MODERN TRIBOLOGY HANDBOOK Volume One Principles of Tribology
The MECHANICS and MATERIALS SCIENCE Series Series Editor
Bharat Bhushan
PUBLISHED TITLES Handbook of Micro/Nano Tribology, Bharat Bhushan Modern Tribology Handbook, Bharat Bhushan
FORTHCOMING TITLES Rolling Mills Rolls and Bearing Maintenance, Richard C. Schrama Thermoelastic Instability in Machinery, Ralph A. Burton
MODERN TRIBOLOGY HANDBOOK Volume One Principles of Tribology
Editor-in-Chief
Bharat Bhushan, Ph.D., D.Sc. (Hon.) Department of Mechanical Engineering The Ohio State University Columbus, Ohio
CRC Press Boca Raton London New York Washington, D.C.
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Library of Congress Cataloging-in-Publication Data Modern tribology handbook / edited by Bharat Bhushan. p. cm. — (Mechanics and materials science series) Includes bibliographical references and index. ISBN 0-8493-8403-6 (alk. paper) 1. Tribology — Handbooks, manuals, etc. I. Bhushan, Bharat, 1949- II. Series. TJ1075.M567 2000 621.8′9 — dc21
00-046869
This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 0-8493-8403-6/01/$0.00+$.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.
© 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-8403-6 Library of Congress Card Number 00-046869 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
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Foreword
The very size of this Modern Tribology Handbook reflects the extent to which the subject has developed since the word tribology was introduced in 1966. While much progress has been recorded in recent decades and several research workers, some of whom are authors of chapters in these volumes, have revealed new facets of the subject and generated valuable data, it is as well to remember that the major users of tribological knowledge are the engineers who design, manufacture, and operate machinery. The general engineer who finds much value in handbooks will welcome the addition of this new compendium of tribological knowledge and data. It is important that the reader and user of this handbook be aware of the well-tried approaches to the measurement of friction and wear and the difficulties sometimes encountered in the interpretation of the results. Throughout the long history of tribology, engineers have sought simple guidance on the magnitude of dominant quantities affecting the performance and life of machinery. Engineers in many fields frequently require estimates of the magnitudes of the friction and wear likely to be experienced by different combinations of materials sliding or rolling together in various environments. The presentation of practical information in the form of data banks for friction and wear based upon current knowledge and experience will thus be warmly welcomed. The frustration experienced by practicing engineers when seeking guidance from expert tribologists on representative values of such quantities is legendary! The basic concepts of contact, friction, wear, and lubrication have been embellished in impressive style by recent analytical and experimental approaches to these subjects, and the outcome is thoroughly reviewed in the initial and major section of the handbook dealing with macrotribology. Impressive studies have greatly enhanced our understanding of the physical and chemical nature of surfaces during the latter half of the 20th century, and the subject which underpins many aspects of tribology thus attracts special attention. Some of the topics, such as wear maps and elastohydrodynamic lubrication, are almost as new as the term tribology itself. Effective lubrication remains the ideal way of controlling friction and wear in most mechanical systems. The science and technology of generating fluid-film lubrication to protect tribological components is now firmly established. However, studies of macrotribology have been supplemented by remarkable investigations of micro-, nano-, and even molecular tribology in recent times. This is illustrated by studies of the physical and chemical properties of surfaces; the contact and adhesion between solids; the effects of surface modifications and coatings upon friction and wear; lubricant rheology; very thin elastohydrodynamic lubricating films; and the nature of boundary and mixed lubrication. This alone justifies the substantial and welcome section of the handbook devoted to micro- and nanotribology. While most of the work is devoted to experimental studies, one chapter is devoted to the fascinating subject of molecular dynamics simulations in this field. v
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Both the conventional and the newer tribological materials are considered in the third section of the handbook. This provides a timely opportunity for the reader to extend his or her knowledge of the advantages and limitations of ceramics, diamond, diamond-like carbon and related films, and a wide range of coating composites. The last major section of the handbook is devoted to industrial components and systems. Familiar components which have typically enjoyed a century or more of development, such as slider bearings, rolling element bearings, gears, and seals are all considered, alongside components and systems encountered in road, rail, marine, and space vehicles. The special tribological problems faced in earth-moving and manufacturing equipment attract individual attention. It is refreshing to see newer applications of tribology included in the handbook. The term biotribology was introduced in 1973 to embrace the application of tribology to biological and particularly medical situations. While the success of joint replacement tends to dominate this field, since it represents a remarkable and dominant feature of orthopedic surgery, there are also an increasing number of examples of the successful transfer of tribological knowledge to the biological field. It is, however, the impact of information technology on society that has promoted major progress in tribology in recent times. The role of tribology has undoubtedly been central to the successful development of magnetic storage and retrieval systems. Spectacular achievements have been recorded in relation to computers, printers, cameras, and scanners, and the reader will welcome the chapters devoted to these developments. The Jost Report1 of 1966 emphasized that losses associated with the shutdown of machinery disabled by the failure of tribological components represented a troublesome economic millstone around the necks of machinery and manufacturing systems. Since that time, maintenance of machinery has changed considerably, with emphasis moving away, in many cases, from routine inspection and component replacement to more effective procedures. It is therefore fitting that the closing chapter of the handbook should be devoted to machinery diagnosis and prognosis. It is now well recognized that the tribologist and maintenance engineer must work closely together in monitoring the health of machinery and the performance of tribological components that might so easily compromise the well-being of our industrial society. The Editor-in-Chief and his team are to be warmly congratulated in bringing together this extensive, timely, and useful Modern Tribology Handbook. Duncan Dowson, CBE, FRS, FREng, CEng, FIMechE FCGI Emeritus/Research Professor School of Mechanical Engineering The University of Leeds U.K.
Reference 1. Department of Education and Science, 1966, Lubrication (Tribology) Education and Research, A Report on the Present Position and Industry’s Needs, HMSO, London.
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Preface
Tribology is the science and technology of interacting surfaces in relative motion and of related subjects and practices. The nature and consequences of the interactions that take place at the moving interface control its friction, wear, and lubrication behavior. Understanding the nature of these interactions and solving the technological problems associated with the interfacial phenomena constitute the essence of tribology. The field of tribology incorporates a number of disciplines, including mechanical engineering, materials science, mechanics, surface chemistry, surface physics and a multitude of subjects, such as surface characterization, friction, wear, lubrication, bearing materials, lubricants, and the selection and design of lubrication systems, and it forms a vital element of engineering. The importance of friction and wear control cannot be overemphasized for economic reasons and long-term reliability. It is important that all designers of mechanical systems use appropriate means to reduce friction and wear, through the proper selection of bearings and the selection of appropriate lubricants and materials for all interacting surfaces. It is equally important that those involved with manufacturing understand the tribological origins of unwanted friction, excessive wear, and lubrication failure in their equipment. The lack of consideration of tribological fundamentals in design and manufacturing is responsible for vast economic losses, including shortened life, excessive equipment downtime, and large expenditures of energy. The recent emergence and proliferation of proximal probes (in particular tip-based microscopies and the surface force apparatus) and of computational techniques for simulating tip-surface interactions and interfacial properties has allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifying and manipulating nanostructures. These advances provide the impetus for research aimed at developing a fundamental understanding of the nature and consequences of the interactions between materials on the atomic scale, and they guide the rational design of material for technological applications. In short, they have led to the appearance of the new field of micro/nanotribology. There are also new applications which require detailed understanding of the tribological processes on macro- and microscales. Since the early 1980s, tribology of magnetic storage systems has become one of the important parts of tribology. Microelectromechanical Systems (MEMS) have begun to appear in the marketplace which present new tribological challenges. Tribology of processing systems such as copiers, printers, scanners, and cameras is important, although it has not received much attention. Along with the new industrial applications, there has been development of new materials, coatings, and treatments, such as synthetic diamond, true diamond, diamond-like carbon films, and chemically grafted films, to name a few. It is clear that the general field of tribology has grown rapidly during the past 50 years or so. Conventional tribology is well established, but micro/nanotribology is evolving and is expected to take center stage for the next decade. New materials are needed, and their development requires fundamental understanding of tribological processes. Furthermore, new industrial applications continue to evolve with their unique challenges. Much of the new tribological information has not made it into the hands vii
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that need to use it. Very few tribology handbooks exist, and these are dated. They have focused on conventional tribology, traditional materials, and already-matured industrial applications. The objective of this handbook is to cover modern tribology with an emphasis on all industrial applications. A large number of leading tribologists from around the world have contributed chapters dealing with all aspects of the subject. The appeal of the subject is expected to be very broad, including researchers and practicing engineers and scientists. The handbook is divided into four sections. The first section, on Macrotribology, covers the fundamentals of conventional tribology. It consists of 15 chapters on topics including surface physics, surface roughness, solid contact mechanics, adhesion, friction, contact temperatures, wear, lubrication and liquid lubricants, friction and wear measurement techniques, design of friction and wear tests, and friction and wear data bank. The second section on Micro/Nanotribology covers the fundamentals of the emerging field of micro/nanotribology. It consists of studies using surface force apparatus, scanning probe microscopy, and molecular dynamic simulations. These studies complement our tribological understanding on the macroscale. The third section on Solid Tribological Materials and Coatings covers the materials; hard, wear-resistant, and solid lubricant coatings; and surface treatments used in tribological applications as well as coating evaluation techniques. The fourth and last section on Tribology of Industrial Components and Systems covers a large range of industrial applications. This section starts out with the most common tribological components followed by tribology of various industrial applications from the “old” and “new” economy. A Glossary of Terms in Tribology is added, which should be of general interest. We embarked on this project in October 1998, and we worked very hard to get all the chapters to the publisher in a record time of a little over 1 year. I wish to sincerely thank the authors for offering to write comprehensive chapters on a tight schedule. This is generally an added responsibility in the hectic work schedules of most researchers today. I also wish to thank the section editors who worked hard to solicit the most competent authors. They are listed in the handbook. I depended on a large number of reviewers who provided critical reviews, in many cases, of more than one chapter in a short time. They are listed in the handbook as well. I also would like to thank Mr. Sriram Sundararajan, a Ph.D. student in my lab, who patiently assisted in the handling of the chapters. I hope the readers of this handbook find it useful. Bharat Bhushan Editor September 2000
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The Editor
Dr. Bharat Bhushan received an M.S. in mechanical engineering from the Massachusetts Institute of Technology in 1971, an M.S. in mechanics and a Ph.D. in mechanical engineering from the University of Colorado at Boulder in 1973 and 1976, respectively, an M.B.A. from Rensselaer Polytechnic Institute at Troy, NY, in 1980, Doctor Technicae from the University of Trondheim at Trondheim, Norway, in 1990, a Doctor of Technical Sciences from the Warsaw University of Technology at Warsaw, Poland, in 1996, and Doctor Honouris Causa from the Metal–Polymer Research Institute of the National Academy of Sciences at Gomel, Belarus. He is a registered professional engineer (mechanical). He is presently an Ohio Eminent Scholar and The Howard D. Winbigler Professor in the Department of Mechanical Engineering as well as the Director of the Computer Microtribology and Contamination Laboratory at the Ohio State University, Columbus. He is an internationally recognized expert in tribology on the macro- to nanoscales, and is one of the field’s most prolific authors. He is considered by some a pioneer in the tribology and mechanics of magnetic storage devices and a leading researcher in the field of micro/nanotribology using single probe microscopy. He has authored 5 technical books, 23 handbook chapters, more than 400 technical papers in reviewed journals, and more than 60 technical reports. He has edited more than 25 books, and holds 10 U.S. patents. He is founding editor-in-chief of the World Scientific Advances in Information Storage Systems Series, the CRC Press Mechanics and Materials Science Series, and the Journal of Information Storage and Processing Systems. He has given more than 200 invited presentations on five continents and more than 50 keynote/plenary addresses at major international conferences. He organized the first symposium on Tribology and Mechanics of Magnetic Storage Systems in 1984 and the first international symposium on Advances in Information Storage Systems in 1990, both of which are now held annually. He is the founder of an ASME Information Storage and Processing Systems Division founded in 1993 and served as the founding chair from 1993 through 1998. His biography has been listed in over two dozen Who’s Who books including Who’s Who in the World, and he has received more than a dozen awards for his contributions to science and technology from professional societies, industry, and U.S. government agencies. Dr. Bhushan is also the recipient of various international fellowships including the Alexander von Humboldt Research Prize for Senior Scientists and the Fulbright Senior Scholar Award. He is a foreign member of the International Academy of Engineering (Russia), the Byelorussian Academy of Engineering and Technology, and the Academy of Triboengineering of the Ukraine, an honorary member of the Society of Tribologists of Belarus, a fellow of ASME and the New York Academy of Sciences, a senior member of IEEE, and a member of STLE, ASEE, Sigma Xi, and Tau Beta Pi. Dr. Bhushan has previously worked for Automotive Specialists, Denver, CO; the R & D Division of Mechanical Technology Inc., Latham, NY; the Technology Services Division of SKF Industries Inc., King of Prussia, PA; the General Products Division Laboratory of IBM Corporation, Tucson, AZ; and the Almaden Research Center of IBM Corporation, San Jose, CA. ix
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Contributors
Dr. Phillip B. Abel
Prof. Herbert S. Cheng
Dr. David I. Fletcher
NASA Glenn Research Center Cleveland, OH
Department of Mechanical Engineering Northwestern University Evanston, IL
Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Richard S. Cowan
Dr. Richard S. Gates
Dr. Koshi Adachi Laboratory of Tribology School of Mechanical Engineering Tohoku University Sendai, Japan
Dr. Xiaolan (Alan) Ai The Timken Company Canton, OH
Dr. Niklas Axén Ångström Laboratory Uppsala University Uppsala, Sweden
Prof. Richard C. Benson Department of Mechanical and Nuclear Engineering The Pennsylvania State University University Park, PA
Dr. Alan D. Berman Seagate Technology Costa Mesa, CA
MultiUniversity Center for Integrated Diagnostics Georgia Institute of Technology Atlanta, GA
Prof. Christophe Donnet École Centrale de Lyon Département de Sciences et Techniques des Matériaux et des Surfaces Laboratoire de Tribologie et Dynamique des Systèmes Écully, France
Prof. Rob S. Dwyer-Joyce Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Dr. Ali Erdemir
National Institute of Standards and Technology Gaithersburg, MD
William A. Glaeser Battelle Columbus, OH
Lois J. Gschwender Wright Patterson Air Force Base Dayton, OH
Dr. Jeffrey A. Hawk U.S. Department of Energy Albany Research Center Albany, OR
Prof. Sture Hogmark Ångström Laboratory Uppsala University Uppsala, Sweden
Argonne National Laboratory Energy Technology Division Argonne, IL
Dr. Kenneth Holmberg
The Ohio State University Columbus, OH
Dr. Peter J. Blau
Dr. John Ferrante
Dr. Hendrik Hölscher
Bharat Bhushan
Tribomaterials Investigative Systems Oak Ridge, TN
David E. Brewe U.S. Army Vehicle Propulsion Directorate NASA Glenn Research Center Cleveland, OH
Department of Physics Cleveland State University Cleveland, OH
Prof. John Fisher School of Mechanical Engineering The University of Leeds Leeds, U.K.
VTT Manufacturing Technology Espoo, Finland
Institute of Applied Physics University of Hamburg Hamburg, Germany
Dr. Stephen M. Hsu National Institute of Standards and Technology Gaithersburg, MD
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Dr. M. Ishida
Brent K. Lok
Dr. A. William Ruff
Railway Technical Research Institute Tokyo, Japan
Chevron Global Lubricants San Francisco, CA
Consultant Gaithersburg, MD
Prof. Jacob N. Israelachvili
Prof. Kenneth C Ludema
Prof. Richard F. Salant
Department of Chemical Engineering and Materials Department University of California at Santa Barbara Santa Barbara, CA
Prof. Staffan Jacobson Ångström Laboratory Uppsala University Uppsala, Sweden
Mark J. Jansen AYT Corporation Brookpark, OH
Dr. William R. Jones, Jr.
Mechanical Engineering Department University of Michigan Ann Arbor, MI
Department of Mechanical Engineering Georgia Institute of Technology Atlanta, GA
Prof. Othmar Marti Experimentelle Physik Universität Ulm Ulm, Germany
Prof. Allan Matthews Research Centre in Surface Engineering The University of Hull Hull, U.K.
Dr. Daniel Maugis
Dr. K. J. Sawley Transportation Technology Centre Pueblo, CO
Dr. F. Schmid Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
CNRS Laboratoire des Materiaux et Structures du Genie Civil Champ sur Marne, France
Dr. Karl J. Schmid
NASA Glenn Research Center Cleveland, OH
Dr. Ajay Kapoor
Prof. Eric Mockensturm
Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Department of Mechanical and Nuclear Engineering The Pennsylvania State University University Park, PA
Prof. Steven R. Schmid
Prof. Koji Kato
Charles A. Moyer
Laboratory of Tribology School of Mechanical Engineering Tohoku University Sendai, Japan
Prof. Francis E. Kennedy Thayer School of Engineering Dartmouth College Hanover, NH
Dr. Padma Kodali Cummins Inc. Columbus, IN
David C. Kramer Chevron Global Lubricants Richmond, CA
Dr. Mats Larsson Balzers Sandvik Coating AB Stockholm, Sweden
The Timken Company (retired) Canton, OH
John Deere Marine Engines Division Waterloo, IA
Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN
Dr. Shirley E. Schwartz General Motors Powertrain Warren, MI
Dr. Martin H. Müser Institute für Physik Johannes Gutenberg-Universität Mainz, Germany
Dr. Malcolm G. Naylor Cummins Inc. Columbus, IN
Dr. Udo D. Schwarz Institute of Applied Physics University of Hamburg Hamburg, Germany
Dr. Shashi K. Sharma
Dr. Martin Priest
Wright Patterson Air Force Base Dayton, OH
School of Mechanical Engineering The University of Leeds Leeds, U.K.
Dr. Ming C. Shen
Prof. Mark O. Robbins Department of Physics and Astronomy The Johns Hopkins University Baltimore, MD
SULZERMEDICA Austin, TX
Carl E. Snyder, Jr. Wright Patterson Air Force Base Dayton, OH
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Prof. Andras Z. Szeri
Dr. Jerry C. Wang
Dr. Rick D. Wilson
Department of Mechanical Engineering University of Delaware Newark, DE
Cummins Inc. Columbus, IN
U.S. Department of Energy Albany Research Center Albany, OR
Dr. Urban Wiklund
Prof. William R. D. Wilson
Mark L. Sztenderowicz Chevron Global Lubricants Richmond, CA
Dr. Simon C. Tung General Motors Research and Development Center Warren, MI
Ångström Laboratory Uppsala University Uppsala, Sweden
Dr. John A. Williams Engineering Department Cambridge University Cambridge, U.K.
Department of Mechanical Engineering University of Washington Seattle, WA
Prof. Ward O. Winer Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA
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Section Editors Section 1: Macrotribology Bharat Bhushan (The Ohio State University, USA) Francis E. Kennedy (Dartmouth College, USA) Andras Z. Szeri (University of Delaware, USA) Section 2: Micro/Nanotribology Bharat Bhushan (The Ohio State University, USA) Othmar Marti (University of Ulm, Germany) Section 3: Solid Tribological Materials and Coatings Bharat Bhushan (The Ohio State University, USA) Ali Erdemir (Argonne National Laboratory, USA) Kenneth Holmberg (VTT Manufacturing Technology, Finland) Section 4: Tribology of Industrial Components and Systems Bharat Bhushan (The Ohio State University, USA) Stephen M. Hsu (National Institute of Standards and Technology, USA)
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Reviewers Prof. George Adams (Northeastern University, Boston, MA) Dr. Paul Bessette (Nye Lubricants Inc., New Bedford, MA) Prof. B. Bhushan (The Ohio State University, Columbus, OH) Prof. Thierry A Blanchett (Rensselaer Polytechnic Institute, Troy, NY) Dr. Peter J. Blau (Oak Ridge National Laboratory, Oak Ridge, TN) Dr. Ken Budinski (Eastman Kodak Co., Rochester, NY) Dr. Nancy Burnham (École Polytechnique Federal de Lausanne, Switzerland) Dr. Jaime Colchero (Universidad Antonoma de Madrid, Spain) Dr. Christopher Dellacorte (NASA Glenn Research Center, Cleveland, OH) Dr. Urs. T. Duerig (IBM Research Division, Zurich, Switzerland) Dr. John Dumbleton (Biomaterials and Technology Assessment, Ridgewood, NJ) Dr. Norman S. Eiss Jr. (Retired) Dr. Ali Erdemir (Argonne National Laboratory, Argonne, IL) Prof. Traugott E. Fischer (Stevens Institute of Technology, Hoboken, NJ) Mr. William A. Glaeser (Battelle Memorial Institute, Columbus, OH) Prof. Steve Granick (University of Illinois, Urbana, IL) Prof. Judith A. Harrison (U.S. Naval Academy, Annapolis, MD) Dr. Jeffrey A. Hawk (U.S. Department of Energy, Albany, OR) Prof. Sture Hogmark (Uppsala University, Sweden) Dr. Kenneth Holmberg (VTT Manufacturing Technology, Finland) Dr. K. L. Johnson (Cambridge University, Cambridge, U.K.) Dr. William R. Jones (NASA Glenn Research Center, Cleveland, OH) Prof. Koji Kato (Tohoku University, Japan) Prof. Francis E. Kennedy (Dartmouth College, Hanover, NH) Dr. Jari Koskinen (VTT Manufacturing Technology, Finland) Dr. Minyoung Lee (G. E. Corp. R&D, Schenectady, NY) Prof. Frederick F. Ling (University of Texas, Austin, TX) Dr. Jean-Luc Loubet (École Centrale de Lyon, France) Prof. Kenneth C Ludema (University of Michigan, Ann Arbor, MI) Dr. William D. Marscher (Mechanical Solutions Inc., Parsippany, NJ) Prof. Ernst Meyer (Institute für Physik, University of Basel, Switzerland) Dr. Sinan Muftu (Massachusetts Institute of Technology, Bedford, MA) Dr. B. Nau (Fluid Sealing Consultant) Prof. Gerhard Poll (Universität Hannover, Germany) Prof. David E. Rigney (The Ohio State University, Columbus, OH) Dr. A. William Ruff (Consultant, Gaithersburg, MD) Prof. Farshid Sadeghi (Purdue University, W. Lafayette, IN) Prof. Steven R. Schmid (University of Notre Dame, Notre Dame, IN) xvi
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Dr. Shashi K. Sharma (Wright Patterson Air Force Base, Dayton, OH) Dr. Simon Sheu (Alcoa, Pittsburgh, PA) Dr. William D. Sproul (Reactive Sputtering Inc., Santa Barbara, CA) Prof. Andras Z. Szeri (University of Delaware, Newark, DE) Dr. John Tichy (Rensselaer Polytechnic Institute, Troy, NY) Prof. Matthew Tirrell (University of California, Santa Barbara, CA) Dr. Andrey A. Voevodin (Wright Patterson Air Force Base, Dayton, OH) Prof. Mark E. Welland (Cambridge University, U. K.) Prof. J. A. Wickert (Carnegie Mellon University, Pittsburgh, PA) Dr. Pierre Willermet (Ford Motor Co., Dearborn, MI) Dr. John A. Williams (Cambridge University, U. K.) Mr. E. Zaretsky (NASA Glenn Research Center, Cleveland, OH) Dr. Ing. K.-H Zum Gahr (Forschungszentrum Karlsruhe, Germany)
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Contents
Volume One SECTION I Introduction
1
Phillip B. Abel and John Ferrante
Introduction ................................................................................................................................ 5 Geometry of Surfaces .................................................................................................................. 6 Theoretical Considerations ...................................................................................................... 10 Experimental Determinations of Surface Structure................................................................ 19 Chemical Analysis of Surfaces .................................................................................................. 23 Surface Effects in Tribology...................................................................................................... 32 Concluding Remarks ................................................................................................................ 40
Surface Roughness Analysis and Measurement Techniques Bharat Bhushan 2.1 2.2 2.3 2.4
3
Bharat Bhushan, Francis E. Kennedy, and Andras Z. Szeri
Surface Physics in Tribology 1.1 1.2 1.3 1.4 1.5 1.6 1.7
2
Macrotribology
The Nature of Surfaces ............................................................................................................. 49 Analysis of Surface Roughness ................................................................................................. 50 Measurement of Surface Roughness ........................................................................................ 81 Closure..................................................................................................................................... 114
Contact Between Solid Surfaces 3.1 3.2 3.3 3.4 3.5 3.6
John A.Williams and Rob S. Dwyer-Joyce
Introduction ............................................................................................................................ 121 Hertzian Contacts ................................................................................................................... 122 Non-Hertzian Contacts .......................................................................................................... 137 Numerical Methods for Contact Mechanics ......................................................................... 140 Experimental Methods for Contact Mechanics..................................................................... 144 Further Aspects ....................................................................................................................... 150
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4
Adhesion of Solids: Mechanical Aspects 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
5
Friction 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11
6
xx
Koji Kato and Koshi Adachi
Introduction ............................................................................................................................ 273 Change of Wear Volume and Wear Surface Roughness with Sliding Distance .................. 274 Ranges of Wear Rates and Varieties of Wear Surfaces.......................................................... 274 Descriptive Key Terms............................................................................................................ 276 Survey of Wear Mechanisms .................................................................................................. 278 Concluding Remarks .............................................................................................................. 299
Wear Debris Classification 8.1 8.2 8.3 8.4 8.5
Francis E. Kennedy
Surface Temperatures and Their Significance....................................................................... 235 Surface Temperature Analysis................................................................................................ 238 Surface Temperature Measurement....................................................................................... 259
Wear Mechanisms 7.1 7.2 7.3 7.4 7.5 7.6
8
Kenneth C Ludema
Introduction ............................................................................................................................ 205 Qualitative Ranges of Friction................................................................................................ 208 Early Concepts on the Causes of Friction.............................................................................. 213 Adhesion, Welding, and Bonding of the Three Major Classes of Solids.............................. 215 The Formation and Persistence of Friction Controlling Surface Films ............................... 216 Experiments that Demonstrate the Influence of Films on Surfaces..................................... 218 Mechanisms of Friction .......................................................................................................... 219 Measuring Friction.................................................................................................................. 220 Test Machine Design and Machine Dynamics ...................................................................... 227 Tapping and Jiggling to Reduce Friction Effects................................................................... 229 Equations and Models of Friction.......................................................................................... 230
Frictional Heating and Contact Temperatures 6.1 6.2 6.3
7
Daniel Maugis
Introduction ............................................................................................................................ 163 Adhesion Forces, Energy of Adhesion, Threshold Energy of Rupture................................. 164 Fracture Mechanics and Adhesion of Solids.......................................................................... 167 Example: Contact and Adherence of Spheres........................................................................ 175 Liquid Bridges ......................................................................................................................... 183 Adhesion of Rough Elastic Solids — Application to Friction .............................................. 186 Kinetics of Crack Propagation................................................................................................ 188 Adhesion of Metals ................................................................................................................. 197 Conclusion .............................................................................................................................. 198
William A. Glaeser
Introduction ............................................................................................................................ 301 How Wear Debris Is Generated ............................................................................................. 302 Collection of Wear Debris ...................................................................................................... 306 Diagnostics with Wear Debris................................................................................................ 308 Conclusions ............................................................................................................................. 312
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9
Wear Maps 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
10
Liquid Lubricants and Lubrication Lois J. Gschwender, David C. Kramer, Brent K. Lok, Shashi K. Sharma, Carl E. Snyder, Jr., and Mark L. Sztenderowicz 10.1 10.2 10.3 10.4
11
Andras Z. Szeri
Basic Equations ....................................................................................................................... 384 Externally Pressurized Bearings.............................................................................................. 391 Hydrodynamic Lubrication.................................................................................................... 398 Dynamic Properties of Lubricant Films................................................................................. 422 Elastohydrodynamic Lubrication........................................................................................... 438
Boundary Lubrication and Boundary Lubricating Films and Richard S. Gates 12.1 12.2 12.3 12.4 12.5 12.6
13
Introduction ............................................................................................................................ 361 Lubricant Selection Criteria ................................................................................................... 361 Conventional Lubricants — The Evolution of Base Oil Technology................................... 366 Synthetic Lubricants ............................................................................................................... 373
Hydrodynamic and Elastohydrodynamic Lubrication 11.1 11.2 11.3 11.4 11.5
12
Stephen M. Hsu and Ming C. Shen
Introduction ............................................................................................................................ 317 Fundamental Wear Mechanisms of Materials....................................................................... 318 Wear Prediction ...................................................................................................................... 319 Wear Mapping......................................................................................................................... 320 Wear Maps as a Classification System ................................................................................... 322 Wear Map Construction for Ceramics .................................................................................. 324 Comparison of Materials ........................................................................................................ 328 Modeling Wear by Using Wear Maps.................................................................................... 341 Advantages and Limitations of Current Wear Map Approach ............................................ 354
Introduction ............................................................................................................................ 455 The Nature of Surfaces ........................................................................................................... 457 Lubricants and Their Reactions ............................................................................................. 459 Boundary Lubricating Films................................................................................................... 468 Boundary Lubrication Modeling............................................................................................ 479 Concluding Remarks .............................................................................................................. 486
Friction and Wear Measurement Techniques Sture Hogmark, and Staffan Jacobson 13.1 13.2 13.3 13.4 13.5
Stephen M. Hsu
Niklas Axén,
The Importance of Testing in Tribology ............................................................................... 493 Wear or Surface Damage ........................................................................................................ 494 Classification of Tribotests ..................................................................................................... 497 Tribotest Planning .................................................................................................................. 498 Evaluation of Wear Processes................................................................................................. 500 xxi
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13.6 13.7 13.8 13.9 13.10
14
Simulative Friction and Wear Testing 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8
15
Tribotests — Selected Examples ........................................................................................... 501 Abrasive Wear ........................................................................................................................ 502 Erosive Wear .......................................................................................................................... 504 Wear in Sliding and Rolling Contacts .................................................................................. 505 Very Mild Wear ..................................................................................................................... 508
Friction and Wear Data Bank 15.1 15.2 15.3 15.4
Introduction
Micro/Nanotribology Bharat Bhushan and Othmar Marti
Microtribology and Microrheology of Molecularly Thin Liquid Films Alan D. Berman and J. N. Israelachvili 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9
xxii
A. William Ruff
Introduction........................................................................................................................... 523 Sources of Data ...................................................................................................................... 523 Materials Found in Data Bank .............................................................................................. 527 Data Bank Format.................................................................................................................. 529
SECTION II
16
Peter J. Blau
Introduction........................................................................................................................... 511 Defining the Problem ............................................................................................................ 512 Selecting a Scale of Simulation.............................................................................................. 514 Defining Field-Compatible Metrics...................................................................................... 516 Selecting or Constructing the Test Apparatus...................................................................... 517 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed.................................................................................................................................... 517 Case Studies............................................................................................................................ 518 Conclusions............................................................................................................................ 522
Introduction........................................................................................................................... 568 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure.................. 568 Adhesion and Capillary Forces ............................................................................................. 572 Nonequilibrium Interactions: Adhesion Hysteresis ............................................................ 574 Rheology of Molecularly Thin Films: Nanorheology .......................................................... 576 Interfacial and Boundary Friction: Molecular Tribology.................................................... 582 Theories of Interfacial Friction ............................................................................................. 587 Friction and Lubrication of Thin Liquid Films.................................................................... 594 Stick-Slip Friction .................................................................................................................. 600
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Measurement of Adhesion and Pull-Off Forces with the AFM Othmar Marti 17.1 Introduction ............................................................................................................................ 617 17.2 Experimental Procedures to Measure Adhesion in AFM and Applications....................... 624 17.3 Summary and Outlook.......................................................................................................... 633
18
Atomic-Scale Friction Studies Using Scanning Force Microscopy Udo D. Schwarz and Hendrik Hölscher 18.1 Introduction ............................................................................................................................ 641 18.2 The Scanning Force Microscope as a Tool for Nanotribology............................................ 642 18.3 The Mechanics of a Nanometer-Sized Contact ................................................................... 644 18.4 Amontons’ Laws at the Nanometer Scale............................................................................. 646 18.5 The Influence of the Surface Structure on Friction ............................................................. 648 18.6 Atomic Mechanism of Friction............................................................................................. 652 18.7 The Velocity Dependence of Friction................................................................................... 658 18.8 Summary ................................................................................................................................ 660
19
Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy Bharat Bhushan 19.1 19.2 19.3 19.4 19.5 19.6 19.7
20
Introduction........................................................................................................................... 667 Description of AFM/FFM and Various Measurement Techniques .................................... 669 Friction and Adhesion ........................................................................................................... 678 Scratching, Wear, and Fabrication/Machining .................................................................... 694 Indentation............................................................................................................................. 703 Boundary Lubrication ........................................................................................................... 708 Closure ................................................................................................................................... 712
Computer Simulations of Friction, Lubrication, and Wear Mark O. Robbins and Martin H. Müser 20.1 20.2 20.3 20.4 20.5 20.6 20.7
Introduction........................................................................................................................... 717 Atomistic Computer Simulations......................................................................................... 718 Wearless Friction in Low-Dimensional Systems.................................................................. 722 Dry Sliding of Crystalline Surfaces ....................................................................................... 734 Lubricated Surfaces................................................................................................................ 740 Stick-Slip Dynamics............................................................................................................... 752 Strongly Irreversible Tribological Processes......................................................................... 755
xxiii
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Volume Two SECTION III Introduction
21
Introduction........................................................................................................................... 827 Tribology of Coated Surfaces ................................................................................................ 828 Macromechanical Interactions: Hardness and Geometry................................................... 835 Micromechanical Interactions: Material Response ............................................................. 839 Material Removal and Change Interactions: Debris and Surface Layers............................ 844 Multicomponent Coatings .................................................................................................... 852 Concluding Remarks ............................................................................................................. 858
Tribology of Diamond, Diamond-like Carbon and Related Films Ali Erdemir and Christophe Donnet 24.1 24.2
xxiv
Ali Erdemir
Introduction........................................................................................................................... 787 Classification of Solid Lubricants ......................................................................................... 792 Lubrication Mechanisms of Layered Solids ......................................................................... 806 High-Temperature Solid Lubricants .................................................................................... 808 Self-Lubricating Composites................................................................................................. 813 Soft Metals.............................................................................................................................. 815 Polymers................................................................................................................................. 817 Summary and Future Directions .......................................................................................... 818
Tribological Properties of Metallic and Ceramic Coatings Kenneth Holmberg and Allan Matthews 23.1 23.2 23.3 23.4 23.5 23.6 23.7
24
Koji Kato and Koshi Adachi
Introduction........................................................................................................................... 771 Pure Metals ............................................................................................................................ 771 Soft Metals and Soft Bearing Alloys...................................................................................... 772 Copper-based Alloys.............................................................................................................. 774 Cast Irons ............................................................................................................................... 774 Steels ....................................................................................................................................... 776 Ceramics................................................................................................................................. 778 Special Alloys.......................................................................................................................... 781 Comparisons Between Metals and Ceramics ....................................................................... 782 Concluding Remarks ............................................................................................................. 783
Solid Lubricants and Self-Lubricating Films 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8
23
Bharat Bhushan, Ali Erdemir, and Kenneth Holmberg
Metals and Ceramics 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10
22
Solid Tribological Materials and Coatings
Introduction........................................................................................................................... 871 Diamond Films ...................................................................................................................... 872
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24.3 24.4 24.5
25
Self-Assembled Monolayers for Controlling Hydrophobicity and/or Friction and Wear Bharat Bhushan 25.1 25.2 25.3 25.4 25.5
26
Diamond-like Carbon (DLC) Films ..................................................................................... 888 Other Related Films............................................................................................................... 897 Summary and Future Direction............................................................................................ 899
Introduction........................................................................................................................... 909 A Primer to Organic Chemistry............................................................................................ 912 Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains ................................................................................................................ 917 Tribological Properties .......................................................................................................... 921 Conclusions............................................................................................................................ 924
Mechanical and Tribological Requirements and Evaluation of Coating Composites Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund 26.1 26.2 26.3 26.4 26.5
Introduction........................................................................................................................... 931 Design of Tribological Coatings............................................................................................ 938 Design of Coated Components............................................................................................. 945 Evaluation of Coating Composites ....................................................................................... 949 Visions and Conclusions ....................................................................................................... 959
SECTION IV Introduction
27
Bharat Bhushan and Stephen M. Hsu
Slider Bearings 27.1 27.2 27.3 27.4
28
Tribology of Industrial Components and Systems
David E. Brewe
Introduction........................................................................................................................... 969 Self-acting Finite Bearings..................................................................................................... 977 Failure Modes....................................................................................................................... 1019 Slider Bearing Materials....................................................................................................... 1027
Rolling Element Bearings 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 28.10
Xiaolan Ai and Charles A. Moyer
Introduction......................................................................................................................... 1041 Rolling Element Bearing Types........................................................................................... 1042 Bearing Materials ................................................................................................................. 1046 Contact Mechanics .............................................................................................................. 1048 Bearing Internal Load Distribution .................................................................................... 1057 Bearing Lubrication ............................................................................................................. 1063 Bearing Kinematics.............................................................................................................. 1067 Bearing Load Ratings and Life Prediction.......................................................................... 1071 Bearing Torque Calculation ................................................................................................ 1074 Bearing Temperature Analysis ............................................................................................ 1079 xxv
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28.11 Bearing Endurance Testing ................................................................................................. 1082 28.12 Bearing Failure Analysis ...................................................................................................... 1083
29
Gears 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8
30
Rotary Dynamic Seals 30.1 30.2 30.3 30.4 30.5
31
Introduction......................................................................................................................... 1187 The Engine ........................................................................................................................... 1188 Transmission and Drive Line.............................................................................................. 1197 The Tire ................................................................................................................................ 1203 The Brakes............................................................................................................................ 1209 Windshield Wipers .............................................................................................................. 1212 Automotive Lubricants........................................................................................................ 1213
Diesel Engine Tribology Jerry C. Wang 33.1 33.2
xxvi
William R. Jones, Jr. and Mark J. Jansen
Introduction......................................................................................................................... 1159 Lubrication Regimes............................................................................................................ 1159 Mechanism Components .................................................................................................... 1161 Liquid Lubricants and Solid Lubricants ............................................................................. 1162 Liquid Lubricant Properties ................................................................................................ 1165 Accelerated Testing and Life Testing .................................................................................. 1175 Summary .............................................................................................................................. 1181
Automotive Tribology Ajay Kapoor, Simon C. Tung, Shirley E. Schwartz, Martin Priest, and Rob S. Dwyer-Joyce 32.1 32.2 32.3 32.4 32.5 32.6 32.7
33
Richard F. Salant
Introduction......................................................................................................................... 1131 Mechanical Seals .................................................................................................................. 1131 Rotary Lip Seal ..................................................................................................................... 1146 Nomenclature ...................................................................................................................... 1154 Defining Terms .................................................................................................................... 1155
Space Tribology 31.1 31.2 31.3 31.4 31.5 31.6 31.7
32
Herbert S. Cheng Introduction......................................................................................................................... 1095 Gear Types............................................................................................................................ 1096 Tribological Failure Modes ................................................................................................. 1097 Full-Film Lubrication Performance.................................................................................... 1101 Mixed Lubrication Characteristics...................................................................................... 1110 Modeling of Tribological Failures in Gears........................................................................ 1115 Failure Tests ......................................................................................................................... 1122 Conclusions.......................................................................................................................... 1124
Malcolm G. Naylor, Padma Kodali, and
Introduction......................................................................................................................... 1231 Power Cylinder Components.............................................................................................. 1233
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33.3 33.4 33.5 33.6 33.7 33.8 33.9
34
Overhead Components ....................................................................................................... 1246 Engine Valves ....................................................................................................................... 1249 Bearings and Bushings......................................................................................................... 1253 Turbomachinery .................................................................................................................. 1255 Fuel System .......................................................................................................................... 1258 Fuels, Lubricants, and Filtration......................................................................................... 1261 Future Trends ...................................................................................................................... 1267
Tribology of Rail Transport Sawley, and M. Ishida
Ajay Kapoor, David I. Fletcher, F. Schmid, K. J.
34.1 Introduction .......................................................................................................................... 1271 34.2 Wheel/Rail Contact.............................................................................................................. 1275 34.3 Diesel Power for Traction Purposes ................................................................................... 1308 34.4 Current Collection Interfaces of Trains.............................................................................. 1314 34.5 Axle Bearings, Dampers, and Traction Motor Bearings.................................................... 1321 34.6 New Developments and Recent Advances in the Study of Rolling Contact Fatigue ....... 1324 34.7 Conclusion ........................................................................................................................... 1325
35
Tribology of Earthmoving, Mining, and Minerals Processing and R. D. Wilson 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8
36
37
Introduction......................................................................................................................... 1331 Wear Processes in Mining and Minerals Processing ........................................................... 1333 Equipment Used in Earthmoving Operations ................................................................... 1339 Equipment Used in Mining and Minerals Processing........................................................... 1344 General Classification of Abrasive Wear ............................................................................ 1347 Tribological Losses in the Mining of Metallic Ores, Coal, and Non-metallic Minerals................................................................................................................................ 1359 Financial Cost of Wear in Earthmoving, Mining, and Minerals Processing.................... 1366 Concluding Remarks ........................................................................................................... 1368
Marine Equipment Tribology 36.1 36.2 36.3 36.4 36.5
Steven R. Schmid and Karl J. Schmid
Introduction......................................................................................................................... 1371 Marine Oil Properties and Chemistry ................................................................................ 1371 Diesel Engine Lubrication ................................................................................................... 1374 Steam and Gas Turbines...................................................................................................... 1380 Ancillary Equipment............................................................................................................ 1381
Tribology in Manufacturing 37.1 37.2 37.3 37.4 37.5
Jeffrey A. Hawk
Steven R. Schmid and William R. D. Wilson
Introduction......................................................................................................................... 1385 Unique Aspects of Manufacturing Tribology .................................................................... 1385 Metal Cutting ....................................................................................................................... 1394 Finishing Operations ........................................................................................................... 1398 Bulk Forming Operations ................................................................................................... 1399 xxvii
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Macro- and Microtribology of Magnetic Storage Devices Bharat Bhushan 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8
39
Macro- and Microtribology of MEMS Materials 39.1 39.2 39.3 39.4
40
Bharat Bhushan
Introduction .......................................................................................................................... 1515 Experimental Techniques ..................................................................................................... 1525 Results and Discussion.......................................................................................................... 1527 Closure................................................................................................................................... 1544
Mechanics and Tribology of Flexible Media in Information Processing Systems Richard C. Benson and Eric M. Mockensturm 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 40.10 40.11 40.12
41
Introduction .......................................................................................................................... 1413 Magnetic Storage Devices and Components ....................................................................... 1415 Friction and Adhesion .......................................................................................................... 1423 Interface Temperatures......................................................................................................... 1447 Wear....................................................................................................................................... 1448 Lubrication ............................................................................................................................ 1482 Micro/Nanotribology and Micro/Nanomechanics............................................................. 1491 Closure................................................................................................................................... 1501
Introduction .......................................................................................................................... 1549 Introduction to Foil Bearings ............................................................................................... 1550 A Simple Foil Bearing Model................................................................................................ 1553 Other Foil Bearing Models ................................................................................................... 1556 Air Reversers.......................................................................................................................... 1558 Introduction to Wound Rolls............................................................................................... 1561 Air Entrainment in Wound Rolls......................................................................................... 1562 Nip-Induced Tension and J-line Slip in Web Winding ...................................................... 1565 Web Tenting Caused by High Asperities............................................................................. 1570 Mechanisms that Cause a Sheet to Jam, Stall, or Roll Over in a Channel ......................... 1576 Micro-slip of Elastic Belts ..................................................................................................... 1579 Transport of Sheets Through Roller/Roller and Roller/Platen Nips.................................. 1582
Biomedical Applications 41.1 41.2 41.3 41.4 41.5 41.6 41.7
xxviii
John Fisher
Introduction .......................................................................................................................... 1593 Tribology in the Human Body ............................................................................................. 1594 Tribology of Artificial Organs and Medical Devices ............................................................. 1596 Natural Synovial Joint and Articular Cartilage ................................................................... 1599 Total Replacement Joints...................................................................................................... 1603 Wear and Wear Debris Induced Osteolysis......................................................................... 1605 Joint Replacement and Repair in the Next Millennium ..................................................... 1607
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42
Technologies for Machinery Diagnosis and Prognosis and Ward O. Winer 42.1 42.2 42.3 42.4 42.5
Richard S. Cowan
Introduction .......................................................................................................................... 1611 Failure Prevention Strategies................................................................................................ 1611 Condition Monitoring Approaches ..................................................................................... 1616 Tribo-Element Applications................................................................................................. 1634 Equipment Asset Management ............................................................................................ 1639
Glossary .......................................................................................................... 1645 Index ............................................................................................................... 1661
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I Macrotribology Bharat Bhushan The Ohio State University
Francis E. Kennedy Dartmouth College
Andras Z. Szeri University of Delaware 1 Surface Physics in Tribology
Phillip B. Abel, John Ferrante .............................................. 5
Introduction • Geometry of Surfaces • Theoretical Considerations • Experimental Determinations of Surface Structure • Chemical Analysis of Surfaces • Surface Effects in Tribology • Concluding Remarks
2 Surface Roughness Analysis and Measurement Techniques Bharat Bhushan ............. 49 The Nature of Surfaces • Analysis of Surface Roughness • Measurement of Surface Roughness • Closure
3 Contact Between Solid Surfaces John A. Williams, Rob S. Dwyer-Joyce ....................... 121 Introduction • Hertzian Contacts • Non-Hertzian Contacts • Numerical Methods for Contact Mechanics • Experimental Methods for Contact Mechanics • Further Aspects
4 Adhesion of Solids: Mechanical Aspects
Daniel Maugis .............................................. 163
Introduction • Fracture Mechanics and Adhesion of Solids • Example: Contact and Adherence of Spheres • Liquid Bridges • Adhesion of Rough Elastic Solids — Application to Friction • Kinetics of Crack Propagation • Adhesion of Metals • Conclusion
5 Friction Kenneth C. Ludema ............................................................................................ 205 Introduction • Qualitative Ranges of Friction • Early Concepts on the Causes of Friction • Adhesion, Welding, Bonding of the Three Major Classes of Solids • The Formation and Persistence of Friction Controlling Surface Films • Experiments that Demonstrate the Influence of Films on Surfaces • Mechanisms of Friction • Measuring Friction • Test Machine Design and Machine Dynamics • Tapping and Jiggling to Reduce Friction Effects • Equations and Models of Friction
6 Frictional Heating and Contact Temperatures Francis E. Kennedy ............................. 235 Surface Temperatures and Their Significance • Surface Temperature Analysis • Surface Temperature Measurement
7 Wear Mechanisms Koji Kato, Koshi Adachi .................................................................... 273 Introduction • Change of Wear Volume and Wear Surface Roughness with Sliding Distance • Ranges of Wear Rates and Varieties of Wear Surfaces • Descriptive Key Terms • Survey of Wear Mechanisms • Concluding Remarks
1
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Macrotribology
8 Wear Debris Classification
William A. Glaeser .............................................................. 301
Introduction • How Wear Debris Is Generated • Collection of Wear Debris • Diagnostics with Wear Debris • Conclusions
9 Wear Maps
Stephen M. Hsu, Ming C. Shen .................................................................... 317
Introduction • Fundamental Wear Mechanisms of Materials • Wear Prediction • Wear Mapping • Wear Maps as a Classification System • Wear Map Construction for Ceramics • Comparison of Materials • Modeling Wear by Using Wear Maps • Advantages and Limitations of Current Wear Map Approach
10 Liquid Lubricants and Lubrication Lois J. Gschwender, David C. Kramer, Brent K. Lok, Shashi K. Sharma, Carl E. Snyder, Jr., M.L. Sztenderowicz ................................... 361 Introduction • Lubricant Selection Criteria • Conventional Lubricants — The Evolution of Base Oil Technology • Synthetic Lubricants
11 Hydrodynamic and Elastohydrodynamic Lubrication
Andras Z. Szeri ...................... 383
Basic Equations • Externally Pressurized Bearings • Hydrodynamic Lubrication • Dynamic Properties of Lubricant Films • Elastohydrodynamic Lubrication
12 Boundary Lubrication and Boundary Lubricating Films Stephen M. Hsu, Richard S. Gates .................................................................................................................... 455 Introduction • The Nature of Surfaces • Lubricants and Their Reactions • Concluding Remarks
13 Friction and Wear Measurement Techniques Niklas Axén, Sture Hogmark, Staffan Jacobson .................................................................................................................... 493 The Importance of Testing in Tribology • Wear or Surface Damage • Classification of Tribotests • Tribotest Planning • Evaluation of Wear Processes • Tribotests — Selected Examples • Abrasive Wear • Erosive Wear • Wear in Sliding and Rolling Contacts • Very Mild Wear
14 Simulative Friction and Wear Testing Peter J. Blau ...................................................... 511 Introduction • Defining the Problem • Selecting a Scale of Simulation • Defining FieldCompatible Metrics • Selecting or Constructing the Test Apparatus • Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed. • Case Studies • Conclusions
15 Friction and Wear Data Bank A. William Ruff .............................................................. 523 Introduction • Sources of Data • Materials Found in Data Bank • Data Bank Format
A
great deal of progress has been made in the past 100 years in the understanding of the fundamentals of tribological phenomena at the macroscopic scale. This section begins with a description of solid surfaces, their physical and chemical structures, and their important effect on tribological behavior (Chapter 1). The topography of solid surfaces is treated in Chapter 2, which includes the treatment of the characterization of surface roughness and details techniques for measuring surface roughness at various scales. The deformation and stress that occur when two solid surfaces come into contact and the geometry of contacts are considered for both smooth and rough surfaces in Chapter 3. The fundamentals of adhesion between solid surfaces are presented in Chapter 4, along with a discussion of the effects of surface roughness and the presence of a thin fluid film on the surface. An important concern in sliding contacts is friction. The mechanisms of friction, its major consequences, and means of measuring and controlling friction are covered in Chapter 5. Frictional heating of contacting surfaces, one of the main consequences of friction, is treated in Chapter 6, along with means for determining the surface temperatures that result from frictional heating. Perhaps the most important effect of frictional sliding is wear of the sliding components. The subject of wear is covered in three chapters. Chapter 7 presents a survey of the various mechanisms of wear of metals, ceramics, polymers, and composites; Chapter 8 follows with the analysis of wear debris, particularly as a tool for machine diagnosis. An important tool for understanding and controlling wear is the wear map; basic information about wear maps and their use is given in Chapter 9.
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Macrotribology
3
The primary method for alleviating the detrimental effects of friction is to use lubrication. Chapter 10 presents the fundamentals of liquid lubricants and their use in the various regimes of lubrication. The fundamentals of fluid film lubrication are accessible in Chapter 11; included are treatments of both hydrostatic and hydrodynamic lubrication of conformal contacts, journal and thrust bearing configurations in which the bearing surfaces are considered rigid, and elastohydrodynamic lubrication of counterformal contacts, rolling element bearings and gears with deforming surfaces. Lubrication of surfaces by boundary films is treated in Chapter 12, which includes a discussion of the chemical and physical phenomena occurring at the interface between lubricant and solid surface. There are two chapters dealing with tribotesting methodology: friction and wear measurement methods are presented in Chapter 13, while in Chapter 14 tribotest program design considerations are discussed. The results of many years of tribotests for metals, ceramics, and polymers are compiled in the friction and wear databank in Chapter 15. The editors of Section I hope that this section will prove to be an effective means of transferring basic tribology science and technology to practicing engineers and scientists in need of this information.
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1 Surface Physics in Tribology 1.1 1.2 1.3
Introduction ........................................................................... 5 Geometry of Surfaces............................................................. 6 Theoretical Considerations.................................................. 10
1.4
Experimental Determinations of Surface Structure .......... 19
Surface Theory • Friction Fundamentals Low-Energy Electron Diffraction • High-Resolution Electron Microscopy • Field Ion Microscopy
1.5
Chemical Analysis of Surfaces............................................. 23 Auger Electron Spectroscopy • X-ray Photoelectron Spectroscopy • Secondary Ion Mass Spectroscopy • Infrared Spectroscopy • Thermal Desorption
Phillip B. Abel
1.6
NASA Glenn Research Center
John Ferrante Cleveland State University
Surface Effects in Tribology................................................. 32 Atomic Monolayer Effects in Adhesion and Friction • Monolayer Effects due to Adsorption of Hydrocarbons • Atomic Effects in Metal-Insulator Contacts
1.7
Concluding Remarks............................................................ 40
1.1 Introduction Tribology, the study of the interaction between surfaces in contact, spans many disciplines, from physics and chemistry to mechanical engineering and material science, and is of extreme technological importance. In this first chapter on tribology, the key word will be surface. This chapter will be rather ambitious in scope in that we will attempt to cover the range from microscopic to macroscopic. We will approach this problem in steps: first considering the fundamental idea of a surface, next recognizing its atomic character and the expectations of a ball model of the atomic structures present. We will then consider more realistic relaxed surfaces and then consider how the class of surface, i.e., metal, semiconductor, or insulator, affects these considerations. Finally, we will present what is expected when a pure material is alloyed and the effects of adsorbates. Following these more fundamental descriptions, we will give brief descriptions of some of the experimental techniques used to determine surface properties and their limitations. The primary objective here will be to provide a source for more thorough examination by the interested reader. Finally, we will examine the relationship of tribological experiments to these more fundamental atomistic considerations. The primary goals of this section will be to again provide sources for further study of tribological experiments and to raise critical issues concerning the relationship between basic surface properties with regard to tribology and the ability of certain classes of experiments to reveal the underlying interactions. We will attempt to avoid overlapping the material presented by other authors in this publication. This chapter cannot be a complete treatment of the physics of surfaces due to space
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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Modern Tribology Handbook
limitations. We recommend an excellent text by Zangwill (1988) for a more thorough treatment. Instead we concentrate on techniques and issues of importance to tribology on the nanoscale.
1.2 Geometry of Surfaces We now examine from a geometric standpoint what occurs when you create two surfaces by dividing a solid along a given plane. We limit the discussion to single crystals, since the same arguments apply to polycrystalline samples except for the existence of grains, each of which could be described by a corresponding argument. This discussion starts by introducing the standard notation for describing crystals given in solid state texts (e.g., Ashcroft and Mermin, 1976; Kittel, 1986). It is meant to be didactic in nature and will not attempt to be comprehensive. In order to establish notation and concepts we limit our discussion to two Bravais lattices, face-centered cubic (fcc) and body-centered cubic (bcc), which are the structures often found in metals. Unit cells, i.e., the structures which most easily display the symmetries of the crystals, are shown in Figure 1.1. The other descriptions that are frequently used are the primitive cells, which show the simplest structures that can be repeated to create a given structure. In Figure 1.1 we also show the primitive cell basis vectors, which can be used to generate the entire structure by the relation
R = n1a 1 + n2a 2 + n3a 3
(1.1)
where n1, n2, and n3 are integers, and a1, a2, and a3 are unit basis vectors. Since we are interested in describing surface properties, we want to present a standard nomenclature for specifying a surface. The algebraic description of a surface is usually given in terms of a vector normal to the surface. This is conveniently accomplished in terms of vectors that arise naturally in solids, namely the reciprocal lattice vectors of the Bravais lattice (Ashcroft and Mermin, 1976; Kittel, 1986). This is convenient since these vectors are used to describe the band structure and diffraction effects in solids. They are usually given in the form
K = hb1 + kb 2 + lb 3
(1.2)
where h,k,l are integers. The reciprocal lattice vectors are related to the basis vectors of the direct lattice by
(
b i = 2π a j × a k
a
) {a ⋅ (a i
j
× ak
)}
(1.3)
b
FIGURE 1.1 (a) Unit cube of face-centered cubic (fcc) crystal structure, with primitive-cell basis vectors indicated. (b) Unit cube of body-centered cubic (bcc) crystal structure, with primitive-cell basis vectors indicated.
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Surface Physics in Tribology
7
a
b
FIGURE 1.2 Projection of cubic face (100) plane for (a) fcc, and (b) bcc crystal structures. In both cases, smaller dots represent atomic positions in the next layer below the surface.
where a cyclic permutation of i,j,k is used in the definition. Typically, parentheses are used in the definition of the plane, e.g., (h,k,l). The (100) planes for fcc and bcc lattices are shown in Figure 1.2 where dots are used to show the location of the atoms in the next plane down. This provides the simplest description of the surface in terms of terminating the bulk. There is a rather nice NASA publication by Bacigalupi (1964) which gives diagrams of many surface and subsurface structures for fcc, bcc, and diamond lattices, in addition to a great deal of other useful information such as surface density and interplanar spacings. A modern reprinting is called for. In many cases, this simple description is not adequate since the surface can reconstruct. Two prominent cases of surface reconstruction are the Au(110) surface (Good and Banerjea, 1992) for metals and the Si(111) surface (Zangwill, 1988) for semiconductors. In addition, adsorbates often form structures with symmetries different from the substrate, with the classic example the adsorption of oxygen on W(110) (Zangwill, 1988). Wood (1963) formalized the nomenclature for describing such structures. In Figure 1.3 we show an example of 2 × 2 structure, where the terminology describes a surface that has a layer with twice the spacings of the substrate. There are many other possibilities, such as structures rotated with respect to the substrate and centered differently from the substrate. These are also defined by Wood (1963). The next consideration is that the interplanar spacing can vary, and slight shifts in atomic positions can occur several planes from the free surface. A recent paper by Bozzolo et al. (1994) presents the results
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Modern Tribology Handbook
FIGURE 1.3 Representation of fcc (110) face with an additional 2 × 2 layer, in which the species above the surface atoms have twice the spacing of the surface. Atomic positions in the next layer below the surface are represented by smaller dots.
1
-3.82% +2.48%
2 3 4 5 Unrelaxed
ECT
FIGURE 1.4 Side view of nickel(100) surface. On the left, the atoms are positioned as if still within a bulk fcc lattice (“unrelaxed”). On the right, the surface planes have been moved to minimize system energy (Bozzolo et al., 1994). The percent change in lattice spacing is indicated, with the spacing in the image exaggerated to illustrate the effect.
for a large number of metallic systems and serves as a good review of available publications. Figure 1.4 shows some typical results for Ni(100). The percent change given represents the deviation from the equilibrium interplanar spacing. The drawing in Figure 1.4 exaggerates these typically small differences in order to elucidate the behavior. Typically, this pattern of alternating contraction and expansion diminishing as the bulk is approached is found in most metals. It can be understood in a simple manner (Bozzolo et al., 1994). The energy for the bulk metal is a minimum at the bulk metallic density. The formation of the surface represents a loss of electron density because of missing neighbors for the surface atoms. Therefore, this loss of electron density can be partially offset by a contraction of the interplanar spacing between the first two layers. This contraction causes an electron density increase between layers 2 and 3 and, thus, the energy is lowered by a slight increase in their interplanar spacing. There are some exceptions to this behavior where the interplanar spacing increases between the first two layers due to bonding effects (Needs, 1987; Feibelman, 1992). However, the pattern shown in Figure 1.4 is the usual behavior for most metallic surfaces. There can be similar changes in position within the planes; however, these are usually small effects (Rodriguez et al., 1993; Foiles, 1987). In Figure 1.5, we show a side view of a gold (110) surface (Good and Banerjea, 1992). Figure 1.5a shows the unreconstructed surface and 1.5b shows a side view of the (2 × 1) missing row reconstruction. Such behavior indicates the complexity that can arise even for metal surfaces and the danger of using ideas which are too simplistic, since more details of the bonding interactions are needed (Needs, 1987; Feibelman, 1992). Real crystal surfaces typically are not perfectly oriented nor atomically flat. Even “on-axis” (i.e., within a fraction of a degree) single crystal low-index faces exhibit some density of crystallographic steps. For
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a
b
FIGURE 1.5 Side view of nickel(110) surface: (a) unreconstructed; (b) 1 × 2 missing row surface reconstruction. (From Good, B.S. and Banerjea, A. (1992), Monte Carlo Study of Reconstruction of the Au(110) Surface Using Equivalent Crystal Theory, in Mat. Res. Soc. Symp. Proc., Vol. 278, pp. 211-216. With permission.)
a gold(111) face tilted one half degree toward the (011) direction, evenly spaced single atomic height steps would be only 27 nm apart. Other surface-breaking crystal defects such as screw and edge dislocations may also be present, in addition to whatever surface scratches, grooves, and other polishing damage remains in a real single crystal surface. Surface steps and step kinks would be expected to show greater reactivity than low-index surface planes. During either deposition or erosion of metal surfaces one expects incorporation into or loss from the crystal lattice preferentially at step edges. More generally on simple metal surfaces, lone atoms on a low index crystal face are expected to be most mobile (i.e., have the lowest activation energy to move). Atoms at steps would be somewhat more tightly bound, and atoms making up a low-index face would be least likely to move. High-index crystal faces can often be thought of as an ordered collection of steps on a low-index face. When surface species and even interfaces become mobile, consolidation of steps may be observed. Alternating strips of two low-index crystal faces can then develop from one high-index crystal plane, with lower total surface energy but with a rougher, faceted topography. Much theoretical and experimental work has been done over the last decade on nonequilibrium as well as equilibrium surface morphology (e.g., Kaxiras, 1996; Williams, 1994; Bartelt et al., 1994; Conrad and Engel, 1994; Vlachos et al., 1993; Redfield and Zangwill, 1992). Semiconductors and insulators generally behave differently (Srivastava, 1997). Unlike most metals for which the electron gas to some degree can be considered to behave like a fluid, semiconductors have strong directional bonding. Consequently, the loss of neighbors leaves dangling bonds which are satisfied by reconstruction of the surface. The classic example of this is the silicon(111) 7 × 7 structure, where rebonding and the creation of surface states gives a complex structure. Until a scanning probe microscope (SPM) provided real-space images of this reconstruction (Binnig et al., 1983) much speculation surrounded this surface. Zangwill (1988) shows both the terminated bulk structure of Si(111) and the relaxed 7 × 7 structure. It is clear that viewing a surface as a simple terminated bulk can lead to severely erroneous conclusions. The relevance to tribology is clear since the nature of chemical reactions between surfaces, lubricants, and additives can be greatly affected by such radical surface alterations. There are other surface chemical state phenomena, even in ultra-high vacuum, just as important as the structural and bonding states of the clean surface. Surface segregation often occurs to metal surfaces and interfaces (Faulkner, 1996, and other reviews cited therein). For example trace quantities of sulfur often segregate to iron and steel surfaces or to grain boundaries in polycrystalline samples (Jennings et al., 1988). This can greatly affect results since sulfur, known to be a strong poisoning contaminant in catalysis, can affect interfacial bond strength. Sulphur is often a component in many lubricants. For alloys, similar geometrical surface reconstructions occur (Kobistek et al., 1994). Again alloy surface composition can vary dramatically from the bulk, with segregation causing one of the elements to be the only component on a surface. In Figure 1.6 we show the surface composition for a CuNi alloy as a function of bulk composition with both a large number of experimental results and some theoretical predictions for the composition (Good et al., 1993). In addition nascent surfaces typically react with the ambient, giving monolayer films and oxidation even in ultra-high vacuum, producing even more pronounced surface composition effects. In conclusion, we see that even in the most simple circumstances, i.e., single-crystal surfaces, the situation can be very complicated.
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Cu (111)
1.0
xCu [surface]
0.8
Y
0.6
0.4
Y
Y
0.2 Y
0.0 0.0
Y
0.2
0.4
0.6
0.8
1.0
xCu [bulk]
BFS [800 K] Ref.31 [923 K] Ref.19 [870-920 K] Ref.19 [823 K] Ref.15 [873 K]
Ref.16 [800 K] Ref.20 [773 K,673 K] Ref.30 [973 K] Y Ref.28 [800 K] ( ) Ref.30 [973 K]
FIGURE 1.6 Copper(111) surface composition vs. copper bulk composition: comparison between the experimental and theoretical results for the first and second planes. (From Good, B., Bozzolo, G., and Ferrante, J. (1993), Surface segregation in Cu–Ni alloys, Phys. Rev. B, Vol. 48, pp. 18284-18287 [and references therein]. With permission © 1993 American Physical Society.)
1.3 Theoretical Considerations 1.3.1 Surface Theory We have shown how the formation of a surface can affect geometry. We now present some aspects of the energetics of surfaces from first-principles considerations. For a long time, calculations of the electronic structure and energetics of the surface had proven to be a difficult task. The nature of theoretical approximations and the need for high-speed computers limited the problem to some fairly simple approaches (Ashcroft and Mermin, 1976). The advent of better approximations for the many body effects, namely for exchange and correlation, and the improvements in computers have changed this situation in the not too distant past. One aspect of the improvements was density functional theory and the use of the local density approximation (LDA) (Kohn and Sham, 1965; Lundqvist and March, 1983). Difficulties arise because, in the creation of the surface, periodicity in the direction perpendicular to the surface is lost. Periodicity simplifies many problems in solid state theory by limiting the calculation to a single unit cell with periodic boundary conditions. With a surface present the wave vector perpendicular to the surface, k⊥ , is not periodic, although the wave vector parallel to the surface, k , still is. Calculations usually proceed by solving the one-electron Kohn–Sham equations (Kohn and Sham, 1965; Lundqvist and March, 1983), where a given electron is treated as though it is in the mean field of all of the other electrons. The LDA represents the mean field in terms of the local electron density at a
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given location. The Kohn–Sham equations are written in the form (using normalized atomic units where the constants appearing in the Schroedinger equation, Planck’s constant and the electron rest mass, along with the electron charge and the speed of light, h = me = e = c ≡ 1).
[−1 2∇ + V(r)]Ψ (k , r) = ε (k ) Ψ (k , r) 2
i
i
i
(1.4)
where Ψi and εi are the one-electron wave function and energy, respectively, and
() ()
[ ( )]
V r = Φ r + Vxc ρ r
(1.5)
where Vxc[ρ(r)] is the exchange and correlation potential, ρ(r) is the electron density (the brackets indicate that it is a functional of the density), and Φ(r) is the electrostatic potential given by
()
()
Φ r = ∫ dr ′ ρ r
r − r′ − Σ j Z j r − R j
(1.6)
in which the first term is the electron–electron interaction and the second term is the electron–ion interaction, Zj is the ion charge and the electron density is given by
( )
()
ρ r = Σ occ Ψi k , r
2
(1.7)
where occ refers to occupied states. The calculation proceeds by using some representation for the wave functions such as the linear muffin tin orbital approximation (LMTO), and iterating self-consistently (Ashcroft and Mermin, 1976). Self-consistency is obtained when either the output density or potential agree to within some specified criterion with the input. These calculations are not generally performed for the semi-infinite solid. Instead, they are performed for slabs of increasing thickness to the point where the interior atoms have essentially bulk properties. Usually, five planes are sufficient to give the surface properties. The values of εi(k) give the surface band structure and surface states, localized electronic states created because of the presence of the surface. The second piece of information needed is the total energy in terms of the electron density, as obtained from density functional theory. This is represented schematically by the expression
[]
[]
[]
[]
E ρ = E ke ρ + Ees ρ + E xc ρ
(1.8)
where Eke is the kinetic energy contribution to the energy, Ees is the electrostatic contribution, Exc is the exchange correlation contribution, and the brackets indicate that the energy is a function of the density. Thus the energy is an extremum of the correct density. Determining the surface energy accurately from such calculations can be quite difficult since the surface, or indeed any of the energies of defects of interest, are obtained as a difference of big numbers. For example, for the surface the energy would be given by
{ ( ) ( )} 2A
Esurface = E a − E ∞
(1.9)
where a is the distance between the surfaces (a = 0 to get the surface energy) and A is the cross-sectional area. The initial solutions of the Kohn–Sham equations for surfaces and interfaces were accomplished by Lang and Kohn (1970) for the free surface and Ferrante and Smith for interfaces (Ferrante and Smith,
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1985; Smith and Ferrante, 1986). The calculations were simplified by using the jellium model to represent the ionic charge. In the jellium model the ionic charge is smeared into a uniform distribution. Both sets of authors introduced the effects of discreteness on the ionic contribution through perturbation theory for the electron–ion interaction and through lattice sums for the ion–ion interaction. The jellium model is only expected to give reasonable results for the densest packed planes of simple metals. In Figures 1.7 and 1.8 we show the electron distribution at a jellium surface for Na and for an Al(111)–Mg(0001) interface (Ferrante and Smith, 1985) that is separated by a small distance. In Figure 1.7 we can see the characteristic decay of the electron density away from the surface. In Figure 1.8 we see the change in electron density in going from one material to another. This characteristic tailing is an indication of the reactivity of the metal surface. In Figure 1.9 we show the electron distribution for a nickel(100) surface for the fully three-dimensional calculations performed by Arlinghouse et al. (1980) and that for a silver layer adsorbed on a palladium(100) interface (Smith and Ferrante, 1985) using self-consistent localized orbitals (SCLO) for approximations to the wave functions. First, we note that for the Ni surface there is a smoothing of the surface density characteristic of metals. For the silver adsorption we can see that there are localized charge transfers and bonding effects indicating that it is necessary to perform three-dimensional calculations in order to determine bonding effects. Hong et al. (1995) have also examined metal ceramic interfaces and the effects of impurities at the interface on the interfacial strength. In Figure 1.10 we schematically show the results of determining the interfacial energies as a function of separation between the surfaces with the energy in Figure 1.10a and the derivative curves giving the interfacial strength. In Figure 1.11 we show Ferrante and Smith’s results for a number of interfaces of jellium metals (Ferrante and Smith, 1985; Smith and Ferrante, 1986; Banerjea et al., 1991). Rose et al. (1981, 1983) found that these curves would scale onto one universal curve and indeed that this result applied to many other bonding situations including results of fully three-dimensional calculations. We show the scaled curves from Figure 1.11 in Figure 1.12. A very useful generalization of the original work can be applied to multicomponent alloy surfaces (Bozzolo et al., 1999). Somewhat surprisingly because of large charge transfer, Hong et al. (1995) found that this same behavior also is applicable to metal–ceramic interfaces. Finnis (1996) gives a review of metal–ceramic interface theory. The complexities that we described earlier with regard to surface relaxations and complex structures can also be treated now by modern theoretical techniques. Often in these cases it is necessary to use “supercells” (Lambrecht and Segall, 1989). Since these structures are extended, it would require many atoms to represent a defect. Instead, in order to model a defect and take advantage of the simplicities of periodicities, a cell is created selected at a size which will mimic the main energetics of the defects. In conclusion, theoretical techniques have advanced substantially and are continuing to do so. They have and will shed light on many problems of interest experimentally.
1.3.2 Friction Fundamentals Friction, as commonly used, refers to a force resisting sliding. It is of obvious importance since it is the energy loss mechanism in sliding processes. In spite of its importance, after many centuries friction surprisingly has still avoided a complete physical explanation. An excellent history of the subject is given in a text by Dowson (1979). In this section we will outline some of the basic observations and give some recent relevant references treating the subject at the atomic level, in keeping with the theme of this chapter, and since the whole topic is much too complicated to treat in such a small space. There are two basic issues, the nature of the friction force and the energy dissipation mechanism. There are several commonplace observations, often considered general rules, regarding the friction force as outlined in the classic discussions of the subject by Bowden and Tabor (1964): 1. The friction force does not depend on the apparent area of contact. 2. The friction force is proportional to the normal load. 3. The kinetic friction force does not depend on the velocity and is less than the static friction force.
FIGURE 1.7 Electron density at a jellium surface vs. position for a Na(011)–Na(011) contact for separations of 0.25, 3.0, and 15.0 au. (From Ferrante, J. (1978), Adhesion of a Bimetallic Interface, NASA TM-78890 National Aeronautics and Space Administration, Washington, D.C.).
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FIGURE 1.8 Electron number density n and jellium ion charge density for an aluminum(111)–magnesium(0001) interface. (From Ferrante, J. and Smith, J.R. (1985), Theory of the bimetallic interface, Phys. Rev. B, Vol. 31, pp. 3427-3434. With permission. © 1985 American Physical Society.)
Historically Coulomb (Dowson, 1979; Bowden and Tabor, 1964), realizing that surfaces were not ideally flat and were formed by asperities (a hill and valley structure), proposed that interlocking asperities could be a source of the friction force. This model has many limitations. For example, if we picture a perfectly sinusoidal interface there is no energy dissipation mechanism, since once the top of the first asperity is attained the system will slide down the other side, thus needing no additional force once set in motion. Bowden and Tabor (1964), recognizing the existence of interfacial forces, proposed another mechanism based on adhesion at interfaces. Again, recognizing the existence of asperities, they proposed that adhesion occurs at asperity contacts and then shearing occurs with translational motion. As can be seen, this model explains a number of effects such as the disparity between true area of contact and apparent area of contact, and the tracking of friction force with load, since the asperities and thus the true area of contact change with asperity deformation (load). The actual arguments are more complex than indicated here and require reading of the primary text for completeness. These considerations also emphasize the basic topic of this chapter, i.e., the important effect of the state of the surface and interface on the friction process. Clearly, adsorbates, the differences of materials in contact, and lubricants greatly affect the interaction. We now proceed to outline briefly some models of both the friction force and frictional energy dissipation. As addressed elsewhere in this volume there have been recently a number of attempts to theoretically model the friction interaction at the atomic level. The general approaches have involved
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FIGURE 1.9 (a) Electronic charge density contours at a nickel(100) surface. (From Arlinghaus, F.J., Gay, J.G., and Smith, J.R. (1980), Self-consistent local-orbital calculation of the surface electronic structure of Ni (100), Phys. Rev. B, Vol. 21, pp. 2055-2059. With permission. © 1980 American Physical Society.) (b) Charge transfer of the palladium (100) slab upon silver adsorption. (From Smith, J.R. and Ferrante, J. (1985), Materials in Intimate Contact, Mat. Sci. Forum, Vol. 4, pp. 21-38. With permission.)
assuming a two-body interaction potential at an interface, which in some cases may only be onedimensional, and allowing the particles to interact across an interface, allowing motion of internal degrees of freedom in either one or both surfaces. Hirano and Shinjo (1990) examine a quasistatic model where one solid is constrained to be rigid and the second is allowed to adapt to the structure of the first, interacting through a two-body potential as translation occurs. No energy dissipation mechanism is included. They conclude that two processes occur: atomic locking where the readjusting atoms change
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FIGURE 1.10 Example of a binding energy curve: (a) energy vs. separation; (b) force vs. separation. (From Banerjea, A., Ferrante, J., and Smith, J.R. (1991), Adhesion at metal interfaces, in Fundamentals of Adhesion, Liang-Huang Lee, (Ed.), Plenum Publishing, New York, pp. 325-348. With permission.)
their positions during sliding, and dynamic locking where the configuration of the surface changes abruptly due to the dynamic process if the interatomic potential is stronger than a threshold value. The latter process they conclude is unlikely to happen in real systems. They also conclude that the adhesive force is not related to the friction force, and discuss the possibility of a frictionless “superlubric” state (Shinjo and Hirano, 1993; Hirano et al., 1997). Matsukawa and Fukuyama (1994) carry the process further in that they allow both surfaces to adjust and examine the effects of velocity with attention to the three rules of friction stated above. They argue, not based on their calculations, that the Bowden and Tabor argument is not consistent with flat interfaces having no asperities. Since an adhesive force exists, there is a normal force on the interfaces with no external load. Consequently, rules of friction one and two break down. With respect to rule three, they find it restricted to certain circumstances. They found
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0
a
-200
-400
-600
-800 (B) Zn(0001)-Zn(0001).
(A) AI(111)-AI(111). 0
-200
ADHESIVE ENERGY, ERG/CM
2
-400
-600
-800 0
.2
.4
.6
.8
1.0
0
.2
.4
.6
.8
1.0
(D) Na(110)-Na(110).
(C) Mg(0001) - Mg(0001).
b -200
-400
Mg(0001) - Na(110)
AI(111) - Mg(0001)
AI(111) - Zn(0001)
-600
-200
-400
AI(111) - Na(110)
Zn(0001) - Mg(0001)
Zn(0001) - Na(110)
-600 0
.2
.4
.6 0
.2
.4
.6
0
.2
.4
.6
SEPARATION a. NM FIGURE 1.11 Adhesive energy vs. separation: (a) commensurate adhesion is assumed; (b) incommensurate adhesion is assumed. (From Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. With permission. © 1983 American Physical Society.)
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0 -.1
SCALED ADHESIVE ENERGY, E*
-.2 -.3 AI-AI Zn-Zn Mg-Mg Na-Na AI-Zn AI-Mg AI-Na Mg-Na Zn-Na Zn-Mg
-.4 -.5 -.6 -.7 -.8 -.9 -1.0 -1
0
1
2
3
4
5
6
7
8
SCALED SEPARATION, a*
FIGURE 1.12 Scaled adhesive binding energy as a function of scaled separation for systems in Figure 1.11. (From Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. With permission. © 1983 American Physical Society.)
that the dynamic friction force, in general, is sliding velocity dependent, but with a decreasing velocity dependence with increasing maximum static friction force. Hence for systems with large static friction forces, the kinetic friction force shows behavior similar to classical rule three, above. Finally, Zhong and Tomanek (1990) performed a first-principles calculation of the force to slide a monolayer of Pd in registry with the graphite surface. Assuming some energy dissipation mechanism to be present, they calculated tangential force as a function of load and sliding position. Sokoloff (1990, 1992, and references therein) addresses both the frictional force and friction energy dissipation. He represents the atoms in the solids as connected by springs, thus enabling an energy dissipation mechanism by way of lattice vibrations. He also looks at such issues as the energy to create and move defects in the sliding process and examines the velocity dependence of kinetic friction based on the possible processes present, including electronic excitations (Sokoloff, 1995), concluding that both velocity-dependent and independent processes contribute to the force of friction (Sokoloff and Tomassone, 1998). Even a simplified model of flat, sliding, featureless dielectric surfaces can generate velocitydependent friction of a magnitude comparable to Van der Waals forces, according to Pendry (1997). Persson (1991) proposes a model for energy dissipation due to electronic excitations induced within a metallic surface, and concludes (Volokitin and Persson, 1999) that, except possibly for physisorbed layers of atoms sliding on a metal surface, this “van der Waals friction” is negligible compared to friction forces due to real areas of contact between macroscopic bodies. Persson (1993a, 1994, 1995) also addresses the effect of a boundary lubricant between macroscopic bodies, modeling fluid pinning to give the experimentally observed logarithmic time dependence of various relaxation processes. He has devoted an entire book (Persson, 1998) as well as a review article (Persson, 1999) to sliding friction, with emphasis on recent theoretical and experimental results. Interestingly, the concept of “elastic coherence length” in sliding friction theory can also be applied to earthquake dynamics (Persson and Tosatti, 1999). Finally, as more fully covered in other chapters of this volume, much recent effort has gone into modeling
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specifically the lateral force component of a probe tip interaction with a sample surface in scanning probe microscopy (e.g., Hölscher et al., 1997; Diestler et al., 1997, and references therein; Lantz et al., 1997). In conclusion, while these types of simulations may not reflect the full complexity of real materials, they are necessary and useful. Although limited in scope, it is necessary to break down such complex problems into isolated phenomena which, it is hoped, can result in the eventual unification in the larger picture. It simply is difficult to isolate the various components contributing to friction experimentally.
1.4 Experimental Determinations of Surface Structure In this section we will discuss three techniques for determining the structure of a crystal surface, lowenergy electron diffraction (LEED), high-resolution electron microscopy (HREM), and field ion microscopy (FIM). The first, LEED, is a diffraction method for determining structure, and the latter two are methods to view the lattices directly. There are other methods for determining structure, such as ion scattering (Niehus et al., 1993), low-energy backscattered electrons (De Crescenzi, 1995), and even secondary electron holography (Chambers, 1992) which we will not discuss. Other contributors to this volume address scanning probe microscopy and tribology, which are also nicely covered in an extensive review article by Carpick and Salmeron (1997).
1.4.1 Low-Energy Electron Diffraction Since LEED is a diffraction technique, when viewing a LEED pattern you are viewing the reciprocal lattice and not atomic locations on the surface. A LEED pattern typically is obtained by scattering low-energy electrons (0 to ~300 eV) from a single crystal surface in ultra-high vacuum. In Figure 1.13 we show the LEED pattern for the W(110) surface with a half monolayer of oxygen adsorbed on it (Ferrante et al., 1973). We can first notice in Figure 1.13a that the pattern looks like the direct lattice W(110) surface, but this only means that the diffraction pattern reflects the symmetry of the lattice. Notice that in Figure 1.13b extra spots appear at 1/2 order positions upon adsorption of oxygen. Since this is the reciprocal lattice, this means that the spacings of the rows of the chemisorbed oxygen actually are at double the spacing of the underlying substrate. In fact the interpretation of this pattern is more complicated since the structure shown would not imply a 1/2 monolayer coverage, but is interpreted as an overlapping of domains at 90° from one another. In this simple case the coverage is estimated by adsorption experiments, where saturation is interpreted as a monolayer coverage. The interpretation of patterns is further
CLEAN
1/2 MONOLAYER OF OXYGEN
FIGURE 1.13 LEED pattern for (a) clean, and (b) oxidized tungsten(110) with one-half monolayer of oxygen. The incident electron beam energy for both patterns is 119 eV. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
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complicated, since with complex structures such as the silicon 7 × 7 pattern, the direct lattice producing this reciprocal lattice is not unique. Therefore it is necessary to have a method to select between possible structures (Rous and Pendry, 1989). We now digress for a moment in order to discuss the diffraction process. The most familiar reference work is X-ray diffraction (Kittel, 1986). We know that for X-rays the diffraction pattern of the bulk would produce what is known as a Laue pattern where the spots represent reflections from different planes. The standard diffraction condition for constructive interference of a wave reflected from successive planes is given by the Bragg equation
2d ⋅ sinθ = nλ
(1.10)
where d is an interplanar spacing, θ is the diffraction angle, λ is the wavelength of the incident radiation, and n is an integer indicating the order of diffraction. Only certain values of θ are allowed where diffractions from different sets of parallel planes add up constructively. There is another simple method for picturing the diffraction process known as the Ewald sphere construction (Kittel, 1986), where it can be easily shown that the Bragg condition is equivalent to the relationship
k − k′ = G
(1.11)
where k is the wave vector (2π/λ) of the incident beam, k′′ is the wave vector of the diffracted beam, and G is a reciprocal lattice vector. The magnitude of the wave vectors k = k′ are equal since momentum is conserved, i.e., we are only considering elastic scattering. Therefore a sphere of radius k can be constructed, which when intersecting a reciprocal lattice point indicates a diffracted beam. This is equivalent to the wave vector difference being equal to a reciprocal lattice vector, with that reciprocal lattice vector normal to the set of planes of interest, and θ the angle between the wave vectors. In complex patterns, spot intensities are used to distinguish between possible structures. The equivalent Ewald construction for LEED is shown in Figure 1.14. We note that the reciprocal lattice for a true two-dimensional surface would be a set of rods instead of a set of points. Consequently the Ewald sphere will always intersect the rods and give diffraction spots resulting from interferences due to scattering between rows of surface atoms, with the number of spots changing with electron wavelength and incident angle. However, for LEED, complexity results from spot intensity modulation by the three-dimensional lattice structure. In X-ray diffraction the scattering is described as kinematic, which means that only single scattering events are considered. With LEED, multiple scattering occurs because of the low energy of the incident electrons; thus, structure determination involves solving a difficult quantum mechanics problem. Generally, various possible structures are constructed, and the multiple scattering problem is solved for each proposed structure. The structure which minimizes the difference between the experimental intensity curves and the theoretical calculations is the probable structure. There are a number of parameters involved with atomic positions and electronic properties, and the best fit parameter is denoted as the “R-factor.” In spite of the complexity, considerable progress has been made, and computer programs for performing the analysis are available (Van Hove et al., 1993). The LEED structures give valuable information about adsorbate binding which can be used in the energy calculations described previously.
1.4.2 High-Resolution Electron Microscopy Fundamentally, materials derive their properties from their make-up and structure, even down to the level of the atomic ordering in alloys. In order to fully understand the behavior of materials as a function of their composition, processing history, and structural characteristics, the highest resolution examination tools are needed. In this section we will limit the discussion to electron microscopy techniques using commonly available equipment and capable of achieving atomic-scale resolution. Traditional scanning electron microscopy (SEM), therefore, will not be discussed, though in tribology SEM has been and should continue to prove very useful, particularly when combined with X-ray spectroscopy. Many modern
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Electron Gun Diffracted Electrons nλ = d sin θ
Fluorescent Screen
θ
1/λ = V/150
Crystal 1/d
Ewald Sphere
Reciprocal Net Rods
FIGURE 1.14 Ewald sphere construction for LEED. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
Auger electron spectrometers (discussed in the next section on surface chemical analysis) also have highresolution scanning capabilities, and thus can perform imaging functions similar to a traditional SEM. Another technique not discussed here is photoelectron emission microscopy (PEEM). While PEEM can routinely image photoelectron yield (related to the work function) differences due to single atomic layers, lateral resolution typically suffers in comparison to SEM. PEEM has been applied to tribological materials, however, with interesting results (Montei and Kordesch, 1996). Both transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) make use of an electron beam accelerated through a potential of, typically, up to a few hundred kilovolts. Generically, the parts of a S/TEM consist of an electron source such as a hot filament or field emission tip, a vacuum column down which the accelerated and collimated electrons are focused by usually magnetic lenses, and an image collection section, often comprised of a fluorescent screen or CCD camera for immediate viewing combined with a film transport and exposure mechanism for recording images. The sample is inserted directly into the beam column and must be electron transparent, both of which severely limit sample size. There are numerous good texts available about just TEM and STEM (e.g., Hirsch et al., 1977; Thomas and Goringe, 1979). An advantage to probing a sample with high-energy electrons lies in the De Broglie formula relating the motion of a particle to its wavelength
(
λ = h 2mE k
)
12
(1.12)
where λ is the electron wavelength, h is the Planck constant, m is the particle mass, and Ek is the kinetic energy of the particle. An electron accelerated through a 100 kV potential then has a wavelength of
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0.04 Ångstom, well below any diffraction limitation on atomic resolution imaging. This is in contrast with LEED, for which electron wavelengths are typically of the same order as interatomic spacings. As the electron beam energy increases in S/TEM, greater sample thickness can be penetrated with usable signal reaching the detector. Mitchell (1973) discusses the advantages of using very high accelerating voltages, which at the time included TEM voltages up to 3 MV. More recently, commercially available instruments have taken advantage of the sub-angstrom electron wavelengths with design advances allowing routine achievement of atomic-scale imaging, though image interpretation becomes an issue at that scale (Smith, 1997). As the electron beam traverses a sample, any crystalline regions illuminated will diffract the beam, forming patterns characteristic of the crystal type. Apertures in the microscope column allow the diffraction patterns of selected sample areas to be observed. Electron diffraction patterns combined with an ability to tilt the sample make determination of crystal symmetry and orientation relatively easy, as discussed in Section 1.4.1 above for X-ray Ewald sphere construction. Electrons traversing the sample can also undergo an inelastic collision (losing energy), followed by coherent rescattering. This gives rise to cones of radiation which reveal the symmetry of the reflecting crystal planes, showing up in diffraction images as “Kikuchi lines,” named after the discoverer of the phenomenon. The geometry of the Kikuchi lines provides a convenient way of determining crystal orientation with fairly high accuracy. Another technique for illuminating sample orientation uses an aperture to select one of the diffracted beams to form the image, which nicely highlights sample area from which that diffracted beam originates (“darkfield” imaging technique). One source of TEM image contrast is the electron beam interacting with crystal defects such as various dislocations, stacking faults, or even strain around a small inclusion. How that contrast changes with microscope settings can reveal information about the defect. For example, screw dislocations may “disappear” (lose contrast) for specific relative orientations of crystal and electron beam. An additional tool in examining extended three-dimensional structures within a sample is stereomicroscopy, where two images of the same area are captured tilted from one another, typically by around 10°. The two views are then simultaneously shown, each to one eye, to reveal image feature depth. For sample elemental composition, an X-ray spectrometer and/or an electron energy-loss spectrometer can be added to the S/TEM. Particularly for STEM, due to minimal beam spreading during passage through the sample the analyzed volume for either spectrometer can be as small as tens of nanometers in diameter. X-ray and electron energy-loss spectrometers are somewhat complementary in their ranges of easily detected elements. Characteristic X-rays are more probable when exciting the heavier elements, while electron energy losses due to light element K-shell excitations are easily resolvable. Both TEM and STEM rely on transmission of an electron beam through the sample, placing an upper limit on specimen thickness which depends on the accelerating voltage available and on specimen composition. Samples are often thinned to less than a micrometer, with lateral dimensions limited to a few millimeters. An inherent difficulty in S/TEM sample preparation is locating a given region of interest within the region of visibility in the microscope, without altering sample characteristics during any thinning process needed. For resolution at an atomic scale, columns of lighter element atoms are needed for image contrast, so individual atoms are not “seen.” Samples also need to be somewhat vacuum compatible, or at least stable enough in vacuum to allow examination. The electron beam itself may alter the specimen either by heating, by breaking down compounds within the sample, or by depositing carbon on the sample surface if there are residual hydrocarbons in the microscope vacuum. In short, S/TEM specimens should be robust under high-energy electron bombardment in vacuum.
1.4.3 Field Ion Microscopy For many decades, field ion microscopy (FIM) has provided direct lattice images from sharp metal tips. Some early efforts to examine contact adhesion used the FIM tip as a model asperity, which was brought into contact with various surfaces (Mueller and Nishikawa, 1968; Nishikawa and Mueller, 1968; Brainard and Buckley, 1971, 1973; Ferrante et al., 1973). As well, FIM has been applied to the study of friction
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FIGURE 1.15 Field ion microscope pattern of a clean tungsten tip oriented in the (110) direction. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
(Tsukizoe et al., 1985), the effect of adsorbed oxygen on adhesion (Ohmae et al., 1987), and even direct examination of solid lubricants (Ohmae et al., 1990). In FIM a sharp metal tip is biased to a high negative potential relative to a phosphor-coated screen in an evacuated chamber backfilled to about a millitorr with helium or other noble gas. A helium atom impinging on the tip experiences a high electric field due to the small tip radius. This field polarizes the atom, potentially creating a helium ion. Ionization is most probable directly over atoms in the tip where the local radius of curvature is highest. Often, only 10 to 15% of the atoms on the tip located at the zone edges and at kink sites are visible. The helium ions are then accelerated to a phosphorescent screen at some distance from the tip, giving a large geometric magnification. Uncertainty in surface atom positions is often reduced by cooling the tip to liquid helium temperature. Figure 1.15 is a FIM pattern for a clean tungsten tip oriented in the (110) direction. The small rings are various crystallographic planes that appear on a hemispherical single crystal surface. A classic discussion of FIM pattern interpretation can be found in Mueller (1969); a review has been published by Kellogg (1994); and a more extensive discussion of FIM in tribology can be found in Ohmae (1993).
1.5 Chemical Analysis of Surfaces In this section we will discuss four of the many surface chemical analytic tools which we feel have had the widest application in tribology, Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), secondary ion mass spectroscopy (SIMS), and infrared spectroscopy (IR). AES gives elemental analysis of surfaces, but in some cases will give chemical compound information. XPS can give compound information as well as elemental. SIMS can exhibit extreme element sensitivity as well as “fingerprint” lubricant molecules. IR can identify hydrocarbons on surfaces, which is relevant because most lubricants are hydrocarbon based. Hantsche (1989) gives a basic comparison of some surface analytic techniques, and surface characterization advances have been reviewed every 2 years since 1977 in the journal Analytical Chemistry (e.g., McGuire et al., 1999). Before launching into this discussion we wish to present a general discussion of surface analyses. We use a process diagram to describe them given as
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EXCITATION (INTERACTION) ⇓ DISPERSION ⇓ DETECTION ⇓ SPECTROGRAM The first step, excitation in interaction, represents production of the particles or radiation to be analyzed. In light or photon emission spectroscopy a spark causes the excitation of atoms to higher energy states, thus emitting characteristic photons. The dispersion stage could be thought of as a filtering process where the selected information is allowed to pass and other information is rejected. In light spectroscopy this would correspond to the use of a grating or prism, for an ion or electron it might be an electrostatic analyzer. Next is detection of the particle which could be a photographic plate for light or an electron multiplier for ions or electrons. And, finally, the spectrogram tells what materials are present and hopefully how much is there.
1.5.1 Auger Electron Spectroscopy The physics of the Auger emission process is shown in Figure 1.16. An electron is accelerated to an energy sufficient to ionize an inner level of an atom. In the relaxation process an electron drops into the ionized energy level. The energy that is released from this de-excitation is absorbed by an electron in a higher energy level, and if the energy is sufficient it will escape from the solid. The process shown is called a KLM transition, i.e., a level in the K shell is ionized, an electron decays from an L shell, and the final
FIGURE 1.16 Auger transition diagram for an atom. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
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electron is emitted from an M shell. Similarly, a process involving different levels will have corresponding nomenclature. The energy of the emitted electron has a simple relationship to the energies of the levels involved, depending only on differences between these levels. The relationships for the process shown are
∆E final = ∆Einitial
(1.13)
Eauger = E K − E L − E M
(1.14)
giving
Consequently, since the energy levels of the atoms are generally known, the element can be identified. There are surprisingly few overlaps for materials of interest. When peaks do overlap, other peaks peculiar to the given element along with data manipulation can be used to deconvolute peaks close in energy. AES will not detect hydrogen, helium, or atomic lithium because there are not enough electrons for the process to occur. AES is surface sensitive because the energy of the escaping electrons is low enough that they cannot originate from very deep within the solid without detectable inelastic energy losses. The equipment is shown schematically in Figure 1.17. The dispersion of the emitted electrons is usually accomplished by any of a number of electrostatic analyzers, e.g., cylindrical mirror or hemispherical analyzers. Although the operational details of the analyzers differ somewhat, the net result is the same. An example spectrum is shown in Figure 1.18 for a wearscar on a pure iron pin worn with dibutyl adipate with 1 wt% zinc-dialkyl-dithiophosphate (ZDDP). This spectrum corresponds to the first derivative of the actual spectral lines (peaks) in the spectrum (Brainard and Ferrante, 1979). Historically, first derivative spectra were taken because the actual peaks were very small compared to the slowly varying background, posing signal to noise problems. The derivative emphasized the more rapidly changing peak, but made quantification more difficult, since the AES peaks are not a simple shape such as Gaussian, where a quantitative relationship exists between the derivative peak-to-peak height and the area under the original peak. The advent of dedicated microprocessors and the ability to digitize the results enable more sophisticated treatment of the data. The signal to background problem can now be handled by modeling the background and subtracting it, leaving an enhanced AES peak. Thus the number of particles present can be obtained by finding the area under the peak, enhancing the quantitative capability of AES. AES can be chemically sensitive in that energy levels may shift when chemical reactions occur. Large shifts can be detected in the AES spectrum or, alternatively, peak shapes may change with chemical reaction. Some examples of these effects will be given later in the chapter.
FIGURE 1.17 Schematic diagram of AES apparatus. (From Ferrante, J. (1982), Practical applications of surface analytic tools in tribology, J. Am. Soc. Lubr. Eng., Vol. 38, pp. 223-236. With permission.)
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FIGURE 1.18 Auger spectrum of wear scar on a pure iron pin run against M2 tool steel disk in dibutyl adipate containing 1-wt% ZDDP. Sliding speed, 2.5 cm/s; load, 4.9 N; atmosphere, dry air. (From Brainard, W.A. and Ferrante, J. (1979), Evaluation and Auger Analysis of a Zinc-Dialkyl-Dithiophosphate Antiwear Additive in Several Diester Lubricants, NASA TP-1544, National Aeronautics and Space Administration, Washington, D.C.)
There are two other techniques that are used in conjunction with AES that should be mentioned: scanning Auger microscopy (SAM) and depth profiling. SAM is simply “tuning” to a particular AES peak and rastering the electron beam in order to obtain an elemental map of a surface. This can be particularly useful in tribology since you are often dealing with rough, inhomogeneous surfaces. We show a sample SAM map in Figure 1.19.
FIGURE 1.19 Example of scanning Auger microscopy results. Sample is silicon carbide fiber reinforced titanium aluminide matrix composite. Single element images as labeled, with higher concentrations represented as brighter regions. (A) SEM mode; (B) silicon; (C) carbon; (D) titanium. (Darwin Boyd, unpublished results.)
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Depth profiling is the process of sputter-eroding a sample by bombarding the surface with ions while simultaneously obtaining AES or other spectra. This enables one to obtain the composition of reactionformed or deposited films on a surface as a function of sputter time or depth, given proper attention to the effects of sputtering itself (Hofman, 1998). Consequently, AES has many applications for studying tribological and other surfaces. Some examples will be given in subsequent sections.
1.5.2 X-ray Photoelectron Spectroscopy The physical processes involved in XPS are simpler than in AES. An X-ray photon ionizes the inner level of an atom directly, and in this case the emitted electron from the ionization is detected, as opposed to AES where several electron energy levels are involved in the final electron production. The dispersion and detection methods are similar to AES. Monochromatic, incoming X-ray photons are generated from an elemental target such as magnesium or aluminum. Measurement of the energy distribution of emitted electrons from the sample permits the identification of the ionized levels by the simple relation
E final = E xray − E binding energy
(1.15)
Since the final energy is measured and the X-ray energy is known one can determine the binding energy and consequently the material. AES peaks are also present in the XPS spectrum. AES peaks can be distinguished from the fact that the energies of the Auger electrons are fixed, since they depend on a difference in energy levels, whereas the XPS electron energies depend on the energy of the incident X-ray. An example XPS spectrum in shown in Figure 1.20, and a schematic diagram of the XPS apparatus would resemble the AES diagram of Figure 1.17, but with incident X-rays replacing electrons impinging on the specimen. XPS can perform chemical as well as elemental analysis. As stated earlier, when an element is in a compound there is a shift in energy levels relative to the unreacted element. Unlike AES where energy level differences are detected, a chemical reaction results in an energy shift of the element XPS peak. For example, the iron peak from Fe2O3 is shifted by nearly 4 eV from an elemental iron peak. Not only are the shifts simpler to interpret, but it is easier to detect peaks directly (as opposed to AES derivative mode
FIGURE 1.20 Example of XPS spectrum. (From Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. With permission.)
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measurements) since the signal to background in XPS is greater than in AES. In addition, the mode of operation in the dispersion step typically enables higher resolution. The surface sensitivity of XPS is similar to AES because the energies of the emitted electrons are similar. Figure 1.21 shows some examples of oxygen and sulfur peak shifts resulting from reactions with iron and chromium for wear scars on a steel pin run with dibenzyl-disulfide as the lubricant additive (Wheeler, 1978).
SULFUR (2p)
FeSO4
SEVERE WEAR SCAR
FeS
FeS
MILD WEAR SCAR UNWORN SURFACE
170
165
160
155
170
SEVERE WEAR SCAR OXYGEN (1s) FeO ADSORBED O2 535
530
165
160
155
ADSORBED O2
Cr2O3
MILD WEAR SCAR
Fe2O3
UNWORN SURFACE
FeO 535
525
530
525
BINDING ENERGY, eV (a) BEFORE SPUTTERING
(b) AFTER 30 seconds OF SPUTTERING Fe2O3 Cr2O3
FeO
ADSORBED O2
535
530
525
BINDING ENERGY, eV (c) OXYGEN (1s) SPECTRAL LINE FROM WEAR TEST SPECIMEN SHOWING BINDING ENERGIES OF 1s ELECTRON IN SEVERAL COMPOUNDS AND RESOLUTION OF PEAK OBTAINED WITH ANALOG CURVE RESOLVER.
FIGURE 1.21 Sulfur 2p and oxygen 1s XPS peaks from unworn steel surfaces and wear scars run in mineral oil with 1% dibenzyl disulfide. (From Wheeler, D.R. (1978), X-ray photoelectron spectroscopic study of surface chemistry of dibenzyl disulfide on steel under mild and severe wear conditions, Wear, Vol. 47, pp. 243-254. With permission. © 1978 Elsevier Science.)
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1.5.3 Secondary Ion Mass Spectroscopy The physical process involved in SIMS differs from both AES and XPS in that both the excitation source and detected particles are ions. Rather than illuminate the sample surface with either electrons (AES) or photons (XPS), ions are used to bombard the sample surface and knock off (sputter) surface particles. The dispersion phase analyzes the emitted particle masses, instead of energy analyzing the emitted electrons as in AES or XPS. Although using sputtering implies an erosion of the sample surface, a compensating advantage for SIMS is extreme sensitivity. Under advantageous conditions, as few as 1012 atoms per cm3 (ppb) have been detected (Gnaser, 1997), with more typical sensitivities for most elements in the ppm range (Wilson et al., 1989). A comprehensive discussion of the SIMS technique has been published by Benninghoven et al. (1987). The SIMS technique typically used in surface studies gives partial monolayer sensitivity using small incident ion currents (“static” SIMS). Higher ion beam currents, often rastered, give species information as a function of sputter depth (“dynamic” SIMS or SIMS depth profiling). SIMS instrumentation can be roughly categorized by the type of ion detector used, e.g., quadrupole, magnetic sector, or time-of-flight, with their inherent differences in sensitivity, lateral and mass resolution. As well, the incident angle, energy, and type (e.g., noble gas, cesium, or oxygen) of primary ion sputtering beam employed can greatly affect the magnitude and character of the secondary ion yield. SIMS has several complexities. SIMS only detects secondary ions, rather than all of the sputtered species, which can lead to difficulty in quantification. Large molecules on the surface such as hydrocarbon lubricants or typical additives can exhibit complex patterns of possible fragments. A knowledge of the adsorbate and cracking patterns is often needed for interpretation. As well, multiply ionized fragments or simply different species may overlap in the spectra, having nearly identical charge-to-mass ratios. As a simple example, carbon monoxide (CO) and diatomic nitrogen (N2) overlap, requiring examination of other mass fragments to distinguish between the two. As with depth profiling for either AES or XPS, depth resolution “smearing” can occur either due to ion beam mixing of near-surface species or due to the development of surface topography after long times under the ion beam. Despite these potential limitations, SIMS should remain the technique of choice for many low detection limit, high surface sensitivity studies (Zalm, 1995).
1.5.4 Infrared Spectroscopy Infrared spectroscopy (IRS) is particularly useful in detecting lubricant films on surfaces. It can provide binding and chemical information for adsorbed large molecules. It has an additional advantage in that it is nondestructive. Incident electrons in AES can cause desorption and decomposition even for aluminum oxide, and can be very destructive for polymers. Similarly, the emitted electrons can cause destruction of some films for both AES and XPS. In IRS, the specimen is illuminated with infrared light of welldefined energy. If the energy of the incident light corresponds to a transition between vibrational energy levels in the specimen, the light can be absorbed. When compared to the reference light beam that has not passed through a sample, the infrared light interacting with the sample will appear at reduced intensity at these vibrational excitation energies. The dispersion step is similar to dispersion in visible photon spectroscopy in that a grating or prism is used to isolate the wavelengths of interest. A variation of IRS which has advantages in sensitivity and resolution is called Fourier transform infrared spectroscopy (FTIR). In FTIR, the incident beams are passed through a Michelson interferometer in which one of the paths is modulated by moving a mirror. As before, one of the modulated beams is passed through the sample and impinges directly on the detector, which is a heat-sensitive device. When nonmonochromatic radiation is used, the Fourier transform of the spatially modulated beam contains all of the information in one signal, as opposed to the dispersion method where each beam must be analyzed separately. A schematic diagram of the equipment is shown in Figure 1.22. IRS can be surface sensitive and has been used in a diverse range of analytical science applications (McKelvy et al., 1998), which we will not address. A primary interest in tribology is the detection of hydrocarbon or additive films on surfaces. AES and XPS, for contrast, would be useful primarily in
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Fixed Mirror Movable Mirror
Sample Compartment Detector
IR Source Reference or Sample Cell Holders Mirror
Mirror Mirror
FIGURE 1.22 Optical arrangement for a Fourier transform infrared spectrometer. (From Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. With permission.)
detecting elemental species and are limited to use in ultrahigh vacuum. IRS can be used in air as well as vacuum. The surface sensitivity of IRS can be enhanced by multiple reflections in the surface films and by using grazing incidence angles. Orientation of adsorbed molecules can be obtained by examining the polarization dependence of the spectrum. There are selection rules for what materials can be detected depending on whether the molecule has a dipole moment and the orientation of the molecule on a metal surface. Sample spectra for micron-thick and less than 200-Ångstrom-thick Krytox films on a metal substrate are shown in Figure 1.23 (Herrera-Fierro, 1993).
1.5.5 Thermal Desorption We mention briefly at this point another useful tool for examining the behavior of adsorbates on surfaces, thermal desorption spectroscopy (TDS). We give only a brief description and for a more complete treatment refer the reader to Zangwill (1988). The methods described so far give little information concerning binding energies of adsorbates to surfaces, a topic of importance when choosing stable lubricants or additives. Many species adsorb strongly but do not react chemically, e.g., by forming an oxide. When the surface is heated they can be removed intact or in some decomposed form. A simple view would be that the binding energy would resemble the curves presented in Figure 1.12, and the adsorbates could be removed by giving them sufficient energy to overcome the energy well depth. This would be accomplished by heating a sample following adsorption and then either observing the surface coverage via AES or monitoring pressure increases in the vacuum system. There can be a variety of bonding states depending on the structure of the surface, e.g., at a step edge one would expect a different binding energy from a surface site. Although the real situation may be quite complex, we describe the simplest case, a single bonding state and no decomposition. The rate of desorption can be described by (Meyers et al., 1996)
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Reflectance Spectrum Krytox Lubricant on a 440-C Bearing Ball
ether 2.2
1.8
C-0-C
C-F Stretch
2.0
(a)
Stretch
}
1.6
C-F2
Reflectance
1.4 1.2
Bend
1.0 0.8 0.6 0.4 0.2 0.0 3000
2600
2200
1800
1400
1000
600
1000
600
Wavenumber (cm-1)
0.02
0.01
H 0 2
}
Reflectance
(b)
0.00
3000
2600
2200
1800
1400
Wavenumber (cm-1)
FIGURE 1.23 IR spectrum of a Krytox film on a 440C bearing showing characteristic absorption corresponding to certain functional groups: (a) micron-thick film; (b) less than 200-Ångstrom-thick film; note the increased sensitivity and the bend from absorbed water from 1400 to 2000 cm–1. (From Herrera-Fierro, P.C. private communication, first published in Ferrante (1993).)
(
r = dθ dt = θν ⋅ exp − Ed kT
)
(1.16)
where θ is the coverage, ν is the pre-exponential frequency factor, Ed is the desorption energy, T is the temperature, and k is the Boltzmann constant. By heating to various temperatures and performing an Arrhenius plot one can extract Ed and determine the strength of bonding to a surface. This technique will be seen to be useful in studying monolayer and submonolayer adsorbed film effects on friction between otherwise clean metal surfaces.
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1.6 Surface Effects in Tribology In this section we will deal with a number of issues, analyzing evidence first for effects at the atomic monolayer or submonolayer level in tribology. We will examine monolayer effects both from a fundamental standpoint as well as a more practical viewpoint. This will not be a comprehensive review of the literature, but in keeping with the objectives of this chapter, will be didactic in nature. The references selected, however, will refer to the relevant literature. In this chapter we are not concerned with the effects of lubricants other than their effects of changing shear strength or adhesion at the interface. Consequently we are interested in issues involving boundary lubrication and interfacial properties (Ferrante and Pepper, 1989; Gellman, 1992; Carpick and Salmeron, 1997; McFadden and Gellman, 1997, 1998). There are a number of issues to address which emphasize the difficulties involved in answering fundamental questions concerning bonding (Ferrante and Pepper, 1989). One clear difficulty is the fact that one cannot observe the interface during the interaction. It is necessary to infer what happened at the interface by examining the states of the surfaces before and after interaction. There are often situations where the locus of failure is not the interface, e.g., shear or adhesive failure can occur in the bulk of one of the materials rather than at the interface, or both effects can occur depending on the region in contact. There are uncertainties regarding the measurement of forces, though some recent efforts nicely relate lateral force sensitivity to normal force sensitivity for a commercial SPM cantilever beam, i.e., for a single asperity contact (Ogletree et al., 1996). Clearly, there are elastic effects in any measuring apparatus and in the materials involved that make measurement of the force distribution at the interface difficult. Materials can change mechanical properties as a result of the forces applied. For example, such properties as hardness, ductility, defect formation, plasticity, strain hardening, and creep must be considered. Surface properties may be altered just by contact with the counterface material (Carpick et al., 1996). Generally, even the true area of contact is not known in macroscopic studies due to the fact that asperities determine the contact area on most materials. There is a great deal yet to be learned concerning the basic interfacial properties in tribology. This is in part due to the complexities involved. As an example of such complexities, in Table 1.1 we show some results of Buckley and Pepper (1971) for metallic transfer of dissimilar metals in sliding contact performed using a pin-on-disk apparatus in an ultra-high vacuum system with AES analysis in the wear track. Both pin and disk specimens were ion sputter cleaned. As we can see, all metals transferred to tungsten, and cobalt transferred in all cases. However, iron and nickel did not transfer to tantalum, molybdenum, TABLE 1.1 Metallic Transfer for Dissimilar Metals in Sliding Contact Disk
Rider
Transfer of Metal from Rider to Disk
Tungsten
Iron Nickel Cobalt Iron Nickel Cobalt Iron Nickel Cobalt Iron Nickel Cobalt
Yes Yes Yes No No Yes No No Yes No No Yes
Tantalum
Molybdenum
Niobium
Source: Ferrante, J. (1989), Applications of surface analysis and surface theory in tribology, Surf. Int. Anal., Vol. 14, pp. 809-822. With permission. © John Wiley & Sons.
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or niobium. The surprising result is that the softer metals did not transfer to the harder in all cases. Pepper explained these results in terms of the mechanical properties of the materials. Tungsten, which is the hardest of the materials, fits the expected pattern. However, since nickel and iron strain harden, transfer and deformation are minimized. Cobalt, which has a hexagonal, close-packed structure, has easy slip planes and thus transferred in all cases. Thus simple explanations based on cohesive and interfacial energies can be misleading if mechanical properties are not taken into account. We give a second example performed by Pepper (1974) demonstrating the care necessary in performing studies of polymer films transferred from polymer pins sliding on an S-Monel disk in UHV. Figure 1.24 shows the AES spectra for polytetrafluoroethylene (PTFE), polyvinyl chloride (PVC), and polychlorotrifluoroethylene (PCTFE) pins sliding on S-Monel. The PTFE spectrum shows large fluorine and carbon peaks and large attenuation of the metal peaks. (Care had to be taken due to electron bombardment desorption of the fluorine.) The friction coefficient was low and smooth, suggesting slip. The combined results indicated that PTFE strands were transferring to the metal surface consistent with the models of Pooley and Tabor (1972). For PVC the AES spectrum shows a large chlorine peak and small attenuation of the metal peaks, suggesting decomposition and chlorine adsorption rather than polymer transfer. The friction coefficient, although reduced, remained large and exhibited some stick slip. For PCTFE the spectrum shows chlorine, carbon, and intermediate attenuation of the metal peaks, but with stability under electron bombardment, suggesting the possibility of both decomposition and some polymer transfer. The friction coefficient was high with stick slip. Consequently, it is difficult to anticipate what is happening, again demonstrating the need for more extensive surface characterization.
1.6.1 Atomic Monolayer Effects in Adhesion and Friction Our primary objective in this and following sections is to explore the evidence for atomic effects on friction. The bulk of the discussion in this section will be based on the recent high-quality experiments of Gellman and collaborators (Gellman, 1992; McFadden and Gellman, 1995a,b, 1997, 1998; Ko et al., 1999) while we acknowledge the pioneering contributions of Buckley and the members of his group (Buckley, 1981). Gellman and collaborators have performed a number of adhesion and friction experiments on single crystals in contact, both for clean and adsorbate-covered interfaces, namely Ni(100)–Ni(100), Cu(111)–Cu(111), and even single-grain Al70Pd21Mn9 quasicrystals. The contacting crystals had a slight curvature in order to prevent contact at the edges of the samples where large concentrations of steps were expected, and to ensure point contact. The vacuum system was also vibration isolated, which is very important for reasons to be discussed below. Normally the experiments were repeated for 10 different points. The normals of the crystals were aligned by lasers. The apparatus provided the ability to sputter clean both contacting surfaces, and LEED and AES could be performed on the surfaces in order to guarantee the crystallinity and to measure contamination and determine concentration of adsorbates. The AES measurements were performed with LEED optics in the old retarding field analyzer mode. Following sputter cleaning, the samples were annealed and analyzed with LEED in order to verify the crystal structure and with AES to verify cleanliness. On copper (111) McFadden and Gellman (1995a) examined the effects of sulfur adsorption, since sulfur is a common antiwear additive. It is often used along with phosphorous to prevent metal-to-metal contact when the lubricant breaks down. Both surfaces were dosed with sulfur using hydrogen sulfide, which decomposes upon heating, desorbing the hydrogen and leaving sulfur behind on the surface. At saturation, sulfur forms an ordered superlattice which has a 7 × 7 R19 degree LEED pattern. This corresponds to a close-packed monolayer of sulfide ions (S2–) on top of the copper(111) lattice with an absolute coverage of .43 monolayers relative to the copper(111) substrate. The results of the adhesion experiments are shown in Figure 1.25. The adhesion coefficient, µad = Fad /FN , which is the ratio of pull-off force to normal force, was found to be .69 ± .21. As little as .05 monolayers (11% of saturation) gave a substantial percentage reduction. The saturation value at one monolayer was .26 ± .07. They also found that there was no dependence of the adhesion coefficient on contact time, separation time, temperature, or normal force. There would be
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(B)
(A)
(C)
dN(E)/dE
N (720 V)
Ni , Cu Ni , Cu
C
F
Ni,Cu
100
1000 100 1000 100 1000 E E E (A) SPUTTERED (B) AFTER SLIDING (C) DISK MOVING WITH DISK. PTFE FOR ONE RE- VELOCITY OF 1 MM/SEC UNDER ELECTRON BEAM. VOLUTION. DISK STATIONARY FOR AUGER ANALYSES.
(B)
dN(E)/dE
(A)
C
CI (X1/5) Ni,Cu
100
E
Ni,Cu
E 1000 100 1000 (B) AFTER SLIDING PVC FOR ONE REVOLUTION.
(A) SPUTTERED DISK.
(B)
dN(E)/dE
(A)
Ni ,Cu
100
(C)
C
C CI (X1/5)
CI (X1/5) Ni ,Cu
1000 100
1000 100
Ni ,Cu
1000
E (A) SPUTTERED DISK.
(B) AFTER SLIDING (C) DISK MOVING WITH VELOCITY OF 1 MM/SEC PCTFE FOR ONE REVOLUTION. UNDER ELECTRON BEAM DISK STATIONARY FOR AUGER ANALYSES.
FIGURE 1.24 AES spectra from an S-Monel disk with transfer films from different polymers. (From Pepper, S.V. (1974), Auger analysis of films formed on metals in sliding contact with halogenated polymers, J. Appl. Phys., Vol. 45, pp. 2947-2956. With permission.)
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1.0
0.9
0.8
adhesion coefficient
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0 0
.11
.22
.33
.44
sulfur coverage (ML)
FIGURE 1.25 Adhesion coefficient vs. sulfur coverage by McFadden and Gellman (1995a). Experimental conditions: temperature = 300 K; normal force = 40 to 60 mN; contact time before separation = 15 to 20 s; separation speed = 50 µm/s. At each coverage the standard deviation of the adhesion coefficient calculated from 10 measurements is plotted.
no expected dependence on normal force since higher loads would simply increase the contact area, and the adhesion coefficient therefore would be expected to track with the normal force. Buckley (1981) reported adhesion coefficients much greater than 1.0 for clean single crystals in contact. As mentioned earlier, it is important to control vibrations in the experiments. Bowden and Tabor (1964) showed that when clean metal surfaces were plastically loaded and then translated, the junction grew, i.e., the true contact area increased until shear occurred. In all probability, the large adhesion coefficients observed by Buckley were caused by increased contact area from junction growth caused by vibrations. In any event, there is strong bonding at clean metal interfaces, and as Gellman and others have shown, the adhesion coefficient can be decreased by submonolayer films. McFadden and Gellman (1995a) performed a somewhat different experiment on the copper(111) surface with regard to static friction measurements. The surfaces were exposed to laboratory atmosphere for several days. As determined by AES, the primary contaminants were sulfur and carbon. Although tenuous, the coverage was estimated to be between 10 to 15 Ångstroms. Then a number of cycles of sputtering followed by annealing with static friction measurements after each cycle were performed. The results are shown in Figure 1.26. The friction coefficient, µs, increased with removal of contaminant to the clean-surface value of 4.4 ± 1.3. Again these results imply submonolayer effects by these contaminants. Wheeler (1976) earlier performed static friction experiments with both chlorine and oxygen adsorbed on polycrystalline surfaces of copper, iron, and steel. The measurements were performed with a pin-ondisk apparatus, with AES used to monitor coverage. The results of these studies are shown in Figure 1.27. Wheeler found that there were no differences between the effects of chlorine and oxygen on any of the surfaces if adsorbate coverage was taken into account. Adsorption at partial monolayer coverages reduced the coefficient of friction in all cases. Wheeler found that he could get a good correlation with a junction
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FIGURE 1.26 Static friction coefficient vs. Auger peak ratios as the contaminated copper(111) surfaces are gradually cleaned by ion bombardment. For each contamination level the average and standard deviation of the friction coefficient calculated from 10 measurements are presented. (From McFadden, C.F. and Gellman, A.J. (1995a), Effect of surface contamination on the UHV tribological behavior of the Cu(111)/Cu(111) interface, Tribology Letters, Vol. 1, pp. 201-210. With permission.)
growth model where the surfaces were partially covered during translation. The values of the coefficient were of comparable magnitude to those of Gellman. Clean single-grain Al70Pd21Mn9 quasicrystal surfaces gave a static friction coefficient of only µs = 0.60 ± 0.08 (Ko et al., 1999), in contrast with the high value reported for clean copper(111) above. Formation on the clean quasicrystal surfaces of about a monolayer of oxide following exposure to oxygen or water did discernibly reduce µs, though never as low as for the uncleaned, air-exposed surfaces with µs = 0.11 ± 0.02. Determining reasons for the differing friction coefficients between surfaces remains an ongoing challenge.
1.6.2 Monolayer Effects due to Adsorption of Hydrocarbons In considering the evidence for monolayer effects on friction, we again start by referring to recent publications by Gellman et al. (Gellman, 1992; McFadden and Gellman, 1995a,b, 1998; Meyers et al., 1996) describing a number of friction experiments performed with hydrocarbon adsorbates. First, we present the effects of ethanol adsorption on a sulfur-covered nickel(100) surface. The sulfur was adsorbed as previously described and produced a c2 × 2 structure on the nickel surface. The sulfur overlayer was used since stable results could not be obtained with ethanol alone, which Gellman found desorbed at very low temperatures. There were a number of different friction states depending on ethanol coverage, shown in Figure 1.28 (Gellman, 1992). These are the classic behaviors observed in friction (Buckley, 1981). The first shown is “slip” where, once a certain transverse force is applied, there is simple sliding. The second is “stick-slip” where rebonding occurs and the simple slip process is repeated between rebonding events, with poor definition of a friction coefficient. This behavior probably results from junction growth with the adsorbate only
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2.5 CHLORINE ON COPPER CHLORINE ON IRON OXYGEN ON IRON OXYGEN ON STEEL
2.0
OXYGEN ON COPPER
(MINIMUM µS)
µs
1.5 BOTH SURFACES COVERED
1.0
.5
0
.2
.4
.6
.8
1.0
C' FIGURE 1.27 The effects of oxygen and chlorine adsorption on static friction for a metal–metal contact. (from Wheeler, D.R. (1976), Effect of adsorbed chlorine and oxygen on the shear strength of iron and copper junctions, J. Appl. Phys., Vol. 47, pp. 1123-1130. With permission. © 1976 American Institute of Physics.)
effective in certain regions, as observed by Wheeler (1976). Finally, “stick” is where the surfaces weld, and it is similar to shearing a bulk solid. The results of Gellman’s studies are shown in Figure 1.29 where the key indicates differences in behavior. For copper(111) a saturated, submonolayer sulfur coating barely reduced µs and gave stick behavior (McFadden and Gellman, 1997). Partial coverages of ethanol gave erratic behavior typically exhibiting stick-slip. Finally at one monolayer the ethanol effectively lubricated the surface giving the desired slip as well as low adhesion (McFadden and Gellman, 1995b). Consequently, a monolayer film can effectively lubricate. Similar behavior was observed for 2,2,2-trifluoroethanol (McFadden and Gellman, 1995b) as well as for butanol and heptafluorobutanol adsorbed on clean copper(111) surfaces (McFadden and Gellman, 1998). Again stick-slip was observed for coverages less than a monolayer and slip for coverages greater than or equal to one monolayer. Similarly, high adhesion was observed for low coverages, and low adhesion for higher coverages. We conclude this discussion with some TDS and IR studies of fluorinated hydrocarbons on copper(111) surfaces by Meyers et al. (1996). Fluorinated hydrocarbons are of interest because of their thermal stability, and therefore are useful for higher temperature lubrication. All of the ethers were found to adsorb molecularly and reversibly on the copper(111) surfaces, exhibiting first-order desorption kinetics. These studies found that fluorination of perfluoropolyalkyl ethers (PFPAE) reduced the desorption energy. The general reason for this behavior was felt to be that bonding occurred with the oxygens on the PFPAE’s.
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120K, L = 10, mN, V = 10 µ/s 20 STICK
Friction Force (mN)
15
10 SLIP
SLIP-STICK
5
0
-5 Time
FIGURE 1.28 Friction force vs. time for three types of sliding behavior observed during shearing of interfaces between ethanol-charged nickel(100) surfaces, by Gellman (1992). The loads on the interface are all 10 mN at the beginning of each trace, and shearing begins at the points marked with the arrows. Temperature = 120 K; load = 10 mN; velocity = 10 µm/s.
5 Stick Stick-Slip
Friction Coefficient
4
Slip
3
2
1
0 10-2
10-1
1 101 102 EtOH Coverage (ML)
103
FIGURE 1.29 Coefficients of friction measured at interfaces between nickel(100)–c(2 × 2)–S surface modified by adsorption of ethanol at coverages from 0 to 300 ML. (From Gellman, A.J. (1992), Lubrication by molecular monolayers at Ni–Ni interfaces, J. Vac. Sci. Technol. A, Vol. 10, pp. 180-187. With permission.)
Fluorine is thought to weaken this interaction. In addition, fluorination changed the adsorbate–adsorbate interaction from repulsive to attractive. FTIR studies showed that the diethyl ethers are oriented with their molecular axes parallel to the copper(111) surface.
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We conclude this section with some elegant experiments performed by Krim et al. (Daly and Krim, 1996; Krim et al., 1995; Mak et al., 1994; Sokoloff et al., 1993) for which Widom and Krim (1986; also Krim and Widom, 1988) originally adapted an apparatus for sliding monolayer and thicker physisorbed films on silver substrates. The true contact area is known in these studies and there is no wear of the surfaces, which are silver deposited with a (111) face on a quartz crystal microbalance. These experiments were designed to investigate the nature of the friction forces. Slipping of physisorbed films, e.g., ethane and ethylene, on the silver surfaces causes shifts in the frequency and amplitude of the quartz crystal vibrations, and film characteristic slip times are obtained from shifts in the quality factor, Q, of the oscillator circuit. Friction results from energy losses due to the interactions at an interface. Typically it is assumed that these losses occur through phonons, vibrations of the lattice which dissipate the energy (Sokoloff et al., 1993), though Persson (1991), followed by Sokoloff (1995), demonstrated that electronic excitations could also be an energy dissipation mechanism here. In these experiments the average friction force per unit area is related to the slip time by
Ff = ρν τ
(1.17)
where Ff is the friction force, ρ and ν are the film density and velocity, respectively, and τ is the slip time. Therefore, a longer slip time implies a smaller friction force. Based on electronic effects alone (Persson, 1993b) ethane on silver is expected to have a longer slip time than ethylene and thus lower friction. Krim’s results are consistent with this prediction although the ability of the theory to predict hard numbers is limited. Monolayer oxygen adsorption on the surface increases the slip time and thus lowers the friction coefficient substantially, consistent with the electronic excitation model. Although these experiments are not completely definitive at this time, they open new areas of investigation for probing the little understood energy loss mechanisms in friction.
1.6.3 Atomic Effects in Metal-Insulator Contacts We now discuss a number of results where monolayer effects have been observed in metal-insulator friction experiments performed by Pepper (1976, 1979, 1982). First, we discuss static friction experiments performed with a copper ball on the basal plane of a diamond flat. The diamond surface is known to be terminated by hydrogen atoms. Pepper (1982) found that the hydrogen could be removed by either electron bombardment or heating in UHV. Following removal of the hydrogen, the LEED pattern for the surface changed from a 1 × 1 to a 1 × 2 pattern. The interesting feature is shown in the static friction results for the two situations given in Figure 1.30. We can see that removal of the hydrogen caused an increase in µs. Pepper found that exposing the surface to excited hydrogen could cause readsorption. Following hydrogen readsorption the static friction was again reduced, although not to its original value. Pepper also performed core level ionization energy loss spectroscopy on the diamond surface and found changes in the electronic structure of the valence band. Therefore, these experiments showed results sensitive to the electronic structure of the surface. In Figure 1.31 we show similar studies performed by Pepper (1979) for copper and nickel balls on the basal plane of sapphire with chlorine and oxygen as adsorbates. Again the balls were cleaned by sputtering and the sapphire was cleaned by heating as verified by AES. In both cases, we see that oxygen increased the interfacial friction and chlorine decreased it compared to the clean metal. For the increased shear strength case, one cannot identify the locus of failure, whether at the interface or in the bulk of one of the materials. Unfortunately, the wear scar area was too small to analyze. In any event, again monolayer adsorption was detectable in friction experiments. Perhaps even more surprising were effects shown in Figure 1.32. Here dynamic friction experiments were performed by Pepper (1976) with a polycrystalline sapphire pin on a polycrystalline iron disk in UHV. We see the same behavior reproduced with dynamic friction. After removing the oxygen or chlorine atmospheres, the friction coefficients returned to their original values.
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POLISHED SURFACE TRANSFORMED SURFACE EXPOSED TO EXCITED HYDROGEN TRANSFORMED SURFACE EXPOSED TO HYDROGEN AND THEN ANNEALED
.8
.7
.6 EXPOSED TO EXCITED HYDROGEN
.5 µ
.4
.3
.2
.1
0 750
800
850
900
950
0
ANNEAL TEMPERATURE, C
FIGURE 1.30 Copper–diamond static friction coefficient as a function of diamond annealing temperature. (From Pepper, S.V. (1982), Effect of electronic structure of the diamond surface on the strength of the diamond-metal interface, J. Vac. Sci. Technol., Vol. 20, pp. 643-646. With permission.)
1.7 Concluding Remarks We have attempted to present a description of issues and techniques in the physics of surfaces of interest in tribology. This field of research is exceedingly difficult, with the effects of a wide variety of materials and phenomena to understand. It is further complicated by the inability to observe the interactions directly, resulting in conclusions from inference. It is clear that there is a great deal of research necessary to obtain a comprehensive understanding of tribology at the nanoscale. It is hoped that the demonstrations in this chapter and in this volume indicate that there is the possibility of gaining rational understanding leading to the design of better materials in this technologically important field.
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OXYGEN
2.4
2.0
1.6
1.2 1.0 CHLORINE
µg / µ c
.8
.4 (A) NICKEL
2.8 2.4 2.0
1.6
1.2 1.0 .8
.4
.1
1
10
100
1000
EXPOSURE (L ) (B) COPPER.
FIGURE 1.31 Static friction coefficient after exposure to gas (µg) ratio to static friction coefficient of clean contact (µc), plotted vs. exposure to oxygen or chlorine for: (A) nickel; and (B) copper. (From Pepper, S.V. (1979), Effect of interfacial species on shear strength of metal-sapphire contacts, J. Appl. Phys., Vol. 50, pp. 8062-8065. With permission.)
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1.5
COEFFICIENT OF FRICTION . µ
1.0
.5
1 REVOLUTION
0 EXPOSE TO 1000 L O2 (A) OXYGEN ADSORBED ON IRON DISK.
1.0
.5
0
EXPOSE TO 200 L Cl2 (B) CHLORINE ADSORBED ON IRON DISK.
FIGURE 1.32 Effect of oxygen or chlorine on the dynamic friction of an iron disk sliding on sapphire. (From Pepper, S.V. (1976), Effect of adsorbed films on friction of Al2O3-metal systems, J. Appl. Phys., Vol. 47, pp. 2579-2583. With permission.)
References Arlinghaus, F.J., Gay, J.G., and Smith, J.R. (1980), Self-consistent local-orbital calculation of the surface electronic structure of Ni (100), Phys. Rev. B, Vol. 21, pp. 2055-2059. Ashcroft, N.W. and Mermin, N.D. (1976), Solid State Physics, Holt, Rinehart and Winston, New York. Bacigalupi, R.J. (1964), Surface Topography of Single Crystals of Face-Centered-Cubic, Body-CenteredCubic, Sodium Chloride, Diamond, and Zinc-Blende Structures, NASA TN D-2275, National Aeronautics and Space Administration, Washington, D.C. Banerjea, A., Ferrante, J., and Smith, J.R. (1991), Adhesion at metal interfaces, in Fundamentals of Adhesion, Liang-Huang Lee, (Ed.), Plenum Publishing, New York, pp. 325-348. Bartelt, N.C., Einstein, T.L. and Williams, E.D. (1994), Measuring surface mass diffusion coefficients by observing step fluctuations, Surf. Sci., Vol. 312, pp. 411-421. Benninghoven, A., Rüdenauer, F.G., and Werner, H.W. (1987), Secondary Ion Mass Spectroscopy, Wiley, New York. Binnig, G., Rohrer, H., Gerber, Ch., and Weibel, E. (1983), 7 × 7 Reconstruction on Si(111) resolved in real space, Phys. Rev. Lett., Vol. 50, pp. 120-123. Bowden, F.P. and Tabor, D. (1964), The Friction and Lubrication of Solids, Oxford University Press, London. Bozzolo, G., Rodriguez, A.M., and Ferrante, J. (1994), Multilayer relaxation and surface energies of metallic surfaces, Surf. Sci., Vol. 315, pp. 204-214.
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Bozzolo, G., Ferrante, J., Noebe, R.D., Good, B., Honecy, F.S., and Abel, P.B. (1999), Surface segregation in multicomponent systems: modeling of surface alloys and alloy surfaces, Computational Materials Sci., Vol. 15, pp. 169-195. Brainard, W.A. and Buckley, D.H. (1971), Preliminary Studies by Field Ion Microscopy of Adhesion of Platinum and Gold to Tungsten and Iridium, NASA TN D-6492, National Aeronautics and Space Administration, Washington, D.C. Brainard, W.A. and Buckley, D.H. (1973), Adhesion and friction of PTFE in contact with metals as studied by auger spectroscopy, field ion and scanning electron microscopy, Wear, Vol. 26, pp. 75-93. Brainard, W.A. and Ferrante, J. (1979), Evaluation and Auger Analysis of a Zinc-Dialkyl-Dithiophosphate Antiwear Additive in Several Diester Lubricants, NASA TP-1544, National Aeronautics and Space Administration, Washington, D.C. Buckley, D.H. and Pepper, S.V. (1971), Elemental Analysis of a Friction and Wear Surface during Sliding using Auger Spectroscopy, NASA TN D-6497, National Aeronautics and Space Administration, Washington, D.C. Buckley, D.H. (1981), Surface Effects in Adhesion, Friction, Wear, and Lubrication, Elsevier Scientific Publishing, Amsterdam. Carpick, R.W., Agrait, N., Ogletree, D.F., and Salmeron, M. (1996), Variation of the interfacial shear strength and adhesion of a nanometer-sized contact, Langmuir, Vol. 12, pp. 3334-3340. Carpick, R.W. and Salmeron, M. (1997), Scratching the surface: fundamental investigations of tribology with atomic force microscopy, Chem. Rev., Vol. 97, pp. 1163-1194. Chambers, S.A. (1992), Elastic scattering and interference of backscattered primary, Auger and X-ray photoelectrons at high kinetic energy: principles and applications, Surf. Sci. Reports, Vol. 16, pp. 261-331. Conrad, E.H. and Engel, T. (1994), The equilibrium crystal shape and the roughening transition on metal surfaces, Surf. Sci., Vol. 299/300, pp. 391-404. Daly, C. and Krim, J. (1996), Sliding friction of solid xenon monolayers and bilayers on Ag(111), Phys. Rev. Lett., Vol. 76, pp. 803-806. De Crescenzi, M. (1995), Structural surface investigations with low-energy backscattered electrons, Surf. Sci. Reports, Vol. 21, pp. 89-175. Diestler, D.J., Rajasekaran, E., and Zeng, X.C. (1997), Static frictional forces at crystalline interfaces, J. Phys. Chem. B, Vol. 101, pp. 4992-4997. Dowson, D. (1979), History of Tribology, Longman, New York. Faulkner, R.G. (1996), Segregation to boundaries and interfaces in solids, Int. Mater. Rev., Vol. 41, pp. 198-208. Feibelman, P.J. (1992), First-principles calculation of the geometric and electronic structure of the Be (0001) surface, Phys. Rev. B, Vol. 46, pp. 2532-2539. Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. Ferrante, J. (1978), Adhesion of a Bimetallic Interface, NASA TM-78890 National Aeronautics and Space Administration, Washington, D.C. Ferrante, J. (1982), Practical applications of surface analytic tools in tribology, J. Am. Soc. Lubr. Eng., Vol. 38, pp. 223-236. Ferrante, J. and Smith, J.R. (1985), Theory of the bimetallic interface, Phys. Rev. B, Vol. 31, pp. 3427-3434. Ferrante, J., Bozzolo, G.H., Finley, C.W. and Banerjea, A. (1988), Interfacial adhesion: theory and experiment, in Mat. Res. Soc. Symp. Proc., Vol. 118, pp. 3-16. Ferrante, J. (1989), Applications of surface analysis and surface theory in tribology, Surf. Int. Anal., Vol. 14, pp. 809-822. Ferrante, J. and Pepper, S.V. (1989), Fundamentals of tribology at the atomic level, in Mat. Res. Soc. Symp. Proc., Vol. 140, pp. 37-50.
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Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. Finnis, M.W. (1996), The theory of metal–ceramic interfaces, J. Phys.: Condens. Matter, Vol. 8, pp. 5811-5836. Foiles, S.M. (1987), Reconstruction of fcc (110) surfaces, Surf. Sci., Vol. 191, pp. L779-L786. Gellman, A.J. (1992), Lubrication by molecular monolayers at Ni–Ni interfaces, J. Vac. Sci. Technol. A, Vol. 10, pp. 180-187. Gnaser, H. (1997), SIMS detection in the 1012 atoms cm–3 Range, Surf. Int. Anal., Vol. 25, pp. 737-740. Good, B.S. and Banerjea, A. (1992), Monte Carlo Study of Reconstruction of the Au(110) Surface Using Equivalent Crystal Theory, in Mat. Res. Soc. Symp. Proc., Vol. 278, pp. 211-216. Good, B., Bozzolo, G., and Ferrante, J. (1993), Surface segregation in Cu–Ni alloys, Phys. Rev. B, Vol. 48, pp. 18284-18287. Hantsche, H. (1989), Comparison of basic principles of the surface-specific analytical methods: AES/SAM, ESCA(XPS), SIMS, and ISS with X-ray microanalysis, and some applications in research and industry, Scanning, Vol. 11, pp. 257-280. Herrera-Fierro, P.C. private communication, first published in Ferrante (1993). Hirano, M. and Shinjo, K. (1990), Atomistic locking and friction, Phys. Rev. B, Vol. 41, pp. 11837-11851. Hirano, M., Shinjo, K., Kaneko, R., and Murata, Y. (1997), Observation of superlubricity by scanning tunneling microscopy, Phys. Rev. Lett., Vol. 78, pp. 1448-1451. Hirsch, P., Howie, A., Nicholson, R.B., Pashley, D.W., and Whelan, M.J. (1977), Electron Microscopy of Thin Crystals, Robert E. Krieger Publishing Co., Malabar, Florida. Hofmann, S. (1998), Sputter depth profile analysis of interfaces, Rep. Prog. Phys., Vol. 61, pp. 827-888. Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1997), Modeling of the scan process in lateral force microscopy, Surf. Sci., Vol. 375, pp. 395-402. Hong, T., Smith, J.R. and Srolovitz, D.J. (1995), Theory of metal–ceramic adhesion, Acta Metall. Mater., Vol. 43, pp. 2721-2730. Jennings, W.D., Chottiner, G.S. and Michal, G.M. (1988), Sulphur segregation to the metal oxide interface during the early stages in the oxidation of iron, Surf. Int. Anal., Vol. 11, pp. 377-382. Kaxiras, E. (1996), Review of atomistic simulations of surface diffusion and growth on semiconductors, Computational Matl. Sci., Vol. 6, pp. 158-172. Kellogg, G.L. (1994), Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces, Surf. Sci. Reports, Vol. 21, pp. 1-88. Kittel, C. (1986), Introduction to Solid State Physics, 6th ed., John Wiley & Sons, New York. Ko, J.S., Gellman, A.J., Lograsso, T.A., Jenks, C.J., and Thiel, P.A. (1999), Friction between single-grain Al70Pd21Mn9 quasicrystal surfaces, Surf. Sci., Vol. 423, pp. 243-255. Kobistek, R.J., Bozzolo, G., Ferrante, J., and Schlosser, H. (1994), Multilayer relaxation and surface structure of ordered alloys, Surf. Sci., Vol. 307-309, pp. 390-395. Kohn, W. and Sham, L.J. (1965), Self-consistent equations including exchange and correlation effects, Phys. Rev., Vol. 140, pp. A1133-A1138. Krim, J. and Widom, A. (1988), Damping of a crystal oscillator by an adsorbed monolayer and its relation to interfacial viscosity, Phys. Rev. B, Vol. 38, pp. 12184-12189. Krim, J., Daly, C., and Dayo, A. (1995), Electronic contributions to sliding friction, Tribology Letters, Vol. 1, pp. 211-218. Lambrecht, W.R.L. and Segall, B. (1989), Efficient direct calculation method for dielectric response in semiconductors, Phys. Rev. B, Vol. 40, pp. 7793-7801. Lang, N.D. and Kohn, W (1970), Theory of metal surfaces: charge density and surface energy, Phys. Rev. B, Vol. 1, pp. 4555-4568. Lantz, M.A., O’Shea, S.J., Hoole, A.C.F., and Welland, M.E. (1997), Lateral stiffness of the tip and tip–sample contact in frictional force microscopy, Appl. Phys. Lett., Vol. 70, pp. 970-972. Lundqvist, S. and March, N.H. (Eds.) (1983), Theory of the Inhomogeneous Electron Gas, Plenum Press, New York.
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Mak, C., Daly, C., and Krim, J. (1994), Atomic-scale measurements on silver and chemisorbed oxygen surfaces, Thin Solid Films, Vol. 253, pp. 190-193. Matsukawa, H. and Fukuyama, H. (1994), Theoretical study of friction: one-dimensional clean surfaces, Phys. Rev. B, Vol. 49, pp. 17286-17292. McFadden, C.F. and Gellman, A.J. (1995a), Effect of surface contamination on the UHV tribological behavior of the Cu(111)/Cu(111) interface, Tribology Letters, Vol. 1, pp. 201-210. McFadden, C.F. and Gellman, A.J. (1995b), Ultrahigh vacuum boundary lubrication of the Cu–Cu interface by 2,2,2-trifluoroethanol, Langmuir, Vol. 11, pp. 273-280. McFadden, C.F. and Gellman, A.J. (1997), Metallic friction: the influence of atomic adsorbates at submonolayer coverages, Surf. Sci., Vol. 391, pp. 287-299. McFadden, C.F. and Gellman, A.J. (1998), Metallic friction: the effect of molecular adsorbates, Surf. Sci., Vol. 409, pp. 171-182. McGuire, G.E., Fuchs, J., Han, P., Kushmerick, J.G., Weiss, P.S., Simko, S.J., Nemanich, R.J., and Chopra, D.R. (1999), Surface characterization, Anal. Chem., Vol. 71, pp. 373R-388R. McKelvy, M.L., Britt, T.R., Davis, B.L., Gillie, J.K., Graves, F.B., and Lentz, L.A. (1998), Infrared spectroscopy, Anal. Chem., Vol. 70, pp. 119R-177R. Meyers, J.M., Street, S.C., Thompson, S., and Gellman, A.J. (1996), Effect of fluorine on the bonding and orientation of perfluoroalkyl ethers on the Cu(111) Surface, Langmuir, Vol. 12, pp.1511-1519. Mitchell, T.E. (1973), High voltage electron microscopy of microstructural analysis, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 125-152. Montei, E.L. and Kordesch, M.E. (1996), Detection of tribochemical reactions using photoelectron emission microscopy, J. Vac. Sci. Technol. A, Vol. 14, pp. 1352-1356. Mueller, E.W. and Nishikawa, O. (1968), Atomic surface structure of the common transition metals and the effect of adhesion as seen by field ion microscopy, Adhesion or Cold Welding of Materials in Space Environment, ASTM Special Tech. Publ. No. 431, American Society for Testing and Materials, Philadelphia, PA, pp. 67-87. Mueller, E.W. (1969), Field Ion Microscopy, American Elsevier, New York. Needs, R.J. (1987), Calculations of the surface stress tensor at aluminum (111) and (110) surfaces, Phys. Rev. Lett., Vol. 58, pp. 53-56. Niehus, H., Heiland, W., and Taglauer, E. (1993), Low-energy ion scattering at surfaces, Surf. Sci. Reports, Vol. 17, pp. 213-303. Nishikawa, O. and Mueller, E.W. (1968), Field ion microscopy of contacts, Proc. of the Holm Seminar on Electric Contact Phenomena, Ill. Inst. Technol., Chicago, IL, pp. 193-206. Ogletree, D.F., Carpick, R.W., and Salmeron, M. (1996), Calibration of frictional forces in atomic force microscopy, Rev. Sci. Instrum., Vol. 67, pp. 3298-3306. Ohmae, N., Umeno, M., and Tsubouchi, K. (1987), Effect of oxygen adsorption on adhesion of W to Au studied by field ion microscopy, ASLE Trans., Vol. 30, pp. 409-418. Ohmae, N., Tagawa, M., Umeno, M., and Koike, S. (1990), High voltage field ion microscopy of solid lubricants, Proc. Jpn. Intl. Tribol. Conf., Nagoya, pp. 1827-1832. Ohmae, N. (1993), Field ion microscopy in tribology studies, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 47-74. Pendry, J.B. (1997), Shearing the vacuum — quantum friction, J. Phys. C: Solid State Phys., Vol. 9, pp. 10301-10320. Pepper, S.V. (1974), Auger analysis of films formed on metals in sliding contact with halogenated polymers, J. Appl. Phys., Vol. 45, pp. 2947-2956. Pepper, S.V. (1976), Effect of adsorbed films on friction of Al2O3-metal systems, J. Appl. Phys., Vol. 47, pp. 2579-2583. Pepper, S.V. (1979), Effect of interfacial species on shear strength of metal-sapphire contacts, J. Appl. Phys., Vol. 50, pp. 8062-8065.
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Pepper, S.V. (1982), Effect of electronic structure of the diamond surface on the strength of the diamondmetal interface, J. Vac. Sci. Technol., Vol. 20, pp. 643-646. Persson, B.N.J. (1991), Surface resistivity and vibrational damping in adsorbed layers, Phys. Rev. B, Vol. 44, pp. 3277-3296. Persson, B.N.J. (1993a), Theory of friction and boundary lubrication, Phys.Rev. B, Vol. 48, pp. 18140-18158. Persson, B.N.J. (1993b), Applications of surface resistivity to atomic scale friction, to the migration of “hot” adatoms, and to electrochemistry, J. Chem. Phys., Vol. 98, pp. 1659-1672. Persson, B.N.J. (1994), Theory of friction: the role of elasticity in boundary lubrication, Phys. Rev. B, Vol. 50, pp. 4771-4786. Persson, B.N.J. (1995), Theory of friction: stress domains, relaxation, and creep, Phys. Rev. B, Vol. 51, pp. 13568-13585. Persson, B.N.J. (1998), Sliding Friction: Theory and Applications, Springer, Heidelberg. Persson, B.N.J. (1999), Sliding friction, Surf. Sci. Reports, Vol. 33, pp. 83-119. Persson, B.N.J. and Tosatti, E. (1999), Theory of friction: elastic coherence length and earthquake dynamics, Solid State Comm., Vol. 109, pp. 739-744. Pooley, C.M. and Tabor, D. (1972), Friction and molecular structure: the behaviour of some thermoplastics, Proc. R. Soc., Vol. A329, pp. 251-274. Redfield, A.C. and Zangwill, A. (1992), Attractive interactions between steps, Phys. Rev. B, Vol. 46, pp. 4289-4291. Richter, R., Gay, J.G., and Smith, J.R. (1985), Spin separation in a metal overlayer, Phys. Rev. Lett., Vol. 54, pp. 2704-2707. Rodriguez, A.M., Bozzolo, G., and Ferrante, J. (1993), Multilayer relaxation and surface energies of fcc and bcc metals using equivalent crystal theory, Surf. Sci., Vol. 289, pp. 100-126. Rose, J.H., Ferrante, J. and Smith, J.R. (1981), Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett., Vol. 47, pp. 675-678. Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. Rous, P.J. and Pendry, J.B. (1989), Applications of tensor LEED, Surf. Sci., Vol. 219, pp. 373-394. Shinjo, K. and Hirano, M. (1993), Dynamics of friction: superlubric state, Surf. Sci., Vol. 283, pp. 473-478. Smith, J.R. and Ferrante, J. (1985), Materials in Intimate Contact, Mat. Sci. Forum, Vol. 4, pp. 21-38. Smith, J.R. and Ferrante, J. (1986), Grain–boundary energies in metals from local-electron-density distributions, Phys. Rev. B, Vol. 34, pp. 2238-2245. Smith, D.J. (1997), The realization of atomic resolution with the electron microscope, Rep. Prog. Phys., Vol. 60, pp. 1513-1580. Sokoloff, J.B. (1990), Theory of energy dissipation in sliding crystal surfaces, Phys. Rev. B, Vol. 42, pp. 760-765. Sokoloff, J.B. (1992), Theory of atomic level sliding friction between ideal crystal interfaces, J. Appl. Phys., Vol. 72, pp. 1262-1269. Sokoloff, J.B., Krim, J., and Widom, A. (1993), Determination of an atomic-scale frictional force law through quartz-crystal microbalance measurements, Phys. Rev. B, Vol. 48, pp. 9134-9137. Sokoloff, J.B. (1995), Theory of the contribution to sliding friction from electronic excitations in the microbalance experiment, Phys. Rev. B, Vol. 52, pp. 5318-5322. Sokoloff, J.B. and Tomassone M.S. (1998), Effects of surface defects on friction for a thin solid film sliding over a solid surface, Phys. Rev. B, Vol. 57, pp. 4888-4894. Srivastava, G.P. (1997), Theory of semiconductor surface reconstruction, Rep. Prog. Phys., Vol. 60, pp. 561-613. Thomas, G. and Goringe, M.J. (1979), Transmission Electron Microscopy of Materials, John Wiley & Sons, New York. Tsukizoe, T., Tanaka, S., Nishizaki, K., and Ohmae, N. (1985), Field ion microscopy of metallic adhesion and friction, Proc. JSLE Intl. Tribol. Conf., Tokyo, pp. 121-126.
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Van Hove, M.A., Moritz, W., Over, H., Rous, P.J., Wander, A., Barbieri, A., Materer, N., Starke, U., and Somorjai, G.A. (1993), Automated determination of complex surface structures by LEED, Surf. Sci. Reports, Vol. 19, pp. 191-229. Vlachos, D.G., Schmidt, L.D., and Aris, R. (1993), Kinetics of faceting of crystals in growth, etching, and equilibrium, Phys. Rev. B, Vol. 47, pp. 4896-4909. Volokitin, A.I. and Persson, B.N.J. (1999), Theory of friction: the contribution from a fluctuating electromagnetic field, J. Phys.: Condens. Matter, Vol. 11, pp. 345-359. Wheeler, D.R. (1976), Effect of adsorbed chlorine and oxygen on the shear strength of iron and copper junctions, J. Appl. Phys., Vol. 47, pp. 1123-1130. Wheeler, D.R. (1978), X-ray photoelectron spectroscopic study of surface chemistry of dibenzyl disulfide on steel under mild and severe wear conditions, Wear, Vol. 47, pp. 243-254. Widom, A. and Krim, J. (1986), Q factors of quartz oscillator modes as a probe of submonolayer-film dynamics, Phys. Rev. B, Vol. 34, pp. 1403-1404. Williams, E.D. (1994), Surface steps and surface morphology: understanding macroscopic phenomena from atomic observations, Surf. Sci., Vol. 299/300, pp. 502-524. Wilson, R.G., Stevie, F.A., and Magee, C.W. (1989), Secondary Ion Mass Spectroscopy, Wiley, New York. Wood, E.A. (1963), Vocabulary of surface crystallography, J. Appl. Phys., Vol. 35, pp. 1306-1312. Zalm, P.C. (1995), Ultra shallow doping profiling with SIMS, Rep. Prog. Phys., Vol. 58, pp. 1321-1374. Zangwill, A. (1988), Physics at Surfaces, Cambridge University Press, Cambridge, U.K. Zhong, W. and Tomanek, D. (1990), First-principles theory of atomic-scale friction, Phys. Rev. Lett., Vol. 64, pp. 3054-3057. Zhu, X.Y., Hermanson, J., Arlinghaus, F.J., Gay, J.G., Richter, R., and Smith, J.R. (1984), Electronic structure and magnetism of Ni (100) films: self-consistent local-orbital calculations, Phys. Rev. B, Vol. 29, pp. 4426-4438.
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2 Surface Roughness Analysis and Measurement Techniques 2.1 2.2
The Nature of Surfaces ........................................................ 49 Analysis of Surface Roughness ............................................ 50 Average Roughness Parameters • Statistical Analyses • Fractal Characterization • Practical Considerations in Measurement of Roughness Parameters
2.3
Mechanical Stylus Method • Optical Methods • Scanning Probe Microscopy (SPM) Methods • Fluid Methods • Electrical Method • Electron Microscopy Methods • Analysis of Measured Height Distribution • Comparison of Measurement Methods
Bharat Bhushan The Ohio State University
Measurement of Surface Roughness................................... 81
2.4
Closure ................................................................................ 114
2.1 The Nature of Surfaces A solid surface, or more exactly a solid–gas or solid–liquid interface, has a complex structure and complex properties depending on the nature of the solids, the method of surface preparation, and the interaction between the surface and the environment. Properties of solid surfaces are crucial to surface interaction because surface properties affect real area of contact, friction, wear, and lubrication. In addition to tribological functions, surface properties are important in other applications, such as optical, electrical and thermal performance, painting, and appearance. Solid surfaces, irrespective of their method of formation, contain irregularities or deviations from the prescribed geometrical form (Whitehouse, 1994; Bhushan, 1996, 1999a,b; Thomas, 1999). The surfaces contain irregularities of various orders ranging from shape deviations to irregularities of the order of interatomic distances. No machining method, however precise, can produce a molecularly flat surface on conventional materials. Even the smoothest surfaces, such as those obtained by cleavage of some crystals, contain irregularities, the heights of which exceed the interatomic distances. For technological applications, both macro- and micro/nanotopography of the surfaces (surface texture) are important (Bhushan, 1999a,b). In addition to surface deviations, the solid surface itself consists of several zones having physicochemical properties peculiar to the bulk material itself (Figure 2.1) (Gatos, 1968; Haltner, 1969; Buckley, 1981). As a result of the forming process in metals and alloys, there is a zone of work-hardened or
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
49
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FIGURE 2.1
Modern Tribology Handbook
Solid surface details: surface texture (vertical axis magnified) and typical surface layers.
deformed material on top of which is a region of microcrystalline or amorphous structure that is called the Beilby layer. Deformed layers would also be present in ceramics and polymers. These layers are extremely important because their properties, from a surface chemistry point of view, can be entirely different from the annealed bulk material. Likewise, their mechanical behavior is influenced by the amount and depth of deformation of the surface layers. Many of the surfaces are chemically reactive. With the exception of noble metals, all metals and alloys and many nonmetals form surface oxide layers in air, and in other environments they are likely to form other layers (for example, nitrides, sulfides, and chlorides). Besides the chemical corrosion film, there are also adsorbed films that are produced either by physisorption or chemisorption of oxygen, water vapor, and hydrocarbons, from the environment. Occasionally, there will be a greasy or oily film derived from the environment. These films are found on metallic and nonmetallic surfaces. The presence of surface films affects friction and wear. The effect of adsorbed films, even a fraction of a monolayer, is significant on the surface interaction. Sometimes, the films wear out in the initial running period and subsequently have no effect. The effect of greasy or soapy film, if present, is more marked; it reduces the severity of surface interaction often by one or more orders of magnitude. This chapter covers the details on the analysis and measurement of surface roughness.
2.2 Analysis of Surface Roughness Surface texture is the repetitive or random deviation from the nominal surface that forms the threedimensional topography of the surface. Surface texture includes (1) roughness (nano- and microroughness), (2) waviness (macroroughness), (3) lay, and (4) flaws. Figure 2.2 is a pictorial display of surface texture with unidirectional lay (Anonymous, 1985). Nano- and microroughness are formed by fluctuations in the surface of short wavelengths, characterized by hills (asperities) (local maxima) and valleys (local minima) of varying amplitudes and spacings. These are large compared to molecular dimensions. Asperities are referred to as peaks in a profile (two dimensions) and summits in a surface map (three dimensions). Nano- and microroughness include those features intrinsic to the production process. These are considered to include traverse feed marks and other irregularities within the limits of the roughness sampling length. Waviness is the surface irregularity
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FIGURE 2.2 Pictorial display of surface texture. (From Anonymous (1985), Surface Texture (Surface Roughness, Waviness and Lay), ANSI/ASME B46.1, ASME, New York. With permission.)
of longer wavelengths and is referred to as macroroughness. Waviness may result from such factors as machine or workpiece deflections, vibration, chatter, heat treatment, or warping strains. Waviness includes all irregularities whose spacing is greater than the roughness sampling length and less than the waviness sampling length. Lay is the principal direction of the predominant surface pattern, ordinarily determined by the production method. Flaws are unintentional, unexpected, and unwanted interruptions in the texture. In addition, the surface may contain gross deviations from nominal shape of very long wavelength, which is known as errors of form. They are not normally considered part of the surface
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FIGURE 2.3
Modern Tribology Handbook
General typology of surfaces.
texture. A question often asked is whether various geometrical features should be assessed together or separately. What features are included together depends on the applications. It is generally not possible to measure all features at the same time. A very general typology of a solid surface is seen in Figure 2.3. Surface textures that are deterministic may be studied by relatively simple analytical and empirical methods; their detailed characterization is straightforward. However, the textures of most engineering surfaces are random, either isotropic or anisotropic, and either Gaussian or non-Gaussian. Whether the surface height distribution is isotropic or anisotropic and Gaussian or non-Gaussian depends upon the nature of the processing method. Surfaces that are formed by cumulative processes (such as peening, electropolishing, and lapping), in which the final shape of each region is the cumulative result of a large number of random discrete local events and irrespective of the distribution governing each individual event, will produce a cumulative effect that is governed by the Gaussian form. It is a direct consequence of the central limit theorem of statistical theory. Single-point processes (such as turning and shaping) and extreme-value processes (such as grinding and milling) generally lead to anisotropic and non-Gaussian surfaces. The Gaussian (normal) distribution has become one of the mainstays of surface classification. In this section, we first define average roughness parameters, followed by statistical analyses and fractal characterization of surface roughness that are important in contact problems. Emphasis is placed on random, isotropic surfaces that follow Gaussian distribution.
2.2.1 Average Roughness Parameters 2.2.1.1 Amplitude Parameters Surface roughness most commonly refers to the variations in the height of the surface relative to a reference plane. It is measured either along a single line profile or along a set of parallel line profiles (surface maps). It is usually characterized by one of the two statistical height descriptors advocated by the American National Standards Institute (ANSI) and the International Standardization Organization (ISO) (Anonymous, 1975, 1985). These are (1) Ra, CLA (center-line average), or AA (arithmetic average) and (2) the standard deviation or variance (σ), Rq or root mean square (RMS). Two other statistical
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FIGURE 2.4
53
Schematic of a surface profile z(x).
height descriptors are skewness (Sk) and kurtosis (K); these are rarely used. Another measure of surface roughness is an extreme-value height descriptor (Anonymous, 1975, 1985) Rt (or Ry , Rmax , or maximum peak-to-valley height or simply P–V distance). Four other extreme-value height descriptors in limited use, are: Rp (maximum peak height, maximum peak-to-mean height or simply P–M distance), Rv (maximum valley depth or mean-to-lowest valley height), Rz (average peak-to-valley height), and Rpm (average peak-to-mean height). We consider a profile, z(x), in which profile heights are measured from a reference line Figure 2.4. We define a center line or mean line such that the area between the profile and the mean line above the line is equal to that below the mean line. Ra, CLA, or AA is the arithmetic mean of the absolute values of vertical deviation from the mean line through the profile. The standard deviation σ is the square root of the arithmetic mean of the square of the vertical deviation from the mean line. In mathematical form, we write
R a = CLA = AA =
1 L
∫
L
z − m dx
(2.1a)
0
and
m=
1 L
∫
L
z dx
(2.1b)
0
where L is the sampling length of the profile (profile length). The variance is given as
σ2 =
1 L
∫ (z − m) L
2
dx
(2.2a)
0
= R q2 − m2
(2.2b)
where, σ is the standard deviation and Rq is the square root of the arithmetic mean of the square of the vertical deviation from a reference line, or
R q2 = RMS2 =
1 L
∫ (z )dx L
0
2
(2.3a)
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TABLE 2.1 Center-Line Average and Roughness Grades Ra Values up to a Value in µm
Roughness Grade Number
0.025 0.05 0.1 0.2 0.4 0.8 1.6 3.2 6.3 12.5 25.0
N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11
For the special case where m is equal to zero,
Rq = σ
(2.3b)
In many cases, the Ra and σ are interchangeable, and for Gaussian surfaces,
σ~
π R ~ 1.25 R a 2 a
(2.4)
The value of Ra is an official standard in most industrialized countries. Table 2.1 gives internationally adopted Ra values together with the alternative roughness grade number. The σ is most commonly used in statistical analyses. The skewness and kurtosis in the normalized form are given as
Sk =
1 σ 3L
∫ (z − m)
1 σ4 L
∫ (z − m)
L
3
dx
(2.5)
dx
(2.6)
0
and
K=
L
4
0
More discussion of these two descriptors will be presented later. Five extreme-value height descriptors are defined as follows: Rt is the distance between the highest asperity (peak or summit) and the lowest valley; Rp is defined as the distance between the highest asperity and the mean line; Rv is defined as the distance between the mean line and the lowest valley; Rz is defined as the distance between the averages of five highest asperities and the five lowest valleys; and Rpm is defined as the distance between the averages of the five highest asperities and the mean line. The reason for taking an average value of asperities and valleys is to minimize the effect of unrepresentative asperities or valleys which occasionally occur and can give an erroneous value if taken singly. Rz and Rpm are more reproducible and are advocated by ISO. In many tribological applications, height of the highest asperities above the mean line is an important parameter because damage may be done to the interface by the few high asperities present on one of the two surfaces; on the other hand, valleys may affect lubrication retention and flow.
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FIGURE 2.5
55
Various surface profiles having the same Ra value.
The height parameters Ra (or σ in some cases) are Rt (or Rp in some cases) are most commonly specified for machine components. For the complete characterization of a profile or a surface, none of the parameters discussed earlier are sufficient. These parameters are seen to be primarily concerned with the relative departure of the profile in the vertical direction only; they do not provide any information about the slopes, shapes, and sizes of the asperities or about the frequency and regularity of their occurrence. It is possible, for surfaces of widely differing profiles with different frequencies and different shapes, to give the same Ra or σ (Rq) values (Figure 2.5). These single numerical parameters are useful mainly for classifying surfaces of the same type that are produced by the same method. Average roughness parameters for surface maps are calculated using the same mathematical approach as that for a profile presented here. 2.2.1.2 Spacing (or Spatial) Parameters One way to supplement the amplitude (height) information is to provide some index of crest spacing or wavelength (which corresponds to lateral or spatial distribution) on the surface. Two parameters occasionally used are the peak (or summit) density, Np (η), and zero crossings density, N0. Np is the density of peaks (local maxima) of the profile in number per unit length, and η is the density of summits on the surface in number per unit area. Np and η are just measures of maxima irrespective of height. This parameter is in some use. N0 is the zero crossings density defined as the number of times the profile crosses the mean line per unit length. From Longuet–Higgins (1957a), the number of surface zero crossings per unit length is given by the total length of the contour where the autocorrelation function (to be described later) is zero (or 0.1) divided by the area enclosed by the contour. This count N0 is rarely used. A third parameter — mean peak spacing (AR) — is the average distance between measured peaks. This parameter is merely equal to (1/Np). Other spacial parameters rarely used are the mean slope and mean curvature, which are the first and second derivatives of the profile/surface, respectively.
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2.2.2 Statistical Analyses 2.2.2.1 Amplitude Probability Distribution and Density Functions The cumulative probability distribution function, or simply cumulative distribution function (CDF), P(h) associated with the random variable z(x), which can take any value between – ∞ and ∞ or zmin and zmax, is defined as the probability of the event z(x) ≤ h, and is written as (McGillem and Cooper, 1984; Bendat and Piersol, 1986)
()
(
P h = Pr ob z ≤ h
)
(2.7)
with P (– ∞) = 0 and P (∞) = 1. It is common to describe the probability structure of random data in terms of the slope of the distribution function given by the derivative
()
pz =
()
dP z
(2.8a)
dz
where the resulting function p(z) is called the probability density function (PDF). Obviously, the cumulative distribution function is the integral of the probability density function p(z), that is,
(
) ∫ p(z)dz = P(h) h
P z≤h =
(2.8b)
−∞
and
(
) ∫ p(z)dz = P(h ) − P(h ) h2
P h1 ≤ z ≤ h 2 =
2
h1
1
(2.8c)
Furthermore, the total area under the probability density function must be unity; that is, it is certain that the value of z at any x must fall somewhere between plus and minus infinity or zmax and zmin. The data representing a wide collection of random physical phenomenon in practice tend to have a Gaussian or normal probability density function,
(
)
z−m − exp pz = 12 2σ 2 σ 2π
()
1
( )
2
(2.9a)
where σ is the standard deviation and m is the mean. For convenience, the Gaussian function is plotted in terms of a normalized variable,
(
)
z* = z − m σ
(2.9b)
which has zero mean and unity standard deviation. With this transformation of variables, Equation 2.9 becomes
( )
p z* =
( )
− z* exp 12 2 2π 1
( )
2
(2.9c)
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which is called the standardized Gaussian or normal probability density function. To obtain P(h) from p(z*) of Equation 2.9c, the integral cannot be performed in terms of the common functions, and the integral is often listed in terms of the “error function” and its values are listed in most statistical textbooks. The error function is defined as
()
erf h =
(2π) ∫ 1
12
0
h
( ) dz *
− z* exp 2
2
(2.10)
An example of a random variable z*(x) with its Gaussian probability density and corresponding cumulative distribution functions is shown in Figure 2.6. Examples of P(h) and P(z* = h) are also shown. The probability density function is bell shaped, and the cumulative distribution function is S-shaped. We further note that for a Gaussian function
( ) P( −2 ≤ z* ≤ 2) = 0.954 P( −3 ≤ z* ≤ 3) = 0.999 P −1 ≤ z* ≤ 1 = 0.682
and
(
)
P −∞ ≤ z* ≤ ∞ = 1 which implies that the probabilities that some number that follows a Gaussian distribution is within the limits of ±1σ, ±2σ, and ±3σ are 68.2, 95.4, and 99.9%, respectively. A convenient method for testing for Gaussian distribution is to plot the cumulative distribution function on probability graph paper to show the percentage of the numbers below a given number; this is scaled such that a straight line is produced when the distribution is Gaussian (typical data to be
FIGURE 2.6
(a) Random function z*(x), which follows Gaussian probability functions.
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FIGURE 2.6 P(z*).
Modern Tribology Handbook
(b) Gaussian probability density function p(z*), and (c) Gaussian probability distribution function
presented later). To test for Gaussian distribution, a straight line corresponding to a Gaussian distribution is drawn on the plot. The slope of the straight line portion is determined by σ, and the position of the line for 50% probability is set at the mean value (which is typically zero for surface height data). The most practical method for the goodness of the fit between the given distribution and the Gaussian distribution is to use the Kolmogorov–Smirnov test (Smirnov, 1948; Massey, 1951; Siegel, 1956). In the Kolmogorov–Smirnov test, the maximum departure between the percentage of the numbers above a given number for the data and the percentage of the numbers that would be above a given number if the given distribution were a Gaussian distribution is first calculated. Then, a calculation is made to determine if the distribution is indeed Gaussian. The level of significance, P, is calculated; this gives the probability of mistakenly or falsely rejecting the hypothesis that the distribution is a Gaussian distribution. Common minimum values for P for accepting the hypothesis are 0.01 to 0.05 (Siegel, 1956). The chisquare test (Siegel, 1956) can also be used to determine how well the given distribution matches a Gaussian distribution. However, the chi-square test is not very useful because the goodness of fit calculated depends too much on how many bins or discrete cells the surface height data are divided into (Wyant et al., 1986).
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For the sake of mathematical simplicity in some analyses, sometimes an exponential distribution is used instead of the Gaussian distribution. The exponential distribution is given as
()
pz =
(
)
z−m 1 exp − σ σ
(2.11a)
or
( )
( )
p z * = exp − z *
(2.11b)
2.2.2.2 Moments of Amplitude Probability Functions The shape of the probability density function offers useful information on the behavior of the process. This shape can be expressed in terms of moments of the function,
mn =
∫
∞
−∞
()
z n p z dz
(2.12)
mn is called the nth moment. Moments about the mean are referred to as central moments,
mnc =
∞
∫ (z − m) p(z) dz n
(2.13)
−∞
The zeroth moment (n = 0) is equal to 1. The first moment is equal to m, mean value of the function z(x), whereas the first central moment is equal to zero. For completeness, we note that
∫
∞
∫
∞
Ra =
()
z − m p z dz
−∞
(2.14)
The second moments are,
m2 =
−∞
()
z 2p z dz = R q2
(2.15)
and
m2c =
∞
∫ (z − m) p(z) dz = σ 2
−∞
= R q2 − m2
2
(2.16a)
(2.16b)
The third moment mc3 is the skewness (Sk). A useful parameter in defining variables with an asymmetric spread, it represents the degree of symmetry of the distribution function (Figure 2.7). It is usual to normalize the third central moment as,
Sk =
1 σ3
∫ (z − m) p(z) dz ∞
−∞
3
(2.17)
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FIGURE 2.7 (a) Probability density functions for random distributions with different skewness, and for (b) symmetrical distributions (zero skewness) with different kurtosis.
Symmetrical distribution functions, including Gaussian, have zero skewness. The fourth moment mc4 is the kurtosis (K). It represents the peakedness of the distribution and is a measure of the degree of pointedness or bluntness of a distribution function (Figure 2.7). Again, it is usual to normalize the fourth central moment as,
K=
1 σ4
∞
∫ (z − m) p(z) dz −∞
4
(2.18)
Note that the symmetric Gaussian distribution has a kurtosis of 3. Distributions with K > 3 are called leptokurtic, and those with K < 3 are called platykurtic. Kotwal and Bhushan (1996) developed an analytical method to generate probability density functions for non-Gaussian distributions using the so-called Pearson system of frequency curves based on the methods of moments (Elderton and Johnson, 1969). (For a method of generating non-Gaussian distributions on the computer, see Chilamakuri and Bhushan [1998].) The probability density functions generated by this method for selected skewness and kurtosis values are presented in Table 2.2. These functions are plotted in Figure 2.8. From this figure, it can be seen that a Gaussian distribution with zero skewness and a kurtosis of three has an equal number of local maxima and minima at a certain height above and below the mean line. A surface with a high negative skewness has a larger number of local maxima above the mean as compared to a Gaussian distribution; for a positive skewness the converse is true, Figure 2.9. Similarly, a surface with a low kurtosis has a larger number of local maxima above the mean as compared to that of a Gaussian distribution; again, for a high kurtosis the converse is true (Figure 2.9).
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TABLE 2.2 Probability Density Functions for Surfaces with Various Skewness and Kurtosis Values Based on the Pearson’s System of Frequency Curves Non-Gaussian Parameters
Number of Type
Probability Density Function, p(z*)
Sk
K
–0.8
3
I
p(z *) = 0.33(1 + z * 3.86)
–0.5
3
I
p(z *) = 0.38(1 + z * 6.36)
–0.3
3
I
p z * = 0.39 1 + z * 10.72
0.0
3
Normal
p(z *) = 0.3989 exp −0.5(z *)
( )
(
2.14
(1 − z * 1.36)
(1 − z * 2.36)
9.21
(
29.80
0.3
3
I
p(z *) = 0.39(1 + z * 4.05)
0.5
3
I
p(z *) = 0.38(1 + z * 2.36)
0.8
3
I
p(z *) = 0.33(1 + z * 1.36)
0.0
2
II
p(z *) = 0.32 1 − (z *) 16
0.0
3
Normal
p(z *) = 0.3989 exp −0.5(z *)
0.0
5
VII
p(z *) = 0.46 1 + (z *) 25
0.0
10
VII
0.0
20
VII
2
(
2
10.64
)
(1 − z * 10.72)
2.79
(1 − z * 6.36)
0.11
(1 − z * 3.86)
)
29.80
9.21
2.14
0.5
( ) p(z *) = 0.49(1 + (z *) 8.20) p(z *) = 0.51(1 + (z *) 5.52) 2
2.79
) (1 − z * 4.05)
10.64
(
0.11
2
)
−4
2
−2.92
2
−2.68
z* = z/σ
In practice, many engineering surfaces have symmetrical Gaussian height distribution. Experience with most engineering surfaces shows that the height distribution is Gaussian at the high end, but at the lower end, the bottom 1 to 5% of the distribution is generally found to be non-Gaussian (Williamson, 1968). Many of the common machining processes produce surfaces with non-Gaussian distribution, Figure 2.10. Turning, shaping, and electrodischarge machining (EDM) processes produce surfaces with positive skewness. Grinding, honing, milling, and abrasion processes produce grooved surfaces with negative skewness but high kurtosis values. Laser polishing produces surfaces with high kurtosis. 2.2.2.3 Surface Height Distribution Functions If the surface or profile heights are considered as random variables, then their statistical representation in terms of the probability density function p(z) is known as the height distribution, or a histogram. The height distribution can also be represented as cumulative distribution function P(z). For a digitized profile, the histogram is constructed by plotting the number or fraction of surface heights lying between two specific heights as a function of height (Figure 2.11). The interval between two such heights is termed the class interval and is shown as dz in Figure 2.11. It is generally recommended to use 15 to 50 class intervals for general random data, but the choice is usually a trade-off between accuracy and resolution. Similarly, from the surface or profile height distribution, the cumulative distribution function is derived. It is constructed by plotting the cumulative number or proportion of the surface height lying at or below a specific height as a function of that height (Figure 2.11). An example of a profile and corresponding histogram and cumulative height distribution on a probability paper for a lapped nickel–zinc ferrite is given in Figure 2.12.
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FIGURE 2.8
Probability density function for random distributions with selected skewness and kurtosis values.
FIGURE 2.9
Schematic illustration for random functions with various skewness and kurtosis values.
Probability density and distribution curves can also be obtained for the slope and curvature of the surface or the profile. If the surface, or profile height, follows a Gaussian distribution, then its slope and curvature distribution also follows a Gaussian distribution. Because it is known that if two functions follow a Gaussian distribution, their sum and difference also follow a Gaussian distribution. Slope and curvatures are derived by taking the difference in a height distribution, and therefore slope and curvatures of a Gaussian height distribution would be Gaussian.
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63
FIGURE 2.10 Typical skewness and kurtosis envelopes for various manufacturing processes (From Whitehouse, D.I. (1994), Handbook of Surface Metrology, Institute of Physics Publishing, Bristol, U.K. With permission.)
FIGURE 2.11 distribution.
Method of deriving the histogram and cumulative distribution function from a surface height
For a digitized profile of length L with heights zi , i = 1 to N, at a sampling interval ∆x=L/(N – 1), where N represents the number of measurements, average height parameters are given as
1 Ra = N
σ2 =
Sk =
1 N
N
∑z −m
(2.19a)
i
i =1
N
∑ (z − m)
1 σ 3N
2
(2.19b)
i
i =1
N
∑ (z − m) i
i =1
3
(2.19c)
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Profile height (nm)
20
10
0
-10 -20 0
56
112
168
224
280
Distance (µm) (a)
Fraction of surface at given height
Rq = 2.2 nm Rt = 34.6 nm 0.4 Histogram
0.3
Gaussian distribution curve
0.2 0.1 0 -20
-10
0 Surface height (nm)
10
20
10
20
Percentage of surface at or below. a given height
99.9 99 90 50 10 1 0.1 -20
-10
0 Surface height (nm) (b)
FIGURE 2.12 ferrite.
(a) Profile and (b) corresponding histogram and distribution of profile heights of lapped nickel–zinc
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K=
N
1 σ 4N
∑ (z − m)
m=
1 N
4
(2.19d)
i
i =1
and N
∑z
(2.19e)
i
i =1
∂z
∂ 2z
Two average spacing parameters, mean of profile slope and profile curvature − 2 of a digitized ∂x ∂x profile, are given as
mean slope =
and mean curvature =
1 N −1
N −1
z i +1 − z i ∆x
∑
1 N−2
i =1
N −1
2z i − z i −1 − z i +1 ∆x 2
∑ i =2
(2.20a)
(2.20b)
The surface slope at any point on a surface is obtained by finding the square roots of the sum of the squares of the slopes in two orthogonal (x and y) axes. The curvature at any point on the surface is obtained by finding the average of the curvatures in two orthogonal (x and y) axes (Nayak, 1971). Before calculation of roughness parameters, the height data are fitted in a least-square sense to determine the mean height, tilt, and curvature. The mean height is always subtracted, and the tilt is usually subtracted. In some cases, curvature needs to be removed as well. Spherical and cylindrical radii of curvature are removed for spherical and cylindrical surfaces, respectively (e.g., balls and cylinders), before roughness parameters are calculated. 2.2.2.4 Bearing Area Curves The real area of contact (to be discussed in the next chapter) is known as the bearing area and may be approximately obtained from a surface profile or a surface map. The bearing area curve (BAC) first proposed by Abbott and Firestone (1933) is also called the Abbott–Firestone curve or simply the Abbott curve. It gives the ratio of air to material at any level, starting at the highest peak, called the bearing ratio or material ratio, as a function of level. To produce a BAC from a surface profile, a parallel line (bearing line) is drawn some distance from a reference (or mean) line. The length of each material intercept (land) along the line is measured and these lengths are summed. The proportion of this sum to the total length, the bearing length ratio (tp), is calculated. This procedure is repeated along a number of bearing lines, starting with the highest peak to the lowest valley, and the fractional land length (bearing length ratio) as a function of the height of each slice from the highest peak (cutting depth) is plotted (Figure 2.13). For a Gaussian surface, the BAC has an S-shaped appearance. In the case of a surface map, bearing planes are drawn, and the area of each material intercept is measured. For a random surface, the bearing length and bearing area fractions are numerically identical. The BAC is related to the CDF. The fraction of heights lying above a given height z (i.e., the bearing ratio at height h) is given by
(
∞
) ∫ p(z) dz
Prob z ≥ h =
h
(2.21a)
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FIGURE 2.13
Modern Tribology Handbook
Schematic of bearing area curve.
which is 1 – P(h), where P(h) is the cumulative distribution function at z ≤ h (Figure 2.6). Therefore, the BAC can be obtained from the height distribution histogram. The bearing ratio histograph at height h is simply the progressive addition of all the values of p(z) starting at the highest point and working down to the height z = h, and this cumulative sum multiplied by the class interval ∆z is
(
)
P z ≥ h = ∆z
∞
∑ p(z)
(2.21b)
z=h
The relationship of bearing ratio to the fractional real area of contact is highly approximate as material is sliced off in the construction of BAC and the material deformation is not taken into account. 2.2.2.5 Spatial Functions Consider two surfaces with sine wave distributions with the same amplitude but different frequencies. We have shown that these will have the same Ra and σ, but with different spatial arrangements of surface heights. Slope and curvature distributions are not, in general, sufficient to represent the surface, as they refer only to one particular spatial size of features. The spatial functions (McGillem and Cooper, 1984; Bendat and Piersol, 1986), namely the autocovariance (or autocorrelation) function (ACVF), structure function (SF), or power spectral (or autospectral) density function (PSDF), offer a means of representing the properties of all wavelengths, or spatial sizes of the feature; these are also known as surface texture descriptors. ACVF has been the most popular way of representing spatial variation. The ACVF of a random function is most directly interpreted as a measure of how well future values of the function can be predicted based on past observations. SF contains no more information than the ACVF. The PSDF is interpreted as a measure of frequency distribution of the mean square value of the function, that is the rate of change of the mean square value with frequency. In this section, we will present the definitions for an isotropic and random profile z(x). Definitions for an isotropic surface z(x,y) can be found in a paper by Nayak (1971). Analysis of an anisotropic surface is considerably complicated by the number of parameters required to describe the surface. For example, profile measurements along three different directions are needed for complete surface characterization of selected anisotropic surfaces. For further details on anisotropic surfaces, see Longuet-Higgins (1957a), Nayak (1973), Bush et al. (1979), and Thomas (1982). Autocovariance and Autocorrelation Functions For a function z(x), the ACVF for a spatial separation of τ is an average value of the product of two measurements taken on the profile a distance τ apart, z(x) and z(x + τ). It is obtained by comparing the function z(x) with a replica of itself where the replica is shifted an amount τ (Figure 2.14),
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FIGURE 2.14
Construction of the autocovariance function.
()
1 L→∞ L
R τ = lim
∫ z(x)z(x + τ)dx L
(2.22a)
0
where L is the sampling length of the profile. From its definition, ACVF is always an even function of τ, that is,
() ( )
R τ = R −τ
(2.22b)
The values of ACVF at τ = 0 and ∞ are,
()
R 0 = R q2 = σ 2 + m2
(2.22c)
and
( )
R ∞ = m2
(2.22d)
The normalized form of the ACVF is called the autocorrelation function (ACF) and is given as
()
C τ = lim
L→∞
[ ( ) ][ ( ) ] [ ( ) ] σ
1 z x − m z x + τ − m dx = R τ − m2 Lσ 2
2
(2.23)
For a random function, C(τ) would be maximum (= 1) at τ = 0. If the signal is periodic, C(τ) would peak whenever τ is a multiple of wavelength. Many engineering surfaces are found to have an exponential ACF,
()
(
C τ = exp − τ β
)
(2.24)
The measure of how quickly the random event decays is called the correlation length. The correlation length is the length over which the autocorrelation function drops to a small fraction of its value at the origin, typically 10% of its original value. The exponential form has a correlation length of β* [C(τ) = 0.1] equal to 2.3 β (Figure 2.15). Sometimes, correlation length is defined as the distance at which value of the autocorrelation function is 1/e, that is 37%, which is equal to β for exponential ACF. The correlation length can be taken as that at which two points on a function have just reached the condition where they can be regarded as being independent. This follows from the fact that when C(τ) is close to unity, two points on the function at a distance τ apart are strongly interdependent. However, when C(τ) attains values close to zero, two points on the function at a distance τ apart are weakly correlated. The correlation length, β* can be viewed as a measure of randomness. The degree of randomness of a surface increases with an increase in the magnitude of β*. The directionality of a surface can be found from its autocorrelation function. By plotting the contours of equal autocorrelation values, one can obtain contours to reveal surface structure. The anisotropy of
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FIGURE 2.15
Modern Tribology Handbook
An exponential autocorrelation function and corresponding power spectral density function.
the surface structure is given as the ratio between the longer and shorter axes of the contour (Wyant et al., 1986; Bhushan, 1996). For a theoretically isotropic surface structure, the contour would have a constant radius; that is, it would be a circle. The autocorrelation function can be calculated either by using the height distribution of the digitized profile or the fast Fourier transform (FFT) technique. In the FFT technique, the first PSDF (described later) is obtained by taking an FFT of the surface height and squaring the results; then an inverse FFT of the PSDF is taken to get ACVF. Structure Function The structure function (SF) or variance function (VF) in an integral form for a profile z(x) is,
()
1 L→∞ L
S τ = lim
∫ [z(x) − z(x + τ)] dx L
2
(2.25)
0
The function represents the mean square of the difference in height expected over any spatial distance τ. For stationary structures, it contains the same information as the ACVF. The two principal advantages of SF are that its construction is not limited to the stationary case, and it is independent of the mean plane. Structure function is related to ACVF and ACF as
() [
( )]
S τ = 2 σ 2 + m2 − R τ
(2.26a)
[ ( )]
= 2σ 2 1 − C τ
(2.26b)
Power Spectral Density Function The PSDF is another form of spatial representation and provides the same information as the ACVF or SF, but in a different form. The PSDF is the Fourier transform of the ACVF, ∞
( ) ( ) ∫ R(τ)exp(−iωτ)dτ
P ω = P −ω = =
∫
∞
−∞
−∞
() (
)
(2.27)
( )
σ 2 C τ exp − iωτ dτ + m2δ ω
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where ω is the angular frequency in length–1 (= 2πf or 2π/λ, f is frequency in cycles/length and λ is wavelength in length per cycle), and δ(ω) is the delta function. P(ω) is defined over all frequencies, both positive and negative, and is referred to as a two-sided spectrum. G(ω) is a spectrum defined over nonnegative frequencies only and is related to P(ω) for a random surface by
( )
( )
G ω = 2P ω , ω ≥ 0
(2.28a)
= 0, ω < 0. Since the ACVF is an even function of τ, it follows that the PSDF is given by the real part of the Fourier transform in Equation 2.27. Therefore, ∞
∞
( ) ∫ R(τ)cos (ωτ)dτ = 2∫ R(τ)cos (ωτ)dτ
Pω =
−∞
(2.28b)
0
Conversely, the ACVF is given by the inverse Fourier transform of the PSDF,
()
Rτ =
1 2π
∞
∫ () ( ) −∞
P ω exp iωτ dω =
1 2π
∞
∫ P(ω)cos (ωτ) dω −∞
(2.29)
For
()
τ = 0, R 0 = R q2 =
1 2π
∞
∫ P(ω) dω
(2.30)
−∞
The equation shows that the total area under the PSDF curve (when frequency in cycles/length) is equal to Rq2 . The area under the curve between any frequency limits gives the mean square value of the data within that frequency range. The PSDF can also be obtained directly in terms of the Fourier transform of the profile data z(x) by taking an FFT of the profile data and squaring the results, as follows:
( )
1 L→∞ L
P ω = lim
z x exp − iωx dx
∫ () ( L
0
)
2
(2.31)
The PSDF can be evaluated from the data either via the ACVF using Equation 2.28 or the Fourier transform of the data (Equation 2.31). Note that the units of the one-dimensional PSDF are in terms of length to the third power, and for the two-dimensional case it is the length to the fourth power. Figure 2.15 shows the PSDF for an exponential ACF previously presented in Equation 2.24. The magnitude of the P(ω) at ω = 1/β is known as the half-power point. For an exponential ACF, the PSDF is represented by white noise in the upper frequencies. The physical meaning of the model is that the main components of the function consist of a band covering the lower frequencies (longer wavelengths). Shorter wavelength components exist, but their magnitude declines with increasing frequency so that, in this range, the amplitude is proportional to wavelength. To cover large spatial range, it is often more convenient with surface data to represent ACF, SF, and PSDF on a log–log scale. Figure 2.16a shows examples of selected profiles. Figures 2.16b and 2.16c show the corresponding ACVF and PSDF (Bendat and Piersol, 1986). (For calculation of ACVF and PSDF, profile length of multiple of wavelengths [a minimum of one wavelength] needs to be used.) The ACVF of a sine wave is a cosine wave. The envelope of the sine wave covariance function remains constant over all time delays,
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FIGURE 2.16 (a) Four special time histories: (i) sine wave, (ii) sine wave plus wide-band random noise, (iii) narrowband random noise, and (iv) wide-band random noise. (b) corresponding idealized autocovariance functions, and (c) corresponding power spectral density functions (From Bendat, J.S. and Piersol, A.G. (1986), Engineering Applications of Correlation and Spectral Analysis, 2nd edition, Wiley, New York. With permission.)
suggesting that one can predict future values of the data precisely based on past observations. Looking at the PSDF of the sine wave, we note that the total mean square value of the sine wave is concentrated at the single frequency, ω0. In all other cases, because of the erratic character of z(x) in Figure 2.16a, a past record does not significantly help one predict future values of the data beyond the very near future. To calculate the autocovariance function for (iii) to (iv) profiles, the power spectrum of the data is considered uniform over a wide bandwidth B. ACVF and PSDF of a sine wave plus wide-band random noise is simply the sum of the functions of the sine wave and wide-band random noise. The moments of the PSDF are defined as
Mn =
1 2π
∫ [P(ω) − m δ(ω)]ω ∞
−∞
2
n
dω
(2.32)
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FIGURE 2.16 (continued)
where Mn are known as the spectral moments of the nth order. We note for a Gaussian function (Nayak, 1971),
M0 = σ 2 =
1 L
∫ (z − m) L
dx
(2.33a)
0
M2 = σ ′ =
( )
1 L
( )
1 L
2
2
∫ (dz dx) dx
(2.33b)
∫ (d z dx ) dx
(2.33c)
L
2
0
and 2
M 4 = σ ′′ =
L
2
2
2
0
where σ′ and σ″ are the standard deviations of the first and second derivatives of the functions. For a surface/profile height, these are the surface/profile slope and curvature, respectively.
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FIGURE 2.16 (continued)
According to Nayak (1971), a random and isotropic surface with a Gaussian height distribution can be adequately characterized by the three-zeroth (M0), second (M2) and fourth moments (M4) of the power spectral density function. Based on the theory of random processes, a random and isotropic surface can be completely characterized in a statistical sense (rather than a deterministic sense) by two functions: the height distribution and the autocorrelation function. A random surface with Gaussian height distribution and exponential autocorrelation function can then simply be characterized by two parameters, two lengths: standard deviation of surface heights (σ) and the correlation distance (β*) (Whitehouse and Archard, 1970). For characterization of a surface with a discrete, arbitrary autocorrelation function, three points C(0), C(h), and C(2h) for a profile, where h is an arbitrary distance and four or more points are needed on the C(τ), depending upon the type of the surface (Whitehouse and Phillips, 1978, 1982). 2.2.2.6 Probability Distribution and Statistics of the Asperities and Valleys Surfaces consist of hills (asperities) of varying heights and spacing and valleys of varying depths and spacing. For a two-dimensional profile, the peak is defined as a point higher than its two adjacent points greater than a threshold value. For a three-dimensional surface map, the summit is defined as a point higher than its four adjacent points greater than a threshold value. A valley is defined in the same way but in reverse order. A threshold value is introduced to reduce the effect of noise in the measured data and ensure that every peak/summit identified is truly substantial. Based on analysis of roughness data
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of a variety of smooth samples, Poon and Bhushan (1995b) recommend a threshold value as one tenth of the σ roughness of smooth surfaces (with σ less than about 50 nm); it should be lower than 10% of the σ value for rougher surfaces. Gaussian surfaces might be considered as comprising a certain number of hills (asperities) and an equal number of valleys. These features may be assessed and represented by their appropriate distribution curves, which can be described by the same sort of characteristics as were used previously for the surface height distributions. Similar to surface height distributions, the height distributions of peaks (or summits) and valleys often follow the Gaussian curve (Greenwood, 1984; Wyant et al., 1986; Bhushan, 1996). Distribution curves can also be obtained for the absolute values of slope and for the curvature of the peaks (or summits) and valleys. Distributions of peak (or summit) curvature follow a log normal distribution (Gupta and Cook 1972; Wyant et al., 1986; Bhushan, 1996). The mean of the peak curvature increases with the peak height for a given surface (Nayak, 1971). The parameters of interest in some analytical contact models of two random rough surfaces to be discussed in the next chapter are the density of summits (η), the standard deviation of summit heights (σp), and the mean radius (Rp) (or curvature, κp) of the summit caps or η, σ, and β*. The former three roughness parameters (η, σp, Rp) can be related to other easily measurable roughness parameters using the theories of Longuet-Higgins (1957a,b), Nayak (1971), and Whitehouse and Phillips (1978, 1982). For a random Gaussian profile, we note that M2(= σ′ 2) and Mr (= σ″ 2) can be calculated from σ, N0, and Np using the following relationship (Longuet-Higgins, 1957a):
σ′ πσ
(2.34a)
σ ′′ 2πσ ′
(2.34b)
N0 = and
Np =
Note that N0 and Np are frequency dependent, for example, if the profile has a high frequency riding on a low frequency, then Np will be higher and N0 will be lower. We now define an auxiliary quantity, bandwidth parameter, α (Nayak, 1971), 2
2N σσ ′′ 2 α = p = 2 N0 σ′
(2.35)
which defines the width of the power spectrum of the random process forming the process from which the profile is taken. The distribution of peak heights and their expected tip curvature as a function of α are shown in Figure 2.17 (Nayak, 1971). z*p (= zp /σ) is the standardized cumulative summit/peak height distribution and κ*p (= κp /σ″) is the standardized mean summit/peak curvature κp . It is observed that high peaks always have a longer expected mean curvature (i.e., a smaller mean radius) than lower peaks. If α = 1, the spectrum consists of a single frequency, where 2Np, total density of peaks and valleys (maxima and minima) equals N0. If α = ∞, the spectrum extends over all frequencies (white noise spectrum). The peak heights have a Gaussian distribution and κp is nearly constant for peaks of all heights and is given by
σp ~ σ
(2.36a)
κ p ~ 1.3 σ ′′
(2.36b)
and
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FIGURE 2.17 (a) Probability density of peak heights and (b) expected dimensionless curvature of peaks. (From Nayak, P.R. (1971), Random process model of rough surfaces, ASME J. Lub. Tech., 93, 398-407. With permission.)
We also note that a profile with a very narrow spectrum has no peaks below a mean line, whereas a white noise profile with infinite spectral width has half of its peaks below this line. From Bush et al. (1976), the standard deviation of the summit/peak height for any α is given by
0.8968 σ p ~ 1 − α
12
σ
(2.37)
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From Nayak (1971), the density of summits per unit area can be related to the spectral moments and number of peaks per unit length by
σ ′′ η = 0.031 σ′
2
(2.38a)
~ 1.2 N p2
(2.38b)
Using discrete random process analysis, Whitehouse and Phillips (1978, 1982) derived the relationship of tribological parameters of interest for a surface that has a Gaussian height distribution. For characterization of a profile, we need standard deviation and just two points on the measured ρ1 and ρ2 spaced h (sampling interval) and 2h from the origin of the normalized autocorrelation function. For characterization of a surface, we need between four and seven points on the ACF, depending upon the type of surface. Tribological parameters that can be predicted are the mean and standard deviation (σp) of the peak height; the mean (κp) and standard deviation (σ″p ) of the peak curvature; the average peak slope; the correlation coefficient between the peak height and its curvature; and the summit density. 2.2.2.7 Composite Roughness of Two Random Rough Surfaces For two random rough surfaces in contact, the composite roughness of interest is defined as the sum of two roughness processes obtained by adding together the local heights (z), the local slope (θ), and local curvature (κ)
z = z1 + z 2 θ = θ1 + θ2
(2.39)
κ = κ1 + κ 2 For two random rough surfaces in contact, an equivalent rough surface can be described of which the values of σ, σ′, σ″, R(τ), P(ω), and M0, M2, and M4 are summed for the two rough surfaces, that is,
σ 2 = σ12 + σ 22 σ ′2 = σ1′ 2 + σ ′2 2 σ ′′2 = σ1′′2 + σ ′′2 2
() () () P(ω ) = P (ω ) + P (ω ) M = (M ) + (M ) R τ = R1 τ + R 2 τ
and
i
1
2
i 1
i 2
(2.40a)
where i = 0, 2, 4. These equations state that variances, autocovariance function, and power spectra are simply additive. Since autocovariance functions of two functions are additive, simple geometry shows that correlation lengths of two exponential ACVFs are related as
1 1 1 = *+ * * β β1 β2
(2.40b)
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FIGURE 2.18
Modern Tribology Handbook
Qualitative description of statistical self-affinity for a surface profile.
2.2.3 Fractal Characterization A surface is composed of a large number of length scales of roughness that are superimposed on each other. As stated earlier, surface roughness is generally characterized by the standard deviation of surface heights. However, due to the multiscale nature of the surface, it is known that the variances of surface height and its derivatives and other roughness parameters depend strongly on the resolution of the roughness measuring instrument or any other form of filter; hence they are not unique for a surface (Ganti and Bhushan, 1995; Poon and Bhushan, 1995a). Therefore rough surfaces should be characterized in such a way that the structural information of roughness at all scales is retained. It is necessary to quantify the multiscale nature of surface roughness. A unique property of rough surfaces is that if a surface is repeatedly magnified, increasing details of roughness are observed right down to nanoscale. In addition, the roughnesses at all magnifications appear quite similar in structure, as is qualitatively shown in Figure 2.18. The statistical self-affinity is due to similarity in appearance of a profile under different magnifications. Such a behavior can be characterized by fractal geometry (Majumdar and Bhushan, 1990; Ganti and Bhushan, 1995; Bhushan, 1999b). The fractal approach has the ability to characterize surface roughness by scale-independent parameters and provides information on the roughness structure at all length scales that exhibit the fractal behavior. Surface characteristics can be predicted at all length scales within the fractal regime by making measurements at one scan length. Structure function and power spectrum of a self-affine fractal surface follow a power law and can be written as (Ganti and Bhushan model)
( 2 D − 3) τ ( 4 −2 D )
()
S τ = Cη
( )
Pω =
(2.41)
( 2 D − 3)
c1η ω
(2.42a)
( 5−2 D )
and
c1 =
(
) [(
)] C
Γ 5 − 2D sin π 2 − D 2π
(2.42b)
The fractal analysis allows the characterization of surface roughness by two parameters D and C which are instrument-independent and unique for each surface. The parameter D (ranging from 1 to 2 for surface profile) primarily relates to the relative power of the frequency contents, and C to the amplitude of all frequencies. η is the lateral resolution of the measuring instrument, τ is the size of the increment (distance), and ω is the frequency of the roughness. Note that if S(τ) or P(ω) are plotted as a function of ω or τ, respectively, on a log-log plot, then the power law behavior results in a straight line. The slope of the line is related to D, and the location of the spectrum along the power axis is related to C.
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FIGURE 2.19 Structure functions for the roughness data measured using AFM and NOP, for a thin-film magnetic rigid disk. (From Ganti, S. and Bhushan, B. (1995), Generalized fractal analysis and its applications to engineering surfaces, Wear, 180, 17-34. With permission.) TABLE 2.3 Surface Roughness Parameters for a Polished Thin-Film Rigid Disk Scan Size (µm × µm)
σ(nm)
D
C(nm)
1(AFM) 10(AFM) 50(AFM) 100(AFM) 250(NOP) 4000(NOP)
0.7 2.1 4.8 5.6 2.4 3.7
1.33 1.31 1.26 1.30 1.32 1.29
9.8 × 10–4 7.6 × 10–3 1.7 × 10–2 1.4 × 10–2 2.7 × 10–4 7.9 × 10–5
AFM — Atomic force microscope NOP — Noncontact optical profiler
Figure 2.19 presents the structure functions of a thin-film magnetic rigid disk measured using an atomic force microscope (AFM) and noncontact optical profiler (NOP). A horizontal shift in the structure functions from one scan to another arises from the change in the lateral resolution. The D and C values for various scan lengths are listed in Table 2.3. Note that fractal dimension of the various scans is fairly constant (1.26 to 1.33); however, C increases/decreases monotonically with σ for the AFM data. The error in estimation of η is believed to be responsible for the variation in C. These data show that the disk surface follows a fractal structure for three decades of length scales.
2.2.4 Practical Considerations in Measurement of Roughness Parameters 2.2.4.1 Short- and Long-Wavelength Filtering Engineering surfaces cover a broad bandwidth of wavelengths, and samples, however large, often exhibit nonstationary properties (in which the roughness is dependent upon the sample size). Surface roughness is intrinsic; however, measured roughness is a function of the bandwidth of the measurement and thus is not an intrinsic property. Instruments using different sampling intervals measure features with different length scales. Roughness is found at scales ranging from millimeter to nanometer (atomic) scales. A surface is composed of a large number of length scales of roughness that are superimposed on each other. Therefore, on a surface, it is not that different asperities come in different sizes but that one asperity comes in different sizes. Distribution of size and shape of asperities is dependent on the short-wavelength limit or the sampling interval of the measuring instrument. When the sampling interval at which the surface is sampled is reduced, the number of asperities detected and their curvature appear to rise without
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FIGURE 2.20
Modern Tribology Handbook
Sinusoidal profiles with different numbers of sampling points per wavelength.
limit down to atomic scales. This means that asperity is not a “definite object.” Attempts are made to identify a correct sampling interval which yields the relevant number of asperities for a particular application. An asperity relevant for contact mechanics is defined as that which makes a contact in a particular application (contacting asperity) and carries some load. The short-wavelength limit or the sampling interval affects asperity statistics. The choice of shortwavelength limit depends on the answer to the following question: what is the shortest wavelength that will affect the interaction? It is now known that it is the asperities on a nanoscale that first come into contact and plastically deform instantly, and subsequently, the load is supported by the deformation of larger-scale asperities (Bhushan and Blackman, 1991; Poon and Bhushan, 1996). Since plastic deformation in most applications is undesirable, asperities on a nanoscale need to be detected. Therefore, the shortwavelength limit should be as small as possible. The effect of the short-wavelength limit on a roughness profile can be illustrated by a sinusoidal profile represented by different numbers of sampling points per wavelength as shown in Figure 2.20. The waveform of the sinusoidal profile is distorted when the number of sampling points decreases. The profile parameters do not change significantly with sampling points equal to 6 or greater per wavelength. Therefore, the minimum number of sampling points required to represent a wavelength structure may be set to 6, i.e., the optimum sampling interval is λ/6, where λ is the wavelength of the sinusoidal profile. By analogy, the suitable sampling interval should be related to the main wavelength structure of a random profile which is represented by β*. However, β* is a function of the bandwidth of the measurement and thus is not an intrinsic property. It is reasonable to select a sampling interval a fraction of β* measured at the long wavelength limit, say 0.25 β* to 0.5 β* (Poon and Bhushan, 1995a). Figure 2.21 demonstrates how the long wavelength limit, also called the cutoff wavelength or sampling length (size), can affect the measured roughness parameters (Anonymous, 1985). The top profile represents the actual movement of the stylus on a surface. The lower ones show the same profile using cutoff wavelength values of 0.8, 0.25, and 0.08 mm. A small cutoff value would isolate the waviness while a large cutoff value would include the waviness. Thomas (1999) has shown that the standard deviation of surface roughness, σ, will increase with an increase in the cutoff wavelength or sampling length L, as given by the following relation,
σ ∝ L1 2
(2.43)
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FIGURE 2.21 The effect of the cutoff wavelength is to remove all components of the total profile that have wavelengths greater than cutoff value.
Ganti and Bhushan (1995) and Poon and Bhushan (1995a) have reported that σ and other roughness parameters initially increase with L and then reach a constant value because engineering surfaces seem to have a long-wavelength limit. Thus, before the surface roughness can be effectively quantified, an application must be defined. Having a knowledge of the application enables a measurement to be planned and in particular for it to be decided to what bandwidth of surface features the information collected should refer. Features that appear as roughness in one application of a surface may well constitute waviness in another. The long-wavelength limit (which is the same as scan size in many instruments) in contact problems is set by the dimensions of the nominal contact area (Figure 2.22). This is simply to say that a wavelength much longer than the nominal contact area will not affect what goes on inside it. In addition, the longwavelength limit of the surface roughness in the nominal contact area, if it exists, should be obtained. The long-wavelength limit can be chosen to be twice the nominal contact size or the long-wavelength limit of the roughness structure in the nominal contact size, if it exists, whichever is smaller. To provide a basis of instrumentation for roughness measurement, a series of cutoff wavelength values has been standardized in a British standard (BS1134-1972), an ANSI/ASME (B46.1-1985), and an ISO Recommendation (R468). The international standard cutoff values are 0.08, 0.25, and 0.8 mm. The preferred value of 0.8 mm is assumed unless a different value is specified. Note that waviness measurements are made without long-wavelength filtering. Long- and short-wavelength filtering in measuring instruments is most commonly accomplished by digital filtering. For example, in a fast Fourier transform (FFT) technique, the FFT of the raw data is taken,
FIGURE 2.22
Contact size of two moving components of different lengths L1 and L2 on the same rough surface.
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FIGURE 2.23
Modern Tribology Handbook
Transmission characteristics of a profiler with low bandpass and high bandpass filters.
the appropriate frequency contents are removed, and the inverse FFT is taken to obtain the filtered data. However, this technique is slow, and one method commercially used is the finite impulse response (FIR) technique. The FIR technique filters by convoluting the trace data with the impulse response of the filter specification. The impulse response is obtained by taking the inverse FFT of the filter specification. Anonymous (1985) also describes the electronic filtering method for short- and long-wavelength filtering, which is accomplished by passing the alternating voltage representing the profile through an electrical wave filter, such as the standard RC filter. The electronic filtering is generally used to filter out short wavelength electronic noise (low band pass filtering). In some profilers (Talysurf by Rank Taylor Hobson, Leicester, England), a skid on a pickup body is traversed along with the stylus arm (Bhushan, 1996). The skid provides a straight reference datum and provides a long-wavelength filtering which is a function of the size and shape of the skid. Mechanical short-wavelength filtering also results from the design and construction of a measuring instrument. For example in the stylus instrument or the atomic force microscope, the stylus removes certain short wavelengths on the order of the stylus tip radius, which is referred to as lateral resolution of the instrument. The stylus is not able to enter the grooves. As the spacing between grooves increases, the stylus displacement will rise, but once it has become sufficient for the stylus to reach the bottom, there will be a full indication. In a digital optical profiler, lateral resolution is controlled by the physical size of the charge-coupled-device (CCD) image sensors at the microscope objective magnifications. A short wavelength limit, if selected, should be at least twice the lateral resolution of the instrument. For the instrument in which a short-wavelength filter is introduced, the output will tend to fall off above a certain frequency, that is below a certain wavelength, for example, as shown by the dotted curve B in Figure 2.23, even though the stylus continues to rise and fall over the irregularities. Dotted curve C in Figure 2.23 also shows the fall off of instrument output at longer wavelength. Only within the range of wavelengths for which the curve is substantially level will the indication be a measure solely of the amplitude and be independent of wavelength curve A in Figure 2.23. 2.2.4.2 Scan Size After the short-wavelength and long-wavelength limits are selected, the roughness measurement must be made on a length large enough to provide a statistically significant value for the chosen locality. The total length involved is called the measuring length, evaluation length, traversing length, or scan length. In some cases, a length of several individual scan lengths (say five) are chosen (Whitehouse, 1994). In most measurements, scan length is the same as the long-wavelength limit. For two-dimensional measurement, a certain area is measured rather than a length. Wyant et al. (1984) and Bhushan et al. (1985) have suggested that in measurement of a random surface, a scan length equal to or greater than 200 β* should be used.
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FIGURE 2.24 SEM micrograph of a trace made by a stylus instrument showing surface damage of electroless Ni–P coating (stylus material, diamond; stylus radius = 0.1 µm; and stylus load = 10 µN or 1 mg). (From Poon, C.Y. and Bhushan, B. (1995a), Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler, Wear, 190, 76-88. With permission.)
2.3 Measurement of Surface Roughness A distinction is made between methods of evaluating the nanoscale to atomic scale and microscale features of surface roughness. Physicists and physical chemists require fine-scale details of surfaces and often details of molecular roughness. These details are usually provided using methods such as low-energy electron diffraction, molecular-beam methods, field-emission and field-ion microscopy, scanning tunneling microscopy, and atomic force microscopy. On the other hand, for most engineering and manufacturing surfaces, microscopic methods suffice, and they are generally mechanical or optical methods. Some of these methods can also be used to measure geometrical parameters of surfaces (Bhushan, 1996, 1999). Various instruments are available for the roughness measurement. The measurement technique can be divided into two broad categories: (a) a contact type in which during measurement a component of the measurement instrument actually contacts the surface to be measured; and (2) a noncontact type. A contact-type instrument may damage surfaces when used with a sharp stylus tip, particularly soft surfaces (Figure 2.24). For these measurements, the normal loads have to be low enough so that the contact stresses do not exceed the hardness of the surface to be measured. The first practical stylus instruments were developed by Abbott and Firestone (1933). In 1939, Rank Taylor Hobson in Leicester, England, introduced the first commercial instrument called Talysurf. Today, contact-type stylus instruments using electronic amplification are the most popular. The stylus technique, recommended by the ISO, is generally used for reference purposes. In 1983, a noncontact optical profiler based on the principle of two-beam optical interferometry was developed and is now widely used in the electronics and optical industries to measure smooth surfaces. In 1985, an atomic force microscope was developed which is basically a nano-profiler operating at ultra-low loads. It can be used to measure surface roughness with lateral resolution ranging from microscopic to atomic scales. This instrument is commonly used in research to measure roughness with extremely high lateral resolution, particularly nanoscale roughness. There exists a number of other techniques that have been either demonstrated in the laboratory and never commercially used or used in specialized applications. We will divide the different techniques into six categories based on the physical principle involved: mechanical stylus method, optical methods, scanning probe microscopy (SPM) methods, fluid methods, electrical method, and electron microscopy methods. Descriptions of these methods are presented, and the detailed descriptions of only three — stylus, optical (based on optical interferometry), and AFM techniques — are provided. We will conclude this section by comparing various measurement methods.
2.3.1 Mechanical Stylus Method This method uses an instrument that amplifies and records the vertical motions of a stylus displaced at a constant speed by the surface to be measured. Following is a partial list of commercial profilers: Rank
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Taylor Hobson (UK) Talysurf profilers, Tencor Instruments AlphaStep and P-series profilers, Veeco/Sloan Technology Dektak profilers, Gould Inc. Instruments Division profilers, and Kosaka Laboratory, Tokyo (Japan) profilers. The stylus is mechanically coupled mostly to a linear variable differential transformer (LVDT), an optical or a capacitance sensor. The stylus arm is loaded against the sample and either the stylus is scanned across the stationary sample surface using a traverse unit at a constant speed or the sample is transported across an optical flat reference. As the stylus or sample moves, the stylus rides over the sample surface detecting surface deviations by the transducer. It produces an analog signal corresponding to the vertical stylus movement. This signal is then amplified, conditioned, and digitized (Thomas, 1999; Bhushan, 1996). In a profiler, as shown in Figure 2.25a, the instrument consists of a stylus measurement head with a stylus tip and a scan mechanism (Anonymous, 1996a). The measurement head houses a stylus arm with a stylus, sensor assembly, and the loading system. The stylus arm is coupled to the core of an LVDT to monitor vertical motions. The core of a force solenoid is coupled to the stylus arm and its coil is energized to load the stylus tip against the sample. A proximity probe (photo optical sensor) is used to provide a soft limit to the vertical location of the stylus with respect to the sample. The sample is scanned under the stylus at a constant speed. In high precision, ultra-low load profilers, shown in Figures 2.25b and 2.25c, the vertical motion is sensed using a capacitance sensor, and a precision stage transports the sample during measurements (Anonymous, 1996b). The hardware consists of two main components: a stylus measurement head with stylus tip and a scan mechanism. The stylus measurement head houses a sensor assembly, which includes the stylus, the appropriate sensor electronics and integrated optics, and the loading system. The capacitance sensor exhibits a lower noise, has a lower mass, and scales well to smaller dimensions as compared to LVDTs. The capacitive sensor assembly consists of a stylus arm suspended by a flexure pivot, connected to a sensor vane that extends through the center of a highly sensitive capacitive sensor. Vertical movement of the stylus arm results in movement of the vane, which is registered by the capacitance sensor. The analog signal of the capacitance sensor output is digitized and displayed in a surface roughness map. The entire stylus assembly is mounted on a plate, which is driven by a motor for coarse vertical motion. In order to track the stylus across the surface, force is applied to the stylus. The ability to accurately apply and control this force is critical to the profiler performance. The measurement head uses a wire coil to set a programmable stylus load as low as 0.05 mg. Attached above the stylus flexure pivot is an arm with a magnet mounted to the end. The magnet is held in close proximity to the wire coil, and the coil, when energized, produces a magnetic field that moves the magnet arm. This applied force pushes the stylus arm past its null position to a calibrated force displacement, where the horizontal position of the stylus arm represents zero applied force to the stylus. The force coil mechanism and a sophisticated digital signal processor are used to maintain a constant applied force to the stylus. The flexure pivot allows the stylus to move easily, but its tension affects the applied force to the stylus as the stylus arm is moved through its vertical range. To locally correct for the pivot tensions during roughness measurement for a constant stylus force, the force is calibrated by serving the drive current to the force coil to move the stylus several regularly spaced positions, with the stylus not in contact with a sample (zero stylus force). A table of stylus position vs. current settings is generated. A digital signal processor uses these data to dynamically change the force setting as the roughness measurements are made. The scan mechanism shown in Figure 2.25c, holds the sensor assembly stationary while the sample stage is moved with a precision lead screw drive mechanism. This drive mechanism, called the X drive, uses a motor to drive the lead screw, which then moves the sample stage with guide wires along an optical flat via PTFE skids. The motion is monitored by an optical encoder and is accurate to 1 to 2 µm. The optical flat ensures a smooth and stable movement of the stage across the scan length, while a guide bar provides a straight, directional movement. This scanning of the sample limits the measurement noise from the instrument, by decoupling the stage motion from vertical motions of the stylus measured using the sensor. Surface topography measurements can be acquired with high sensitivity over a 205-mm scan. Three-dimensional images can be obtained by acquiring two-dimensional scans in the X direction while
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ce For
l
Coi
t
gne
Ma
ne
r Va
so Sen
d hiel c S w) i t e agn n vie er M sectio ( Out
lus
Sty
s ate xis r Pl nt) o A s t o Sen pare Piv nce trans a t i ac own Cap (sh
Sample Plate (Theta Plate)
X Leadscrew
Y (3D) Leadscrew
Optically Flat Reference
FIGURE 2.25 Schematics of (a) stylus measurement head with loading system and scan mechanism used in Veeco/Sloan Dektak profilers. (Courtesy of Veeco/Sloan Technology, Santa Barbara, CA.) (b) Stylus measurement head with loading system and (c) scan mechanism used in Tencor P-series profilers. (Courtesy of Tencor Instruments, Milpitas, CA.)
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FIGURE 2.26
Modern Tribology Handbook
Schematic of a diamond conical stylus showing its cone angle and tip radius.
stepping in the Y direction by 5 µm with the Y lead screw used for precise sample positioning. When building a surface map by parallel traversing, it is essential to maintain a common origin for each profile. This can be achieved by a flattening procedure in which the mean of each profile is calculated separately and these results are spliced together to produce an accurate surface map. The surface maps are generally presented such that the vertical axis is magnified by three to four orders of magnitude as compared to the horizontal scan axis. Measurements on circular surfaces with long scan lengths can be performed by a modified stylus profiler (such as Talyround) in which a cylindrical surface is rotated about an axis during measurement. Styli are made of diamond. The shapes can vary from one manufacturer to another. Chisel-point styli with tips (e.g., 0.25 µm × 2.5 µm) may be used for detection of bumps or other special applications. Conical tips are almost exclusively used for microroughness measurements (Figure 2.26). According to the international standard (ISO 3274–1975), a stylus is a cone of a 60° to 90° included angle and a (spherical) tip radius of curvature of 2, 5, or 10 µm. The radius of a stylus ranges typically from 0.1 to 0.2 µm to 25 µm with the included angle ranging from 60° to 80°. The stylus is a diamond chip tip that is braised to a stainless steel rod mounted to a stylus arm. The diamond chip is cleaved, then ground and polished to a specific dimension. The radius of curvature for the submicrometer stylus tip, which is assumed to be spherical, is measured with an SEM, or against a standard. The portion of the stylus tip that is in contact with the sample surface, along with the known radius of curvature, determines the actual radius of the tip with regard to the feature size. The stylus cone angle is determined from the cleave and grind of the diamond chip and is checked optically or against a standard. Maximum vertical and spatial (horizontal) magnifications that can be used are on the order of 100,000× and 100×, respectively. The vertical resolution is limited by sensor response, background mechanical vibrations, and thermal noise in the electronics. Resolution for smooth surfaces is as low as 0.1 nm and 1 nm for rough surfaces for large steps. Lateral resolution is on the order of the square root of the stylus radius. The step height repeatability is about 0.8 nm for a step height of 1 µm. The stylus load ranges typically from 0.05 to 100 mg. Long-wave cutoff wavelengths range typically from 4.5 µm to 25 mm. Short-wave cutoff wavelengths range typically from 0.25 µm to several millimeters. The scan lengths can be typically as high as 200 mm, and for three-dimensional imaging, the scan areas can be as large as 5 mm × 5 mm. The vertical range typically ranges from 2 to 250 µm. The scan speed ranges typically from 1 µm/s to 25 mm/s. The sampling rate ranges typically from 50 Hz to 1 kHz. 2.3.1.1 Relocation There are many situations where it would be very useful to look at a particular section of a surface before and after some experiment, such as grinding or run-in, to see what changes in the surface roughness have occurred. This can be accomplished by the use of a relocation table (Thomas, 1999). The table is bolted to the bed of the stylus instrument, and the specimen stage is kinematically located against it at three points and held in position pneumatically. The stage can be lowered and removed, an experiment of some kind performed on the specimen, and the stage replaced on the table. The stylus is then relocated to within the width of the original profile.
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FIGURE 2.27
85
Distortion of profile due to finite dimensions of stylus tip (exaggerated).
2.3.1.2 Replication Replication is used to obtain measurements on parts that are not easily accessible, such as internal surfaces or underwater surfaces. It is used in compliant surfaces because direct measurement would damage or misrepresent the surface (Thomas, 1999). The principle is simply to place the surface to be measured in contact with a liquid that will subsequently set to a solid, hopefully reproducing the detail of the original as faithfully as a mirror image or a negative. Materials such as plaster of paris, dental cement, or polymerizing liquids are used. The vital question is how closely the replica reproduces the features of the original. Lack of fidelity may arise from various causes. 2.3.1.3 Sources of Errors A finite size of stylus tip distorts a surface profile to some degree (Radhakrishnan, 1970; McCool, 1984). Figure 2.27 illustrates how the finite size of the stylus distorts the surface profile. The radius of curvature of a peak may be exaggerated, and the valley may be represented as a cusp. A profile containing many peaks and valleys of radius of curvature of about 1 µm or less or many slopes steeper than 45° would probably be more or less misrepresented by a stylus instrument. Another error source is due to stylus kinematics (McCool, 1984). A stylus of finite mass held in contact with a surface by a preloaded spring may, if traversing the surface at a high enough velocity, fail to maintain contact with the surface being traced. Where and whether this occurs depends on the local surface geometry, the spring constant to the mass ratio, and the tracing speed. It is clear that a trace for which stylus contact has not been maintained presents inaccurate information about the surface microroughness. Stylus load also introduces error. A sharp stylus even under low loads results in an area of contact so small that the local pressure may be sufficiently high to cause significant local elastic deformation of the surface being measured. In some cases, the local pressure may exceed the hardness of the material, and plastic deformation of the surface may result. Styli generally make a visible scratch on softer surfaces, for example, some steels, silver, gold, lead, and elastomers (Poon and Bhushan, 1995a; Bhushan, 1996). The existence of scratches results in measurement errors and unacceptable damage. As shown in Figure 2.24 presented earlier, the stylus digs into the surface and the results do not truly represent the microroughness. It is important to select stylus loads low enough to minimize plastic deformation.
2.3.2 Optical Methods When electromagnetic radiation (light wave) is incident on an engineering surface, it is reflected either specularly or diffusely or both (Figure 2.28). Reflection is totally specular when the angle of reflection is equal to the angle of incidence (Snell’s law); this is true for perfectly smooth surfaces. Reflection is totally
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FIGURE 2.28 Modes of reflection of electromagnetic radiation from a solid surface, (a) specular only, (b) diffuse only, and (c) combined specular and diffuse. (From Thomas, T.R. (1999), Rough Surfaces, 2nd ed., Imperial College Press, London, U.K. With permission.)
diffuse or scattered when the energy in the incident beam is distributed as the cosine of the angle of reflection (Lambert’s law). As roughness increases, the intensity of the specular beam decreases while the diffracted radiation increases in intensity and becomes more diffuse. In most real surfaces, reflections are neither completely specular nor completely diffuse. Clearly, the relationships between the wavelength of radiation and the surface roughness will affect the physics of reflection; thus, a surface that is smooth to radiation of one wavelength may behave as if it were rough to radiation of a different wavelength. The reflected beams from two parallel plates placed normal to the incident beam interfere and result in the formation of the fringes (Figure 2.29). The fringe spacing is a function of the spacing of the two plates. If one of the plates is a reference plate and another is the engineering surface whose roughness is to be measured, fringe spacing can be related to the surface roughness. We have just described so-called twobeam optical interference. A number of other interference techniques are used for roughness measurement. Numerous optical methods have been reported in the literature for measurement of surface roughness. Optical microscopy has been used for overall surveying, which only provides qualitative information. Optical methods may be divided into geometrical and physical methods (Thomas, 1999). Geometrical methods include taper sectioning and light sectioning methods. Physical methods include specular and diffuse reflections, speckle pattern, and optical interference. 2.3.2.1 Taper-Sectioning Method In this technique, a section is cut through the surface to be examined at a shallow angle θ, thus effectively magnifying height variations by a factor cot θ, and is subsequently examined by an optical microscope.
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FIGURE 2.29
87
Optical schematic of two-beam interference.
The technique was first described by Nelson (1969). The surface to be sectioned has to be supported with an adherent coating that will prevent smearing of the contour during the sectioning operation. This coating must firmly adhere to the surface, must have a similar hardness, and should not diffuse into the surface. For steel surfaces, about 0.5-mm-thick electroplated nickel can be used. The specimen is then ground on a surface grinder at a typical taper angle between 1° and 6°. The taper section so produced is lapped, polished, and possibly lightly etched or heat tinted to provide good contrast for the optical examination. The disadvantages of this technique include destruction of the test surface, tedious specimen preparation, and poor accuracy. 2.3.2.2 Light-Sectioning Method The image of a slit (or a straight edge such as a razor blade) is thrown onto the surface at an incident angle of 45°. The reflected image will appear as a straight line if the surface is smooth, and as an undulating line if the surface is rough. The relative vertical magnification of the profile is the cosecant of the angle of incidence, in this case 1.4. Lateral resolution is about 0.5 µm. An automated system for three-dimensional measurement of surface roughness was described by Uchida et al. (1979). Their system consists of using the optical system to project the incident slit beam and then observing the image with an industrial television camera projected through a microscope; the table for the test surface is driven by a stepping motor. 2.3.2.3 Specular Reflection Methods Gloss or specular reflectance (sometimes referred to as sheen or luster) is a surface property of the material, namely, the refractive index and surface roughness. Fresnel’s equations provide a relationship between refractive index and reflectance. Surface roughness scatters the reflected light, thus affecting the specular reflectance. If the surface roughness σ is much smaller than the wavelength of the light (λ) and the surface has a Gaussian height distribution, the correlation between specular reflectance (R) and σ is described by (Beckmann and Spizzichino, 1963) 2 2 4 πσ cos θi 4 πσ cos θi R = exp − ~ 1− R0 λ λ
(2.44)
where θi is the angle of incidence measured with respect to the sample normal, and R0 is the total reflectance of the rough surface and is found by measuring the total light intensity scattered in all
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FIGURE 2.30 Schematic of a glossmeter. (From Budde, W. (1980), A reference instrument for 20°, 40°, and 85° gloss measurements, Metrologia, 16, 1-5. With permission.)
directions including the specular direction. If roughness-induced, light-absorption processes are negligible, R0 is equal to the specular reflectance of a perfectly smooth surface of the same material. For rougher surfaces (σ ≥ λ/10), the true specular beam effectively disappears, so R is no longer measurable. Commercial instruments following the general approach are sometimes called specular glossmeters (Figure 2.30). The first glossmeter was used in the 1920s. A glossmeter detects the specular reflectance (or gloss) of the test surface (of typical size of 50 mm × 50 mm), which is simply the fraction of the incident light reflected from a surface (Gardner and Sward, 1972). Measured specular reflectance is assigned a gloss number. The gloss number is defined as the degree to which the finish of the surface approaches that of the theoretical gloss standard, which is the perfect mirror, assigned a value of 1000. The practical, primary standard is based on the black gloss (refractive index, n = 1.567) under angles of incidence of 20°, 60°, or 85°, according to ISO 2813 or American Society for Testing and Materials (ASTM) D523 standards. The specular reflectance of the black gloss at 60° for unpolarized radiation is 0.100 (Fresnel’s equation, to be discussed later). By definition, the 60° gloss value of this standard is 1000 × 0.10 = 100. For 20 and 85°, Fresnel reflectances are 0.049 and 0.619, respectively, which are again by definition set to give a gloss value of 100. The glossmeter described by Budde (1980), operates over the wavelength range from 380 to 760 nm with a peak at 555 nm. There are five different angles of incidence that are commonly used — 20°, 45°, 60°, 75°, and 85°. Higher angles of incidence are used for rougher surfaces and vice versa. Glossmeters are commonly used in the paint, varnish, and paper-coating industries (Gardner and Sward, 1972). These are also used in magnetic tapes at 45° or 60° incident angles, depending on the level of roughness (Bhushan, 1996). It is very convenient to measure the roughness of magnetic tape coatings during manufacturing by a glossmeter. The advantage of a glossmeter is its intrinsic simplicity, ease, and speed of analysis. Other than accuracy and reproducibility, the major shortcoming of the gloss measurement is its dependence on the refractive index. Specular reflectance of a dielectric surface for unpolarized incident radiation increases with an increase in the refractive index according to Fresnel’s equations (Hecht and Zajac, 1974),
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R=
(R + R ) 1
2
(2.45a)
2
where
( (
2 2 cos θi − n − sin θi R1 = 2 2 cos θi + n − sin θi
) )
12
12
2
(2.45b)
and
( (
2 2 2 n cos θi − n − sin θi R2 = 2 2 2 n cos θi + n − sin θi
) )
12
12
2
(2.45c)
where n is the refractive index of the dielectric material, θi is the angle of incidence with respect to surface normal, and R1 and R2 are the reflectance in the perpendicular and the parallel to the incident plane, respectively. For θi = 0 (normal incidence), Equation 2.45 reduces to
1− n R= 1+ n
2
(2.46)
From Equations 2.45 and 2.46, we can see that a slight change of refractive index of the surface can change the gloss number. A change in the refractive index can come from a change in the supply of the raw material used in manufacturing the test surface (Fineman et al., 1981), a change in the composition of the surface (Wyant et al., 1984), or the aging of the surface (Alince and Lepoutre, 1980; Wyant et al., 1984). We therefore conclude that use of a glossmeter for roughness measurement is not very appropriate; however, for luster or general appearance, it may be acceptable. 2.3.2.4 Diffuse Reflection (Scattering) Methods Vision depends on diffuse reflection or scattering. Texture, defects, and contamination causes scattering (Bennett and Mattson, 1989; Stover, 1995). It is difficult to obtain detailed roughness distribution data from the scattering measurements. Its spatial resolution is based on optical beam size, typically 0.1 to 1 mm in diameter. Because scatterometers measure light reflectance rather than the actual physical distance between the surface and the sensor, they are relatively insensitive to changes in temperature and mechanical or acoustical vibrations, making them extremely stable and robust. To measure large surface areas, traditional methods scan the roughness of several, relatively small areas (or sometimes just a single scan line) at a variety of locations on the surface. On the other hand, with scatterometers, the inspection spot is quickly and automatically rastered over a large surface. The scattering is sometimes employed to measure surface texture. This technique is particularly suitable for on-line roughness measurement during manufacture because it is continuous, fast, noncontacting, nondestructive, and relatively insensitive to the environment. Three approaches have been used to measure defects and roughness by light scattering. Total Integrated Scatter The total integrated scatter (TIS) method is complementary to specular reflectance. Instead of measuring the intensity of the specularly reflected light, one measures the total intensity of the diffusely scattered
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FIGURE 2.31 Schematic of the total integrated scatter apparatus with a diffuse integrated sphere. (From Stover, J.C., Bernt, M., and Schiff, T. (1996), TIS uniformity maps of wafers, disks and other samples, Proc. Soc. Photo-Opt. Instrum. Eng., 2541, 21-25. With permission.)
light (Bennett, 1978; Stover, 1995). In the first TIS instrument, an aluminized, specular Coblentz sphere (90° integrating sphere) was used (Bennett and Porteus, 1961). Another method, shown in Figure 2.31 uses a high-reflectance diffuse integrated sphere. The incident laser beam travels through the integrated sphere and strikes the sample port at a few degrees off-normal. The specular reflection traverses the sphere again and leaves through the exit port where it is measured by the specular detector, D2. The inside of the sphere is covered with a diffuse white coating that rescatters the gathered sample scatter throughout the interior of the sphere. The sphere takes on a uniform glow regardless of the orientation of the scatter pattern. The scatter signal is measured by sampling this uniform glow with a scatter detector, D1, located on the right side of the sphere. The TIS is then the ratio of the total light scattered by the sample to the total intensity of scattered radiation (both specular and diffuse). If the surface has a Gaussian height distribution and its standard deviation σ is much smaller than the wavelength of light (λ), the TIS can be related to σ as given by Equation 2.41 (Bennett, 1978):
TIS =
2 2 R0 − R 4 πσ cos θi 4 πσ cos θi = 1 − exp − ~ R0 λ λ
(2.47a)
2
4 πσ = , if θi = 0 λ
(2.47b)
Samples of known specular reflectance are used to calibrate the reflected power (R0) signals. The same samples, used to reflect the beam onto the sphere interior, can be used to calibrate the scattered power (R0 – R) measurement signals (Stover et al., 1996). Several commercial instruments, such as a Surfscan (Tencor Instruments, Mountain View, CA), Diskan (GCA Corp., Bedford, MA), and Dektak TMS-2000 (Veeco/Sloan Technology, Santa Barbara, CA) are built on this principle. In these instruments, to map a surface, either the sample moves or the light beam raster scans the sample. These instruments are generally used to generate maps of asperities, defects, or particles rather than microroughness distribution. Diffuseness of Scattered Light This approach relies on the observation that, over a large roughness range, the pattern of scattered radiation becomes more diffuse with increasing roughness. Hence, the goal here is to measure a parameter that characterizes the diffuseness of the scattered radiation pattern and to relate this parameter to the surface roughness. The ratio of the specular intensity to the intensity at one off-specular angle is measured.
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Since this ratio generally decreases with increasing surface roughness, it provides a measure of the roughness itself. Peters (1965) used this technique with the detector held 40° off-specular to determine the roughness of cylindrical parts while they were being ground. His results show a good correlation between the diffuseness and Ra over a range up to 0.3 µm. Using a pair of transmitting/receiving fiber-optic bundles set at different angles, the roughness measurements can be made with optics and instrumentation located remotely (North and Agarwal, 1983). Angular Distributions In principle, the entire angular distribution (AD) of the scattered radiation contains a great deal of information about the surface roughness. In addition to σ roughness, measurements of the angular distributions can yield other surface parameters, such as the average wavelength or the average slope. The angle of incidence is normally held constant and the AD is measured by an array of detectors or by a movable detector and is stored as a function of the angle of scattering. The kind of surface information that may be obtained from the AD depends on the roughness regime. For σ > λ and surface spatial wavelength >λ (rough-surface limit), one is working in the geometrical optics regime, where the scattering may be described as scattering from a series of glints or surface facets oriented to reflect light from the incident beam into the scattering direction. This AD is therefore related to the surface slope distribution, and its width is a measure of the characteristic slope of the surface. As σ and surface spatial wavelength decrease, the distribution becomes a much more complicated function of both surface slopes and heights and is difficult to interpret. For σ < λ (smooth-surface limit), the scattering arises from the diffraction of light by the residual surface roughness viewed as a set of sinusoidal diffraction grating with different amplitudes, wavelengths, and directions across the surface. The intensity of the scattered light is determined by the vertical scale of the roughness and its angular width by the transverse scale; both scales are measured in units of the radiation wavelengths. It can be shown theoretically that the AD should directly map the power spectral density function of the surface roughness (Hildebrand et al., 1974; Stover, 1975; Church, 1979). Figure 2.32 shows a sketch of various texture classes (in the smooth surface limit) on the left and their scattering signatures or power spectral densities on the right. The final sketch in the figure is the sum of the preceding ones, representing a real diamond-turned surface. Such signatures can be easily seen by reflecting a beam laser light from the surface onto a distant screen in a dark room (Church, 1979). Figure 2.33 shows the measured scattered intensity distribution from a diamond-turned gold surface using He–Ne laser light. He used a nonconventional method of scanning the scattering angle and the incident angle simultaneously by holding both the source and the detector fixed and rotating the specimen. The upper curve in Figure 2.33 shows the AD in the plane of incidence and perpendicular to the predominant lay of the surface. The sharp peak in the center is the specular reflection; a broad scattering distribution is due to the random component of the roughness; and a series of discrete lines are due to a periodic component roughness caused by the feed rate of the diamond tool. The lower curve in Figure 2.33 is an AD measured parallel to the lay direction, and it shows another broad distribution characteristic of the random roughness pattern in this direction. In principle, then, one can distinguish between effects due to periodic and random roughness components and can detect the directional property of surfaces. A number of experimental systems have been developed. Clarke and Thomas (1979) developed a laser scanning analyzer system to measure rough surfaces; and scattered light was empirically related to the roughness. In their technique, a laser beam is reflected from a polygonal mirror rotating at high speed onto a surface where it is reflected into a fixed photodetector receiver masked to a narrow slit. The angular reflectance function is produced as the spot scans the strip. At a given moment in any scan, the fixed detector receives light scattered from the single point on the strip which happens at that instant to be illuminated by the deflected beam. The spot diameter can be set from 200 µm upward at a scan width of 623 mm, and the scanning speed is 5 kHz maximum.
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FIGURE 2.32 Texture classes and their scattering signatures when illuminated by coherent light. The final sketch is the sum of the preceding ones representing a real diamond-turned surface. (From Church, E.L. (1979), The measurement of surface texture and topography by differential light scattering, Wear, 57, 93-105. With permission.)
In the measurements reported by Clarke and Thomas (1979), all reflection curves were symmetrical and roughly the same shape irrespective of finish and resembled a Gaussian error curve (similar to the upper curve as shown in Figure 2.33). The surface roughness was found to be related to the width of the curve at half the maximum amplitude. Half-width tends to increase fairly linearly with the arithmetic average roughness and varies as about the fourth power of the mean absolute profile slope (Figure 2.34). Vorburger et al. (1984) developed an AD instrument shown in Figure 2.35 in which a beam from an He–Ne laser illuminates the surfaces at an angle of incidence that may be varied. The scattered light distribution is detected by an array of 87 fiber-optic sensors positioned in a semicircular yoke that can be rotated about its axis so that the scattered radiation may be sampled over an entire hemisphere. They compared the angular scattering data with theoretical angular scattering distributions computed from digitized roughness profiles measured by a stylus instrument and found a reasonable correlation. The three scattering methods described so far are generally limited by available theories to studies of surfaces whose σ are much less than λ. With an He–Ne laser as the light source, the preceding constraint means that these techniques have been used mainly on optical quality surfaces where σ < 0.1 µm. Within that limited regime, they can provide high-speed, quantitative measurements of the roughness of both isotropic surfaces and those with a pronounced lay. With rougher surfaces, AD may be useful as a comparator for monitoring both amplitude and wavelength surface properties. The ultimate vertical
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FIGURE 2.33 Experimental AD scattering spectrum of a diamond-turned surface. The upper curve shows a scan mode perpendicular to the lay direction. The lower curve shows a scan parallel to the lay direction. (From Church, E.L. (1979), The measurement of surface texture and topography by differential light scattering, Wear, 57, 93-105. With permission.)
resolution is 1 nm or better, but the horizontal range is limited to fairly short surface wavelengths. Both the vertical and horizontal ranges can be increased by using long wavelength (infrared) radiation, but there is an accompanying loss of vertical and horizontal resolution. 2.3.2.5 Speckle Pattern Method When a rough surface is illuminated with partially coherent light, the reflected beam consists, in part, of random patterns of bright and dark regions known as speckle. Speckle is the local intensity variation between neighboring points in the overall AD discussed earlier. One means of clarifying the distinction between speckle and the AD is to note that speckle is the intensity noise that is usually averaged out to obtain the AD. The technique used to relate speckle and surface roughness is the speckle pattern correlation measurement. Here, two speckle patterns are obtained from the test surface by illuminating it with different angles of incidence or different wavelengths of light. Correlation properties of the speckle patterns are then studied by recording the patterns. Goodman (1963) and others have shown that the degree of correlation between speckle patterns depends strongly on the surface roughness (σ) (see e.g., Ruffing and Fleischer, 1985). 2.3.2.6 Optical Interference Methods Optical interferometry is a valuable technique for measuring surface shape, on both a macroscopic and microscopic scale (Tolansky, 1973). The traditional technique involves looking at the interference fringes and determining how much they depart from being straight and equally spaced. With suitable computer analysis, these can be used to completely characterize a surface. Bennett (1976) developed an interferometric system employing multiple-beam fringes of equal chromatic order (FECO). FECO are formed when a collimated beam of white light undergoes multiple reflections between two partially silvered surfaces, one of which is the surface whose profile is being measured and the other is a super-smooth reference surface. Based upon a television camera for the detection of the positional displacement of the fringes, this technique has yielded accuracies of σ on the order of 0.80 nm for the measurement of surface profiles. Lateral resolution of this system has been reported to be between 2 and 4 µm, over a 1 mm profile length. Both the differential interference contrast (DIC) and the Nomarski polarization interferometer techniques (Francon, 1966; Francon and Mallick, 1971) are commonly used for qualitative assessment of surface roughness. While those interferometers are very easy to operate, and they are essentially insensitive to vibration, they have the disadvantage that they measure what is essentially the slope of the surface
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FIGURE 2.34 Variation of half-width with (a) average roughness and (b) mean absolute slope: A, milled: B, turned; C, spark eroded; D, shaped; E, ground; F, criss-cross lapped; G, parallel lapped. (From Clarke, G.M. and Thomas, T.R. (1979), Roughness measurement with a laser scanning analyzer, Wear, 57, 107-116. With permission.)
errors, rather than the surface errors themselves. A commercial Nomarski type profiler based on the linearly polarized laser beam is made by Chapman Instruments, Rochester, New York. The Tolansky or multiple-beam interferometer is another common interferometer used with a microscope. The surface being examined must have a high reflectivity and must be in near contact with the interferometer reference surface, which can scratch the surface under test. One of the most common optical methods for the quantitative measurement of surface roughness is to use a two-beam interferometer. The actual sample can be measured directly without applying a highreflectivity coating. The surface-height profile itself is measured. The option of changing the magnification can be used to obtain different values of lateral resolution and different fields of view. Shortwavelength visible-light interferometry and computerized phase-shifting techniques can measure surfaceheight variations with resolutions better than 1/100 of a wavelength of light. The short wavelength of visible light is a disadvantage, however, when measuring large surface-height variations and slopes. If a single wavelength is used to make a measurement and the surface-height difference between adjacent measurement
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FIGURE 2.35 Schematic of angular-distribution scatter apparatus. (From Vorburger, T.V., Teague, E.C., Scire, F.E., McLay, M.J., and Gilsinn, D.E. (1984), Surface roughness studies with DALLAS array for light angular scattering, J. Res. of NBS, 89, 3-16. With permission.)
points is greater than one-quarter wavelength, height errors of multiple half-wavelengths may be introduced. The use of white light, or at least a few different wavelengths, for the light source can solve this height ambiguity problem. Two techniques can extend the range of measurement of surface microstructure where the surface slopes are large. One technique, measuring surface heights at two or more visible wavelengths, creates a much longer nonvisible synthetic wavelength, which increases the dynamic range of the measurement by the ratio of the synthetic wavelength to the visible wavelength. Increases in the dynamic range by factors of 50 to 100 are possible. Another more powerful method uses a white-light scanning interferometer, which involves measuring the degree of fringe modulation or coherence, instead of the phase of the interference fringes. Surface heights are measured by changing the path length of the sample arm of the interferometer to determine the location of the sample for which the white-light fringe with the best contrast is obtained. Vertical position at each location gives the surface height map. Various commercial instruments based on optical phase-shifting and vertical scanning interferometry are available (Wyko Corp., Tucson, AZ; Zygo Corp., Middlefield, CT; and Phase Shift Technology, Tucson, AZ). Next, we describe the principles of operation following by a description of a typical commercial optical profiler. Phase Shifting Interferometry Several phase-measurement techniques (Wyant, 1975; Bruning, 1978; Wyant and Koliopoulos, 1981; Creath, 1988) can be used in an optical profiler to give more accurate height measurements than are possible by simply using the traditional technique of looking at the interference fringes and determining how much they depart from going straight and being equally spaced. One mode of operation used in commercial profilers is the so-called integrated bucket phase-shifting technique (Wyant et al., 1984, 1986; Bhushan et al., 1985). For this technique, the phase difference between the two interfering beams is changed at a constant rate as the detector is read out. Each time the detector array is read out, the time variable phase α(t), has changed by 90° for each pixel. The basic equation for the irradiance of a two-beam interference pattern is given by
[ ( ) ( )]
I = I1 + I2 cos φ x , y + α t
(2.48)
where the first term is the average irradiance, the second is the interference term, and φ(x, y) is the phase distribution being measured. If the irradiance is integrated while α(t) varies from 0 to π/2, π/2 to π, and π to 3π/2, the resulting signals at each detected point are given by
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( ) [ ( ) ( )] B( x , y ) = I′ + I′ [− cos φ ( x , y ) − sin φ ( x , y )] C( x , y ) = I′ + I′ [− cos φ ( x , y ) + sin φ ( x , y )] A x , y = I1′ + I2′ cos φ x , y − sin φ x , y 1
2
1
2
(2.49)
From the values of A, B, and C, the phase can be calculated as
( )
[( (
) ( )) (A(x, y ) − B(x, y ))]
φ x , y = tan−1 C x , y − B x , y
(2.50)
The subtraction and division cancel out the effects of fixed-pattern noise and gain variations across the detector, as long as the effects are not so large that they make the dynamic range of the detector too small to be used. Four frames of intensity data are measured. The phase φ(x, y) is first calculated, by means of Equation 2.50, using the first three of the four frames. It is then similarly calculated using the last three of the four frames. These two calculated phase values are then averaged to increase the accuracy of the measurement. Because Equation 2.50 gives the phase modulo 2π, there may be discontinuities of 2π present in the calculated phase. These discontinuities can be removed as long as the slopes on the sample being measured are limited so that the actual phase difference between adjacent pixels is less than π. This is done by adding or subtracting a multiple of 2π to a pixel until the difference between it and its adjacent pixel is less than π. Once the phase φ(x, y) is determined across the interference field, the corresponding height distribution h(x, y) is determined by the equation
λ h x, y = φ x, y 4π
( )
( )
(2.51)
Phase shifting interferometry using a single wavelength has limited dynamic range. The height difference between two consecutive data points must be less than λ/4, where λ is the wavelength of the light used. If the slope is greater than λ/4 per detector pixel, then height ambiguities of multiples of halfwavelengths exist. One technique that has been very successful in overcoming these slope limitations is to perform the measurement using two or more wavelengths λ1 and λ2 , and then to subtract the two measurements. This results in the limitation in height difference between two adjacent detector points of one quarter of a synthesized equivalent wavelength λeq,
λ eq =
λ1λ 2 λ1 − λ 2
(2.52)
Thus, by carefully selecting the two wavelengths it is possible to greatly increase the dynamic range of the measurement over what can be obtained using a single wavelength (Cheng and Wyant, 1985). While using two wavelength phase-shifting interferometry works very well with step heights, it does not work especially well with rough surfaces. A much better approach is to use a broad range of wavelengths and the fringe modulation or coherence peak sensing approach, whose description follows. Vertical Scanning Coherence Peak Sensing In the vertical scanning coherence peak sensing mode of operation, a broad spectral white light source is used. Due to the large spectral bandwidth of the source, the coherence length of the source is short,
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FIGURE 2.36 Irradiance at a single sample point as the sample is translated through focus. (From Caber, P. (1993), An interferometric profiler for rough surfaces, Appl. Opt., 32, 3438-3441. With permission.)
and good contrast fringes will be obtained only when the two paths of the interferometer are closely matched in length. Thus, if in the interference microscope the path length of the sample arm of the interferometer is varied, the height variations across the sample can be determined by looking at the sample position for which the fringe contrast is a maximum. In this measurement there are no height ambiguities and, since in a properly adjusted interferometer the sample is in focus when the maximum fringe contrast is obtained, there are no focus errors in the measurement of surface texture (Davidson et al., 1987). Figure 2.36 shows the irradiance at a single sample point as the sample is translated through focus. It should be noted that this signal looks a lot like an amplitude modulated (AM) communication signal. The major drawback of this type of scanning interferometer measurement is that only a single surface height is being measured at a time and a large number of measurements and calculations are required to determine a large range of surface height values. One method for processing the data that gives both fast and accurate measurement results is to use conventional communication theory and digital signal processing (DSP) hardware to demodulate the envelope of the fringe signal to determine the peak of the fringe contrast (Caber, 1993). This type of measurement system produces fast, noncontact, true threedimensional area measurements for both large steps and rough surfaces to nanometer precision. A Commercial Digital Optical Profiler Figure 2.37 shows a schematic of a commercial phase shifting/vertical sensing interference microscope (Wyant, 1995). For smooth surfaces, the phase shifting mode is used since it gives subnanometer height resolution capability. For rough surfaces and large steps, up to 500-µm surface height variations, the
CCD Camera
Spectral or Neutral Density Filter
Magnification Selector Microscope Objective
White Light Source Test Surface
Translator Mirau Interferometer
FIGURE 2.37 Optical schematic of the three-dimensional digital optical profiler based on phase-shifting/vertical sensing interferometer, Wyko HD-2000. (From Wyant, J.C. (1995), Computerized interferometric measurement of surface microstructure, Proc. Soc. Photo-Opt. Instrum. Eng., 2576, 122-130. With permission.)
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vertical scanning coherence sensing technique is used, which gives an approximately 3-nm height resolution. The instrument operates with one of several interchangeable magnification objectives. Each objective contains an interferometer, consisting of a reference mirror and beams splitter, which produces interference fringes when light reflected off the reference mirror recombines with light reflected off the sample. Determination of surface height using phase-shifting interferometry typically involves the sequential shifting of the phase of one beam of the interferometer relative to the other beam by known amounts, and measuring the resulting interference pattern irradiance. Using a minimum of three frames of intensity data, the phase is calculated and is then used to calculate the surface height variations over a surface. In vertical scanning interferometry when short coherence white light is used, these interference fringes are present only over a very shallow depth on the surface. The surface is profiled vertically so that each point on the surface produces an interference signal and the exact vertical position where each signal reaches its maximum amplitude can be located. To obtain the location of the peak, and hence the surface height information, this irradiance signal is detected using a CCD array. The instrument starts the measurement sequence by focusing above the top of the surface being profiled and quickly scanning downward. The signal is sampled at fixed intervals, such as every 50 to 100 nm, as the sample path is varied. The motion can be accomplished using a piezoelectric transducer. Low-frequency and DC signal components are removed from the signal by digital high bandpass filtering. The signal is next rectified by square-law detection and digitally lowpass filtered. The peak of the lowpass filter output is located and the vertical position corresponding to the peak is noted. Frames of interference data imaged by a video camera are captured and processed by high-speed digital signal processing hardware. As the system scans downward, an interference signal for each point on the surface is formed. A series of advanced algorithms are used to precisely locate the peak of the interference signal for each point on the surface. Each point is processed in parallel and a three-dimensional map is obtained. The configuration shown in Figure 2.37 utilizes a two-beam Mirau interferometer at the microscope objective. Typically the Mirau interferometer is used for magnifications between 10 and 50×, a Michelson interferometer is used for low magnifications (between 1.5 and 5×), and the Linnik interferometer is used for high magnifications (between 100 and 200x) (Figure 2.38). A separate magnification selector is placed between the microscope objective and the CCD camera to provide additional image magnifications. High magnifications are used for roughness measurement (typically 40×), and low magnifications (typically 1.5×), are used for geometrical parameters. A tungsten halogen lamp is used as the light source. In the phase shifting mode of operation a spectral filter of 40-nm bandwidth centered at 650 nm is used to increase the coherence length. For the vertical scanning mode of operation the spectral filter is not used. Light reflected from the test surface interferes with light reflected from the reference. The resulting interference pattern is imaged onto the CCD array, with a size of about 736 × 480 and pixel spacing of about 8 µm. The output of the CCD array can be viewed on the TV monitor. Also, output from the CCD array is digitized and read by the computer. The Mirau interferometer is mounted on either a piezoelectric transducer (PZT) or a motorized stage so that it can be moved at constant velocity. During this movement, the distance from the lens to the reference surface remains fixed. Thus, a phase shift is introduced into one arm of the interferometer. By introducing a phase shift into only one arm while recording the interference pattern that is produced, it is possible to perform either phase-shifting interferometry or vertical scanning coherence peak sensing interferometry. Major advantages of this technique are that its noncontact and three-dimensional measurements can be made rapidly without moving the sample or the measurement tool. One of the limitations of these instruments is that they can only be used for surfaces with similar optical properties. When dealing with thin films, incident light may penetrate the film and can be reflected from the film-substrate interface. This reflected light wave would have a different phase from that reflected from the film surface. The smooth surfaces using the phase measuring mode can be measured with a vertical resolution as low as 0.1 nm. The vertical scanning mode provides a measurement range to about 500 µm. The field of view depends on the magnification, up to 10 mm × 10 mm. The lateral sampling interval is given by the detector spacing divided by the magnification; it is about 0.15 µm at 50× magnification. The optical
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FIGURE 2.38 ferometer.
99
Optical schematics of (a) Michelson interferometer, (b) Mirau interferometer, and (c) Linnik inter-
resolution which can be thought of as the closest distance between two features on the surface such that they remain distinguishable, is given by 0.61 λ/(NA), where λ is the wavelength of the light source and NA is the numerical aperture of the objective (typically ranging from 0.036 for 1.5× to 0.5 for 40×). In practice, because of aberrations in the optical system, the actual resolution is slightly worse than the optical resolution. The best optical resolution for a lens is on the order of 0.5 µm. The scan speed is typically up to about 7 µm/s. The working distance, which is the distance between the last element in the objective and the sample, is simply a characteristic of the particular objective used. Church et al. (1985) measured a set of precision-machined smooth optical surfaces by a mechanicalstylus profiler and an optical profiler in phase measuring mode. They reported an excellent quantitative agreement between the two profilers. Boudreau et al. (1995) measured a set of machined (ground, milled, and turned) steel surfaces by a mechanical stylus profiler and an optical profiler in the vertical scanning mode. Again, they reported an excellent quantitative agreement between the two profilers.
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Typical roughness data using a digital optical profiler can be found in Wyant et al. (1984, 1986), Bhushan et al. (1985, 1988), Lange and Bhushan (1988), Caber (1993), and Wyant (1995).
2.3.3 Scanning Probe Microscopy (SPM) Methods The family of instruments based on scanning tunneling microscopy (STM) and atomic force microscopy (AFM) are called scanning probe microscopies (SPM). 2.3.3.1 Scanning Tunneling Microscopy (STM) The principle of electron tunneling was proposed by Giaever (1960). He envisioned that if a potential difference is applied to two metals separated by a thin insulating film, a current will flow because of the ability of electrons to penetrate a potential barrier. To be able to measure a tunneling current, the two metals must be spaced no more than 10 nm apart. In 1981, Dr. Gerd Binnig, Heinrich Rohrer, and their colleagues introduced vacuum tunneling combined with lateral scanning (Binnig et al., 1982; Binnig and Rohrer, 1983). Their instrument is called the scanning tunneling microscope (STM). The vacuum provides the ideal barrier for tunneling. The lateral scanning allows one to image surfaces with exquisite resolution, laterally less than 1 nm and vertically less than 0.1 nm, sufficient to define the position of single atoms. The very high vertical resolution of the STM is obtained because the tunnel current varies exponentially with the distance between the two electrodes, that is, the metal tip and the scanned surface. Very high lateral resolution depends upon the sharp tips. Binnig et al. overcame two key obstacles for damping external vibrations and for moving the tunneling probe in close proximity to the sample. An excellent review of this subject is presented by Bhushan (1999b). STM is the first instrument capable of directly obtaining three-dimensional images of solid surfaces with atomic resolution. The principle of STM is straightforward. A sharp metal tip (one electrode of the tunnel junction) is brought close enough (0.3 to 1 nm) to the surface to be investigated (second electrode) that, at a convenient operating voltage (10 mV to 2 V), the tunneling current varies from 0.2 to 10 nA, which is measurable. The tip is scanned over a surface at a distance of 0.3 to 1 nm, while the tunnel current between it and the surface is sensed. Figure 2.39 shows a schematic of one of Binnig and Rohrer’s designs. The metal tip was fixed to rectangular piezodrives Px, Py, and Pz made out of commercial piezoceramic material for scanning. The sample was mounted on either a superconducting magnetic levitation or two-stage spring system to achieve the stability of a gap width of about 0.02 nm. The tunnel current JT is a sensitive function of the
FIGURE 2.39 Principle of the operation of the scanning tunneling microscope. (From Binnig, G. and Rohrer, H. (1983), Scanning tunnelling microscopy, Surf. Sci., 126, 236-244. With permission.)
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-Y PZT tube scanner -X
Y
X V
Z
Tip i
Sample
FIGURE 2.40 Principle of operation of a commercial STM; a sharp tip attached to a piezoelectric tube scanner is scanned on a sample.
gap width d, that is, JT ∝ VT exp(–Aφ1/2d), where VT is the bias voltage, φ is the average barrier height (work function), and A ~ 1 if φ is measured in eV and d in Å. With a work function of a few eV, JT changes by an order of magnitude for every angstrom change of h. If the current is kept constant to within, for example, 2%, then the gap h remains constant to within 1 pm. For operation in the constant current mode, the control unit (CU) applies a voltage Vz to the piezo Pz such that JT remains constant when scanning the tip with Py and Px over the surface. At the constant work function φ, Vz(Vx, Vy) yields the roughness of the surface z(x,y) directly, as illustrated at a surface step at A. Smearing of the step, δ (lateral resolution) is on the order of (R)1/2, where R is the radius of the curvature of the tip. Thus, a lateral resolution of about 2 nm requires tip radii of the order of 10 nm. A 1-mm-diameter solid rod ground at one end at roughly 90° yields overall tip radii of only a few hundred nanometers, but with closest protrusion of rather sharp microtips on the relatively dull end yields a lateral resolution of about 2 nm. In situ sharpening of the tips by gently touching the surface brings the resolution down to the 1-nm range; by applying high fields (on the order of 108 V/cm) during, for example, half an hour, resolutions considerably below 1 nm can be reached. There are a number of commercial STMs available on the market. Digital Instruments Inc. introduced the first commercial STM, the Nanoscope I, in 1987. In the Nanoscope III STM for operation in ambient air, the sample is held in position while a piezoelectric crystal in the form of a cylindrical tube scans the sharp metallic probe over the surface in a raster pattern while sensing and outputting the tunneling current to the control station (Figure 2.40) (Anonymous, 1992a). The digital signal processor (DSP) calculates the desired separation of the tip from the sample by sensing the tunneling current flowing between the sample and the tip. The bias voltage applied between the sample and the tip encourages the tunneling current to flow. The DSP completes the digital feedback loop by outputting the desired voltage to the piezoelectric tube. The STM operates in both the “constant height” and “constant current” modes depending on a parameter selection in the control panel. In the constant current mode, the feedback gains are set high, the tunneling tip closely tracks the sample surface, and the variation in the tip height required to maintain constant tunneling current is measured by the change in the voltage applied to the piezo tube (Figure 2.41). In the constant height mode, the feedback gains are set low, the tip remains at a nearly constant height as it sweeps over the sample surface, and the tunneling current is imaged (Figure 2.41). A current mode is generally used for atomic-scale images. This mode is not practical for rough surfaces. A three-dimensional picture [z(x,y)] of a surface consists of multiple scans [z(x)] displayed laterally from each other in the y direction. Note that if atomic species are present in a sample, the different atomic species within a sample may produce different tunneling currents for a given bias voltage. Thus the height data may not be a direct representation of the texture of the surface of the sample. Samples to be imaged with STM must be conductive enough to allow a few nanometers of current to flow from the bias voltage source to the area to be scanned. In many cases, nonconductive samples can be coated with a thin layer of a conductive material to facilitate imaging. The bias voltage and the tunneling
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FIGURE 2.41 Scanning tunneling microscope can be operated in either the constant current or the constant height mode. The images are of graphite in air.
current depend on the sample. The scan size ranges from a fraction of a nanometer each way to about 125 µm × 125 µm. A maximum scan rate of 122 Hz can be used. Typically, 256 × 256 data formats are used. The lateral resolution at larger scans is approximately equal to scan length divided by 256. The standalone STMs are available to scan large samples which rest directly on the sample. The STM cantilever should have a sharp metal tip with a low aspect ratio (tip length/tip shank) to minimize flexural vibrations. Ideally, the tip should be atomically sharp, but in practice, most tip preparation methods produce a tip that is rather ragged and consists of several asperities with the one closest to the surface responsible for tunneling. STM cantilevers with sharp tips are typically fabricated from metal wires of tungsten (W), platinum-iridium (Pt–Ir), or gold (Au) and sharpened by grinding, cutting with a wire cutter or razor blade, field emission/evaporator, ion milling, fracture, or electrochemical polishing/etching (Ibe et al., 1990). The two most commonly used tips are made from either a Pt–Ir (80/20) alloy or tungsten wire. Iridium is used to provide stiffness. The Pt–Ir tips are generally mechanically formed and are readily available. The tungsten tips are etched from tungsten wire with an electrochemical process. The wire diameter used for the cantilever is typically 250 µm with the radius of curvature ranging from 20 to 100 nm and a cone angle ranging from 10 to 60° (Figure 2.42a). For calculations of normal spring constant and natural frequency of round cantilevers, see Sarid and Elings (1991). Controlled geometry (CG) Pt/Ir probes are commercially available (Figure 2.42b). These probes are electrochemically etched from Pt/Ir (80/20) wire and polished to a specific shape which is consistent from tip to tip. Probes have a full cone angle of approximately 15° and a tip radius of less than 50 nm. For imaging of deep trenches (>0.25 µm) and nanofeatures, focused ion beam (FIB) milled CG milled probes with an extremely sharp tip radius (<5 nm) are used. For electrochemistry, Pt/Ir probes are coated with a nonconducting film (not shown in the figure). 2.3.3.2 Atomic Force Microscopy (AFM) STM requires that the surface to be measured is electrically conductive. In 1985, Gerd Binnig and his colleagues developed an instrument called the atomic force microscope, capable of investigating surfaces
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FIGURE 2.42 Schematics of (a) a typical tungsten cantilever with a sharp tip produced by electrochemical etching, and (b) CG Pt/Ir.
FIGURE 2.43
Principle of operation of the atomic force microscope.
of both conductors and insulators on an atomic scale (Binnig et al., 1986). Like the STM, the AFM relies on a scanning technique to produce very high resolution, three-dimensional images of sample surfaces. AFM measures ultrasmall forces (less than 1 nN) present between the AFM tip surface and a sample surface. These small forces are measured by measuring the motion of a very flexible cantilever beam having an ultrasmall mass. In the operation of high-resolution AFM, the sample is generally scanned instead of the tip as an STM, because AFM measures the relative displacement between the cantilever surface and reference surface, and any cantilever movement would add vibrations. However, AFMs are now available where the tip is scanned and the sample is stationary. As long as the AFM is operated in the so-called contact mode, little if any vibration is introduced. The AFM combines the principles of the STM and the stylus profiler (Figure 2.43). In the AFM, the force between the sample and tip is detected rather than the tunneling current to sense the proximity of the tip to the sample. A sharp tip at the end of a cantilever is brought into contact with a sample surface by moving the sample with piezoelectric scanners. During initial contact, the atoms at the end of the tip experience a very weak repulsive force due to electronic orbital overlap with the atoms in the sample surface. The force acting on the tip causes a lever deflection which is measured by tunneling, capacitive, or optical detectors such as laser interferometry. The deflection can be measured to within ±0.02 nm, so for a typical lever force constant at 10 N/m a force as low as 0.2 nN (corresponding normal pressure ~200 MPa for an Si3N4 tip with a radius of about 50 nm against single-crystal silicon) could be detected. This operational mode is referred to as “repulsive mode” or “contact mode” (Binnig et al., 1986). An
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alternative is to use “attractive force imaging” or “noncontact imaging,” in which the tip is brought into close proximity (within a few nanometers) to, and not in contact with, the sample (Martin et al., 1987). A very weak van der Waals attractive force is present at the tip–sample interface. Although in this technique the normal pressure exerted at the interface is zero (desirable to avoid any surface deformation), it is slow and difficult to use and is rarely used outside research environments. In either mode, surface topography is generated by laterally scanning the sample under the tip while simultaneously measuring the separation-dependent force or force gradient (derivative) between the tip and the surface. The force gradient is obtained by vibrating the cantilever (Martin et al., 1987; Sarid and Elings, 1991) and measuring the shift of resonance frequency of the cantilever. To obtain topographic information, the interaction force is either recorded directly or used as a control parameter for a feedback circuit that maintains the force or force derivative at a constant value. Force derivative is normally tracked in noncontact imaging. With AFM operated in the contact mode, topographic images with a vertical resolution of less than 0.1 nm (as low as 0.01 nm) and a lateral resolution of about 0.2 nm have been obtained. With a 0.01-nm displacement sensitivity, 10 nN to 1 pN forces are measurable. These forces are comparable to the forces associated with chemical bonding, e.g., 0.1 µN for an ionic bond and 10 pN for a hydrogen bond (Binnig et al., 1986). For further reading, see Bhushan (1999b). STM is ideal for atomic-scale imaging. To obtain atomic resolution with AFM, the spring constant of the cantilever should be weaker than the equivalent spring between atoms on the order of 10 Nm. Tips have to be as sharp as possible. Tips with a radius ranging from 5 to 50 nm are commonly available. “Atomic resolution” cannot be achieved with these tips at the normal force in the nanoNewton range. Atomic structures obtained at these loads have been obtained from lattice imaging or by imaging of the crystal periodicity. Reported data show either perfectly ordered periodic atomic structures or defects on a large lateral scale, but no well-defined, laterally resolved atomic-scale defects like those seen in images routinely obtained with STM. Interatomic forces with one or several atoms in contact are 20 to 40 or 50 to 100 pN, respectively. Thus, atomic resolution with AFM is possible only with a sharp tip on a flexible cantilever at a net repulsive force of 100 pN or lower. The first commercial AFM was introduced in 1989 by Digital Instruments. Now there are a number of commercial AFMs available on the market. Major manufacturers of AFMs for use in an ambient environment are: Digital Instruments Inc., Santa Barbara, CA; Park Scientific Instruments, Mountain View, CA; Topometrix, Santa Clara, CA; Seiko Instruments, Japan; Olympus, Japan; and Centre Suisse D’Electronique et de Microtechnique (CSEM) S.A., Neuchâtel, Switzerland. Ultra-high vacuum (UHV) AFM/STMs are manufactured by Omicron Vakuumphysik GmbH, Germany. Personal STMs and AFMs for ambient environment and UHV/STMs are manufactured by Burleigh Instruments Inc., Fishers, NY. We describe here the commercial AFM for operation in ambient air, with scanning lengths ranging from about 0.7 µm (for atomic resolution) to about 125 µm (Figure 2.44a) (Anonymous, 1992b). This is the most commonly used design and the multimode AFM comes with many capabilities. In this AFM, the sample is mounted on a PZT tube scanner which consists of separate electrodes to scan precisely the sample in the X-Y plane in a raster pattern as shown in Figure 2.44b and to move the sample in the vertical (Z) direction. A sharp tip at the end of a flexible cantilever is brought into contact with the sample. Normal and frictional forces being applied at the tip–sample interface are measured using a laser beam deflection technique. A laser beam from a diode laser is directed by a prism onto the back of a cantilever near its free end, tilted downward at about 10° with respect to a horizontal plane. The reflected beam from the vertex of the cantilever is directed through a mirror onto a quad photodetector (split photodetector with four quadrants). The differential signal from the top and bottom photodiodes provides the AFM signal, which is a sensitive measure of the cantilever vertical deflection. Topographic features of the sample cause the tip to deflect in the vertical direction as the sample is scanned under the tip. This tip deflection will change the direction of the reflected laser beam, changing the intensity difference between the top and bottom photodetector (AFM signal). In the AFM operating mode of the “height mode,” for topographic imaging, or for any other operation in which the applied normal force is to be kept a constant, a feedback circuit is used to modulate the voltage applied to the PZT scanner to adjust the height of the PZT, so that the cantilever vertical deflection (given by the intensity difference
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Mirrored prism Diode laser & lens
AFM signal (A+B) - (C+D)
Mirror
FFM signal (A+C) - (B+D) Split-diode photodetector
Cantilever & substrate
Sample
z
(a)
x
y
xyz PZT tube scanner
FIGURE 2.44 (a) Principle of operation of a commercial atomic force/friction force microscope, sample mounted on a piezoelectric tube scanner is scanned against a sharp tip and the cantilever deflection is measured using a laser beam deflection technique, and (b) schematic of triangular pattern trajectory of the AFM tip as the sample is scanned in two dimensions. During imaging, data are recorded only during scans along the solid scan lines.
between the top and bottom detector) will remain almost constant during scanning. The PZT height variation is thus a direct measure of surface roughness of the sample. This AFM can be used for roughness measurements in the “tapping mode,” also referred to as dynamic force microscopy. In the tapping mode, during scanning over the surface, the cantilever is vibrated by a piezo mounted above it, and the oscillating tip slightly taps the surface at the resonant frequency of the cantilever (70 to 400 kHz) with a 20 to 100 nm oscillating amplitude introduced in the vertical direction with a feedback loop keeping the average normal force constant. The oscillating amplitude is kept large enough so that the tip does not get stuck to the sample because of adhesive attraction. The tapping mode is used in roughness measurements to minimize the effects of friction and other lateral forces and to measure the roughness of soft surfaces. There are several AFM designs in which force sensors using both the optical beam deflection method and scanning unit are mounted on the microscope head; then these AFM designs can be used as standalones. Lateral resolution of these designs is somewhat poorer than the designs in which the sample is scanned instead of the cantilever. The standalone AFMs can be placed directly on the large samples which cannot be fitted into the AFM assembly just described. There are other designs which head can adopt larger samples. A schematic of one such design is shown in Figure 2.45. The head both scans and generates the cantilever deflection. The beam emitted by the laser diode reflects off the cantilever and is detected by a quad photodetector.
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Split-diode photodetector
Laser diode, collimator & lens
Adjustable mirror Laser path Fixed mirror
Lens Mirror Lens
y
Camera objective lens
x
xyz PTZ tube scanner
z
Cantilever holder Sample
Motorized stage X Y
FIGURE 2.45 Principle of operation of a commercial atomic force/friction force microscope; the head both scans and generates the cantilever deflection. (From Anonymous (1994), Dimension 3000 Instruction Manual, Digital Instruments, Santa Barbara, CA. With permission.)
Roughness measurements are typically made using a sharp tip on a cantilever beam at a normal load on the order of 10 nN. The tip is scanned in such a way that its trajectory on the sample forms a triangular pattern. Scanning speeds in the fast and slow scan directions depend on the scan area and scan frequency. The scan sizes available for this instrument range from 0.7 µm × 0.7 µm to 125 µm × 125 µm. A maximum scan rate of 122 Hz can typically be used. Higher scan rates are used for small scan length. 256 × 256 data points are taken for each image. For example, scan rates in the fast and slow scan directions for an area of 10 µm × 10 µm scanned at 0.5 Hz are 10 µm/s and 20 nm/s, respectively. The lateral resolution at larger scans is approximately equal to scan length divided by 256. At first glance, scanning angle may not appear to be an important parameter for roughness measurements. However, the friction force between the tip and the sample will affect the roughness measurements in a parallel scan (scanning along the long axis of the cantilever). Therefore, a perpendicular scan may be more desirable. Generally, one picks a scanning angle that gives the same roughness data in both directions; this angle may be slightly different than that for the perpendicular scan. The most commonly used cantilevers for roughness measurements in contact AFM mode are microfabricated plasma enhanced chemical vapor deposition (PECVD) silicon nitride triangular beams with integrated square pyramidal tips with a radius on the order of 30 to 50 nm. Four cantilevers with different sizes and spring stiffnesses (ranging from 0.06 to 0.6 N/m) on each cantilever substrate made of boron silicate glass are shown in Figure 2.46a. Etched single-crystal n-type silicon rectangular cantilevers with square pyramidal tips with a radius of about 10 nm are used for contact and tapping modes (Figure 2.46b). The cantilevers used for contact mode are stiff. For imaging within trenches by AFM, high-aspect ratio tips (HART) are used. An example of a probe is shown in Figure 2.46c. The probe is approximately 1 µm long and 0.1 µm in diameter. It tapers to an extremely sharp point (the radius is better than the resolution of most SEMs).
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FIGURE 2.46 Schematics of (a) triangular cantilever beam with square pyramidal tips made of PECVD Si3N4, (b) rectangular cantilever beams with square pyramidal tips made of single-crystal silicon, and (c) high-aspect ratio Si3N4 probe.
2.3.4 Fluid Methods Such techniques are mainly used for continuous inspection (quality control) procedures in service as they function without contact with the surface and are very fast. These provide numerical data that can only be correlated empirically to the roughness. The two most commonly used techniques are the hydraulic method and the pneumatic gaging method. In the hydraulic method, sometimes called the outflow meter method, an open-bottomed vessel with a compliant annulus at its lower end is placed in contact with the surface to be measured and filled with water to a predetermined level. The time taken for a given volume of water to escape through the gap between the compliant annulus and the rough surface is measured (Thomas, 1999). A simple relationship exists between the standard deviation of asperity heights, σp , and the flow time, t,
σ p = at n
(2.53)
where a and n are constants determined by the characteristics of the method employed. This method was initially developed to measure road surfaces but can be used for any large roughness pattern. The pneumatic gaging method is used for finer-scale roughness, such as machined metal surfaces. An outflow meter is used with air rather than water as the working medium, and surface roughness is measured by means of pneumatic resistance between the compliant annulus and the surface. For a constant rate of air flow, the pressure drop is determined by the overall surface roughness (Thomas, 1999).
2.3.5 Electrical Method An electrical method used is the capacitance method based on the parallel capacitor principle. The capacitance between two conducting elements is directly proportional to their area and the dielectric
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FIGURE 2.46 (continued)
constant of the medium between them, and inversely proportional to their separation. If a rough surface is regarded as the sum of a number of small elemental areas at different heights, it is fairly easy to work out the effective capacitance between it and a smooth surface disk for various deterministic models. The capacitance between a smooth disk surface and the surface to be measured is a function of the surface roughness. A commercial instrument is available based on this principle (Brecker et al., 1977). The capacitance method is also used for the continuous inspection procedures (quality control).
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2.3.6 Electron Microscopy Methods 2.3.6.1 Reflection Electron Microscopy Electron microscopy, both reflection and replica, can reveal both macroscopic and microscopic surface features (Halliday, 1955). But they have two major limitations: first, it is difficult to derive quantitative data; and second, because of their inherently limited field of view, they show only few asperities, whereas in fact the salient point about surface contact is that it involves whole populations of contacting asperities. The use of SEM requires placing specimens in vacuum. In addition, for insulating specimens, conductive coating (e.g., gold or carbon) is required. 2.3.6.2 Integration of Backscattered Signals Sato and O-Hori (1982) have shown that the profile of a surface can be obtained by processing backscattered electron signals (BES) using a computer connected to a scanning electron microscope (SEM). A backscattered electron image is produced by a BES, which is proportional to the surface inclination along the electron beam scanning. This means that the profile of the surface roughness can be derived by integrating the intensity of a BES, which varies along the scanning. Three-dimensional measurements of roughness are possible by making several scans. Disadvantages of the technique are that it requires the sample to have a conductive coating and the time taken to make measurements is fairly long. 2.3.6.3 Stereomicroscopy The application of stereomicroscopy to obtain surface roughness information is based on the principle of stereo effects. The stereo effects can be obtained by preparing two images of the same surface with slightly different angular views (typically less than 10°). The result is a parallax shift between two corresponding image points of the same feature relative to some reference point, due to a difference in the elevation between the feature and the reference point. By measuring the parallax shift, one can extract the height information from these stereo-pair images. Consider a point P on the specimen (Figure 2.47). Point O is an arbitrary reference point. After a clockwise rotation of angle θ, the point of interest is P′. The horizontal position of the feature is x1 before rotation and x2 after rotation. The distance x2 – x1 is known as parallax p. Simple trigonometry shows that the height of the feature P″ relative to the reference point O, z is given as (Boyde, 1970)
z=
p 2 sin θ 2
( )
(2.54)
Image matching is the major step in stereomicroscopy. Given a stereo pair of images, we have to select a picture element (pixel), for example, the left image, and locate the corresponding conjugate pixel of
FIGURE 2.47
Surface height calculation model from stereo-pair images.
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the right image. From the corresponding x positions, the z position of the pixel can be determined (relative to some arbitrary reference). This procedure is then repeated for all pixels of interest. In the procedure of pixel matching, a window (array of pixels) is first set up in the left image. Then, a window array of the same size is placed around a potential pixel in the right image and a measure of image agreement between these two windows is computed. This procedure is repeated by moving the window in the right image until the best image content agreement is reached. The degree of image matching can be obtained by calculating the sum of the squared difference between the two comparing windows. This method calculates the sum of the squared intensity difference for all the pixels within the two windows. The smallest sum corresponds to the maximum image agreement. The stereomicrographs are taken using an SEM with suitable resolution. The measurement technique requires several steps: obtaining SEM stereo pairs, stereo-pair image digitization (conversion of the analog data into digital form in the image so that they can be processed by a computer), and finally parallax analysis from which roughness information is deduced. Since an SEM is typically used to obtain the pair of stereo images, the lateral resolution is limited by the electron beam size, which is typically 5 nm. Vertical resolution is a function of lateral parallax resolution and the angle φ.
2.3.7 Analysis of Measured Height Distribution The measured height distribution across the sample can be analyzed to determine surface roughness statistics and geometrical parameters of a surface. The following surface roughness statistics can be obtained from the height distribution data: surface height distributions; surface slope and curvature distributions in x, y, and radial directions; heights, absolute slopes, and curvatures of all summits and the upper 25% summits; summit density and the upper 25% summit density; number of zero crossings per unit length in x, y, and two dimensions; and a three-dimensional plot of the autocovariance function with a contour of the autocovariance function at 0 and 0.1 (Wyant et al., 1986; Bhushan, 1996). The following geometrical parameters of a surface, for example, the radii of spherical curvature and cylindrical curvature, can be measured by fitting spherical and cylindrical surfaces, respectively.
2.3.8 Comparison of Measurement Methods Comparison of the various methods of roughness measurement may be made on a number of grounds, such as ease of use, whether quantitative information can be obtained, whether three-dimensional data of topography can be obtained, lateral and vertical resolutions, cost, and on-line measurement capability. Table 2.4 summarizes the comparison of the relevant information. The final selection of the measurement method depends very much on the application that the user has in mind. For in-process inspection procedures, measurement methods employing specular reflection, diffuse reflection, or speckle pattern are used. For continuous inspection (quality control) procedures requiring limited information, either fluid or electrical methods can be used. For procedures requiring detailed roughness data, either the stylus profiler, digital optical profiler or atomic force microscope is used. For a soft or super-finished surface, the digital optical profiler or AFM is preferred. Roughness plots of a disk measured using an atomic force microscope (spatial resolution ~15 nm), noncontact optical profiler or NOP (spatial resolution ~1 µm), and a stylus profiler (spatial resolution ~0.2 µm), are shown in Figure 2.48. The figure shows that roughness is found at scales ranging from millimeters to nanometers. The measured roughness profile depends on the spatial and normal resolutions of the measuring instrument. Instruments with different lateral resolutions measure features with different length scales. It can be concluded that a surface is composed of a large number of length scales of roughness that are superimposed on each other. Figure 2.49 shows the comparison of AFM, NOP, and SP profiles extracted from the measurements with about the same profile lengths and sampling intervals. The roughness measurements are affected by the spatial (lateral) resolution of the measuring instrument.
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TABLE 2.4
Comparison of Roughness Measurement Methods
Method
Quantitative Information
ThreeDimensional Data
Vertical
On-line Measurement Capability
Resolution (nm) Spatial
Limitations
Stylus instrument
Yes
Yes
15–100
0.1–1
No
Contact type can damage the sample, slow measurement speed in 3D mapping
Optical methods Taper sectioning
Yes
No
500
25
No
Limited No Limited
Yes No Yes
500 105–106 105–106
0.1–1 0.1–1 0.1–1
No Yes Yes
Limited
Yes
Destructive, tedious specimen preparation Qualitative Semiquantitative Smooth surfaces (<100 nm) Smooth surfaces (<100 nm)
Optical interference Scanning tunneling microscopy
Yes Yes
Yes Yes
500–1000 0.2
0.1–1 0.02
No No
Atomic force microscopy Fluid/electrical Electron microscopy Reflection/replication Integration of backscattered signal Stereomicroscopy
Yes No
Yes No
0.2–1
0.02
No Yes
No Yes
Yes Yes
5 5
10–20 10–20
No No
Yes
Yes
5
50
No
Light sectioning Specular reflection Diffuse reflection (scattering) Speckle pattern
Yes
Requires a conducting surface; scans small areas Scans small areas Semiquantitative Expensive instrumentation, tedious, limited data, requires a conducting surface, scans small areas
It refers to the stylus size of AFM and stylus profiler and the pixel size used in NOP for roughness measurement. For AFM and stylus profiler instruments, the ability of the stylus to reproduce the original surface features depends on the stylus size. The smaller the stylus, the closer it will follow the original profile. The stylus tip radius of AFM is smaller than SP and therefore AFM measurement is expected to be more accurate. A profile measured by AFM is used to assess the effect of the stylus size on the accuracy of roughness measurements (Poon and Bhushan, 1995a,b). Figure 2.50 shows the loci of different stylus radii on an AFM profile. By increasing the stylus size, the original profile is distorted, resulting in the underestimation of σ and the overestimation of β*. σ drops from 4.70 nm to 4.06 nm by 14% and β* increases from 0.16 µm to 0.44 µm by 175% when the stylus tip radius increases to 5 µm. NOP is an optical technique to measure surface roughness using the optical interference technique. The light intensity of the fringes is related to the surface height. In the optical system, the fringe pattern is discretized into pixels. Within one pixel or one sampling interval, the light intensity represents the average value of surface heights within the pixel. Effectively, the optical probe acts as an optical filter to remove highfrequency details using a cutoff length equal to the sampling interval. In the NOP measurement, the sampling interval is 1 µm. Therefore, the AFM profile in Figure 2.50a can be used to simulate the profile given by NOP by splitting the profile into a number of cutoff lengths equal to 1 µm. The mean of each cutoff length represents the surface height measured by NOP. A cubic spline curve is obtained to go through the mean points and shown in Figure 2.50e. σ for the simulated NOP profile is about 50% underestimated, and β* is 45% overestimated as compared with the AFM profile. Various roughness parameters of the disk measured using the AFM with two scan sizes are presented in Table 2.5. As stated earlier, surface roughness is generally characterized by σ, sometimes along with other parameters. From the profiles in Figures 2.49 and 2.50, vertical roughness parameters σ, Rp, and P – V
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FIGURE 2.48 Surface roughness plots of a glass–ceramic disk measured using an atomic force microscope (spatial resolution ~15 nm), noncontact optical profiler (spatial resolution ~1 µm), and stylus profiler (tip radius ~0.2 µm).
FIGURE 2.49 Comparison of surface plots of a glass–ceramic disk measured using AFM (~0.16 µm), SP (~0.2 µm), and NOP (~1 µm) drawn on a same scale.
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FIGURE 2.50 Simulated profiles of different stylus sizes sliding on the original AFM profile and the simulated NOP profile. (From Poon, C.Y. and Bhushan, B. (1995a), Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler, Wear, 190, 76-88. With permission.)
are seen to increase with the measuring instruments in the following order: NOP < SP < AFM. On the other hand, the spatial parameter β* is seen to increase in the reverse order, i.e., AFM < SP < NOP. σ and β* as functions of scan size for three instruments shown in Figure 2.51 show a similar trend and are related to different instrument spatial resolutions. We also note that the σ initially increases with the scan size and then approaches a constant value, whereas β* increases monotonically with the scan size. The result of σ as a function of scan size suggests that the disk has a long-wavelength limit. It is expected that β*, which is a measure of wavelength structure, should also approach a constant value. In contrast, β* generally increases with the scan size. As the sampling interval increases with increasing scan size, high-frequency details of the original profile gradually disappear, resulting in high β*. σ is a vertical parameter not sensitive to sampling interval, but it generally increases with scan size. β* is a spatial parameter affected by both sampling interval and scan length. If the sampling interval can be kept the same for all scan sizes, β* will be expected to approach a constant value (Figure 2.52) (Poon and Bhushan, 1995a). The question often asked is what instrument should one use for roughness measurement? For a given instrument, what scan size and sampling interval should one use? Deformation of asperities depends on the roughness, mechanical properties, and loading. Nanoasperities deform by plastic deformation, which is undesirable (Bhushan and Blackman, 1991; Poon and Bhushan, 1996). Therefore an instrument that can measure high frequency, such as AFM, should be used, particularly in low-load conditions. As stated earlier, a sampling interval equal to 0.25 and 0.50 times the correlation length at the selected scan size should be selected. A scan size equal to or greater than the value at which σ approaches a constant value, or twice the nominal contact size of the physical problem, whichever is smaller, should be used.
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TABLE 2.5 Various Roughness Parameters of a Glass-Ceramic Disk Measured Using AFM at Scan Sizes Scan Size (µm2) Roughness Parameters σ, surface height (nm) Skewness Kurtosis σ, profile slope x (mrad) σ, profile slope y (mrad) σ, surface slope (mrad) σ, profile curvature x (mm–1) σ, profile curvature y (mm–1) σ, surface curvature (mm–1) Summit height (nm) Mean σ Summit curvature (mm–1) Mean σ Summit-valley distance (nm) Summit-mean distance (nm) Summit density (µm–2) Profile zero crossing x (mm–1) Profile zero crossing y (mm–1) Mean correlation length (µm)
8×8
32 × 32
5.13 –0.24 6.01 53.5 67.7 86.3 1635 3022 1950
5.42 0.24 4.1 22 25.2 33.5 235.5 291.2 228.3
2.81 5.56
4.26 5.08
3550 1514 45.9 22.9 15.6 2794 4157 0.32
384 225.5 48.5 24.2 2.97 1279 1572 0.67
x and y are along radial and tangential directions, respectively; summit threshold is taken as 0.5 nm.
2.4 Closure The solid surfaces, irrespective of the method of formation, contain deviations from the prescribed geometrical form, ranging from macro- to nanoscale. In addition to surface deviations, the solid surface consists of several zones having physicochemical properties peculiar to the bulk material itself. Surface texture, repetitive deviation from the nominal surface, includes roughness (nano- and microroughness, waviness, or macroroughness and lay). Surface roughness is most commonly characterized with two average amplitude parameters: Ra or (σ) Rq and Rt (maximum peak-to-valley height). However, the amplitude parameters alone are not sufficient for complete characterization of a surface, and spatial parameters are required as well. A random and isotropic surface can be completely characterized by two functions — the height distribution and autocorrelation functions. A random surface with Gaussian height distribution and exponential autocorrelation function can be completely characterized by two parameters σ and β*; these parameters can be used to predict other roughness parameters. A surface is composed of a large number of length scales of roughness superimposed on each other. Hence, commonly measured roughness parameters depend strongly on the resolution of the measuring instrument and are not unique for a surface. The multiscale nature of rough surfaces can be characterized using a fractal analysis for fractal surfaces. Various measurement techniques are used for off-line and on-line measurements of surface roughness. Optical techniques such as specular reflection and scattering, are commonly used for on-line semiquantitative measurements. Commonly used techniques for off-line measurements are either contact profiler — stylus profilers and atomic force microscopes- or noncontact profilers — optical profilers based on two-beam interference. Contact–stylus based profilers are the oldest form of measuring instruments and are most commonly used across the industry. However, the stylus tip can scratch the delicate
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FIGURE 2.51 Variation of σ and β* with scan size for a glass–ceramic disk measured using AFM (scan length/256 data points), NOP (~1 µm), and SP (~0.2 µm).
surface during the course of the measurement. They also suffer from slow measurement speed, where three-dimensional mapping of the surfaces is required. Optical profilers are noncontact and can produce three-dimensional profiles rapidly and without any lateral motion between the optical head and the sample. Optical profilers can be used for surfaces with homogeneous optical properties, otherwise they need to be coated with a 10- to 20-nm-thick reflective coating (e.g., gold) before measurement. Lateral resolutions of profilers with sharp tips are superior to optical profilers. Nanoscale roughness with atomicscale resolutions can be measured using atomic force microscopes which are used at ultralow loads. However, these are more complex to use. Three-dimensional roughness height data can be processed to calculate a variety of amplitude and spatial functions and parameters. Without the use of long-wavelength filtering, waviness data can be obtained and analyzed.
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FIGURE 2.52 Variation of correlation length with scan size with a constant sampling interval (40 nm) for a glass–ceramic disk measured using AFM.
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Bhushan, B. (1999a), Principles and Applications of Tribology, Wiley, New York. Bhushan, B. (1999b), Handbook of Micro/Nanotribology, 2nd edition, CRC, Boca Raton. Bhushan, B. and Blackman, G.S. (1991), Atomic force microscopy of magnetic rigid disks and sliders and its applications to tribology, ASME J. Trib., 113, 452-457. Bhushan, B., Wyant, J.C., and Koliopoulos, C.L. (1985), Measurement of surface topography of magnetic tapes by Mirau interferometry, Appl. Opt., 24, 1489-1497. Bhushan, B., Wyant, J.C., and Meiling, J. (1988), A new three-dimensional digital optical profiler, Wear, 122, 301-312. Binnig, G. and Rohrer, H. (1983), Scanning tunnelling microscopy, Surf. Sci., 126, 236-244. Binnig, G., Rohrer, H., Gerber, Ch., and Weibel, E. (1982), Surface studies by scanning tunneling microscopy, Phys. Rev. Lett., 49, 57-61. Binnig, G., Quate, C.F., and Gerber, Ch. (1986), Atomic force microscope, Phys. Rev. Lett., 56, 930-933. Boudreau, B.D., Raja, J., Sannareddy, H., and Caber, P.J. (1995), A comparative study of surface texture measurement using white light scanning interferometry and contact stylus techniques, Proc. Amer. Soc. Prec. Eng., 12, 120-123. Boyde, A. (1970), Practical problems and methods in the three-dimensional analysis of scanning electron microscope images, Scanning Electron Microscopy, Proc. of the Third Annual SEM Symposium, IITRI, Chicago, IL, 105-112. Brecker, J.N., Fromson, R.E., and Shum, L.Y. (1977), A capacitance based surface texture measuring system, Annals CIRP, 25, 375-377. Bruning, J.H. (1978), Fringe scanning interferometers, in Optical Shop Testing, Malacara, D. (Ed.), Wiley, New York, 409-437. Buckley, D. H. (1981), Surface Effects in Adhesion, Friction, Wear and Lubrication, Elsevier, Amsterdam. Budde, W. (1980), A reference instrument for 20°, 40°, and 85° gloss measurements, Metrologia, 16, 1-5. Bush, A.W., Gibson, R.D., and Keogh, G.P. (1976), The limit of elastic deformation in the contact of rough surfaces, Mech. Res. Commun., 3, 169-174. Bush, A.W., Gibson, R.D., and Keogh, G.P. (1979), Strongly anisotropic rough surfaces, ASME J. Trib., 101, 15-20. Caber, P. (1993), An interferometric profiler for rough surfaces, Appl. Opt., 32, 3438-3441. Cheng, Y.Y. and Wyant, J.C. (1985), Multiple-wavelength phase-shifting interferometry, Appl. Opt., 24, 804-807. Chilamakuri, S. and Bhushan, B. (1998), Contact analysis of non-gaussian random surfaces, Proc. Instn. Mech. Engrs., Part J: J. Eng. Trib., 212, 19-32. Church, E.L. (1979), The measurement of surface texture and topography by differential light scattering, Wear, 57, 93-105. Church, E.L., Vorburger, T.V., and Wyant, J.C. (1985), Direct comparison of mechanical and optical measurements of the finish of precision-machined optical surfaces, Opt. Eng., 24, 388-395. Clarke, G.M. and Thomas, T.R. (1979), Roughness measurement with a laser scanning analyzer, Wear, 57, 107-116. Creath, K. (1988), Phase-shifting interferometry techniques, in Progress in Optics, 26, Wolf, E. (Ed.), Elsevier, New York, 357-373. Davidson, M., Kaufman, K., Mazor, I., and Cohen, F. (1987), An application of interference microscopy to integrated circuit inspection and metrology, Proc. Soc. Photo-Opt. Instrum. Eng., 775, 233-247. Elderton, P.E. and Johnson, L.J. (1969), System of Frequency Curves, Cambridge University Press, London, U.K. Fineman, I., Engstrom, G., and Pauler, N. (1981), Optical properties of coated papers in relation to base papers and coating raw materials, Paper Tech. and Indus., March, 59-65. Francon, F. (1966), Optical Interferometry, Academic Press, San Diego, CA. Francon, F. and Mallick, S. (1971), Polarization Interferometers, Wiley Interscience, New York. Ganti, S. and Bhushan, B. (1995), Generalized fractal analysis and its applications to engineering surfaces, Wear, 180, 17-34.
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Poon, C.Y. and Bhushan, B. (1996), Nano-asperity contact analysis and surface optimization for magnetic head slider/disk contact, Wear, 202, 83-98 Radhakrishnan, V. (1970), Effects of stylus radius on the roughness values measured with tracing stylus instruments, Wear, 16, 325-335. Ruffing, B. and Fleischer, J. (1985), Spectral correlation of partially or fully developed speckle patterns generated by rough surfaces, J. Opt. Soc. Amer., 2, 1637-1643. Sarid, D. and Elings, V. (1991), Review of scanning force microscopy, J. Vac. Sci. Technol. B, 9, 431-437. Sato, H. and O-Hori, M. (1982), Surface roughness measurement by scanning electron microscope, Annals CIRP, 31, 457-462. Siegel, S. (1956), Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill, New York. Smirnov, N. (1948), Table for estimating the goodness of fit of empirical distributions, Annals of Mathematical Statistics, 19, 279-281. Stover, J.C. (1975), Roughness characterization of smooth machined surfaces by light scattering, Appl. Opt., 14, 1796-1802. Stover, J.C. (1995), Optical Scattering: Measurement and Analysis, 2nd ed., SPIE Optical Engineering Press, Bellingham, WA. Stover, J.C., Bernt, M., and Schiff, T. (1996), TIS uniformity maps of wafers, disks and other samples, Proc. Soc. Photo-Opt. Instrum. Eng., 2541, 21-25. Thomas, T.R. (1999), Rough Surfaces, 2nd ed., Imperial College Press, London, U.K. Tolansky, S. (1973), Introduction to Interferometers, Wiley, New York. Uchida, S., Sato, H., and O-Hori, M. (1979), Two-dimensional measurement of surface roughness by the light sectioning method, Annals CIRP, 28, 419-423. Vorburger, T.V., Teague, E.C., Scire, F.E., McLay, M.J., and Gilsinn, D.E. (1984), Surface roughness studies with DALLAS array for light angular scattering, J. Res. of NBS, 89, 3-16. Whitehouse, D.J. (1994), Handbook of Surface Metrology, Institute of Physics Publishing, Bristol, U.K. Whitehouse, D.J. and Archard, J.F. (1970), The properties of random surfaces of significance in their contact, Proc. R. Soc. Lond. A, 316, 97-121. Whitehouse, D.J. and Phillips, M.J. (1978), Discrete properties of random surfaces, Phil. Trans. R. Soc. Lond. A, 290, 267-298. Whitehouse, D.J. and Phillips, M.J. (1982), Two-dimensional discrete properties of random surfaces, Phil. Trans. R. Soc. Lond. A, 305, 441-468. Williamson, J.B.P. (1968), Topography of solid surfaces, in Interdisciplinary Approach to Friction and Wear, Ku, P.M. (Ed.), SP-181, NASA Special Publication, NASA, Washington, D.C., 85-142. Wyant, J.C. (1975), Use of an ac heterodyne lateral shear interferometer with real time wavefront corrections systems, Appl. Opt., 14, 2622-2626. Wyant, J.C. (1995), Computerized interferometric measurement of surface microstructure, Proc. Soc. Photo-Opt. Instrum. Eng., 2576, 122-130. Wyant, J.C. and Koliopoulos, C.L. (1981), Phase measurement system for adaptive optics, Agard Conference Proceedings, No. 300, 48.1-48.12. Wyant, J.C., Koliopoulos, C.L., Bhushan, B., and George, O.E. (1984), An optical profilometer for surface characterization of magnetic media, ASLE Trans., 27, 101-113. Wyant, J.C., Koliopoulos, C.L., Bhushan, B., and Basila, D. (1986), Development of a three-dimensional noncontact digital optical profiler, ASME J. Trib., 108, 1-8.
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3 Contact Between Solid Surfaces 3.1 3.2
Introduction ....................................................................... 121 Hertzian Contacts .............................................................. 122 Contact of Spheres • Contact of Two Cylinders with Axes Parallel • Contact of Two Cylinders with Inclined Axes • Contact of Bodies of Arbitrary Shape • Surface and Subsurface Stresses • Surface Tractions and Sliding Contact • Cylinder Sliding Perpendicular to Its Axis and Sliding Spheres
3.3
Non-Hertzian Contacts...................................................... 137 Flat Rigid Planar Punch • Flat Rigid Axisymmetric Punch • Indentation by an Angular Wedge • Indentation by a Cone
3.4
Numerical Methods for Contact Mechanics .................... 140 Matrix Inversion Method • Variational Method • Finite Element Method
3.5
Real and Nominal Area of Contact Measurement • Experimental Contact Stress Analysis
John A. Williams Cambridge University
Rob S. Dwyer-Joyce The University of Sheffield
Experimental Methods for Contact Mechanics ............... 144
3.6
Further Aspects................................................................... 150 Contact of Rough Surfaces • Loading Beyond the Elastic Limit • Repeated Contacts — The Role of Residual Stresses and Shakedown • Contacts on Layered Solids
3.1 Introduction When two solid surfaces are loaded together there will always be some distortion of each of them. Deformations may be purely elastic or may involve some additional plastic, and so permanent, changes in shape. Such deflections and modifications in the surface profiles of the components can be viewed at two different scales. Consider, for example, the contact between a heavily loaded roller and the inner and outer races in a rolling element bearing. The degree of flattening of the rollers can be expressed as a proportion of their radii, i.e., at a relatively macroscopic scale. On the other hand, since on the microscale no real surface, such as those of either the roller or the race, can be truly smooth, it follows that when these two solid bodies are pushed into contact they will touch initially at a discrete number of points or asperities. Some deformation of the material occurs on a very small scale at, or very close to, these areas of true contact. It is within these regions that the stresses are generated whose total effect is just to balance the applied load. Classical contact mechanics assumes the deforming materials to be isotropic and homogeneous; in principle, its results can be applied both to global contacts and to those between interacting asperities.
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3.2 Hertzian Contacts When any two curved bodies of different radii of curvature are brought into contact they will initially touch at either a point or along a line. With the application of the smallest load, elastic deformation enlarges these into contact areas across which the loads are distributed as pressures. The first analysis of this situation was presented by Heinrich Hertz in 1881 and is based on the following assumptions: i. The surfaces are continuous, smooth, nonconforming and frictionless, ii. The size of the contact area is small compared to the size of the bodies, i.e., the strains associated with the deformations are small, iii. Each solid can be considered to behave as an elastic half-space in the vicinity of the contact zone, and iv. The gap h between the undeformed surfaces can be approximated by an expression of the form
h = Ax 2 + By 2
(3.1)
where x and y are orthogonal coordinates lying in the common tangent plane to the two surfaces. Although strictly, idealization (iv) requires parabolic surface profiles, by implication Hertzian analysis is relevant to the contact of spheres, cylinders, and ellipsoids. Progress over the last century in contact mechanics can be seen as the gradual relaxation of the restrictions imposed by the original Hertzian treatment; for an exhaustive review, see Johnson (1985).
3.2.1 Contact of Spheres If two elastic spheres 1 and 2 of radii R1 and R2 are pressed into contact with force P, as in Figure 3.1(a), then the resultant circular contact area has radius a such that
{
a = 3PR 4E
}
13
(3.2)
where E* is the contact modulus defined by
1 1 − v12 1 − v22 = + E* E1 E2
(3.3)
and R, the reduced radius of curvature, is related to those of the individual components by the relation
1 1 1 = + R R1 R2
(3.4)
Convex surfaces are taken to have positive radii of curvature; those of concave surfaces are negative. The resulting pressure distribution p(r) is semielliptical, i.e., of the form
()
{
p r = p0 1 − r 2 a 2
}
12
, where r 2 = x 2 + y 2
(3.5)
Such a distribution is shown in Figure 3.1b and is characteristic of Hertzian contacts. The maximum pressure p0 which occurs on the axis of symmetry and the mean pressure pm are given by
p0 =
3 p = 3P 2πa 2 2 m
(3.6)
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P R2 2
2a
R1
1
(a)
P
p0
p(r)
a
a
(b)
FIGURE 3.1
(a) Spheres in elastic contact; (b) the resulting semi-elliptical pressure distribution.
p0 is sometimes known as the Hertz stress. Under this loading, the centers of the two spheres move together by the small displacement ∆ where
{
∆ = a 2 R = aπp0 2E * = 9P 2 16 RE *2
}
13
(3.7)
If one of the loaded solids is, in fact, a plane surface then its effective radius becomes infinite so that the reduced radius of the contact is numerically equal to that of the opposing sphere.
3.2.2 Contact of Two Cylinders with Axes Parallel If two circular cylinders with radii R1 and R2 are pressed together by a force per unit length of magnitude P with their axes parallel, as shown in Figure 3.2, then the contact patch will be of half-width b such that
{
}
b = 2PR πE *
12
(3.8)
where R and E* are the reduced radius of contact and the contact modulus defined by Equations 3.3 and 3.4, respectively. Contact pressure is again semielliptical such that
()
{
p x = p0 1 − r 2 b2
}
12
(3.9)
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1oad P
R2
2b R1
FIGURE 3.2
Parallel cylinders in elastic contact; the intensity of the loading is P per unit length.
where peak pressure
{
}
p0 = PE * πR
12
(3.10)
and coordinate x is measured in a direction perpendicular to that of the cylinder axes. The mean pressure pm over the contact strip is equal to P/2b and is given by
pm = πp0 4 The axes of the cylinders move together by a small distance ∆ where
(
)[ (
)
]
(
)[ (
)
]
∆ = 1 − v12 ln 4 R1 b − 1 2 E1 + 1 − v22 ln 4 R2 b − 1 2 E2
(3.11)
Once again, if one of the surfaces is planar, then the value of R will be equal to the radius of curvature of the other.
3.2.3 Contact of Two Cylinders with Inclined Axes Suppose the lower cylinder is of radius R1 and the upper of R2, as shown in Figure 3.3. The cylinders touch at the point O but their axes are inclined at an angle θ. Ox1y1 is a set of Cartesian axes with Oy1 along a generator of the lower cylinder, and Ox2 a second similar set with Oy2 along a generator of the upper cylinder. Close to the origin we can approximate the circular section of each cylinder by a parabolic profile and so write that the separation h of the two solid surfaces at the point P, which has coordinates (x1,y1) in the first coordinate system or (x2,y2) in the second, is given by
h≈
x12 x2 + 2 2R1 2R2
(3.12)
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R2
+
x1 y2
h x2
y1
+ R1
y2 x1
θ
P
·
x2 y1
FIGURE 3.3
The geometry of two circular cylinders in skewed contact.
It is possible to choose a common set of axes (Oxy), in which Ox is inclined to the Ox1-direction by the angle α, such that Equation 3.1 is recovered, provided that A and B satisfy the conditions
B−A =
{
(
)
}
1 1 R12 + 1 R22 + 2 R1R2 cos 2θ 2
12
(3.13)
and
B+A =
{
1 1 R1 + 1 R2 2
}
(3.14)
)
(3.15)
and α is given by the solution of
(
R2 sin 2α = sin 2 θ − α R1 Equation 3.1 can then be written as
h=
x2 y2 + 2R′ 2R′′
(3.16)
by defining
R′ = 1 2A and R′′ = 1 2B
(3.17)
R′ and R″ are known as the principal radii of relative curvature. It is evident from Equation 3.16 that contours of constant gap h between the undeformed surfaces will be ellipses, the lengths of whose axes are in the ratio (R′/R″)1/2.
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When a normal load P is applied, the point of contact spreads into an elliptical area with semi-axes a and b, such that the eccentricity, i.e., the ratio b/a, is independent of the load and depends only on the ratio of R′/R″. For mildly elliptical contacts, i.e., A/B < 5, then the ratio b/a is given by
(
b a≈ A B
)
2 3
(3.18)
An “equivalent” radius Re can be defined as
(
Re = R′′ × R′
)
12
=
( )
1 AB 2
−1 2
(3.19)
and this used to estimate the contact area or Hertz stress by using the circular contact equations with R replaced by Re. The approach of the bodies can be calculated using Equation 3.7 but with R replaced by (AB)–1/2 rather than Re. If the two cylinders make contact with their axes parallel so that θ = 0, it follows from Equations 3.13, 3.14, and 3.17 that
1 1 1 = + R′ R1 R2 i.e. Equation 3.3 is recovered. On the other hand, if the axes of the two cylinders are perpendicular to one another θ = 90°; then R′ = R1 and R″ = R2. It follows that
h=
x2 y2 + 2R1 2R2
(3.20)
Consequently, for the particular case of a pair of equal cylinders crossing at an angle of 90°, contours of constant surface separation close at the contact point will be circles.
3.2.4 Contact of Bodies of Arbitrary Shape Suppose that the profile of each body closer to the origin can be expressed as
x12 y2 + 1 2R1′ 2R1′′ x 2 y 2 z 2 = − 2 + 2 2R2′ 2R2′′ z1 =
(3.21)
where the directions of the axes of each body are chosen to coincide with the principal curvatures of that body. In general the two sets of axes may be inclined to each other at an arbitrary angle θ, as shown in Figure 3.4a. The coordinates can be transformed to a common set of axes (Oxy) inclined at α to x1 and β to x2, as shown. The gap h between the surfaces can then be written as
h = z1 − z 2 = Ax 2 + By 2 + Cxy where C = 0.5{(1/R′2 ) – (1/R ″2 )}sin2β – 0.5{(1/R′1) – (1/R″1)}sin2α.
(3.22)
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(a)
y1
x2
x
1_ 1_ - 1_ 2 R'1 R"1
b
y
2
)
(
y
B-A 2a
a q
2q
x1
2b
1_ 1_ - 1_ 2 R'2 R"2
FIGURE 3.4
)
(
(b)
(a) Arbitrary curved bodies in contact; (b) geometric relations.
The condition that C should vanish, so that Equation 3.1 is recovered, is satisfied by the triangle shown in Figure 3.4b with the result that
{
}
{
[
] [
}
B − A = 0.5 1 R1′ − 1 R1′′ sin 2α + 0.5 1 R2′ − 1 R2′′ sin 2β 2 = 0.5 1 R1′ − 1 R1′′ + 1 R2′ − 1 R2′′
] [ 2
][
]
12
+ 1 R1′ − 1 R1′′ 1 R2′ − 1 R2′′ cos 2θ
Finally,
{
A + B = 0.5 1 R1′ + 1 R1′′ + 1 R2′ + R2′′
}
(3.23)
from which the values of A (= 1/2R′) and B (= 1/2R″) can be found.
3.2.5 Surface and Subsurface Stresses Stresses that develop in conditions of nonconformal contacts can be among the most severe in any mechanical device; the situation of a Hertzian contact is of particular interest because the most heavily loaded elements of material, and thus the site of initial plastic yielding, lies not at the surface but a small distance beneath it. (This is in contrast to the situation when the curvature of the surfaces is not continuous, for example in circumstances in which one of the bodies has the profile of a wedge or cone, when the site of maximum stress lies adjacent to its apex [see Section 3.3]). Closed form analytical solutions for subsurface stresses are known for only a limited number of special cases. Nominal Point Contacts In the case of two spheres pressed into contact (or the equivalent geometry of two circular cylinders with their axes inclined perpendicularly to each other), the pressure within the contact patch (i.e., when r ≤ a) is given by Equation 3.5 and the surface stresses (i.e., at z = 0) are given in polar coordinates by the expressions
( (
σ θθ
12 2 2 − 1− r a 3 2 1 2 2 2 − 2ν 1 − r a 12 2 2 p0 = − 1 − r a
) ( ) (
1 − 2v 2 2 a r 1 − 1 − r 2 a 2 3 1 − 2v 2 2 p0 = − a r 1 − 1 − r 2 a 2 3
σ rr p0 =
()
σ zz p0 = − p r
) )
32
(
)
(
(
)
(3.24)
)
Outside the contact patch (r ≥ a)
(
)
σ n p0 = − σ θθ p0 = 1 − 2ν a 2 3r 2
(3.25)
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s zz s xx
P0
,
s zz P0
1
P0
0.8 0.6 s yy P0
0.4 s qq P0
0.2 compressive
-1.5
x ,r
-1
-0.5
tensile
0.5
0
s rr P0
1.5 b a
1
FIGURE 3.5 Stress distributions at the surface of a line contact (left-hand side) and point contact (right-hand side); Poisson’s ratio ν = 0.3.
The form of these surface stress distributions is illustrated in Figure 3.5 for the case ν = 0.3. The radial stress is tensile outside the loaded circle and has its maximum value at the edge of the loaded zone when r = a. This is the site of the largest tensile stress occurring anywhere in the material and is held responsible for the ring cracks often observed in the contact of brittle materials. At the center of the contact the radial stress is compressive and of magnitude (1 – 2ν)p0/2. Thus for an incompressible material, with ν = 0.5, the stress at the origin is hydrostatic. Within the material stresses along the axis of symmetry (r = 0) are given by
( ){ ( )
( )} 12 (1 + z a )
σ rr p0 = σ θθ p0 = − 1 + ν 1 − z a arctan a z −
(
σ zz p0 = − 1 + z 2 a 2
)
2
2
−1
−1
(3.26)
This stress distribution for a half space with ν = 0.3 is shown in Figure 3.6a. Along the z-axis, σrr , σθθ , and σzz are principal stresses and so the principal shear stress τ1 is of magnitude 1--- σzz – σrr and this is also 2 shown in the figure: its maximum value lies at a depth of 0.48a below the surface and here τmax /p0 = 0.31.
0
0 0
0.2
0.4
0.6
0.8
-0.2
-0.2
σ rr σθθ p0,p
-0.4
-0.4
0
-0.6
-0.6 -0.8 -1
σ zz p
τ1 p0
0.8
1
σxx p0
0
σ zz p0
-1
-1.4 -1.6
-1.6
-2
1
0.6
-1.2
-1.4
z a
τ p
0.4
σ yy p0
-0.8
0
-1.2
-1.8
0.2
0
1
-1.8
(a)
z a
(b)
-2
FIGURE 3.6 (a) Elastic contact of spheres; subsurface stresses along the axis of symmetry; (b) elastic contact of cylinders; subsurface stresses along the axis of symmetry.
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r/a -0.75 0
-0.5
-0.25
0.25
0.5
0.75
0.4 0.35 0.34 0.32 0.30 0.28 0.26 0.24
0.8 z/a 1.2
0.21 0.18
1.6
0.15
2.0
0.12
FIGURE 3.7 Contours of maximum shear stress normalized by Hertz stress p0, beneath nominal circular point contact of radius a in material with ν = 0.3.
TABLE 3.1 Normalized Maximum Shear Stress τmax /p0 and Its Location for Materials with Various Poisson’s Ratios Poisson’s Ratio
Material
τmax /p0
z/a
0.2 0.30 0.33 0.5
Glass Steel Aluminium Rubber
0.335 0.310 0.303 0.267
0.45 0.48 0.50 0.55
Since this is the greatest shear stress in the material, its position is the likely site of the initiation of plasticity. The value of τmax /p0 and its location is somewhat influenced by the value of Poisson’s ratio (Table 3.1). Away from the axis of symmetry the stresses can be computed in a number of ways, such as those described by Hamilton and Goodman (1966), Hamilton (1983), and Sackfield and Hills (1983); these are discussed in Hills, Nowell, and Sackfield (1993). Contours of maximum shear stress, plotted as τmax/p0, for such a nominal circular point contact are shown in Figure 3.7. Nominal Line Contacts If the axes of the cylinders are taken to lie parallel with the y-axis, then surface stresses are given by the equations
() {
p x = p0 1 − x 2 b2
}
12
{
( ) p = − p ( x ) p = −(1 − x b )
together with σ yy p0 = −2ν 1 − x 2 b2 and σ zz
2
0
}
where peak pressure p0 = PE * πR
0
2
12
12
12
(3.27)
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Along the line of loading symmetry, (i.e., the z-axis)
(
)(
)
− 2z b −1 2 σ zz p0 = − 1 + z 2 b2 −1 2 and τ1 p0 = z b − z 2 b2 1 − z 2 b2
σ xx p0 = − 1 + 2z 2 b2 1 + z 2 b2
( (
)
)(
−1 2
(3.28)
)
The value of τmax /p0 is now 0.30 and occurs now at a depth of z = 0.78b as illustrated in Figure 3.6b. The stresses σxx , σzz , and τmax are all independent of the value of v although not so the third, out-ofplane, stress σyy ; for plane strain conditions
(
so that σ yy
)
12 2 2 p0 = −2v 1 + z b + z b
σ yy = v σ xx + σ zz
(
)
(3.29)
Away from the axis of symmetry the stress components can be evaluated using the method of complex potentials (Muskhelishvili, 1949), although solutions to the problem in a real form have been published by several authors (Beeching and Nichols, 1948; Poritsky, 1950; Smith and Liu, 1953; Sackfield and Hills 1983). McEwen (1948) expresses the stress at a general point (x,z) in terms of m and n defined by 12 2 m2 = 0.5 b2 − x 2 + z 2 + 4 x 2 z 2 + b2 − x 2 + z 2 12 2 2 2 2 2 2 2 2 2 2 n = 0.5 b − x + z + 4 x z − b − x + z
(
)
(
(
)
(
)
)
(3.30)
where the signs of m and n are the same as the signs of x and z, respectively; then
{ ( ) (m + n )} b + 2z b p = − m {1 − ( z − n ) (m + n )} b p = n {(m − z ) (m + n )} b
σ xx p0 = m 1 + z 2 + n2 σ zz τ xz
2
2
2
2
2
0
2
2
2
2
(3.31)
2
0
Contours of maximum shear stress under such a line contact in a material with Poisson’s ratio 0.3 are shown in Figure 3.8. Elliptical Contacts Where the contact geometry leads to an elliptical contact patch, it is more difficult to find explicit solutions for the internal stress field. Thomas and Hoersch (1930) examined the problem on the axis of symmetry and later Fessler and Ollerton (1957) and Ollerton and Morley (1963) determined in closed form values of σzz and τ1. A more general solution is due to Sackfield and Hills (1983), and Figure 3.9, taken from this, illustrates the change in location of the point of severest stress along the axis x = y = 0 in terms of the eccentricity parameter k equal to the ratio of b/a, the minor to major axes of the contact patch.
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0
-3
-2
-1
0
1
2
3
x/b
0.03
1 0.26 0.33
z/b 2
0.18
3 FIGURE 3.8 Contours of maximum shear stress normalized by Hertz stress p0, beneath nominal line contact in material with ν = 0.3.
0.7 z/a
0.6
0.5
0.2
FIGURE 3.9
0.4
0.6
eccentricity a/b or b/a
0.8
1
Effect of ellipticity of contact patch measured as ratio a/b or b/a on location of point of severest stress.
3.2.6 Surface Tractions and Sliding Contact Relative Motion of Surfaces: Rolling, Sliding, and Spin Two solid bodies in contact are said to roll together if there is a difference in the components of their angular velocities measured along an axis parallel to their common tangent plane. Consider two cylinders 1 and 2 touching along a common generator, as shown in Figure 3.10a. If the angular velocity ω1 is not equal to ω2, both in magnitude and sense (i.e., clockwise or counterclockwise), the two cylinders are in rolling contact. The angular velocity of roll has a magnitude which is equal to the difference between ω1 and ω2. In this figure, the Oxy plane is the common tangent plane; if there is any difference in the components of the linear velocities of the two points in contact at O within this plane, then, as well as rolling on one another, the surfaces also have a relative sliding velocity. In Figure 3.10a this sliding velocity is equal in magnitude to U1 – U2 and thus equal to R1ω1 – R2ω2 . – The term rolling velocity U must be carefully defined, especially if the point of contact between the solid surfaces is not at rest, in other words if one or both of the centers of the cylinders has a linear motion. – If, however, bodies 1 and 2 are rotating about fixed centers then the rolling velocity U = 1--- |U1 + U2|. 2 In the case of a more general three-dimensional contact, e.g., that of two spheres in contact Figure 3.10b, or of a sphere on a plane, there can also be a difference in the components of the angular velocities of the two bodies in the direction of the common normal, i.e., at right angles to the common tangent plane. This represents a spinning motion, and in Figure 3.10b is of magnitude ω1z – ω2z .
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ω2z
ω2
z
y
y
z O
U2 ω1
x
U1 x ω1z
FIGURE 3.10 (a) Two cylinders 1 and 2 in contact with their axes parallel: there can be rolling and sliding at the point of contact; (b) in the three-dimensional case, Body 2 can also spin relative to Body 1.
In the effectively two-dimensional case of Figure 3.10a, when the cylinders are pressed together by a normal load, the contact will spread over a finite area which can be determined for this nonconformal contact by Hertz theory (Equations 3.8 through 3.11). Once account is taken of the fact that the contact spreads into a strip which has a finite width, rather than occurring along a line, the specification of “sliding” is not quite so straightforward. This is because, in the presence of friction (or traction) between the surfaces, some pairs of points in contact at the interface may “slip” relative to one another while others “stick.” A difference between the tangential surface strains in the two bodies in the region of “stick” can lead to a small degree of overall relative movement, which is known as creep.
3.2.7 Cylinder Sliding Perpendicular to Its Axis and Sliding Spheres Gross Sliding The simplest case is one in which there is gross sliding of the interface. If the contact is frictionless, then the contact stresses, both surface and subsurface, are unaffected by the sliding motion. However, if there is an imposed sliding force, this affects both the distribution of stresses and the contact geometry. If the two solids have the same elastic constants, then any tangential force transmitted between them gives rise to equal and opposite normal displacements of any point on the interface. Thus any “warping” of one surface conforms exactly to that of the other and does not disturb the distribution of normal pressure. The size and shape of the contact are then fixed by the profiles of the two surfaces, and the normal load is independent of the traction. With solids of differing elastic properties this is no longer the case, and tangential tractions do interact with the normal pressure so that the contact area and pressure distribution is no longer symmetrical (Buffler, 1959). However, these effects are generally small, especially if the coefficient of friction is small so that in practical cases it can usually be assumed that the stresses and deformations due to normal and tangential loadings are independent of one another and can be superposed to find resultant values. Assuming that Amontons’ law holds at every point at the interface, i.e., that the local surface tangential stress q(x) is given by
()
()
q x =µp x where p(x) is given by Equation 3.27. Hence
()
qx =
{
2πP 1 − x 2 b2 πb2
}
12
(3.32)
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q(x)/p0 2 1
(a)
0
-1
1
x/b
-1 -2 (b)
0
-3
-2
-1
0
1
3 0.06
0.02 0.06 0.1
1
2
x/b
0.1 0.14 0.3
0.14 0.26
z/b
0.22
2 0.18
3 FIGURE 3.11 (a) Surface stresses due to friction traction at a nominal line contact; (b) contours of principal shear stress beneath a sliding elastic line contact with µ = 0.2.
The stress components generated by the application of this form of loading have been evaluated by several workers (McEwen, 1949; Poritsky, 1950; Smith and Liu, 1953; Sackfield and Hills, 1983b). At the surface (z = 0) the stress component parallel to the surface reduces to the expressions
1 2 2 2 µp0 = −2 x b ± x b − 1 for x > b σ xx µp0 = − 2x b for x ≤ b
and σ xx
(
)
(3.33)
These are illustrated in Figure 3.11a. Whatever the coefficient of friction, the maximum resultant surface tensile stress in sliding occurs at the trailing edge of the contact and is of magnitude 2µp0. The application of a surface traction has two effects: first, it disrupts the symmetry of the subsurface stress distribution of Figure 3.8, and, second, it increases the level of stress at any given depth and gradually moves the location of the most highly stressed element of material toward the loaded surface, as illustrated in Figure 3.11b. In the case of sphere sliding on a flat, again neglecting any interference between normal pressure and tangential loading arising from a difference in elastic constants of the two solids, the distribution of traction is given by
()
qr =
(
3µP 1 − r 2 a2 2πa 3
)
12
(3.34)
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where a is the contact patch radius. Explicit equations for subsurface stresses are available in Goodman and Hamilton (1966), Hamilton (1983), and Sackfield and Hills (1983). Once again, as the coefficient of friction increases, so the region of maximum shear stress both moves from a subsurface location toward the surface and becomes more intense. The site of potential yield occurs at the surface when µ exceeds about 0.3. The normal contact of elastic spheres introduces a radial tension at r = a of magnitude (1 – 2ν)/3 ≈ 0.3p0. The effect of the tangential traction is to add to the tension at one side of the contact and to subtract from it at the other. The maximum tension, which occurs at the point (–a,0) rises to 0.5p0 and 1.0p0 for µ = 0.25 and µ = 0.5, respectively. This result is comparable to that from the two-dimensional case. The analysis has been extended to elliptical contacts by Bryant and Keer (1982) and Sackfield and Hills (1983b), who show that the contact pressure for first yield is almost independent of the shape of the contact ellipse. Incipient Sliding — Microslip The application of a tangential force which is less than the limiting force of friction will not give rise to sliding motion but will induce interfacial frictional tractions and elements of relative shearing or microslip at the interface. In general, over the center of the contact region, normal stresses may be sufficient to prevent relative motion at the interface so that the surfaces are effectively within a “stick” region. However, at the periphery of the contact, there may be relative surface displacements as a result of interfacial “slip.” Difficulty arises in the solution of such problems because the division of the contact into “stick” and “slip” regions is not known ab initio: a useful first step is to assume that slip occurs nowhere in the contact zone. Slip is then most likely in those regions where the local tangential stress, so found, exceeds its possible limiting values. In the case of two cylinders in line contact, slip occurs first at the edges of the contact: over the central region, the greater values of normal pressure inhibit any tangential motion. In these circumstances the interfacial shear stress q(x) is given by
(
q x = µp0 1 − x 2 b2
()
) − (1 − x c ) 12
2
2
12
(3.35)
where b is the half width of the whole contact, and c the half-width of the central sticking region. This distribution is illustrated in Figure 3.12a. The width of the central zone, i.e., the value of dimension c, is dependent on the magnitude of the applied tangential force Q,
{
}
12
c b = 1 − Q µP
(3.36)
The physical behavior of the contact is summarized by this equation. If the normal load P is kept constant while the tangential force on the junction Q is varied, as soon as Q increases from zero, microslip begins at the edges of the contact. As Q grows, so this slipping region spreads inward according to Equation 3.36. When Q approaches the limiting value of µP the sticking region has degenerated to a line at x = 0. When Q reaches magnitude µP gross sliding at the interface is initiated. The change in the relative size of the sticking region with the increase in the applied tangential load is illustrated in Figure 3.12b. A similar argument in the case of a sphere sliding on a flat leads to a central circular “sticking” region of radius c, whose value can be found from the applied tangential force Q by the equation
{
}
c a = 1 − Q µP
13
(3.37)
Contact analyses of this sort (Johnson, 1985) are particularly relevant when the applied forces vary or oscillate with time. Microslip at the interface between two surfaces which are subjected to vibration, often in combination with corrosion, produces the characteristic surface damage known as “fretting.” In components which also carry a high steady stress, fretting can lead to premature failure by fatigue.
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(a)
p Q
Hertzian pressure P(x)
R
q(x) x slip
slip
stick
c
c
b
b
(b)
1
0.75
c/b 0.5
0.25
0 0.6
0.25
0.5
0.75
1
Q/P FIGURE 3.12 (a) Contact between cylinders with parallel axes: surface traction due to the application of traction load of intensity Q; (b) reduction of central sticking region with applied tangential load for two cylinders in nominal line contact.
Free and Tractive Rolling The term free rolling is usually used for conditions in which there is no net traction, while tractive rolling is reserved for those situations in which such tangential forces exist. Tractive rolling is typified by the driving or braking wheels of a vehicle, where the interfacial tangential or frictional force acts to change the velocity of the mass in motion. If there is no transmission of torque between two cylinders in line contact, then the distribution of shear stress at the interface is given by the equation
( )=β
qx p0
{1 − x b } π 2
2
12
(
log b + x
) (b − x )
(3.38)
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TABLE 3.2 Values of the Parameter b for Various Materials; Body 2 is Steel β
Body 1 Rubber Perspex/Plexiglas Glass Duralumin Cast iron
~0 0.19 0.21 0.12 –0.24
in which β is a factor which depends on the elastic constants of the two materials, where
(
)(
)
(
)(
)
1 1 − 2v1 1 + v1 E1 − 1 − 2v2 1 + v2 E2 β= 2 1 − v12 E1 + 1 − v22 E2
(
)
(
)
(3.39)
If the two solids are different, then β > 0. The values of β for a number of fairly common materials chosen as Body 1 are given in Table 3.2; in each case Body 2 is steel. Tractive Rolling When either a driving or braking torque is transmitted through a rolling contact, the contact zone between the solids will, in general, contain both sticking and slipping zones, but, unlike the situation in sliding contact, the sticking zone will not be symmetrically disposed about the line joining the geometric centers of the cylinders. Consider a case in which two elastically similar cylinders, loaded together by a normal force of intensity of P per unit length, are rotating so that a torque is transmitted across the interface. Referring to Figure 3.13, we suppose that cylinder 1 is the driving roller and cylinder 2 the driven.
load torque
ω2
2
2b 1
ω1 driving torque
FIGURE 3.13 Rolling contacts; the lower cylinder 1 drives the upper cylinder 2 through frictional effects at the interface which is of width 2b: in free rolling there is no load torque applied to the driven cylinder.
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q(x)/p0 1
b c -2.0
-1.5
-1
-0.5
0.5
d
stick
1.5
1
x/b
slip
FIGURE 3.14 Distribution of surface traction under tractive rolling of similar cylinders plotted for the case c/b = 0.6 and Q/µP = 0.64.
By analogy with the stationary situation, the contact area will be divided into regions of “stick” and “slip”. In the static case there was a central sticking region, extending from –c < x < +c, with side slip zones disposed symmetrically. Under tractive rolling the pattern is displaced so that there is no slipping at the leading edge, as illustrated in Figure 3.14. The distribution of surface tractive stresses is then given by
()
{(
q x = µp0 1 − x 2 b2
)}
12
( ){ ( ) }
− µp0 c d 1 − x + d 2 c 2
12
for − b < x < c − d
and
{
()
q x = µp0 1 − x 2 b2
}
12
for c − d < x < b
(3.40)
Dimensions c and d are related to the applied normal load P and tangential load Q by the relations
{
}
c d = 1 − d b = 1 − Q µP
12
3.3. Non-Hertzian Contacts The preceding section has described analysis for the contact of curved bodies where the gap between the undeformed surfaces can be expressed as a quadratic (i.e., by Equation 3.1). In this section, elastic contacts between some bodies of other shapes are considered.
3.3.1. Flat Rigid Planar Punch Consider a flat-ended punch, of width 2b and of infinite length in the y-direction, pressed onto an elastic half-space with a force per unit length P, as shown in Figure 3.15. The surface of the punch is assumed frictionless so there is no restriction to lateral displacement of material under the punch. Contact occurs across the width of the punch, 2b. A theoretically infinite value of the contact stress is reached at the shoulders of the punch. The pressure distribution is given by:
( ) Pπ {b − x }
px =
2
2
−1 2
(3.41)
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P
p(x) p0
b
x
b z
FIGURE 3.15
Indentation by a flat-ended rigid planar punch.
The mean pressure over the contact strip is given by:
pm = P 2b = πp0 2
(3.42)
As in all line contact problems, the deflection can only be presented relative to some datum. The normal deflection uz of the surface, outside the contact region, is given by:
uz = δ −
(
)
2 1− v2 P πE
( ) {
}
ln x b + x 2 b2 − 1
12
(3.43)
where δ is the normal deflection at an arbitrary datum point.
3.3.2 Flat Rigid Axisymmetric Punch In this case the punch has a circular section of radius a. It is pressed onto an elastic half-space with a force P. Again the surface of the punch is assumed frictionless. Contact occurs across a circle of radius a and the resulting pressure distribution (Figure 3.16) is (Timoshenko and Goodier, 1951)
()
pr =
{
P a2 − r 2 2 πa
}
−1 2
(3.44)
The mean pressure pm over the contact circle is given by
pm = P πa 2 =
p0 2
(3.45)
The penetration ∆ of the punch is given by
(
)
∆ = P 1 − v 2 2Ea
(3.46)
3.3.3 Indentation by an Angular Wedge If a two-dimensional wedge of semi-angle α is pressed onto a frictionless elastic half-space with a force per unit length, P then contact is made over a rectangular region of semi-width b, such that
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P
p(r) p0
r
a
a z
FIGURE 3.16
Indentation by a flat-ended rigid axisymmetric punch.
P p(x) x
b
b z
FIGURE 3.17
Indentation by a two-dimensional blunt wedge.
(
b = P E * cotα
)
(3.47)
This time the pressure distribution (Figure 3.17) has a singularity at the wedge apex and is given by
()
px =
E * cot α cosh −1 b x π
( )
(3.48)
Equations 3.47 and 3.48 are appropriate for blunt wedges only (α is close to 90°) such that deformations are small and linear elastic theory is applicable.
3.3.4 Indentation by a Cone If a cone of semi-angle α is pressed onto a frictionless elastic half-space with a force per unit length equal to P, then contact is made over a circular region of radius a, 12
2P a= πE * cotα
(3.49)
The pressure distribution again has a singularity at the cone apex and is given by (Love 1939)
()
pr =
E * cot α cosh −1 a r 2
( )
(3.50)
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The extent of the penetration ∆ of the cone is given by
∆ = P 4E * a
(3.51)
Equations 3.49 to 3.51 are appropriate for large angle cones only (α is close to 90°) such that deformations are small and linear elastic theory is applicable.
3.4 Numerical Methods for Contact Mechanics Many contact problems will not fall into the preceding categories (Hertzian elastic or frictionless cones/punches) and require modeling by some numerical means. Common problems of this sort are those that involve friction and partial slip, complex geometry, nonlinearity of elastic properties, or plasticity.
3.4.1 Matrix Inversion Method For contact problems where the half-space assumption holds (i.e., the surfaces deform under contact loading as if they were elastic half-spaces), then a surface discretization method may be employed. The basic principle involves dividing the surface into a number of discrete elements. Some form of pressure distribution is then assumed to act on each element (Bentall and Johnson, 1967). Figure 3.18 shows three possible unit pressure distributions for a two-dimensional (i.e., line contact) problem; point loading, uniform pressure, or an overlapping triangular pressure distribution. The normal displacement at anode point i due to the loading at node point j is then expressed from the appropriate elasticity equation for the chosen unit loading. Hills et al. (1993) provide a useful summary of these traction elements. For example, for the uniform pressure elements (Figure 3.18b) the normal displacement at element i by a pressure applied at node j is given by
1− v p ( ) ( πE ) (x + a) ln[(x + a) a] − (x − a) ln[(x − a) a] + constant 2
2
i
uz = −
2
i
(3.52)
where 2a is the spacing between nodal points and x is the distance between nodes i and j. The constant is usually removed by considering the displacements relative to some arbitrary datum. The displacement (uz )i of the point i due to the summation of the loadings at each of the points j is then expressed by a matrix equation of the form n
(u ) = ∑C p z i
ij
j
(3.53)
i =1
The influence coefficient matrix Cij is obtained from the appropriate expressions for the deflection caused by the chosen elemental pressure distribution. For the uniform pressure element example, this gives
()
Cij k =
( ) ( ) ( ) ( )
2 2 1 k + 1 ln k + 1 − k − 1 ln k − 1 + constant 2π
(3.54)
where k is the number of elements between nodes i and j (i.e., k = i – j). In many cases the region of contact will not initially be known and an interactive procedure is adopted. A region of contact is guessed and a set of displacements u determined from the interpenetration of the
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(a)
Pj j
(b)
ui
Pj j
(c)
ui
Pj j
ui
FIGURE 3.18 Discretization of a contact surface and the application of element loading; (a) point loading at each node; (b) uniform pressure acting on each element; (c) overlapping triangular pressure distributions.
two bodies. Some numerical matrix inversion procedure then gives the corresponding pressures p. The set of pressures will contain some negative values; these are removed from the assumed contact area for the next iteration. A solution is found when the pressure is positive at all points within the region of contact and zero elsewhere. The total load is then found from the sum of the elemental pressures n
P=A
∑p
j
(3.55)
j =1
where A is a constant depending on the pressure element chosen (for the uniform pressure element example A is simply the width of the element, and the load is expressed per unit contact length). This method has been used extensively for determining the contact of rough surfaces (Webster and Sayles, 1986; Snidle and Evans, 1994). Real digitized surface roughness data are recorded, and this method used to determine real areas of contact when the profile is loaded against some counterface. Figure 3.19 shows the results from one such model; a rough surface has been loaded against a smooth cylindrical body. The resulting displaced surfaces and pressure distributions are shown. Once a surface distribution is known it is straightforward to determine the subsurface stress field (again assuming linear elastic behavior). The stress at any location is the summation of the stresses caused by each of the surface pressure elements. Again for the line contact uniform pressure element example,
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FIGURE 3.19 Numerical model of the contact between a planar rough surface and a smooth cylinder; (a) the predicted pressure distribution is shown compared to the Hertz smooth surface solution; (b) original and deformed surfaces.
the stresses at point (x,z) beneath a single pressure element, p, located at the surface (z = 0) and –a < x < +a are (Johnson 1985)
{(
) (
)}
{(
) (
)}
σ xx = −
p 2 θ1 − θ2 + sin 2θ1 − sin 2θ2 2π
σ zz = −
p 2 θ1 − θ2 − sin 2θ1 − sin 2θ2 2π
τ xz =
{
p cos 2θ1 − cos 2θ2 2π
(
tan θ1 = z x − a
)
(3.56)
} (
and tan θ2 = z x + a
)
Figure 3.20 shows a contour plot of the von Mises stress beneath the contact between a rough sphere and a smooth half-space (Lee and Ren 1994) determined using this numerical approach. The stress peaks associated with the roughness tend to be restricted to the near-surface region: the deeper stresses are similar to those for a smooth contact.
3.4.2 Variational Method It is possible to use the approach described above in cases where friction is present at the interface. In these cases both shear and normal tractions result in surface displacements. However, this further complicates the solution method since the regions of stick and slip within the contact must also be determined. The matrix inversion method is then very intensive in computational time. An alternative approach which is more useful in these cases is the variational method (Kalker, 1990). The variational principle states that the true stress field within a solid, loaded at its boundary, exists when the complementary potential energy is at a minimum value. The complementary potential energy V*
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r/a 0
-0.75
-0.5
-0.25
0.25
0.5
0.75
0.4 0.365 0.36 0.34 0.32 0.30 0.28 0.26 0.24
0.8
z/a 1.2
0.21 0.18
1.6
0.15
2.0
0.12
FIGURE 3.20 Numerically determined contour plot of von Mises stress beneath the contact between a rough sphere and a smooth half-space. (From Lee, S.C. and Ren, N. (1994), The sub-surface stress field created by three-dimensional rough bodies in contact with traction, Tribol. Trans., 37, 615-621. With permission.)
can be expressed in terms of the stored strain energy and the forces and displacements prescribed at the surface
1 V* = 2
n
∫ p(u
z1
)
∫(
)
+ uz 2 dS + p hi − δ dS
i =1
(3.57)
S
where δ is the overlap of the two surfaces and h(x,y) is their initial separation. S is the surface over which the pressure p acts, causing normal displacements uz. Again this can be written in a discretized form as
V* =
1 p 2 i
n
pi
n Cij p j + A pi hi − δ j =1 i =1 n
∑ ∑ j =1
∑ (
)
(3.58)
where A is a constant depending on the pressure element used. The solution proceeds by determining the values of pi which minimize V* subject to pi > 0. This has been done using a simplex method (Kalker and van Randen, 1972) or by using a direct quadratic programming technique (Tian and Bushan, 1996); the latter being more computationally efficient. Figure 3.21 shows the deformed surface predicted when this method is applied to the three-dimensional contact of a rough surface an a rigid sphere.
3.4.3 Finite Element Method Where the contact problem involves nonlinear material behavior such as plasticity or when the half-space assumption is no longer valid (i.e., when the dimensions of the body are not large compared with the regions of contact), then it may be necessary to employ a finite element method. A number of commercial finite element codes are available which are suitable for the solution of frictional contact problems (e.g., ABAQUS, DYNA3D, MARC, NASTRAN, RADIOSS, ANSYS).
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The contacting bodies are divided into an array of either two-dimensional axisymmetric or planar elements or three-dimensional brick elements. A set of gap or contact elements is defined between the surface nodes which are likely to come into contact during loading. A friction coefficient may be defined for the contact. Appropriate materials properties, boundary conditions, and nodal loadings are also specified. Modern programs have graphical interfaces to assist in the generation of meshes. The “preprocessing” program then generates an input file to use with the main analysis program. Also available are “postprocessing” packages, which generate graphical presentations of results such as stress or strain contours and deformed mesh shapes. Typically, contact problems involve loads distributed over small areas of contact. This results in rapid changes in stress in the elements surrounding the contact. Therefore, the mesh in this region must be refined adequately to describe these high stress gradients. Thus even a simple Hertz contact analysis needs a fine mesh for accurate results (Figure 3.22). The nonlinearities associated with contact, stick–slip behavior, and plasticity mean that the solution is loading-path dependent. This requires that the applied load is divided into a number of small steps and a solution found at each iteration. These two features can often lead to long computation times. The availability and ease of use of commercial FEA codes has led to their widespread adoption in both industrial and academic environments. Many fundamental tribological phenomena have been investigated by this method (e.g., elastic plastic contact, layered bodies, repeated contact cycles, indentation and hardness testing, impacts, metal forming, rough surface contact, and crack propagation). Likewise, countless industrial products and processes with contact aspects are modeled with these techniques.
3.5 Experimental Methods for Contact Mechanics In the experimental analysis of contact problems for machine element design, it is likely that the measurement of contact (both real and apparent) and contact stress are of interest. There are several experimental techniques for determining these parameters.
3.5.1 Real and Nominal Area of Contact Measurement Where the surfaces of the bodies are rough, contact is made only at the asperity summits. The true area of contact can be significantly lower than the geometrical (or nominal) area of contact. The techniques of determining this real area of contact can be categorized into electrical, optical, acoustic, and surfacecoating methods. Electrical and Thermal Resistance Measurement of the electrical resistance between contacting surfaces can give information about the true area of contact (Holm, 1967; Bowden and Tabor, 1939). This must be achieved by means of a currentpotential method because the resistance of the contact is small (of the order 10–3 to 10–6 ohms) compared with that of the leads. If the region of contact between two bodies is made up of n discrete contact points of radius ai , the total contact resistance is n
R = ρ÷
∑a
i
(3.59)
i =1
where ρ is the resistivity of the material (ohm/m). The resistance R depends on the contact spot radius (and not on the spot area). It is therefore not possible to determine the real area of contact directly, using this method, unless some assumption is made about either the size or number of individual contact spots. Equation 3.59 only holds if the contact points are far apart. In addition, the presence of surface
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Load = 0.026 N
nm 50 0 -50 100 75
100
µm
75
50 50
25
25 0
µm
0
Load = 0.149 N
nm 50 0 -50 100 75
100
µm
75
50 50
25
µm
25 0
0
Load = 0.395 N
nm 50 0 -50 100 75
µm
100 75
50 50
25
25 0
µm
0
FIGURE 3.21 Numerical model of the contact between a three-dimensional rough surface and a smooth rigid sphere. (From Tian, X. and Bhushan, B. (1996), A numerical three-dimensional model for the contact of rough surfaces by variational principle, Trans. ASME J. Trib., 118, 33-42. With permission.)
oxide films can have a significant effect on the contact resistance, and it is for these reasons the electrical resistance method is restricted to qualitative measurement. A similar method is the measurement of heat flux across the interface (Newcomb, 1957). This method has the advantage of being less susceptible to surface films. However, heat flow is not limited to junctions, as some may occur across air gaps. Optical Methods If one of the contacting bodies is transparent to light, then the regions of contact can be observed directly. There are a number of ways in which this principle has been realized, including direct methods, frustrated internal reflection and optical interference.
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MISES
VALUE +9.30E–01 +7.24E+01 +1.44E–02 +2.15E–02 +2.87E–02 +3.58E–02 +4.30E–02 +5.01E–02 +5.73E–02 +6.44E–02 +7.16E–02 +7.87E–02 +8.59E–02 +9.30E–02
FIGURE 3.22 (a) A typical finite element mesh for use with a planar frictional contact problem; (b) contour plots of von Mises stress obtained by finite element method.
A soft metal may be pressed against a glass surface and the number and size of the regions of contact measured directly (Dyson and Hirst, 1954). On the other hand, if both bodies are transparent, then a light beam may be directed through the interface. The beam will pass through regions of contact without deflection but will be scattered at air gaps. Contact areas then show up as bright spots against a grey background (Kragelsky, 1965). Alternatively, the specimen surface may be loaded against a prism and a parallel beam of light directed at the interface at grazing incidence (Kragelsky and Demkin, 1960). At regions of noncontact the beam is internally reflected, while at the contact spots this is frustrated. Contact spots are then viewed in the reflected light. A third method relies on the optical interference between two light beams, one of which is reflected from the top surface and one from the bottom (Bailey and Courtney-Pratt, 1955). The two surfaces,
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FIGURE 3.23 Optical interferogram of the contact between a flat disk and a glass lens. The real area of contact is related to the proportion of light spots in the image. (From Bhushan B. and Dugger M. T. (1990) Real contact area measurements on magnetic rigid discs, Wear, 37, 41-50. With permission.)
which must be transparent, are coated with thin metallic films so that they are partially reflective. A beam of light is directed through the transparent specimen. Interference occurs between that part of the beam which reflects at the first surface and that which reflects at the second. Constructive interference occurs when the gap between the two specimens is equal to a whole number of wavelengths. Figure 3.23 shows an optical interferogram of the contact between a flat disc and a glass lens (Bhushan and Dugger, 1990). Ultrasonic Reflection A wave of ultrasound incident at an interface between two materials will transmit through regions of contact and be reflected back at air gaps. This phenomenon can be used to investigate the true area of contact at an interface (Kendall and Tabor, 1971; Drinkwater and Dwyer-Joyce, 1996). An ultrasonic transducer is mounted on one of the bodies and is excited to emit a broad band (typically 5 to 20 MHz) longitudinal pulse. The reflected pulse is received by the same transducer, amplified, and its signal stored on a computer. The amplitude of the reflected pulse can be divided by that if the incident pulse to give a reflection coefficient R. Provided that the wavelength of the signal is large compared with the size of the asperity contact, this is dependent on K the stiffness of the interface
(
)
2 R = 1 + 2K ωz
−1 2
(3.60)
where ω is the angular frequency of the wave, and z is the acoustic impedance of the material (the product of the wave speed and density). The stiffness of the interface is defined as the contact pressure required to cause unit approach of the surfaces; this depends on both the number and size of individual contact spots as well as their proximity. The stiffness varies from zero to infinity as the ratio of the real to nominal area of the contact varies from zero to 100%. This method may also be used to determine the extent of a contact region. An ultrasonic transducer is scanned across the interface. Where contact is made the wave will be transmitted; reflection occurs at regions of noncontact. The resolution of this technique is relatively coarse and is currently of most use in applications where the contact region is relatively large. Figure 3.24 shows a scan of the interface between a rough rubber sphere and a smooth steel flat. The resolution of the method is such that
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FIGURE 3.24 Ultrasonic scan of the contact between a steel ball and a steel flat (diameter 1.3 nm). The levels of shading indicate the reflection coefficient (the proportion of an incident wave reflected at the interface). Thus regions of higher pressure will result in increased conformity of the roughness and thus reduced reflection.
individual contact regions are not visible; rather regions of conformity (high percentage contact) are observed. Thin Surface Coatings A thin, soft metal (e.g., copper, silver, or gold) coating is applied to one of the surfaces by chemical or physical deposition and the bodies are then loaded together as required. The thin layer within the region of contact is deformed. The extent of the contact region can be observed by a change in the appearance of the deposited film. Alternatively, a radioactive or thin fluorescent paint coating may be applied to one surface. This is then loaded against the counterface. The extent of transfer can be determined quantitatively by, for example, use of some form of radioactivity counter.
3.5.2 Experimental Contact Stress Analysis Photoelasticity and Caustics The contacting bodies are modeled in photoelastic material, such as polycarbonate or epoxy resin. For two-dimensional applications a planar model is fabricated and loaded in a polariscope (a light source
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149
FIGURE 3.25 Photoelastic fringe pattern of the contact between a cylinder and half-space. Images have been obtained by a stress freezing method and are digitized for an automated analysis. (From Burguete, R.L. and Patterson, E.A., (1997), A photoelastic study of contact between a cylinder and a half-space, Exp. Mech., 37, 314-323. With permission.)
with two polarizing filters). The isochromatic fringe pattern gives contours of principal stress difference (σ1 – σ2). For three-dimensional models a stress freezing technique must be employed. The most common method is to apply the loading to the model at elevated temperature and allow to cool under load. The deformation remains frozen into the structure, which may then be cut into appropriate slices for analysis in a polariscope. This method has been used by Ollerton and Haines (1963) to study elliptical contact subjected to normal and tangential traction. Full field imaging and automated stress separation of contact problems has been studied by Burguete and Patterson (1997). Figure 3.25 shows a photoelastic fringe pattern from the contact between a cylinder and a flat surface compared with the theoretical solution. A related application is the method of caustics. The application of stresses causes deflection and a change in the refractive index of the material. If a planar specimen is illuminated with parallel incident light, rays which pass through the stressed regions are deflected. The light distribution on an image plane behind the specimen is no longer uniform. The boundary between the light and dark regions is known
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as the caustic curve. This analysis is generally carried out by finding the boundary loading which gives a theoretical caustic curve closest to that observed (Theocaris and Stassinakis, 1978). Contact Pressure Pads and Films For larger-scale contacts, commercially available thin film pressure transducers can have an application. The transducer consists of a matrix of conductive elements whose resistance varies with applied load. The elements are mounted on a thin flexible sheet which is placed between the contacting bodies. Typically, the smallest transducers are of the order of 1 mm2 and are sensitive to pressures up to 150 MPa. They are used routinely in the motor industry to study human interactions with the vehicle. Die impregnated films can also be used as pressure-sensitive devices. The film is placed between the contacting bodies, which are then loaded. The film releases a die at controlled pressure levels. After unloading, the film is then removed and examined; the color depth is proportional to applied pressure. Resistive Microtransducers Small elements of manganin or titanium are deposited onto a surface. When this microtransducer is located inside a contact, the pressure causes the resistance to increase. Typically the transducers are deposited through a shaped mask by radio frequency sputtering (for metal surfaces a thin layer of insulating silica is deposited first). They have been used to measure pressures in rolling and sliding lubricated contacts (Hamilton and Moore 1971, Kannel et al. 1965). The transducers are also sensitive to temperature rises which must be taken into consideration during any measurement.
3.6 Further Aspects 3.6.1 Contact of Rough Surfaces Nominally Flat Surfaces Having established the modes of behavior of a single contact spot, it is now possible to consider what happens when two real surfaces, that is, those carrying a large number of asperities with a range of summit heights, are brought into loaded contact. The elastic stresses depend on the relative profiles of the surfaces, described by the reduced radius of curvature R and the contact modulus E*. This means that, for the purposes of analysis, all the deformable surface imperfections can be considered to be concentrated on one surface, while the second surface is both rigid and plane. Suppose the rough surface to consist of N hills or asperities whose heights z above the mean level vary in some statistical fashion. This distribution can be described by the probability density function φ(z), which must be such that +∞
∫ φ(z ) dz = 1
(3.61)
−∞
so that all the summits are included. In their often-quoted treatment, Greenwood and Williamson (1966) assumed that the tips or summits of the asperities were spherical and all had the same characteristic radius of curvature Rs. When a normal load is applied, the rigid surface moves toward the mean level of the rough surface so that, when the separation is d, it will have made contact with all the asperities for which zs > d. The number n of such contacts will be given by ∞
∫ ()
n = N φ z dz
(3.62)
d
In the case of a rough surface that exhibits perfect plasticity, deformation of each contact spot will occur at the same normal pressure pm. It follows immediately that as long as pm remains constant the
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total real area of contact between the two solids will be in direct proportion to the applied load W. The actual number of individual contact points will depend very much on the nature of the function φ(z). However, when the contact is purely elastic, each asperity contact spot can be treated as a separate Hertzian contact between a sphere and a flat. This might occur either because the normal load is insufficiently large to cause significant plastic flow, or perhaps more realistically, because after repeated loading, the shakedown mechanism has given rise to elastic conditions (see Section 3.6.3). The total load W is given by summing up all n such contacts, so that ∞
∫ ( )( )
4 W = NE * Rs1 2 φ z z − d 3
32
dz
(3.63)
d
and the total real area of contact A is the sum of all the n contacts, so that ∞
∫ ( )( )
A = NπRs φ z z − d dz
(3.64)
d
The numerical values of n, W, and A given by Equations 3.62, 3.63, and 3.64, clearly depend on the form of the function of φ(z). In their original paper Greenwood and Williamson considered a random or Gaussian distribution of summit heights and evaluated these integrals numerically; however, they also suggested that an analytical treatment is possible if we make use of the observation that, whatever the precise form of the bell shaped distribution of φ(z), it is only the most prominent asperities, i.e., those of large z, which will take part in the surface interactions. Within this region we can reasonably model φ(z) by an exponential expression of the form
()
( )
φ z = λ exp − λz
where λ is a suitable constant. In such a case, the number of points of contact n, and the real contact area A, are both strictly proportional to the applied load W. As the separation of the surfaces decreases, although the area of any particular contact spot grows, more asperities make contact so that the average size of the patches of real contact, i.e., A/n, remains constant. Provided the surface contains a range of surface roughnesses the direct proportionality between applied load and area of contact extends throughout the elastic range of material response as well as the plastic regime. A consequence of the area of real contact being proportional to the load is that the actual mean contact pressure is constant. Its value pm is equal to the load W divided by the area of contact A
pm =
W 4 E* = C A 3π Rs1 2 1
(3.65)
and is therefore independent of the separation of the surfaces. When the numerical value of the coefficient C1 is substituted, Equation 3.65 becomes
pm ≈ 0.39E * σ s Rs
(3.66)
where σs is the standard deviation of the surface roughness. Since each asperity contact is being modeled as being equivalent to that between a sphere and a plane, the results of the Hertz analysis can be used to predict those conditions which will just lead to the initiation of plastic deformation. In such a Hertzian contact the maximum shear stress occurs beneath the surface and is of magnitude 0.47pm. Setting this
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shear stress equal to the flow stress of the material k, we can see that the critical value of pm to cause yielding is equal to 2.15k. Since the flow stress is simply related to the hardness of the material H (≈5.6k) there is likely to be some plastic yielding if
pm ≥
2.15 × H 5.66
(3.67)
Combining this with the expression for pm from Equation 3.65 the condition for the onset of plasticity becomes that
E* σ s Rs ≥ C H
(3.68)
where C is a constant which, although depending to some extent on the form of the height distribution, is of the order of unity. The nondimensional group on the left-hand side of Equation 3.68 is sometimes known as the plasticity index Ψ, and neatly describes the likely deformation characteristics of a rough surface. If its value is very much less than unity, then asperity deformation is likely to be entirely elastic; on the other hand, if Ψ is significantly greater than 1 the response is predominantly plastic. The factor σ s ⁄ Rs is associated with the mean slope of the surface and can be obtained, approximately at least, from the profilometry data. Elastic Contact of Rough Curved Surfaces Most tribological contacts are between nonconforming or curved surfaces. The question then naturally arises, under what circumstances can the surface roughnesses on such loaded curved surfaces be safely neglected in calculating the contact stresses (using, for example, the Hertzian analysis) and under what circumstances can they not. For the situation to be amenable to quantitative treatment it is necessary for the two ranges of scales involved to be very different. These are typified on the one hand by the radius of curvature of the mean level of the surfaces, say R, and on the other by height and spatial distribution of the asperities. The nominal contact area will contain many deforming asperities, and these then act as a compliant layer lying over the surface of the body. Contact extends over a larger area than would be the case if the solids were perfectly smooth. The details of the quantitative solution are beyond the scope of this discussion. They can be found in Johnson (1985) and examples in Bhushan (1996, 1998). However, the conclusions can be conveniently expressed if a nondimensional parameter χ is defined to describe the influence of the surface roughness by the relation
{
χ = σ s R a 2 = σ s 16 RE *2 9W 2
}
13
(3.69)
here a is the contact radius for smooth surfaces according to the Hertz analysis. The smoother the surfaces, then the smaller the value of χ (since it depends on σs). The influence of χ on the effective pressure distribution for point contacts can be seen in Figure 3.26, which illustrates the extent of the contact zone for two values of χ which correspond to smooth (χ = 0.05) and rough (χ = 2) engineering surfaces. In this plot the pressure is normalized by the maximum Hertz pressure for smooth surfaces, the radial distance by the Hertzian contact radius a, and the dotted curve represents the Hertzian semi-ellipse. With a rough surface the peak pressure is much below the normal Hertzian value and falls more or less asymptotically to zero over an area very much greater than the Hertzian area. However, if χ is less than about 0.1 both the pressure curve and the contact radius are really quite close to Hertzian values. Thus the Hertz theory for perfectly smooth surfaces can be used to calculate the contact stresses on real engineering surfaces without introducing numerical errors of more than a few percent, provided the nondimensional group (σsR/a2) is less than about 0.1.
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contact pressure p/p0
1
x =0.05 0.5
x=2 0
1
2
3
r/a FIGURE 3.26
The effect of the contact parameter χ on the contact between rough, curved surfaces.
3.6.2 Loading Beyond the Elastic Limit Limit of Elasticity There must be some value of load for which the material of the weaker surface of the contact pair starts to deform plastically rather than elastically: to estimate this critical value an appropriate yield criterion must be applied. The yield of ductile metals is usually taken to be governed by either the Tresca maximum shear stress criterion or the von Mises strain energy criterion. In the case of the axial contact of cylinders the condition of plane strain deformation ensures that the stress component σyy is the intermediate principal stress. The Tresca criterion involves equating the maximum principal shear stress (which from Section 3.2.5) is equal to 0.30p0 to the shear yield stress k (which is numerically equal to Y/2). Hence, the critical value of the peak pressure p0Y is given by
p0Y = 3.3 k = 1.67 Y
(3.70)
The corresponding value of the mean pressure pmY is, from Equation 3.10,
p0Y =
π Y p ≈ 2.59 k = 1.3Y 4 0
(3.71)
The load per unit length of the contact PY required to bring material to the point of yield can be found from Equation 3.10,
PY =
πR Y 2 RY 2 p0 = 8.76 E* E*
(3.72)
Even when some yielding has taken place, the scale of the changes of shape must be small. This is because initial yield has occurred beneath the surface so that the plastic zone is still totally surrounded by a region in which the stresses and strains are still elastic: this limits the extent of plastic deformation
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since the plastic strains must be of the same order as the adjacent elastic strains. The material displaced by the flattening of the contact is accommodated by an elastic expansion of the surrounding hinterland. If the normal load on the contact is increased still further, beyond P Y, then the plastic zone grows until eventually it breaks out at the free surface. Once this occurs the constraint on the scale of the plastic deformation offered by the elastic hinterland is much reduced; the plastic strains can become very much larger with significant changes in the surface profile. In an analysis of this situation, it is then reasonable to consider the elastic strain components to be negligibly small in comparison to the plastic. Provided the material does not strain harden to any appreciable extent, it may be idealized as a rigid perfectly plastic solid which flows under a constant shear flow stress k. The situation can now be analyzed by one of the standard methods for dealing with large strain plastic forming processes; for example the slip line field technique in two dimensions, or the approximate, but more readily applied, upper bound method in both two- and three-dimensional geometries (see, for example, Johnson and Mellor, 1964, or Hosford and Caddell, 1983). The upper bound method depends on postulating some mechanism of plastic flow which is compatible with both the external constraints on the body and with volume constancy. Equating the rate at which the external load does work to the rate at which energy is absorbed within the material provides an upper bound on the true maximum load the contact can sustain. In the case of a single, loaded line contact the upper bound theorem leads to estimates of the form
pm = 5.66k = 2.83Y .
(3.73)
When the same methods are applied to other indentation geometries, it is found that although the numerical value of the ratio pm/Y depends to some extent both on details of the geometry and the frictional conditions on the surface it is always close to the value 3. Thus we can see that after subsurface yielding is initiated (at an interfacial mean pressure of about Y) there is a transitional range, involving values of pm between Y and 3Y, when the plastic flow is constrained by the surrounding elastic material and within which the elastic strains cannot be neglected in comparison with the plastic. These three ranges of loading — elastic, elastic/plastic, and fully plastic — are characteristic of nearly all engineering structures subjected to loadings of increasing severity. The pressure pm can be thought of as a measure of the indentation hardness H of the material, that is, the smallest value of normal pressure required to bring about significant plastic deformation under a rigid indenter. Elastic/Plastic Contact While problems in the intermediate elastic–plastic region are, in principle, susceptible to analysis, solutions are difficult to obtain in all but the simplest of geometries. Difficulties arise in finding solutions which satisfy both the equations of equilibrium and compatibility on both sides of the boundary between elastically and plastically stressed material because the size and shape of the elastic/plastic boundary is not known a priori. In the case of the contact between a flat surface and a comparatively blunt indenter, i.e., one with an included angle of more than about 140°, the experimental observation that the subsurface displacements are approximately radial from the point of first contact, with roughly cylindrical or spherical contours of equal strain, has led to a simplified approximate model (Johnson, 1970). The pressure beneath the indenter is a function of the single nondimensional group Etanθ/Y where θ is the angle between the face of the indenter of its local tangent and the surface. This group can be interpreted as the ratio of the strain imposed by the indenter (which is related to its “sharpness” or the value of tanθ) to the strain capacity of the material as measured by the elastic strain at yield (i.e., Y/E); the group Etanθ/Y is thus a measure of the severity of the loading. The three regions of behavior, elastic, elastic–plastic, and fully plastic, can be displayed on a graph of pm /Y vs. Etanθ/Y. The elasticity of the indenter can be taken into account by replacing E by E* (defined as in Equation 3.3). Such a “map” of material behavior is shown in Figure 3.27. First yield for a spherical indenter occurs at about pm /Y = 1.1 and for a cone at about pm /Y = 0.5. The fully plastic state is reached when the group E*tanθ/Y has a numerical value in the range of 30 to 40.
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3
pm 2 Y
cone
Sphere
1 elastic
0
elastic-plastic
1
plastic
10
100
E*tanθ Y FIGURE 3.27 Indentation of a half-space by spheres and cones. pm/Y is the ratio of the mean contact pressure to the material yield stress, and E*tanθ/Y is a measure of the severity of loading.
The same gradual transition from purely elastic contact to fully plastic behavior occurs when the contact is subject to a tangential load applied simultaneously with the normal pressure. The presence of a surface traction moves the point of initial yield from the Oz axis of symmetry and brings it closer to the surface as shown by comparing Figures 3.8 and 3.11. As the frictional traction at the surface gets larger, a stage is reached when the position of maximum shear occurs actually at the surface rather than beneath it. This effect is illustrated in Figure 3.28 curve A in which the ratio of the maximum Hertz pressure to the shear flow stress, i.e., to p0 /k, which is just sufficient to cause initial plastic flow, is plotted against the traction or friction or traction coefficient Q/P. Figure 3.28 is thus effectively a second map 5 sub-surface flow
load intensity p /k 0
4
surface and sub-surface flow sub-surface flow
elastic shakedown surface flow
3 elastic
2
1
0
elastic limit A elastic-perfectly plastic shakedown limit B kinematic hardening shakedown limit C
0.1
0.2 0.3 0.4 surface traction Q/P
0.5
0.6
FIGURE 3.28 Effect of surface traction Q/P on the maximum Hertz pressure p0 for either yielding or shakedown of material with shear flow stress k: curve A elastic contact, first yield, Tresca; curve B elastic-perfectly plastic behavior; curve C, after shakedown, for a kinematically hardening material. (From Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press, Cambridge. With permission.)
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which can be used to determine both the likelihood of plastic deformation and whether this is at or below the surface. It applies to a single contact at which the severity of the loading, described by both the ratio of the peak Hertzian pressure to the uniaxial yield strength and the traction coefficient Q/P, is known. In the case of a line contact there is a slight complicating factor in that it is possible for deformation to occur by spread of material in the out-of-plane, or Oy-direction; however, this mode of lateral flow is favored only over a fairly narrow range of traction coefficients. Figure 3.28 illustrates an important general point: if the friction or traction coefficient is less than about 0.3 then the plastic zone beneath a sliding contact is contained within the bulk and does not break through to the free surface. The plastic strains must therefore be comparatively small and of the order of the elastic strains. But if the traction coefficient exceeds 0.3 then the flow field extends to the surface for both line and point contacts. Having lost the constraining effect of the elastic boundary it follows that the plastic strains can now become much larger.
3.6.3 Repeated Contacts — The Role of Residual Stresses and Shakedown In many practical contacts the loaded surfaces have to withstand many repeated passes of the load. If, in the first pass, the elastic limit is exceeded (so that the operating point of the contact is above curve A in Figure 3.28) an element of plastic deformation will take place, and thus when the load is removed some system of residual stresses will remain in the material. In the second pass of the load the material is subjected to the combined action of the applied contact stresses and the system of residual stress left behind from the first pass. Generally speaking, such residual stresses are protective, in the sense that they will make yielding less likely in the second pass than was the case in the first. It is possible that after a few passes the residual stress system builds up to such an extent that the applied load can be carried entirely elastically. This process is known as elastic shakedown. Shakedown can be investigated either by repeated application of numerical stress analysis (usually FEM, see Section 3.4.3 and, for example Ham et al., 1988, or Kulkarni et al., 1991) or by appealing to an important theorem in stress analysis; this states that if any distribution of residual stress can be found which, together with the elastic stresses due to the load, constitute a system of stress which is everywhere within the elastic limit of the material then the system will shake down. The strength of the theorem lies in the fact that the system of residual stress that is used for the calculation does not have to be the real one — as long as it is a possible one. The important practical implication is that, providing a suitable set of residual stresses is possible, the material will find them. When this argument is applied to the case of a repeated Hertzian contact between cylinders, the condition for elastic shakedown to occur turns out to be that the peak Hertzian pressure p0 must be no greater than 4.00k. Using the Tresca criterion the critical value of p0 for yield on the first application of the load is 3.3k. This means that if the repeated load is such that 3.3k < p0 < 4.0k then, although there will be some yield in the first cycle of operation, shakedown will occur. As the total load P on the contact is proportional to (p0)2 it follows that the ratio of the shakedown limit PS to the elastic limit P Y is given by 2
P S 4.0 = = 1.47 P Y 3.3
(3.74)
In other words the load on such a contact can be nearly 50% greater than that needed to bring about yield on the first cycle before conditions are so severe that continuous plastic deformation will be produced on every subsequent cycle. A similar analysis can be made of a Hertzian line contact which also carries tractive load Q. As the traction on the surface is increased, so the limiting value of the maximum Hertz pressure for which shakedown is possible reduces. This effect is illustrated in Figure 3.28 curve B, from which it can be seen that as the traction grows, so the allowable interval between the load for first yield and that for shakedown becomes narrower.
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The effect of strain hardening can also lead to an apparent shakedown phenomenon irrespective of the contact geometry. With repeated deformation the effective value of k, the material shear strength, may rise in the surface layers, so that a load which initially exceeds the shakedown limit subsequently lies below it. Further refinements of the shakedown argument are possible for materials which strain harden in particular ways. For example, Figure 3.28 curve C illustrates the shakedown curve for a material that exhibits kinematic hardening. In a material which exhibits some form of nonlinear strain-hardening (which is typical of many engineering alloys) the situation of incremental plastic collapse or plastic ratchetting can arise; here gross deformation of the surface and close-to-surface material may accumulate after millions of repeated loading cycles, each of which contributes an element of plastic strain. Shakedown can also play a part in rolling contacts, such as a ball on a flat, in which with repeated traversals an originally plane surface becomes grooved, so increasing the contact area and reducing the contact stresses (see Williams, Dyson, and Kapoor, 1999).
3.6.4 Contacts on Layered Solids Stress and deformation analyses for the case of a rigid cylindrical indenter making contact with a halfspace carrying an elastic surface layer with differing mechanical properties from the bulk have been carried out by a number of authors (Burminster, 1945; Hannah, 1951; Gladwell, 1976; Chen, 1971; Chen and Engel, 1972; Jaffar and Savage, 1988). The usual method of solution is to first calculate the local surface deformations from the degree of nominal overlap of the two surfaces and then to solve, either analytically or numerically, the stress-deformation integral equation, so arriving at a consistent distribution of normal pressure at the interface: this can then be integrated to give the normal load. Gupta and Walowit (1974) and Kannel and Dow (1986) obtained generalized solutions for elastic cylindrical indenters against layered elastic solids. Walowit and Pinkus (1982) and King and O’Sullivan (1987) analyzed the stress field associated with an elastic cylindrical indenter sliding with traction over an elastic halfspace with a single surface layer (see Figure 3.29a), and this analysis was extended to multiple layers by Elsharkaway and Hamrock (1993). O’Sullivan and King (1988) examined the case of a spherical indenter loaded sliding over a single layered surface. Results from analyses of this sort can be validated and extended by finite element analyses such as those of Ihara (1986), Komvopoulos (1988), and Arnell (1993, 1994). Figure 3.29, taken from O’Sullivan and King, illustrates the effect of both harder and softer elastic layers on the surface pressure distribution and local deformation. In these results Poisson’s ratio is taken as 0.3 throughout and the indenter is assumed rigid and of radius R. In Figure 3.29b the pressure is normalized by p0 which is the Hertz pressure under the center of the indenter for the case E1 = E2 when the radius of contact a is equal to layer thickness. Figure 3.29c illustrates the variation with indentation depth δ with the normal load P; this is normalized by load P0, the load for the situation when E1 = E2 and a = h. The more compliant layer gives, as expected, enhanced penetration depths and significant changes to the pressure profile. Subsurface stress components, σxx , σzz , and τxz , are also much modified by the presence of both the surface layer and any surface friction or traction. A stiffer surface layer behaves rather like a thin elastic plate bonded to the substrate, large bending stresses can develop giving a tensile σxx at the interface, which can be significant for the growth of cracks normal to the interface. The shear stress τxz is also enhanced by the stiffness of the surface layer, although its magnitude decays rapidly with depth z. High interface shear stress can adversely effect the bonding between layer and substrate. Layers which are of lower modulus than the bulk generally lead to reduced stresses but, since they are also likely to be of lower hardness, provide lower resistance to wear or surface damage. To fully exploit the superior tribological properties of harder (and generally stiffer) surface coatings, softer intermediate layers may be appropriate. Similar effects have been found in the case of nominal point rather than line contacts (Kral et al., 1997; Lovell, 1998). Relatively little work has been done on the analysis of the elastic–plastic contact of layered surfaces despite the fact that plastic deformation is a major concern in the design and performance of engineering components. Failure of a hard coating–soft substrate system under some tribological situations may be caused not by conventional wear but rather by debonding of the coating from the substrate (adhesive
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p
Q
slider
x δ
h
E1, v1
z
E2, v2
25 20
2
p/p0
E1
=
1.5
4E2
E1
=
E1
1
p/p0 15
2E2 =
E1
0
=
0.5E2
E1
0.5 0.2 0.4
0.6 0.8
x/a0
1
1.2
E1 = 2E2 E1 = E2 E1 = 0.5E2
10
E2
=
0.25E2
1.4
1.6
5 0
0.2
0.4
0.6
0.8
δ/h
FIGURE 3.29 (a) Spherical or cylindrical indenter in contact with a layered half-space; (b) normal contact pressure profiles beneath a frictionless rigid spherical indenter for an elastic layered half-space with different values of E1E2, a0 is the Hertzian semi-dimension when E1 = E2; (c) indentation depth vs. applied load, P0 is the normal load for the case E1 = E2 and a0 = h. (Adapted from O’Sullivan, T.C. and King, R.B. (1988), Sliding contact stress field due to a spherical indenter on a layered elastic half-space, Trans. ASME J. Trib., 110, 2345-240. With permission.)
failure), fracture of the coating (cohesive failure), or even subsurface fracture (substrate failure). Accordingly, it is valuable to have a picture of the spatial distribution of plastic stresses and of the position of the initiation and subsequent development of the plastic zone. Based on an FEM analysis of a hard coating (TiN) on a soft substrate (Ti) indented by a rigid cylinder, Komvopoulos (1989) found that coating thickness has a significant effect on the initiation and development of the plastic zone. Deformation maps can be constructed which define the deformation mode (elastic or plastic) in terms of such parameters as maximum pressure and coating thickness. More recent work (see Mao et al.,1994) has used a rigorous elastic–plastic FEM analysis to study the initiation and development of the plastic zone in various TiN coating–substrate systems, including TiN–Al, TiN–Ti, and TiN–HSS (high-speed steel) indented by a rigid ball of 100 µm diameter. The results confirm that both the coating thickness and substrate strength have a significant influence on both the plastic deformation behavior and the load-bearing capacity. In most coating–substrate systems, plastic deformation is initiated first in the substrate at the coating–substrate interface; plastic deformation does not initiate in the harder coating until a large plastic zone has been developed in the substrate. Increasing the coating thickness and/or substrate strength increases the resistance of the composite to plastic deformation. When the substrate is relatively soft and the coating is relatively thin, plastic deformation is concentrated in the substrate. With increasing coating thickness and substrate strength, plastic deformation in the coating becomes more evident, such that when a very thick TiN coating on (relatively strong) HSS is indented by the rigid ball, plastic deformation is initiated in the coating rather than the
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0
0 E1 = 2E2 E1 = E 2 E1 = 0.5E2
1
z/h 2
z/h
2
3
3
4
4
5
0
-0.5
-1.5
-1 σz /p
0
E1 = 0.5E2 E1 = E2 E1 = 2E2
1
-2
5 0.4
0
-0.8 -0.4 σz /p 0
-1.2
-1.6
FIGURE 3.30 Normal and shear stress components under the center of a rigid spherical frictionless indenter sliding over a layered elastic half-space with different values of E1/E2; the radius of contact a0 is equal to layer thickness h when E1 = E2 .
substrate. Only when the coating is very thin does its presence degrade the load-bearing capacity of HSS. This indicates the importance of depositing a sufficiently thick coating in order to optimize the tribological performance of coated systems. Tian and Saka (1991) also investigated the interaction between a rigid cylinder and a two-layer elastic–plastic half-space. As the normal load increases, plastic deformation initiates in the substrate for a thin interlayer (specifically when the interlayer thickness was less than 0.7% of cylinder radius), whereas, for a thicker interlayer, plastic deformation could be initiated at the interface between the top layer and the interlayer. In the elastic–plastic regime, the contact pressure distribution became flatter and the peak pressure moved slightly away from the contact center as the plastic zone breaks out to the contact interface. Sliding contact was also considered and it was found that surface deformation, location of initial yielding, as well as the values of the stresses and strains along the interfaces between layers strongly depended on the coefficient of friction. Yielding initiated on the surface when the friction coefficient was high and in the subsurface when the friction coefficient was low. Surface strains, especially shear strains, were large owing to the element of unconstrained deformation. The completion of further analyses of the contact of such multilayered solids with representative surface topographies, especially under conditions of repeated loading, should enable their optimization to be more readily achieved than by empirical developments, which are currently most commonly used.
References Arnell, R.D. (1994), Stress distribution in layered surfaces subject to tribological forces, Phys. Stat. Sol.(a),145, 247-254. Arnell, R.D. and Djabella, H. (1993), Two-dimensional finite element analysis of elastic stresses in doublelayer systems under combined surface normal and tangential loads, Thin Solid Films, 226, 65-73. Beeching, R. and Nichols, W. (1948), Theoretical discussion of pitting failure in gears, Proc. Instn Mech. Engrs., 158, 317-324. Bentall, R.H. and Johnson, K.L. (1967), Slip in the rolling contact of two dissimilar elastic materials, Int. J. Mech. Sci., 9, 389-397. Bhushan B. and Dugger M. T. (1990) Real contact area measurements on magnetic rigid discs, Wear, 37, 41-50. Bhushan, B. (1996), Contact mechanics of rough surfaces in tribology: single asperity contact, Appl. Mech. Rev., 49(5), 275-298. Bhushan, B. (1998), Contact mechanics of rough surfaces in tribology: multiple asperity contact, Trib. Lett., 4, 1-35.
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Bowden, F.P. and Tabor, D. (1939), The area of contact between stationary and moving surfaces, Proc. R. Soc. A, 169, 391-402. Bryant, M. D. and Keer, L. M. (1982), Rough contact between elastically and geometrically similar curved bodies, ASME J. Appl. Mech., 49, 435-441. Bufler, H. (1959), Zur theorie der rollenden reibung, Ing. Arch., 27, 137-142. Burguete, R.L. and Patterson, E.A., (1997), A photoelastic study of contact between a cylinder and a halfspace, Exp. Mech., 37, 314-323. Burminster, D. M. (1945), General theory of stresses and displacements in layered systems, J. Appl. Phys., 16, 89-94. Chen W.T. (1971), Computation of stresses and displacements in a layered elastic medium, Int. J. Engng. Sci., 9, 775-800. Chen W.T. and Engel, P.A. (1972), Impact and contact stress analysis in multi-layered media, Int. J. Solids Struc., 8, 1257-1281. Dyson, J. and Hirst, W., (1954), The true area of contact between solids, Proc. Phys. Soc. (London), 67B, 309-312. Elsharkaway, A.A. and Hamrock, B.J. (1993), Numerical solution for dry sliding line contact of multilayered elastic bodies, ASME J. Tribology, 115, 237-245. Fessler, H. and Ollerton, E. (1957), Contact stresses in toroids under radial loads, Brit. J. Appl. Phys., 8, 387-393. Gladwell, G.M.L. (1976), Some unbounded problems in plane elasticity theory, ASME J. Appl. Mech., 43, 263-267. Gladwell, G.M.L. (1980) Contact Problems in the Classical Theory of Elasticity, Sijhoff and Noordhoff, Amsterdam. Greenwood, J.A. and Williamson, J.P.B. (1966), Contact of nominally flat surfaces, Proc. R. Soc. A, 295, 300-330. Gupta P.K. and Walowit, J.A. (1974) Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lub. Tech., 96, 259-257. Ham, G., Rubin, C.A., Hahn, G.T., and Bhargave, V. (1988), Elasto-plastic finite element analysis of repeated two-dimensional rolling sliding contacts, ASME J. Trib., 110, 44-49. Hamilton, G.M. (1983), Explicit equations for the stresses beneath a sliding spherical contact, Proc. Instn. Mech. Engrs., 197C, 53-61. Hamilton, G.M. and Goodman, L.E. (1966), The stress field created by a circular sliding contact, ASME J. Appl. Mech., 33, 371-376. Hamilton, G.M. and Moore, S.L., (1971), Deformation and pressure in an elasto-hydrodynamic contact, Proc. R. Soc., 332A, 313-330. Hannah, M. (1951) Contact stress and deformation in a thin elastic layer, Quart. J. Appl. Maths., 4, 94-105. Hills, D. A., Nowell, D., and Sackfield, A. (1993), Mechanics of Elastic Contacts, Butterworth-Heinemann, Oxford. Holm, R. (1967), Electric Contacts, Springer-Verlag, New York. Hosford, W.F. and Caddell, R.M. (1983), Metal-forming. Mechanics and Metallurgy, Prentice-Hall, New York. Ihara, T., Shaw, M.C., and Bhushan, B. (1986), Finite element analysis of contact stress and strain in an elastic film on a rigid substrate, ASME J. Trib., 108, 527-533 and 534-539. Jaffar, M.J. and Savage, M.D. (1988), On the numerical solution of line contact problems involving bonded and unbonded strips, J. Strain Anal., 23, 67-77. Johnson, K.L. (1970), The correlation of indentation experiments, J. Mech. Phys. Solids, 18, 115-123. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press, Cambridge. Johnson, W. and Mellor, P.B. (1964), Engineering Plasticity, van Nostrand, New York. Kalker, J.J. and van Randen, Y. (1972), A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems, J. Engng. Math., 6 193-206.
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Kalker, J.J. (1990), Three Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Dordrecht. Kannel, J.W. and Dow, T.A. (1986), Analysis of traction forces in a precision traction drive, ASME J. Trib., 108, 403-410. Kannel, J.W., Walowit, J.A., Bell, J.C., and Allen, C.M. (1965), The determination of stresses in rolling contact elements, Trans. ASME J. Lub. Tech., 89, 453-465. Kendall, K. and Tabor, D. (1971), An ultrasonic study of the area of contact between stationary and sliding surfaces, Proc. R. Soc. A, 323, 321-340. King, R.B. and O’Sullivan, T.C. (1987), Sliding contact stresses in a two-dimensional layered elastic halfspace, Int J. Sol. Structs, 23, 581-697. Komvopoulos, K. (1988), Finite element analysis of a layered elastic solid in normal contact with a rigid surface, Trans. ASME J. Trib., 110, 477-485. Komvopoulos, K. (1989), Elastic-plastic finite element analysis of indented layered media, Trans ASME J. Trib., 111, 430. Kragelsky, I.V. (1965), Friction and Wear, Butterworths, London. Kragelsky, I.V. and Demkin, N.B. (1960), Determination of the true area of contact of elastic solids, Trans. ASME, Friction and Wear in Machinery, New York, 14, 30-53. Kral, E.R. and Komvopoulos, K. (1997), Three dimensional finite element analysis of subsurface stress and strain fields due to sliding contact on an elastic-plastic layered medium, Trans. ASME J. Trib., 111, 332-341. Kulkarni, S., Hahn, G.T., Rubin, C.A., and Bhargave, S. (1991), Elasto-plastic finite element analysis of three dimensional pure rolling contact above the shakedown limit, ASME J. Appl. Mech., 58, 347-353. Lee, S.C. and Ren, N. (1994), The sub-surface stress field created by three-dimensional rough bodies in contact with traction, Tribol. Trans., 37, 615-621. Love, A.E.H. (1939), Bousinesq’s problem for a rigid cone, Quart. J. Math., 10, 161-170. Lovell, M.R. (1998), Analysis of contact between transversely isotropic coated surfaces, Wear, 214, 165-174. Mao, K., Sun, Y., and Bell, T. (1994), Contact mechanics of engineering surfaces: state of the art, Surface Engng., 10(4), 297-306. McEwen, E. (1949), Stresses in elastic cylinders in contact along a generatrix, Philos. Mag., 40, 454-463. Muskhelishvili, N.I. (1949), Some Basic Problems of the Mathematical Theory of Elasticity, 3rd ed., Moscow (English translation, by J.R.M. Radok, Noordhoff, 1953). Newcomb, T.P. (1957), Communication, Proc. Conf. Lubrication and Wear, Inst. Mech. Eng., London, 837-838. Ollerton, E. and Haines, D.J. (1963), Contact stress distributions on elliptical contact surfaces subjected to radial and tangential forces, Proc. Instn. Mech. Engrs., 177, 95-101. Ollerton, E. and Morley, J.W.W. (1963), Fatigue strength of rail steel in rolling contact, in Proc. Symposium on Fatigue in Rolling Contact, IMech E, London. O’Sullivan, T.C. and King, R.B. (1988), Sliding contact stress field due to a spherical indenter on a layered elastic half-space, Trans. ASME J. Trib., 110, 235-240. Poritsky, H. (1950), Stresses and deflections of cylindrical bodies in contact, Trans. ASME J. Appl. Mech., 17, 191-201. Sackfield, A. and Hills, D. A. (1983a), Some useful results in the classical Hertz contact problem, J. Strain Anal., 18, 101-108. Sackfield, A. and Hills, D.A. (1983b), A note on the Hertz contact problem: correlation of standard formulae, J. Strain Anal., 18, 195-201. Smith, J.O. and Liu, C.K. (1953) Stresses due to tangential and normal loads on an elastic solid, Trans. ASME J. Appl. Mechs., 20, 157-166. Snidle, R.W. and Evans. H.P. (1994), A simple method of elastic contact simulation, Proc. Insn. Mech. Engrs. Part J, 208, 291-293.
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Theocaris, P.S. and Stassinakis, C.A., (1978), The elastic contact of two disks by the method of caustics, Exp. Mech., 18, 409-415. Thomas, H.R. and Hoersch, V.A. (1930), Stresses due to the pressure of one elastic solid on another, Univ. of Illinois Engng. Exptal. Station Bulletin No 212. Tian, H. and Saka, N. (1991), Finite element analysis of an elastic-plastic two-layer half-space; normal contact, Wear, 148, 47-68. Tian, H. and Saka, N. (1991), Finite element analysis of an elastic-plastic two-layer half-space; sliding contact, Wear, 148, 261-272. Tian, X. and Bhushan, B. (1996), A numerical three-dimensional model for the contact of rough surfaces by variational principle, Trans. ASME J. Trib., 118, 33-42. Timoshenko, S.P. and Goodier, J.N. (1951), Theory of Elasticity, McGraw-Hill, New York. Walowit, J.A. and Pinkus, O. (1982), Effect of friction between cylinders and rubber staves of finite thickness, Trans. ASME J. Lub. Tech., 104, 255-261. Webster, M.N. and Sayles, R.S. (1986), A numerical model for the elastic frictionless contact of real rough surfaces, Trans. ASME J. Trib., 108, 314-320. Williams, J.A., Dyson, I.N., and Kapoor, A. (1999), Repeated loading, residual stresses, shakedown and tribology, J. Mater. Res., 14(4) 1548-1559.
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4 Adhesion of Solids: Mechanical Aspects 4.1 4.2 4.3
Introduction ....................................................................... 163 Adhesion Forces, Energy of Adhesion, Threshold Energy of Rupture.............................................................. 164 Fracture Mechanics and Adhesion of Solids.................... 167 Energy Aspects, Energy Release Rate • Example of the Flat Punch • Mechanical Aspects
4.4
Example: Contact and Adherence of Spheres .................. 175 Hertz Solution • JKR Solution • DMT Solution • JKR–DMT Transition in a Dugdale Model • Application to a Liquid Meniscus
4.5 4.6 4.7
Liquid Bridges .................................................................... 183 Adhesion of Rough Elastic Solids — Application to Friction................................................................................ 186 Kinetics of Crack Propagation .......................................... 188 Case of Viscoelastic Solids • Experiments of Fixed Cross-Head Velocity — Tackiness • Branch with Negative Resistance: Velocity Jump and Stick-Slip • Examples of the Additivity of Dissipations • Short Historical Background
4.8
Daniel Maugis Laboratoire des Matériaux et des Structures du Génie Civil
Adhesion of Metals ............................................................ 197 Adhesion of Microcontacts • Cold Welding • Adhesion of Metals at High Temperature
4.9
Conclusion.......................................................................... 198
Abstract Adhesion and adherence of solids are reviewed in the framework of fracture mechanics. The main concepts are recalled: surface energy, thermodynamic work of adhesion, energy release rate, stable and unstable equilibrium of cracks, controlled propagation, stress intensity factors, J integral, and Dugdale model. An example of application is given for the adherence of spheres (based on various models). Kinetics of crack propagation for viscoelastic solids is presented in terms of G(v) curves, tackiness, stickslip, and velocity jumps. Examples of additivity of various losses are given, which include viscous drag, bulk dissipation, extraction of chains, and the problems of threshold values and hysteresis are discussed. Finally, the case of metals (cold welding and high-temperature adherence) is examined.
4.1 Introduction When two solids approach each other, they undergo attraction forces (adhesion forces) which can be long or short ranged and of variable strength, corresponding to energies from a few mJ/m2 to some J/m2. We
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deal here with solid-state physics and surface physicochemistry. When we want to characterize the force or the mechanical resistance of bonds so established between the two solids, we are faced with a more complicated problem. The separation never occurs spontaneously across the entire sample, but by propagation of a crack. It is accompanied with deformation and energy loss, which is more important the stronger the adhesion force. The force needed to separate the two solids depends of course on the density of bonds, but in addition, to the geometry of the samples and to the velocity at which separation occurs. The energy consumed can reach, in some cases, many hundreds of kJ/m2. It is thus necessary to seek analyses that apply to many geometries, how to employ fracture mechanics in various situations, and how to account for various energies that come into play. If the surfaces are rough or if they are not clean, adhesion is generally not strong. If one introduces a liquid which wets the surfaces, it increases adhesion. In some cases, the liquid hardens afterward by cooling, evaporation, polymerization. If this liquid is a polymer one speaks of gluing, if it is a liquid alloy between two metals one speaks of brazing (opposed to welding which is done without addition of matter).
4.2 Adhesion Forces, Energy of Adhesion, Threshold Energy of Rupture Besides the Young’s modulus E and the Poisson’s ratio ν, an isotropic elastic solid has a surface γ. Young’s modulus and Poisson ratio reflect the behavior of intermolecular forces for small displacements of atoms around their equilibrium points, and 2γ is the work per unit area necessary to break the bonds along an imaginary plane and to separate reversibly two parts of a solid. Surface energy thus characterizes the nature of bonds which ensure the cohesion of the solid through this imaginary plane. So, metals and covalently bonded solids have a high surface energy (1000 to 3000 mJ·m–2); the ionic crystals (100 to 500 mJ·m–2) or molecular crystals (γ < 100 mJ·m–2) have a lower surface energy. To calculate the surface energy of a solid, let us take the example of the Lennard–Jones potential between two atoms
U =−
C D + r 6 r12
where C is the London constant. By a simple integration, one obtains the stress between two half-spaces (two plates) separated by a distance z : 3 9 A Z 0 Z 0 σz = − 6 πZ 03 z z
()
Z 3 Z 9 3 3 = σ 0 − 0 2 th z z
(4.1)
where Z0 is the interatomic equilibrium distance. The constant A = π2n2C is called the Hamaker constant (n, the number of atoms per unit volume, is assumed to be constant, independent of the distance z, so that we can deal with the interaction of two rigid solids not strained by the stress σ). This curve is displayed in Figure 4.1. At z = Zc it passes through a maximum termed the theoretical stress σth , which is extremely high if compared to the elastic limit at 0.5%, for example. The part of the curve at the lefthand side of the maximum represents the elastic field, and the slope at z = Z0 is the Young’s modulus. The part at right of the maximum corresponds to two half-spaces in interaction; we term this portion of the curve the adhesion field. The area below the curve from z = Z0 up to infinity represents 2γ, and we see that to create two new surfaces one must first supply a work 2γ ′ against the elastic restoring forces (going from Z0 to Zc) and then a work 2γ ″ against the adhesion forces (going from Zc to infinity)
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FIGURE 4.1 Lennard–Jones potential. Stress between two half-spaces. Jumps such as A to B and C to D are observed if a spring of insufficient stiffness is used to measure the force.
2γ =
∞
∫ () Z0
σ z dz =
∫ () Zc
σ z dz +
Z0
∞
∫ σ(z )dz
(4.2)
Zc
For two solids 1 and 2 in contact, the work necessary to reversibly separate them may be written as
w = γ 1 + γ 2 − γ 12 W is the Dupré energy of adhesion and γ12 is the interfacial energy (which can be the grain boundary energy between two grains, or the twin boundary energy between two twins). The reversibility required in the definition of surface energy or adhesion energy is an important point which must be emphasized.
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FIGURE 4.2 Schematic view of a crack tip. The last nonbroken bond is the bond CB sustaining the theoretical stress. In the mechanics of continuous media the contour of the J integral just around the “cohesive zone” is the line AED with a cusp. This contour should be ABCD in a discrete model.
In fact it is impossible to maintain the surfaces parallel down to the contact, and the symmetry is broken. Only a part of the single crystals is in contact, and the separation instead, to occur on a whole, occurs along a line where bonds are broken one after another. We thus deal with a crack (Figure 4.2, where the trace of this line is the point E). The theoretical stress σth, instead of extending across the whole crystal at the moment of separation, is localized at the crack tip, on the bond BC. Elastic forces appear ahead of the crack tip, and adhesion (or cohesion) forces extend on some length, the cohesion zone, beyond which surfaces are interaction free. The stresses necessary to create a unit area of new surface are much less, and the crack can be seen as a stress transformer. The surface energy 2γ is thus the work necessary to reversibly transfer an internal surface from a point where it is submitted to no stress (z = Z0) to the crack walls beyond the range of adhesion forces:
2γ =
dz ∫ σ[z(x )] dx dx x2
(4.3)
x1
The problem of the reversibility is less crucial. The crack advances by a lattice mesh each time a bond such as BC is broken. This rupture is accompanied by a jump (the more important the shorter the cohesion zone), during which energy is lost (phonons emission, for example). Similar jumps occur during healing of the crack. The crack thus may be trapped (“lattice trapping”) by an energy barrier (as a dislocation by Peierls–Nabarro forces) and may not be completely reversible. We will term G+0 and G –0 these threshold energies to advance or recede the crack with G 0– < w < G +0. This theory of “lattice trapping,” in which a lattice of point masses is linked by spring resistant to both traction and flexion, has been developed by Thomson et al. (1971), and Fuller and Thomson (1978). It must be noted that due to the elastic “fretting” around this bond, the amplitude of jumps is less, but is very sensitive to the shape of the crack. This effect is probably small or negligible in inorganic materials, as experimentally shown on glass or mica (Wan et al., 1990) where hysteresis between advance and recession is not observed. On the other hand, it can be important for macromolecular solids, if we replace the word bond by the word chain. We recover the argument proposed by Lake and Thomas (1967) for the rupture of elastomers, i.e.,
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to advance, the adhesion has to break C–C bonds, but the work is much higher than the dissociation energy of that bond because it is necessary to stretch all the bonds of the chain (molecular mass Mc) between two cross-linking points, and all the stored energy is irreversibly dissipated at the instant of rupture. The calculation leads to:
G0 = NnU = k Mc
(4.4)
where N is the number of chains cutting the fracture plane per unit area (proportional to 1/ M c ), n is the number of bonds between two cross-link points (proportional to Mc), and U is the dissociation energy of a C–C bond. G0 thus is not an adhesion energy but a threshold rupture energy of with representative values of the order of 50 to 100 J/m2. Such a proportionality between G0 and M c was effectively observed by Genet and Tobias (1982) or in an equivalent manner between G0 and 1/ E (Bhowmick et al., 1983) where E is the Young’s modulus. This argument is also valid for elastomers adhering to a solid by strong bonds: G0 must increase with the density N of bonds up to a value G 0* corresponding to the rupture of the bulk elastomer, and this effect was also observed by Ahagon and Gent (1975) and Chang and Gent (1981), G 0* is weaker the more cross-linked the elastomer.
4.3 Fracture Mechanics and Adhesion of Solids 4.3.1 Energy Aspects, Energy Release Rate The work needed to extend the area of a crack by dA is 2γdA. This work is taken to the elastic and/or potential energy of the system. Irwin and Kies, (1952) introduced the strain energy release rate, noted G by Irwin (1957) (initial of Griffith); elastic energy returned when the area of the crack increases by dA,
∂U E ∂U E ∂U P G= + = ∂A P ∂A δ ∂A
(4.5)
where δ is an imposed displacement, and Up = –Pδ represents the potential energy in the case where P is constant. Equilibrium at constant temperature and fixed load (dT = 0, dP = 0) corresponds to an extremum of Gibbs free energy , whereas equilibrium at constant temperature and fixed grips (dT = 0, dδ = 0) corresponds to an extremum of Helmholtz free energy F. In both cases equilibrium is given by
G=w
(4.6)
which we will term Griffith’s criterion of equilibrium and which links two of the three variables δ, P, A of the state equations, so that equilibrium curves δ(A), A(P), P(δ) are functions of w. If G ≠ w, the area of contact spontaneously changes to decrease the thermodynamic potential. If G < w, A must increase for the potential to decrease: the crack recedes. If G > w, the area of contact must decrease to have d < 0 or dF < 0, and the crack advances. GdA is the mechanical energy released when the crack extends by dA. As the rupture of bonds requires the work wdA, the excess (G – w)dA is changed into kinetic energy if there is no dissipation. G – w is the crack extension force, per unit length of crack; it is zero at equilibrium. The equilibrium given by G = w can be stable, unstable, or neutral. A thermodynamic system under a given “constraint” is stable if the corresponding potential is minimum, i.e., if its second derivative is positive. Stability at constant temperature (dT = 0) and fixed grips (dδ = 0) is given by:
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∂2 F ∂G ∂A2 = ∂A > 0 δ ,T δ Similarly, at fixed load, stability will be defined by:
∂2 ∂G ∂A2 = ∂A > 0 P ,T P An important point is that the stability of equilibrium is generally not the same at fixed load and at fixed grips, and at fixed ∆ it depends on the stiffness km of the measuring apparatus. Its stiffness km is that of the spring. A displacement ∆ can be imposed by turning the screw (which is thermodynamically equivalent to apply a load P to the spring, and then to clamp it without external work), and can be divided into a spring elongation δm and a displacement δ of the two solids in contact. The spring exerts a force P = kmδm on the two solids, and we have:
∆ = δ + δm = δ +
P km
(4.7)
Equilibrium at fixed ∆ is still given by G = w, and the stability by:
∂G >0 ∂A ∆
(4.8)
but this stability depends on the stiffness km. Equilibrium can be unstable at fixed load, and stable at fixed grips. Another important concept is that of controlled rupture. Let us consider a stable equilibrium defined by G = w and (∂G/∂A) > 0. If a fluctuation decreases the area of contact (dA < 0), G decreases and we have G < w; the crack recedes to return to its equilibrium position. We have the same return to equilibrium if the fluctuation increases the area of contact (the system of loading remaining the same). The crack will move only if the load P or the displacement δ is modified, and it will move such as to bring back G to its value w. We deal thus with a controlled rupture, but for the crack to be always in equilibrium with the loading, it is necessary that the variations of P or δ are very slow, so, we deal with a quasistatic transformation. The fact that G remains constantly equal to w during this controlled propagation is written:
∂G ∂G dG = dA + d∆ = 0 ∂A ∆ ∂∆ A
(4.9)
Starting from a stable equilibrium with the two solids compressed (P > 0, δ > 0), let us decrease progressively the imposed displacement ∆. One encounters generally a progressive reduction of the area of contact A, i.e., a controlled rupture with G = w and (∂G/∂A)∆ > 0 until a critical displacement ∆c where (∂G/∂A)∆ = 0. Beyond this point the equilibrium becomes unstable, and the crack spontaneously propagates at ∆c = const. until the complete separation. It propagates with a crack extension force G – w which increases in proportion as A decreases (since (∂G/∂A)∆ < 0). This instability point on the equilibrium curve P(δ) corresponds to the point where d∆/dδ = 0, i.e., after Equation 4.7 to:
km +
dP =0 dδ
(4.10)
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On the equilibrium curve P(δ) the stability ends with a horizontal tangent at fixed load P (km = 0), and with a vertical tangent at fixed displacement δ (km = ∞). The critical load Pc corresponding to the limit of stability of the system:
G=w ∂G ≤0 ∂A defines the pull-off force of the two solids in contact, force which generally depends on the stiffness km of the measuring apparatus. In some geometries and in some loading conditions, the equilibrium is always unstable; as soon it is reached the crack propagates spontaneously (at constant loading conditions), and the criterion defining adherence is simply reduced to G = w. It is the case, as we will see, for the double cantilever beam at fixed load, or the flat punch on an elastic half-space. It is also the case for the classical Griffith crack in an infinite solid, as seen above.
4.3.2 Example of the Flat Punch The problem of the adherence of a flat punch was solved for the first time by Kendall (1971) by a balance of energy. Let us consider, Figure 4.3, an axisymmetric punch with a flat end, of radius a, pressing an elastic half-space. The penetration δ of the punch and the stress distribution in the area of contact were computed by Boussinesq in 1885, and are:
δ=
σz = −
2P 3aK
P 1 2πa 2 1 − r 2 a 2
(4.11)
(4.12)
where
1 3 1 − ν12 1 − ν22 = + K 4 E1 E2
(4.13)
(E and ν are the Young’s modulus and Poisson’s ratio of the elastic half-space). Note that the compressive stress is infinite on the edge of the contact. The same formulae can be applied when adhesion forces maintain the contact over a circle of radius a, while one pulls with a force P (Figure 4.3b). Compressive stresses become tensile stresses, infinite on the edge. To compute the energy release rate G, one must compute the mechanical energy (elastic plus potential) and its variation when the area of contact varies by dA. To vary the radius of the punch to study the variations of mechanical energy may not be the obvious way to proceed, but examination of Figure 4.3c shows that Equation 4.11 applies to the cause where the radius of contact a is smaller than the radius of the punch. One can thus study variations of elastic and potential energies for fluctuations of areas of contact at constant load P. For a load P and a radius of contact a, the energy release rate is:
G=
3Kδ 2 P2 = 3 8πa 6 πa K
Note that Equations 4.11 and 4.14 are the two equations of state of the system.
(4.14)
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P P b r δ a
uz
uz
[a]
δ a
[b]
Pc δc
a
P1 P2
δ
[uz] a
v1 v2
δ1
δ2
[d]
[c]
FIGURE 4.3 Analogy between the adherence of a circular flat punch to a half-space and the rupture of a deeply notched cylindrical bar.
The equilibrium defined by G = w is always unstable, for we have:
∂G ∂G P2 9 Kδ 2 <0 = 3 = − 2 5 = − ∂A δ ∂A P 4π a K 16 π2 a 3 Let us consider the unstable equilibrium of Figure 4.3c, under the load P. If a fluctuation temporarily increases the area of contact, G decreases, and as G < w, the crack recedes and the area of contact increases, reducing G still more. One deviates more and more from equilibrium, and the process stops when one reaches the edge of the punch. If, on the contrary, a fluctuation decreases the area of contact, G increases, and as G > w, the crack propagates and the area of contact decreases, increasing G more. The process stops only when a complete separation is obtained under this load P. Let us return to the adherence of the punch of Figure 4.3b. For P = 0, we have G = 0, but the area of contact cannot increase further. In proportion, the traction force P is increased, G decreases at constant a, until the equilibrium (unstable) G = w is reached under a critical load Pc. At this moment, a fluctuation can only decrease the area of contact, and this decrease continues until complete rupture under this load, Pc defined by G = w, i.e.,
Pc = 6 πa 3Kw
(4.15)
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Mode I
Mode II
Mode III
FIGURE 4.4
The three modes of displacement at a crack tip.
which is, by definition, the adherence force of a punch of radius a. Similarly, at fixed displacement, instability will appear at the critical displacement:
δc =
8πaw 3K
(4.16)
Note that this adherence force is not proportional to the area of contact, nor to the perimeter, nor to the energy of adhesion.
4.3.3 Mechanical Aspects 4.3.3.1 Stress Intensity Factors From the beginning, a crack was considered as a flattened cavity with stress-free walls. In this case the stress on the edge becomes infinite. The singularity in 1/ r of the stresses at a crack tip was pointed out by Sneddon (1946), and Irwin (1958) introduced the stress intensity factors KI, KII, KIII characterizing the force of the singularity for the three components of displacement at the crack tip* (Figure 4.4): mode I or opening mode, mode II or sliding mode, mode III or screw mode.
*One must beware of the fact that thee modes are defined by the local state at the crack tip, and cannot be deduced directly from the external loading. For example, when an axisymmetric punch is pressed onto the surface of a brittle solid, a vertical crack (Hertzian fracture) appears on the edge of the contact which is opened in mode I and not in mode II, as might be suggested by the geometry.
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Let us consider the Inglis elliptical cavity, with semi-axes a and b, and traversing a plate submitted at infinity to biaxial stresses: σ along Oy′ and kσ along Ox′. The ellipse centered at O has its major axis along Ox, which makes an angle β with Oy′. One knows the exact solution as well in stresses as in displacements (see Maugis, 1992b). When b tends toward zero, one obtains the Griffith crack, and the stresses around the crack tip, at
x = a + r cos θ y = r sin θ can be written
σx =
3θ 3θ θ θ θ θ 12 K I cos 1 − sin sin − K II sin 2 + cos cos + σn cos 2β + 0 r 2 2 2 2 2 2 2πr
σy =
3θ 3θ θ θ θ cos K I 1 + sin sin + K II sin cos + 0 r 1 2 2 2 2 2 2 2πr
τ xy =
θ θ 3θ θ 3θ cos K I sin cos + K II 1 + sin sin + 0 r 1 2 2 2 2 2 2 2πr
( ) ( )
1
( )
1
(4.17)
( )
1
with
KI =
(
)
1 m − n cos 2β σ πa 2
(4.18)
1 K II = n sin 2β 2
(4.19)
and m = 1 + k, n = 1 – k. These angular variations of stresses in mode I and II were given by Sneddon (1946) and Irwin (1958), and the stress intensity factors by Eftis and Subramonian (1978), generalizing the results of Sih et al. (1962) for uniaxial loading. The discontinuities of displacements ux , and uy , between the upper wall (θ = +π) and the lower wall (θ = –π) at a point of the crack are given by:
[u ] = κ µ+ 1 K y
[u ] = κ µ+ 1 K x
( )
(4.20)
( )
(4.21)
I
r +0 r3 2 2π
II
r +0 r3 2 2π
where µ is the shear modulus, ν is Poisson’s ratio and
κ=
3− ν 1+ ν
in plane stress
κ = 3 − 4 ν in plane strain
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In mode I, a crack opens with a parabolic shape. Equations 4.18 and 4.19 show that stress intensity factors are expressed in Pa· m. They must not be confused with stress concentration factors which are nondimensional. For a crack in mode I (β = π/2), we have simply
K I = σ πa
(4.22)
(but σx depends on the biaxiality of the constant term, also named the T-stress). It can be shown that terms in 1/ r for the stresses and terms in r for the displacements depend on the geometry of the system only by the KI and KII . The other terms of the power expansion are specific to the studied problem. These stress intensity factors play an important role in fracture mechanics, an interesting property arising from the superposition principle: for a given mode stress intensity factors are additive. They can be obtained directly, without knowing the exact solution, and one can compute them for a large number of geometries and loadings. Let us consider another example, useful for the following, that of an exterior circular crack (case of a deeply notched bar). Paris and Sih (1965) gave the stress intensity factor for a force P or a stress σ applied at infinity:
1 P P K I = σ πa = πa = 2 2 2πa 2a πa
(4.23)
Note that this is the result obtained by the power expansion of Equation 4.12 in function of t = a – r, with a sign plus since it is a traction, giving
σz =
P
1
2a πa
2πt
=
KI 2πt
Let us also examine the case where a uniaxial and constant pressure p is applied inside the crack on a length d = c – a such that it opens and propagates it. This internal loading leads to a stress intensity factor (Maugis, 1992a)
KI =
pa 2 m − 1 + m2 tan −1 m2 − 1 πa
(4.24)
with m = c/a > 1. The stress in the area of contact (ρ = r/a < 1) and the elastic displacement of the crack walls (ρ = r/a > 1) are given by
( )
σz r , 0 =
(
KI πa
1 1 − ρ2
)
+
2p m2 − 1 tan −1 π 1 − ρ2
(4.25)
min ( ρ , m ) 2 1 − ν2 ρ2 − t 2 2 −1 1 −1 1 2 2 uz = dt − 2 pa m − 1 ρ − 1 − cos K I πa cos −m 2 2 2 πE ρ ρ (4.26) t m −t 1
We will use these results for the contact of spheres.
∫
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4.3.3.2 Irwin Formula The work GdA to make the crack advance or recede corresponds to the work of stresses at the crack tip to open or close that crack. Irwin (1957) has shown the equivalence between the thermodynamic aspect and the mechanical aspect (or more precisely between G and K, since the notion of surface energy does not appear in the mechanical aspect), by computing the work of the singular stress, Equation 4.17, to close on da a crack of parabolic shape, Equation 4.20 and found
G=
1 − ν2 2 K1 E
K2 G= 1 E
plane strain (4.27) plane stress
This result is obtained with the following hypotheses: (1) propagation of the crack in its plane, (2) linear relationship between stress and strain, and (3) no interaction between crack walls. It must be emphasized that Equations 4.27 are not a definition of G, but an estimation of G within the above hypotheses. Their domain of validity is limited; it is that of the linear elastic fracture mechanics, LEFM. In a number of cases, stress intensity factors can be written in the form KI ≈ σ πa . If, in the absence of a crack, the sample is submitted to a constant stress σ, the density of elastic energy at any point is W = σ2/2E, and one can write G under the form G = kaW. We will see below how the Rice Jintegral will generalize the use of that elastic energy density. 4.3.3.3 Dugdale and Barenblatt Models The origin of these infinite stresses, physically unacceptable, arises from the purely elastic analysis of the problem, analysis in which the adhesion forces between neighboring surfaces (at right of the peak in Figure 4.1) are not taken into account. In fact they cannot be taken into account directly since they are not restoring forces: the stress decreases when the distance increases. One must use a stratagem. Dugdale (1960) and Barenblatt (1962) have shown how to eliminate these singularities: the adhesion or cohesion stresses acting between the walls of the crack can be seen as an inner loading, leading to a stress intensity factor Km compensating the stress intensity factor KI due to external loading. The terms in 1/ r for the stresses and in r for the opening of the crack disappear. Under loading, the crack takes the shape of a cusp (terms in r 3/2) and is no longer parabolic. The relation KI + Km = 0 ensures the continuity of stresses and determines the length d of the cohesion zone, but an equation is missing to calculate G since Equation 4.27 is no longer valid. This last equation was given by Rice (1968a,b). 4.3.3.4 Rice J-Integral Rice has introduced the following integral:
∫
J = Wdy − T ⋅ r
∂u ds ∂x
(4.28)
Where Γ is an open contour starting from the lower crack face and extending counterclockwise around the crack tip to a point on the upper surface (see Figure 4.5), starting point and arrival point being on → → free surfaces. T and u are stress traction vectors and displacements on the contour Γ, oriented along the outward normal. W is the density of elastic energy in any point of the solid (linear elasticity or not). This integral is independent of the contour Γ. Taking for Γ the external contour of the solid, one can show that J is identified with G. In the case where the walls of the crack are assumed to be without interaction (LEFM), it suffices to take for the contour a circular contour or radius r around the crack tip; when r tends toward zero only singular terms give a contribution and one recovers the Irwin result, Equation 4.29.
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E
D y
F A
B
FIGURE 4.5
h
x
Γ
C
Contours of Γ for the J integral.
If one now introduces a cohesion zone of length d such that singular terms disappear (Dugdale and Barenblatt models), and in which the stresses σ(u) are tensile stresses along Oy and function of the opening u, it suffices to take as contour Γ a line enclosing this cohesion zone. With dy = 0 (in undeformed state), and T = δ(u) on Γ, the J-integral reduces to:
J ≡G =
∂δ
∫ σ(u) ∂x dx d
(4.29)
0
with δ = u+ – u– the crack displacement. Let δt be the opening of the crack beyond which cohesion forces no longer act, termed the COD (crack opening displacement). We get
J ≡G =
δt
∫ σ(δ)dδ
(4.30a)
0
In the case where σ(u) = σ0 is constant in the cohesion zone (Dugdale model), we get:
J ≡ G = σ 0δ t
(4.30b)
4.4 Example: Contact and Adherence of Spheres Let us examine now how all the notions introduced in section 2 apply in the case of the contact and adherence of spheres. This problem is central in contact mechanics and tribology, and must be studied with great care.
4.4.1 Hertz Solution Assuming an elliptical distribution of pressure in the area of contact, Hertz showed in 1882 that the area of contact aH and the approach δH of two spheres of radius R1 and R2 under a load P just as the stress distribution in the area of contact were given by:
a H3 =
PR K
(4.31)
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δH =
σH = −
a H2 R
3P r2 1− 2 2 2πa H aH
(4.32)
(4.33)
with K given by Equation 4.13 and
1 1 1 = + R R1 R2 We limit ourselves to the case of a rigid sphere on an elastic half-space. Note that: (a) the penetration δH of the sphere in the half-space is twice the thickness of the portion of sphere of chord 2aH ; (b) that the radius of contact is zero under zero load; and (c) that the stresses cancel on the edge of the contact, which imposes a tangential connection between the sphere and the half-space. Note also (d) that the forcedisplacement relation is not linear and that the stored elastic energy under the load P is:
2 U E = Pδ H 5
(4.34)
Boussinesq showed in 1885 that, in the general case of a frictionless convex punch indenting an elastichalf space, the area of contact is generally unknown and that the problem can be solved by adding the condition that the normal stress σ2 cancels on the edge of the contact, which ensures a tangential connection between the punch and the half-space and determines the penetration δ of the punch. Any different value of the penetration leads to infinite stresses and to a discontinuity of displacements at the edge. Compressive singular stresses are impossible since they lead to interpenetration, whereas tensile singular stresses need the solids to be endowed with adhesion. This remark was apparently forgotten for almost a century.
4.4.2 JKR Solution It was only in 1971 that Johnson, Kendall, and Roberts (1971) published their theory of adherence of spheres (or sphere onto a plane), by making a balance of elastic energy UE, potential energy UP and surface energy US = –πa2w of the system. The calculation of elastic energy is rendered difficult by the fact that the surfaces are not conformal: adhesion forces distort the neighboring surfaces, and elastic energy is stored even under zero load. To evaluate it, JKR used a clever strategy. Let P1 be the apparent Hertzian load which would give the same radius of contact a as the one observed in the presence of surface energy. By definition, we have:
P1 =
a 3K R
(4.35)
To determine the penetration δ and the elastic energy UE stored under the load P, JKR used the loading path of Figure 4.6. Assuming no adhesion, apply the apparent Hertzian load P1 (point L). The radius of contact is then a, the penetration δ1 = a2/R, and the stored elastic energy the area OLMO. Reduce the load from P1 to P, making the radius of contact a constant and increasing the energy of adhesion up to w (point B). This unloading curve is a straight line (LB) since one works at constant area. Although we deal with a sphere, we have a flat punch displacement since the motion is made as a whole. The variation of penetration is thus given by Equation 4.11:
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FIGURE 4.6 JKR loading path. G = 0 from O to L, then da = 0 from L to B. The elastic energy stored at point B is the area OLBJO.
∆δ =
(
2 P1 − P
)
3aK
and the variation of elastic energy is given by the area of the trapezium LBJM. So, at point B, under the load P and in the presence of adhesion we get the elastic energy UE and the penetration
δ=
a2 2P + 3R 3aK
(4.36)
Derivating UE at constant displacement δ, or introducing the potential energy Up = –Pδ, the energy release rate is: 2
a 3K 2 R − P P1 − P 3K a2 = − = δ G= 8πa R 6 πa 3K 6 πa 3K
(
)
2
(4.37)
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Equations 4.36 and 4.37 are the equations of state of the system. At this stage the radius of contact a under the load P is still unknown. It will be determined by Griffith equilibrium condition G = w, which is the supplementary condition of Boussinesq, necessary to solve the problem. For w = 0 one recovers, as expected, Hertz results. Note that the loading path is the only one that allows us to obtain the elastic energy from a diagram (P, δ). Here also we can note that G could be obtained directly from the knowledge of the stresses on the edge of the contact. The distribution of normal stresses in the contact area results from the superposition on the same area of Hertzian stresses under the load P1, and the tensile stresses due to the flat punch movement, Equation 4.12, under the unloading P1 – P:
( )
σ z r ,0 =
P1 − P 1 3 P1 − 1 − ρ2 2 2 2 πa 2 2πa 1 − ρ
ρ <1
(4.38)
The stresses are compressive in the center and tensile on the edge, becoming infinite at r = a. The principal term of the power expansion in function of ρ = a – r is a function only of the punch unloading, and we have:
KI =
P1 − P
(4.39)
2a πa
hence Equation 4.37 by using the Irwin formula, Equation 4.27, which can be written for two different materials in the form:
1 1 − ν12 1 − ν22 2 G= + K E2 I 2 E1
(4.40)
We are correctly in the field of linear fracture mechanics. Stresses and displacement discontinuities in the JKR theory can be written:
( )
σ ρ, 0 =
[ ]
uz =
(
2 1− v2 πE
)K
I
KI πa
πa cos −1
1 1− ρ
2
−
3aK 1 − ρ2 2πR
ρ <1
1 a2 2 1 ρ − 1 + ρ2 − 2 cos −1 + ρ πR ρ
(
)
(4.41)
ρ >1
(4.42)
The connection between the sphere and the elastic half-space is now a vertical connection (opening of the crack in r ) The equilibrium relation G = w links two of the three variables, a, P, and δ, of the equation of state (36), and draws equilibrium curves a(P), P(δ), δ(a). In Figure 4.6 the equilibrium curve is the curve BCDO. One notes that, if starting from L, one regularly decreases the load, one cannot go beyond point C, whereas if one regularly decreases the penetration one cannot go beyond point D. These two instability points are defined by (∂G/∂A)P = 0 and (∂G/∂A)δ = 0. We get, for the adherence force:
3 Pc = − πwR at fixed load 2
(4.43a)
5 Pc = − πwR at fixed grips 6
(4.43b)
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FIGURE 4.7 Equilibrium relations between penetration δ and radius of contact a, in reduced coordinates. Superimposed are the curves at constant P, independent of w.
If the measuring apparatus has a stiffness km the limit of stability will be placed between C and D at a point where the tangent of the curve is –km, in agreement with Equation 4.10. Figure 4.7 displays the equilibrium relation δ(a), function of w, on which are superimposed the curves δ(a, P) independent of w, Equation 4.36. If, starting from the point L (P = 10), one decreases very slowly the load down to P = 0 (point N), one makes a controlled rupture at G = w following the equilibrium curve LN. If, on the other hand, one abruptly imposes an unloading at P = 0, one will observe an instantaneous elastic displacement at constant radius a from L to M, a point where G > w, then a crack propagation at P = 0 with a progressive return to equilibrium at point N. The curve marked “slowing down-acceleration” represents the locus of the points where (∂G/∂A)P = 0. If from point L one imposes an abrupt unloading at P = –5, one will observe a slowing down of the crack, followed by an acceleration until complete separation. Note that if one imposes an abrupt loading from N to L, one does not follow a path similar to LMN, since one cannot have G < 0. One will observe an instantaneous penetration NS at constant a, then the path ST at G = 0, along the Hertz curve, and finally a crack recession at P = constant, up to the point L (Maugis and Barquins, 1978a, 1980). We will return later to these crack propagation kinetics at fixed load. The JKR theory has been verified a number of times. The variation of contact area at zero load with the concentration of surfactant in a liquid allows us to draw the Gibbs adsorption isotherms (Haidara et al., 1995).
4.4.3 DMT Solution However, the JKR theory presents a difficulty: the adherence force Pc = – 3 πwR, independent of the 2 Young’s modulus, was incompatible with an old calculation by Bradley in 1932 giving an adherence force Pc = –2πwR between a rigid sphere and a rigid plane in point contact. In 1975 Derjaguin et al. (1975) gave a completely different theory, the DMT theory, in which adhesion forces act in an annular zone around the contact but do not deform the profile. In this theory, there are no singular stresses, the
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connection is tangent, and separation occurs when the contact is reduced to a point (thus without abrupt instability) under an adherence force Pc = –2πwR. A long controversy occurred when Tabor (1977), comparing both theories, emphasized that the main defect of the DMT theory was to neglect the deformations due to adhesion forces outside of the contact, whereas that of the JKR theory was to neglect these adhesion forces. Considering the height h of the discontinuity of displacements in the JKR theory, he proposed that one must pass continuously from one theory to the other in function of a parameter w2R/E2Z 03 where Z0 is the equilibrium distance between atoms. After an exchange of notes with Tabor, Muller et al. (1980) gave a self-consistent numerical calculation, using the Lennard–Jones potential and abandoning the hypothesis that adhesion forces do not deform the Hertzian profile. The result was a continuous transition from the DMT theory to the JKR theory when a parameter µ, proportional to the parameter introduced by Tabor, increases. The DMT theory applies when µ 1 (hard solids, small radii, weak adhesion) and that of JKR for µ 1 (soft solids, large radii, strong adhesion). As shown later (Muller et al., 1980), neither limit theory depends on the exact form of the interaction potential between the surfaces.
4.4.4 JKR–DMT Transition in a Dugdale Model In 1982, Barquins and Maugis (1982), used the theory of Sneddon (1965) for the contact of axisymmetric punches, in which a rigid body displacement χ(1) was cancelled to have zero stresses on the edge of the contact. They showed that, if χ(1) ≠ 0, the singularities of stresses and the discontinuities of displacement which appear are those of the fracture mechanics, with a stress intensity factor KI proportional to χ(1). Writing the classical relation between G and KI2, Equation 4.41, for plane deformation,* the JKR results appear immediately, not those of DMT. In fact, as recalled above, this relation is valid only in linear elastic fracture mechanics, when the interaction zone is negligible compared to a characteristic dimension of the system, here the radius of contact. Applying a Dugdale model (Barenblatt model where adhesion forces are assumed constant and equal to σ0 on an annulus of width d around the contact), one recovers the JKR–DMT transition, but this time with the advantages of analytic formulae (Maugis, 1992a). The method consists in calculating two stress intensity factors, the one KI due only to external loading (Equation 4.39) is that of the JKR theory; the other corresponds to a constant pressure acting on a length d = c – a in an external circular crack (Equation 4.24). Comparison of Equations 4.25 and 4.26 with Equations 4.41 and 4.42 shows that terms in KI are identical. If we replace the pressure p by –σ0 one obtains a negative stress intensity factor Km. One then adds the two loadings making
K I + Km = 0
(4.44)
which cancels the singular stresses, ensures the continuity of stresses, and fixes the length d. One can thus calculate the profile of the crack, and in particular its opening δt at the end of the cohesion zone at r = c (i.e., ρ = m)
δt =
(
)
a2 2 m − 1 + m2 − 2 tan−1 m2 − 1 πR +
(
4 1− v2 πE
)σ a 0
(4.45)
(
)
m2 − 1 tan−1 m2 − 1 − m − 1
The energy release rate is computed by the J-integral, which reduces here to σ0 δt , and the problem is solved by writing the equilibrium equation, G = w. In the calculation it appears as a parameter *Deformations are plane in the vicinity of an axisymmetric crack.
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FIGURE 4.8
JKR–DMT transition. Surface stress distribution for P = 3πwR and for various values of the parameter λ.
λ=
(
2σ 0 πwK 2 R
)
13
(4.46)
When λ → ∞, (c/a → 1) one recovers the JKR theory, and when λ → 0, (c/a → ∞), the DMT theory with an energy release rate
a 3K −P G= R 2πR
(4.47)
We have seen in Figure 4.1 that surface energy represents the work against two types of forces: first elastic forces, then adhesion forces. It could seem physically incompatible to have tensile stresses in an area of contact and no adhesion forces outside (JKR), or to have only compressive forces in an area of contact and adhesion forces outside (DMT). Figure 4.8, which displays the stress distribution in surface, allows us to understand the difficulties carried by these two limit cases. The JKR theory which is an LEFM theory, corresponds to the limit λ → ∞, and we see that adhesion stresses outside the area of contact are reduced to a peak infinitely narrow of zero measure. (One could say that the joining point of stresses on the edge of the contact is reported at infinity.) The total adhesion force outside the contact being zero, the integral of stresses in the area of contact is equal to the applied load P, and negative loads are sustained by tensile elastic stresses. In the theory of DMT (λ → 0) the stress distribution is assumed to be Hertzian in the contact. The adhesion forces must tend toward zero to have the continuity of stresses on the edge, but their integral is finite and the total attraction force outside the contact is 2πwR. The integral of normal stresses in surface is then P + 2πwR, and negative loads are sustained by adhesion forces outside the area of contact. Figure 4.9 displays the equilibrium curves a(P) as a function of the parameter λ. One observes a continuous transition from the JKR theory to the DMT theory when λ decreases. The last equilibrium
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FIGURE 4.9 Equilibrium radius of contact vs. applied load, in reduced coordinates, for various values of the parameter λ. The Hertz curve is shown for comparison.
FIGURE 4.10 Profile of the air gap for P = 0 and for various values of the parameter λ. This is also the shape of an elastic sphere on a rigid half space. The dashed line shows the increase of the crack opening displacement δt and of the ratio c/a when λ decreases. The parabolic approximation for the JKR profile is also given in the dashed line.
radii of contact at fixed load or fixed grips (defining the corresponding adherence forces) are depicted by dotted lines on the JKR curve. The Hertz curve is given for comparison. Figure 4.10 displays the crack profile for P = 0 and the transition of the crack tip shape from the vertical to the tangential when λ decreases.
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4.4.5 Application to a Liquid Meniscus A liquid meniscus at the edge of a contact is a perfect example of a Dugdale zone where the constant pressure σ0 is the Laplace pressure, and, as a matter of fact, experiments with crossed mica cylinders (geometry similar to sphere/plane geometry) had shown that a liquid meniscus changes the shape of the profile in the vicinity of the contact (Israelachvili, 1992; Christenson, 1985, 1988). These experiments have been repeated with great precision by Maugis and Gauthier-Manuel (1994) and are in good agreement with the above theory.
4.5 Liquid Bridges When the contact between the solids has disappeared, the meniscus is transformed into a liquid bridge which also give an adherence. The exact calculation of that force is difficult but is simplified for small volumes of liquids for which one can use a circular approximation of the meniscus. This attraction force is due both to the Laplace pressure and to the surface tension of the liquid (Fischer, 1926; Heady and Cahn, 1970), but as the second term is negligible for small volumes, one can evaluate the adherence force by fracture mechanics (Maugis, 1987b, 1991), using a Dugdale model with a Laplace pressure σ0 = γ/ρ (where ρ is the radius of the meniscus) acting at the tip of an external crack with an opening of δt = 2ρ cos θ. We get
G = σ 0δ t = 2γ cos θ
(4.48)
Let us take a rigid punch with a profile f(r) and let b equal the wetted radius and z the separation between the punch and a rigid plane. One can compute the energy release rate G from the potential energy Up = –Pz:
∂U P P dz G= =− 2πb db ∂A P As a first approximation, take a cylindrical liquid bridge of constant volume V:
() ∫
V = πzb2 z +
()
b z
()
2πrf r dr
0
With the condition dV/dz = 0, G becomes
G=
()
P z+ f b πb2
(4.49)
Equating Equations 4.48 and 4.49 one obtains the force P as a function of the separation z. For a flat punch, f (r) = 0, we get the classical result:
P=
2πb2 γ cos θ z
(4.50)
For a sphere, f (r) = r2/2R:
P=
a result given by Israelachvili (1992).
4 πγR cos θ 2zR 1+ 2 b
(4.51)
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For a cone of semi-angle β, f (r) = r/tan β:
P=
1πγb tan β z tan β 1+ b
(4.52)
This last equation is an approximation for large β of an expression given by Coughlin et al. (1982) for the case z = 0. For two spheres, evaluation of the liquid volume leads to
P=
2πγR cos θ zR 1+ 2 b
(4.53)
Since experiments are generally made at constant volume, let us introduce the volume V in the previous equations, with V = πb2z for two parallel plates, V = πb2z + πb4/4R for a sphere and a plane, V = πb2z + πb4/2R for two spheres. Equations 4.50, 4.51, and 4.53 become
P=
2Vγ cos θ z2
1 P = 4 πγR cos θ1 − V 1+ πRz 2
1 P = 2πγR cos θ 1 − 2V 1+ πRz 2
two plates
(4.54)
sphere plane
(4.55)
sphere sphere
(4.56)
which are decreasing functions of z. Figure 4.11 displays the equilibrium curves P(z) for a sphere and a plane. The stability of equilibrium depends on the stiffness km of the measuring apparatus and can be studied either by (∂G/∂A)∆ or by Equation 4.10. The second method is more direct and shows that equilibrium is stable if km > –dP/dz. For a liquid bridge between a sphere and a plane, for example, the initial slope is
dP πR 3 = −k0 = − 4 πγ cos θ V dz z = 0 It is only if km > k0 that the curve can be entirely followed, eventually up to the point where dP/dz = –km again, as for the curve drawn in the dashed line. This shape arises from the fact that, for a given volume, there are two solutions for the gorge radius (Erle et al., 1971; Fortes, 1982; Boucher et al., 1982; Lian et al., 1993). The criterion of stability at fixed grips is the point where the two solutions converge (Lian et al., 1993), the point with a vertical tangent on the curve P(z). If km < k0 the equilibrium at fixed ∆ is unstable for z = 0, and one jumps along the straight line
P = 4 πγR cos θ − km z
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FIGURE 4.11 Force-displacement equilibrium curve for liquid bridges between a sphere and a plane for various values of the reduced volume V/πR3 of the liquid bridge. Stable equilibria can only be observed for stiffness km of the measuring apparatus larger than –dP/dz.
down to the point where it cuts the equilibrium curve, which can be followed until the rupture. If this straight line does not intersect the equilibrium curve, the adherence force is simply P = 4πγR cos θ. Some experimenters have observed an instability at z = 0 (McFarlane and Tabor, 1950; O’Brien and Hermann, 1973; Fisher and Israelachvili, 1980), others extended equilibrium curves (Mason and Clark, 1965; Hotta et al., 1974). When one studies the contact of a sphere with a meniscus, one can thus expect two jumps: the first at the limit of stability of the solid–solid contact, the second at the limit of the stability of the liquid bridge (depending on the volume of the liquid). We must note that in this cylindrical approximation of the liquid bridge, the adherence force at z = 0 is independent of the volume of the liquid bridge. In fact a circular approximation for the meniscus or an exact solution (Mazzone et al., 1986) shows that it decreases with the volume. In such experiments one must take care to avoid viscous effects. For a liquid bridge between two parallel plates, for example, the Stefan law, modified by Healey (1926) tells us that the time to separate two plates from z1 to z2 with a force F is
t=
3πηb 4 1 1 − 2 2 8F z1 z 2
i.e., that the viscous force is:
F=
3ηV 2 dz 2πz 5 dt
an equation given by Dienes and Klemm (1946) (see also Trahan et al., 1987). For a liquid bridge between a sphere and a plane, the viscous force was given by Matthewson (1988) under the form
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2
2zR z˙ F = 6 πηR2 1 − 2 b z The influence of the viscosity on the adherence due to liquid bridges was clearly shown by McFarlane and Tabor (1950) and can be suspected in experiments by Mason and Clark (1965) on oil bridges.
4.6 Adhesion of Rough Elastic Solids — Application to Friction The JKR theory is well verified on soft elastic materials, like rubber, but experiments on harder materials only revealed a very weak adherence. The explanation was given by Johnson (1975) and Fuller and Tabor (1976). On rough surfaces there is a competition between compressive forces exerted by the contact of higher asperities and the attraction force exerted by the contact of lower asperities, so that on hard elastic solids the least roughness decreases the adherence force. Fuller and Tabor (1976) used the model of Greenwood and Williamson (1966): a surface of nominal area A0 having N asperities is in contact with a smooth rigid plane. Asperities have all the same radius of curvature R and have a Gaussian distribution of height with a standard deviation σ
()
φz =
z2 exp − 2 2σ σ 2π 1
Where φ(z)dz is the probability for an asperity to have a height between z and z + dz above the plane defined by the mean height of asperities. If all the spheres were at the same level (σ = 0), the adherence force should be NPc = 3 NπwR. If σ ≠ 0, the more stretched asperities pull off first, as soon as their 2 elongation reaches δc, critical elongation at fixed grips (roughnesses individually behave as if they are submitted to a fixed grips motion). The pull-off force between the two surfaces is given in the dotted line in Figure 4.12, as a function of the adhesion parameter σ/δc. The modified parameter
θ=
9π σ E * R1 2σ 3 2 = wR 8 3 δc
32
Where E* = E/(1 – ν2), is, except for a coefficient, the ratio of the force needed to deform the asperity by a quantity δ = σ to the adherence force of that asperity. For metals, even clean, the Young’s moduli are so large that standard deviations less than a few tens of Ångströms should be necessary to have an adhesion parameter less than one. There is no difficulty in making a similar calculation for contacts of the DMT type. The result (Maugis, 1996) is rather similar and is displayed in the solid line in Figure 4.12. Due to adhesion forces around the contact, an overload Z appears which must be added to the load P applied by the experimenter. This overload certainly plays an important role in the friction of solids. An analogy can be made with magnetic forces. The friction coefficient f = T/P of steel on steel is about 0.2, but if the rider is magnetized, the friction coefficient increases enormously. The mechanisms of dissipation have not changed, but the load on asperities is now the applied load plus the overload due to magnetic forces. If T is the friction force and P the applied load, the friction coefficient µ should be defined by
(
T =µ P+Z
)
(4.57)
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FIGURE 4.12 Elastic contact of a rough surface on a smooth rigid plane. Normalized adherence force F/NPc as a function of the parameter σ/δc. In the dotted line, the theory of Fuller and Tabor for JKR contacts; in the solid line, the theory for DMT contacts.
FIGURE 4.13 DMT contacts. The total load Z + P as a function of the applied load P, for various values of the adhesion parameter θ. Normalized coordinates. Dashed line: the limit of stability (pull-off force).
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and the shape of the friction curve T vs. P should be that of Figure 4.13. A similar equation has been repeatedly proposed in the past with Z a constant adherence force, so that the equation looks like the two-term Coulomb law
T = k + µP
(4.58)
(see Tabor, 1975 and Derjaguin, 1988). Such equations account for friction under negative load. In the present theory Z is not the adherence force and it increases with the applied load P since the number of contacts increases, and thus the overload.
4.7 Kinetics of Crack Propagation We have seen that a crack in an elastic solid is in equilibrium if G = w. If G > w the crack advances, if G < w the crack recedes. G – w is the thermodynamic force which makes the crack advance. In a solid without dissipation, a crack subjected to a constant force G – w would constantly accelerate until the Rayleigh waves velocity is reached. However, such nondissipative materials do not exist. First, a real material can have a term of static friction ψ such that the crack only advances if G – w > ψ, giving the appearance of a large energy of adhesion G0 = w + ψ, and leading to hysteresis between crack advance and crack recession. This is the case when there is plastic deformation or polymer chain extraction. Secondly, when G > G0, the crack assumes a velocity depending on dissipative processes, as a ball falling in oil. (Of course, if (∂G/∂A) ≠ 0, G varies during propagation with the velocity.) So we are led to write in a very general manner
G −w =
dU d1 dU d 2 dU K + +L+ dA dA dA
(4.59)
where Ud1, Ud2, … are the dissipation energies (depending or not on the velocity) and UK the kinetic energy. A first type of dissipation, very general, can be understood from the Barenblatt model. When a crack propagates at a velocity ν, the peak of stress at its tip moves with it, and a volume element neighboring its trajectory undergoes a cycle stress when the crack tip moves near it,* cycle whose characteristic duration is about d/ν (where d is the width of the stress peak) and whose magnitude is proportional to the theoretical stress, hence to w. Energy is lost in such a cycle,** and the crack undergoes a drag proportional to w (as proposed for the first time by McLean [1957] for plastic dissipation in intergranular fracture of metals), and function of the crack velocity. Besides internal friction in the vicinity of the crack tip, other types of dissipation can be added. When the crack propagates in a liquid medium, viscosity can impede the opening of the crack and cause a Newtonian drag which can be larger than the internal drag above a given velocity (see Michalske and Frechette [1980] for fracture of glass and Carré and Schultz [1985] for peeling). One can also have dissipation in the bulk of the material, at a distance from the crack. In the case of the peeling of a *One can make the analogy with the drag of a cylinder (nonadhesive) rolling on a viscoelastic material. This drag arises from the energy dissipated in bulk during the passing of compressive stresses below the roller. This drag tends toward zero at very low or very high velocities and is maximum for velocities around a/τ where a is half the contact width and τ the relaxation time. This maximum correlates with the maximum of tan δ taking as period T = 3.4 a/V is the duration of passage of a volume element below the roller (see Hunter, 1961; Johnson, 1985). **This internal friction can have various origins: thermal diffusion between compressed and stretched volume elements (thermoelasticity), diffusion of interstitial atoms toward octahedric sites in face-centered crystals (Snoek effect), stress-induced migration of alkali cations in glasses, oscillations of pinned dislocations in metals (Granato–Lucke effect), etc.
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viscoelastic band, for example, energy can be dissipated in the transitory flexion of the band when the interfacial crack advances, and whose importance depends on the band thickness. In the case of a ball or cylinder rolling on an elastomer, losses by deformation of the bulk must be added to dissipation at the edge of the contact (Roberts, 1979, Zaghzi et al., 1987). Finally, in the case of polymers the essential part of the dissipation can arise from the work of extraction of fibrils (crazes) or polymeric chains. For some years a great deal of attention has been focused on the role of these connectors (Raphaël and De Gennes, 1992; Creton et al., 1992, 1994; Brown, 1993; Brochard-Wyart et al., 1994; Deruelle et al., 1994).
4.7.1 Case of Viscoelastic Solids Let us examine first the case of adherence of viscoelastic solids where the only dissipations are localized at the crack tip. As said above, a crack submitted to a constant force G – w undergoes a drag proportional to w and function of its velocity ν and one can write the phenomenologic equation (Mueller and Knauss 1971; Andrews and Kinloch, 1973; Maugis and Barquins, 1978b).
( )
G − w = wφ aT ν
(4.60)
which generalizes for any geometry the equation given by Gent and Schultz (1972) for the peeling in various liquids. aT is the WLF translation factor (Williams et al., 1955) for the velocity–temperature equivalence, given by
log aT = −
(
8.86 T − TS
)
101.6 + T − TS
(4.61)
where TS = Tg + 50 (Tg is the temperature of viscous transition), used for the first time in fracture mechanics by Mullins (1959) for tearing of rubber, and by Kaelble (1960) for peeling. So, in Equation 4.60 surface properties (w) and viscoelastic properties are completely decoupled from elastic properties, geometry, and applied loadings which appear in G. The dimensionless function φ(aTν) is characteristic of crack propagation in mode I. Once this function is known, Equation 4.60 allows us to predict the kinetics of pull-off at fixed load, fixed grips, or fixed cross-head velocity. Equation 4.60 has been verified for adherence of glass/polyurethane on various geometries where G could be computed (sphere, flat punch, flat-ended sphere, peeling) at various temperatures. Whatever the studied geometry, one obtains the same master curve, which shows the advantage of fracture mechanics. Adsorption of water decreases the Dupré energy of adhesion w, and thus viscoelastic losses in agreement with Equation 4.60. This point was verified by measuring the rolling resistance of a glass cylinder rolling on an inclined plane as a function of the velocity for various room humidities (Roberts, 1979; Maugis and Barquins, 1980). In this geometry we have essentially a π/2 peeling at the rear of the cylinder (the points of the cylinder follow a cycloid). The result is a translation of the logG–logν curves with humidity. As in these experiments we have G w, this translation clearly arises from the multiplicative term w in the right-hand side of Equation 4.60, in agreement with earlier results for peeling in various liquids (Gent and Schultz, 1972) or on various substrates (Andrews and Kinloch, 1973). So, logG–logν curves are horizontally shifted to the right when temperature increases (due to the aT factor) and shifted down when the Dupré energy of adhesion decreases.
4.7.2 Experiments of Fixed Cross-Head Velocity — Tackiness Adherence of solids is more often studied with a testing machine at constant cross-head velocity than at fixed load or fixed grips, but the kinetics of detachment is more difficult to interpret since the testing machine makes two parameters vary simultaneously: displacement ∆ and crack length. The variation of G with time is given by:
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FIGURE 4.14 Adherence of a glass ball on polyurethane measured with a traction machine. Influence of the cross· · head velocity δ on the recorded force. The JKR equilibrium curve (for δ → 0) is shown in the dotted line. Points C and D correspond to quasistatic adhesion force at fixed load and at fixed grips. (Modified from Barquins, M. and Maugis, D. (1981), Tackiness of elastomers, J. Adhesion, 13:53-65.)
dG ∂G ˙ ∂G ˙ = ∆+ A dt ∂∆ A ∂A ∆
(4.62)
At the beginning G is low and the crack advances slowly, the first term prevails, and the recorded force increases. Then, as the crack accelerates, the second term prevails and the recorded force decreases. The maximum which results from the competition between the two effects has no physical signification. · Let us examine the case of a glass ball on a rubber half-space, pulled with the velocity ∆ by a testing machine of stiffness km (Barquins and Maugis, 1981). This experiment corresponds to the practical determination of tackiness, a normalized test since it depends on a number parameters and is without a theoretical model, and whose simplified version is the thumb test (one puts a thumb on a material and withdraws it to see if it sticks). To solve the problem we have the two equations of state of the system, · · Equations 4.36 and 4.37, the equation of propagation Equation 4.60, and the relation between δ and ∆ extracted from Equation 4.7. A numerical computation allows us to have P as a function of t (i.e., of ∆). The comparison between theory and experiment is very good. Figure 4.14 (for km infinite) shows that · the maximum force recorded essentially depends on the imposed velocity δ. The dotted curve corresponds to quasistatic unloading (see Figure 4.6) and the point D is the adherence force at fixed grips (F = 65 πwR). One can see that great influence of the viscoelastic dissipation on the adherence and how much care
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FIGURE 4.15 G(ν) curve seen as the superposition of an elastic solution with G increasing as the Rayleigh velocity is approached, and a broad peak due to viscoelastic losses.
· must be taken when using a testing machine. Confusion between the curve at δ = 1 µm/s with the equilibrium curve would lead to a very large apparent adhesion energy.
4.7.3 Branch with Negative Resistance: Velocity Jump and Stick-Slip The relation between the form of the function φ(aTν) and the viscoelastic properties of a material is a problem still unsolved. Mullins (1959) had shown, for the tearing of various elastomers, that there is a linear relation between rupture energy G at given temperature and velocity with the imaginary part of the complex shear modulus measured at the same temperature and a given frequency. For the adherence of glass on polyurethane a strong correlation was found by Maugis (1982) between variation of G with crack velocity, G ∝ (aTν)0.6, and variation of the imaginary part of the Young’s modulus E″ ∝ ω0.6, at low frequency. Let us study the implications of such a negative resistance branch in the G(ν) curve. This curve can be seen as the superposition of an elastic solution with G increasing when ν approaches the velocity cR of Rayleigh waves and a wide peak due to viscoelastic losses (Figure 4.15). Branches with positive slopes correspond to stable propagation, i.e., if a small perturbation temporarily increases the velocity, the dissipation increases and the crack returns to its initial velocity. The branch AC, on the other hand, corresponds to unstable propagations and cannot be observed. In fact, the behavior depends on the stability of the studied geometry. If geometry and loading are such that (∂G/∂A) < 0, G and thus ν increase with the crack length up to a value Gc , νc (point A) where the velocity abruptly jumps (with acoustic emission) on the second branch with positive slope. This value Gc is the critical energy release rate for catastrophic fracture, and is a characteristic of the material. We are thus faced with three characteristic values of G: w, G0 , Gc . This catastrophic fracture is thus always preceded by a slow propagation (subcritical) as clearly noted, perhaps for the first time, by Rivlin and Thomas (1953) in the case of the rupture of rubber. This subcritical propagation can pass unnoticed if νc is low and extends a fraction of mm only. This criterion of catastrophic propagation for ν = νc can be written G = wc (with wc a thousand times w in the case of rubber) but absolutely cannot be confused with the Griffith criterion of equilibrium. The value Gc must not be deduced from the maximum of the recorded force in a tensile machine at constant cross-head velocity, since this maximum can be observed in the subcritical crack propagation regime (Margolis et al., 1976, Maugis, 1985). For many decades, velocity jumps have been observed by a number of experimenters (see Maugis, 1985), and a hysteresis between the velocity jump AB for an accelerating crack and the velocity jump CD for a crack which decelerates was observed by Kobayashi and Dally (1977) in epoxy resins.
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If the geometry and the loading are such that (∂G/∂A) > 0, the crack propagation can be controlled and the crack velocity imposed. If, however, one tries to impose a velocity V between νc and ν2 in the negative resistance branch, a phenomenon of stick-slip motion appears. According to the simple model of relaxation oscillations proposed a number of times (Clark and Irwin 1966; Williams et al., 1968; Williams, 1984), and classical in friction, the first branch is followed up to Gc (point A, Figure 4.15) where the velocity νc is too low, so that the velocity jumps to ν1 (point B) where it is too fast; the crack slows down until point C where the velocity ν2 is still too fast. Then the velocity jumps to point D where the crack appears arrested. Therefore the velocity increases up νc, and so on. In this periodic stick-slip motion, most of the time is spent on the branch DA of low velocities and the recorded force has a sawtooth shape, with Pmax giving classically Gi or Ki for crack initiation and Ga and Ka for crack arrest. Maugis and Barquins (1988) have studied the stick-slip in peeling using adhesive rollers and the results were in agreement with the above model. This model accounts for the frequencies observed in the range of velocities V, for the acoustic emission at each jump, for the marks let on the band at each cohesive–adhesive transition (allowing an independent period measurement), but does not explain why the amplitude of oscillations decreases when V increases, why oscillations are sinusoidal, or why the marks on the band disappear at high velocity. For that purpose it is necessary to introduce the inertia of the system. The relaxation cycles are replaced by limit circling including point A or point C, or both, with the possibility of chaotic motion when a third degree of freedom is added, like the peel angle (Maugis, 1987a; Hong and Yue, 1995).
4.7.4 Examples of the Additivity of Dissipations 4.7.4.1 Viscous Drag When a crack propagates in the presence of a viscous liquid, this liquid can decrease the energy of adhesion at the crack tip, giving a translation of G(ν) curves, as seen above. But beyond a given velocity, the drag due to hydrodynamic phenomena inside the crack can be larger than the drag wϕ(ν) due to internal friction. In this case a knee arises in the G(ν) curve and one follows the curve corresponding to viscous drag until cavitation appears. The crack then propagates without contact with the liquid medium, and one follows the G(ν) curve for propagation in air, as shown by Carré and Schultz (1985) for peeling of elastomers in oils of various viscosities. The curve for viscous drag can even cross the G(ν) curve for propagation in air, with a velocity jump when cavitation occurs, as observed by Michalske and Frechette (1980) for the fracture of glass in water. 4.7.4.2 Bulk Dissipations Let us take the example of a cylinder of mass M and length b rolling on an elastomer inclined by an angle β on the horizontal. The energy (potential) release rate is G = Mg sin β/b (Roberts and Thomas 1975, Kendall 1975). (One can view the rolling cylinder as an adhesive roller which unglues by rolling down: we have a peeling at π/2 under the load P = Mg sin β). Two types of dissipation exist. The first, in the bulk, as discussed in note 4 and which is independent of surface properties, the second in the vicinity of the crack tip, as in peeling. By decreasing the mass of the cylinder toward zero, the bulk term disappears, whereas, by spreading talc powder onto the surface, adhesion disappears. Zaghzi et al. (1987) have clearly shown that the two types of dissipation must be added, with the same factor aT , to have
( )
G = G0Φ aT ν
(4.63)
Figure 4.16 illustrates rolling on EPDM. For a mass of 15 g, bulk losses are negligible, and that curve, which can be represented by the equation
(
G = w 1 + αν0, 6
)
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FIGURE 4.16 LogG–logν curves for cylinders of various masses rolling on an elastomer (EPDM). For 15g the losses in the bulk are almost negligible, and this curve corresponds to peeling. (Modified from Zaghzi, N., Carré, A., Shanahan, M.E.R., Papirer, E., and Schultz, J. (1987), A study of spontaneous rubber/metal adhesion. I. The rolling cylinder test, J. Polym. Sci. Polym. Phys., 25:2393-2402.)
with w = 0,25 J/m2, corresponds to peeling alone. We must note that in Equation 4.63 G0 is not a true multiplicative factor since in a log–log diagram curves are not shifted in parallel when one changes G0. It is more explicit to retain the form
( )
G = w 1 + α aT ν
0, 6
( )
+g ϕ a ν 2 2 T
4.7.4.3 Chains or Fibrils Extraction When one has strong bonds between a substrate and a polymer, separation can occur with chains or fibrils extraction as in the fracture of bulk polymers. Energy dissipated in this process is to be added to the energy dissipated by internal friction by moving stresses (Maugis, 1995). Let us consider, as an example, the results of Ahagon and Gent (1975) concerning the peeling of polybutadiene on treated glass (Figure 4.17). These authors increased the density of covalent bond (primary bonds) by increasing the proportion of vinylsilane in ethylsilane during the glass treatment, so that the density of vinyl groups used for the bonding to glass could vary from 0 to 100%. They observed that curves are not shifted parallel to themselves in log–log coordinates, when one changes the density of primary bonds, but they converge at a high velocity of peeling, and that the upper curve is the same as for tearing of the elastomer. (Recall that Chang et Gent [1981] have shown that G0 linearly increases with the density of primary bonds up to a limit value G*0 characteristic of the bulk elastomer, and that the less the elastomer is crosslinked the higher G*0 , in agreement with the model of Lake and Thomas [1967].) Assume that two dissipative mechanisms coexist with the same factor aT for the velocity–temperature correspondence, but with different sensitivity to velocity, as for rolling seen above, and that the lower curve for 0% of vinylsilane (and thus no chemical bonds) corresponds to internal friction. Let us subtract from the three upper
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FIGURE 4.17 LogG–logν curves for the peeling of an elastomer on glass surfaces treated with a mixture of ethylsilane and vinylsilane: (0% vinylsilane [O], 50% vinylsilane [∆], 100% vinylsilane [] or nontreated [+]). (Data from Ahagon, A. and Gent, A.N. (1975), Effect of interfacial bonding on the strength of adhesion, J. Polym. Sci. Polym. Phys. Ed., 13:1285-1300.)
curves the values of the lower curve: one obtains three curves (dotted lines) which are vertically shifted when one increases the density of chemical bonds. We are thus tempted to write schematically
( )
( )
G − w = wϕ aT ν + Nf aT ν l
(4.64)
where the Nfl term is that proposed by de Gennes (1982) in his theory of chain suction (l is the chain length, f the force to extract it, and N the number of chains crossing the fracture plane unit area). Notice that this nonparallelism of logG–logν curves is observed only if the two dissipative phenomena are of the same order of magnitude. If dissipation by internal friction is negligible compared to the work of chain or fibril extraction, the curves would appear parallel and one would be tempted to write
( )
G = G0 Φ aT ν
(4.65)
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where G0 is, this time, a multiplicative factor and where Φ → 1 when ν → 0. At zero velocity Equation 4.64 is written
G0 = w + Nf0l
(4.66)
Note that the term Nf0l is identical to the σ0σt term of the Dugdale model (Equation 4.30b). In summary, it seems that two regimes must be distinguished. The first is where adherence is low, there are only losses by internal friction at the crack tip, and where equation
( ) [
( )]
G = wF aT ν = w 1 + ϕ aT ν
(4.67)
is well verified, giving parallel log–log curves when surfaces energy is modified. The second is where adherence is high, due principally to chain or fibril extraction and where Equation 4.65 is verified, giving parallel log–log curves when the measure of primary bonds is modified, but with ∆(aTν) ≠ F(aTν). 4.7.4.4 Remarks on Hysteresis It is clear that the dissipations at crack tip or in the bulk in a viscoelastic solid are of hysteresis origin; a volume element submitted to cycles of stresses dissipates more or less energy according to the imposed frequency. Another type of hysteresis, often described, that we will name static hysteresis, concerns the threshold fracture energy G0. We have seen above that hysteresis between advancing or receding cracks was negligible in glass or mica. In the case of JKR contacts we will say that a static hysteresis occurs if the contact area under load P is larger when obtained by unloading (crack advance) than by loading (crack receding). Very low crack velocity or very long times must be reached to ascertain whether hysteresis occurs or not. However, there are a number of cases where there is no doubt (see Kendall [1974] where hysteresis is very neat.) One generally admits that values of G obtained after increase of the contact area (receding crack) correspond to Dupré energy of adhesion, w, whereas the higher values G0 obtained by decrease of the crack area arise from a mechanism of chain extraction. Shanahan and Michel (1991) have shown, for glass-elastomer contacts, that the more the elastomer is cross-linked the lower G0, the value of w being independent of the degree of cross-linking, and that hysteresis disappears at high degrees of crosslinking. When loading and unloading are carried out in a quasistatic manner one obtains two curves a(P) both obeying the JKR relation (Chaudhury and Whiteside, 1991). Thus, when one speaks of adherence energy during advancing or receding, one must understand that equilibrium or pseudoequilibrium has been reached. Note that there always exists a dissymmetry between advancing and receding cracks. The thermodynamic “motive” G – w for crack advancing can be as high as demanded. On the other hand, as G cannot be negative, the motive w – G for crack receding cannot exceed w (so that the velocity of crack closing remains low). We have seen in Figure 4.7 that if one starts from an equilibrium point on the JKR curve and applies an overload, most of the path follows the Hertz curve (G = 0). The joining is tangent; there is no dissipation on the edge of the contact; and this path is almost instantaneous (Maugis and Barquins, 1978a). It is only after this quasi-instantaneous increase of the area of contact that a true crack slowly recedes. This dissymmetry explains the difference of kinetics between coming on and coming off experiments, but has no relation to the static hysteresis which could be observed.
4.7.5 Short Historical Background After Griffith, fracture mechanics expanded in a rather anarchic manner in various fields (glass, elastomers, metals) and the history of appearance of different concepts is rather involved. The first geometries studied were unstable. The Griffith criterion of equilibrium was confused for a long time with a criterion of catastrophic fracture, particularly for glasses where the critical fracture energy Gc for brutal fracture is slightly above the 2γ0 of glass in a vacuum. For other materials Gc can be higher by many orders of
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magnitude. For the catastrophic rupture of metals, Irwin (1948) and Orowan (1949) have generalized the Griffith relation by replacing surface energy with a fracture energy γp . Similarly but independently, the criterion of catastrophic rupture of rubber was written as
∂U E ∂A ≥ Tc δ by Rivlin and Thomas (1953), where Tc is the tear energy characteristic of the material and considerably larger than surface energy. However, they noted that catastrophic fracture was preceded by a slow propagation above a characteristic threshold T0 well below Tc (They obtained T0 = 3700 J/m2, compared with Tc = 13,000 J/m2.) Later, Greensmith and Thomas (1965) observed that T has not an single value but depends on the tear velocity, and gave the first G(ν) curves of the literature. In the field of glass, due to the confusion of the criterion for brutal rupture with the Griffith criterion, the slow propagation preceding brittle fracture (studied for the first time by Grenet, 1899), remained mysterious, as reflected by its names: static fatigue, retarded fractured, stress corrosion. The time to rupture in a static fatigue experiment was seen as the time for a defect to increase from subcritical size to the Griffith critical size (subcritical propagation). However the problem was that a crack of this size should close instead of propagate. Shand (1961) was probably the first, in the field of glasses, to draw the crack velocity as a function of the energy release rate (so, eliminating the crack length and the geometry) followed by Wiederhorn and Bolz (1870). Shand (1961) was also the first to affirm that this was the threshold value G0 , and not Gc , which was to compare with surface energy. (Nowadays the idea of a drag by internal friction to explain the subcritical growth, and despite the analogy with problems of adhesion [Maugis 1985, 1986], is not yet accepted by the scientific community working on glasses and ceramics, which prefers to keep the stress corrosion.) Concerning the kinetics of crack propagation in rupture and adherence of elastomers, it was remarked early that the peeling or tearing force strongly depends on velocity (Rivlin, 1944; Busse et al., 1946). Then Mullins (1959) for tearing and Kaelble (1960) for peeling used the WLF translation factor aT to have master curves. Introducing the energy release rate (named rupture energy θ), Gent and Kinloch (1971) showed that G(aTν) curves were independent of the tested geometry.* Gent and Schultz (1972), working with peeling elastomer bands at various velocities in various liquids, observed that log–log curves giving the peeling force as a function of velocity were parallel shifted by a quantity predicted by the reduction of Dupré energy of adhesion w, i.e., that the work of detachment W was proportional to w:
() (
W = wF ν = w 1 + kνn
)
(4.68)
Similarly Andrews and Kinloch (1973) studied adherence of rubber to various polymer substrates. They obtained, in log–log coordinates G(aTν) curves, all parallel to the tearing curve of rubber. From the threshold tear energy, they deduced the threshold adherence θ0, compatible either with a Dupré energy of adhesion when secondary bonds are present at the interface, or higher in the presence of covalent bonds, and proposed to write
( )
(4.69a)
( )
(4.69b)
G = w Φ aT ν or
G = G0Φ aT ν
*Following Rivlin and Thomas (1953), the interfacial or cohesive rupture energy, for a nonlinear elastic solid was evaluated from the density of stored elastic energy in the sample at the moment of propagation, a method not applicable to all geometries, particularly the adherence of a flat punch.
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An equation similar to Equation 4.69b was also given by Mueller and Knauss (1971) for the tearing of an elastomer. Maugis and Barquins have rewritten Equations 4.68 and 4.69a in the form of Equation 4.60, in order to separate clearly the thermodynamic driving force from the drag term. We have seen that one of the problems was the identity of the mechanisms and the dissipative functions in Equations 4.68 and 4.69. It remains to predict the form of functions F(aTν) and Φ(aTν) from the rheological properties of the materials.
4.8 Adhesion of Metals Metals have an elastoplastic behavior which complicates further adherence problems. Furthermore, clean metallic surfaces have high surface energies and make strong metallic bonds when in contact. Separation generally occurs by ductile rupture of the softer material, and adherence depends on rheological properties. If impurities are adsorbed onto the surfaces, the metallic bonds are screened, adhesion decreases strongly, and rupture will be adhesive rather than cohesive. Contact of clean surfaces must be avoided in friction, but is a necessary condition in cold welding.
4.8.1 Adhesion of Microcontacts When a hard sphere is progressively pressed on an elastoplastic half-space, it begins to elastically deform the half-space; then plastic deformations appear at the Hertz point (0, a/2) for a mean pressure pm = 1.1σ0 (σ0 is the elastic limit). The mean pressure continues to increase as the plastic zone develops, then remains constant and approximately equal to pm = 3σ0 = H when plastification reaches the surface (H is the hardness). In the presence of adhesion forces these deformations are enhanced. One can even have plastic deformation under zero load. After elastoplastic or full plastic contact (radius of contact af ) and elastic recovery, the adherence force F depends on the type of observed rupture. This rupture can be cohesive if the energy of adhesion is high, or interfacial, occurring after reduction or not of the radius of contact. These various points have been discussed in Maugis and Pollock (1984) and play an important role in the adhesion of particles (Rimai et al., 1994).
4.8.2 Cold Welding Milner and colleagues from 1959 to 1969 made a major contribution in explaining the mechanisms of cold welding (Milner and Rowe, 1962; Tylecote, 1968). It is the fragmentation of the oxide film and the extrusion of underlying clean metal through the cracks which explains cold-welding by co-rolling (Vaidyanath et al., 1959), punching, or torsion–compression. This extrusion is obtained above a deformation threshold varying from 10 to 90% depending on the metals. This threshold is lowered by preliminary scratch brushing with a metallic brush, by working in a vacuum (Sherwood and Milner, 1969), or by the reduction of oxide thickness (Cantalejos and Cuminski, 1972). Cave and Williams (1973) have shown in scanning microscopy how the metal was progressively extruded through fractured scratch-brushed layers in proportion as deformation increases, in cold welding by rolling. Adherence is more important the cleaner the metal in contact. A large proportion of virgin surface is immediately contaminated by impurities trapped at the interface and adheres poorly. It is necessary to have large deformation to disperse contaminants or to work in a vacuum (Sherwood and Milner, 1969). An important point is that if the friction coefficient between oxide films is high, these films break up coherently, extruding clean metal (Cantalejos and Cuminski, 1972; Osias and Tripp, 1966). This point was shown in an elegant manner by Osias and Tripp (1966) on plasticine models covered with brittle varnish.
4.8.3 Adhesion of Metals at High Temperature (Maugis, 1980) Experiments show that above a threshold temperature, adherence of metals strongly increases with temperature and contact time. This threshold decreases when the load increases, but a representative value is about 0.3 Tf where Tf is the absolute melting temperature. So, room temperature experiments are high-temperature experiments for indium, tin, and lead.
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When two metals come into contact under a given load, asperities compress one another and undergo plastic deformation and creep; the area of contact increases with temperature and contact time, as in a hot hardness experiment. Then, when the stress has sufficiently decreased, the area of contact increases by surface diffusion or diffusion along grain boundaries as in a sintering experiment. As these various mechanisms are thermally activated, the increase of the area of contact with temperature can be written:
A = A0e − QA
RT
(4.70)
where the activation energy QA can be deduced from the activation energies of these various mechanisms. In high-temperature contacts, strong metallic bonds are easily developed and separation generally occurs by creep rupture (cohesive rupture), so that the adherence force can be written, as for cold welding:
F = kAσ u
(4.71)
where σu is the ultimate tensile strength and k a factor linearly decreasing from 2 to 1 when the real area of contact increases. The proportionality between tensile strength and hardness (H ≅ 3σu ) is maintained at high temperature, so that σu has the same activation energy t QH as the hot hardness. In creep rupture, as in hot hardness, there is an equivalence between time and temperature, and master curves can be obtained by using the Sherby–Dorn parameter θ = t exp(–Q/RT) where Q is the activation energy for self-diffusion. Thus, creep rupture depends on time to rupture t, and the adherence force decreases when the rupture time increases. The adherence at high temperature is thus characterized by a competition between the increase of the area of contact by creep and sintering with time and temperature, and the decrease of mechanical properties with those parameters. These effects can be separated by measuring adherence at a constant temperature lower than that of contact, as in experiments by Polke (1969) or Gras (1989). In fact, the problem is rendered more complex by phenomena such as oxidation, oxide dissolution, segregation of impurities, interdiffusion, and phase transformation. Mutual solubility is not a condition of high adherence as believed some years ago, and insoluble pairs like Ag–Fe, Ag–Ni, and Pb–Au can have better adherence than soluble pairs like Ag–Au. Interdiffusion changes only the mechanical properties in the vicinity of the junction so formed; if they are improved, adherence increases, but the formation of brittle intermetallic compounds or the development of porosities by Kirkendall effect can reduce that adherence.
4.9 Conclusion This overview of mechanical aspects of adhesion leads to a rather coherent image. But in the details a number of points remain to be elucidated. One should know how to predict the threshold energy G0 and more generally the G(ν) curves from the mechanical properties of materials. Phenomena such as cavitation and crazes at crack tip remain to be clarified, and stick-slip is more complex that initially thought (Ryschenkoff and Arribart, 1996). Crack propagation in mixed mode is a subject still debated. Finally, despite recent progress (Kim and Kim, 1988; Williams, 1993; Moidu et al., 1995), we are still unable to take accurately into account elastoplastic deformations in the adherence of solids.
References Ahagon, A. and Gent, A.N. (1975), Effect of interfacial bonding on the strength of adhesion, J. Polym. Sci. Polym. Phys. Ed., 13:1285-1300. Andrews, E.H. and Kinloch, A.J. (1973), Mechanics of adhesive failure. I, Proc. London Ser. Soc. A., 332:385-399. Barenblatt, G.I. (1962), The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7:55-129.
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Barquins, M. and Maugis, D. (1981), Tackiness of elastomers, J. Adhesion, 13:53-65. Barquins, M. and Maugis, D. (1982), Adhesive contact of axisymmetric punches on an elastic half-space: the modified Hertz–Huber stress tensor, J. Méc. Théor. Appl., 1:331-357. Bhowmick, A.K., Gent, A.N., and Pulford, C.T.R. (1983), Tear strength of elastomers under threshold conditions, Rubber Chem. Technol., 56:226-282. Boucher, E.A., Evans, M.J.B., and McGarry, S. (1982), Capillary phenomena. XX. Fluid bridges between horizontal solid plates in a gravitational field, J. Colloid Interface Sci., 89:154-165. Brochard-Wyart, F., De Gennes, P.G., Léger, L., Marciano, Y., and Raphaël, E. (1994), Adhesion promoters, J. Phys. Chem., 98:9405-9410. Brown, H.R. (1993), Effects of chain pull-out on adhesion of elastomers, Macromolecules, 26:1666-1670. Busse, W.F., Lambert, J.M., and Verdery, R.B. (1946), Tackiness of GR-S and other elastomers, J. Appl. Phys., 17:376-385. Cantalejos, N.A. and Cuminski, G. (1972), Morphology of the interface of roll-bonded aluminium, J. Inst. Metals, 100:20-28. Carré, A. and Schultz, J. (1985), Polymer–aluminium adhesion. IV. Kinetics aspects of the effect of a liquid environment, J. Adhesion, 18:207-216. Cave, J.A. and Williams, J.D. (1973), The mechanisms of cold pressure welding by rolling, J. Inst. Metals, 101:203-207. Chang, R.J. and Gent, A.N. (1981), Effect of interfacial bonding on the strength of adhesion of elastomers. I. Self adhesion, J. Polym. Sci. Polym. Phys. Ed., 19:1619-1633. Chaudhury, M.K. and Whiteside, G.M. (1991). Direct measurement of interfacial interactions between semispherical lenses and flat sheets of poly(dimethylsiloxane) and their chemical derivatives, Langmuir, 7:1013-1025. Christenson, H.K. (1985), Capillary condensation in systems of immiscible liquids, J. Colloid Interface Sci., 104:234-249. Christenson, H.K. (1988), Adhesion between surfaces in undersaturated vapors. A reexamination of the influence of meniscus curvature and surface forces, J. Colloid Interface Sci., 121:170-178. Clark, A.B.J. and Irwin, G.R. (1966), Crack propagation behaviors, Exp. Mech., 6:321-330. Coughlin, R.W., Elbirli, B., and Vergara-Edwards, L. (1982), Interparticle force conferred by capillarycondensed liquid at contact points. I. Theoretical considerations, J. Colloid Interface Sci., 87:18-30. Creton, C., Brown, H.R., and Shull, K.R. (1994), Molecular weight effects in chain pullout, Macromolecules, 27:3174-3183. Creton, C., Kramer, E.J., Hui, C.Y., and Brown, H.R. (1992), Failure mechanisms of polymer interfaces with block copolymers, Macromolecules, 25:3075-3088. De Gennes, P.G. (1982), The formation of polymer/polymer junctions, in Microscopic Aspects of Adhesion and Lubrication, George, J.M. (Ed.), Elsevier, Amsterdam, 355. Derjaguin, B.V. (1988), Mechanical properties of the boundary lubrication layer, Wear 128:19-27. Derjaguin, B.V., Muller, V.M., and Toporov, Yu. P. (1975), Effect of contact deformation on the adhesion of particles, J. Colloid Interface Sci., 53: 314-326. Deruelle, M., Tirrell, M., Marciano, Y., Hervet, H., and Léger, L. (1994), Adhesion energy between polymer networks and solid surfaces modified by polymer attachment, Faraday Disc., 98:55-65. Dienes, G.J. and Klemm, W.H. (1946), Theory and application of the parallel plate plastometer, J. Appl. Phys., 17:458-471. Dugdale, D.S. (1960), Yielding of sheets containing slits, J. Mech. Phys. Solids, 8:100-104. Eftis, J. and Subramonian, N. (1978), The inclined crack under biaxial loading, Engng. Fracture Mech., 10:43-67. Erle, M.A., Dyson, D.C., and Morrow, N.R. (1971), Liquid bridges between cylinders, in a torus and between spheres, A.I.Ch.E.J., 17:115-121. Fischer, R.A. (1926), On the capillary force in an ideal soil: corrections of formulae given by W.B. Haines, J. Agric. Sci., 16:492-505.
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Fisher, L.R. and Israelachvili, J.N. (1980), Determination of the capillary pressure in menisci of molecular dimensions, Chem. Phys. Lett., 76:325-328. Fortes, M.A. (1982), Axisymmetric liquid bridges between parallel plates, J. Colloid Interface Sci., 88:338-352. Fuller, B.W. and Thomson, R.M. (1978) Lattice theories of fracture, in Fracture Mechanics of Ceramics, Vol. 4, Bradt, R.C., Hasselman, D.P.H., and Lange, F.F. (Eds.), Plenum Press, 507. Fuller, K.N.G. and Tabor, D. (1976), The effect of surface roughness on the adhesion of elastic solids, Proc. R. Soc. A, 345:327-342. Gent, A.N. and Kinloch, A.J. (1971), Adhesion of viscoelastic materials to rigid substrates. III. Energy criterion for failure, J. Polym. Sci., A-2. 9:659-668. Gent, A.N. and Schultz, J. (1972), Effect of wetting liquids on the strength of adhesion of viscoelastic materials, J. Adhesion, 3:281-294. Gent, A.N. and Tobias, R.H. (1982), Threshold tear strength of elastomers, J. Polym. Sci. Polym. Phys. Ed., 20:2051-2058. Gras, R. (1989). Etude de l’adhérence et du frottement à haute température du Nickel. Thèse d’Etat, Paris. Greensmith, H.W. and Thomas, A.G. (1955), Rupture of rubber. III. Determination of tear properties, J. Polym. Sci., 18:189-200. Greenwood, J.A. and Williamson, J.B. (1966), Contact of nominally flat surfaces, Proc. R. Soc. A, 295:300-319. Grenet, M. (1899), Recherches sur la résistance mécanique des verres, Bull. Soc. Encour. Ind. Nat., 4:838-848. Haidara, H., Chaudhury, M.K., and Owen, M.J. (1995), A direct method of studying adsorption of a surfactant at solid–liquid interface, J. Phys. Chem., 99:8681-8683. Heady, R.B. and Cahn, J.W. (1970), An analysis of the capillary forces in liquid-phase sintering of spherical particles, Metall. Trans., 1:185-189. Healey, A. (1926), Trans. Inst. Rubber Ind. 1-334. Hong, D.C. and Yue, S. (1995), Deterministic chaos in failure dynamics: dynamic of peeling of adhesive tape, Phys. Rev. Lett., 74:254-257. Hotta, K., Takeda, K., and Ilnoya, K. (1974), The capillary binding force of a liquid bridge, Powder Technol., 10:231-242. Hunter, S.C. (1961), The rolling contact of a rigid cylinder with a viscoelastic half space, Trans. ASME, J. Appl. Mech., 28:611-617. Irwin, G.R. (1948), Fracture dynamics, in Fracturing of Metals, Trans. ASM, Vol. 40 A, 147-166. Irwin, G.R. (1957), Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., 24:361-364. Irwin, G.R. (1958), Fracture, in Encyclopedia of Physics, Vol. IV: Elasticity and Plasticity, Flugge, S. (Ed.), Springer-Verlag, Berlin, 551. Irwin, G.R. and Kies, J.A. (1952), Fracturing and fracture dynamics, Welding Journal, 31:95-100. Israelachvili, J.N. (1992), Intermolecular and Surface Forces, 2nd ed., Academic Press, New York. Johnson, K.L. (1975), Non-Hertzian contact of elastic spheres, in The Mechanics of the Contact Between Deformable Bodies, ed. de Pater, A.D. and Kalker, J.J. (Eds.), Delft University Press, 26. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press, U.K. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London, Vol. A, 324:301-313. Kaelble, D.H. (1960), Peel adhesion, Adhesive Age, 3:37-42. Kendall, K. (1971), The adhesion and surface energy of elastic solids, J. Phys. D: Appl. Phys., 4:1186-1195. Kendall, K. (1974), Kinetics of contact between smooth solids, J. Adhesion, 7:55-72. Kendall, K. (1975), Rolling friction and adhesion between smooth solids, Wear, 33:351-358. Kim, K.S., and Kim, J. (1988). Elasto-plastic analysis of the peel test for thin film adhesion, Trans. ASME, 110:266-273. Kobayashi, T. and Dally, J.W. (1977), A system of modified epoxies for dynamic photoelastic studies of fracture, Exp. Mech., 17:367-374. Lake, G.J. and Thomas, A.G. (1967), The strength of highly elastic materials. Proc. R. Soc. Ser. A, 300:108-119.
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Lian, G., Thornton, C., and Adams, M.J. (1993), A theoretical study of the liquid bridge force between two rigid spherical bodies, J. Colloid Interface Sci., 161:138-147. Margolis, R.D., Dunlap, R.W., and Markovitz, H. (1976), Fracture toughness testing of glassy plastics, in Cracks and Fracture, ASTM STP 601, Philadelphia, 391. Mason, C. and Clark, W.C. (1965), Liquid bridges between spheres, Chem. Eng. Sci., 20:859-866. Matthewson, M.J. (1988), Adhesion of spheres by thin liquid films, Philos. Mag., 57:207-216. Maugis, D. (1980), Creep, hot hardness and sintering in the adhesion of metals at high temperature, Wear, 62:349-386. Maugis, D. (1985), Subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement, J. Mater. Sci., 20:3041-3073. Maugis, D. (1986), Subcritical crack growth, surface energy and fracture toughness of brittle materials, in Fracture Mechanics of Ceramics, Vol. 8, Bradt, R.C., Evans, A.G., Hasselman, D.P.H., and Lange, F.F. (Eds.), Plenum Publishing, New York, 255. Maugis, D. (1987a), Propagation saccadée de fissure en pelage, rôle de l’inertie, C. R. Acad. Sci. Paris, Série II, 304:775-778. Maugis, D. (1987b), Adherence of elastomers: fracture mechanics aspects, J. Adhesion Sci. Technol., 1:105-134. Maugis, D. (1991), Adherence and fracture mechanics, in Adhesive Bonding, Lee, L.H. (Ed.), Plenum Publishing, New York, 303. Maugis, D. (1992a), Adhesion of spheres: the JKR–DMT transition using a Dugdale model, J. Colloid Interface Sci., 150:243-269. Maugis, D. (1992b), Stresses and displacements around cracks and elliptical cavities: exact solutions, Engng Fracture Mech., 43:217-255. Maugis, D. (1995), On the additivity of losses of propagating cracks in polymer adhesion and tearing, J. Adhesion Sci. Technol., 9:1005-1008. Maugis, D. (1996), On the contact and adhesion of rough surfaces, J. Adhesion Sci. Technol., 10:161-175. Maugis, D. (May 1997), Adherence des solides. Aspects mécaniques, La Revue de Métallurgie–CIT Sciences et Génie des Matériaux, 655-690. Maugis, D. and Barquins, M. (1978a), Adhérence d’une bille de verre sur un massif viscoélastique: étude du recollement, C. R. Acad. Sci. Paris, Sér. B, 287:49-52. Maugis, D. and Barquins, M. (1978b), Fracture mechanics and the adherence of viscoelastic bodies, J. Phys. D: Applied Phys., 11:1989-2023. Maugis, D. and Barquins, M. (1980), Fracture mechanics and adherence of viscoelastic solids, in Adhesion and Adsorption of Polymers, Part A, Lee, L.H. (Ed.), Plenum Press, New York, 203. Maugis, D. and Barquins, M. (1988). Stick-slip and peeling of adhesive tapes, in Adhesion 12, Allen, K.W. (Ed.), Elsevier, London, 205. Maugis, D. and Gauthier-Manuel, B. (1994), JKR–DMT transition in the presence of a liquid meniscus, J. Adhesion Sci. Technol., 8:1311-1322. Maugis, D. and Pollock, H.M. (1984), Surface forces, deformation and adherence at metal microcontacts, Acta Metall., 32:1323-1334. Mazzone, D.N., Tardos, G.I., and Pfeffer, R. (1986), The effect of gravity on the shape and strength of a liquid bridge between two spheres, J. Colloid Interface Sci., 113:544-556. McFarlane, J.S. and Tabor, D. (1950), Adhesion of solids and the effect of surface films, Proc. R. Soc. London. A, 202:224-243. McLean, D. (1957), Grain Boundaries in Metals, Clarendon Press, Oxford. Michalske, T.A. and Frechette, V.D. (1980), Dynamic effect of liquids on crack growth leading to catastrophic failure of glass, J. Am. Ceram. Soc., 63:603-609. Milner, D.R. and Rowe, G.W. (1962), Fundamentals of solid phase welding, Metall. Rev., 7:433-480. Moidu, A.K., Sinclair, A.N., and Spelt, J.K. (1995), Analysis of the peel test: prediction of adherent plastic dissipation and extraction of fracture energy in metal-to-metal adhesive joints, J. Testing Eval., 23:241-253.
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Mueller, H.K. and Knauss, W.G. (1971a), The fracture energy and some mechanical properties of a polyurethane elastomer, Trans. Soc. Rheol., 15:217-233. Mueller, H.K. and Knauss, W.G. (1971b), Crack propagation in a linearly viscoelastic strip, J. Appl. Mech., 38:483-488. Muller, V.M., Yushenko, V.S., and Derjaguin, B.V. (1980), On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane, J. Colloid Interface Sci., 77:91-111. Mullins, L. (1959), Rupture of rubber, part IX: role of hysteresis in the tearing of rubber, Trans. Inst. Rubber Ind., 35:213-222. O’Brien, W.J. and Hermann, J.J. (1973), The strength of liquid bridges between dissimilar materials, J. Adhesion, 5:91-103. Orowan, E. (1949), Fracture and strength of solids, Rep. Prog. Phys., 120:185-232. Osias, J.R. and Tripp, J.H. (1966), Mechanical disruption of surface films on metals, Wear, 9:388-397. Paris, P.C. and Sih, G.C. (1965), Stress analysis of cracks, in Fracture Toughness and Testing Applications, ASTM STP 381, Philadelphia, 30. Polke, R. (1969), Adhesion of solids at elevated temperatures, in Adhésion et Physico-Chimie des Surfaces Solides, Colloque CNRS/DGRST, Soc. Chim. de France, p. 51-54. Raphaël, E. and De Gennes, P.G. (1992), Rubber-rubber adhesion with connector molecules, J. Phys. Chem., 96:4002-4007. Rice, J.R. (1968a), A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 90:379-386. Rice, J.R. (1968b), Mathematical analysis in the mechanics of fracture, in Fracture, Vol. 2, H. Liebowitz (Ed.), Academic Press, 191. Rimai, D.S., Demejo, L.P., and Bowen, R.C. (1994), Mechanics of particle adhesion, J. Adhesion Sci. Technol., 8:1333-1355. Rivlin, R.S. (1944), The effective work of adhesion, Paint Technol., 9:215-216. Rivlin, R.S. and Thomas, A.G. (1953), Rupture of rubber. I. Characteristic energy of tearing, J. Polymer Sci., 10:291-318. Roberts, A.D. (1979), Looking at rubber adhesion, Rubber Chem. Technol., 52:23-42. Roberts, A.D. and Thomas, A.G. (1975), The adhesion and friction of smooth rubber surfaces, Wear, 33:45-64. Ryschenkow, G. and Arribart, H. (1996), Adhesion failure in the stick-slip regime: optical and AFM characterizations and mechanical analysis, J. Adhesion, 58:143-161. Shanahan, M.E.R. and Michel, F. (1991), Physical adhesion of rubber to glass: cross-link density effects near equilibrium, Int. J. Adhesion Adhesives, 11:170-176. Shand, E.B. (1961), Fracture velocity and fracture energy of glass in the fatigue range, J. Am. Ceram. Soc., 44:21-26. Sherwood, W.C. and Milner, D.R. (1969), The effect of vacuum machining on the cold welding of some metals, J. Inst. Metals, 97:1-5. Sih, G.C., Paris, P.C., and Erdogan, F. (1962), Crack-tip stress intensity factors for plane extension and plate bending problems, J. Appl. Mech., 29:306-312. Sneddon, I.N. (1946), The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc. R. Soc. A, 187:229-260. Sneddon, I.N. (1965), The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, Int. J. Engng. Sci., 150:243-269. Tabor, D. (1975), Interactions between surfaces: adhesion and friction, in Surface Physics of Materials, Vol. II, Blakely, J.M. (Ed.), Academic Press, New York, 475. Tabor, D. (1977), Surface forces and surface interactions, J. Colloid Interface Sci., 58:2-13. Thomson, R., Hsieh, C., and Rana, V. (1971), Lattice trapping of fracture cracks, J. Appl. Phys., 42:3154-3160. Trahan, J.F., Wehbeh, E.G., and Hussey, R.G. (1987), The limits of lubrication theory for a disk approaching a parallel plane wall, Phys. Fluids, 30:939-943.
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Tylecote, R.F. (1968), The Solid Phase Welding of Metals, Arnold, London. Vaidyanath, L.R., Nicholas, M.G., and Milner, D.R. (1959), Pressure welding by rolling, Brit. Weld. J., 6:13-28. Wan, K.T., Lathabai, S., and Lawn, B.R. (1990), Crack velocity functions and the thresholds in brittle solids, J. Eur. Ceram. Soc., 6:259-268. Wiederhorn, S.M. and Bolz, L.H. (1970), Stress corrosion and static fatigue of glass, J. Am. Ceram. Soc., 53:543-548. Williams, J.G. (1984), Fracture Mechanics of Polymers, Ellis Horwood, New York. Williams, J.G. (1993), A review of the determination of energy release rates for strips in tension and bending. Part I — Static solutions, J. Strain Analysis, 28:237-246. Williams, J.G., Radon, J.C., and Turner, C.E. (1968), Designing against fracture in brittle solids, Polym. Eng. Sci., 4:130-141. Williams, M.L., Landel, R.F., and Ferry, J.D. (1955), The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, J. Am. Chem. Soc., 77:3701-3707. Zaghzi, N., Carré, A., Shanahan, M.E.R., Papirer, E., and Schultz, J. (1987), A study of spontaneous rubber/metal adhesion. I. The rolling cylinder test, J. Polym. Sci. Polym. Phys., 25:2393-2402.
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5 Friction 5.1 5.2
Introduction ....................................................................... 205 Qualitative Ranges of Friction .......................................... 208 Lubricated Friction • Rolling Friction • The Elastic Case • The Plastic Case • The Viscoelastic Case • Effect of Fracture Properties of Materials
5.3 5.4 5.5 5.6 5.7 5.8
Early Concepts on the Causes of Friction........................ 213 Adhesion, Welding, and Bonding of the Three Major Classes of Solids.................................................................. 215 The Formation and Persistence of Friction Controlling Surface Films ...................................................................... 216 Experiments that Demonstrate the Influence of Films on Surfaces ............................................................... 218 Mechanisms of Friction ..................................................... 219 Measuring Friction............................................................. 220 Unsteady Data and Vibration of Test Machines • The Sources of Unsteady Data • Interaction of Inherent Unsteady Data with the Dynamics of a Test Machine
Kenneth C Ludema University of Michigan
5.1
5.9 Test Machine Design and Machine Dynamics................. 227 5.10 Tapping and Jiggling to Reduce Friction Effects ............. 229 5.11 Equations and Models of Friction .................................... 230 Static Friction • The Stribeck Curve
Introduction
Friction is the resistance to the sliding of one solid body over or along another, as solid bodies are ordinarily understood in the macroscopic world. High friction is desirable between tires and roads (coefficients of which range from about 0.5 to 1.2), between mechanical parts that are bolted together and in countless other examples. Low friction is desirable between sliding parts in computer hard disk systems, in engines, in door latches and in many other mechanical devices. Whether friction is low or high is of little consequence in many applications, provided it is predictable (i.e., reasonably constant) and does not cause noise or vibrations. The most notable exception to the latter is the stringed instrument that uses a bow to create music. Friction often seems constant, regular, and well behaved, but that is observed mostly in mechanical devices that operate under relatively constant sliding conditions averaged over time. Actually, virtually every sliding condition produces a different level of friction. One reason is that surface materials continually change with time. Even in a vacuum, the surfaces of materials A and B are likely not really A and B, but rather have a higher composition of an alloying element that has migrated to the free surface from an alloyed substrate. Then, surfaces in air are likely to oxidize: even some oxide ceramics will oxidize and some also hydrolyze on their surfaces. These coatings or films will alter frictional behavior. Further, in “clean” air, surfaces attract gases to adsorb upon them, producing a layer of partially oriented liquid
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that has very different properties from the amorphous condensed phase of the gas. In addition, in the usual atmosphere in which parts slide, there is water vapor, and there are hydrocarbons (e.g., turpenes from trees and oil vapor from machinery) and other “contaminants” (e.g., human fingerprints) of every description that find their way into sliding contacts. The substances that settle on A and B may be specific to A and B, but A and B rarely “touch” each other. In this sense, tires do not actually “meet the road” either, but rather are separated by thin films of water and other substances. Very thin films of water can produce the high friction of tires, even at low shear rates: at 10 mph, on a water film 10–6 inch thick, the ratio of viscous retarding force to normal force (µ?) is about 0.66. If high friction of wet surfaces seems incongruous, consider another common human experience: everyone who plays softball or baseball knows that the bat is less likely to slip from the hands if the hands (and bat handle) are moistened a bit (Murakami et al., 1995). (Viscous friction is a much better explanation for this phenomenon than is the influence of “meniscus forces” discussed in Section 5.5 below.) The magnitude or “level” of friction is often expressed in terms of the coefficient of friction, µ, which is the force, F, to slide divided by the force or load, W, pressing the two solid bodies together, µ = F/W. Where an object is set upon a flat and horizontal plane, this load is the weight of the object: it is often referred to as the normal load, or the applied load. Expressing friction in terms of a “coefficient” is a misleading practice, suggesting possibly that the “coefficient” is an intrinsic property of materials, and that friction force is always proportional to the applied load. The latter may be true over narrow ranges of applied load but is not generally true. For example, sliding resistance has been measured when no external load is applied: clean metal surfaces can be drawn together by atomic bonding forces only, and two wetted surfaces can be drawn together by meniscus forces, both of which are described in following sections. Friction had long been assumed to be invariant under all conditions (i.e., independent of load, sliding speed, contact area, and all other operational variables) and graced with the term “Coulomb friction.” It is safe to say that Coulomb friction is an unusual phenomenon, safe because a few tests will prove it so. (The Baldwin Testing Company, the manufacturer of tensile test machines, at one time distributed bronze plaques on which were the words, “One Test is Worth a Thousand Opinions.”) One goal in this introduction is to point out the futility of trying to find useful values of coefficient of friction in books or published papers. Most published values were measured in research laboratories, usually with simple devices (though perhaps controlled by a computer), and rarely at practical sliding speeds and contact conditions. The data in themselves are usually reliable and highly reproducible, but they apply only to the conditions in that test. The tests may have been designated as standard tests by ASTM or other standards-making bodies, but such standards apply only to the methods of doing the test. Tabular values of friction are also frequently found in computer-based design packages, which seems to add a measure of legitimacy to the values. Most often only a single value of coefficient of friction is admissible or allowed to be entered into the algorithms and equations, some have room for two values, a “static” (or starting) coefficient of friction and a “dynamic” (or kinetic, or sliding) coefficient of friction, and a few can accommodate more complete frictional behavior as discussed in Section 5.11. The unresolved issue remains, however, of finding valid values. Though fixed (single) values of friction are attractive and widely available, ranges of values taken from measurements over wide ranges of sliding conditions are more realistic. A chart of friction ranges is given in Figure 5.1. Even these data have little meaning since specific values of friction are not connected with specific sliding conditions. For example, though handbooks often publish values for dry steel at 0.2, one can measure values ranging from 0.1 to 1.1, and perhaps even higher, depending on sliding conditions. The value 0.2 is probably correct for several applications, but no one knows a priori whether the application at hand is one of the well-characterized applications. In order to infer this to be the case one must make sure that the application at hand is similar in every detail to previous, well-behaved applications. Many published papers state, or strongly infer, that similitude is sufficiently shown by matching some combination of contact pressure and sliding speed only: rarely do these papers show supporting data or mention the importance of the ever-present oxides, adsorbed gases, and contaminants. No papers have yet provided methods to predict the coefficient of friction for any dry sliding pair within an order of 10 of measured values without introducing some questionable assumptions.
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FIGURE 5.1
A table of values of the coefficient of friction of various materials and conditions of sliding.
A topic closely related to the values of the coefficient of friction is the tendency or likelihood of sliding surfaces to vibrate or make noise. Sometimes this is called stick-slip, which will be discussed in Sections 5.8 and 5.9. Vibration is often seen as a system problem and, indeed, noisy vibrations can often be suppressed by applying damping somewhere in the system surrounding the sliding members. However, it seems more sensible to avoid initiating the vibration by choosing appropriate sliding materials. This is not readily done because there is almost never enough information in tables of friction coefficient that indicate the tendency for materials to cause vibration during sliding. This problem, too, requires close attention to proper simulation between old and new designs, and may also require some testing to resolve. Though we usually separate discussions of lubrication from discussions of friction, this is unreasonable to do. Friction is the resistance to sliding, and fluid films also offer resistance to sliding. Furthermore, all surfaces in air are lubricated, but by invisible layers of “lubricant.” The term “lubricated” appears to have two meanings, either “not dry,” or “having deliberately exposed a sliding pair to a lubricant.” Thick film lubrication is a very well developed field, whereas “thinner film” lubrication, or “boundary film” lubrication often involves some chemistry and is somewhat more of an empirical art. Lubrication-bycontaminant film or by “residual” films is scarcely mentioned, probably because they are invisible and few people appear to know what to do with these films even if their presence is acknowledged. Actually
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films of deliberately applied lubricants are sometimes thinner and less effective than films of “contaminants,” but one advantage of deliberate lubrication is that the chemistry of the interface region can be influenced by choice of lubricant. Furthermore, a continuous stream of lubricant can be supplied if desired, whereas a “contaminant” film is less reliably re-formed. Friction will be influenced by the thickness and mechanical properties of all these films. Furthermore, the entire chemistry in the contact region between two solids changes with time, that is, time of both sliding and of standing still. During sliding time the sliding speed, ambient temperature, contact pressure, duty cycles, changes in the roughness of the solids, and several more variables influence the chemistry. Chemistry can also change while surfaces are not sliding, whether contacting or not. The following paragraphs will expand on the points summarized above. The major purpose of this chapter is to discuss the many variables that influence friction so that designers may have confidence that friction values cannot be reliably predicted. This is an amazingly liberating concept and it encourages designers to focus their attention on the important aspects of frictional similitude between old products and “upgraded” products. Where similitude is questionable, testing should be done, and testing must be “simulative” testing, i.e., testing components that are very nearly like production parts in the way they will eventually operate. Testing can be a lengthy, expensive and risky procedure, if it is not guided by good conceptual or physical models of friction, and this tends to deter good testing. A frequent consequence of confused thinking on friction (and wear) is that these issues are postponed to very late in the design process, or perhaps ignored until warranty claims on production parts become very high.
5.2
Qualitative Ranges of Friction
Though absolute values of friction cannot be predicted, general ranges of friction are fairly easy to define. Very low friction can be achieved either by rolling, or by “elastic contact” between solid surfaces that have low bonding force between them. Low friction can be achieved by fluid film lubrication. Intermediate friction levels are found in materials that are moderately hard and not carefully cleaned. The highest friction is usually found with soft metal parts that are well cleaned, though “clean” is a relative term: high friction is usually accompanied by much plastic flow in surfaces. Ceramic material pairs often have higher friction as a class than do metals, though they are generally much harder than most metals, but this is usually because many metals have soft oxide coatings on them, whereas few ceramics do. Solid lubricants often produce friction at intermediate-to-high levels (and are used primarily for the prevention of galling and other severe forms of wear rather than for low friction). Rubber has high friction when sliding against almost any other solid, and the friction is inversely related to the hardness of the rubber. The friction of plastics, particularly “filled” plastics, against almost any other material can be low but usually is not very high either. The friction of rubber and plastics often varies in a manner that reflects their viscoelastic properties, which properties are not prominent in polymer-based composites (filled plastics).
5.2.1 Lubricated Friction The most completely studied mode of sliding is the liquid lubricated state. Longest life is achieved by maintaining complete separation of the sliding members with a “thick fluid film,” which is accomplished by selecting combinations of lubricant viscosity, bearing length, and shaft/bearing clearance to suit the geometry, the speed of shaft rotation, and the load on the system. (Cameron [1966] and Barwell [1979] are two good books on the practical aspects of hydrodynamic lubrication.) Generally the coefficient of friction is to be minimized for system efficiency, but there is little return on achieving values of coefficient of friction much less than about 0.1. Relatively few systems are expected to operate continuously at optimum friction conditions: most systems start and stop often or are overloaded on occasion. At low speeds a thick fluid film cannot be sustained, leading to wear of the shaft and/or bearing, and the friction usually increases. A curve widely attributed to Stribeck (Stachowiak et al., 1993) portrays the variations in friction over a range of the ratio ZN/p, where Z is the viscosity of the lubricant, N is the rotational speed of the shaft, and p is the
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log of friction coefficient
boundary lubrication
Friction
hydro-dynamic "friction" mixed lubrication (undefined) axis
log of ZN/p
FIGURE 5.2 A Stribeck curve showing the variation in sliding resistance of a shaft in a bearing over a range of viscosity, Z, shaft speed, N, and contact pressure, p, between the shaft and bearing.
nominal contact pressure between the shaft and bearing. A typical Stribeck curve is shown in Figure 5.2, which is often used to show zones or regimes of operation of a shaft in a bearing, in terms of the effectiveness of lubrication. The thick fluid film, or hydrodynamic regime is of the form of calculations by Petrov showing increased viscous losses as ZN/p increases. At some point, when ZN/p diminishes, it is thought that some asperities on each surface collide and “adhere” together, to cause higher friction: in the extreme, sufficient adhesion causes seizure of the sliding members. The region in which asperity collision is thought to occur is referred to as the “mixed-film” region because contacting bodies are thought to be supported on a mixture or combination of asperity–asperity contact points and fluid regions between asperities. In the mixedfilm region the friction is high and totally unpredictable: published Stribeck curves often suggest values of 0.2 or more but this is largely speculation. The value of 0.2 is the most common assumption for dry sliding of steel and brass, which is probably taken as typical of very poor lubrication. The left-hand section of the mixed lubrication region is called the “boundary lubrication” regime when there are active chemical compounds or “additives” in the lubricant. This region is identified by the lack of serious wear problems even though the surfaces are not totally separated. The additives are referred to as “boundary additives” because they form substances that coat the boundaries of the sliding pairs with a “protecting” substance. The existence of such films is verified, but their thickness and mechanical properties have not been well characterized. The usual Stribeck curve is a composite of the analytical Petrov type of curve on the right, and the empirical work by McKee and McKee (1929) for minimally lubricated surfaces on the left. The major value of the Stribeck representation is that when tests or experiments are run in the lower ranges of ZN/p, variations in friction can be used to estimate the adequacy of lubrication and likelihood of progression of surface damage.
5.2.2 Rolling Friction (Tabor, 1955) A hard ball or cylinder that rolls along the surface of a softer material (or a soft roller on a hard surface) deforms the softer material. This requires energy, which is particularly evident when the softer material deforms plastically. Energy is also required to deform materials in the elastic and viscoelastic ranges of strain, but in the case of these latter materials some energy is restored when the roller moves on and the material returns to its near original state. All materials consume energy when cyclically strained in the elastic range, in amounts ranging from 0.5 to ≈4% of the input strain energy for ceramic materials and metals, and about 20% in the case of the rubber in auto tires.
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Rolling balls and tires slide a small amount against a contacting flat surface because the softer body is deforming laterally in the contact region while rolling, sliding in one direction in the “front half ” of contact and in the opposite direction in the “back half ” of contact. (Sliding between regions of a tire against a flat surface may be demonstrated by rolling a tire over a sheet of paper.) Lubrication reduces this sliding friction and results in lower overall rolling loss, as in the case of automobile tires on wet roads. The effect is small because the sliding losses are much smaller than deformation losses in the materials substrate.
5.2.3 The Elastic Case (McClelland and Glosli, 1992) When two clean asperities of very low slope (<2°) are in atomic contact, and where the bonding forces of the atoms are weak (as with most covalently and ionically bonded solids where lattice matching of exposed lattice planes is rare), there is not likely to be very high sliding resistance. When an atom in one asperity moves from one location on the opposing surface to an adjacent location, significantly less force is required than to pull the asperities apart in a direction normal to the surface. The reason is that as a laterally moving atom is being pulled away from one stationary surface atom, it moves into the force field of an adjacent atom, increasing the energy of the atom left behind while decreasing the energy of the one ahead. The transition occurs with little net energy rise on the overall surface, particularly if laterally moving atoms move between equivalent atomic positions. The transition is likely not smooth. Rather, the separating atoms “snap apart” from each other and the approaching atoms will “snap together.” The result is a ripple of vibrations in atomic lattices, which vibrations are not totally conservative: some energy is lost in each cycle of the vibration, and eventually vibration ceases. As a historical note, the idea that frictional energy might be dissipated as lattice vibrations was introduced in 1929. G.A. Tomlinson (1929) published a paper on friction in which he proposed an irreversibility of atomic bonding due to energy lost in lattice vibrations. His model was rather mathematical in nature and he predicted the friction of several materials based on their lattice properties. Beare and Bowden (1935) measured the friction of these same materials and found no connection: they concluded that it was not possible to predict friction in the mathematical format of Tomlinson. It appears today as if Tomlinson’s intuition was correct, but he picked the wrong properties or the wrong materials in his paper. Research by Israelachvili (1995) is under way on finding material pairs that have much lower friction than any material pair has today. One important condition for low friction is that the asperities not be stressed beyond the elastic limit. (The presumed elastic behavior of asperities at the beginning of sliding is discussed in Section 5.11.) Contact stresses can be minimized by limiting the slope of the sides of asperities (as with smooth surfaces), or in the ultimate by contacting on flat crystallographic planes.
5.2.4 The Plastic Case If the combined normal and friction force is great enough, it will cause plastic flow in the asperities. Asperities of high slope (>2°), as in the case of rough surfaces, will plastically deform readily upon application of a normal load alone (Tabor, 1952). Then, from solid mechanics we learn that when the ratio of shear stress to normal stress on asperities is less than about 0.3 (Childs, 1992), passing asperities will “iron” each other down by plastic deformation so that the surface becomes smoother on average, and the surfaces harden as sliding continues. When the ratio of shear to normal stress is greater than 0.3, asperities are likely to be stretched (plastically deformed) in the direction of sliding, sometimes producing a rougher surface than before sliding. These surfaces harden more quickly than do the previously mentioned surfaces, and plastic deformation energy will appear as friction. It would seem that the friction of very ductile (soft) materials, on average should be greater than that of hard materials because of the great amount of plastic flow in the surfaces during sliding, except that very ductile materials are also usually weaker materials. (In air and other lubricants, the thickness and structure of surface substances will likely be influenced by the substrate material on which the films form, and that will also influence friction.)
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FIGURE 5.3 of load.
The viscoelastic response of two different arrays of springs and dashpots to imposed loads and release
FIGURE 5.4 Sketch of two properties, tangent modulus, and damping loss of a viscoelastic material during cyclic tensile or torsion tests.
5.2.5 The Viscoelastic Case When sliding a very smooth plastic (linear polymer) material against any other smooth solid, the friction shows no patterns that can be identified with substrate properties: the properties of the physically adsorbed films are more prominent. When the asperities of a hard surface, or when a spherical slider slides along a surface of the plastic materials, clear viscoelastic effects are seen in the friction measurements. Viscoelastic effects are often modeled as various arrays of springs and dashpots (Ferry, 1980), as shown in Figure 5.3, and there are two prominent results, as sketched in Figure 5.4. One is that in cyclic straining the effective elastic (tangent) modulus is seen to increase very considerably (2 to 3 orders of 10) when increasing the strain rate (or frequency of oscillation at constant strain). The other is that the damping loss (loss modulus) is low at the low and at high strain rates, but much higher in an intermediate range of strain rate. The full range of these variations covers about 8 orders of 10 of strain rate, and the highest damping loss can be about 8 times higher than the low values. Pin-on-disk friction of plastics varies also by 5 to 1, or even 10 to 1 over a wide range of sliding speeds. Thus, whereas the coefficient of friction of Teflon® is widely reported as 0.17, it has been measured to
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FIGURE 5.5 Sketch of the movement of waves of detachment (Schallamach waves) during sliding of soft rubber along a flat surface.
cover a range from 0.10 to 0.80! A plotted curve of friction vs. sliding speed has the same appearance as a curve of damping loss vs. strain rate, which can be taken as strong evidence that the viscoelastic properties of the plastic influences the friction. Furthermore, temperature has the same influence on measured values of friction (Grosch, 1963) as on the measured values of damping loss. This is shown in Figure 5.4. It is likely, however, that damping loss is not the relevant viscoelastic property to connect with friction, but rather the connection can be made through the tangent modulus property (Ludema and Tabor, 1966). Soft rubber exhibits interesting behavior when sliding on a smooth counterface, which was described by A. Schallamach (1963) and is sketched in Figure 5.5. Upon the start of sliding with uniform contact applied pressure, there is shear throughout the body of the rubber, but because the contact pressure is reduced at the rear of contact the rubber slips first at the rear. This slipping alters the stress state in the rubber, such that the contact pressure just ahead of the slipped region to the rear is reduced. Slip then occurs in this region, which then alters the contact pressure further ahead. A wave of slip occurs and moves forward at about 10 times the sliding speed. With continued sliding, standing waves are established, which often have frequencies in the audible range. In the case of very soft rubber the waves of slip become waves of detachment in that the rubber actually separates from the flat plate. Good lubrication reduces the Schallamach waves such that sliding is quiet at moderate sliding speeds, but the waves are reestablished when the sliding speed becomes low and the lubricant film is thin. The viscoelastic component of rubber friction is also diminished when there is good lubrication, as shown in Figure 5.6 (Wassink, 1996). The surface of the rubber does not slide the distance of translation of the entire body, so that Schallamach waves diminish friction: the reduction is not exactly proportional to the “slip distance reduction” due to the waves because some energy is expended in the passage of the waves along the rubber, which is measured as friction.
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3
2.5
dry sliding 1.5
2.5 orders of ten
coefficient of friction
2
1
0.5
lubricated sliding
0 10
-5
0
10 sliding speed, mm/s
10
5
10
10
FIGURE 5.6 The viscoelastic nature of rubber friction, in dry sliding and as progressively attenuated by incursion of lubricant into the contact region as sliding speed increases. The curves are constructed by viscoelastic transformation, using data over ranges of temperature and sliding speed.
5.2.6 Effect of Fracture Properties of Materials Some friction is due to the loosened particles in the sliding interfaces. Metal surfaces (except gold) have oxides on them which come loose during sliding, and over time some substrate metal is removed as well, either by adhesive tearing or by fatigue failure. Ceramic materials are more likely to have grains loosened because of poor bonding, which will fragment into smaller bits and cover a surface: grains can be loosened after only a few cycles of shear strain. Brittle polymers fragment somewhat also but bits of the softer polymers will be removed by adhesion and circulate within the contact region. The nature of the loosened particles is difficult to express. Some oxides scratch the metal surfaces beneath, which suggests that the oxide is abrasive: others are not abrasive. The general definition of the hardness and brittleness of materials in the sliding interface becomes unclear when a high contact pressure is applied. These terms are usually mentioned in the context of tensile properties of materials where no hydrostatic pressure is applied. For example, the true strain at fracture of 1018 annealed steel is somewhat larger than 1, but from hardness tests of surfaces that have been sliding together for a long time it would appear that the metal had strained to a true strain as high as 10. Some work has been done on the strain accumulations and fracturing of materials under the conditions that exist in a sliding contact (Kapoor, 1994).
5.3
Early Concepts on the Causes of Friction
In the earlier days, friction was thought to be due to the “interlocking of asperities” (Ludema, 1979). Asperities are the very small (usually microscopic) bumps or protuberances on most surfaces, which constitute the “roughness” of surfaces. Actually, asperities “interfere” with each other’s passage rather than interlock, but interestingly one modern author explained the “interlocking” mechanism as equivalent to the action of the fabric Velcro® (Victor, 1961), found in many garments, shoes, floor mats, and other products. There were some objections to the “interlocking” theory over 100 years ago (Bowden and Tabor, 1954): some pointed out that once a group of asperities on one surface had ascended the slopes of the asperities
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FIGURE 5.7 Sketch of real contact area between two bodies of surface dimension A and B: the summation of the small regions in this sketch is about 0.07AB and is referred to as the “real” area.
on the opposite surface, which required energy to do, no further energy would be required to continue sliding. Rebuttals developed but none were persuasive, probably because the necessary tools to observe the discussed phenomena (asperities, etc.) were not available. Some “interlocking” likely does occur where one surface has hard grains, constituents, or compounds protruding from the surface, which plow grooves in the opposite surface. Such plowing produces plastic deformation in the opposite surface, which consumes energy. The most serious doubts about the interlocking concept came with the experiments of W.B. Hardy (1923). He transferred a single molecular layer of a fatty acid from the surface of water to a glass plate. From his work on the sizes of these molecules he was sure that a monolayer was thinner by at least an order of 10 than the average height of the roughness (asperities) on the glass surface. When sliding clean glass on clean glass he measured a coefficient of friction of about 0.6, whereas when sliding clean glass on the glass plate coated with a thin film of fatty acid the coefficient of friction was about 0.06. Interlocking or interference could clearly not explain such great difference in friction. Adhesion, cohesion, atomic attraction, molecular attraction, and similar terms were used then to explain friction. F.P. Bowden and D. Tabor (1964) and several others vigorously pursued the idea of adhesion as the source of friction. Bowden and Tabor and their many Ph.D. students showed that friction was proportional to the real area of contact between two surfaces, which was taken as strong support of the adhesion concept. This was a formidable task because the real area of contact is ultimately the summation of thousands of microscopic points of contact within a nominal area of contact, as sketched in Figure 5.7: these details cannot be seen while sliding occurs. Further, the actual shear strength within those microscopic areas of contact was not known either, and is not really known to this day. Bowden, Tabor, and students used very many methods to estimate and infer what was occurring on surfaces, and the preponderance of their evidence surely showed that friction is not primarily due to mechanical interlocking of asperities. They and several others developed physical models of friction, usually around the assumption that friction is the product of real contact area and the shear strength of the material in the asperities. One model is expressed in the following terms: µ = AsS/Aw3Y (Greenwood et al., 1955), where µ is the coefficient of friction, S is the shear strength of the bond between asperities, 3Y is the pressure hardness of the weakest of the sliding materials, Y is the yield strength, and A is the cross-sectional area of shear (As) and the area carrying the normal load (Aw). Assuming that Aw ≈ As, µ ≈ S/3Y, which is about 0.16 or 0.2 depending on which flow rules of metal one favors. The major problem with this conclusion is that µ of all materials would be about the same. Tabor recognized this as erroneous, and over 40 years ago (Tabor, 1959) developed a model in which the sliding resistance is offered by shearing of a substance between sliding bodies, a solid substance with a flow (shear) strength. This model could be adapted for the case of viscous substances in the interface, but whether solid or viscous, the properties of the interfacial substances could only be assumed. This model further assumes that the real contact area will grow as shear stresses develop in the asperities.
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Though adhesion appears to be a better explanation for friction than is interlocking of asperities, it is probably the major mechanism only when surfaces are clean and sliding in a vacuum. Analysis of many published papers that invoke the “adhesion theory” of friction suggests that most authors believe adhesion to be complete and full-strength welding or bonding at every asperity contact site. This cannot be a valid general assumption for two reasons: 1. Bonding of atomically clean ceramics and polymers is seldom “full strength,” and, 2. Most systems function in atmospheres that provide substances (contaminants) that adsorb to solid surfaces, which diminishes bonding strength considerably. Bond strength and persistence of surface contaminants will be discussed in the following two sections.
5.4
Adhesion, Welding, and Bonding of the Three Major Classes of Solids
Adhesion, welding, etc., usually refer to resistance to separating bodies from each other in the direction normal to these surfaces. When two atomically clean, smooth, and conforming pieces of the same metal are brought into contact in a perfect vacuum, against matching atomic or lattice arrays, they will become one piece leaving no evidence of the former boundaries or surfaces. There is no need to apply pressure, heat or rubbing energy: atomic bonding occurs spontaneously. This is called “adhesion,” though some argue that the term “cohesion” should be used where identical materials bond together. The original two pieces of metal will not readily “slide” over or along each other, and in fact no definable interface survives along which sliding can occur in preference to shearing of substrate material. For most common metals (there are a few exceptions among the metals), if the lattice arrays are even significantly misaligned they will still bond with high strength. By contrast, ceramic materials will bond together at high strength only when lattice arrays are perfectly matched and aligned. Mismatch occurs where ceramics of different atom spacing are in contact or where the lattices in contacting asperities are rotated or tilted (ever so) slightly relative to each other. The strength (Van Vlack, 1959) of bond ranges is as low as 2.5% of the maximum if lattices are mismatched, so that when multicrystalline ceramics slide over each other there will be varying degrees of lattice matching, and therefore varying friction with distance of sliding. For the third class of materials, linear polymers, bond strength will be fairly high whatever the relative alignment. Bonding between atoms may be described in terms of their electron structures (VanVlack, 1959). In the current “shell theory” of electrons the number of electrons with negative charge should balance the positive charge on the nucleus, and there should be no net electrostatic attraction between atoms. However, within clusters of atoms the valence electrons (those in the outer shell) take on two different duties. In the case of some elements, particularly those that do not conduct heat or electricity very well and are referred to as insulators, a pair of electrons orbit around two adjacent nuclei and constitute the “s” bond. These bonds are very specific as to allowed angle between pairs of nuclei, and any attempt to displace an atom from its “assigned” position results in much reduced bonding strength. This explains the brittle nature of most monolithic insulators (including ceramic materials), and the difficulty in bonding one group of ceramic atoms to another. The few additional electrons in insulators and all of the electrons of conducting elements (the metals mostly) become “delocalized,” that is, they do not retain allegiance to any single or pair of nuclei. These delocalized electrons set up standing waves among a wide group of nuclei: the average energy state of the delocalized electrons is lower than the energy state of valence electrons of single atoms, and this is the energy of bonding between atoms within a solid. This group bonding is known as “π bonding,” and not referred to as “a bond.” The angular relationship between pairs of atoms in π bonding is influenced more by atomic packing than by variations in bond strength, which explains both the ductile nature of most metals and their ability to bond well under most conditions of misalignment.
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Some solid materials such as polymers are made up of long chains as a “backbone” (usually carbon or silicon) of a molecule. Bond angles along this chain are very specific. For example, the bond angle of carbon is 109.5°, and considerable effort is required to bend this bond to any other static angle. These bonds do vibrate, however, over a range of angle around the central value of 109.5°, and they also vibrate in rotational modes. But, a long chain of carbon atoms, as in a polymeric material, does not satisfy the potential bond energy of carbon atoms. Carbon can connect with up to four other atoms usually; two of which are satisfied by connection to others in the chain, leaving two bonds to connect with side atoms or chains of atoms. In this array some electrons are not involved in the “s” bonds and these develop the π bonding. Where segments of two or more adjacent molecules lie moderately parallel to each other, π bonding is particularly strong, packing these molecular segments into a crystalline order and imparting more elastic than viscous behavior to these regions.
5.5
The Formation and Persistence of Friction Controlling Surface Films
After a “new” solid surface has been created it exists in a high state of energy, of the order of 1 J/m2 (VanVlack, 1959). The energy state of electrons at the surface of a solid is higher (less delocalized) than that in the substrate, which is seen in the form of surface atoms (ions) being ≈ 95% the “size” of substrate atoms. This energy constitutes the potential for bonding of one solid body to another solid body or to a liquid or a gas. Surface energy can be reduced by bringing any atom or molecule to that surface. The first layer of adsorbed atoms reduces the surface energy the most, but if that layer is nearly the same material as the new surface, then that layer becomes the new high energy surface. Molecules of liquid or gas approaching an energetic surface will surely not have the same atomic arrangement as the solid surface and will therefore not reduce the surface energy of that surface very much: of the order of 10% of the surface energy. The first molecular layer is aligned as best it can, which is to say that some order is imposed upon this first group of otherwise randomly oriented molecules. The first layer of molecules does not totally satisfy the surface free energy of the solid, so energy is available to attract a second layer and impose some order within it as well, and so it transpires in 4 or 5 more layers. Order in these layers has actually been observed and experiments have shown that the viscosity of these layers is directly related to the degree of order (vanAlsten et al., 1990; Pashley and Israelachvili, 1984; Gee et al., 1990). The viscosity of the first layers of the liquid is very high, perhaps 1000 times its “bulk” viscosity. The viscosity of succeeding layers decreases as films become thicker, apparently getting to bulk viscosity at about 5 to 10 molecular-layer thickness. The affected films might be 10 to 20 nm thick (e.g., 0.3 nm for computer hard disks), which is small compared with the height of asperities on very smooth technological surfaces, which would be about 25 nm. It is apparent that these “fluid” films could be very tenacious, that is, hard to displace even by repeated sliding. Consider the persistence of grease or other high-viscosity substances on a glass plate: continued rubbing with a finger over such substances does decrease their thickness but requires much effort to remove entirely. Of course, the layer may be regularly renewed if sliding occurs in an atmosphere containing the proper molecules. The liquid nature of adsorbed water is seen in the behavior of heads and the hard disks of computers. While the disk is rotating the read/write head “flies” over the disk and adsorbed gas with very small spacing. When the disk stops for a short time, the slider settles closely enough to the disk so that the adsorbed films on each surface “wets” the other (Li, 1989). This is shown in Figure 5.8. The force pulling the head to the disk is sometimes referred to as a “meniscus force” and is equivalent to the action of a meniscus in contact with the wall of a container or the surface of tubes inserted vertically into a liquid. This is shown in Figure 5.9. If the wetting angle of the liquid to the material of a tube is less than 90°, the meniscus will lift a column of liquid in a tube, whereas if the wetting angle is greater than 90°, the meniscus will suppress the liquid in the tube below the general level of liquid outside of
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SLIDER
meniscus
FLAT DISK OR PLATE
liquid that wets the beaker and tube
FIGURE 5.9
tube
Sketch of the “liquid bridge” that forms when two films of adsorbed liquid touch each other.
tube
FIGURE 5.8
liquid that does not wet the beaker or tube
Sketch of the effects of surface tension or meniscus forces acting on a liquid surface at a solid boundary.
the tube. The wetting angle is equivalent to the “contact angle” at the edge of contact between a drop of liquid and a horizontal flat plane. Meniscus forces can influence friction by drawing two bodies together, sometimes with a greater force than an applied external force. The result will be a simultaneous enlarging of the “wetted” area, and a thinning of the fluid film, two conditions that increase the force required to shear the fluid. The drive motor of a typical hard disk drive (particularly those in laptop computers) does not have sufficient torque to start rotation when there is a high sliding resistance: this phenomenon is known as “stiction” (sticktion?). The problem can be alleviated by deliberately roughening a “track” on which the slider is programmed to “park.” Meniscus forces also have a significant effect on the sliding friction of very soft lubricated rubber. This occurs by the meniscus force attracting the rubber to the other surface and thereby increasing the area of close proximity between the two. Meniscus forces also “hold” a thin polymeric film to a glass surface and allow many insects to walk on vertical surfaces. Adsorbed films of liquid and gas build up at very great rates in Earth’s atmosphere. About 99% of a solid surface will be covered by a monolayer of adsorbed gas in about 1.2 × 10–8 sec (Ludema, 1996). After about 10 seconds the film is about 1.5 nm thick. After a day these films grow to thicknesses in the range of 4 to 12 nm. Adsorbed gas films can usually be driven off surfaces by heating, in which case the surface energy of the solid surface beneath returns to a higher energy state. This reversible process is referred to as physical adsorption. Films of ordinary liquids can also be “driven off ” by heating, as is the case with solvents. Many other liquids such as oil, are more likely to dissociate or oxidize rather than to simply boil off. When a surface is covered with adsorbed O2, CO2, or H2O, the oxygen in these adsorbates is available to oxidize the substrate surface. About 10 times the energy is released in oxidation as in physical adsorption. Oxidation begins on metals (except on gold) and some ceramic material in approximately 10–7 seconds: in about 10–4 seconds a monolayer of oxide (or other compounds) has formed (Evans, 1960) and the films grow at about the same rate as physically adsorbed films grow. The oxidation process cannot be reversed by heating alone. When chemical reactions occur during adsorption the process is known as chemical adsorption, or more simply, chemisorption. Physically adsorbed films form on top of the oxide. Most of the above-described films are invisible to the unaided eye or by microscopy (light or electron). Neither are they detectable with many instruments: for example, even several layers of water on a
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crystalline solid cannot be detected by infrared spectroscopy, but ellipsometry can detect fractions of a monolayer of water. The properties of oxides cover a wide range, but the ratio of the mechanical properties of the oxides to those of the substrate is the relevant quantity. For coatings (including oxides) that are softer (lower shear strength) than the substrate, the friction is lowered. The opposite could probably be said of hard coatings on soft substrates, but the picture in this case is less clear. Hard coatings debond or fragment at some load, causing higher friction than for sliding on a solid body of high hardness. At very high loads the soft substrate will plastically deform, which also contributes to high friction.
5.6
Experiments that Demonstrate the Influence of Films on Surfaces
One of the mysterious aspects of research reports and published papers is that sliding surfaces are discussed as if they have no contaminant or other substances on them, whereas virtually everyone else, educated and uneducated, child and adult, knows that such substances are ubiquitous. Films of “contaminants” accumulate on windows and mirrors to the point of being visible as a haze, and they form without people touching them. (These may be films of water from vapor or films of condensed hydrocarbon gases emitted from nylon, vinyl polymers, etc.) Fingerprints appear on all objects handled by people, and since they are often visible their thicknesses must be in the range of the wavelength of light (≈1 µm). It is common knowledge that fingerprint films and other films influence friction. When these films are removed, the surfaces are “squeaky clean,” a term taken from the practice of rubbing a (clean) finger along the wetted edge of a glass container: if the friction is low, the glass is “dirty,” but if squeaking (stick-slip) is heard and friction is high, the glass is considered “clean.” Very thin films do indeed influence friction, but the published evidence is sparse. Measures of cleanliness are not often discussed in research papers, but cleaning methods are. A frequent litany of how surfaces have been cleaned, might include the following, “sprayed with acetone, held in ultrasonically agitated isopropanol for 10 minutes, dried with an electric hair dryer, and held in a desiccator for 24 hours.” Of course, one problem in measuring cleanliness is that there are no convenient instruments that can detect very thin films of contaminants, and if such measurements were to be made, the measurements would need to be made in an atmosphere where the contaminants in the laboratory would not form a new contaminant film! A few experiments were run to measure the influence of contaminant films on the friction of steel on steel at low contact pressures (100 MPa) and very low sliding speed (23 µm/s). The experiments were done with a 6.2-mm-diameter cylinder (roller from a roller bearing) sliding on a disk of 50 mm diameter. The cylinder was steel of 58Rc, the disks were steel of 51Rc, with a roughness in the range of 0.06 µm Ra or better. The disks were “contaminated” by several means, and cleaned by several common laboratory methods as indicated in Table 5.1. The thickness of the films was measured with an ellipsometer that displayed its results in the form of the Mueller Matrix transformation between four incident Stokes parameters and four reflected Stokes parameters. The internal consistency of the numbers in the transformation assured that valid film thickness measurements were made, and at the same time the index of refraction of each film was displayed. The coefficient of friction vs. measured film thickness is plotted in Figure 5.10. The overwhelming trend is toward lower friction with thicker films. The reason for some inconsistency is probably that each type of contaminant, before and after being diluted or converted by cleaning fluids, has a different viscosity or molecular ordering. However, the data from each type of contaminant and cleaning methods do show some order. The clear point in Figure 5.10 is that friction is not as much controlled by the properties of the substrate material as by the varied thickness and (probably) composition of invisible contaminant films. Handbook values of friction, which were taken from surfaces covered with one type and thickness of contaminant cannot be applied to surfaces covered with another type and thickness of contaminant.
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TABLE 5.1 Sample Data on the Cleaning Method, Thickness of Film, Index of Refraction of the Films, and Coefficient of Friction of Steel Covered with the Films Contaminant Vacuum pump oil
Light mineral oil
Normal finger print
Greasy finger print
Cleaning Method
Film Thickness, Å
Refractive Index
Friction Coefficient
None Acetone spray Isopropanol-soaked paper None Isopropanol spray Sprayed with acetone None Toluene spray Acetone spray Ultrasonic acetone bath Isopropanol-soaked paper None Acetone spray
2461.4 5.374 <1 2524.6 13.95 <1 156.4 59.44 24.19 7.053 <1
1.085 2.476
120.2
1.79
0.082 0.296 0.467 0.262 0.522 0.552 0.0337 0.191 0.314 0.482 0.528 0.351 0.07
1.077 1.071 1.835 2.167 2.51 2.48
Note: Thickness and friction data are plotted in Figure 5.10.
FIGURE 5.10
5.7
The effect of four contaminants on the friction of steel.
Mechanisms of Friction
The simple model in which friction is the product of real contact area times the strength of bond in that area was appropriate in the early days of friction knowledge but is clearly limited in light of modern understanding of surface geometry, surface chemistry, and strains in surface materials. But papers continue to be published in which the limited concepts continue to be advanced, probably arising from limited perspective of friction mechanisms. Adhesion concepts are often used in attempts to understand “mixed film” or “boundary film” lubrication. The common assumption was that lubricant films could be thick enough to prevent most asperities on one surface contacting asperities on the other surface, but a few stand high enough to “contact” each other. Friction is then explained in terms of a combination of adhesion of “contacting asperities” plus
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FIGURE 5.11
Three sources of sliding resistance (friction) between lubricated surfaces.
the viscous drag in regions that are not in “contact.” Even this concept needs to be updated to account for the influence of the very thin films of lubricant, which reduce the strength of bond between asperities and have their own distinctive shear-resisting properties (either viscous or solid). A measurement of electrical resistance across the interface of nominal contact regions is sometimes made to estimate the relative amount of asperity (adhesive) contact, but the results are strongly influenced by the high resistivity of very thin layers of contaminant (lubricants) on most asperities. Likely the greater part of the applied load is carried on these thin layers. Sliding with sufficient speed or applied load will, of course, change the nature of the insulating layer and will expose more asperities to atomic contact, but the extent of the change is usually not even approximately indicated by electrical contact resistance measurements. In summary, friction of surfaces that are not rigorously clean is seen to consist of the following three components, which may be visualized with the aid of Figure 5.11: 1. Shear of those real contact (load carrying) regions that are in (solid) atom–atom (adhesive) contact 2. Shear of those real contact (load carrying) regions where the solid asperities are not in atom–atom (adhesive) contact but are separated by interposing films of contaminant/boundary/chemisorbed/etc., substances 3. Viscous shear of fluid between the noncontacting regions of the apparent area of contact. The nature of surface roughness influences some of these components and so will the amount, shape, and properties of loosened particles of substrate material and oxides (e.g.) in the nominal contact area.
5.8
Measuring Friction
The measurement of the coefficient of friction involves measuring two quantities, namely F, the force required to initiate and/or sustain sliding, and N, the normal force holding two surfaces together. (Recall that atomic bonding forces and/or meniscus forces may also be present as an unmeasured normal force.) Some of the earliest measurements of the coefficient of friction were done by an arrangement of pulleys and weights shown in Figure 5.12. Increasing load P is applied until sliding begins and one obtains the
FIGURE 5.12
A device for measuring static or starting friction.
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FIGURE 5.13
The inclined plane method of measuring the static coefficient of friction. F
static, or starting coefficient of friction, with µs = Ps /N = -----s . If the kinetic coefficient of friction, µk is W desired, a weight is applied to the string and the slider is moved manually and released. If sliding ceases, more weight is applied to the string for a new trial until sustained sliding of uniform velocity is observed. F In this case, the final load Pk is used to obtain µ k = Pk /N = ----k- . W A second convenient system for measuring friction is the inclined plane shown in Figure 5.13. The measurement of the static coefficient of friction consists simply in increasing the angle of tilt, α, of the plane until the object begins to slide down the inclined plane: the tangent of the angle of tilt, tan α, is the coefficient of static friction. If the kinetic coefficient of friction is required, the plane is tilted at some chosen angle and the slider is advanced manually: if the object stops sliding, the proper angle of tilt has not been set. When an angle of tilt is found at which sustained sliding of uniform velocity occurs, the tangent of that angle is the kinetic coefficient of friction. Data will vary according to one’s judgment of the uniformity of sliding speed. Other friction force measuring devices range from the simple spring scale to transducers that produce an electrical signal in proportion to an applied force. The deflection of the holder of one of the sliding members can be measured by capacitance sensors, inductance sensors, piezoelectric materials, optical interference, moire fringes, light beam deflection, and several other methods. The strain in the specimen holder can be measured by strain gages, acoustic emission, etc. The most widely used, because of its simplicity and reliability is the strain gage system. Just as there are many sensing systems available, there are also many designs of friction measuring machines: these can be classified in terms of range of load, range of speed, atmosphere in which they function, reciprocating vs. continuous motion, rotating vs. linear motion, spherical or cylindrical or flat (e.g.) shapes of sliding members, etc. Many machine configurations are available for purchase but all are variants of the basic motion-producing and force-measuring components. Only the pin-on-disk (pin-on-flat plate) geometry will be discussed here, where a round-tip pin is held by a cantilever-shaped force transducer and it slides against a disk. The disk is usually rotated by a drive system, either directly from a motor as sketched in Figure 5.14, or through gears or belts. The disk is held on a pedestal, which is held on a shaft that is supported by bearings. This geometry is among the least useful for purposes of simulating practical hardware but it is easy to explain: and the results are quickly available for publication!
5.8.1 Unsteady Data and Vibration of Test Machines The focus in the following paragraphs is on the dual problem of unsteady data from test machines, and vibration of test machines. Virtually all test machines produce unsteady and time-varying data, which behavior is disconcerting where smooth and constant values of friction are expected (to accuracies of ±0.01!). The variations range from about ±5% for most practical sliding pairs to more than ±35% for dry sliding of soft metals. Unsteady friction force appears in the test machine as a vibration, which may
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FIGURE 5.14
Modern Tribology Handbook
The components of a pin-on-disk friction test machine.
range in amplitude from very small to very large: the latter may be annoying to the operator, or even damaging to the machine. Smooth data can sometimes be obtained by artificial means. One way is by changing the test conditions, such as by changing the applied load or the sliding speed. Machine vibrations can be reduced by increasing its stiffness, or by applying damping in appropriate places. Smooth data can also be artificially obtained by filtering the data stream or by using a data acquisition system with low frequency response to eliminate the higher frequencies so that the data appear more stable. Where data are displayed in rough form, as with a chart recorder, it is tempting to obtain a “best estimate” line through the traces to obtain a single value of friction. This is reasonable to do where variations are small, but when variations are larger and approach the stick-slip state, reasonable values of friction cannot be obtained. True stick-slip is uncommon, though frictional vibrations are commonly referred to as stick-slip. In the actual stick-slip condition the sliding bodies momentarily stop sliding and then slide some short distance before becoming stationary again. In such cases, the value of µs may possibly be estimated from the maximum force measured when slip starts, as indicated by the arrow in Figure 5.15a. The shape of the curve in Figure 5.15b, prior to the maximum, reflects only the system stiffness and intended speed of sliding. When slip begins, the slip portion is usually not recorded in sufficient detail to determine µk, however. In general, it is incorrect to assume that µk is the average of
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(b)
(c)
(d)
applied force velocity
(a)
applied force velocity
Friction
time
in actual stick slip there is virtually zero sliding speed at the "stick" point in the cycle
time
time
time
frictional oscillations occur without "stick" but is a quasi-harmonic motion imposed upon an average velocity
FIGURE 5.15 The momentary sliding speed and force applied to a slider in the stick-slip condition (a and b) and in the more common sliding condition (c and d).
peaks and minima in the excursions though such estimates would not introduce much error if the data were in the form of Figures 5.15c and d. Neither of the above solutions is wise without consideration of the effects of the solution. If the lab tester is to be used to simulate production hardware in service, filtering the data from the lab tester will not produce stable sliding in the production hardware, and the same logic applies to the other solutions to unsteady data. More important, the average friction values in a vibrating machine are usually different from the friction values in a quiet machine for nominally identical test conditions: instantaneous contact pressures and sliding speeds are different in the two.
5.8.2 The Sources of Unsteady Data Unsteady data may be classified as two major types, those that are independent of machine dynamics and those that result from interaction between inherent frictional behavior and machine dynamics. There are at least four sources of unsteady data that are independent of machine dynamics. These are: 1. Surface roughness, with wavelength of the order of, or larger than, the size of contact regions, which usually produces high frequency variations in friction. 2. Inherent and repeatable variation of friction along a sliding path, under all steady-state conditions with ideal specimens and machines, usually producing high frequency variations in friction. These variations are greatest in the case of dry metals, ceramics, and hard polymers: they are the least in the case of well-lubricated surfaces or when a metal sphere slides on a soft plastic. A sketch of such data is shown in Figure 5.16a. 3. Inherent and repeatable variations of low frequency that are cyclical in nature due to misaligned test machine parts, bad bearings, poorly made specimens, or vibrations transmitted from outside the machine, etc. Figure 5.16b shows such cyclical variations superposed upon noncyclical data. 4. A long-term change due to changing conditions in the contact region of specimens. This is shown in Figure 5.16c.
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FIGURE 5.16
Modern Tribology Handbook
Three forms of surface traces and read-out.
5.8.3 Interaction of Inherent Unsteady Data with the Dynamics of a Test Machine Unsteady data can interact with the dynamics of test machines to produce two affects: one is to alter the dynamic content of inherent friction data, and the other is to “feed back” sliding conditions upon the sliding pair that are different from the intended conditions. The data from transducers in friction test machines usually contain a range of frequencies (which can be separated by Fourier analysis). Some of these frequencies will be below and some above the several natural frequencies of a transducer and test machine system. The frequencies that are lower than the natural frequency of the test machine components will induce vibrations in those components in phase with the driving frequency; those near but still below the natural frequency of the components will induce very large amplitudes. The frequencies that are higher than the natural frequency of the machine components will induce vibrations that are 180° out of phase from the driving amplitude, which amplitudes will increase near the natural frequencies again. This phenomenon is shown in Figure 5.17. Several causes of machine coupled vibration are described: 1. Vibrations resulting from the coupling between the elasticity of a machine and a negative slope of friction vs. sliding speed. When a mechanical driver within an elastic frame or machine exerts force upon some other part of the system to slide it, the system will distort in proportion to the resistance to slide. A “prime mover” is represented in Figure 5.18 as pulling a sliding body with an elastic coupler or spring. Beginning with zero force in the spring, the prime mover moves,
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amplitude
amplitude of the driving force
natural frequency of vibration of the system
driving force
frequency of the imposed force
M the mass vibrates in the mass vibrates 180° out phase with the driver of phase from the driver
FIGURE 5.17 Amplitude of motion of a mass, M, subjected to a force of constant amplitude and variable frequency, through a spring, without damping.
prime mover spring FIGURE 5.18
sliding object
Schematic sketch of the important elements of a typical elastic machine in which sliding occurs.
stretching the spring. The slider moves only when sufficient force has developed in the spring to meet the static friction force to slide the body. After sliding begins, and assuming a negative slope of dynamic friction vs. sliding speed, the stretched spring exerts more force upon the slider than is required to keep the object moving, so the excess spring force accelerates the object. The object now moves faster than the prime mover, shortening the spring beyond the point required to keep the object moving at the speed of the prime mover: it “overshoots” and slows down. At the new lower speed its friction increases which hastens further slowing, eventually to a speed less than that of the prime mover. This oscillation continues as long as there is sliding in the general speed range in which there is a negative slope of friction, as sketched in Figure 5.19. From the general principles of mechanical dynamics, the frequency will depend on the mass of the slider, the stiffness of the spring and on the nature of damping in the sliding interface and in the overall system. These events take place in all noisy and vibrating brakes and clutches, for example. Where the spring is very flexible and the slope of friction curve is steep, the slider speed may range from zero to some finite value, and this behavior is commonly referred to as stick-slip, as speed of the prime mover
µ
range of speed variation of the slider sliding speed
FIGURE 5.19
One frictional behavior that encourages frictional oscillations.
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mica ordered molecular layers disorder due to shearing ordered molecular layers mica FIGURE 5.20 A sketch of the ordered array of molecules near a solid surface, with some disorder occurring in the center of the film due to shearing.
noted before. Most practical sliding systems that vibrate do so without the sliding velocity actually diminishing to zero: actual stick-slip is not common in machinery. Zero velocity is, of course, a relative term. For most people, it is a velocity that is too slow to “see.” Section 2 below discusses motion on the molecular scale, and Section 5.11.1 discusses “breakaway” friction in µm dimensions, both of which are difficult to “see.” The description above applies to the case where all points on an interface oscillate in phase with each other. More likely every contact point on a surface acts quite independently, due to the random physical interaction between asperities and due to local variations in friction, such that there are many interacting elastic waves in the sliding surfaces, which produces the noise discernible from all sliding and rolling solids. The above paragraphs describe the case of dry sliding. If lubricant is present in adequate quantity, the lubricant film is likely to be thicker at high sliding speed than at rest. This will have the effect of increasing the (negative) slope of friction vs. sliding speed, and generate frictional vibrations more readily or more severely. 2. Frictional oscillations have also been seen when shearing films of a solvent of a few molecules thick between two molecularly smooth flat surfaces. When there is no sliding the atoms of the solid impose structure or lattice order upon the molecules of the liquid, extending to three or more molecular dimensions from each solid surface: such a system is sketched in Figure 5.20. Shear displacement of that ordered structure requires a progressively larger force with an increase in displacement. When the “shear strength” of the ordered solvent is reached, the lattice order changes progressively toward the unordered liquid structure in a manner equivalent to the generation of dislocations in plastically shearing metal. The shear resistance diminishes as shear progresses. This behavior is equivalent to a negative slope of the friction vs. velocity curve. Whether or not frictional oscillations (stick-slip) on the scale related to order–disorder phenomenon in nanodimension-thick solvents could couple with the larger–scale phenomenon remains to be seen. Few machines are lubricated with solvents, of course, but there is likely to be a similar order–disorder phenomenon in hydrocarbon lubricants, particularly in the lubricants containing molecules with branched side-chains (boundary additives). These molecules form strong bonds with metal ions (in the oxides), which then assume the lattice order in the oxides. The order–disorder phenomenon in these molecules will be of much larger dimension than that of solvents, likely increasing the possibility of some synchronized vibrational modes with the vibration frequencies in machinery. 3. A general increase in coefficient of friction with increase in normal load (or pressure) produces the same type of behavior as that produced by a decrease in friction with an increase in sliding speed. 4. Sometimes “hot spots” may be generated on surfaces, which produce variations in friction. Hot spots are local regions on a nominal contact region that heat and expand quickly, which propels the regions of the sliding bodies apart momentarily. Hot spots occur because in most machines, sliding components do not contact each other with uniform contact pressure, either because they do not conform to each other geometrically, or because they are not held rigidly. A hot spot
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exacerbates the inherent nonuniformity of contact which develops increasing amplitude of vibration and variation of friction as time progresses. Clutches and brakes are subject to this type of vibration because their surface temperatures rise quickly to rather high values. 5. Second-order effects arise from the effects of specimen waviness, for example, where the upper specimen bounces along the plate. These impulses may have the effect of providing impulses in both contact pressure and sliding speed, which often have their separate effects on µ.
5.9
Test Machine Design and Machine Dynamics
Likely, someday, the fundamental frictional behavior for some sliding pairs will be found, but that appears to be a distant prospect. Until then, testing will be necessary and product design would be greatly simplified if any convenient test machine could be used and operated in any convenient manner to measure that friction. Sometimes useful data can be derived from a simple test machine, but not often, and rarely for a novice. A skilled operator can often interpret laboratory data in a way that applies to production hardware, but not always. The shape of specimens, the manner of preparing surfaces, the manner of “break-in” at the beginning of sliding, the sliding cycles and stopping times, and several other issues can be important and must be considered in simulative testing. Furthermore, the dynamics of a test machine influences test results, particularly the severity and nature of the vibrations and variations in data. These variations in turn influence the data obtained from a sliding pair to varying degrees. It is instructive to operate two machines with identical specimens and observe the differences in the results between the two: even two identical machines can produce different results, depending on the condition of the bearings, the fit of the components, etc. As to test machines, adequate simulation requires careful attention to the dynamics of data acquisition systems as well as to machine dynamics. These are rather specialized topics beyond the scope of this chapter, but a simple discussion of the behavior of two cantilevered force transducers will introduce the subject of dynamics adequately for present purposes. One common cantilevered force transducer is sketched in Figure 5.21. The cantilever is firmly fixed to, and projects from a vertically adjustable base. The adjustable base lowers the pin into contact with
FIGURE 5.21
A simple cantilever force transducer for measuring friction.
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FIGURE 5.22
Modern Tribology Handbook
The hinged friction force transducer.
the disk, and is adjusted downward still more to produce a normal load between the two. The disk rotates and applies a force, F, to the pin. The force, F, bends the cantilever, which produces a maximum strain near the root of the cantilever. Strain gages are applied on the vertical surfaces of the cantilever. The vertical force can also be measured by strain gages applied near the root of the cantilever, on the horizontal (upper and lower) surfaces (not shown in Figure 5.21). One advantage of this configuration is that specimen (vertical) loading can be varied by moving the base up or down with a servomotor. One disadvantage is that the specimen loading will vary where the disk surface is not flat or not perpendicular to its support shaft. (Servo systems could be devised to compensate for such machine errors.) Another common type of cantilevered force is the hinged cantilever transducer system sketched in Figure 5.22. The load is applied directly in some manner upon the cantilever or pin holder. Either a mass or a force can be applied anywhere along the cantilever, or upon an extension of the cantilever beyond the pin holder. A mass will alter the vibration characteristics of the cantilever, whereas a low-mass force, as applied by a mass hanging on a weak spring or a force applied by an air cylinder, will have less effect. An important feature of both designs sketched in Figures 5.21 and 5.22 is that the contact area between the pin and specimen plate is usually located on neither the vertical nor the horizontal center line of the transducer bar. This is seen in detail in Figure 5.23, and it is apparent that a friction force applies a
FIGURE 5.23
View of the end of a friction force transducer showing three positions of the pin.
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FIGURE 5.24
Sketch of a tilted transducer bar.
moment to the cantilever. When the pin is in the leading position relative to the vertical axis of the transducer, a frictional impulse rotates the transducer counterclockwise, imparting a lifting impulse upon the transducer, which increases the vertical load on the sliding contact region (by bending the cantilever upward in Figure 5.21 and by accelerating a mass upward in Figure 5.22). This action constitutes a coupling between the vertical and horizontal mode of deflection of the transducer, which exacerbates the effect of inherent variations in friction force (depending to some extent on the match between the spacing of inherent frictional variations and natural frequency of bar vibration). By contrast, a frictional impulse upon a slider in the lagging position will also couple the vertical and horizontal deflection modes but in a manner that will diminish the effect of inherent variations in friction force. When the slider is in the middle position a small impulse would produce very little coupling. Where the contact region between the pin and specimen plate is above the centerline of the transducer bar, the effect is the opposite of that described above. A second type of coupling may occur when the root of a transducer in Figure 5.21 is tilted in the manner shown in Figure 5.24, and the stiffness in the horizontal direction is lower than that in the vertical direction. When the disk surface moves in the direction shown, a friction force, F, will be exerted that will bend the transducer in a direction having an upward component, by an amount dependent on the angle ε. In the case shown, a friction force will have the effect of reducing the vertical load on the sliding contact. When ε is in the opposite sense, a friction force will have the opposite effect. The above discussions focus on the vibration of a flexible transducer bar alone. The influence of the surrounding support structure and the influence of damping is a much more complicated matter, particularly where there is damping in the contacting interface between the sliding specimens.
5.10
Tapping and Jiggling to Reduce Friction Effects
One of the practices in the use of instruments is to tap and/or jiggle to obtain accurate readings. Tapping the face of a meter or gage probably causes the sliding surfaces in the gage to separate momentarily, reducing friction resistance to zero. The sliding surfaces (shafts in bearings, or racks on gears) will advance some distance before contact between the surfaces is reestablished. Continued tapping will allow the surfaces to progress until the force to move the gage parts is reduced to zero.
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Jiggling is best described by using the example of a shaft advanced axially through an O-ring. Such motion requires the application of a force to overcome friction. Rotation of the shaft also requires overcoming friction, but rotation reduces the force required to effect axial motion. In lubricated systems the mechanism may involve the formation of a thick fluid film between the shaft and the O-ring. In a dry system an explanation may be given in terms of components of forces. Frictional force usually acts in the exact opposite direction from the direction of relative motion between sliding surfaces. If the shaft is rotated at a moderate rate, there will be very little frictional resistance to slow axial motion. Jiggling, fiddling, and coaxing would appear to be an anachronistic practice in this age of computerbased data acquisition systems. To some extent, instruments are better and more precise than they were only 20 years ago, but friction remains unchanged. It is instructive to tap transducer heads and other sensors now and then, even today.
5.11
Equations and Models of Friction
There are many equations in the technical literature relating the coefficient of friction, µ, to various material properties and sliding conditions (Meng and Ludema, 1995). Virtually all of them are empirical in nature, having been derived from experimental data, with a constant or two to correspond with measured values of friction. Most friction tests are done over a range of sliding speed, V, a range of applied load, W, two or three harnesses, H, and often temperature, T. The resulting equations would be of the form, µ = kWaVbHcTd, and the exponent on each variable is likely to have some value other than one. Most often an equation is constructed by varying the load, for example, over some range while holding H, V, and T constant at some convenient value, and then treating each other variable in turn. This is done in the unrealistic expectation that the effect of each variable is independent of the others. The most curious variable to include is temperature, as if temperature by itself has some effect. It probably influences several other quantities in the contact region which, in turn, influences friction. Temperature, both from ambient heating and from frictional energy, affects lubricant viscosity and oxidation rate, for example, and the latter is likely not to be reversible. The major value of a complete friction equation for a particular system is to characterize the functioning of that system under dynamic conditions, that is, when operating under nonsteady-state conditions. Examples of such systems are artificial skeletal joints, robot joints, automotive steering assist devices (power steering), and computer hard disks as mentioned before. Modelers of such systems search in vain for equations with “friction as an output.” They generally prefer linear models or apply effort to linearize existing nonlinear models; apparently, stability of the mathematical expressions becomes an issue with nonlinear models. A complete equation for a “new” system requires extensive testing to derive. It is highly unlikely that an equation developed for one mechanical system can, at all, be applied to any other system. An example of friction modeling is seen in the designing of industrial robots and automotive power steering systems. Robot joints operate at fairly constant temperature but cover a wide range of sliding speed, stopping, starting, reversing, etc. Where a robot is used to place an object precisely at some location in a short time, the motor drive must ramp down at the proper rate, and this rate depends on the rate of change of friction as sliding speed changes. In essence, the motor must be programmed to meet the frictional resistance to be encountered in the joint as well as to accommodate the momentum (and inertia) of all moving masses. In automotive power steering systems, control is employed to multiply the effort of a human operator to turn the direction of a car in a predictable manner; control is made more difficult in this case by large temperature changes and, in hydraulic systems, by the wide range of friction in the shaft seals due to the wide ranges of hydraulic pressures required to meet highly variable turning resistances. Convenient representations of lubricated friction used by control designers are of the form shown in Figure 5.25 (Armstrong-Hélouvry, 1991). The first curve shows the force required to initiate sliding. This is a curve dominated by the elastic “wind-up” of the system between the power source and the sliding surfaces. The second applies to the sliding condition and is divided into four regimes: static friction, a transition from standing to the sliding condition, a level of friction at low sliding speed known as the
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friction force
friction force
static friction
time (distance)
kinetic friction
viscous friction
sliding speed
Representation of friction in lubricated joints used by control engineers.
static friction
FIGURE 5.25
transition region between static and kinetic friction
standing time FIGURE 5.26
Representation of the increase in static friction with time of standing.
kinetic friction, and a regime with positive slope labeled as viscous friction. The curve in Figure 5.25 has the appearance of a Stribeck curve with a spike at zero velocity representing static friction.
5.11.1
Static Friction
The magnitude of the static or starting friction of lubricated systems varies considerably according to standing time, or time at rest, as shown in Figure 5.26. This is most easily, but not totally satisfactorily explained as resulting from the squeezing out of lubricant during the standing time so that asperities continue to come into contact over the start-up time; it is surely not connected with the change in solidto-solid adhesion forces with shear rate. The transition from the static condition, before sufficient force is applied to slide is not expressed in terms of sliding speed but rather in terms of displacement by control engineers. The events at start-up are described in terms of breakaway or frictional lag. Some displacement, perhaps as large as 5 µm in the case of lubricated metals, may be required to effect complete breakaway. The breakaway phenomenon is described by Dahl (1987) in terms similar to the fracture of a brittle tensile specimen: two bonded asperities shear elastically until the bond fractures between the two, and a lower friction follows. Apparently, in the Dahl model, new points of adhesion are less firmly bonded during sliding than after standing for some time. The Dahl model is difficult to validate but some expression of the type of the Dahl model provides a link between force-displacement (static) behavior and force-velocity (dynamic) behavior after breakaway, through information on the acceleration of the body. The “stopping” phenomenon is the inverse of the breakaway phenomenon, but the magnitude of the displacement involved is usually too small to affect robot accuracy. The magnitude is readily measurable, however, in the case of a rubber seal on a shaft. Stick-slip is ordinarily described as involving alternate stopping and sliding of one body along another. Close examination shows that supposed zero velocity of a sliding interface during continuous movement of a prime mover is actually very slow sliding and just not perceptible moving. It is then interesting to speculate what is the minimum velocity of sliding in other noisy systems such as in the case of squeaking floor boards in an old house, or squeaking plastic panels above the instrument panel in a car, or squealing tires of cars.
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sliding speed
FIGURE 5.27
5.11.2
Hysteresis effect in lubricated sliding when the sliding speed varies.
The Stribeck Curve
The mixed or boundary lubrication region of the Stribeck curve (see Section 5.2) is a negative slope which tends to induce frictional vibrations (see Sections 5.8 and 5.9). This slope can be minimized, by a properly formulated lubricant. The lowest value of friction is taken as the kinetic friction, and to the right the Petrov form of curve is approximated as a straight line. This reflects the behavior of a lubricated shaft in a bearing with fixed spacing or clearance between the two, rather than the elastohydrodynamic case where film thickness varies with sliding speed. Most lubricated systems exhibit a hysteresis effect, that is, the friction follows a different path when the velocity is decreasing compared with increasing velocity. A simple hysteresis curve is shown also in Figure 5.27, but in some practical systems, the two curves are quite different from each other, producing different vibration characteristics. Whether or not this effect is included in control algorithms depends on the magnitude of allowed control error.
References Armstrong-Hélouvry, B. (1991), Control of Machines with Friction, Kluwer Academic Publishers, Boston. Barwell, F.T. (1979), Bearing Systems, Oxford University Press, Oxford, UK, chapter 1. Beare, W.G. and Bowden, F.P. (1935), Physical properties of surfaces I. Kinetic friction, Philos. Trans. R. Soc. London Ser. A, 234, 329-354. Bowden, F.P. and Tabor, D. (1954), Friction and Lubrication of Solids, Oxford University Press, Oxford, UK. Bowden, F.P. and Tabor, D. (1964), Friction and Lubrication of Solids, II, Oxford University Press, Oxford, UK. Cameron, A. (1966), Principles of Lubrication, John Wiley & Sons, New York, chapter 12. Childs, T.H.C. (1992), Deformation and flow of metals in sliding friction, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), NATO Applied Science Series, v. 220, Kluwer Academic Publishers, Boston, 209. Dahl, P.R. (1987), A solid friction model, TOR-158(3107)-18, The Aerospace Corporation, El Segundo, CA (a reference taken from Armstrong-Hélouvry, 1991). Evans, U.R. (1960), The Corrosion and Oxidation of Metals, Edward Arnold Publishers, London. Ferry, J.D. (1980), Viscoelastic Properties of Polymers, 3rd ed. John Wiley & Sons, New York, 15. Gao, D., Kuhlmann-Wilsdorf, D., and Makel, D.D. (1992), Moisture effects including stiction resulting from adsorbed water films, J. Tribology (ASME), 114, 174. Gee, M.L., McGuiggan, P.M., and Israelachvili, J. (1990), Liquid to solid-like transitions of molecularly thin films under shear, J. Chem. Phys., 93(3), 1895. Greenwood, J.A. and Tabor, D. (1955), Deformation properties of friction junctions, Proc. Phys. Soc. A, 68, 609-619. Grosch, K.A. (1963), The relation between the friction and visco-elastic properties of rubber, Proc. R. Soc. A, 274, 21.
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Hardy, W.B. (1923), Collected Works, Rideal, E.K. (Ed.), under the auspices of the Colloid Committee of the Faraday Society, Cambridge Press, Cambridge, U.K. Israelachvili, J.N. (1995), Surface forces and micro-rheology of molecularly thin liquid films, in Handbook of Micro/Nano Tribology, Bhushan, B. (Ed.), CRC Press, Boca Raton, 267. Kapoor, A. (1994), A re-evaluation of the life to rupture of ductile metals by cyclic plastic strain, Fatigue and Fracture of Engineering Material and Structures, 17, 2, 79-89. Li, Z., Rabinowicz, E., and Saka, N. (1989), The stiction between magnetic recording heads/slider interface, Tribology and Mechanics of Magnetic Storage Systems, STLE-SP 26, 64. Ludema, K.C. and Tabor, D. (1966), The friction and visco-elastic properties of polymeric solids, Wear, 9, 329. Ludema, K.C. (1979), J.J. Bikerman, friction and adhesion, Wear, 53, 1. Ludema, K.C. (1996), Friction, Wear, Lubrication: a Textbook in Tribology, CRC Press, Boca Raton, FL, 45. McClelland, G.M. and Glosli, J.N. (1992), Friction at the atomic scale, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), NATO Applied Science Series, v. 220, Kluwer Academic Publishers, Boston, 405. McKee, S.A. and McKee, T.R. (1929), Trans. ASME, APM, 57.15, 161. Meng, H.C. and Ludema, K.C. (1995), Wear models and predictive equations: their form and content, Wear, 181-183, 443-457. Murakami, T., Ohtsuki, N., and Hugaki, H. (1995), The adaptive multimode lubrication in biotribological systems, Proceedings of the International Tribology Conference, Yokohama, 1981-1986. Pashley, R.M. and Israelachvili, J. (1984), Molecular layering of water in thin films between mica surfaces and its relation to hydration forces, J. Colloid and Interface Science, 101, 51. Schallamach, A. (1963), A theory of dynamic rubber friction, Wear, 6, 375. Stachowiak, G.W. and Batchelor, A.W. (1993), Engineering Tribology, Elsevier Tribology Series #24, Amsterdam, 21821. Tabor, D. (1952), Plastic contact of rough surfaces, Proc. Roy. Soc. A, 212, 482. Tabor, D. (1955), The mechanism of rolling friction, Proc. R. Soc. A, 229, 181-220. Tabor, D. (1959), Junction growth in metallic friction: the role of combined stresses and surface contamination, Proc. R. Soc. A, 251, 378-393. Tomlinson, G.A. (1929), A molecular theory of friction, Phil. Mag, Series 7, 7, 905. vanAlsten, J. and Granick, S. (1990), Origins of static friction in ultra thin liquid films, Langmuir, 6, 876. VanVlack, L. (1959), Elements of Materials Science, Addison Wesley Publishing Co., Reading, MA. Victor, E. (1961), Friction, A Follet Beginning Science Book, Chicago. Wassink, D. (1996), Friction Dynamics in Low Speed Lubricated Sliding of Rubber: A Case Study of Lip Seals, Ph.D. thesis, University of Michigan, Ann Arbor.
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6 Frictional Heating and Contact Temperatures 6.1 6.2
Surface Temperatures and Their Significance.................. 235 Surface Temperature Analysis............................................ 238 Analytical Methods for Flash Temperature Rise Calculations • Numerical Methods for Surface Temperature Determination
6.3
Francis E. Kennedy Dartmouth College
6.1
Surface Temperature Measurement .................................. 259 Thermocouples, Thermistors, and Related Temperature Sensors • Radiation Detection Techniques • Ex Post Facto Methods
Surface Temperatures and Their Significance
Friction occurs whenever two solid bodies slide against each other. It takes place by a variety of mechanisms in and around the real area of contact between the sliding or rolling/sliding bodies. It is through frictional processes that velocity differences between the bodies are accommodated. It is also through these processes that mechanical energy is transformed into internal energy or heat, which causes the temperature of the sliding bodies to increase. The exact mechanism by which this energy transformation occurs may vary from one sliding situation to another, and the exact location of that transformation is usually not known for certain. It is known that solid friction and related frictional processes, including frictional heating, are concentrated within the real area of contact between two bodies in relative motion. Some investigators contend that these processes occur by atomic-scale interactions within the top several atomic layers on the contacting surfaces (Landman et al., 1993), while others believe that most energy dissipation occurs in the bulk solid beneath the contact region by plastic deformation processes (Rigney and Hirth, 1979). Experimental work has shown that at least 95% of the energy dissipation occurs within the top 5 µm of the contacting bodies (Kennedy, 1982). Although there may be disagreement about the exact mechanism of the energy transformation, most tribologists agree that nearly all of the energy dissipated in frictional contacts is transformed into heat (Uetz and Föhl, 1978). This energy dissipation, called frictional heating, is responsible for increases in the temperatures of the sliding bodies, especially within the contact region on their sliding surfaces where the temperatures are highest. For the purposes of this discussion, it will be assumed that all frictional energy is dissipated as heat which is conducted into the contacting bodies at the actual contact interface. Frictional heating and the resulting contact temperatures can have an important influence on the tribological behavior and failure of sliding components. Surface and near-surface temperatures can become high enough to cause changes in the structure and properties of the sliding materials, oxidation of the surface, and possibly even melting of the contacting solids. These temperature increases can often be responsible for changes in the friction and wear behavior of the material or the behavior of any
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lubricant present in the contact. Among the most important effects of frictional heating on tribological processes are the following: • Sliding friction of materials with low melting points is often dominated by frictional heating effects. The low sliding friction of ice and snow is due to the presence of a thin lubricating layer of meltwater which results from frictional heating of contacting ice crystals (Bowden and Hughes, 1939; Oksanen and Keinonen, 1982; Akkok et al., 1987). The low friction brought about by meltwater lubrication is critical for winter sports such as skiing, ice skating, and bobsledding. The temperature rise at the contacting ice asperities may not be sufficient to cause melting at very low sliding speeds; as a result the friction coefficient of ice and snow at very slow velocities may be as high as 0.6 to 0.8, but as soon as higher sliding velocities cause sufficient melting of the surface to produce a lubricating layer, the friction coefficient drops below 0.1 (Kennedy et al., 1999). • Even metallic components can have contact temperatures which are sufficiently high to melt the sliding surfaces within the real area of contact if the sliding speeds are high enough. As is the case with ice, this results in a thin lubricating layer of molten material which lowers the friction significantly and increases wear (Montgomery, 1976; Carignan and Rabinowicz, 1980). Such a condition occurs with rocket sleds and with projectiles traveling in gun barrels. • Elastomers and polymers also have friction and wear behavior which is significantly affected by interface temperatures. This regime of tribological behavior has been called the “thermal control regime” (Ettles, 1986). Frictional heating can cause surface temperatures to reach the melting or softening temperature of thermoplastic polymers, and this results in a drastic change in the friction and wear behavior of the polymer (Lancaster, 1971; Kennedy and Tian, 1994). In fact, Lancaster showed that the “PV limit,” which is often used in the design of dry plastic bearings, is in reality a “critical surface temperature limit”; i.e., the combination of contact pressure and sliding velocity causes the surface temperature to reach the critical temperature of the material (Lancaster, 1971). Even if the surface temperature does not reach the critical temperature, the viscoelastic behavior of the polymer or elastomer can be significantly affected and the resulting friction can be altered (Ettles and Shen, 1988). Design methodology has been developed for polymer bearings based on the avoidance of surface temperatures which could be detrimental to their tribological performance (Floquet et al., 1977). • In normal circumstances, most metallic tribological components do not have contact temperatures which approach their melting or softening point, but the temperatures can still have a very major effect on their tribological behavior. • The phenomenon of galling or seizing of metals results from a combination of contact temperature and contact pressure at asperity junctions sufficient to cause microwelding of the two surfaces at those points. A galling criterion based on thermal considerations was developed by Ling and Saibel (1957/58). • The oxidation which occurs on sliding metallic surfaces exposed to air or to oxygen-containing lubricants is of great practical importance. When the oxide film is coherent and well bonded to the surface, it is beneficial because it prevents metal–metal contact and thus lowers wear and friction. When the oxide film is easily removed from the surface, however, oxidation is detrimental because it promotes wear by third-body abrasion by hard oxide particles. The subject of oxidation in sliding components and its relation to surface temperatures was reviewed by Quinn (1983) and Quinn and Winer (1985). • Contact temperatures and the resulting thermal stresses can play an important role in wear of sliding metallic components. The fact that temperature gradients around the contacts are very large can be responsible for softening and shear failure of the near-surface layer of the material in many situations (Rozeanu and Pnueli, 1978). The thermomechanical stress field around a sliding contact can be responsible for wear of the contacting materials, and it can be an
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Frictional Heating and Contact Temperatures
•
•
•
•
•
237
important wear mechanism for both ceramics and metals; such wear can be modeled by the “thermomechanical wear theory” (Ting, 1988). • “Wear mechanism maps” have been developed in recent years to show graphically the transitions between the different mechanisms of dry sliding wear of metals (Lim and Ashby, 1987). Many of the wear mechanisms, such as mild oxidational wear, severe oxidational wear, and melt wear are very much affected by temperature, and the transitions can be dominated by contact temperature effects. As a result, the wear mechanism maps are, to a large extent, based on surface temperature maps (Lim and Ashby, 1987; Ashby et al., 1991). Owing to the high hardness and low thermal conductivity of many ceramics, the real contact areas of sliding ceramic components are often very small and very hot (Griffioen et al., 1986). The high contact temperatures and large temperature gradients can be responsible for large thermomechanical stresses which cause thermocracking and wear of the sliding ceramic surfaces. These phenomena are particularly important for ceramics such as zirconia which are susceptible to thermoelastic instability and thermocracking (Lee et al., 1993). Contact temperatures may play an even greater role in wear transitions for ceramics than in those for metals (Hsu and Shen, 1996). Scuffing or scoring is an important failure mode for lubricated sliding or rolling/sliding components such as gears or cams. Most models for scuffing failure are based on a critical contact temperature which causes scuffing by either weakening the lubricant film so it is unable to support the load (Blok, 1937; Dyson, 1975) or increasing the shear stress in the film to a limiting value (Jacobsen, 1990). The effect of temperature on the lubricant and its additives is also important (Enthoven et al., 1993). The effectiveness of boundary lubrication is strongly dependent on contact temperature. Friction and wear with lubricants containing physically or chemically adsorbed additives deteriorate rapidly when the contact temperature reaches a critical value at which the additive molecules desorb (Fein et al., 1959). The role of frictional heat in the lubricant transition has been well established (Ettles et al., 1994). Lubricants containing extreme pressure (EP) additives rely on high contact temperatures to promote the formation of protective films on the contact surfaces (Spikes and Cameron, 1974). The thermal deformations around frictionally heated contacts can give rise to the phenomenon known as thermoelastic instability (TEI). The disturbances in contact geometry, temperature, and stress which accompany TEI can have a significant effect on the performance of brakes (Dow, 1980; Barber et al., 1986), mechanical face seals (Banerjee and Burton, 1979; Kennedy and Karpe, 1982), electrical contacts (Dow and Kannel, 1982), and gas path seals (Kennedy, 1984). The development of TEI involves the interaction of frictional heating, surface deformation, and wear, and its avoidance requires an understanding of those three phenomena and their interaction. In addition to the effects noted above, excessive surface temperatures can contribute to the operational failure of many tribological components. One important example is magnetic storage devices. Failure of magnetic tape systems is frequently influenced by the temperature of the head/tape interface (Bhushan, 1987b), and magnetic disk storage systems are subject to degradation of protective coatings and/or lubricant, owing to high temperatures at the head/disk interface (Bhushan, 1992).
The ability to predict and measure the surface temperatures of actual contacting bodies is important if failure of tribological components is to be avoided. In addition, frictional heating has such an important influence on the tribological behavior of so many sliding systems that all tribotests must be designed with thermal considerations in mind (Floquet, 1983), and frictional heating must be considered in interpreting the results of tribotests. Before describing the methods used for surface temperature determination, it may be useful to review the geometric and temporal conditions under which the contact temperatures occur. As is shown in Figure 6.1, there are three levels of temperature in sliding contacts. The highest contact temperatures,
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FIGURE 6.1
Schematic diagram of temperature distribution (isotherms) around sliding contact.
Tc, occur at the small (perhaps on the order of 10 µm diameter) contact spots between surface roughness peaks or asperities on the sliding surfaces. These temperatures can be very high (over 1000°C in some cases) but last only as long as the two asperities are in contact. This could be less than 10 µs. The asperity contacts are often confined to a small portion of the surface of the bodies, which could be called the nominal contact patch. An example of this is a typical elliptical Hertzian contact area of several hundred µm length between two contacting gear teeth. At any instant, there are usually several short-duration flash temperature rises (∆Tf ) at the various asperity contact spots within a nominal contact patch. The integrated (in space and time) average of the temperatures of all points within the contact patch could be called the nominal (or mean) contact temperature (Tnom). The nominal contact temperature can be over 500°C for severe sliding cases, such as in brakes, but is usually much lower. The temperature diminishes as one moves away from the contact patch, and it generally decreases to a rather modest bulk volumetric temperature (Tb) several mm into the contact bodies. That temperature is generally less than 100°C. The total contact temperature (Tc) at a given point is given by the total of the three contributions:
Tc = Tb + ∆Tnom + ∆Tf
(6.1)
In the remainder of this chapter, methods will be discussed for determining the interfacial contact temperatures, Tc, in tribological systems. This temperature determination can be made by either analytical prediction or experimental measurement, and both of these methods will be discussed.
6.2
Surface Temperature Analysis
Consider a general two-body sliding (or rolling/sliding) contact in which Body 1 is moving with velocity V1 relative to the contact area and Body 2 is moving with velocity V2 relative to the same contact area. The rate of total energy dissipated in the sliding contact is determined by the friction force and the relative sliding velocity. If it is assumed that all of this energy is dissipated as heat on the sliding surfaces within the real area of contact, then the rate of heat generated per unit area of contact, qtotal , is given by:
q total = µ pU where µ is the coefficient of friction p is the contact pressure (which may vary within the contact area) U is the relative sliding velocity = V2 – V1
(6.2)
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Fourier’s law for heat conduction in an isotropic solid which is moving with velocity V may be written:
∂T DT ∇⋅ k∇T + Q˙ = ρC = ρC + V ⋅∇T Dt ∂t
(6.3)
· where Q is internal heat generation rate per unit volume, k is thermal conductivity, ρ is density, and C is specific heat. If there is no internal heat generation and if k is uniform and constant:
∂T k∇ 2T = ρC + V ⋅∇T ∂t
(6.4)
or
∇ 2T =
1 DT κ Dt
(6.5)
k - = thermal diffusivity. where κ = -----ρC
The problem in surface temperature analysis is to determine the solution to (Equation 6.5) subject to boundary conditions which include the heat generation (Equation 6.2) at the contact interface and other thermal boundary conditions suitable for the operating conditions and geometry of the contacting solid bodies. Both analytical and numerical methods have been used to solve for the surface temperatures resulting from frictional heating.
6.2.1 Analytical Methods for Flash Temperature Rise Calculations Most surface temperature analyses have been based on the pioneering work of Blok (1937) and Jaeger (1942), both of whom used heat source methods. Similar methods were later used by many other investigators, such as Kuhlmann-Wilsdorf (1987) and others. Heat source methods are most useful for determining the flash temperature rise component of contact temperature. 6.2.1.1 Flash Temperature Rise due to Stationary Heat Source on a Stationary Body 6.2.1.1.1 Continuous Point Heat Source on Surface of Stationary Semi-infinite Body Assume that a heat source with constant heat supply rate Q is activated at time t = 0 at a point x = x′, y = y′, z = 0, as shown in Figure 6.2. Let the surface z = 0 be insulated except at the heat source. It is shown in Carslaw and Jaeger (1959) that the solution for this transient problem is given by
(
)
∆T x , y , z , t =
t
Q ρC
( )
− r 2 4κ t − t ′
( ) ∫ (t − t ′) e
32
4 πκ
32
dt ′
(6.6)
t′ = 0
where r = [(x – x′)2 + (y – y′)2 + z2]1/2 is the radius from the heat source to the point of interest. Using the definition of the complementary error function
( )
erfc X =
2 π
∫
∞
X
2
e − X dX
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FIGURE 6.2
Modern Tribology Handbook
Point source of heat on a stationary half-space.
Equation 6.6 becomes
∆T =
r Q ρC erfc 2πκr 4κt
(6.7)
The complementary error function erfc(X) shows a variation of the form shown in Figure 6.3. Therefore, erfc(0) = 1, so the steady-state temperature (for t → ∞ or X → 0) is given by
∆Tss =
Q ρC Q = 2πκr 2πkr
(6.8)
Note: this solution is not valid at the origin, where r = 0. This implies that the surface temperature becomes extremely high at the concentrated point heat source. In actuality, though, the heat input cannot be concentrated at an infinitesimally small point. It must be distributed over a finite area (the real area of contact).
FIGURE 6.3
Complementary error function, erfc (X).
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6.2.1.1.2 Distribution of Continuous Heat Flux on Surface of Stationary Half-Space Let q equal the rate of heat supply per unit area. We can treat a distributed heat flux as a collection of continuous point heat sources. A heat source Q = q dx ′ dy ′ can be considered to act at point x ′, y ′. The steady-state temperature at point P(x,y,z) due to that source is found, using Equation 6.8, to be
dT =
qdx ′dy ′
(
) (
)
2 2 2πk x − x ′ + y − y ′ + z 2
(6.9)
1 2
By superposition, the steady state temperature rise at P due to all heat sources is the integral
∆T =
∫∫
qdx ′dy ′ A′
(
2πk
) (
(6.10)
)
2
2
x − x′ + y − y′ + z2
where the heat flux q may be a function x ′ and y ′, and A′ is the area over which q(x ′, y ′) is distributed. Similarly, the transient temperature rise at P due to q is found (from Equation 6.7) to be
∆T =
∫∫
A′
2πk
(
(
) (
)
1
2 2 2 x − x′ + y − y′ + z2 q dx ′dy ′ erfc 2 2 4κt x − x′ + y − y′ + z2
) (
)
(6.11)
6.2.1.1.2.1 Constant Heat Supply Over Entire Surface z = 0 (–∞ < x′ < ∞, –∞ < y′ < ∞) If q is constant (uniform heat flux) over the entire surface of a half space, Equation 6.11 integrates to give
2q κt − z 2 e k π 12
∆T =
4 κt
z z − erfc 2 2 κt
(6.12)
This is the case of linear heat transfer in a rod due to a heat flux q at the end (Carslaw and Jaeger, 1959). The temperature rise at the heated end, z = 0, is given by
∆T =
2q κt k π
12
t = 2q πρCk
12
(6.13)
From Equation 6.13 we can see that the surface temperature rise for this case of linear heat transfer is directly proportional to the heat flux and that an increase in either thermal conductivity or heat capacity will lead to a decrease in surface temperature. Constant Heat Supply on Infinite Strip – b ≤ x′ ≤ b, – ∞ ≤ y′ ≤ ∞ 6.2.1.1.2.2 For this case of a band heat source on the surface of a semi-infinite solid, the temperature distribution on the surface z = 0 is given by (Carslaw and Jaeger, 1959)
q κt ∆T = k π
12
b+x b+x b−x b+x + erf − Ei − erf 4κt 2 κt 2 πκt 2 κt
( ) − 2
( )
b−x Ei − 4κt 2 πκt b−x
2
(6.14)
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FIGURE 6.4 Temperature distribution across a heated strip of width 2b on the surface of a stationary semi-infinite solid. Curve is for case κt = b2.
where the error function
( )
erf X =
π∫
2
X
2
e − u du
0
and the exponential integral
( ) ∫
Ei − X = −
∞
X
e −u du u
A plot of Equation 6.15 is given in Figure 6.4. It can be seen that the peak temperature rise occurs at the center of the strip (x = 0) and is given by
∆Tmax
2q κt = k π
12
erf
b 4κt
b2 Ei − 4 πκt 4κt b
−
(6.15)
At large times (t → ∞) Equation 6.15 approaches a steady-state value
∆Tmax SS =
2qb k π
(6.16)
6.2.1.1.2.3 Constant Heat Supply q on Circular Region of Radius a on Surface z = 0 (Figure 6.5) In this case the steady-state temperature rise inside the heated circle on the surface z = 0 is given by:
2qa ∆T = πk where x2 + y2 = r2 and r ≤ a.
∫
π 2
ϕ=0
2
r 1 − sin2 ϕ dϕ a
(6.17)
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Frictional Heating and Contact Temperatures
FIGURE 6.5
Circular heat source on surface of stationary body.
FIGURE 6.6
Point source of heat on the surface of a semi-infinite solid moving in x-direction with velocity V.
At the center of the circle, r = 0 and the temperature rise reaches a maximum
∆Tmax =
qa k
(6.18)
We note that for each of the cases of distributed heat flux, the temperature on the surface where heat is being applied remains finite. 6.2.1.2 Stationary Heat Source on Moving Body (or Moving Heat Source on Stationary Body) This problem is treated by Carslaw and Jaeger (1959). The problem of a moving heat source on a stationary body is equivalent to the problem of a stationary heat source on a moving body. The important concept is that there is relative motion between the source of heat and the body into which the heat flows (convective diffusion). 6.2.1.2.1 Moving Semi-infinite Body with Stationary Continuous Point Heat Source (Figure 6.6) Following the treatment of Carslaw and Jaeger (1959), define two coordinate systems as follows: • Fixed x, y, z system, with origin at the stationary heat source • Moving x′, y′, z′ system, fixed in body moving with velocity V The two coordinate systems are related by the expressions:
x ′ = x − Vt
y′ = y
z′ = z
Therefore, the temperature at a point P at time t is T(x,y,z,t) = T(x′ + Vt, y, z, t). Fourier’s law for heat conduction in the moving body is Equation 6.3, where now the material derivative is given by
DT ∂T ∂T = +V Dt ∂t ∂x
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Assume that the surface of the moving body is insulated except at the point heat source, which has strength Q. (Note: Gecim and Winer (1985) and others have found that convective cooling of the surface causes a negligible effect on flash temperature rise, so it is appropriate to assume an insulated surface when determining ∆Tf .) The solution for this case is (Carslaw and Jaeger, 1959) Vx
∆T =
Q ρC 2 κ e π 3 2κR
∫
∞
ξ= R
e−ξ
κt
2
−V 2 R 2 16 κ 2 ξ 2
dξ
(6.19)
where R = x2 + y2 + z2 As time t → ∞, the temperature rise ∆T approaches its quasi-steady-state value ∆Tss.
∆TSS =
Q − V ( R− x ) e 2πkR
2κ
(6.20)
As was the case with the stationary body, these solutions are not valid at the heat source (R = 0), which was assumed to act at an infinitesimally small point. A more realistic condition is the case of a distributed heat source, with the heat being distributed in some manner over a finite area. Any problem involving a distributed heat source on the surface of a moving semi-infinite body can be solved by integrating Equation 6.20 for the quasi-steady-state case or Equation 6.19 for the transient case. 6.2.1.2.2 Uniform Band Source Acting Over –b ≤ x ≤ b, – ∞ ≤ y ≤ ∞ on Moving Body Consider a semi-infinite body moving with velocity V in the x-direction, with a stationary heat source providing a flux q over the band (Figure 6.7). The quasi-steady-state temperature rise for this case is found by integrating the point source solution Equation 6.20. The result is (Carslaw and Jaeger, 1959):
∆T =
∫
b
q e π −b k
(
V x− x′ 2κ
)
1 2 V 2 K 0 x − x ′ + z 2 dx ′ 2 κ
(
)
(6.21)
where K0( ) is the modified Bessel function of the second kind, order 0. This result (Equation 6.21) is plotted in Figure 6.8. It can be seen that the results depend very much on the nondimensional Peclet number
Pe ≡
FIGURE 6.7
Vb 2κ
(6.22)
Uniform band heat supply on surface of semi-infinite solid moving in x-direction with velocity V.
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10
κ q)
T (π k V / 2
Pe = 10 8
6
5 2
4
1 0.5
2
0.2 -2
-1
0
1
2
3
4
x/b
FIGURE 6.8 Surface temperature rise for a semi-infinite solid caused by friction at a contact of width 2b over which it slides with velocity V.
At large values of the Peclet number, say Pe ≥ 10, the maximum temperature is seen to occur at the trailing edge. In such a case the maximum temperature rise at the trailing edge x = b is given by
∆Tmax =
2qb k πPe
(6.23)
where Pe ≥ 10. It can be noted from Equation 6.23 that for constant q the maximum surface temperature decreases as the velocity increases (or Pe increases). This is due to the nature of heat transfer to a moving body. The material entering the heat source at the leading edge (x = –b) is at the relatively cool nominal surface temperature. That material has a finite heat capacity and thermal diffusivity, so a finite time is required to absorb the heat that causes an increase in its temperature. As the body’s velocity increases, there is less time spent beneath the heat source by a given volume of material, and thus the temperature increase of the material will be smaller. If the temperature is evaluated at different depths z, one would find that the temperature decreases very rapidly as z > 0, especially at high sliding velocities or high Pe. The heat that enters the moving body beneath the heat source is concentrated in a thin zone (the thermal boundary layer) under the heat source. This is shown in Figure 6.9. For values of Peclet number less than 10, a closed-form expression for maximum temperature rise (equivalent to Equation 6.23) is not as easily found, but approximate expressions have been developed
FIGURE 6.9 Temperature distribution in a moving body at low and high Peclet numbers. (From Stachowiak, G.W. and Batchelor, A.W. (1993), Engineering Tribology, Elsevier, Amsterdam. With permission.)
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by Kuhlmann-Wilsdorf (1987), Greenwood (1991), and Tian and Kennedy (1994). For a uniform band source of heat on the surface of a body moving relative to the heat source with velocity V, the maximum flash temperature rise can be approximated as follows (Tian and Kennedy, 1994):
∆Tmax ≈
2qb
(
k π 1 + Pe
(6.24)
)
6.2.1.2.3 Moving Source with Uniform Heat Flux on Circular Region of Radius a The solution for the case of uniform circular heat source on a moving body can be found using the results of Jaeger (1942). The maximum flash temperature rise for high Peclet number (Pe > 10) is:
∆Tmax ≈
2qa
(6.25)
k πPe
where in this case the Peclet number is defined as:
Pe ≡
Va 2κ
(6.26)
For the entire range of Peclet number, the maximum steady-state flash temperature rise can be approximated as (Greenwood, 1991):
∆Tmax ≈
(
2qa
k π 1.273 + Pe
)
(6.27)
6.2.1.3 Summary of Solutions for Maximum Temperature Rise with Heat Sources of Various Shapes The maximum flash temperature rise for a number of different contact shapes and pressure distributions has been determined by many investigators, including Blok (1937), Jaeger (1942), Archard (1958/59), Kuhlmann-Wilsdorf (1987), Greenwood (1991), Tian and Kennedy (1994), and Bos and Moes (1994). Generally they integrated expressions for the temperature rise due to a single heat source on a stationary or moving body (Equations 6.8 or 6.20, respectively) to obtain the maximum surface temperature within the heated region. A compilation of their solutions is given in Table 6.1 for the entire range of Peclet number, which is defined by Equation 6.22 for the case of band or square heat source or by Equation 6.26 for circular or elliptical heat source (Figure 6.10). It should be noted that contacting asperities which are plastically deformed have a contact pressure distribution which is approximately uniform, giving a uniform heat flux, whereas elastic contacts have a Hertzian contact pressure distribution, which results in a parabolic or semi-ellipsoidal heat flux distribution. Expressions for average temperature rise in the contacts can also be determined, and such expressions can be found in Archard (1958/59), Greenwood (1991), Tian and Kennedy (1994), and Bos and Moes (1994). The expressions given in Table 6.1 can be used in the determination of contact temperature by the methodology to be described below. 6.2.1.4 Flash Temperature Transients Although methodology is presented above for determining either transient or steady-state flash temperature rises, the expressions in Table 6.1 are for steady or quasi-steady-state conditions. Since the initial work by Blok (1937) and Jaeger (1942), nearly all investigators have assumed that steady conditions prevail. There are two reasons for using the steady-state or quasi-steady-state assumption:
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TABLE 6.1 Expressions for Maximum Flash Temperature Rise for Various Heat Source Distributions Maximum Flash Temperature Rise (Steady State) Shape of Heat Source
Heat Flux Distribution
Stationary or Low Speed Pe < 0.1
Figure No.
High Speed Pe > 10
2qb
2qb
k π
k πPe
Band
Uniform
6.7
Square
Uniform
6.10a
1.122qb k
Circular
Uniform
6.5
qa k
k πPe
Circular
Parabolic
6.10b
3πqa 8k
k πPe
Elliptical
Uniform
6.10c
Elliptical
Semi-ellipsoidal
6.10d
2qb k πPe 2qa
2.32qa
Approximate Expression for All Velocities 2qb k π(1 + Pe ) 2qb k π(1.011 + Pe ) 2qa k π(1.273 + Pe ) 2.32qa k π(1.234 + Pe ) 2qa
qa
2qa
k Se
k πPe
k π(1.273Se + Pe )
3πqa
2.32qa
2.32qa
8k Se
k πPe
k π(1.234Se + Pe )
Pe is the Peclet number given by Equation 6.22 for band or square contacts and by 6.26 for – circular or elliptical contacts, q is the mean heat flux, Se is a shape function for elliptical heat sources, given by Se =
(
16e1.75
)(
3 + e 0.75 1 + 3e 0.75
)
and e = b/a is the aspect ratio of the elliptical source. Source: Adapted from Jaeger, 1942; Kuhlmann-Wilsdorf, 1987; Greenwood, 1991; Tian and Kennedy, 1994; and Bos and Moes, 1994.
1. The steady-state temperature is the largest flash temperature rise that can occur, so that assumption will result in conservative estimates of maximum surface temperatures. 2. The steady-state condition is reached in a very short time after sliding commences, so nearly all of the time of sliding is spent in steady-state conditions. It is of interest to confirm the validity of the second assumption and to know how long it takes for steady-state conditions to be reached. Jaeger (1942) evaluated the transient temperature at the center of a square heat source moving at a velocity V over a surface, and the results are shown in Figure 6.11. It can be seen that the temperature rapidly approaches the steady-state value at a rate that is dependent on Peclet number. Bhushan (1987a) analyzed those results and concluded that the flash temperature reaches its steady-state value after moving a distance of only 1.25 times the length of the heat source. More recently, Yevtushenko et al. (1997) studied the transient temperature rise for a moving circular heat source and concluded that the temperature reaches at least 87% of its steady-state value almost instantaneously (within approximately one heat source length for a Peclet number of 1) and then asymptotically approaches the steady state. The duration required to reach steady-state conditions decreases as the sliding velocity (or Peclet number) increases; the longest duration is that for a stationary heat source. Gecim and Winer (1985) analyzed the case of a stationary circular source and concluded that the surface temperature is a function of the Fourier number, F = κt/R2. The maximum temperature (at the center
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FIGURE 6.10 Diagrams of heat sources used in Table 6.1. (a) Square heat source with uniform heat flux distribution. (b) Circular heat source with parabolic heat flux distribution. (c) Elliptical heat source with uniform heat flux distribution. (d) Elliptical heat source with semi-ellipsoidal heat flux distribution.
FIGURE 6.11 Surface temperature at center of a moving square heat source as function of time and Peclet number. (Adapted from Jaeger, J.C. (1942), Moving sources of heat and the temperature of sliding contacts, Proc. R. Soc. NSW, 76, 203-224.)
of the source) reaches about 95% of its steady-state value before F = 25 and then gradually approaches the steady value by the time F = 100 (Gecim and Winer, 1985). Based on these considerations, in nearly all frictional heating situations it can be safely assumed that the steady-state (or quasi-steady-state) conditions prevail, and the solutions listed in Table 6.1 can be used. In cases involving contacts of very short duration, however, it may be necessary to use transient solutions of the heat source equations. For example, Hou and Komanduri (1998) found that in threebody abrasive finishing operations the contact times between an abrasive grit and a surface being polished or ground are so short that transient surface temperature solutions may be required.
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6.2.1.5 Nominal Surface Temperature Rise If a single concentrated heat source does not repeat the same path over the contact surface, and if the body is very large, there is no significant nominal surface temperature rise because all heat generated at the contact spot is transferred into the three-dimensional heat sink. The contact temperature in that case can be found, without significant error, by adding the local (flash) temperature rise to the bulk temperature of the body, as was done in Blok’s (1937) analysis. However, if the heat source passes repeatedly over the same point on the surface, there unavoidably exists an extra surface temperature rise because the frictional heat generated during one pass cannot all flow away from the contact area before the next generation of heat at the same spot. The extra surface temperature rise is the nominal surface temperature rise. (Some others, such as Ashby, et al. (1991), have referred to this as a bulk surface temperature rise.) In determining the nominal surface temperature rise, an imaginary heat flux could be considered to be evenly distributed across the entire nominal contact area on the stationary body and another imaginary heat flux applied to the contacting surface of the moving body (Tian and Kennedy, 1993). The thermal response of the bodies to those heat fluxes would then be analyzed. For the case of a fast-moving heat source which repeatedly sweeps over the same path (as for a pin on a wear track on a disk or a brake pad on a rotor), or for a heat source which oscillates over the same contact path, the heat flux on the moving body should be applied to the entire area swept out by the contact. For a slow speed case, the imaginary heat flux would be applied only to the nominal contact area. While surface heat convection has little influence on the local temperature rise, the nominal temperature rise is affected by large-scale boundary conditions such as convection or conduction, as well as the total heat entering the body. Therefore, the nominal surface temperature rise on one of the contacting bodies can be expressed as:
(
∆Tnom = f Q, Anom , h, t , G
)
(6.28)
where Q is the total heat entering the contact surface of the body due to friction and other heat sources, Anom is the nominal contact area, h is heat convection coefficient at boundaries, t is the time during which the frictional heat is applied, and G is a geometrical and material factor related to the shape of the finite body and thermal properties of the material. In most cases the nominal temperature rise can be determined by an approximate one-dimensional analysis in which the heat flux is spread over the nominal contact area Anom if the body is not moving relative to the heat source. If the body is moving relative to the heat source, Anom is replaced by Aswept, which is the entire area swept out by the heat source. This concept is best illustrated by examples. Consider the case of a stationary pin of circular crosssection sliding against a rotating disk (Figure 6.12). The pin, which is stationary with respect to the contact zone, will be considered first. It is assumed to be held in place by a large heat sink at bulk temperature Tb1 and has heat flux q1 entering the real area of contact Ar on its surface. The nominal area Force
Heat Sink Tb1
Disk properties k2, K2
DISK
FIGURE 6.12
Sink/Pin contact properties Ac1, hc1
PIN Pin properties k1, K1
l1
2a
Schematic diagram of a typical pin-on-disk contact.
velocity V
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of contact is Anom1 = πa2. If the nominal area of contact is larger than the real area of asperity contact, the nominal heat flux into the stationary pin is:
qnom1 = q1 Ar Anom
(6.29)
Assuming that the pin has been in contact long enough to come to thermal steady state, then the heat flow in the pin is approximately linear and the nominal surface temperature rise for that body is given by (Ashby et al., 1991):
∆Tnom1 = Tnom1 − Tb1 = qnom1 lb1 k1
(6.30)
If there is very good thermal contact between pin and heat sink, the heat conduction length lb1 is equal to the pin length l1. Imperfect thermal contact between pin and heat sink can lead to higher nominal temperature rises for the stationary body. This can be taken into account by adjusting the heat conduction length using the method of Ashby et al. (1991). If the effective heat transfer coefficient between pin and clamp is hc1 (units: W/m2K), then simple continuity of heat fluxes gives:
lb1 = l1 +
Ank1 Ac1hc1
(6.31)
where Ac1 is the nominal area of the clamp contact. Ashby et al. (1991) found that the effective heat conduction length lb1 can often be double the actual length l1. The nominal heat flow into the moving disk can be determined in several ways. Ashby et al. (1991) consider that the heat source is injecting heat into a point on the disk surface for only a transit time, after which the heat diffuses into the bulk of the body before the same point is heated again on the next traversal past the heat source. They determine an effective diffusion distance lb2, which is given by the following expression (Ashby et al.,1991):
lb2 =
2πκ 2 a tan−1 12 π aV
12
(6.32)
Then the nominal surface temperature rise for the moving body is determined by:
∆Tnom2 = Tnom2 − Tb 2 = qnom2 lb 2 k2
(6.33)
An alternative approach which is particularly useful for relatively rapidly moving bodies was suggested by Tian and Kennedy (1993). The nominal heat flux for a moving body can be modeled as an imaginary, evenly distributed, stationary heat source over the whole sliding surface (Aswept). The imaginary average stationary heat flux in this case equals (from Equation 6.29):
qnom2 = q2 Ar Aswept
(6.34)
where Aswept is the total surface area swept out by the nominal sliding track on the contact surface of the moving disk. For example, if the wear track on a disk surface has a mean radius rm (Figure 6.13) then the swept area is Aswept = 2π rm (dn), where dn is the nominal width of the contact in the direction perpendicular to sliding. The solution for the nominal surface temperature using the imaginary heat flux Equation 6.24 can usually be found by solving a one-dimensional heat conduction problem for the thickness of the disk, resulting in Equation 6.33.
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FIGURE 6.13
View of normal sliding track (wear track) on moving disk surface.
FIGURE 6.14
Stationary band heat source on outside surface of rotating cylinder.
251
If convection occurs over the surface of the moving disk, and if the average convection coefficient over the whole contact surface is h, it can be shown that the steady-state temperature rise above the background temperature is (Tian and Kennedy, 1993):
∆Tnom2 = Tnom2 − Tb 2 = qnom2 h
(6.35)
A similar equation results for the case of a stationary heat source acting on the surface of a fast-rotating cylinder as shown in Figure 6.14. Assume that the nominal width of the heat source is equal to the width of the cylinder and that there is no heat loss from the circular ends of the cylinder. The average convection coefficient over the contacting surface is h. Using the present surface temperature model, the swept area on the cylinder surface is Aswept = 2π ro (w), where ro is the mean radius of the cylinder and w is the axial width of the nominal contact area (and of the cylinder). Equations 6.34 and 6.35 are still valid for determining the nominal heat flux and nominal surface temperature rise, respectively, for this case (Tian and Kennedy, 1993). 6.2.1.6 Partition of Frictional Heat When frictional heating occurs at a contact interface during sliding, it is necessary to determine the partition of frictional heat between the two contacting bodies in order to predict the surface temperature rise using the aforementioned solutions for temperature in a single body.
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We will assume that all of the frictional heat, given by Equation 6.2, is generated at the contact interface within the real area of contact. Some of the generated heat goes into Body 1, which is moving at velocity V1 relative to the contact area, and some into Body 2, which is moving at velocity V2 relative to the contact. Define q1 = heat flux (heat per unit time per unit area) into Body 1 q2 = heat flux into Body 2 Then
q1 + q2 = qtotal = µpU
(6.36)
where U = V2 – V1. Let us define heat partitioning factor α:
α = q1 qtotal
and
1 − α = q2 qtotal
(6.37)
Then
q1 = αµpU
and
(
)
q2 = 1 − α µpU
(6.38)
In general, α is a function of position (α = α (x, y)) and both q1 and q2 can vary with position. In fact, qtotal may also vary within the contact because the contact pressure is not necessarily constant and because the sliding velocity may vary with position. 6.2.1.6.1 Complete Solutions for Heat Partition Function If contact between the two bodies is perfect within the real contact area, no temperature jump should be expected across the contact interface within the real area of contact. The most accurate heat partition function α(x,y) can be obtained by matching the surface temperatures of the two contacting solids at all points within the real contact area. This has been done by several investigators, particularly Ling (1959) and Bos and Moes (1995). Ling’s methodology involved an iterative solution in which transform solutions are used for the temperatures on each surface (see Section 6.2.2.1 below) and then the contact temperature is matched at each point on the two surfaces (Ling, 1973). Bos and Moes (1995) developed a numerical algorithm to determine the heat partitioning function for arbitrarily shaped contact by matching the surface temperatures of the two contacting bodies at all points within the contact area. They used heat source methods for determining the temperature solutions for each surface. An example of the result of a temperature-matching algorithm is shown in Figure 6.15. The dashed lines show the surface temperature rise for a square heat source on moving and stationary bodies, as determined using expressions given in Table 6.1. Those results have been normalized to give the same maximum temperature rise. The solid curve shows the temperature distribution for the same conditions using Ling’s iterative procedure. It is apparent that the actual temperature distribution is between those predicted for the stationary and moving surfaces. Most of the frictional heat dissipated at the leading edge of the contact flows into the moving body, because the material of that body is cool when it enters the contact and it needs to be brought quickly up to the temperature of the stationary surface with which it is in contact. On the other hand, by the time the moving surface reaches the trailing edge of the contact, much less of the frictional heat enters the already heated moving surface. 6.2.1.6.2 Approximate Solutions for Heat Partition Using the Blok Postulate Owing to the difficulty of determining the complete heat partitioning function α(x,y), most investigators have made use of an approximation first made by Blok (1937), in which it is assumed that the heat partitioning function is a constant factor. Blok postulated that overall heat partitioning factor can be
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2.2
1.8
T( πk/qb)
2
1
2.0
3
1.6
1.4
1.2
1.0
0.8
0.6 -1.0
-0.6
-0.2
0
0.2
0.6
1.0
X/b FIGURE 6.15 Temperature distributions resulting from square heat source at interface between moving and stationary bodies. Curve 1: stationary body solution; Curve 2: moving body; Curve 3: iterative solution with temperature matching everywhere in contact. (From Ling, F.F. (1973), Surface Mechanics, John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
estimated by setting the maximum surface temperature of the two bodies equal within the contact (Blok, 1937; Ling, 1973). Various analyses have been carried out by others to determine the exact heat partitioning function; it was found that the computed values of partitioning factor were in good agreement with the results obtained using Blok’s postulate (Ling, 1973; Bos and Moes, 1995). Case of Band Contact (Two-Dimensional Heat Flow) 6.2.1.6.2.1 Consider two large bodies, one of which is stationary (V1 = 0), the other of which is moving with velocity U (V2 = U). The bodies are in contact along the band –∞ ≤ y ≤ ∞ and –b ≤ x ≤ b, and the two bodies have the same sum of bulk temperature and nominal surface temperature rise (that sum could be equal to 0). The temperature on the surface of the stationary body is given by Equation 6.14 and Figure 6.4. For the moving body the surface temperature is given by Equation 6.21 and Figure 6.8. By comparing the temperature distributions in Figures 6.4 and 6.8 one can see that they are quite different in shape, so equating the temperatures at all points within the region – b ≤ x ≤ b is not possible using those distributions. Instead, we will make use of the Blok postulate and set Tmax equal on moving and stationary surfaces. For the band contact case, Equations 6.16 and 6.24 can be used and this gives: for the stationary body
Tmax =
2q1b
(6.16a)
k1 π
and for the moving body
Tmax =
2q2b
(
k2 π 1 + Pe
)
(6.24a)
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where
Pe =
Ub 2κ 2
Equating these gives
1
α= 1+
(6.39)
k2 1 + Pe k1
As can be seen, for high sliding velocities Pe is large and α is small. Thus, at high sliding velocities most of the heat enters the moving body (the body moving with respect to the heat source). This is because the moving body presents more new material per unit time to the heat source, where it must then be heated up to Tmax . The surface of the stationary body is always at temperature Tmax and need not receive much heat from the source to remain at that temperature. Using the Blok postulate, then
q1 =
µpU k 1 + 2 1 + Pe k1
(6.40)
and this can be used in Equation 6.16a to find the surface temperature. It might be noted that if sliding speeds are very low (Pe < 0.1), then at each position within the contact there is ample time for the temperature distribution in the moving body to approach that of the stationary body. In that case, one finds
α=
1 k 1+ 2 k1
(6.41)
So, at very low sliding speeds the conductivities of the sliding bodies govern the partitioning of the frictional heat. The majority of the frictional heat enters the body with the highest thermal conductivity. Case of Circular Contact Spots (Three-Dimensional Heat Flow) 6.2.1.6.2.2 In most actual sliding situations, the real area of contact is composed of a number of small circular or elliptical junctions. If one assumes that the contact spots are well separated and their temperature fields do not interact, the contact temperature solution requires use of an expression such as Equation 6.27 for both bodies. As was shown above for the band contact case, the two expressions could then be equated using the Blok postulate, as long as there is no nominal temperature rise for either body (∆Tnom2 = ∆Tnom1 = 0) and both bodies have the same bulk temperature (Tb1 = Tb2). Let us consider the case of contacting hemispherical asperities, both of which are moving with respect to the circular contact area where heat is being generated. The Peclet number Pei of each of the two bodies is found by using its relative velocity Vi in Equation 6.26. The contact radius is a. Using the solution for the case of a uniform circular heat source of radius a (as in Equation 6.27) for each body, the maximum interface temperature is given by
Tc max =
2aµpU π k1 1.273 + Pe1 + k2
(
)
(1.273 + Pe ) 2
(6.42)
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This is the case encountered when there is contact between hemispherical asperities of two materials and there is plastic deformation of the softer of the two contacting materials. In this case, p = the indentation hardness of the softer material. For elastic contact between hemispherical asperities, there is a Hertzian contact pressure distribution, and the maximum interface temperature can be derived using the solution for the case of a parabolic heat source, Table 6.1.
Tc max =
1.31aµpU
(
)
π k1 1.2344 + Pe1 + k2
(1.2344 + Pe )
(6.43)
2
–
where p is the mean pressure of elastic contact. 6.2.1.6.3 General Contact Case In general, the maximum contact temperature for a surface can be found using Equation 6.1. Using the Blok postulate, the maximum temperature is set equal for the two surfaces, giving:
Tcmax1 = Tb1 + ∆Tnom1 + ∆T fmax 1 = Tb 2 + ∆Tnom2 + ∆T fmax 2 = Tcmax 2
(6.44)
The nominal temperature rise and maximum flash temperature rise for Body i can be found as a linear function of an unknown heat flux qi entering that surface, using the methods of Section 6.2.1.5 for ∆Tnom and Table 6.1 for ∆Tfmax . This will give expressions of the form ∆Tnom1 = A1q1, ∆Tnom2 = A2q2, ∆Tfmax1 = B1q1 and ∆Tfmax2 = B2q2, where Ai and Bi are influence coefficients which depend on contact geometry, sliding velocity and thermal properties. For example, if the contact is circular and the pressure distribution is uniform, from Table 6.1:
B1 =
(
2a
k1 π 1.273 + Pe1
)
and B2 =
(
2a
k2 π 1.273 + Pe2
)
Using the Ai and Bi in Equation 6.44, one gets
Tcmax = Tb1 + A1q1 + B1q1 = Tb 2 + A2q2 + B2q2
(6.45)
Defining the heat partition factor α as above, expressions 6.38 can be used to get 6.45 in terms of α, and the total heat flux rate, qtotal = µpU. Solving for α, one gets:
α=
(T
b2
)
(
− Tb1 + qtotal A2 + B2
(
qtotal A1 + A2 + B1 + B2
)
)
(6.46)
It can be seen easily that Equation 6.46 reduces to 6.39 for the case of band contact with Tb1 = Tb2 and ∆Tnom1 = ∆Tnom2 = 0 (so that A1 = A2 = 0). Therefore, for the general contact case, one can determine the heat partition factor using Equation 6.46 and then use it, A1 and B1, along with the heat flux q1 = αqtotal = α µpU, in Equation 6.45 to find the maximum contact temperature.
6.2.2 Numerical Methods for Surface Temperature Determination Several important assumptions were implicit in the development of the heat source equations in Section 6.2.1 above. Of particular importance are the assumptions that the body is very large and is
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homogeneous (since the heat source solutions are for a homogenous, semi-infinite, half-space. Real contacting bodies may be large relative to the contact size, but they are not infinitely large, and they often contain more than one material. To overcome that difficulty, numerical methods have been developed to solve the heat conduction equation (6.3) for bodies of finite dimensions involving frictional heating over a portion of their surface. These include integral transform methods, finite element methods, and hybrid methods which combine both integral transforms and finite elements. When used appropriately, these methods allow natural temperature matching on the two contacting surfaces without resorting to artificial assumptions concerning heat partitioning. They also allow the determination of contact temperatures in layered bodies and determination of temperature distribution throughout the contacting solids. This makes them a valuable companion to numerical stress analysis programs for the determination of thermomechanical effects (deformation and stress distributions) for sliding systems subjected to frictional heating. This generally is not possible (or is inconvenient) with the heat source methods described above. 6.2.2.1 Integral Transform Methods Integral transform methods for surface temperature determination were first developed by Ling and coworkers (Ling, 1973), and were later applied by Floquet et al. (1977) and others. Of particular importance in sliding contact problems are Fourier transform-based methods. The method enables the solution of the heat conduction equation (6.5) in each of the two contacting bodies, subject to appropriate boundary conditions. Temperatures are matched at the contact interface between the bodies, making it unnecessary to specify the heat partition function, and the total heat flux distribution, qtotal , is applied at the contact interface. A transform which is appropriate to the geometry of the problem is applied to the equations and boundary conditions, the transformed equations are solved, and then the solution is inverted to obtain the temperature distribution. Transform methods have been found to give good results for contact temperatures and temperature distributions for the complete range of velocities which are encountered in tribological applications of real solid bodies. An example of the use of integral transform techniques is shown in Figure 6.16 (Floquet et al., 1977). Both shaft and housing are cylindrical, and different types of motion were prescribed for the system. The results point out that surface temperatures are greater if the more conductive component (the shaft) is stationary than if the same component is moving relative to the contact zone. Integral transform methods have proven very useful and accurate for determining contact temperatures in cylindrical bearings in both two dimensions (Floquet et al., 1977) and three dimensions (Floquet and Play, 1981). Other examples of integral transform applications are given by Ling (1973). Several investigators have combined integral transform solutions for temperature distributions with transform solutions of the elasticity equations to determine thermoelastic contact stress distributions for various contact problems (e.g., Ling, 1973; Ju and Huang, 1982). Although transform techniques do not generally require large computational times or storage requirements, there is no readily available transform-based software for performing the analysis, so considerable time is required to generate the computer code. Another major disadvantage is that the integral transform techniques are only applicable to simple geometries (cylindrical shaft and housing, rectangular bodies, etc.), and this limits their usefulness. 6.2.2.2 Finite Element Methods Many commercial finite element codes enable solution of heat conduction problems. They can be used to solve Equation 6.3, but in just about all cases they assume that the body is not moving relative to the heat source (V = 0 in Equation 6.3). They can still be used for surface temperature analysis, but only if a transient problem is solved, with the heat source being considered fixed for a given time increment and moved for the next increment. A better way is to use a finite element program specifically written to solve the quasi-steady heat conduction equations (Equation 6.4 with ∂T/∂t = 0). One such program is described by Kennedy (1981).
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frictional interface housing frictional material
4
shaft 3
R
ω 1
ro a e
curves run max. table temperat. I 3 88.1 II 19 84.9 III 11 61.3
Geometry G1 Thickness liner 0.0004 m
100
oscillation motion, I moving housing, II moving shaft, III 50
entrance x
x/2
exit 0
x/2 angular position
x
FIGURE 6.16 (a) Geometry used in transform-based analysis of surface temperatures in dry bearing. (b) Results of analysis for different types of motion (contact temperature vs. angular position). (From Floquet, A., Play, D., and Godet, M. (1977), Surface temperatures in distributed contacts: application to bearing design, ASME J. Lubrication Technology, 99, 277-283. With permission.)
The essence of the finite element method for surface temperature determination is as follows: finite element meshes are defined for the two contacting bodies. Those meshes share nodes within the real area of contact, and those nodes (contact nodes) enable temperature matching for the contacting surfaces throughout the contact region. The finite element meshes should be very fine in the contact region, where temperature gradients are highest. An example of such a mesh is shown in Figure 6.17. The desired distribution of frictional heat flux qtotal is prescribed at the contact interface. That heat flux flows naturally into the two contacting bodies, so no heat partitioning function needs to be prescribed. The velocity of each body is used in the finite element version of Equation 6.5 to get the finite element equations for each element of that body. The finite element equations for the entire system are solved, using the appropriate boundary conditions, to find the temperature distributions in both bodies. An example of a temperature distribution determined by finite element methods is shown in Figure 6.18. The particular case being analyzed is a ceramic-coated metallic face seal ring in contact with a carbon–graphite seal ring. The contact is assumed to be moving with the rotating metallic ring, so it is moving with respect to the stationary carbon–graphite ring (shown on the bottom in Figure 6.18). The temperature distribution in that case was used as input for a finite element stress analysis (thermoelasto-plastic) program to study the thermal stresses that develop in the vicinity of a frictionally heated contact.
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FIGURE 6.17
Modern Tribology Handbook
Typical finite element mesh for surface temperature analysis.
FIGURE 6.18 Finite element results for temperature distribution (isotherms) ceramic-coated metallic seal ring (top) in contact with carbon graphite seal ring (bottom). Circumferential direction is horizontal in figure; axial direction is vertical. Contact patch extends from –0.05 to +0.05 cm. Ceramic coating is 0.02 cm thick. (From Kennedy, F.E. and Hussaini, S.Z. (1987), Thermo-mechanical analysis of dry sliding systems, Computers and Structures, 26, 345-355. With permission from Elsevier Science.)
Finite element methods have proven very useful in a variety of frictional heating calculations, and they have many advantages for such calculations. They can be used with bodies of finite dimensions, and of real irregular geometries; they do not require artificial heat partitioning assumptions, and guarantee temperature matching throughout the contact region. Their output can be input easily to stress analysis programs, so they can be quite suitable for use in combined temperature-stress models. Finite elements are not problem-free for surface temperature determination. In particular, at high sliding speeds, or high Peclet number, the results are subject to numerical instability (Kennedy et al., 1984). Those instabilities are caused by the convective-diffusion term (V · ∇T) in Equation 6.4. Methods have been developed to help minimize those problems, but difficulties remain at high Peclet numbers (Kennedy et al., 1984). 6.2.2.3 Hybrid Methods Integral transform methods are very useful for determining contact temperature distributions in simple geometries for any sliding velocities, but many tribological components, such as bearing housings, have relatively complex geometries which cannot be studied easily using integral transforms. On the other hand, finite element methods can easily be used for complex geometries but have problems with bodies moving at high sliding velocities. A hybrid technique which can address these difficulties was developed
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by Colin and Floquet (1986), who took advantage of the fact that most moving tribological components, such as a rotating journal, have a relatively simple shape, while those which are stationary, such as a bearing housing, tend to be more complex in shape. The hybrid technique uses transform methods for the moving component and finite element methods for the stationary component. Both finite element and integral transform methods give a relation between heat input and temperature. In the hybrid method, the stationary body is discretized with a finite element mesh and the moving body with a surface mesh whose nodes correspond with nodes of the finite element mesh within the contact zone. Similar interpolation functions are prescribed for temperature of the two surfaces within the contact zone, and the total heat flux distribution is prescribed on the contact interface. The methodology is described in detail by Colin and Floquet (1986). An example of the application of the hybrid technique is shown in Figure 6.19. It is seen that even with a coarse finite element mesh, it is possible to get valid results for a wide range of sliding velocities. It should be noted, however, that there is no readily available software for use in determining sliding contact temperatures using the hybrid method.
6.3 Surface Temperature Measurement Although surface temperature analysis methods, both analytical and numerical, are well developed and widely used, they all suffer from a major difficulty: their use requires knowledge of the area within which the frictional heat is being generated. Seldom is that real area of contact known with any certainty a priori. As a result, it is often necessary to measure surface temperatures experimentally. Surface temperature measurement techniques could be grouped under three categories: point temperature sensors (e.g., thermocouples and thermistors), field radiation-based sensors (e.g., infrared sensors), and ex post facto observations. The various temperature measurement methods were described in several recent publications (Kennedy, 1992; Bhushan, 1999). A brief description of the techniques follows.
6.3.1 Thermocouples, Thermistors, and Related Temperature Sensors 6.3.1.1 Embedded Subsurface Thermocouples Thermocouples are probably the most commonly used sensors for measuring temperatures, including those resulting from frictional heating. Their operation is based on the findings of Seebeck, who demonstrated in 1821 that a specific electromotive force (emf) potential exists as a property intrinsic to the composition of a wire, the ends of which are kept at two different temperatures. The simplest measuring circuitry for thermocouple thermometry involves wires of two dissimilar metals connected together so as to give rise to a total relative Seebeck potential. This emf is a function of the composition of each wire and the temperatures at each of the two junctions. This circuit can be well characterized such that, if one junction is held at a known reference temperature, the temperature of the other “measuring” junction can be inferred by comparison of the measured total emf with an empirically derived calibration table (Reed, 1982). Generally, when the thermocouple technique is to be used to measure contact temperature, a small hole is drilled into a noncontacting surface, usually the rear side, of the stationary component of a frictional pair. The hole may extend to, or just beneath, the sliding surface. An adhesive is put in the hole, either ceramic cement for components encountering high sliding temperatures or a polymeric adhesive such as epoxy for lower temperature components. Ideally, the adhesive should be an electrical insulator but a reasonably good thermal conductor. A small thermocouple is then inserted in the hole so that its measuring junction rests either at or just beneath the sliding surface and is held in position by the cement, which also serves to insulate the thermocouple wires from the surrounding material. A diagram of a typical embedded thermocouple installation is shown in Figure 6.20. Several such thermocouples can be embedded at different depths and at various locations along the sliding path to get information about surface temperature distribution and temperature gradients. By monitoring the thermocouple(s) throughout a sliding interaction, the transient nature of the surface temperatures can be
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FIGURE 6.19 Hybrid numerical analysis of temperature distribution in bearing. Finite element mesh was used for bearing support, Fourier transforms for rotating shaft. Model configuration is at left. Resulting temperatures, as function of velocity, are at right. (From Colin, F. and Floquet, A. (1986), Combination of finite element and integral transform techniques in a heat conduction quasi-static problem, Int. J. Numer. Methods in Engg., 23, 13-26. Reproduced by permission of John Wiley & Sons, Limited.)
deduced. It should be mentioned that subsurface thermocouples can also be embedded in the moving component of a friction couple, but slip rings or a similar means will be required to gain access to the thermocouple output. Embedded thermocouples have been found to give a good indication of the transient changes in frictional heat generation which accompany gross changes in contact area (Ling and Simkins, 1963; Santini and Kennedy, 1975). They cannot, however, give a true indication of surface temperature peaks. Subsurface thermocouples have a limited ability to respond to flash temperatures owing to their finite thermal mass and distance from the points of intimate contact where heat is being generated. A thermocouple can be made part of the sliding surface by placing it in a hole which extends to the surface and then grinding the thermocouple flush with the surface. Even in that case, however, the finite mass of the thermocouple junction prevents it from responding to very short-duration flash temperature pulses
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F V
Moving Slider (Material 2)
Hot Thermocouple Junctions
Stationary Material 1 Dielectric Adhesive Holes (< 0.5 mm diameter)
Cold Junctions
Instrumentation
FIGURE 6.20 Typical installation of embedded thermocouples for measuring surface and near-surface temperatures resulting from frictional heating.
(Suzuki and Kennedy, 1988). In addition, the thermocouple and the hole in which it resides can create a disturbance in the normal heat flow distribution, so the measurement may not be a good indication of the temperature that would exist at the same location in the absence of the thermocouple. Although these problems are not as severe with fast-response microthermocouples, the best use for embedded thermocouples is to measure bulk temperatures within the sliding bodies, and not flash temperatures. The bulk temperatures can be used effectively in determining boundary conditions for an analytical study or for calculating the distribution of frictional heat between the two contacting bodies (Berry and Barber, 1984). This is most easily done if temperatures are measured at several depths beneath the sliding surface, enabling the determination of heat flux values. 6.3.1.2 Dynamic Thermocouples In the dynamic thermocouple technique, sometimes called the Herbert–Gottwein technique, a thermocouple junction is formed at the sliding interface by the contacting bodies themselves. It was originally developed to study contact temperatures at the interface between a cutting tool and workpiece during metal cutting (Shore, 1925). Later it was used to make measurements of surface temperature in a variety of sliding contacts (e.g., Cook and Bhushan, 1973). As long as the two contacting materials are dissimilar and produce a well-characterized thermal emf as a function of temperature, the two rubbing materials can be used as part of a thermocouple circuit. An example of the use of this technique is shown in Figure 6.21. In one typical application, a constantan ball formed one element of the thermocouple and the steel (iron) cylinder was the other (Furey, 1964). A measuring junction was formed wherever there was intimate contact between the ball and cylinder, and the measured temperature was the average temperature at the contact interface.
F Wire V
Moving Slider (Material 2)
Hot Thermocouple Junction
Stationary Material 1
Cold Junction
Wire Instrumentation
FIGURE 6.21 Schematic diagram of a dynamic thermocouple to measure temperature at contact between moving and stationary bodies made of dissimilar metals.
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In a modification of the technique, a single thin wire of constantan (or similar material) could be embedded within the stationary sliding element, emerging at the contact surface. After insulating the wire from the surrounding material, using ceramic cement or epoxy, its end can be ground smooth with the remainder of the sliding surface. In that way, a dynamic thermocouple junction will be formed whenever the end of the wire is in contact with the other surface, and the contact location can be known with certainty (Kennedy, 1984). Dynamic thermocouples have a very thin junction which consists of only the actual contact zone. As a result, they can respond very rapidly to changes in surface temperature. Because they can respond to flash temperatures as well as nominal contact temperatures, dynamic thermocouples have been found to give higher measurements than embedded thermocouples and faster transient response (Kennedy, 1984). The measurements are often lower than theoretical predictions, however (Furey, 1964), and questions persist about the accuracy and meaning of the thermal emf produced by the thermocouple. The emf is produced by a weighted average of all temperatures across the sliding thermocouple junction, and that average may differ from the peak contact temperature (Tc), especially when the thermocouple junction contains more than one contact spot and the junction size is changing with time (Shu et al., 1964). In addition, there is frequently some electrical noise generated at the contact interface, and the thermocouple output must be discriminated from this noise. 6.3.1.3 Thin Film Temperature Sensors In recent years, microelectronic fabrication techniques, such as vapor deposition, have begun to be used to make surface temperature sensors. The advantage of using such techniques is that very small sensors, with rapid response time, can be formed on the surfaces. The earliest vapor-deposited surface temperature sensors were thermistors used to measure surface temperatures on elastohydrodynamically lubricated components such as gear teeth. One such sensor consisted of a thin strip of titanium coated onto an alumina insulator on the surface of one of a pair of meshing teeth (Kannel and Bell, 1972). The resistance of the titanium strip is sensitive to temperature, so by monitoring the change in resistance the transient surface temperature changes could be measured. By nature the strip has a finite length and responds to all temperature changes along its length. Thus, it gives an integrated average measure of temperature and not a pointwise temperature measurement. A recent embodiment of thin film fabrication techniques in surface temperature measurement has been the development of thin film thermocouples. Some of the earliest work on thin film thermocouples described the use of vapor deposition to produce thermocouple pairs from thin films of nickel and iron, copper and iron, copper and nickel, copper and constantan, and chromel and alumel (Marshall et al., 1966). More recently, similar techniques have been used successfully for measuring sliding surface temperatures (Tong et al., 1987; Schreck et al., 1992; Tian et al., 1992). The production of a thin film thermocouple (TFTC) involves the deposition of thin films (typically <1 µm thick) of two different metals, such as nickel and copper, sandwiched between thin layers (also <1 µm thick) of a hard, dielectric material such as Al2O3. The measuring junction of the TFTC is deposited on the surface where frictional heat is generated. The dielectric layer beneath the thermocouple junction is necessary to electrically insulate the TFTC device from the underlying metallic surface. Owing to the softness of the thin metal films making up the thermocouple and connecting leads, it is also necessary to deposit a hard protective layer above the junction to limit damage to the TFTC device. The metal and dielectric films can be grown by physical vapor deposition techniques, with junction sizes as small as 10 µm2 or smaller and thicknesses less than 1 µm. TFTC devices have been found to have extremely rapid (<1 µs) response to a sudden temperature change, and there have been reports of response as fast as 60 ns for Pt–Ir TFTC (Tong et al., 1987). It has also been shown that TFTC do not significantly disturb the heat flow from sliding contacts (Tian et al., 1992). Such sensors can measure the actual temperature of the contact interface, especially when the protective layer is very thin, and the small size of the measuring junctions enables them to respond rapidly to temperature changes at a specific point on the surface. If that point happens to be a flash temperature location, they can give a measure of maximum contact temperature (Tc). As with all thermocouples or thermistors, however, thin film devices cannot give a complete picture of surface
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FIGURE 6.22 junctions.
Thin film thermocouple with three measuring junctions. Line width = 80 µm at the thermocouple
TABLE 6.2 Representative Values of Total Emissivity of Solid Surfaces at 25°C Material
Total Emissivity at 25°C
Copper, polished Copper, oxidized Iron, polished Iron, oxidized Carbon Blackbody
0.03 0.5 0.08 0.8 0.8 1.0
Source: Adapted from Bedford, 1991.
temperature distribution, since that requires the measurement of temperature at a large number of points simultaneously. More recently, arrays of thin film thermocouples have been used to measure the temperature at multiple points on the surface simultaneously (Kennedy et al., 1997). This enables the determination of a portion of the surface temperature field in a sliding contact and can be useful in determining real contact area and pressure distribution. A typical thin film thermocouple array is shown in Figure 6.22. TFTC arrays have been developed with up to 64 thermocouple junctions in an area as small as 500 µm square.
6.3.2 Radiation Detection Techniques Some of the most successful measurements of sliding contact temperatures have used techniques involving the detection of thermal radiation. It is well known that any surface with a temperature above absolute zero is a natural radiator of thermal energy. The radiation emitted by the object is a unique function of its temperature, with the Stefan–Boltzmann law (Equation 6.47) showing that much more power is emitted by a body at high temperatures than at low.
Φ = ε σT 4 A
(6.47)
where Φ is the power (energy rate), T is the absolute temperature, σ is the Stefan–Boltzmann constant, A is the area of the heat source, and ε is the total emissivity of the surface emitting the radiation. ε is temperature-dependent and is also very dependent on the characteristics of the surface. Some typical emissivity values at room temperature are listed in Table 6.2. The radiation is composed of photons of many wavelengths and, according to Planck’s law, the monochromatic emissive power of a blackbody in a vacuum is:
(
w b, λ = 2πHc 2 λ−5 ecH
KλT
)
−1
(6.48)
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140
Wb.l (T) x 10-3 (watt cmm-3)
120
100
80
g f
60 c d
40
b
e
20 a
0
VISIBLE
5
10
15
20
l (mm) FIGURE 6.23 Spectral radial emittance of a blackbody (Equation 6.48) at various temperatures: (a) 800 K, (b) 1200 K, (c) 1600 K, (d) 6000 K, (e) 10,000 K. (From Bedford, R.E. (1991), Blackbody radiation, in Encyclopedia of Physics, Lerner, R.G. and Trigg, G.L. (Eds.), VCH Publishers, Inc., New York, 104. Reprinted by permission of John Wiley & Sons, Inc.)
where λ is wavelength, c is the velocity of light in a vacuum, and H and K are Planck and Boltzmann constants, respectively. wb,λ is defined as the energy emitted per unit area at wavelength λ per unit wavelength in a small interval around λ. Integration of Equation 6.48 over all wavelengths leads to Equation 6.47 for the case of a blackbody (ε = 1). Planck’s law (Equation 6.48) is plotted in Figure 6.23 for some representative temperatures (Bedford, 1991). It can be noted that wb,λ is very low at small and long wavelengths, so most emissive power is found at wavelengths in the range 1 µm < λ < 10 µm. For this reason, most successful attempts to measure temperature by detecting thermal radiation have concentrated on the infrared region of the spectrum (wavelengths of 0.75 µm to 500 µm). If the surface temperature T is high enough, radiation in the visible part of the spectrum (400 nm to 750 nm) can also be detected. Several different radiation measurement techniques have been used with success in measuring surface temperatures, including photography, pyrometry, thermal imaging, and photon detection. 6.3.2.1 Optical and Infrared Photography A photographic technique utilizing infrared-sensitive film was developed by Boothroyd (1961) for studying the temperature distribution in metal cutting. Similar methods have since been used in other studies of surface temperatures in machining, as well as for sliding components such as brakes (Santini and Kennedy, 1975) and in pin-on-disk sliding (Quinn and Winer, 1985). In most cases the camera is focused on the moving body as it emerges from a sliding contact, but successful photographs have also been made through a transparent window to a sapphire/metal or sapphire/ceramic contact (Quinn and Winer, 1985). Sapphire is a useful material for such studies because its mechanical and thermal properties are similar to those of steel and it is essentially transparent to radiation in the visible and near-infrared regions. A photograph showing hot spots on a tool steel pin sliding at high speed on a sapphire disk is shown in Figure 6.24 (Quinn and Winer, 1985). Temperatures of the spots were estimated to range from 950°C to 1200°C. The temperature distribution is best determined by measuring the optical density of the developed negative. The system must be calibrated to determine the density–temperature relationship of the film in the test configuration. This is usually accomplished by photographing specimens of the same material which had been heated to known temperatures and then comparing the optical density
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FIGURE 6.24 Photograph of hot spots on a steel pin (diameter = 6 mm) sliding at 2 m/s on a sapphire disk with a load of 26 N. Photo taken after 25 min of sliding. Exposure time = 1 s. (From Quinn, T.F.J. and Winer, W.O. (1985), The thermal aspects of oxidational wear, Wear, 102, 67-80. With permission.)
of the test film to that of the calibrated film. The same magnification and exposure time must be used in both calibration and test. When careful procedures are used, the method can give good indications of the surface temperature distribution on a sliding contact. In general, however, methods involving IRsensitive film require exposure times (5 s or more) which are longer than the duration of flash temperatures, so they probably do not give a true indication of the highest temperature in a sliding contact. Shorter exposure times (<1 s) can be achieved with normal high-speed color film, as in Figure 6.24, but such film operates with visible light, so is restricted to detection of high temperatures, perhaps 800°C or higher. IR film can respond to mean contact temperatures as low as 300°C, but even those temperatures occur only in rather severe sliding situations. An alternative is to use a modern infrared camera, which is essentially a scanning infrared detector. This will be described below. 6.3.2.2 Infrared Detectors Infrared (IR) detection techniques have been widely used and improved since Parker and Marshall (1948) used an optical pyrometer to measure the surface temperature of a railroad wheel as it emerged from a brake shoe. Early pyrometers used the eye as a detector to match the brightness of the subject body with that of a standard lamp incorporated in the instrument. Improved models were later developed which employed a photoelectric detector in place of the eye. The detector essentially integrates Equation 6.48 over all wavelengths within its spectral range and over the surface area viewed by the detector. Since the temperature is generally not constant over the field of view, the detector output is a function of the average temperature over the area. In order to improve the accuracy of the temperature measurement and to approach a point measurement, most modern detectors are equipped with optics which limit the field of view to a small spot size, perhaps on the order of 100 to 500 µm diameter. The result is an infrared radiometric (IR) microscope, an example of which is shown schematically in Figure 6.25. The IR microscope shown in Figure 6.25 uses a liquid nitrogen-cooled detector made of indium antimonide (InSb), which has a spectral band of 2 to 5.6 µm. IR microscopes can measure transient temperature changes at a rate of up to 20 kHz or greater. They have been used effectively both with metallic components, where the detector can be focused on a spot just emerging from the contact zone (Griffioen et al., 1986), or
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Microscope unit lnSb detector and cooling system
Electronic control unit
Operator
Eyepiece IR channel
Ac signal Preamp
Chopper
Amp
To output recorder
Synchronous demodulator circuitry Output meter
IR energy IR / visible optical element
Visible channel Visible energy
IR + visible energy Target specimen
FIGURE 6.25
Schematic diagram of infrared radiometric microscope.
with a transparent sapphire component, in which case the detector would be focused through the sapphire onto the contact zone between sapphire and metal (Floquet and Play, 1981). By limiting the field of view to a single small spot, the IR microscope can miss many contact events which occur at other spots within the area of contact. To overcome this limitation, investigators in recent years have been using a scanning infrared camera to study sliding surface temperatures (Griffioen et al., 1986; Gulino et al., 1986). A scanning IR camera, or infrared micro-imager, has a detector similar to that shown in Figure 6.25, but the detector is optically scanned over the contact surface in either of two modes, line scan or area scan. In the line scan mode, a fixed line, perhaps several mm in length, is scanned continuously at a rate of up to 2500 line scans per second. In the area scan mode, the rotation of a prism advances the line for each scan to produce a field consisting of typically 100 scan lines. The output is a video voltage map which is a function of the infrared radiation detected at that instant. The output from a complete area scan for the case of a silicon nitride pin sliding against a sapphire disk is shown in Figure 6.26. It should be noted that, even at a scan rate of 2500 lines per second, it takes 40 ms to complete an area scan composed of 100 lines. This is considerably longer than the duration of flash temperatures, so it is unlikely that a field plot similar to Figure 6.26 is fully representative of the surface temperature distribution at any instant. It does, however, give a good indication of the contact conditions within the target area and the approximate temperatures reached at the hot spots. A better indication of transient temperatures at a given point can be achieved in the line scan mode, by continuously sweeping over the same line. Even in that mode, however, the transient times of the temperature fluctuations have been found to be less than the time required to complete a single line scan, and the flash temperature intervals may, in fact, be less than the 5 µs or so between consecutive temperature measurements on the same scan line. Thus, measured contact temperatures may be less than actual flash temperatures, particularly if the hot spot is smaller than the detector’s spot size and is very short-lived. Methods have been devised to correct for the instantaneous temperature averaging that occurs within an IR detector (Griffioen et al., 1986), but those techniques are only approximate. As was stated earlier, an IR detector essentially integrates Equation 6.48, multiplied by the emissivity, over the area of the
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AN
SC
E SID
1.5 3 m / s
8.9 0 N
PIN
T
187 2
NG IDI
OU
SL
T /C
0
1.5 mm
2.7
mm
FIGURE 6.26 Temperature distribution on surface of silicon nitride pin in sliding contact with sapphire disk at velocity of 1.53 m/s and normal load of 8.9 N. Pin bulk temperature = 96°C. Area scan mode with infrared scanning camera. (From Griffioen, J.A., Bair, S., and Winer, W.O. (1986), Infrared surface temperature measurements in a sliding ceramic-ceramic contact, Mechanisms and Surface Distress, Dowson, D. et al. (Eds.), Butterworths, London, 238. With permission.)
detector’s target spot and within its spectral range to get the equivalent of Equation 6.47. If a small hot spot whose temperature is desired is contained within a larger target spot, it is necessary to know the area of the spot so that its contribution to the summed detector output can be determined. Since hot spot areas are usually not known with certainty, the hot spot temperature may be inaccurately determined. A better technique, utilizing two separate detectors, was devised by Bair et al. (1991). If the emitted radiation is split between the two detectors and a different bandpass filter is placed in front of each detector, different values of radiated power will be measured at each of the two wavelengths, and each will be a function of two variables, hot spot area and temperature. The ratio of detected power at the two wavelengths can be used to determine the maximum temperature within the field of view (Bair et al., 1991). The hot spot area can also be determined, once its temperature has been calculated. The optical setup for this method is shown in Figure 6.27. One factor that can lead to inaccuracies in temperature determination using any of the IR techniques is uncertainty about the emissivity of contacting surfaces during the sliding process. It is apparent from Table 6.2 that the total emissivity of a metallic (or nonmetallic) surface can vary considerably owing to oxidation, wear, or other changes in the surface characteristics. In order to get an accurate temperature reading from a radiating surface, an accurate value of emissivity must be known at that temperature. This can be accomplished by carefully determining the emissivity of reference surfaces similar to the contacting surfaces at temperatures throughout the range of interest. Methods can also be developed to handle the emissivity and transmissivity of any lubricant between the surfaces. Despite these procedures, emissivity remains an accuracy-limiting variable in many IR measurements of sliding surface temperatures, especially when the emissivity changes during the sliding process. These difficulties have been partially removed by the technique of Bair et al. (1991), for which the calculated temperature is independent of the emissivity as long as the spectral distribution of emissivity remains unchanged.
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Detector Dewars
4.5-5.5 µm 1-4.5 µm
Shutter
Beam splitter / filter Spherical mirrors
Sapphire
FIGURE 6.27 Optical arrangement for infrared temperature measurement system employing two detectors. (From Bair, S., Green, I., and Bhushan, B. (1991), Measurements of asperity temperatures of a read/write head slider bearing in hard magnetic recording disks, ASME J. Tribol., 113, 547-554. With permission.)
There are several other limitations of infrared detectors when used to measure flash temperature rises. One is that if the size of the hot spot is smaller than the field of view of the detector, there will be a significant loss of accuracy in the temperature measurement. For current infrared detectors, the lower limit of hot spot size for which accurate measurements can be made is 1 to 2 µm (Chung and Wahl, 1992). Another potential limitation of infrared temperature measurement is that the time response (integration time) of the detector may be longer than the duration of the hot spot being measured. This can be a problem for small, rapidly moving hot spots. As an alternative to infrared detectors, a surface temperature measurement method has been developed which uses a photomultiplier to collect photons emitted by a hot contact spot (Suzuki and Kennedy, 1991). Contact temperatures generally need to be a minimum of 400 to 500°C in order to get photons with enough energy to be detected by the photomultiplier, but the response time of the photomultiplier is very rapid (<30 ns). Therefore, the technique can be used for detecting flash temperatures of very short duration (2 µs or less), but it is not too useful for measuring mean contact temperatures, which are generally lower than 500°C. A further restriction is that the sliding test must be run in complete
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darkness to eliminate noise which can dominate the output signal. This method is subject to a limitation similar to that of most infrared detectors, i.e., the area of the spot emitting the photons must be known in order to accurately determine the spot’s temperature.
6.3.3 Ex Post Facto Methods 6.3.3.1 Metallographic Techniques By examining the microstructure of sections of bodies which have undergone frictional heating, information can be gained about the temperatures the bodies witnessed in service. These techniques are generally dependent on the microstructural changes that occur as a result of the surface and near-surface temperatures. This change in microstructure can be detected after metallurgically sectioning the sliding body in a plane normal to the sliding direction. For some materials, etching of the near surface region of the cross-sectioned body can reveal a visible change in microstructure (Wright, 1978). For other materials, microhardness surveys have been found to be effective in determining the near-surface temperature distribution that the material had witnessed in service (Wright and Trent, 1973). In either case, the temperature contours are constructed by comparing the hardness or structural appearance variations with those of standard reference specimens that had been heat treated to known temperatures for known lengths of time (Wright, 1978). Metallographic techniques generally require destruction of the sliding body for sectioning. Such post mortem investigations can give substantial information about what bulk surface and volumetric temperatures had occurred during earlier sliding, but they cannot provide instantaneous temperature measurements. They can only be used successfully with those materials which undergo a known change in microstructure or microhardness at the temperatures encountered in sliding. Another shortcoming is that microhardness and some microstructural changes can also be affected by plastic deformation in the contact region.
References Akkok, M., Ettles, C.M.M., and Calabrese, S.J. (1987), Parameters affecting the kinetic friction of ice, ASME J. Tribol., 109, 552-561. Archard, J.F. (1958/59), The temperature of rubbing surfaces, Wear, 2, 438-455. Ashby, M.F., Abulawi, J., and Kong, H.S. (1991), Temperature maps for frictional heating in dry sliding, Tribology Trans., 34, 577-587. Bair, S., Green, I., and Bhushan, B. (1991), Measurements of asperity temperatures of a read/write head slider bearing in hard magnetic recording disks, ASME J. Tribol., 113, 547-554. Banerjee, B.N. and Burton, R.A. (1979), Experimental studies of thermoelastic effects in hydrodynamically lubricated face seals, ASME J. Lubrication Technology, 101, 275-282. Barber, J.R., Beamond, T.W., Waring, J.R., and Pritchard, C. (1986), Implications of thermoelastic instability for the design of brakes, ASME J. Tribol., 107, 206-210. Bedford, R.E. (1991), Blackbody radiation, in Encyclopedia of Physics, Lerner, R.G. and Trigg, G.L. (Eds.), VCH Publishers, Inc., New York, 104. Berry, G.A. and Barber, J.R. (1984), The division of frictional heat — a guide to the nature of sliding contact, ASME J. Tribol., 106, 405-415. Bhushan, B. (1987a), Magnetic head-media interface temperatures — part 1: analysis, ASME J. Tribol., 109, 243-251. Bhushan, B. (1987b), Magnetic head-media interface temperatures — part 2: application to magnetic tapes, ASME J. Tribol., 109, 252-256. Bhushan, B. (1992), Magnetic head-media interface temperatures — part 3: application to rigid disks, ASME J. Tribol., 114, 420-430. Bhushan, B. (1999), Principles and Applications of Tribology, John Wiley & Sons, New York.
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Blok, H.A. (1937), Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating conditions, Proc. General Discussion on Lubrication and Lubricants, I.Mech.E., London, 222-235. Boothroyd, G. (1961), Photographic technique for the determination of metal cutting temperatures, Br. J. Appl. Physics, 12, 238. Bos, J. and Moes, H. (1994), Frictional heating of elliptic contacts, in Dissipative Processes in Tribology, Dowson, D. et al. (Eds.), Elsevier Science, Amsterdam, 491. Bos, J. and Moes, H. (1995), Frictional heating of tribological contacts, ASME J. Tribol., 117, 171-177. Bowden, F.P. and Hughes, T.P. (1939), The mechanism of sliding on ice and snow, Proc. R. Soc., A172, 280-298. Carignan, F.J. and Rabinowicz, E. (1980), Friction and wear at high sliding speeds, ASLE Trans., 24, 451-459. Carslaw, H.S. and Jaeger, J.C. (1959), Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford. Chung, Y-W. and Wahl, K.J. (1992), Fundamental limits of flash temperature measurements of asperities using infrared detectors, Tribology Trans., 35, 447-450. Colin, F. and Floquet, A. (1986), Combination of finite element and integral transform techniques in a heat conduction quasi-static problem, Int. J. Numer. Methods in Engg., 23, 13-26. Cook, N.H. and Bhushan, B. (1973), Sliding surface interface temperatures, ASME J. Lubrication Technology, 96, 59-64. Dow, T.A. (1980), Thermoelastic effects in brakes, Wear, 59, 213-221. Dow, T.A. and Kannel, J.W. (1982), Thermomechanical effects in high current density slip rings, Wear, 79, 93-105. Dyson, A. (1975), Scuffing — a review, Tribology Int’l., 8, 77-87. Enthoven, J.C., Cann, P.M., and Spikes, H.A. (1993), Temperature and scuffing, Tribology Trans., 36, 258-266. Ettles, C.M.M. (1986), The thermal control of friction at high sliding speeds, ASME J. Tribol., 108, 98-104. Ettles, C.M.M. and Shen, J.H. (1988), The influence of frictional heating on the sliding friction of elastomers and polymers, Rubber Chemistry and Technology, 61, 119-136. Ettles, C.M.M., Dinc, O.S., and Calabrese, S.J. (1994), The effect of frictionally generated heat on lubricant transition, Tribology Trans., 37, 420-424. Fein, R.S., Rowe, C.N., and Kreuze, K.L. (1959), Transition temperatures in sliding systems, ASLE Trans., 2, 50-57. Floquet, A., Play, D., and Godet, M. (1977), Surface temperatures in distributed contacts: application to bearing design, ASME J. Lubrication Technology, 99, 277-283. Floquet, A. and Play, D. (1981), Contact temperatures in dry bearings. Three-dimensional theory and verification, ASME J. Tribol., 103, 243-252. Floquet, A. (1983), Thermal considerations in the design of tribometers, Wear, 88, 45-56. Furey, M.J. (1964), Surface temperatures in sliding contact, ASLE Trans., 7, 133-146. Gecim, B. and Winer, W.O. (1985), Transient temperatures in the vicinity of an asperity contact, ASME J. Tribol., 107, 333-342. Greenwood, J.A. (1991), An interpolation formula for flash temperatures, Wear, 150, 153-158. Griffioen, J.A., Bair, S., and Winer, W.O. (1986), Infrared surface temperature measurements in a sliding ceramic-ceramic contact, Mechanisms and Surface Distress, Dowson, D. et al. (Eds.), Butterworths, London, 238. Gulino, R., Bair, S., Winer, W.O., and Bhushan, B. (1986), Temperature measurements of microscopic areas within a simulated head/tape interface using infrared radiometric technique, ASME J. Tribol., 108, 29-34. Hou, Z-B. and Komanduri, R. (1998), Magnetic field assisted finishing of ceramics — part 1: thermal model, ASME J. Tribol., 120, 645-651. Hsu, S.M. and Shen, M.C. (1996), Ceramic wear maps, Wear, 200, 154-175. Jacobsen, B. (1990), Mixed lubrication, Wear, 136, 99-116.
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Jaeger, J.C. (1942), Moving sources of heat and the temperature of sliding contacts, Proc. R. Soc. NSW, 76, 203-224. Ju, F.D. and Huang, J.H. (1982), Heat checking in the contact zone of a bearing seal, Wear, 79, 107-118. Kannel, J.W. and Bell, J.C. (1972), A method for estimation of temperatures in lubricated rolling-sliding gear or bearing elastohydrodynamic contacts, Proc. I.Mech.E. EHD Symposium, London, 118-130. Kennedy, F.E. (1981), Surface temperatures in sliding systems — a finite element analysis, ASME J. Lubrication Technology, 103, 90-96. Kennedy, F.E. (1982), Single-pass rub phenomena — analysis and experiment, ASME J. Lubrication Technology, 104, 582-588. Kennedy, F.E. (1984), Thermal and thermomechanical effects in dry sliding, Wear, 100, 453-476. Kennedy, F.E. (1992), Surface temperature measurement, Friction, Lubrication and Wear Technology, Metals Handbook, 4, 10th ed., Blau, P.J. (Ed.), ASM International, Metals Park, OH, 438. Kennedy, F.E. and Hussaini, S.Z. (1987), Thermo-mechanical analysis of dry sliding systems, Computers and Structures, 26, 345-355. Kennedy, F.E. and Karpe, S.A. (1982), Thermocracking of a mechanical face seal, Wear, 79, 21-36. Kennedy, F.E. and Tian, X. (1994), The effect of interfacial temperature on friction and wear of thermoplastics in the thermal control regime, in Dissipative Processes in Tribology Dowson, D. et al. (Eds.), Elsevier Science, Amsterdam, 235. Kennedy, F.E., Colin, F., Floquet, A., and Glovsky, R. (1984), Improved techniques for finite element analysis of sliding surface temperatures, Developments in Numerical and Experimental Methods Applied to Tribology, Dowson, D. et al. (Eds.), Butterworths, London, 138. Kennedy, F.E., Frusescu, D., and Li, J. (1997), Thin film thermocouple arrays for sliding surface temperature measurement, Wear, 207, 46-54. Kennedy, F.E., Schulson, E.M., and Jones, D.E. (2000), The friction of ice on ice at low sliding velocities, Phil. Mag. A, 80, 1093-1110. Kuhlmann-Wilsdorf, D. (1987), Temperatures at interfacial contact spots: dependence on velocity and on role reversal of two materials in sliding contact, ASME J. Tribol., 109, 321-329. Lancaster, J.K. (1971), Estimation of the limiting PV relationships for thermoplastic bearing materials, Tribology, 4, 82-86. Landman, U., Luedtke, W.D., and Ringer, E.M. (1993), Molecular dynamics simulations of adhesive contact formation and friction, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, 463. Lee, S.W., Hsu, S.M., and Shen, M.C. (1993), Ceramic wear maps: zirconia, J. Am. Ceram. Soc., 76, 1937. Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metall., 35, 1-24. Ling, F.F. and Saibel, E. (1957/58), Thermal aspects of galling of dry metallic surfaces in sliding contact, Wear, 1, 80-91. Ling, F.F. (1959), A quasi-iterative method for computing interface temperature distributions, Z Agnew. Math. Physik., X, 461-474. Ling, F.F. and Simkins, T.E. (1963), Measurement of pointwise junction condition of temperature at the interface of two bodies in sliding contact, ASME J.Basic Eng., 85, 481-487. Ling, F.F. (1973), Surface Mechanics, John Wiley & Sons, New York. Marshall, R., Atlas, L., and Putner, T. (1966), The preparation and performance of thin thermocouples, J. Sci. Instrum., 43, p. 144. Montgomery, R.S. (1976), Friction and wear at high sliding speeds, ASLE Transactions, 36, 275-298. Oksanen, P. and Keinonen, J. (1982), The mechanism of friction of ice, Wear, 78, 315-324. Parker, R.C. and Marshall, P.R. (1948), The measurement of the temperature of sliding surfaces with particular reference to railway blocks, Proc., Inst. Mech. Eng. London, 158, 209-229. Quinn, T.F.J. (1983), Review of oxidational wear, Tribology Intl., 16, 257-271. Quinn, T.F.J. and Winer, W.O. (1985), The thermal aspects of oxidational wear, Wear, 102, 67-80. Reed, R.P. (1982), Thermoelectric thermometry: a functional model, in Temperature — Its Measurement and Control in Science and Industry, Schooley, J.F. (Ed.), American Inst. of Physics, New York, 5, 915.
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Rigney, D.A. and Hirth, J.P. (1979), Plastic deformation and sliding friction of metals, Wear, 53, 345-370. Rozeanu, L. and Pnueli, D. (1978), Two temperature gradients models for friction failure, ASME J. Lubrication Technology 100, 479-484. Santini, J.J. and Kennedy, F. E. (1975), An experimental investigation of surface temperatures and wear in disk brakes, Lubr. Eng., 31, 402-417. Schreck, E., Fontana, R.E., and Singh, G.P. (1992), Thin film thermocouple sensors for measurement of contact temperatures during slider asperity interactions on magnetic recording disks, IEEE Trans. on Magnetics, 28, 2548-2550. Shore, H. (1925),Thermoelectric measurement of cutting tool temperature, J. Wash. Acad. Sci., 15, 85-88. Shu, H.H., Gaylord, E.W., and Hughes, W.F. (1964), The relation between the rubbing interface temperature distribution and dynamic thermocouple temperature, ASME J. Basic Engg., 86, 417-422. Spikes, H.A. and Cameron, A. (1974), Additive interference in dibenzyl disulphide extreme lubrication, ASLE Trans., 16, 283-289. Stachowiak, G.W. and Batchelor, A.W. (1993), Engineering Tribology, Elsevier, Amsterdam. Suzuki, S. and Kennedy, F.E. (1988), Friction and temperature at head-disk interface in contact start/stop tests, Tribology and Mechanics of Magnetic Storage Systems, 5, 30-36. Suzuki, S. and Kennedy, F.E. (1991), The detection of flash temperatures in a sliding contact by the method of tribo-induced thermoluminescence, ASME J. Tribol., 113, 120-127. Tian, X., Kennedy, F.E., Deacutis, J.J., and Henning, A.K. (1992), The development and use of thin film thermocouples for contact temperature measurement, Tribology Trans., 35, 491-499. Tian, X. and Kennedy, F.E. (1993), Contact surface temperature models for finite bodies in dry and boundary lubricated sliding, ASME J. Tribol., 115, 411-418. Tian, X. and Kennedy, F.E. (1994), Maximum and average flash temperatures in sliding contacts, ASME J. Tribol., 116, 167-174. Ting, B.Y. (1988), Thermomechanical wear theory, Ph.D. dissertation, Georgia Institute of Technology, Atlanta, GA. Tong, H.M., Arjavalingam, G., Haynes, R.D., Hyer, G.N., and Ritsko, J.J. (1987), High temperature thinfilm Pt-Ir thermocouple with fast time response, Re Sci. Instrum., 58, 875. Uetz, H. and Föhl, J. (1978), Wear as an energy transformation process, Wear, 49, 253-264. Wright, P.K. and Trent, E.M. (1973), Metallographic methods of determining temperature gradients in cutting tools, J. Iron Steel Inst., 211, 364-388. Wright, P.K. (1978), Correlation of tempering effects with temperature distribution in steel cutting tools, ASME J. Engineering for Industry, 100, 131-136. Yevtushenko, A.A., Ivanyk, E.G., and Ukhanska, O.M. (1997) Transient temperature of local moving areas of sliding contact, Tribology Intl., 30, 209-214.
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7 Wear Mechanisms 7.1 7.2
Koji Kato Tohoku University
7.3 7.4 7.5
Adhesive Wear • Abrasive Wear • Fatigue Wear • Corrosive Wear • Mechanical Wear of Ceramics under Elastic Contact
Koshi Adachi Tohoku University
7.1
Introduction ....................................................................... 273 Change of Wear Volume and Wear Surface Roughness with Sliding Distance ......................................................... 274 Ranges of Wear Rates and Varieties of Wear Surfaces..... 274 Descriptive Key Terms ....................................................... 276 Survey of Wear Mechanisms ............................................. 278
7.6
Concluding Remarks.......................................................... 299
Introduction
Wear has been recognized as meaning the phenomenon of material removal from a surface due to interaction with a mating surface. Almost all machines lose their durability and reliability due to wear, and the possibilities of new advanced machines are reduced because of wear problems. Therefore, wear control has become a strong need for the advanced and reliable technology of the future. Wear rate changes drastically in the range of 10–15 to 10–1 mm3/Nm, depending on operating conditions and material selections (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). These results mean that design of operating conditions and selection of materials are the keys to controlling wear. As one way to meet these requirements, wear maps have been proposed for prediction of wear modes and wear rates (Lim and Ashby, 1987; Hokkirigawa and Kato, 1988). A wear map is considered one of the best descriptions of tribological conditions and is useful in selecting materials in a wide range of operating conditions. In order to design tribosystems and select materials based on the wear map, an understanding of wear rate, varieties of wear modes, and wear mechanisms is essential. Wear is the result of material removal by physical separation due to microfracture, by chemical dissolution, or by melting at the contact interface. Furthermore, there are several types of wear: adhesive, abrasive, fatigue, and corrosive. The dominant wear mode may change from one to another for reasons that include changes in surface material properties and dynamic surface responses caused by frictional heating, chemical film formation, and wear. Wear mechanisms are described by considering complex changes during friction. In general, wear does not take place through a single wear mechanism, so understanding each wear mechanism in each mode of wear becomes important. Our present understanding of the mechanisms of the four representative wear types is described in the following sections.
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FIGURE 7.1
Three representative types of wear curves in repeated contacts.
FIGURE 7.2
Three representative types of surface roughness changes in repeated contacts.
7.2
Change of Wear Volume and Wear Surface Roughness with Sliding Distance
Wear volume, wear surface roughness, and wear particle shape give us important information in characterizing wear. Three representative types of wear volume curves are shown schematically in Figure 7.1. Type I shows a constant wear rate throughout the whole process. Type II shows the transition from an initially high wear rate to steady wear at a low rate. This type of wear is quite often observed in metals (Chiou et al., 1985). Type III shows catastrophic transition from initial wear of low wear rate to wear of a high rate, such as fatigue fracture. This type of wear is often observed in ceramics (Cho et al., 1989). The amount of sliding before catastrophic wear is the period at which crack initiation takes place and depends on the initial surface finish, material properties, and frictional conditions. On the other hand, three representative types of roughness curves on wear surfaces are shown in Figure 7.2. Type I shows the case of steady wear, where the surface roughness does not change from the initial value. Type II shows the case of steady wear, where surface roughness increases to a certain value and stays there. Type III illustrates initial running-in and steady wear, where surface roughness decreases drastically in the running-in process. It is typically observed in lapping and polishing for surface finishing.
7.3
Ranges of Wear Rates and Varieties of Wear Surfaces
In general, wear is evaluated by the amount of volume lost and the state of the wear surface. The degree of wear is described by wear rate, specific wear rate, or wear coefficient. Wear rate is defined as wear
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FIGURE 7.3 Distribution of specific wear rate of metallic materials in sliding contact under different lubrication conditions. (Data from Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980).
FIGURE 7.4 themselves.
Distribution of specific wear rates and friction coefficients of ceramics in unlubricated sliding against
volume per unit distance, which corresponds to the slope of the wear volume curve shown in Figure 7.1. Specific wear rate is defined as wear volume per unit distance and unit load. Wear coefficient is defined as the product of specific wear rate and the hardness of the wearing material. The distributions of specific wear rates of metallic materials in sliding contact under different lubrication conditions are summarized in Figure 7.3 (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). Observed specific wear rates show a wide distribution in the range of 10–15 to 10–1 mm3/Nm by the differences in lubrication states. Figure 7.4 shows the distributions of specific wear rates and friction coefficients measured in unlubricated sliding of four kinds of ceramics against themselves under different normal loads, sliding velocities, and temperatures. The specific wear rates range from 10–9 to 10–2 mm3/Nm, depending on materials and friction conditions, even in the case of contact between similar materials. Figure 7.5 shows the varieties of wear surfaces of ceramics observed under different contact conditions. Wear surfaces look quite different depending on materials and friction conditions. This means that wear can change drastically when small changes in contact conditions are introduced into the tribosystem. The results shown in Figures 7.3, 7.4, and 7.5 clearly illustrate the following remark about wear (Bayer, 1994): “Wear is not a material property. It is a system response.” Wear changes drastically even with a relatively small change in a tribosystem, which is composed of dynamic parameters, environmental parameters, and material parameters.
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FIGURE 7.5 Variety of worn surface morphologies of three kinds of ceramics under different operating conditions. The arrows indicate relative sliding directions of counterfaces.
7.4
Descriptive Key Terms
There are many terms used to describe wear, and they are not always well differentiated. This sometimes makes understanding wear mechanisms confusing and difficult. Further effort must be given to achieve greater clarity in our approach to the analysis of wear mechanisms. In this section, descriptive key words of wear and their interrelations are summarized. This summary is shown in Figure 7.6 Wear is sometimes investigated from the viewpoint of the types of contact interaction of solid surfaces. There are many different contact configurations in practice. Normal or inclined compression and detachment,
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FIGURE 7.6
277
Descriptive key words of wear and their interrelations.
unidirectional sliding, unidirectional rolling, reciprocal sliding, reciprocal rolling, and rolling with slip are all different contact configurations classified from the viewpoint of motion of contacting bodies. Furthermore, free solid particles sometimes become unique substances, which attack interacting surfaces. This is also a contact configuration. Wear in these contact types is described as sliding wear, rolling wear, impact wear, fretting wear, or slurry wear. These descriptions of wear are all technical and based on the appearance of the contact type. They do not represent wear mechanisms in a scientific way. In order to focus on the wear mechanisms from the viewpoint of contact configurations, apparent and real contact conditions at the contact interface are introduced without particularizing about these contact configurations. Severity of contact, such as elastic contact or plastic contact, is the simplest and most direct way to think about wear mechanisms, and is a tribosystem response determined by dynamic parameters, material parameters, and atmospheric parameters. The following four wear modes are generally recognized as fundamental and major ones (Burwell, 1957/58): 1. 2. 3. 4.
Adhesive wear Abrasive wear Fatigue wear Corrosive wear
Adhesive wear and abrasive wear are wear modes generated under plastic contact. In the case of plastic contact between similar materials, the contact interface has adhesive bonding strength. When fracture is supposed to be essentially brought about as the result of strong adhesion at the contact interface, the resultant wear is called adhesive wear, without particularizing about the fracture mode. In the case of plastic contact between hard and sharp material and relatively soft material, the harder material penetrates to the softer one. When the fracture is supposed to be brought about in the manner of micro-cutting by the indented material, the resultant wear is called abrasive wear, recognizing the interlocking contact configuration necessary for cutting, again without particularizing about adhesive forces and fracture mode.
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In the case of contact in the running-in state, fatigue fracture is generated after repeated friction cycles. When surface failure is generated by fatigue, the resultant wear is called fatigue wear. In the case of contact in corrosive media, the tribochemical reaction at the contact interface is accelerated. When the tribochemical reaction in the corrosive media is supposed to be brought about by material removal, the resultant wear is called corrosive wear. In air, the most dominant corrosive medium is oxygen, and tribochemical wear of metals in air is generally called oxidative wear. Fatigue wear and corrosive wear can be generated in both plastic and elastic contacts. The material removal in adhesive, abrasive, or fatigue wear is governed by deformation and fracture in the contact region, where fracture modes are fatigue, brittle, or ductile fracture. Such deformation and fracture are generated by mechanically induced strains and stresses. Therefore, this type of wear is generally described as mechanical wear. The material removal in corrosive wear is governed by the growth of chemical reaction film or its chisolution on wear surface, where chemical reactions are highly activated and accelerated by frictional deformation, frictional heating, microfracture, and successive removal of reaction products. This type of wear is generally described as chemical wear or tribochemical wear. In some cases, material removal is governed by surface melting caused by frictional heating or by surface cracking caused by thermal stress. These types of wear are described as thermal wear, where frictional heating and partial high temperature govern the process. The macroscopic classifications in terms of mechanical, chemical, and thermal wear are useful to a comprehensive understanding of wear because almost all models of wear are included in these three types. The descriptions of wear by different definitions are summarized in Figure 7.6 to show the relative relations.
7.5
Survey of Wear Mechanisms
As the traditionally accepted representative wear modes, the four wear modes shown in Figure 7.7 are considered, and the wear mechanisms based on those wear modes are explained in detail. In addition, the wear mechanism based on mechanical wear of ceramics is explained.
7.5.1 Adhesive Wear If the contact interface between two surfaces under plastic contact has enough adhesive bonding strength to resist relative sliding, large plastic deformation caused by dislocation is introduced in the contact region under compression and shearing. As a result of such large deformation in the contact region, a
FIGURE 7.7
Schematic images of four representative wear modes.
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crack is initiated and is propagated in the combined fracture mode of tensile and shearing. When the crack reaches the contact interface, a wear particle is formed and adhesive transfer is completed. This type of wear, which occurs when there is enough adhesive bonding at the contact interface, is called adhesive wear. 7.5.1.1 Estimation of Adhesive Wear Volume If it is assumed that the real contact is composed of n contact points of equal size and if a new contact point is formed after the disappearance of the former one, the total number of contacts n stays constant during sliding. By supposing a circular contact area of radius a, the possible volume of wear particles generated after sliding the distance of 2a is assumed as the half sphere volume described by 2πa3/3. Based on these assumptions, the possible wear volume V for n contact points after sliding the distance L is given by:
L 2 V = n ⋅ πa 3 ⋅ 3 2a
(7.1)
Since the normal contact pressure with plastic deformation is almost equal to the hardness value H of the wearing material, the total real contact area for n contact points nπa2 is expressed by:
nπa 2 =
W H
(7.2)
By substituting Equation 7.2 into Equation 7.1, possible wear volume V under normal load W after sliding distance L is given by:
1 WL V= ⋅ 3 H
(7.3)
Equation 7.3 shows that the adhesive wear volume is proportional to the normal load and the sliding distance, and is inversely proportional to the hardness of the wearing material. Considering the relationship of Equation 7.2, it is proportional to the total real contact area during sliding. In practice, however, adhesive wear can occur through various modes, as shown in Figure 7.8 (Kayaba and Kato, 1981), and the size of the wear particles does not simply correspond to the size of the contact. Furthermore, a wear particle is not always generated only from the relatively soft material but can come from both materials. The probability of wear particle generation at each contact point is also not equal. It depends on the microscopic shape of the contact, microstructure of the material in the contact region, microscopic surface contamination, and other disturbances in the surroundings. In order to accommodate all these variables, a parameter Kad is introduced in Equation 7.3 as a modifier, and the wear volume is described by:
V = K ad ⋅
WL H
(7.4)
where Kad is called the wear coefficient for adhesive wear. It is a principal value for a friction pair to describe its wear rate. The physical meaning of Kad is the wear volume fraction at the plastic contact zone, and it is strongly affected by the material properties and the geometry of the zone in compression and shearing. In the adhesive wear of metals (Archard, 1953; Hirst, 1957), wear coefficient Kad varies between 10–7 and 10–2 depending on the operating conditions and material properties. It should be recognized that a wear coefficient Kad is not a constant value but is a possible value in the range of adhesive wear rate.
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FIGURE 7.8 Schematic diagram of representative adhesive transfer process observed in the adhesive wear process; adhesive transfer of a thin flake-like wear particle (a) and a wedge-like wear particle (b). (From Kayaba, T. and Kato, K. (1981), The adhesive transfer of the slip-tongue and the wedge, ASLE Trans., 24, 2, 164-174. With permission.)
7.5.1.2 Adhesive Wear Mode Tangential shear under compression at the contact interface of strong adhesive bonding generates slips along slip planes in the contact region. As a result of the slips, flake-like shear tongues are formed, as shown in Figure 7.8a, and are followed by a crack initiation and propagation in the combined fracture mode of tensile and shear in the leading region of the contact. The large plastic deformation in the contact region sometimes forms a wedge-like shape, which is followed by crack initiation and propagation in the combined fracture mode of tensile and shear in the trailing region of the contact, as shown in Figure 7.8b. Fractographic analysis of the fracture surfaces of wear particles of Figure 7.8a and b indicates that the larger part of the fracture surface of the flake-like wear particle shows the fracture mode of compression and shear, and that all parts of the fracture surface of the wedge-like wear particle in Figure 7.8b shows a tensile and shear fracture mode. Both wear modes which produce flake-like and wedge-like wear particles are basic ones in adhesive wear. In the adhesive wear process, transfer and retransfer from one surface to the mating surface take place in many cases. As a result, relatively large wear particles composed of two surfaces are formed. This is another basic part of the adhesive wear mechanism (Sasada, 1979). In the successive process of repeated sliding, these wear particles leave the contact interface as free particles or stay on either surface and form prows to scratch the counterface (Vingsbo and Hogmark, 1980; Chen and Rigney, 1985). Even if the contact is made between flat surfaces of similar materials and
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FIGURE 7.9 Abrasive wear of ductile material, which is dominated by plastic deformation (a) and one of brittle fracture, which is dominated by brittle fracture (b). (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.)
the contact interface is at first parallel to the sliding direction, the interface rotates and becomes inclined and wavy as a result of the combined effect of normal and tangential forces in sliding (Cocks, 1962). This is another aspect of deformation at a contact interface which explains why the adhesive wear mode of Figure 7.8a or Figure 7.8b occurs commonly in practice.
7.5.2 Abrasive Wear If the contact interface between two surfaces has interlocking of an inclined or curved contact, ploughing takes place in sliding. As a result of ploughing, a certain volume of surface material is removed and an abrasive groove is formed on the weaker surface. This type of wear is called abrasive wear. Here, we assume a single contact point model where a hard, sharp abrasive is indented against the flat surface and forms a groove on it by ploughing. When wearing material has a ductile property, a ribbonlike, long wear particle is generated by the mechanism of microcutting. In the case of brittle material, however, a wear particle is generated by a crack propagation (Evans and Marshall, 1981). These differences are summarized schematically in Figures 7.9a and b. 7.5.2.1 Abrasive Wear of Ductile Material Even in the case of sliding contact between smooth surfaces of the same ductile material, parallel grooves are generally found on the wear surface after sliding. The peak and the valley coincide well with the mating surfaces, as shown in Figure 7.10. This result means that the hard abrasive asperities are formed on the mating surface because of, for example, work hardening, phase transitions, and third-body formation at the contact interface during repeated sliding contact. Therefore, abrasive wear is recognized as a more representative wear mode of ductile material in repeated sliding. 7.5.2.1.1 Estimation of Abrasive Wear Volume The first point to understand in the abrasive wear mechanism is the estimation of wear volume from which wear particles can be generated. Here, we assume a simplified contact model in which the abrasive has a conical shape with an angle θ, and the indentation depth of the abrasive is d, as shown in Figure 7.11.
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FIGURE 7.10 sliding.
The cross-sectional profiles of two mating wear surfaces of 0.45% carbon steel after pin-on-ring
FIGURE 7.11
Typical model of abrasive wear by a conical indentor.
Based on this assumption model, the possible wear volume V, which is ploughed by harder asperities after sliding a distance of L, is given by:
V = d 2 ⋅ tan θ ⋅ L
(7.5)
Since the normal contact pressure under plastic contact can be assumed to be equal to the hardness value H of the wearing material, real contact area of π(dtanθ)2/2 is expressed by:
(
)
2 1 W π d ⋅ tanθ = 2 Hv
(7.6)
By substituting Equation 7.6 into Equation 7.5, possible wear volume V under normal load W and after sliding distance L is given by:
V=
2 WL ⋅ π ⋅ tanθ H v
(7.7)
Equation 7.7 gives the wear volume for the case of ideally plastic abrasive grooving in microcutting shown in Figure 7.12a. There are two other modes of wedge forming and ploughing in abrasive grooving, as shown in Figures 7.12b and c (Hokkirigawa and Kato, 1988) where the wedge does not grow from its initial size in Figure 7.12b, and no wear particles are generated in Figure 7.12c. It means that wear volume in abrasive grooving is not always equal to the groove volume. In order to accommodate all these meanings, a parameter Kab is introduced in Equation 7.7 as a modifier, and the wear volume is described by:
V = K ab ⋅
WL H
(7.8)
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FIGURE 7.12 Three different modes of abrasive wear observed by SEM: Cutting mode (a), steel pin on brass plate; wedge-forming mode (b), steel pin on stainless steel plate; ploughing mode (c), steel pin on brass plate. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, 51-57. With permission.)
FIGURE 7.13 Effect of hardness on the relative wear resistance of pure metals. (From Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., 655-659. With permission.)
Equation 7.8 shows that the abrasive wear volume is proportional to the normal load and the sliding distance, and it is inversely proportional to the hardness of the wearing material. In fact, abrasive wear resistance is linearly proportional to hardness of wearing metals, as shown in Figure 7.13 (Khruschov, 1957). The proportional constant Kab is called the wear coefficient for abrasive wear. It is a principal value for a friction pair in describing its wear rate. The physical meaning of Kab is the wear volume fraction against the nominal groove volume zone, and it depends on the ductility of wearing material, shear strength at the contact interface, and the shape of the abrasive asperity. In the abrasive wear of metal (Rabinowicz, 1980), wear coefficient Kab varies between 10–4 and 10–1, depending on the contact conditions and material parameters. It should be recognized from these data that wear coefficient Kab is not a constant value in abrasive wear. By comparing Kab with Kad in adhesive
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FIGURE 7.14
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Schematic diagram of effect of hardness ratio on wear rate of abraded material against abrasive.
wear, it is clear that abrasive wear gives a relatively large wear coefficient. That is why abrasive wear is recognized as severe wear. Abrasive grooving by the hard and sharp asperity is possible only when the asperity is not flattened or fractured in sliding. Therefore, the abradability of the hard, sharp asperity must be evaluated. 7.5.2.1.2 Hardness Ratio and Shape of Abrasive Asperity The hardness of the abrasive asperity is important in abrasive wear. Generally, when the hardness ratio r (mating material hardness/abrasive hardness) stays below a certain critical value rc1 (0.5 to 0.8; Khruschov, 1974; Rabinowicz, 1983), abrasive wear clearly takes place. However, with the increase in hardness ratio r above the critical value rc1, wear volume of mating material decreases, and finally almost no wear is observed when r is close to a critical value rc2 (1 to 1.4; Rabinowicz, 1983). This relation is shown schematically in Figure 7.14. The results in Figure 7.14 require consideration as to the yield criterion of asperity in grooving action. Theoretical analysis was made by the slip line field theory, and the critical condition for the yield of an asperity is given in Figure 7.15 (Kayaba et al., 1983) between the hardness ratio r and the critical asperity tip angle θc. The parameter f in Figure 7.15b is the ratio of the shear strength of the interface to the shear strength of the softer material, and Figure 7.15a shows the relation at f = 0. Plastic grooving by the asperity is possible when its tip angle θ is larger than the critical value θc, and this value changes depending on the values of hardness ratio r of two surfaces and f, as shown in Figure 7.15b. These figures show that the asperity with large θ can plough the mating surface even when the hardness ratio r is very close to unity theoretically. This is evidence of the high possibility of groove formation at the sliding interface between similar ductile materials. 7.5.2.1.3 Abrasive Wear Mode As mentioned above, abrasive wear takes three different modes: microcutting, wedge forming, and ploughing, as shown in Figure 7.12. Wear particles are formed differently depending on these three modes. In the cutting mode, long and curled ribbon-like wear particles are formed. Low friction assists in this wear mode. In the wedge-forming mode, a wedge-like wear particle is formed at the tip of the grooving asperity as shown in Figure 7.12b and stays there working as a kind of built-up wedge to continue grooving. Sliding takes place at the bottom of the wedge where adhesive transfer of a thin layer from the underlying counterface continues to grow the wedge slowly. This wear mode appears as a combined effect of adhesion at an inclined or curved contact interface and shear fracture at the bottom of the wedge. High friction or strong adhesion assists in this wear mode. In the ploughing mode, a wear particle is not
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FIGURE 7.15 Relationship between the critical tip angle θc and the hardness ratio r where the normalized shear strength f is zero in (a) and changes from zero to 1.0 in (b). (From Kayaba, T., Kato, K., and Hokkirigawa, K. (1983), Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 87, 151-161. With permission.)
generated by a single pass of sliding and only a shallow groove is formed. Repeated sliding and accumulation of plastic flow at the surface is necessary for the generation of wear particles. These three abrasive wear modes are theoretically predictable with two dimensional models of the slip line field theory (Challen and Oxley, 1979). Theoretical predictions agree well with experimental results of spherical pin-on-disk tests, which are shown in the abrasive wear mode diagram of Figure 7.16 (Hokkirigawa and Kato, 1988) by introducing the following parameter Dp for the degree of penetration:
Dp = R
πH 2 πH − R −1 2W 2W
(7.9)
where R is the pin tip radius, H the hardness of the wearing material, and W the load. The parameter f in Figure 7.16 has the same meaning as that in Figure 7.15. Theoretical solid lines are drawn according to the theory (Challen and Oxley, 1979) by substituting the relationship of Dp = 0.8 (1 – cosθ)/sinθ where θ is the attack angle. In all these three abrasive wear modes, grooves are formed as the result of wear particle generation and plastic flow of material to form ridges on both sides of a groove. If we introduce the groove volume ∆Vg per unit sliding distance observed below the initial surface level and the ridge volume ∆Vr per unit sliding distance observed above the initial surface level on both sides of the groove, (∆Vg — ∆Vr) gives the wear volume at one groove in one pass of sliding. With these descriptions, the concept of degree of wear β at one groove is introduced, as shown in Figure 7.17 and is given as follows:
β=
∆Vg − ∆Vr ∆Vg
(7.10)
where β = 1 corresponds to the state of ideal material removal without forming ridges, and β = 0 means the ideal ploughing of no material removal.
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FIGURE 7.16 Abrasive wear mode diagram: abrasive wear modes of ductile material as a function of degree of penetration Dp and normalized shear strength f at the contact interface. Solid lines are theoretically induced with modified two-dimensional model. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, 51-57. With permission.)
FIGURE 7.17 Schematic diagram of cross-sectional profile of groove formed after scratching. ∆Vg: groove volume and ∆Vr: two side ridges’ volume of two sides.
The degree of wear β defined in this way is a function of the hardness H of the wearing material and the degree of penetration Dp as shown in Figure 7.18 (Hokkirigawa and Kato, 1989) for heat treated steels. This β is related to the abrasive wear coefficient Kab mentioned above at one groove as follows:
K ab = β
∆Vg H W
(7.11)
It is clear in Equation 7.11 that β represents the fracture property of the wearing material and (∆VgH/W) represents the deforming property of the wearing material under the effect of f and the shape of the indentor.
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FIGURE 7.18 Degree of wear β as a function of degree of penetration Dp observed with heat-treated steel of different hardness H (kgf/mm2). (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)
The parameter β and ∆Vg are given from the result of a pyramidal scratch test as (Zum Gahr, 1987):
H 1 3 ε β = 1 − exp −2 0 ln s εc H
(7.12)
where H0 is the original hardness of the wearing material, H is the hardness after deformation by grooving, εs is the strain on the groove surface, and εc is the strain above which material is removed from the groove. εs in Equation 7.12 is given by:
13 23 2 W E 1 + 10µ ε s = 2 ln 6 HR2 3
(
)
12
θ tan 2
(7.13)
where E is the Young’s modulus of the wearing material, µ is the friction coefficient, θ is the angle of the pyramid, and R is the tip radius of the pyramid:
W 1 ∆Vg = 1 + 10µ 2 H 5
(
)
12
θ tan π HR 2 − 1 + θ 2 W tan 2 2
(7.14)
By introducing Equations 7.12, 7.13, and 7.14 into Equation 7.11, the wear coefficient Kab is expressed theoretically in terms of material parameters, geometrical parameters, and frictional conditions of load and friction coefficient. If the expression for volumetric is introduced by defining the inverse of wear rate (sliding distance/wear volume), it is given by (β∆Vg)–1. The comparisons of experimental and theoretical values of the volumetric wear resistance show good agreement, as shown in Figure 7.19 (Zum Gahr, 1987). The expressions of Equations 7.9 through 7.14 and Figures 7.15 through 7.19 are all for simple abrasive scratching. But in practical abrasive contact, there are many abrasive contact points at the same time,
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FIGURE 7.19 Theoretical abrasive wear resistance vs. experimental abrasive wear resistance measured on different materials by using a diamond scratch of attack angle θ = 90° and tip radius r = 8 mm under load W = 2N. (From Zum Gahr, K.H. (1987), Microstructure and wear of materials, Tribology series, Elsevier, 132-148. With permission.)
FIGURE 7.20 Relationship between abrasive wear resistance and hardness of worn material observed experimentally and estimated theoretically. (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)
and each of them is at a different state of deformation and wear. Therefore, it becomes necessary to introduce a model for the distribution of contact geometry, contact load, and the resultant abrasive wear mode. If we know the distribution of Dp at multiple abrasive contacts of a surface, the total wear rate of the surface can be introduced by summarizing all the values of β at all contact points. Figure 7.20 (Hokkirigawa and Kato, 1989) shows the experimental data and theoretical solid and broken lines obtained in this way. Good agreement of experimental data and theoretical lines is confirmed. 7.5.2.2 Abrasive Wear of Brittle Material In the case of brittle material, which is indented and ploughed by the abrasive, a wear particle is generated due to mainly brittle fractures caused by initiation and propagation of cracks, such as the median and
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FIGURE 7.21 Relationship between abrasive wear resistance and fracture toughness of yttria-doped zirconium oxide. (From Fischer, T.E., Anderson, M.P., and Jahanmir, S. (1989), Influence of fracture toughness on the wear resistance of yttria-doped zirconium oxide, J. Am. Ceram. Soc., 72, 2, 252-257. With permission.)
FIGURE 7.22
Abrasive wear model for brittle material.
lateral cracks shown in Figure 7.10b. Therefore, wear rate of the brittle material is strongly dependent on fracture toughness. Figure 7.21 (Fischer et al., 1989) shows the effect of fracture toughness on the wear rate of zirconium oxide under abrasive contact. It is clear that fracture toughness is an important parameter to determine the abrasive wear rate of the brittle material. Wear volume in scratching the brittle material is described by the model shown in Figure 7.22 (Evans and Marshall, 1981). It is assumed that a wear particle is generated by lateral crack propagation which
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reaches to the surface. If the crack is propagated by the residual stress, crack length c is defined by the function of normal load W, fracture toughness Kc, hardness H, and Young’s modulus E as follows:
c = α1
W5 8 E K c1 2 H 1 8 H
35
(7.15)
where α1 depends on the shape of the abrasive and is determined by calibration on a material with wellcharacterized fracture properties. The depth b of lateral fracture is estimated by the radius of plastic contact zone, and is given by:
E b = α2 H
2 5
W H
12
(7.16)
where α2 is a material-independent constant. Based on these assumptions, the wear volume V in scratching of the brittle material with a hard asperity is given by the following equation:
V = α3
W9 8 E K c1 2 H 5 8 H
4 5
L
(7.17)
where L is the sliding distance and α3 is a material-dependent constant determined by calibration on a material with well-characterized fracture properties. Another analysis (Evans and Wilshaw, 1976) on a similar model with different assumptions gives a slightly different equation of abrasive wear volume of brittle materials as follows:
V = α4
W5 4 L K c3 4 H 1 2
(7.18)
where α4 is a constant. It is clear from Equations 7.17 and 7.18 that abrasive wear rate depends strongly on both hardness and toughness. Wear rate predicted by both equations agrees well with experimental data, as shown in Figure 7.23 (Evans and Marshall, 1981) and Figure 7.24 (Buljan and Sarin, 1985).
7.5.3 Fatigue Wear Repeated cycles of contact are not necessary in adhesive and abrasive wear for the generation of wear particles. There are other cases of wear where a certain number of repeated contacts are essential for the generation of wear particles. Wear generated after such contact cycles is called fatigue wear. When the number of contact cycles is high, the high-cycle fatigue mechanism is expected to be the wear mechanism. When it is low, the low-cycle fatigue mechanism is expected. 7.5.3.1 Fatigue Wear in Rolling and Sliding Contact under Elastic Contact In the case of the elastic contact generally observed in rolling elements, the main wear mechanism is high-cycle fatigue fracture in the contact region. The critical number of rolling cycles Nf for the generation of wear particles by spalling or flaking is given experimentally as follows (Lundberg and Palmgren, 1952):
Nf ∝
1 Wn
(7.19)
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FIGURE 7.23 Correlation between abrasive wear resistance and (hardness)5/8 × (toughness)1/2. (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.)
FIGURE 7.24 Relationship between abrasive wear resistance and (toughness)3/4 × (hardness)1/2. (From Buljan, S.T. and Sarin, V.K. (1985), The future of silicon nitride cutting tools, Carbide Tool J., May/June, 4-7. With permission.)
where W is the normal load and n is a constant which depends on the shape of the rolling element. In the case of rolling bearings, the value of n is about 3. This empirical law has been widely accepted in the design of rolling bearings. Its basic premise is that spalling or flaking can be treated as statistical fracture phenomena following the modified theory (Weibull, 1930). Although the apparent practical contact pressure is not so high as to introduce yield in the contact region, local yield is generated in the contact region because of the existence of microdefects in the material. A single crystal has slip planes for preferential sliding under shear stress. A polycrystal has grain boundaries, inclusions, and vacancies. Because of these inhomogeneities, the local stress in the contact
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FIGURE 7.25 The change in the hardness distribution beneath the surface during the repeated rolling of steel (0.45C, 0.27 Si, 0.85 Mn). (From Kayaba, T. and Suzuki, S. (1976), An investigation of surface damages by rolling contact, Technology Report, Tohoku Univ., 41, 1, 21-46.)
region exceeds the yield stress of the material even when the theoretical stress for the homogeneous material does not exceed the yield stress (Dufrane and Glaeser, 1976). There is a state where a plastically deformed region appears beneath the interface without reaching the surface. In this case, work hardening takes place in the yield region as a result of repeated contact. This is shown in Figure 7.25 (Kayaba and Suzuki, 1976), where the hardness peak is located about 130 µm beneath the surface, and the value of maximum hardness increases with an increase in the number of rolling cycles. The maximum hardness value of about 400 kgf/mm2 is reached after about 2 × 106 cycles, when pits start to appear on the surface. Repeated friction under elastic or elastoplastic contact causes the accumulation of local plastic strain around some stress concentration points, and cracks are generated after reaching a certain number of frictional cycles. The mechanism of crack initiation and propagation in such a situation is that of fatigue fracture, which is a kind of rate process controlled by the inhomogeneity of the microstructure of a material. 7.5.3.2 Fatigue Wear in Sliding Contact under Plastic Contact In the friction between metallic materials, conformity at the contact interface without catastrophic wear is easily observed as the ploughing mode shown in Figure 7.12c (Hokkirigawa and Kato, 1988). In this mode, a wear particle is not generated by a single pass of sliding and only a shallow, conformable groove is formed. In the case of repeated contact of abrasive sliding at the same grooves, plastic burnishing (ploughing mode in Figure 7.12c) becomes predominant. In this ploughing mode, fatigue fracture is expected to take place after a critical number Nf of plastic strain cycles in the wave. Figure 7.26 (Akagaki and Kato, 1987) shows the effect of repeated sliding on the growth of plastic flow wear particles of steel under boundary lubrication. It is seen that a thin surface layer protrudes in the
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FIGURE 7.26 Flow wear process for steel during repeated sliding in boundary lubrication. (From Akagaki, T. and Kato, K. (1987), Plastic flow process of surface layers in flow wear under boundary lubricated conditions, Wear, 117, 179-196. With permission.)
FIGURE 7.27 Amount of flow wear of the surface layer as a function of sliding cycles under the same sliding conditions. (From Akagaki, T. and Kato, K. (1988), Simulation of flow wear in boundary lubrication using Vickers indentation method, STLE, Trib. Trans., 31, 3, 311-316. With permission.)
direction of sliding, and grows as the number of sliding cycles increases. Figure 7.27 shows the amount of plastic flow of the surface layer as a function of the sliding cycles for the two different contact pressures (Akagaki and Kato, 1988). The flow rate observed is a few micrometers per 104 cycles of sliding. Conforming between two sliding surfaces occurs by this gradual surface plastic flow and wear in metallic triboelements. This phenomenon is representative of low fatigue wear under plastic contact.
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If we suppose that the plastically deformed layer is detached as wear particles by low-cycle fatigue failure, Nf would be given by the modified Coffin–Manson relationship:
C Nf = s ∆γ s
D
(7.20)
where Cs is the monotonic effective shear strain, ∆γs is the effective shear strain increment per wave pass, and D is a constant usually taken as 2. By considering the plastic work needed to produce unit volume of wear and introducing the relationship of Equation 7.20, the specific wear rate ws defined by wear volume/load/distance is described by Challen et al. (1986) as follows:
ws =
rpµ kC ∆γ 1s− D D s
(7.21)
where rp is the ratio of plastic to total work of sliding and k is the average shear flow stress of the wearing material. By introducing the relation of k = H(Hardness)/(3 × 31/2) into Equation 7.21, the fatigue wear coefficient Kf, defined in the same way as Kad and Kab mentioned above, can be expressed as:
K f = ws H =
3 × 31 2 rpµ C D ∆γ 1s− D
(7.22)
The three parameters of ∆γs, rp, and µ are functions of the attack angle α (= π/2 – θ), where θ is defined in Figure 7.11, and the normalized shear strength f. The parameter f has the same meaning as in Figures 7.15 and 7.16; it is the ratio of shear strength τ at the contact interface to the shear flow stress k of the wearing material, i.e., f = τ/k. From Figure 7.28 (Challen et al., 1986), which shows the calculated values of Kf by changing the values of θ and f, it can be seen that Kf is predicted to vary in the range from 10–6 to nearly 1 for α and f values ranging from 0.1° to 10° and from 0 to 0.99, respectively. The contact between a hard asperity and a groove generally becomes milder in repeated sliding as a result of deformation and wear in the groove surface layer. Better conformity between asperity and groove surfaces is attained where the contact pressure is decreased and elastic strains have to be considered. If the maximum Hertzian contact pressure is above the critical value of the elastic shakedown limit in an elastic–plastic half-space of the wearing body, repeated plastic deformation takes place in the form of “cyclic plasticity” or “ratcheting” (Johnson, 1994). In cyclic plasticity, a cycle of axial plastic strain which comprises a reversing (fatigue) component ∆εa acts parallel to the surface. If it were acting alone, the number Nf of cycles to surface failure would be given by the Coffin–Manson relationship as follows:
2C Nf = ∆ε a
2
(7.23)
where C is the monotonic fracture strain. In ratcheting, unidirectional plastic shear strain ∆γr per cycle acts and is accumulated until the total strain reaches a critical value C where surface failure is generated. The number Nr of cycles to failure in ratcheting is given by Johnson (1994) and Kapoor and Johnson (1994) as:
C Nr = ∆γ r
(7.24)
where ∆γr is the ratcheting shear strain per cycle. In this ratcheting region, however, it is not quite clear whether ultimate failure would be caused by fatigue or by ductile fracture. It would be reasonable to
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FIGURE 7.28 Variation of wear coefficient Kf in sliding friction assuming a low-cycle fatigue wear mechanism with attack angle α and normalized shear strength f. (From Challen, J.M., Oxley, P.L.B., and Hockenhull, B.S. (1986), Prediction of Archard’s wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism, Wear, 111, 275-288. With permission.)
suppose that each fatigue wear mode described by Equation 7.20, 7.23, or 7.24 has the possibility of being the prevailing wear mode depending upon the contact condition, and two or three of them may coexist in some cases. Careful experimental observation (Black et al., 1996) gives the value of D = 1.67, which suggests the possibility of a mixture of these two modes of fatigue wear.
7.5.4 Corrosive Wear When sliding takes place, especially in corrosive liquids or gases, reaction products are formed on the surface mainly by chemical or electrochemical interactions. If these reaction products adhere strongly to the surface and behave like the bulk material, the wear mechanism should be almost the same as that of the bulk material. In many cases, however, such reaction products behave very differently from the bulk material. Therefore, wear is quite different from that of the bulk material, and is dominated by the reaction products formed by the interaction of solid materials with the corrosive environment. This kind of tribochemical wear accelerated by corrosive media is called corrosive wear. In corrosive wear, tribochemical reaction produces a reaction layer on the surface. At the same time, such layer is removed by friction. Therefore, relative growth rate and removal rate determine the wear rate of the reaction layers and, as a result, of the bulk material. Therefore, models of the reaction layer growth and those of the layer removal become very important. 7.5.4.1 Oxidative Wear of Metals Oxidative wear is the most representative mode of corrosive wear of metals. Based on the oxidative reaction between steel and normal atmospheric air and assuming the film removal model where an oxide film of steel is supposed to detach from the surface at a certain critical thickness, corrosive wear coefficient Kc defined in the same way as Kad and Kab has been expressed by Quinn (1987) as:
Kc =
Q dA exp − 2 2 ξρv RgT
(7.25)
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where A is the Arrhenius constant, Q the activation energy, Rg the gas constant, T the absolute temperature, ρ the density of oxide, v the sliding velocity, and L the distance along which a wearing contact is made. It is generally assumed that activation energy does not vary substantially between static and sliding conditions. Making this assumption, the experimental wear results for oxidation of steels give a value of the Arrhenius constant in Equation 7.25 which is 103 – 1010 times larger than one in static oxidation (Quinn, 1987). This means that oxidation is much more rapid under sliding contact than in the static condition. This seems to be supported by another experimental result where the thickness of oxidative wear layers of steel and titanium are more than 500 times larger than those grown under static conditions (Krause and Scholter, 1978). Therefore, estimation of real activation energy at the sliding surface becomes important. Furthermore, the real temperature at the real contact interface is important in the determination of the wear rate, because the reaction rate required to form a chemical product is strongly affected by the temperature induced by friction. On the other hand, if the reaction rate is not high enough to grow an oxide film to the critical thickness within a cycle of sliding, oxidative wear of the steel may not occur. Even in this case, the reaction rate also determines the wear rate. 7.5.4.2 Oxidative Wear of Ceramics — Tribochemical Wear of Ceramics The hydroxide of silicon nitride in water is very weakly bonded on the surface, is easily removed from the surface by rubbing, and it dissolves in water (Fischer and Tomizawa, 1985). If the reaction rate is high, a lot of silicon nitride hydroxide can be formed and worn away quickly. The reaction rate determines the wear rate in this case. If it is assumed that friction heating also accelerates chemical reaction at the contact interface, the wear coefficient Kc of nonoxidative ceramics sliding against themselves is explained by Kitaoka et al. (1997) as:
Kc =
Q Ac exp − ρv RgT
(7.26)
where Q is the activation energy, Rg the gas constant, T the reaction temperature, ρ the density of oxide, and v the sliding velocity. It is clear from both models (Quinn, 1967; Kitaoka et al., 1997), that the corrosive wear mechanism is difficult to understand without first understanding the process of the formation of the reaction layer from the viewpoint of the combined effect of mechanical activation and chemical reaction, namely, from the viewpoint of tribochemistry.
7.5.5 Mechanical Wear of Ceramics under Elastic Contact In the contact of ceramics, wear particles are generated mechanically without the mechanism of fatigue wear even under elastic contact. It is the wear governed by the microscopic brittle fracture at surface microcracks under nominal elastic contact. This is the representative wear mechanism of ceramics when specific wear rate is larger than 10–6 mm3/Nm (Adachi et al., 1997). Figure 7.29 shows a schematic diagram of the model, where a wear particle is generated by the propagation of a predominant surface crack in brittle manner. Such crack propagation can be enhanced by the tensile stress induced by friction under elastic contact. Based on the linear elastic fracture mechanics model, the critical condition for the crack propagation is expressed by the following equation:
Bσ max πd ≥ K c
(7.27)
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µp Hertzian Contact
(a)
Tensile stress
(b)
(c)
(d)
FIGURE 7.29 Wear model of brittle material, in which wear particles are generated by propagation of preexistent crack under elastic sliding contact: (a) sliding contact under elastic contact; (b) application of tensile stress to crack tip; (c) propagation of crack; and (d) generation of wear particle.
where σmax is the maximum tensile stress at the crack tip, d preexistent crack length, Kc fracture toughness of the wearing material, and B constant. Sliding generates the friction force which introduces the shear stress at the contact interface in addition to the compressing stress. As the result, the maximum tensile stress σmax is induced at the trailing edge of the contact, which is expressed by the following equation (Hamilton, 1983) in the case of the Hertzian contact:
1 − 2ν 4 + ν σ max = Pmax + πµ 8 3
(7.28)
where Pmax is the maximum Hertzian contact pressure, ν Poisson’s ratio, and µ friction coefficient. Assuming that the Poisson’s ratio is 0.25, Equation 7.28 is simplified as follows:
σ max =
(
Pmax 1 + 10µ
)
6
(7.29)
Substituting Equation 7.29 into Equation 7.27, the critical condition for surface crack propagation is given by the parameter Sc,m defined as follows:
Sc , m =
(1 + 10µ)P
max
KC
d
≥ Cm
(7.30)
where Cm (= 6/(Bπ1/2)) is a constant. Sc,m gives mechanical severity of contact from the viewpoint of contact stress and its concentration against Kc. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact when Sc,m exceeds the threshold value Cm.
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On the other hand, sliding generates heat pulses by friction heating, which in turn generates thermal strain at the contact. The thermal stress σmax induced at a crack tip as a tensile stress σmax is given by the following equation:
σ max =
Eα ∆T 1− ν
(7.31)
where E is Young’s modulus, α the coefficient of thermal expansion, ν Poisson’s ratio, and ∆T the temperature difference due to the heat pulse. If temperature difference ∆T is assumed to be proportional to the flash temperature, the critical condition for crack propagation is given by the parameter Sc,t defined as follows:
Sc , t =
γµ ∆Ts
vWH ≥ Ct kρc
(7.32)
where γ is the heat partition ratio, µ the friction coefficient, ∆Ts the thermal shock resistance, v the sliding velocity, W the normal load, H hardness, k thermal conductivity, ρ density, c specific heat, and Ct constant. Sc,t gives thermal severity of contact from the viewpoint of thermal stress and its concentration against Kc. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact when Sc,t exceeds the threshold value Ct. With these two parameters of Sc,m and Sc,t describing the severity of contact, the region for surface crack propagation is separated from the region of no crack propagation on the wear map shown in Figure 7.30 (Adachi et al., 1997). The state of wear in the region of crack propagation is generally called severe wear, and that in the region of no crack propagation is generally called mild wear. Experimental specific wear rate in the severe wear region varies from 10–6 to 10–2 mm3/Nm, and that in mild wear region from 10–9 to 10–6 mm3/Nm. The experimental critical values of Sc,m and Sc,t at the boundaries between the severe and mild wear regions in Figure 7.30 are 6 and 4.0 × 10–2, respectively.
Wear mode Mild Severe
Material
Sc,m (=
(1+10µ) Pmax d KIC
)
20
Ceramics against themselves
Al2O3
15
10
ZrO2 SiC
Severe wear with Crack propagation
Mild wear without Crack propagation
5
0 10-3
10-2 Sc,t (=
10-1 γµ Ts
vWHV kρc
100
)
FIGURE 7.30 Wear map of ceramics, which shows the possible region of brittle fracture dominated wear under elastic contact. The regions of mild wear and severe wear are clearly shown by the critical values of Sc,m and Sc,t . (From Adachi, K., Kato, K., and Chen, N. (1997), Wear map of ceramics, Wear, 203-204, 291-301. With permission.)
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299
Concluding Remarks
Wear types of adhesive, abrasive, fatigue, and tribochemical wear are introduced and their wear mechanisms are explained with wear models in this chapter. In practical wear of triboelements, some of these wear types are involved at the same time, and major wear type changes in some cases from one to another during running as a result of wear itself. On the other hand, wear is sensitive to the change of various system parameters such as mass, shape, stiffness, material properties, and environment. Because of such multiparameter sensitivity of wear, quantitative prediction of wear rate in practice is still far from reality. It becomes important, therefore, to recognize the major wear type and its typical wear mechanism in relation to system parameters.
References Adachi, K., Kato, K., and Chen, N. (1997), Wear map of ceramics, Wear, 203-204, 291-301. Akagaki, T. and Kato, K. (1987), Plastic flow process of surface layers in flow wear under boundary lubricated conditions, Wear, 117, 179-196. Akagaki, T. and Kato, K. (1988), Simulation of flow wear in boundary lubrication using Vickers indentation method, STLE, Trib. Trans., 31, 3, 311-316. Archard, J.F. (1953), Contact and rubbing of flat surfaces, J. Appl. Phys., 24, 981-988. Bayer, R.G. (1994), Mechanical Wear Prediction and Prevention, Marcel Dekker, New York, 280. Bhansali, K.J. (1980), Wear coefficients of hard-surfacing materials, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, 373-383. Black, A.J., Kopalinsky, F.M., and Oxley, P.L.B. (1996), Sliding metallic wear test with in-process wear measurement: a new approach to collecting and applying wear data, Wear, 200, 30-37. Buljan, S.T. and Sarin, V.K. (1985), The future of silicon nitride cutting tools, Carbide Tool J., May/June, 4-7. Burwell, J.T. (1957/58), Survey of possible wear mechanisms, Wear, 1, 119-141. Challen, J.M. and Oxley, P.L.B. (1979), An explanation of the different regimes of friction and wear using asperity deformation models, Wear, 53, 229-243. Challen, J.M., Oxley, P.L.B., and Hockenhull, B.S. (1986), Prediction of Archard’s wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism, Wear, 111, 275-288. Chen, L.H. and Rigney, D.A. (1985), Transfer during unlubricated sliding wear of selected metal systems, Wear, 105, 47-61. Chiou, Y.C., Kato, K., and Kayaba, T. (1985), Effect of normal stiffness in loading system on wear of carbon steel — part 1: severe-mild wear transition, ASME, J. Tribology, 107, 491-495. Cho, S.J., Hockey, B.J., and Lawn, B.R. (1989), Grain-size and R-curve effects in the abrasive wear of alumina, J. Am. Ceram. Soc., 72, 7, 1949-1952. Cocks, M. (1962), Interaction of sliding metal, J. Appl. Phys., 33, 2152. Dufrane, K.F. and Glaeser, W.A. (1976), Rolling-contact deformation of MgO single crystals, Wear, 37, 21-32. Evans, A.G. and Wilshaw, T.R. (1976), Quasi-static solid particle damage in brittle solids, I. Observations, analysis and implications, Acta Metal., 24, 939-956. Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. Fischer, T.E., Anderson, M.P., and Jahanmir, S. (1989), Influence of fracture toughness on the wear resistance of yttria-doped zirconium oxide, J. Am. Ceram. Soc., 72, 2, 252-257. Fischer, T.E. and Tomizawa, H. (1985), Interaction of tribochemistry and microfracture in the friction and wear of silicon nitride, Wear, 105, 29-45. Hamilton, G.M. (1983), Explicit equations for the stresses beneath a sliding spherical contact, in Proceedings Instn. Mech. Engrs., 197C, 53-58. Hirst, W. (1957), in Proceedings of the Conference on Lubrication and Wear, IMechE, London, 674.
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Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, 51-57. Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. Hokkirigawa, K. (1997), Wear maps of ceramics, Bulletin of the Ceramic Society of Japan, 1, 19-24. Holm, R. (1946), Electric Contact, Almquist and Wiksells, Stockholm, Section 40. Johnson, K.L. (1994), Contact mechanics and the wear of metals, Wear, 190, 162-170. Kapoor, A. and Johnson, K.L. (1994), Plastic ratchetting as a mechanism of metallic wear, Proc. R. Soc. A, 445, 367-381. Kayaba, T. and Suzuki, S. (1976), An investigation of surface damages by rolling contact, Technology Report, Tohoku Univ., 41, 1, 21-46. Kayaba, T. and Kato, K. (1981), The adhesive transfer of the slip-tongue and the wedge, ASLE Trans., 24, 2, 164-174. Kayaba, T., Kato, K., and Hokkirigawa, K. (1983), Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 87, 151-161. Khruschov, M.M. (1974), Principles of abrasive wear, Wear, 28, 69-88. Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., 655-659. Kitaoka, S., Tsuji, T., Yamaguchi, Y., and Kashiwagi, K. (1997), Tribochemical wear theory of non-oxide ceramics in high-temperature and high-pressure water, Wear, 205, 40-46. Krause, H. and Scholter, J. (1978), Wear of titanium and titanium alloys under conditions of rolling stress, ASME, J. Lub. Tech., 100, 199-207. Lancaster, J.K. (1978), Trans. Inst. Metal Finish., 56, 4, 145. Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metallurgica, 35, 1, 1-24. Lundberg, G. and Palmgren, A. (1952), Dynamic capacity of roller bearings, Ingenicorsrenten-skapsakademiens, Nr. 210. Quinn, T.F.J. (1967), The effect of hot-spot temperatures on the unlubricated wear of steel, ASLE Trans., 10, 158-168. Quinn, T.F.J. (1987), in Proc. Int. Conf. on Tribology-Friction, Wear and Lubrication, Inst. Mech. Engrs. Conf. Series, 253-259. Rabinowicz, E. (1980), Wear coefficients — metals, Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, 475. Rabinowicz, E. (1983), The wear of hard surfaces by soft abrasive, in Proc. Int. Conf. on Wear of Materials, ASME, 12-18. Sasada, T. (1979), The role of adhesion in wear of materials, Journal of Japan Society of Lubrication Engineering, 24, 11, 700-705. Vingsbo, O. and Hogmark, S. (1980), Wear of steels, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 373. Weibull, W. (1930), A statistical theory of the strength of materials, IVA Handlinger, (Royal Swedish Academy of Engineering Sciences, Proceedings) Nr. 151. Zum Gahr, K.H. (1987), Microstructure and wear of materials, Tribology series, Elsevier, 132-148.
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8 Wear Debris Classification 8.1 8.2 8.3 8.4
Particle Counting • Biological Debris Sampling • Reworked Wear Debris
William A. Glaeser 8.5
Battelle
8.1
Introduction ....................................................................... 301 How Wear Debris Is Generated......................................... 302 Collection of Wear Debris ................................................. 306 Diagnostics with Wear Debris........................................... 308 Conclusions ........................................................................ 312
Introduction
Wear generates debris. The debris comes in a wide variety of sizes and shapes. Wear debris turns motor oil black. You can see it on your hands if you shake hands with your garage mechanic. The black in used oil is like a pigment — it is nanometer-size colloidal metal particles (and carbon) suspended in the oil. If you take an oil filter apart, you will find other types of wear debris. Some are shiny metal particles visible to the naked eye and in the millimeter size category. If you are in the surface mining business, you will find even larger metal particles in the gravel produced by rock crushers. This is metal that is gouged from the metal jaws in the crusher. In a factory grinding room, dust swept up from the floor and examined in a scanning electron microscope will show perfect micron-size metal spheres from rapidly solidifying drops of molten metal generated by the grinding wheel. Examples of these unique debris particles will be found later in this chapter. Wear debris represents loss of geometric accuracy of moving contacting parts. It can also foul orifices and close spaced parts. Although the total material lost as wear debris in a machine is minute compared to the volume and weight of the moving parts, it can signal failure of gears or bearings, and expensive repairs or warranty payments. Because wear debris can be carried in a circulating oil lubrication system, the condition of an engine or a critical machine can be diagnosed by analyzing a sample of the oil. Debris can be removed from the oil by centrifuging or by a magnetic process. The separated debris can then be examined in a microscope to determine morphology, or it can be chemically analyzed. A standard test, the spectrographic oil analysis program (SOAP), has been used for condition monitoring by railroads, truck fleets, and the military for tanks and aircraft. Until the Industrial Revolution and the development of steam and internal combustion engines, wear was taken for granted. When wear of machinery and tools became a problem, the development of wearresistant materials and the study of wear itself increased rapidly. Now we have a large body of information developed from experience and scientific investigation that can be used in the design and maintenance of more reliable and economical machinery.
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How Wear Debris Is Generated
Early wear theory, as related by Bowden and Tabor (1964) and Holm (1946) indicated that real surfaces contact at high spots in the surface microtopography (asperities) and wear was caused by the shearing off of these contacts. The theory was not clear, however, on how the wear particles were separated from contacting asperities. One obvious mechanism is cutting, as in machining. Under abrasive wear conditions, it is presumed that hard particles embedded in one surface will plow through a softer counterface and produce microchips. The debris thus generated looks like the example shown in Figure 8.1. The curled form that the debris particles assume reminds one of chips from machining. In fact this signals a severe type of abrasive wear. The attack angle, hardness, and depth of penetration of abrading particles determine whether cutting-type abrasion will occur as shown by Mulhearn and Samuels (1962). A frequency distribution of attack angles for abrasive particles on SiC bonded abrasive is shown in Figure 8.2. A number of metals are listed in Table 8.1 together with their critical attack angles — or the
FIGURE 8.1 SEM micrograph of cutting-type debris from abrasive wear, M2 tool steel. (From Rigney, D.A. (1992), The role of characterization in understanding debris generation, Tribology Series, 21, Wear Particles: From the Cradle to the Grave, Elsevier. With permission.)
100
Frequency
80 Critical attack angle
60
α 40
20 Cutting points
Noncutting points
0
0
20
40
60
80
100
120
140
160
Attack angle - α
FIGURE 8.2
Diagram showing the effect of cutting angle on hard particle cutting wear.
180
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TABLE 8.1 Material
HV kg/mm2
Critical Attack Angle
Lead α-brass Aluminum Aluminum alloy Copper Nickel 1040 steel, annealed 1082 steel, quenched and tempered Tool steel, quenched and tempered
5 180 35 145 120 350 180–260 860 760
50° to 60° 50° to 60° 80° to 90° ~35° 40° to 50° 60° to 70° 40° to 90° ~30° ~30°
angle above which cutting will occur. Note that the lower the critical angle, the greater the percentage of particles that will cut. Note also that hardened steel is quite susceptible to cutting abrasion. In general, the higher the hardness of the metal, the more susceptible to cutting wear it is. In order for cutting abrasion to take place, the hardness of the abrasive medium must be over 1.2 times that of the material being abraded. Contact load between sliding surfaces does not have to be large for cutting wear to take place. In fact, Zhao and Bhushan (1998) have demonstrated that cutting abrasion can occur with normal loads of 40 to 80 µN using a diamond pyramidal point on single crystal silicon. The debris produced was similar in morphology to metal-cutting debris (curly and stringy). The size of the chips was about 50 nm wide by 200 nm long. Wear debris can also be generated by plastic deformation. Hard asperities, plowing over a softer surface without cutting will produce ridges. Ridges can then be flattened by further contact. Extrusions or lips are formed. These lips are broken off and become flat wear flakes. The process is illustrated in Figure 8.3. Extrusions can also occur at the exit border of a wear scar formed by a curved surface rotating against a flat surface. An example is shown in Figure 8.4. The example in Figure 8.4 is from a block-on-ring test in which a ring rotates against a block. Wear debris can also be generated by material transfer from one surface to another. An asperity plowing through a surface will cold weld to the mating surface and the weld will shear off, leaving some of the asperity stuck to the mating surface. An in situ scanning electron microscope (SEM) wear experiment by Glaeser (1981) demonstrated this process. A SEM photomicrograph shows this in Figure 8.5. You can see the track the asperity made as it penetrated the other surface. Then, suddenly, adhesion occurs and a piece of the asperity breaks off and sticks to the surface as a lump. Figure 8.6 shows the lump after the rubbing surface has passed over it many times. The lump has been squashed and is breaking up into smaller particles. A unique type of wear debris is found in grinding swarf and from electric spark discharge damage to metal surfaces. It is shown in Figure 8.7. Each particle is spherical. A dendritic microstructure is often visible on the sphere surface. The particles are formed from molten droplets caused by frictional heating of the grinding process. They can also be produced by the hot arc developed in electric discharge damage to metal surfaces or from electric arc welding. Spherical debris can be found in oil samples from machinery operating in the vicinity of grinding operations. Rubber produces wear particles by a different process than metals. During abrasion, the rubber is heated by frictional energy, softens, and sticks to the abrading surface. The rubber then stretches and forms abrasion ridges oriented normal to the direction of sliding. An example is shown in Figure 8.8. Debris comes from these ridges in the form of rolled up particles. A familiar example is the debris that a rubber eraser produces. Most of the wear debris formed by the above mechanisms is visible using light microscopy. Submicron debris can be found in SEM analysis of material filtered from used oil. In a series of experiments designed to observe the generation of wear debris under lubricated conditions, a block-on-ring wear tester was used by Glaeser (1983). The block was Cu-3.2 wt% Al alloy and the ring was carburized steel. A drop of
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PLOWING
MICRO CUTTING
EXTRUSION
EXTRUSION
WEDGING
FORWARD EXTRUSION
GOUGING FIGURE 8.3
Ways in which wear debris is formed by plowing action.
FIGURE 8.4
SEM micrograph of stainless steel extrusions.
silicone oil was applied to the ring so that it clung to the bottom of the ring. The configuration is shown in Figure 8.9. The drop was illuminated with a light source and was observed through a microscope. As the ring rotated, oil from the drop circulated through the block contact and back to the drop, carrying any debris generated into the drop. At the beginning of rotation, the oil drop began to fill with metal flakes that sparkled as they tumbled in the drop. Later in the test, the drop became cloudy. At this point, the experiment was terminated and the drop removed for analysis. The large wear debris was removed by centrifuging. The still cloudy oil was then filtered through a Nucleopore polycarbonate filter.
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305
FIGURE 8.5 SEM micrograph of in-SEM wear experiment, showing asperity plowing, adhesion, and shear off. Transfer of iron to copper–nickel alloy.
FIGURE 8.6
SEM micrograph of transfer lump after being run over many times by the mating surface.
The filter was mounted on a carbon grid for an electron microscope and the filter dissolved with a solvent. The remaining material was then examined in a transmission electron microscope and was found to consist of equiaxed nanoparticles embedded in a gel. An example of the debris is shown in an STEM micrograph, Figure 8.10. The size of the round solid particle indicated in Figure 8.10 is about 130 nm. EDX analysis of the particle showed it to be 80% Cu, 1.6% Fe, and 2% Al. The balance was silicon. The
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FIGURE 8.7
Spherical wear debris from grinding swarf.
FIGURE 8.8
Rubber abrasion pattern.
silicone oil had formed a gel with the submicron metal particles. The large bronze flakes that appeared initially were from the wear-in process as the roughness in the bronze surface was removed. Heavy surface flow produced smeared layers. As these layers were subjected to increasing numbers of rubbing cycles, particles broke off and were trapped in the surface. These particles were reduced to very small particles by comminution, as happens in the ball milling process. SEM analysis revealed particle reduction in progress on the aluminum bronze block as shown in Figure 8.11. The submicron particles produced reacted with the oxidizing lubricant to form a gel which clouded the oil drop. This type of wear is often found in boundary-lubricated or very thin film elastohydrodynamic-lubricated contacting surfaces.
8.3
Collection of Wear Debris
In circulating oil systems, the SOAP (spectrographic oil analysis program) process of debris monitoring has proved valuable in certain applications. Instead of extracting the debris from the oil, the whole oil
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FIGURE 8.9
FIGURE 8.10
307
Experimental setup for viewing wear particles in an oil drop in a block-on-ring wear tester.
TEM micrograph of a submicron wear particle embedded in a gel.
sample is subjected to spectrographic analysis. A summary of this type of oil analysis was reported by Lukas and Anderson (1998). Metal content is measured in ppm. The following potential failures can be detected in this way: • • • • • •
Broken piston rings, worn or scuffed cylinder walls, and worn valve guides Worn ball or roller bearings and/or retainers Worn journal bearings Worn spline couplings Worn cams and followers Scored pistons in hydraulic pumps
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FIGURE 8.11
Wear scar of aluminum bronze block showing the process of comminution of wear debris.
This method works well for colloidal suspensions of metals in oil. However, it is not practical for analysis of larger pieces. By examining the shape, surface texture, and chemistry of larger particles, one can obtain supplemental information on failure of mechanical components. Wear debris can be collected by allowing it to fall on a glass slide. The debris can then be fixed to the slide and examined under a microscope. In a circulating oil system, a filter in the line can be used to collect debris. Debris can be washed out of the filter with solvent, or the filter element, if of an organic material, can be dissolved by an appropriate solvent and the remaining metallic debris collected. Ferrography, developed in the 1970s and described by Seifert, Westcott, and Bowen (1972), uses a magnetic field to collect ferromagnetic particles from a fluid. The fluid with suspended metal particles is allowed to flow over a glass slide inclined at a low angle. The glass slide is held to a strong permanent magnet in such a way that a magnetic gradient is developed along the length of the slide. In this way, the particles are separated by size. Ferrous particles separate in strings, with the largest particles at one end. Weak magnetic particles deposit randomly on the slide. A complete issue of the journal Wear (1983) was devoted to ferrography. Centrifuging suspensions of wear debris in oil-solvent solutions will separate metal particles according to mass. The particles will be distributed in layers. Once the centrifuging is complete, the fluid is decanted from the vessel and the wear particles removed by washing out with solvent. The solvent volume can be reduced by evaporation, the wear particles suspended by ultrasound and the remaining fluid poured out on a glass slide. The wear particles will be well dispersed on the slide when the solvent evaporates. If one wishes to separate the particles by mass, the layers can be removed by pipette and deposited on separate slides. Wear tests will often leave wear debris on one of the wear specimens. For instance in a fretting test in which a ball is oscillated against a flat, debris will appear at the edges of the wear scar. The debris can be picked up with a cellulose acetate film dampened with solvent. The film can then be dissolved, leaving the debris free for examination.
8.4
Diagnostics with Wear Debris
As has been noted, wear debris comes in all sizes and shapes. The way in which the debris has been formed can be deduced from size, shape, and surface texture. For instance, cutting wear debris is unique in having a curly and stringy shape. The presence of cutting wear debris in an oil sample signals a severe wear problem needing immediate attention.
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120 110 100 90 80
Iron
ppm
70 60 50 40 30
Chromium
20 10 0
10
20
30
40
50
60
70
80
90
100 110 120
Hours
FIGURE 8.12 Plot of iron and chromium content as a function of hours of engine operation. (From spectrographic analyses of oil samples.)
Use of wear debris as a diagnostic tool for the health of operating machinery is difficult. Recognition of significant morphological characteristics, color, and chemical make up of the variety of particles and elements that turn up in a sample requires experience. The SOAP program has proven effective for truck, tank, and railroad diesels, hydraulic systems, gear boxes, and compressors. The diagnosis is based on the history of concentration of specific elements found in oil samples. The particles involved are under 10 µm in size and more likely to be of submicron size. They are detected by spectrographic methods which give quantitative results, usually in ppm. The quantitative results are plotted as a function of running hours. An example of such a plot is shown in Figure 8.12. The trends for several metals are compared with the original oil sample taken at hour one. By experience, these trends (for instance, sudden continuing increase in iron content) can be related to pending wear failures of certain components.
8.4.1 Particle Counting Particles from a given sample of oil separated by ferrograph or other methods can be classified as to size and a size-frequency distribution plot made. Assuming that the larger particles are related to severe wear, significant increases in their content compared with the running-in plot should signal shut down and maintenance. A sample plot from a review by Lockwood and Dally (1992) is shown in Figure 8.13. It shows the change in size distribution as running hours accumulate. The shape, thickness, and chemistry of a wear particle can tell much about how it was formed. Individual particles can be examined by SEM. An atlas of particle types has been assembled by Anderson (1982) and contains a wide variety of wear particles collect by ferrography. Micrographs, some in color, are presented together with the conditions that produced the wear particles. A page from the atlas is shown in Figure 8.14. The figure shows the way in which the particles line up in strings in the ferrographs. Individual particles can be seen in SEM micrographs in Figures 8.15 and 8.16. Some of the more easily recognized characteristics of wear particles include: • Wear-in conditions. Flat, fairly smooth particles about 10 µm or smaller formed from broken off lips and extrusions produced by machining. • Cutting. Curled strings and crumpled flakes resulting from abrasive wear process. • Deformation. Flat flakes with parallel striations from breakout of deformed surface material caused by heavy sliding contact.
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m
e
Catastrophic failure Advanced failure mode Onset of severe wear mode Benign wear
Ti
Wear particle concentration. particles/10 mL
Modern Tribology Handbook
0.1
FIGURE 8.13
1
10 100 103 Wear particle size, µm
Plot of wear particle size distribution from oil analysis.
• Contact fatigue. Chunk-like particles 50 µm in size resulting from contact fatigue spalls. Some investigators, including Douglas Scott (1983) found spherical debris 1 to 5 µm in size having the same composition as the steel of ball bearings in engine oil and attributed them to contact fatigue. One must be careful in drawing conclusions from spherical debris. It has been found in hydraulic systems and engines having no rolling contact bearing in the oil stream. J.E. Davies (1986) found spherical particles in diesel engine oil. A dendritic pattern was shown on the particle surfaces as shown in Figure 8.7. These were solidified liquid drops. The spherisurface features and their composition should be determined to diagnose their source. • Babbitt fatigue. Silver-colored flakes of babbitt analyzing for tin or lead (by EDS). • Fretting. For iron base materials, orange powder with particle size on the order of 100 nm and containing alpha Fe2O3 (hematite). Under heavy load, surface features can be produced that are peculiar to the surface morphology. For instance, Sarkar (1983) noted that the surface of an Al–Si alloy pin which had been run against a hardened disk had developed “inclined shear plates” on the surface. A particle, extracted from the wear debris showed the same morphology. Therefore, it was recognized as a piece of the pin surface broken out during heavy sliding contact. The pin and particle are shown in Figure 8.15. Ferrographs will also collect nonmagnetic and nonmetallic particles. They will tend to precipitate out of the fluid as it moves over the glass slide. The same analysis can be performed on wear particles separated from oil by other means (filters, centrifuging). Organic materials can be detected by viewing the slide with transmitted light. Polarized light will show up crystalline minerals.
8.4.2 Biological Debris Sampling Human joints are similar to lubricated mechanical components. The hip joint is a ball-in-socket configuration with cartilage sliding against cartilage, lubricated with a slippery lubricant called synovial fluid. As these joints age, the cartilage is worn away until exposed bone slides on bone. This causes irritation of the joint and inflammation and pain. In the last 25 to 30 years, worn joints have been replaced with artificial components. One part of the joint prosthesis is made of a tough plastic compatible with body tissue (ultra-high-molecular weight polyethylene). The other component is a metal alloy (titanium alloy or cobalt base alloy). The combination operates with relatively low friction but is subject to wear. Both the original human joint or the prosthesis can be tested for wear by using the ferrographic method as shown by Mills and Hunter (1983). An example of extracted cartilage particles is shown in Figure 8.16.
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Wear Debris Classification
FIGURE 8.14
Opt. M
225X
100µm
Opt. M
450X
50µm
Opt. M
1000X
20µm
S.E.M.
1000X
20µm
S.E.M. 2500X
10µm
S.E.M.
2500X
10µm
Opt. M
50µm
Opt. M
1000X
20µm
450X
Page from Wear Particle Atlas.
In biological joints, samples of synovial fluid were extracted and treated with a magnetizing solution by Evans and Bowen (1980). The particles recovered by ferrography can be identified by stains or X-ray analysis. Examination of tissues around failed total hip replacements for UHMWPE wear debris requires a special process described by Campbell, Ma, Yeom et al. (1995). Tissue samples were processed and the polymer wear debris extracted and deposited on Nucleopore polycarbonate filters. The filter plates
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FIGURE 8.15 features.
SEM micrographs of a wear scar and a wear debris particle showing the same surface roughness
FIGURE 8.16
SEM micrograph of cartilage particles extracted from a human joint and separated by ferrography.
containing the wear debris were sputter coated with gold palladium and examined in an SEM. A typical SEM micrograph of the debris is shown in Figure 8.17.
8.4.3 Reworked Wear Debris It must be assumed that debris collected from a wear process is as it was when separated from a surface if one is to deduce how it was generated. This often is not the case. Wear debris can go through a contact zone many times and in the process be altered in size and shape. This is true in roller bearings, reciprocating flat-on-flat sliders, splines, gear couplings, and wet clutches. Ductile metals can be mashed out into extremely thin flakes — thin enough to transmit electrons. When these submicron particles are examined in a transmitting electron microscope (TEM), they appear transparent. An example is shown in Figure 8.18. In experiments to produce this type of particle, iron powders were ball milled under lubricated conditions by Glaeser (1991) and similar submicron flakes produced as shown in Figure 8.19.
8.5
Conclusions
Wear debris comes in many sizes and shapes. Study of wear debris morphology and chemistry can provide clues to the condition of various lubricated parts in a machine and the wear mechanisms extant — all
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FIGURE 8.17
SEM micrograph of UHMWPE wear debris from a human joint prosthesis.
FIGURE 8.18
TEM micrograph of a very thin submicron wear flake.
313
this without tearing an engine down. By monitoring the amounts of given metals in a circulating oil system as a function of running time, one can detect the onset of a mechanical part (bearing, gear, piston ring, or seal) failure. This program (SOAP) has been successfully used for a number of years for condition monitoring of engines. Individual wear particles can provide clues to the wear mechanism that produced them. For instance, a sudden increase in bronze particles from an engine with bronze bearings may be the result of ingestion of abrasive contaminants. Just monitoring the increase in copper in the oil would not indicate the change in wear mode. Bronze particle size and shape would suggest this. Failure analyses can be enhanced by the examination of wear particle size and shape.
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FIGURE 8.19 TEM micrograph of an iron particle subjected to ball milling to simulate wear debris subject to repeated passage through a rolling contract.
Researchers can use wear particle analysis as a tool to follow the wear process as it changes with changes in operating conditions (bearing load, change in environment, increased sliding velocity). Classification of wear debris according to size, thickness, shape, color, and chemistry and relating debris types to wear mechanisms or failure of mechanical components has been the goal of debris atlases. However, care must be exercised in using this information since the character of wear debris is often influenced by factors other than wear mode or parts failure. Diagnostics with wear debris requires experience in interpreting and recognizing significant characteristics.
References Anderson, D.P. (1982), Wear Particle Atlas, NAEC Report 92-163, Lakehurst, NJ. Bowden, F.P. and Tabor, D. (1964), The friction and lubrication of solids, Part 1 (1950) and Part II, Oxford Press, London. Bowen, E.R., Scott, D., Seifert, W.W., and Westcott, V.C. (1964), Ferrography, Tribology International, 9(3), 109-115. Campbell, P, Ma, S., Yeom, B., McKellop, H., Schmalzried, T.P., and Amstuz, H.C. (1995), Isolation of predominantly submicron sized UHMWPE particles from periprosthetic tissue, J. Biomed Material Res., 29, 127-131. Davies, J.E. (1986), Spherical debris in engine oil, Wear, 107-189. Evans, C.H., Bowen, E.R. et al. (1980), Synovial fluid analysis by ferrography, J. Biochem. Biophys. Meth., 2, 11-18. Glaeser, W.A. (1981), Wear experiments in the scanning electron microscope, Wear, 73, 371-386. Glaeser, W.A. (1983), The nature of wear debris generated during lubricated wear, ASLE Transactions, 26, 517-522. Glaeser, W.A. (1991), Ball mill simulation of wear debris attrition, Proceedings, 18th Leeds–Lyon Symposium on Tribology, Tribology Series 21, Elsevier, 515-521. Holm, R. (1946), Electric Contacts, Almquist and Wicksells, Uppsala, Sweden. International Conference on Advances in Ferrography (1983), Wear, 90, 1-181. Lockwood, F.F. and Dally (1992), Lubricant Analysis, 18th edition, Metals Handbook, Tribology, ASM, 19, 300-312. Lukas, M. and Anderson, D.P. (1998), Laboratory used oil analysis methods, Lubrication Engineering, STLE, 31-35.
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Mills, G.H. and Hunter, J.A. (1983), A preliminary use of ferrography in the study of arthritic diseases, Wear, 90, 107-111. Mulhearn, T.O. and Samuels, L.E. (1962), Abrasion of metals, Wear, 5, 478-498. Rigney, D.A. (1992), The role of characterization in understanding debris generation, Tribology Series 21, Wear Particles: From the Cradle to the Grave, Elsevier, 405-412. Sarkar, A., D. (1983), The role of wear debris in the study of wear, Wear, 90, 39-47. Scott, D. (1983), The application of ferrography to the condition monitoring of gas turbines, Wear, 90, 21-29. Seifert, W.W. and Westcott, V.C. (1972), A method for the study of wear particles in lubricating oil, Wear, 21, 22-42. Zhao, X. and Bhushan, B. (1998), Material removal mechanisms of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78.
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9 Wear Maps 9.1 9.2 9.3
Introduction ....................................................................... 317 Fundamental Wear Mechanisms of Materials.................. 318 Wear Prediction.................................................................. 319
9.4 9.5
Wear Mapping .................................................................... 320 Wear Maps as a Classification System .............................. 322
9.6
Wear Map Construction for Ceramics ............................. 324
Simulation Model and Materials Selection
Parameters and Forms Used in Wear Maps Experimental Procedures and Materials • Ceramic Wear Maps
9.7
Comparison of Materials................................................... 328 Dry Sliding Conditions • Paraffin Oil-Lubricated Conditions • Water-Lubricated Conditions • Wear Transition Diagrams • Implications and Use of the Maps
9.8 National Institute of Standards and Technology
Ming C. Shen SULZERMEDICA
Modeling Wear by Using Wear Maps ............................... 341 Metals • Ceramics • Modeling Approaches • Correlation of Data According to Wear Maps • Materials Normalization • Summary
Stephen M. Hsu 9.9
Advantages and Limitations of Current Wear Map Approach............................................................................. 354 Future Wear Maps Research Needs
9.1 Introduction Wear is not an intrinsic material property. Wear is a complex function of the system which includes material properties, operating conditions (load, speed), contact geometry, surface roughness, and environment (lubrication, temperature). Therefore, for a given pair of material combination, wear can vary over several orders of magnitude depending on the conditions. This makes evaluation of materials in terms of wear resistance difficult. Common practice is to conduct simulation wear tests to rank materials under the same operating conditions. If the relationship between wear and the operating conditions (load and speed) are linear, relative ranking of materials will hold. Under the influence of chemistry or environment, unfortunately, wear transitions often occur and the relationship between wear and the operating conditions is often not linear. The relative ranking of materials, therefore, will change when the operating conditions are changed. At the same time, material variations abound. Small changes in the alloying elements and processing conditions change the wear characteristics. So even though the material designation is the same, there is no assurance that the chemical composition and microstructure are identical. Because of these factors, literature reports on material wear characteristics have wide ranges, as shown for ceramics in Table 9.1. For metals, similar ranges are observed for data from all sources. The metal wear data in Table 9.1 show the effect of lubricants on different metals on a single wear tester in a laboratory (Fein, 1975). This makes selection of materials for wear applications difficult.
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317
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TABLE 9.1
Wear Data from the Literature Al2O3
Ceramics
Si3N4
SiC
PSZ
AVG
Range
AVG
Range
AVG
Range
AVG
Range
Fracture toughness, MPa·m Hardness, GPa Elastic modulus, GPa Density (g/cm3) Wear coefficient (K = HW/FDa) Dry air Humid/H2O Lubricant
4 16 370 3.9
2–6 11–12 340–410 3.8–3.9
4.4 16.3 313 3.2
1.4–6 13–17 290–333 3.1–3.4
2.9 25 397 3.0
1.5–4 13–34 390–402 2.8–3.2
8 12 206.0 5.9
5–15 10–14 196–216 5.7–6.0
10–5 10–7 10–3
10–9–10–3 10–7–10–6 10–7–10–2
10–4 10–5 10–6
10–5–10–4 10–9–10–4 —
10–3 10–5 10–6
10–6–10–2 — —
10–4 10–6 10–7
10–7–10–4 — 10–8–10–6
Wear Surface
Opposing Surface
Atmosphere
Lubricant
Wear Coeff.
52100 steel 52100 steel 52100 steel 52100 steel 52100 steel Mild steel Carburized steel Carburized steel
Dry air Air Air Air Air Air Air Air
None None Paraffinic oil Paraffinic oil/TCP Engine oil None Gear oil Gear lubricant
1.0 × 10–3 1.0 × 10–3 3.2 × 10–7 3.3 × 10–9 <2.0 × 10–10 2.3 × 10–3 1.6 × 10–9 2.5 × 10–8
0.5
52100 steel 52100 steel 52100 steel 52100 steel 52100 steel Mild steel Carburized steel Aluminum bronze a
K = wear coefficient, H = hardness, W = wear volume, F = load, D = distance slid.
Current typical industrial practice is to make actual components and put them in actual field trials over a period of time. This way, there can be no dispute with respect to the effectiveness of the materials or material treatment. However, cost and duration make such practice prohibitive, and a very low percentage of new materials are tested. A better way to select and design materials for wear resistance is needed. This chapter discusses the use of the wear map concept to help resolve some of these issues and provide a means to systematically compare and select materials on a common basis. While the discussion will focus on materials in general, the predominant data available are in the area of ceramics. So ceramic wear maps will be used to illustrate the basic concept and applications of wear maps. The applicability of the concept, however, should not be restricted to ceramics.
9.2
Fundamental Wear Mechanisms of Materials
Before we discuss the concept of wear maps as an effective way to understand the various aspects of wear, we need to understand the fundamental wear mechanisms of materials in general. A large number of wear mechanisms has been identified in the literature. For metals, they include deformation, adhesion, abrasion, delamination, fatigue, fracture, corrosion, stress corrosion, and oxidative wear. For brittle solids such as ceramics, they are fracture, abrasion, tribochemical wear, grain pullout, intergranular fracture, and corrosion. Broadly speaking, these can be classified into physical and chemical processes and their interplay. In most cases, several wear mechanisms occur simultaneously, and it is difficult to ascertain specific proportional contributions to wear from different mechanisms. Ying (1996) conducted a series of two-ball collision experiments designed to understand the fundamental relationship between friction, materials deformation, and wear at the single asperity contact basis. The results are summarized in Figures 9.1 and 9.2. For metals, wear is controlled by the accumulation of the shear strain underneath the contact, lubrication tends to redistribute the stress over a much larger area, therefore delaying the onset of wear. For ceramics, wear is controlled by the stress intensity which induces crack propagation. These observations, while useful, are based on single asperity contact experiments. In real contacts, there are multiple asperities and the situation is considerably more complex. Contact asperity temperatures and wear debris interactions to form transfer layers all influence wear. Tribochemical reaction products will exert great influence on friction and wear of materials.
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FIGURE 9.1
Wear mechanisms of metals.
FIGURE 9.2
Wear mechanisms of ceramics.
9.3
Wear Prediction
Modeling of wear in metals has been conducted by many researchers (see Ling and Pan, 1988, and Ludema and Bayer, 1991, for some approaches). Over the years, many models have been proposed for different materials and applications. Unfortunately, most models are correlational in nature and therefore system
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specific: they only work for the particular materials pair, contact geometry, operating condition range, and the particular environment and lubricant. The inability of the models to transcend these restrictions results in a divergent collection of parameters and constants. This situation can be illustrated using erosion as an example, which has been summarized by Ludema (Meng and Ludema, 1995). A total of 32 parameters was found to have been used by various authors to describe their erosion data. There is a lack of consensus on the critical parameters that can describe a phenomenon such as erosion. Such confusion also exists for most other wear phenomena, e.g., abrasion (Rabinowicz, 1965; Hokkirigawa and Kato, 1989; Larsen-Basse, 1991; Komvopoulos et al., 1986). As a result, given the material properties and contact information, there is no model currently available that can predict wear a priori.
9.3.1 Simulation Model and Materials Selection Bayer (1991) discusses at length the essential elements for design-oriented model building and testing. The key is simulation — for all critical aspects of the application environment. The range of applicability of any model must be defined. The ruggedness of the model (does it behave properly when parameters are expanded somewhat out of the usual ranges) needs to be tested. Most important, the overall approach must be system-oriented, not merely focused on materials, or lubricants, or mechanics. Other discussions of this approach can be found in the literature. Godet (1988) has identified the essential elements of simulation wear testing. He includes the need to measure the stiffness and damping characteristics of the test system as well as its wear behavior, all under a controlled mechanical environment. The aim is to ensure that the operating environment is adequately represented in the model and its validation. In the summary of a workshop on this subject (Ling and Pan, 1988), it was noted that design-oriented modeling also requires knowledge and identification of failure mechanisms, possibly in the form of maps that relate failure boundaries to operating parameters.
9.4
Wear Mapping
Measuring and understanding the wear of a material are complex and difficult tasks. There is a general recognition that wear of a material depends on load, speed, temperature, time, contact geometry, surface roughness, oxygen availability, lubricant chemistry, and material surface compositions. The dependence on such a large number of variables has been a significant barrier in achieving a comprehensive representation of wear. Furthermore, for advanced materials such as ceramics, the variations in materials themselves make comparisons of wear test results of the “same” material unusually difficult. Therefore, there is a strong need for a methodology to define and measure wear of a material in definitive terms. Wear mechanism studies and wear modeling efforts also suffer from this lack of definition. To minimize these effects, wear studies are often done under a single set of conditions as a function of time. However, mechanistic interpretations and models proposed on the basis of such data have limited significance. The dominant wear mechanism in one operating region may not be the dominant mechanism in another. While this difficulty is recognized by many, proposed solutions are few. Lim and Ashby (1987) have demonstrated the use of a wear map to correlate the massive literature data on wear of steels. Their wear map is shown in Figure 9.3. Normalized parameters based on an assumed dominant variable were used to construct the map. The asperity temperature at the contact is assumed to dominate the dry sliding of steels on pin-on-disk wear testers. Wear regions based on the asperity temperatures they calculated are developed. Based on the temperature, various dominant wear mechanisms and models are developed. These wear regions, however, describe fairly severe wear levels. In engineering applications, acceptable wear levels are orders of magnitude lower. Beerbower proposed a conceptual wear mechanism diagram for steel under lubricated conditions as a function of the specific oil film thickness as shown in Figure 9.4 (Beerbower, 1972). While the various mechanisms were reported in the literature, the diagram was constructed based on inferences and isolated data. However, it illustrates the complex nature of lubricated wear of steel.
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FIGURE 9.3 Wear map for steel under dry sliding conditions. (From Lim, S.C. and Ashby, M.F. (1987), Wearmechanism maps, Acta Metall., 35(1):1-15. With permission.)
FIGURE 9.4 Wear map for steel under lubricated conditions. (From Beerbower, A. (1972), Boundary Lubrication, U.S. Army, Office of the Chief of Research and Development, Contract No. DAHC19-69-C-0033.)
deGee (1989) proposed a simpler system on steel under well-lubricated conditions based on a large body of data generated under a set of standardized conditions. He referred to his maps as transition diagrams. He pointed out that as the severity of the wear test increases, as reflected by speed and load,
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the wear of steel under well-lubricated conditions progresses from no wear to mild wear, and then to scuffing. Similar to Lim and Ashby’s work, deGee found the concept of flash temperature useful in explaining the wear behavior. These studies illustrate the complexity of examining wear in a comprehensive and systematic manner.
9.5
Wear Maps as a Classification System
The concept of wear maps can be used to classify wear based on the recognition that there are many variables involved. The dependent variable is wear. The independent variables can be divided into two types: continuous variables (speed, load, temperature, and time) and discrete variables (dry, nonreactive lubricant, reactive lubricant, environment, and contaminants). For a given material pair and a fixed discrete variable, there are five three-dimensional wear maps that can be used to describe wear systematically: wear vs. speed and load; wear vs. speed and temperature; wear vs. speed and time; wear vs. load and temperature; and wear vs. load and time. Therefore, for a given material pair, a set of 20 wear maps will systematically define the wear behavior. These maps include: five wear maps under dry sliding conditions; five wear maps under nonreactive fluid (to avoid chemical reactions but to remove the heat at the interface so that the true wear behavior can be observed); five wear maps under reactive lubricant conditions (formation of chemical films similar to industrial applications); five wear maps under the same environment and contaminants conditions (e.g., engine blowby gases, soot particles, and oxygen starvation conditions as in a typical diesel engine ring wear simulation). In many instances, a complete set of wear maps is not needed in order to define the wear behavior but a selected set of maps will serve to define the critical limits and operational boundaries for the materials pair in terms of acceptable wear behavior within those ranges. Within each discrete parameter, the wear characteristics of the material pair will exhibit wear transitions, tribochemical reactions, oxide formation, plastic deformation, and fracture. The location of the speed and load (contact pressure, asperity temperature profile, surface roughness evolution) at which such phenomena occur will differ as the discrete parameter changes from one to the other. Some phenomena will occur in one set of environments but will not occur in another set of environments. These variations of wear behavior actually take place in many experiments; some are controlled and some occur accidentally. While these explain the wide variation in wear results and mechanisms reported in the literature, the resulting confusion about the definitive wear behavior inhibits theoretical development in effective wear modeling. When the wear behavior for a material pair is fully defined by these maps, it will become obvious that a single wear model will not be sufficient to describe or predict wear behavior for a material pair in general. Separate models will be required to describe the wear behavior under different operating conditions and environments.
9.5.1 Parameters and Forms Used in Wear Maps Lim and Ashby (1987) proposed using normalized parameters such as the following to describe wear results:
˜ = W′ W An F˜ =
F An H 0
Vr V˜ = o a where W ′ = wear volume per unit distance slid, An = apparent contact area, ro = radius of the apparent contact area, F = normal force, H0 = room temperature hardness, V = sliding velocity, and a = thermal diffusivity.
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In their work on metals, Lim and Ashby suggested that these parameters were able to correlate data from different sources, using specimens of different shapes and sizes. W can be considered as a dimensionless wear coefficient; F is the nominal pressure divided by the surface hardness; V is the sliding velocity divided by the velocity of heat flow. Rabinowicz (1965) defined an alternative wear coefficient, k, in the following form:
k=
WH o FD
where W = wear volume, F = normal force, D = distance slid, and H0 = room temperature hardness. Thus, k could also be expressed as:
˜ W k= ˜ F Rabinowicz suggested that “wear coefficient represents the probability that, during the contact of the two surfaces at an asperity, a sizeable wear particle is produced.” While these parameters have some intrinsic advantages in representing wear, they also carry with them some hidden assumptions about the wear behavior and also assume other parameters are not critical (such as grain size and microstructure in ceramics). What parameter to use in plotting the wear maps and the form of representation are important considerations in constructing wear maps. To understand this, one needs to examine the actual wear processes in a wear test as a function of time. Figure 9.5 shows typical relationships among wear volume, contact pressure, and the normal force. The pressures include the Hertzian pressure for ideal elastic contacting surfaces and the mean contact pressure calculated as the applied normal force divided by the actual wear scar area measured at the end of each wear step. Neither of these common measures of contact stress in a wear junction accounts for the microscopic morphology. Both measures assume conforming surfaces. Thus, the wear transition that occurred at 180 N normal force in Figure 9.5 is not reflected by the Hertzian pressure at all, and is seen as a sudden decrease in the mean pressure. In contrast, some results (Hisakado, 1986) seem to suggest that as the machine load is increased, the real contact area for ceramic-on-ceramic increases only fractionally, and hence the actual pressures at the tip of the microscopic asperities increase rapidly. This situation is quite different from ductile metals. For metals, surface conformity can be very high under certain speed and load regions, approaching 70 to 80% of the theoretical nominal contact area, and hence mean pressure may be a reasonable measure of the stress at the contact. For ceramics, the conformity typically is about 10 to 15%, and the resulting mean contact
FIGURE 9.5 alumina.
Relationship among wear volume, measures of pressure and normal force illustrated with data on
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pressure, therefore, is not a good representation of the relevant contact stress. Consequently, it is preferable to use the normal force divided by the initial contact area to represent the load without any assumption about the microscopic contact morphology. Wear volume, W, may be less susceptible to misinterpretation than other measures. Normalized measures of sliding speed have a similar difficulty in practice. The relevant thermal diffusivity is the value at the elevated contact temperature for which estimates are difficult to make. Again, it may be preferable to use linear velocity to represent the sliding speed.
9.6
Wear Map Construction for Ceramics
9.6.1 Experimental Procedures and Materials Wear data from a single laboratory are selected to illustrate the wear map concepts. Four ceramic materials are used to create a self-consistent database to construct the maps. The materials are selected for their representative behavior within each material class. In ceramics, given a generic name and chemical composition such as silicon nitride, there are numerous variations in mechanical properties, microstructures, sintering aids, and surface properties. Tribologically, they may behave very differently for a given set of operating conditions and environments. Yet there are some general patterns of characteristics associated with each class of material. This chapter focuses on these general patterns, but we caution the reader that each ceramic material should be treated as a unique sample. The material properties and the mechanical properties of the ceramics studied are listed in Table 9.2. The alumina used is a sintered α-alumina with a density close to the theoretical density. The grains are equiaxed and the average grain size is about 5 µm with the range from 2 to 15 µm. The zirconia ceramic used is a pressureless-sintered polycrystalline zirconia doped with 4.7 weight percent yttria. The as-received material is 100% tetragonal. The grain size is about 1 µm in diameter. The density is 99% of theoretical, resulting in porosity of about 1%. The silicon nitride used is a hot-isostatically-pressed silicon nitride. The material is a mixture of α-Si3N4 and β-Si3N4. The α-phase is primarily in equiaxial grains of size ≈0.5 µm, while the β-phase forms elongated grains, up to 1 µm in diameter and 2 to 5 µm in length. Examination of the fractured surface by energy dispersive X-ray analysis indicates that trace amounts of magnesium, iron, and tungsten are present.
TABLE 9.2
Material Properties of the Ceramics in Wear Map Studies
Description Process Sintering aid/Impurities Density, g/cm3 Phase Average grain size, m Elastic modulus, GPa Poisson’s ratio Hardness, GPa (20°C) (500°C) (1000°C) Fracture toughness, MPa.m1/2 Compressive strength, GPa Specific heat, J/g°C Thermal conductivity, W/m°C Thermal expansion, 1/°C
Al2O3 Sintered — 3.9 2–15 372 0.22 16 ± 0.8 8 ± 0.4 4 ± 0.2 4.5 2.6 0.88 35.6 7.1 × 10-6
Y-TZP Sintered Al2O3, Y2O3 6.05 t-ZrO2 ~1.0 220 0.28 13 ± 0.7 4 ± 0.2 3 ± 0.2 8.5 1.9 0.4 1.8 10 × 10-6
SiC
Si3N4 a
Sintered and post-HIP Al > 3.17
HIP Mg, Fe, Al, W 3.25
3–8 430 0.16 31 ± 1.6 18 ± 0.9 10 ± 0.5 3.2 2.5 0.95 110 4.1 × 10-6
0.3–2 310 0.28 24 ± 1.2 17 ± 0.9 13 ± 0.7 5.4 3.0 0.65 33.0 3.5 × 10-6
(Hardness values are measured by Vicker’s indentation with 1-kg load and a duration of 15 s). a HIP = hot-isostatically-pressed
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The silicon carbide used in this study is a sintered and post-HIPped silicon carbide mixed with equiaxed grains and elongated (rod-shape) grains. Elongated grains are up to 2 µm in diameter and about 10 to 20 µm in length. Wear experiments are conducted on a Four-Ball Wear Tester using a ball-on-three-flats contact geometry. The ball and the flats used are made of the same ceramic material. The diameter of the ball is 12.7 mm. The flats are circular discs of 6.35 mm in diameter with a thickness of 1.59 mm. The final polish is done by using 1-µm diamond paste. Prior to testing, the ball and the flat specimens are cleaned in an ultrasonic bath by using successive solvents of hexane and acetone followed by a detergent wash in water. Afterwards, the specimens are rinsed with deionized water, then blown dry with dry nitrogen. The test procedure used is a step-loading procedure at several fixed sliding speeds. At each sliding speed, the applied load increases in a stepwise manner. For loads lower than 20 N, the load steps follow a sequence of 2 N, 4 N, 8 N, 12 N, and 20 N. Beyond 20 N, the load increment of each step is 20 N. The maximum load is 360 N. The duration of each load step is 5 min. Wear tests sometimes are terminated before 360 N is reached due to extreme wear, such as in the dry sliding case. The sliding speeds are 1.9, 14.4, 38, 190, 380, and 570 mm/s. Additional speeds have also been used in some cases. In lubricated tests, an amount of 1.5 ml fresh lubricant is used in each load step. The worn surfaces are not washed before examination. All tests are conducted at room temperature with the room air at a relative humidity of 50 to 55%. For dry air conditions, dry cylinder air is circulated through the wear tester at a rate of 0.76 L/min. The wear scar diameters on the three flat specimens are measured after each load step. For lubricated cases, purified paraffin oil (PPO, 4 Cst viscosity oil percolated through an activated alumina column prior to wear tests) is used as the nonreactive lubricant for ceramics. (Separate studies had been done to demonstrate that paraffinic oil did not chemically react with ceramics to form chemically active boundary lubricating films.) Water is used as the reactive fluid. Constant condition tests had also been conducted to cross check the step loading procedure. Similar wear results were obtained. For detailed discussion on the test procedures, see Shen and Hsu, 1996. The precision of the wear measurement is generally within ±10%. When the data are plotted in a three-dimensional plot, some data smoothing occurs. The data smoothing tends to reduce the uncertainty and throw out the outliers.
9.6.2 Ceramic Wear Maps Three-dimensional wear maps showing wear as a function of speed and load for alumina, zirconia, silicon carbide, and silicon nitride were constructed. 9.6.2.1 Alumina Figure 9.6 shows the wear maps of alumina under dry air, purified paraffin oil (PPO, nonreactive fluid), and water (reactive fluid)-lubricated conditions. Figure 9.6a shows the alumina wear as a function of speed and load in room temperature and atmosphere conditions (dry air was supplied to the sample holder throughout the test). The map illustrates the simultaneous functional dependence of wear with respect to speed and load. If both speed and load influence wear, the interaction of the speed and load on wear can usually be observed in the surface topographical features such as valleys and plateaus. In this case, it can be seen that this alumina under this set of conditions has very strong load dependence. Wear increases rapidly as load increases at low speed. When the speed reaches about 20 mm/s, the load dependence accelerates and an abrupt sharp increase in wear occurs. This wear transition is probably due to the introduction of additional thermal shock stresses (Shen and Hsu, 1996). The speed dependence is mild under low load but a wear transition occurs due to speed when the load reaches 80 to 90 N. Therefore a low wear region in the shape of a rectangle is defined. There is probably some tribochemical influence in the middle of the speed range as reflected in a “valley.” When PPO was used, basically the speed (thermal shock) effects are minimized (Figure 9.6b); the map shows basically load dependence of wear with some speed influences. When water is used, the effect of speed is much more pronounced than
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(a) Dry air
(b) PPO
FIGURE 9.6
(c) Water
Wear maps of Al2O3 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
in PPO’s case. This is probably due to the tribochemical reactions that occurred between the alumina and water under certain speeds (Gates et al., 1989). 9.6.2.2 Zirconia Specific to zirconia material is the possibility of phase transformation from the tetragonal phase to the monoclinic phase with an accompanying increase in volume. Also, water is known to react with zirconia, causing embrittlement and aging-related fracture (Rühle et al., 1984). The phase transformation could be beneficial to wear if the stresses at the trailing edge of the contact are high enough to cause instantaneous
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FIGURE 9.7
Wear maps of Y-TZP under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
phase transformation, the resulting volume increase will produce a compressive stress on the surface, thus resisting the tensile cracks produced by the contact. However if the phase transformation occurs beneath the surface under hydrostatic pressure, then the volume increase will create an internal stress that is detrimental to wear resistance. The wear maps of zirconia are presented in Figure 9.7. The wear characteristics of Y-TZP under dry sliding conditions are shown in Figure 9.7a. Wear data are not available at the high-speed, high-load corner because the severity of the test conditions caused rapid seizure. A relatively low wear region is bound by 20 N load and 20 mm/s speed. Beyond this region, wear increases rapidly as a function of load and speed. The load dependence is rapid and increases in stepwise fashion. The speed dependence within the experimental conditions appears to approach a steady-state plateau at low loads. Under high loads (~80 N+), the speed effect is very dramatic, resulting in an exponential rise in wear. Under purified
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paraffinic oil (PPO) lubricated conditions (nonreactive fluid), the speed sensitivity is essentially eliminated. This confirms the existence of thermal shock and temperature effects observed in dry sliding conditions. The wear is almost linearly dependent on load. Under water-lubricated conditions (reactive fluid), complex surface topographic features can be seen, suggesting the influence of chemical reactions between water and zirconia producing reaction products that influence friction and wear. At low loads and speeds, the tribochemical reactions protect the surfaces, effectively creating a low wear region that is the lowest among the three conditions. At high loads and high speeds, the presence of water exacerbates the wear rate and it exhibits an exponential rise in wear at both the critical speed and load. At high speeds, rapid wear with increasing sliding speed for this material has been attributed to accelerated stress corrosion due to frictional heating (Nakayama and Hashimoto, 1991). Formation of Y(OH)3 may also contribute to the overall destabilization of Y-TZP by yttria depletion producing monoclinic nucleus. The individual contributions of stress corrosion and hydroxide formation to wear are, however, difficult to ascertain. Increased speed also introduces additional stress from thermal shock at localized hot spots. Consequently, the rapid increase in wear rate as speed is increased beyond the low-wear region may be due to the combination of thermal shocks and cracking from hydrolysis. 9.6.2.3 Silicon Nitride Figure 9.8 presents the wear maps of silicon nitride under dry air, water, and purified paraffinic oil (PPO)lubricated conditions. The wear behavior of silicon nitride in dry air exhibits both speed and load dependence with a low-wear region in the form of a valley. Wear transitions can be observed on both the speed and load axes when a critical load and a critical speed are reached. At those critical loads and speeds, wear rises exponentially, thus defining an unusable region for tribological applications. When the same material couple is under PPO-lubrication conditions (nonreactive fluid), one can see the effects of speed almost disappear within the range of the test conditions at most of the loads. At high loads, the frictional heating begins to influence the wear. The disappearance of the topographical features by the use of PPO is illustrative of the effects of surface temperatures on the wear of the silicon nitride couple. For the water-lubricated case, again, tribochemical reactions exert a major influence (Mizuhara and Hsu, 1992; Tomizawa and Fischer, 1987). Silicon nitride reacts with water to form Si(OH)4, which under certain speed and load conditions further reacts to form silicic acids and high-molecular-weight products. The hydrides, as demonstrated in Tomizawa and Fischer (1987), could form solid cylinders perpendicular to the direction of sliding. Figure 9.8c shows that the tribochemical reactions are activated by speed, or interfacial temperatures at the asperity tips. There is a load limit beyond which the tribochemical products are not able to protect the surface. 9.6.2.4 Silicon Carbide The wear maps of silicon carbide are presented in Figure 9.9. The wear characteristics are similar to those of silicon nitride. The major difference is that the tribochemical influence is different from those of silicon nitride. This may be reasonable since chemically, the two materials have been observed to exhibit different responses to the same chemistry (Hsu, 1991). Some results (Nakayama and Hashimoto, 1991) suggest that silicon nitride emitted far more electrons, charged particles from wear, than silicon carbides. Although the link between emission intensity and lubrication has not been clearly established, this lends support to the observation that silicon nitride and silicon carbide exhibit different chemical responses to water.
9.7
Comparison of Materials
Once the wear maps have been constructed for the materials, the maps can be used as effective tools to compare materials under the same environmental conditions.
9.7.1 Dry Sliding Conditions Figure 9.10 presents the wear maps of the four ceramics for the dry sliding case. The scale of the wear rate is the same for all four materials, from 10–10 to 10–2 mm3/s. There are low-wear regions in the low-speed,
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(a) Dry air
(b) PPO
FIGURE 9.8
(c) Water
Wear maps of Si3N4 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
low-pressure corners for all four materials. As the severity of the contact increases (an increase in speed and/or pressure), a rapid increase in wear takes place when the conditions approach the transition zones. The locations of the transition zones and the slopes of the increase depend on the individual material. Wear accelerates as conditions become more severe. All four materials show both speed and load dependence and rapid transitions to severe wear. Alumina has a different speed dependence than the other three, probably because of the inadvertent reaction with water in the air. Zirconia shows more dependence on both speed and load than the other three. Therefore for zirconia, overdesign is necessary to protect the component/system. The silicon-based materials are relatively “tougher” in that the sensitivity to speed and/or load changes is less compared with either zirconia or alumina (Hsu et al., 1994). Under dry sliding conditions, material properties such as hardness, thermal conductivity, and density are important in determining wear resistance. Table 9.2 shows that in terms of hardness and thermal
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Wear maps of SiC under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
conductivity, silicon carbide has the highest value and zirconia has the lowest value. In terms of fracture toughness, zirconia has the highest value and silicon carbide has the lowest. This may explain the high sensitivity of zirconia with respect to change in speed and load yet zirconia has some of the lowest wear rates at low-load and low-speed regions. Microstructural features such as grain size (He et al., 1993), grain size distributions (Hsu et al., 1995), and grain shapes (He, 1995; Zutshi et al., 1994) all have significant effects on the wear of ceramics. For the four samples examined in this study, both silicon nitride and silicon carbide have duplex grains (elongated grains mixed with small and medium-size equiaxed grains). This kind of grain design usually has a slightly higher wear rate under low load, but a lower wear rate under high load. Zirconia has the smallest equiaxed grains among the four materials; therefore it has some of the lowest wear rates at the low-speed and low-load region. The equiaxed grain structure, however, once it begins to crack, is difficult to stop, and wear accelerates rapidly (Liu and Hsu, 1996; Wang and Hsu, 1996a). The picture that is emerging is that wear is a function of many parameters even for materials properties and microstructures. There are no simple rules to predict wear behavior.
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(a) Al 2O3
(c) SiC FIGURE 9.10
(b) Y-TZP
(d) Si3N4.
Wear maps under dry sliding conditions.
9.7.2 Paraffin Oil-Lubricated Conditions Figure 9.11 shows the wear maps of the four materials under purified paraffin oil-lubricated conditions. For these four ceramics, the purified paraffin oil itself does not react with the ceramics nor does it contain impurities that will react with the ceramics (Wang and Hsu, 1996b; Deckman et al., 1991; Gates and Hsu, 1991; Deckman et al., 1999). Therefore the effect of the presence of the paraffin oil is to remove the high interfacial temperatures and lower the flash temperatures in the contact. Therefore the most dominant effect should be the moderation of the speed dependence under low or moderate loads. This is indeed the case. Figure 9.11 shows that the addition of paraffin oil clearly removes most of the speed dependence at low loads. For Si-based ceramics, the wear rates at low loads and speeds are much lower now than those of zirconia and alumina. In addition, at high loads and speeds, both alumina and zirconia exhibit rapid transitions to high wear. For alumina, the wear transition is basically load induced with some speed effects beyond the
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(a) Al 2O3
(c) SiC FIGURE 9.11
(b) Y-TZP
(d) Si3N4
Wear maps under paraffin oil-lubricated conditions.
critical speed. This probably reflects the fracture behavior of large grain sized microstructures (Liu and Hsu, 1996; Cho et al., 1992). For zirconia, both speed- and load-induced wear transitions are evident. The duplex microstructure of silicon nitride and carbide avoids the wear transitions (Hsu et al., 1995).
9.7.3 Water-Lubricated Conditions Water is a chemically reactive agent to alumina (Gates et al., 1989), zirconia (Michalske et al., 1986), SiC, and Si3N4 (Mizuhara and Hsu, 1992; Tomizawa and Fischer, 1987) under certain tribological conditions. The wear maps in Figure 9.12 reveal different wear regimes directly contradictory to the wear characteristics observed for the same material under the dry sliding and or the paraffin oil-lubricated cases. This can be illustrated using the silicon nitride case. At low loads, the wear increases with speed up to about 15 mm/s, then the wear decreases as speed increases. Tribochemical reactions producing silicon hydroxides
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FIGURE 9.12
(a) Al 2O3
(b) Y-TZP
(c) SiC
(d) Si 3N4
Wear maps under water-lubricated conditions.
have been observed (Tomizawa and Fischer, 1987). For the four materials, wear increases significantly in terms of the baseline data. This agrees with observations made by others (Sasaki, 1989). Water has been observed to produce very low friction under certain operating conditions but accelerates the wear processes by corrosion and stress corrosion cracking. In the alumina case, the tribochemical reactions change the primarily load induced transition to more of a load- and speed-induced transition compared to the paraffin oil-lubricated case. Different aluminum hydrides can be produced, and they have different “lubrication” characteristics (Gates et al., 1989). Therefore, different wear zones are observed as a function of load and speed. In fact, for all four materials, speed dependence comes back in as in the dry case. This suggests that speed activates the tribochemical reactions, and the reaction products change the wear behavior. In the Si3N4 case, a low-wear zone occurs in the low-load, high-speed regime. In this regime, the wear is accompanied by an extremely low friction coefficient (< 0.04). Silicon hydroxides have been found in this region in the form of slender rollers inside the contact zone. The reaction products are thought to provide some limited hydrodynamic lift to lower friction. However, the reaction in a water environment
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FIGURE 9.13
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Wear transition diagrams of Al2O3 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
seems to be somewhat corrosive because the wear level is noticeably higher than the one in the same regime when paraffin oil is present. In the SiC case, an extremely low coefficient of friction is also measured in the high-speed, low-pressure regime. But the resulting wear does not show any noticeable reduction as in the Si3N4 case. Based on the wear maps shown so far, wear maps of different lubrication environments are clearly required in order to describe fully the complete spectrum of wear characteristics for the same material pair under different environments.
9.7.4 Wear Transition Diagrams Wear transitions can be defined as the sudden increase in wear over a small increment of the operating conditions (speed, load, temperature, time). They usually signify a change in wear mode accompanied by a change in the dominant wear mechanism, e.g., onset of third-body wear induced by the generation of wear particles. Wear transitions have been observed in both metals and ceramics under unlubricated and lubricated conditions. Because the onset of transitions can often lead to rapid wear and eventual catastrophic failures, the transition phenomena have been extensively studied. In ceramics, the transition
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phenomena have been studied by many (He et al., 1993; Liu and Hsu, 1996; Wang and Hsu, 1996a,b; Cho et al., 1992; Wang et al., 1995). The locations of the transition zone with respect to the operating parameters are important to design engineers to safeguard proper material selection and design. Given a set of three-dimensional wear maps, the maps can be sliced at a plane to produce a set of contour maps of different wear rates as a function of speed, load, or any other parameter such as temperature and time under different environmental conditions. From the contour maps, the wear transition zone can be easily identified on the contour map as the lines of constant wear rates bunch together to represent a steep ascend. These boundaries then can be plotted to show where the transitions occur. There may be one or more wear transitions in a given map, usually from mild to severe wear or a transition from severe wear to ultra-severe wear. The locations of these wear transition zones change with different lubricants. Figures 9.13 through 9.15 show the wear transition diagrams of the four ceramics under different lubrication conditions. The effects of lubrication on the locations of the wear transition zones can be clearly seen. In addition, the functional dependence of the wear transition lines on speed and load can also be observed.
FIGURE 9.14
Wear transition diagrams of Y-TZP under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
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FIGURE 9.15
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Wear transition diagrams of Si3N4 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
Figure 9.13 shows such wear transition diagrams for alumina under dry sliding conditions; there is a critical speed and a critical load that will precipitate the transition from mild to ultra-severe wear. For the PPO-lubricated case (Figure 9.14), it is basically a series of critical loads under different speeds. In the presence of water, (Figure 9.15), the transition loads are much lower, and another transition from severe to ultra-severe wear occurs at the high-speed and high-pressure region. The transition behaviors for zirconia under the three lubrication conditions are shown in these figures. The transitions depend on both speed and load due to the low thermal conductivity. Note the location of the mild to severe transition moves from the dry case to PPO’s case. This measures the effects of the PPO on the transition behavior. For silicon nitride and silicon carbide, the behaviors are similar. The effects of PPO are quite dramatic. Water, in terms of wear, moderates the ultra-severe wear transition but does not change the mild to severe wear transition that much for silicon nitride. These figures also compare the transition diagrams of the four materials under the same lubrication condition. The locations of the transition zones as well as the functional dependence provide powerful
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tools to compare different materials for a given application. Transient spikes in an application can be estimated and examined in the transition diagrams to assess the potential of premature failure. The results shown above demonstrate the need to construct wear maps to better describe the wear characteristics of a material under a particular lubrication condition. Without such maps, it will be very difficult to grasp the complicated interactions of operating parameters, lubrication conditions, and materials microstructures and properties. The results also reveal that significant differences are present in the wear characteristics of a material under different lubrication environments.
9.7.5 Implications and Use of the Maps Once the wear maps for a given pair of materials are constructed, they can be used as material selection guides as well as design guides for different engineering applications. The wear maps can be used to construct wear mechanism maps by performing additional experiments in various regions to understand the dominant wear mechanism taking place as defined by the operating conditions, environment, and contact conditions. Given the understanding of the detailed wear mechanisms and their processes, wear models for different regions for the same materials pair may be constructed. Models developed based on a single set of operating conditions and environment clearly have limited applicability. Such models and methods have failed to address the real needs of the engineering community (Meng and Ludema, 1995). Wear maps therefore can give rise to the concept of a set of models for a given materials pair based on operating conditions and environment. 9.7.5.1 Wear Mechanism Maps The availability of the wear transition diagrams provides the opportunity to study the different wear mechanisms in each region for a material under a lubrication environment. The transition diagram defines the minimum number of dominant wear mechanisms operating for a given system. By examining the contour maps (lines of constant wear rate), lines of equal spacing and lack of curvature usually indicate the same dominant wear mechanism. Valleys and plateaus usually suggest some change in the wear mode. In this way, regions with potentially different wear mechanisms can be identified. Critical experiments can then be conducted within those regions to identify the dominant wear mechanism. In this way, wear mechanism maps were constructed (Hsu et al., 1991). The experimental verification process is illustrated below. Based on the wear map and wear transition diagram of Y-TZP under paraffin oil-lubricated conditions, two sets of operating conditions can be chosen to examine the dominant wear mechanism in each region. Figure 9.16 shows two worn surfaces under high pressure but at different speeds, one is in the mild-wear regime and the other one is in the severe-wear regime. The worn surface taken from the mild wear case shows mostly grooves, indicative of microabrasion and asperity scale fracture being the dominant wear mechanisms. Meanwhile, the worn surface taken from the severe-wear regime exhibits evidence of microfracture and brittle fracture. Brittle fracture has become the dominant wear mechanism. The onset of the brittle fracture is caused by intergranular cracks giving rise to wear particles in the interface. A series of separate experiments has been conducted to follow the onset of such transitions for alumina (Cho et al., 1992). These results suggest that significant wear increase as well as change in wear mechanism is associated with this wear transition. In this manner, wear mechanism maps for the four ceramics are constructed and are shown in Figures 9.17 through 9.19. These wear mechanism maps serve as a powerful tool to compare different materials and their wear behaviors as functions of wear mechanisms under the same operating conditions. Materials properties are used to understand the wear behaviors rather than being used to judge the wear behaviors. Figure 9.17 shows the wear mechanisms maps for the four materials under dry sliding conditions. When Figure 9.17 is compared with Figure 9.13, one can see there are zones within each region in which the wear mechanisms are different, but the change in wear mechanisms does not increase wear to the
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50um
100um FIGURE 9.16
SEM micrographs of representative worn surfaces of Y-TZP under paraffin oil-lubricated condition.
extent that wear transitions are formed. In a way, it can be pointed out that within a wear zone, there is a severity issue or a progression of severity until some events occur to trigger the wear transition. Figure 9.18 shows more delineation of the mild wear mechanisms of the materials when a nonreactive lubricant such as PPO is used. The functional dependence of some of these mechanisms is also important. For example, for alumina, in the presence of a lubricant, the transition and severity progressions are almost linearly load dependent. The influence of speed is minimum. For silicon-based ceramics, tribochemical zones are both speed and load dependent with speed having a higher influence. When the fluid is changed to water (Figure 9.19), most of the mechanisms are influenced by both speed and load, and the detailed mechanisms are difficult to determine because of the complexity of reactions taking place between water and the ceramics. This suggests that modeling tribochemical wear will be most difficult because of the lack of detailed mechanistic understanding of the processes. Based on these mechanistic results, effective prediction of wear for a single material pair under different lubrication conditions will require a set of equations classified according to the wear regime and dominant mechanisms. This is similar in concept to Ashby’s map; wear equations are developed based on the different wear mechanisms. So, the first conclusion of wear mapping is that a family of equations is required to predict wear accurately. At the same time, it must be pointed out that it is an issue of precision of prediction. As will be seen later in the wear modeling section in this chapter, for one or two orders of magnitude prediction, all
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FIGURE 9.17
Wear mechanism maps under dry sliding conditions.
four ceramics can be treated as a single material pair under a particular lubricating condition. This is the global model based on fracture mechanics. Of course, the global wear model cannot predict some of the wear mechanisms. 9.7.5.2 Material Design and Selection Guide If we take the wear transition diagrams for different materials, we can superimpose them on a single diagram to compare the locations of the transition lines under different conditions. Figure 9.20 illustrates such diagrams for the four ceramics under dry sliding, PPO, and water-lubricated cases. The stress and the speed of the application can be calculated and examined in light of the transition diagrams. For a given safety margin, material pairs that can safely operate in a specified region can be estimated. Conversely, given the three-dimensional representations of the four materials, for a given contact pressure, these three-dimensional maps can be sliced along the constant contact pressure lines and the four materials’ wear levels superimposed in a single diagram for comparison. Figure 9.21a is such a
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FIGURE 9.18 Wear mechanism maps under paraffin oil-lubricated conditions. (The boundaries are derived from wear contour maps and verified experimentally. Not all zones had been verified.).
diagram for 1 GPa contact pressure under dry sliding conditions. For this contact pressure, alumina has the lowest wear of the four materials. Similarly, the maps can be sliced along a single speed; then the wear rate as a function of load or contact pressure can be examined. Figure 9.21b shows the case for the four ceramics at 10 mm/s linear sliding speed under dry sliding conditions. In this case, alumina will work fine in the low-pressure region; SiC will be more suitable at higher pressures. Figure 9.21c illustrates the speed and contact pressure ranges that are available for use with these four materials under dry sliding conditions given a wear rate of 10–7 mm3/s. Similarly, Figure 9.22 illustrates the case for these four materials under PPO-lubricated conditions. At 2 GPa contact pressure, SiC has the lowest wear (Figure 9.22a). Note the intersections of the constant wear lines among the four materials. Figure 9.22b shows the comparison of materials at a constant speed of 100 mm/s. For a constant wear rate of 10–7 mm3/s, Figure 9.22c shows the safe operating regions for the four materials. These derivative maps illustrate how one can select materials for a particular operating condition under a specific lubricating environment.
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FIGURE 9.19 Wear mechanism maps under water-lubricated conditions. (The boundaries are derived from wear contour maps and verified experimentally. Not all zones had been verified.).
9.8
Modeling Wear by Using Wear Maps
9.8.1 Metals Lim and Ashby (1987) used pin-on-disk (steel on steel) wear data under dry sliding conditions from the literature and constructed a wear mechanism map (Figure 9.14). The map uses normalized load and speed as parameters, and the data are successfully partitioned into different regions. Asperity temperatures are the key underlying parameter for the wear mechanisms, e.g., delamination wear, oxidation wear, melt wear, and seizure. Even though the asperity temperature calculation is based on the asperity scale, the coefficients of friction used are the average values for the macrocontact. Wear equations are developed for each mechanism, and these equations are shown in Table 9.3. As discussed before, this approach is successful for severe wear regimes where high asperity temperatures dominate wear mechanisms. For mild wear and lubricated
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FIGURE 9.20 Material comparison based on mild-to-severe wear transitions under (a) dry air, (b) PPO, and (c) water-lubricated conditions.
cases, asperity temperatures are important parameters but not controlling (boundary lubricating films, tribochemical wear, elastohydrodynamic lubrication, etc.); such an approach is not effective. The asperity level temperatures are also critical in analyzing chemical reactivity and surface film formation (Hsu, 1991). The use of measured “average” friction coefficients to estimate asperity temperatures has been shown to be inadequate (Hsu et al., 1988). When the localized wear event and the accompanying measured asperity friction (based on a two-ball collision experimental set up) was incorporated in a mechanical wear model, the resulting temperature became consistent with those estimated from chemical reactivity analysis (Hsu et al., 1994). This suggests that, for an asperity model, the asperity coefficients of friction are needed. The linkage between asperity events and system parameters such as load, temperatures, and speed, for each lubricating environment, lies in the concept of relative surface “conformity.” The actual surface roughness during wear is an ever-changing parameter. When lubrication remains effective, a steady-state conformity of the two contacting surfaces is usually reached (Wang et al., 1991). From the degree of surface conformity, one could possibly link asperity contact conditions to the measured macrocontact conditions. Wear mapping has pointed to the fact that a family of equations is needed to account for wear for a given materials pair in a given environment. No effective wear models for metals are available for the mild-wear and well-lubricated conditions.
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FIGURE 9.21 Material selection guides by using (a) fixed contact pressure, (b) fixed sliding speed, and (c) wear rate level. (The condition is dry sliding.).
9.8.2 Ceramics 9.8.2.1 Basic Wear Mechanisms The dominant wear mechanisms for different regimes are different. These mechanisms are summarized in Table 9.4. The stress intensity in the contact is a critical parameter that underlies the formation of different wear regimes. In mild wear, the nominal contact produces stress intensity insufficient to cause macroscopic scale fracture. Wear occurs primarily at the asperity scale in the form of abrasion and microfracture. This micro-abrasion will generate subsurface damage/cracking at the micron scale. As the localized stress intensity exceeds K1C of the material, microfracture occurs and generates intergranular cracks. This leads to subsequent grain pullouts. In severe wear, the nominal contact produces stress intensity that exceeds K1C and causes macroscopic fracture such as tensile cracks (Hsu et al., 1994). The edge effect of those tensile cracks represents a source of wear particles (Ying et al., 1997). These particles form third bodies in the contact zone and cause more localized fracture and grain pullouts. The combined
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FIGURE 9.22 Material selection guides by using (a) fixed contact pressure, (b) fixed sliding speed, and (c) wear rate level. (The condition is paraffin oil-lubricated sliding.)
wear particles and pulled-out grains are commonly observed in all four ceramics in the severe wear regime. In the ultra-severe wear regime, intragranular fracture is commonly observed. High loads, high sliding speed, and/or their combination cause the much increased stress intensity beyond K1C. The end results are the presence of large quantities of large wear debris. 9.8.2.2 Theoretical Analysis of Critical Parameters Based on Wear Mechanisms Figure 9.23 shows the schematic of the different contact configurations in different wear regimes. In the mild wear regime, wear is caused primarily by abrasion at the asperity scale. So the wear at the asperity contact can be quantified by the product of wear depth, contact width, and length of this contact within each “sliding cycle,” as illustrated in Figure 9.23a. The sliding cycle can be described by the total distance slid l divided by the Hertzian contact width 2a, i.e., l/2a. Under this set of assumptions, wear can be expressed by the following equation:
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TABLE 9.3
Wear Equations Derived from Wear Mechanism Maps in Lim and Ashby, 1987 F˜ =
Seizure
1
(1 + á ì ) 2
12
t
(
)
T − To 106 1 − b ln ˜ 20 Tm âí
Melt wear
˜ = Tm − To H0 1 áì Fí ˜˜ T *â − 1 W T * L âí˜ Tm To
Mild oxidational wear
2 ˜ = C A oro exp − Q o W Z a c RTf
Severe oxidational wear
˜ =f W m
(
Plasticity-dominated wear
(
L oxa
12
12 F˜ ˜ aHoâ áì í -1 K T ox − T N ox m b
(
áì
)
˜ = 2a˜ of v F˜ W f A*
Definitions of the terms: Ao Arrhenius constant for oxidation C constant used in the model for mild oxidation wear F normalized pressure on sliding surface H0 room temperature hardness of metal Kox thermal conductivity of oxide L latent heat of fusion per unit volume for metal Lox latent heat of fusion per unit volume for oxide N total number of contacting asperities Q0 activation energy for oxidation R molar gas constant T* an equivalent temperature for metal To 300°K Tb bulk temperature Tf flash temperature γ cumulative plastic shear strain µ coefficient of friction
TABLE 9.4
F˜ ˜ í
)( )
˜ K ox Tmox − Tb FN
)
Tm Tmox W Zc a fA* fm fv r0 ν α αt β
melting temperature melting temperature of oxide normalized wear rate critical thickness of oxide film thermal diffusivity of metal critical area fraction of voids volume fraction of molten material during sliding volume fraction of inclusions radius of pin normalized velocity heat distribution coefficient constant in Tabor’s junction growth equation dimensionless parameter for bulk heating
Classification of the Wear Map Data under Dry Sliding Conditions Wear (mm3)
Wear Mechanism
Mild wear (stress intensity < K1C)
10–7–10–4
Severe wear (stress intensity > K1C)
10–5–10–2
Ultra-severe wear (stress intensity K1C)
10–3–101
(Asperity scale failure mode) Abrasion Intergranular cracks Subsurface damage/cracks Grain pullout Tribochemical (Nominal scale failure mode) Fracture mechanics Tensile cracks → edge effects 3rd-bodies (linked to grain pullout) (Nominal scale + few pieces large debris) Thermal shock (nominal scale)
Wear Regime
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FIGURE 9.23 Illustrations of the contacts for modeling wear in different wear regimes. (a) asperity scale abrasion in mild wear regime, (b) tensile cracks inside the nominal contact in severe wear regime, and (c) gross fracture in the nominal contact in ultra-severe wear regime.
WearVol ∝
Pm
∑ H i
v
l ∗ Cidi ∗ di ∗ 2a ∗ 2a
(9.1)
where Pm = mean Hertzian pressure, Hv = hardness, Ci = dimensionless geometric factor, and di = asperity contact width. The terms in the parentheses represent the wear depth, which is assumed to be proportional to the ratio of Pm and hardness and a fraction of the contact width di. The 2a term inside the brackets represents the upper bound of length li of such asperity-scale abrasive wear within a single cycle. Since the ratio of Pm /Hv is constant throughout all the asperity contacts, the summation term will be proportional to the real contact area. In the literature, the real contact area between rough surfaces has been modeled by many (Lee and Cheng, 1992; Greenwood and Williamson, 1966). The results appear to vary due to different assumptions, but the functional dependence of real contact area can be expressed as follows:
Areal ∝
(
)
N ∗ f roughness parameters E′
where N = load and E′ = composite Young’s modulus. The roughness parameters include asperity radius (Greenwood and Williamson, 1966), r.m.s. roughness (Lee and Cheng, 1992; Greenwood and Williamson, 1966), and/or autocorrelation length (Lee and Cheng, 1992). By substituting the real contact area into Equation 9.1, the mild wear can be represented by the following equation:
Wear Vol ∝
(
)
Pm N ∗ ∗ f roughness parameters ∗ l Hv E′
(9.2)
For the data set considered here, the surface roughness of all specimens for the four ceramics is controlled to the same roughness; therefore f can be considered as a constant in this analysis. Hence, the mild wear is directly proportional to Pm∗N∗l, which relates to the operating conditions, and inversely proportional to material properties, Hv and E′.
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In severe wear regime, because of the presence of cracks, edge effects from those cracks, and thirdbody wear particles, the asperity contacts have very different characteristics, as illustrated in Figure 9.23b. The total wear volume may be expressed as follows:
Wear Vol ∝
∑ i
l σ MAX d50 T * ∗ bidi ∗ di ∗ 2a ∗ K1C 2a To
(9.3)
where σMAX = maximum tensile stress (Adachi et al., 1997), T* = interfacial temperature of the nominal contact (Archard, 1958-9), To = ambient temperature at 20°C, K1C = fracture toughness, d50 = mean grain size, bi = geometric factor, di = contact width. Here the wear depth is assumed to be proportional to the contact width di by using the ratio of a stress intensity from tensile stress divided by K1C and another geometric factor bi . The crack length in the measure of the stress intensity is assumed to be equivalent to the mean grain size d50. Because of the potential thermal effects from frictional heating, the tensile stress is further modified by multiplying a temperature ratio of (T*/To). The interfacial temperature T* is calculated by using Archard’s temperature equation (Archard, 1958-9). In so doing, the nominal contact is treated as a single asperity and the interfacial temperature is applicable within a layer thickness of half of the Hertzian contact width, i.e., this temperature exists within a thickness of a. The multiple of the two di inside the bracket appears to represent the real contact area, as in the mild wear case. However, in the severe wear situation, a different interpretation may be needed to account for the edge effects due to cracking and third-body wear. This area is assumed to be proportional to the ratio of N/Hv (Wang and Hsu, 1996a). As a result, Equation 9.3 can then be rewritten as follows:
Wear Vol ∝
σ MAX d50 T * N ∗ ∗l K1C To H V T *
( )
(9.4)
In Equation 9.4, the hardness value is the hardness at the asperity temperature. Equation 9.4 is quite similar to the tensile crack model proposed by Hsu (Wang and Hsu, 1996a). But the temperature effects have been added. Also, the use of fracture toughness eliminates the need for a special material property σD , which is the critical damage stress (Wang and Hsu, 1996a). In the ultra-severe wear regime, one assumes that the thermal shock is attributed to a temperature gradient between the heated interface and cold substrate or a hot spot with its surrounding surface area. Since the interfacial temperature exists in a layer with a thickness of half Hertzian width, the wear equation in Equation 9.4 can be extended by substituting the d50 term with a. Namely, the crack length that determines the stress intensity is equivalent to a, as illustrated in Figure 9.23c. This gives rise to the following:
Wear Vol ∝
σ MAX a T * N ∗ ∗l K1C To H V T *
( )
(9.5)
Apparently, the increased (T*/To) ratio and crack length a and a decrease in Hv(T*) will push wear to much elevated levels, as compared to the severe wear described in Equation 9.4.
9.8.3 Modeling Approaches For brittle materials, wear can be linked to the stress intensity as described previously. One approach will be to examine and correlate wear data according to a severity scale, i.e., as the conditions of contact become more severe, higher wear should result. After the data are lined up according to the contact severity, then the materials will be normalized using material property data. In principle, this normalization process will make different materials appear to be the same. Wear for these materials that experienced similar wear mechanisms will be similar, as if they are a single material.
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9.8.3.1 Severity Index The contact severity can be defined in terms of the operating conditions. Let us examine each of the wear equations derived from simple theoretical analysis. In mild wear, Equation 9.2 contains two sets of factors. The Pm∗N∗l term is directly related to the operating conditions. The Hv∗E′ is just a product of material properties. Similarly, the σMAX∗(T*/To)∗N∗l term in Equation 9.4 and the σMAX∗ a ∗(T*/To)∗N∗l term in Equation 9.5 are directly linked to the operating conditions. Meanwhile, the d 50/(K1C∗Hv(T*)) is the material property term in Equation 9.4 and K1C∗Hv(T*) in Equation 9.5. Up to this point, one can plot the wear data in each wear regime against the corresponding severity parameter and observe data scatter among different materials. If the above equations are valid, the degree of data scatter will measure the deviations from the “ideal.” For a global approach, the severity parameters from the three wear regimes are not the same. In order to employ a unified severity parameter across all three wear regimes, some adjustments are needed. First, the common factor in all three wear regimes is N∗l. The uncommon term in mild wear is Pm, and σMAX∗(T*/To) in severe wear, and σMAX∗ a ∗(T*/To) in ultra-severe wear. However, the Pm and σMAX are related through the friction coefficient (Ying et al., 1997). Moreover, the (T*/To) is relatively close to unity in the mild wear regime for the four ceramics, except for Y-TZP. Therefore, the severity parameter can be generalized to σMAX∗(T*/To)∗N∗l. 9.8.3.2 Materials Normalization Materials are characterized by their material properties such as hardness, elastic modulus, toughness, thermal conductivity, thermal diffusivity, and their temperature dependence. In wear, the issue of material properties at the proper scale is very important. While the bulk material properties influence wear, the local properties at the asperity scale often control the wear process. For example, under mild wear conditions, the macrocontact pressure is less than the K1C; therefore, fracture of the contact due to the macrocontact pressure induced tensile stresses will not take place. The asperity contact pressure, however, may exceed K1C and may cause local, grain level fracture. This fracture behavior is governed by local hardness, local fracture toughness, grain size, the ratio of grain boundary energy release rate to grain energy release rate (He and Hutchinson, 1989), residual thermal stress in the grain boundary from the sintering, and the crack length. If the microstructure is a duplex structure, i.e., elongated grains intermixed with equiaxed grains, crack deflection by the elongated grains has to be taken into account, i.e., the aspect ratio of grain defined by grain length divided by grain diameter. If the detailed wear mechanism in each regime for each material is known, many of these material properties can be considered. Whether there is a set of universal material normalization parameters for the four ceramics or not is open to question. Iteration between the severity index and material normalization parameters will help to define what parameters are important and what parameters can be set aside. The optimized combination of parameters will best describe the wear data.
9.8.4 Correlation of Data According to Wear Maps In the following sections, various severity parameters will be tested with the wear map database, followed by the generalized severity parameter determined above. 9.8.4.1 Historical Severity Indexes There are several versions of the so-called severity index (Adachi et al., 1997; Kim et al., 1986; Kim et al., 1994). They are described below.
Sc =
Po RMAX K1C
.
where Po = maximum Hertzian pressure and RMAX = maximum surface roughness. The Sc is originally derived from modeling stress intensity factor by using the maximum Hertzian pressure and a crack length
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equivalent to the maximum surface roughness (Kim et al., 1986). Subsequently, the severity index has been modified by incorporating stresses introduced by friction, and a slightly different form was derived (Kim et al., 1984), as shown below:
SCF =
Po
(1 + µ )R 2
MAX
K1C
where µ = friction coefficient and the rest of the parameters are the same as in SC. More recently, a new severity index has been derived from using the maximum tensile stress in estimating the threshold stress intensity, Scm (Adachi et al., 1997). The maximum tensile stress is simplified in Scm as shown below:
Scm =
(1 + 10µ)P
o
RMAX
K1C
where (1+10µ)Po is the simplified tensile stress. The maximum surface roughness, RMAX, is the same for all specimens tested in our database. Because it represents the equivalent crack length in the estimate of stress intensity, one can employ an alternative interpretation of this term by using the mean grain size. Figure 9.24 shows the effects of the various severity indexes to correlation plots of the wear map data for the four ceramics under dry sliding conditions. The data for the mean grain size, d50, of the four ceramics are listed in Table 9.5. SC and SCF have similar results. Within each material, different wear levels can be present at the same severity index. Wear is primarily correlated by the maximum Hertzian pressure in SC, and friction coefficient has some contributions in SCF . When all four materials are combined, they form two groups. Alumina and SiC are in one group at a higher severity. Silicon nitride and zirconia are in a lower severity group. These are due to the combination of larger mean grain size and relatively lower fracture toughness in the alumina and SiC. On the other hand, Figure 9.24c shows that the wear data mingle more by using Scm. Because all these severity indexes already contain material properties, no material normalization can be applied. Therefore, one may conclude that these parameters do not correlate with the entire wear database adequately. Figure 9.25 shows the application of a single parameter of mean Hertzian pressure to the database. Again, the results show that it is inadequate to represent a unified severity parameter for this database. 9.8.4.2 New Correlation Parameters Figure 9.26a shows the wear data plotted against σMAX∗(T*/To). This parameter has a range of about three orders of magnitude. As compared to the total range of wear volume of nine orders of magnitude, this parameter is extremely sensitive to the wear level. On the other hand, Figure 9.26b shows the results of using the severity parameter σMAX∗(T*/To)∗N∗l. This parameter has a range of seven orders of magnitude, much more compatible to the wear levels. Also the data in each wear regime appear to form clusters, suggesting the severity parameter has the ability to order the wear process. Inclusion of d 50 and a has also been tested. Only slight change is obtained.
9.8.5 Materials Normalization There are different ways to normalize the wear results for the purpose of direct comparisons. One way is to normalize all materials with respect to a particular material. Another is to determine the average value, and then all materials will be normalized with respect to the average. The latter approach is taken here. Figure 9.27a shows the mild wear data only plotted against the severity parameter. This will be the baseline to begin the material normalization process. Figure 9.27b shows the data being normalized against the average HV and average E′. The average HV for the four materials is 21 ± 8 GPa and the average E′ is 176 ± 44 GPa. Because wear in this regime is inversely proportional to HV and E′ (Equation 9.2),
Correlational results from using historical severity indexes: (a) SC, (b) SCF, and (c) Scm. These indexes were defined in the text.
350
FIGURE 9.24
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TABLE 9.5
Microstructural Parameters of the Four Ceramics
Mean grain size, d50 (µm) Grain size ratio, d90/d50 Aspect ratio, A
FIGURE 9.25
Al2O3
Y-TZP
SiC
Si3N4
5 3 1
1 2 1
3 2.6 5
0.5 2 4
Correlational results from using mean Hertzian contact pressure.
the material normalization is carried out by multiplying the wear volume by the ratios of E′/E′mean and HV/HV,mean. For example, the wear volume data of SiC are multiplied by 1.48 and 1.26, since its hardness and Young’s modulus are both higher than the mean values. Figure 9.27b displays that, after material normalization, the Si-based ceramics are separated from the oxides. Because the functional dependence on the severity parameter is different between these two groups of data, a different wear mechanism is controlling the wear. One possible interpretation is that this may be caused by the presence of tribochemical reactions which are not taken into account in the mechanism-based modeling. Figure 9.27c presents a conventional material normalization scheme using the wear coefficient, defined as wear volume∗HV/(N∗l). The results appear to suggest that it is not adequate for this large database. Figure 9.28 shows the material normalization carried out for data in the severe wear regime. According to Equation 9.4, wear volume is inversely proportional to the product of HV(T*)∗K1C / d 50 . The average fracture toughness for the four materials is 5.4 ± 2.3 MPa.m1/2, and the average d50 is 2.4 ± 2 µm. Figure 9.28b shows that the wear data among the two Si-based ceramics and Y-TZP appear to be more packed, but the alumina data fall farther away from the line. Again, this may be caused by tribochemical reactions with the wear debris generated in this regime. The material normalization used in Evans and Marshall (1980) that correlated the grinding data among different ceramics is also tested, i.e., (K1C0.625∗Hv0.5)(8/9), but only slight shifts are found. Figure 9.29 shows the material normalization carried out for the ultra-severe wear data. The material normalization includes the product of hardness and fracture toughness. The improvement from the material normalization appeared to be slight. The material normalization schemes discussed above show that different degrees of data shifts are obtained for data in the different wear regimes. Clearly, the process of selecting a severity parameter and
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FIGURE 9.26 Correlational results from using (a) maximum tensile stress multiplied by a temperature ratio of T*/T0 to take into account the thermal effects, and (b) a severity parameter derived from the current study.
the material normalization process for that severity parameter will have to be an iterative one. At this time, the overall data scatter after the material normalization is about ±1 order of magnitude.
9.8.6 Summary The large wear database used to construct ceramic wear maps presents a unique opportunity to test correlational wear parameters. The database consists of self-consistent data with wide variations in operating conditions and material properties. This database was used to test the concept of test severity
FIGURE 9.27 Material normalization in the mild wear regime: (a) baseline (no normalization), (b) wear volume normalized by using the product of modified hardness and Young’s modulus, and (c) normalization by using the wear coefficient.
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FIGURE 9.28 Material normalization in the severe wear regime: (a) baseline (no normalization), and (b) wear volume normalized by the product of modified HVK1C / d 50 .
parameters to separate the different wear regimes. The determination of the severity parameters is based on the understanding of the wear mechanisms derived from the wear maps. After the wear data of all four ceramics have been separated by using the severity parameter, material normalization is carried out for the data in the individual wear regimes. Results show that grouping of data among different ceramics can be achieved through using the first sets of severity parameter and material normalization parameters. This is quite promising, in light of the huge variations present in the experimental conditions and materials. Further refinements through iterations will be necessary to improve the result.
9.9
Advantages and Limitations of Current Wear Map Approach
There are two ways to approach a systematic construction of wear maps. One is to capture the key variable and divide the regions based on that parameter. This essentially is the Ashby approach. His wear map is constructed based on the fact that wear is controlled by the asperity temperatures due to sliding. Equations
FIGURE 9.29 Material normalization in the ultra-severe wear regime: (a) baseline (no normalization), (b) wear volume normalized by the product of modified hardness and fracture toughness, and (c) normalization by using wear coefficient.
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can then be developed to describe wear according to the asperity temperature scales such as mild oxidation, severe oxidation, and melt wear. The shortcoming of this approach is that regions not dominated by this parameter lose their importance. The choice of parameters to construct the wear maps reflects the approach taken. The other approach is the one described in this chapter. As can be seen, the wear maps, once constructed, can be very powerful in mechanistic determination and materials selection. The wear maps can also provide a design guideline for contact geometry, lubrication environment, and wear life estimation. There are limitations to this approach as well. First of all, many wear experiments are needed to construct the wear maps. In fact, how much data are “sufficient” for a wear map is a real issue. Using the step-loading test procedures saves a tremendous amount of work, but the test procedure itself has limitations. The steploading takes advantage of the fact that a steady state of wear rate is often achieved for most systems under mild wear conditions. This assumption is true for most lubricated systems but may or may not be true for some high-wear regions. One needs to check the validity of this assumption periodically and perform experiments under constant loading conditions to validate the step-loading results. Long-term time effects such as low-cycle fatigue on wear are difficult to include in the current wear maps. Tribochemical reactions that require an induction time period to be effective are hard to deal with using a step-loading procedure. Many of these phenomena require a long-duration constant machine setting condition to measure properly. The test procedures effective in measuring lubrication (tribochemical effects) are not the same as those procedures useful for measuring materials wear. There are many operating wear mechanisms in a wear test. Sometimes several mechanisms coexist in a region to render relatively mild wear, such as deformation, tribochemical wear, and microabrasion. The individual contributions from these coexisting wear mechanisms are difficult to separate. In order to collect critical data for wear modeling, more consistent, careful experiments are required. In addition, accumulation of wear damages by microfracture and microabrasion mechanisms is potentially a fatigue process. Therefore, time effects on wear will also need to be addressed. Microstructural parameters such as grain size, grain size distribution, grain boundary phase, etc., have noticeable effects on the wear characteristics of polycrystalline ceramics (Hsu et al., 1995). How to account for them is a challenge. Furthermore, there are many possible lubrication chemistries for a single ceramic (Gates and Hsu, 1995a,b, 1997). Each chemistry is unique, so it is difficult to map out all the possible permutations of lubrication chemistries for a given material pair.
9.9.1 Future Wear Maps Research Needs Wear map research was originally developed in an attempt to provide a wear classification system for ceramics as well as to provide a sufficient database for the development of wear models. So far the first goal has been met. The progress in wear model development is ongoing. A single universal parameter to fit all the data has been demonstrated to be unrealistic, but one may ask if such parameter(s) exists in each wear mechanism zone. This question remains unanswered at this time. The current database is limited to a narrow speed and load range because of the need to simultaneously measure wear and lubricant chemistry effects. To extend the speed and load ranges will necessitate the use of several wear testing machines. How this will affect the internal consistency needs to be investigated. In summary, wear mapping represents a new approach to examining the age-old issue of wear and has shown it presents an integrated view of wear that cannot be seen otherwise. Much more work needs to be done to fully develop this approach for practical applications.
References Adachi, K., Kato, K., and Chen, N. (1997), Wear map of ceramics, Wear, 203-204:291. Archard, J.F. (1958-9), The temperature of rubbing surfaces, Wear, 2: 438-446. Bayer, R.G. (1991), Comments on engineering needs and wear models, in Tribological Modeling for Mechanical Designers, ASTM STP 1105, Ludema, K.C. and Bayer, R.G. (Eds.), American Society for Testing and Materials, Philadelphia, 3.
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Beerbower, A. (1972), Boundary Lubrication, U.S. Army, Office of the Chief of Research and Development, Contract No. DAHC19-69-C-0033. Cho, S.J., Moon, H., Hockey, B.J., and Hsu, S.M. (1992), Wear transition mechanism in alumina during sliding, Acta Metall. Mater., 40(1):185-192. Deckman, D.E., Jahanmir, S., and Hsu, S.M. (1991), Wear mechanisms of α-alumina lubricated with a paraffin oil, Wear, 149:155-168. Deckman, D.E., Chen, C.I., and Hsu, S.M. (1999), Effects of selected chemical compounds on the lubrication of silicon carbide, in Tribology Trans., 42, 3, 619-625. deGee, A.W.J. (1989), Wear research for industry — examples of application of the irg transition diagram technique, ASME Wear of Materials, 753-763. Dong, X., Jahanmir, S., and Hsu, S.M. (1991), Tribological characteristics of α-alumina at elevated temperatures, J. Am. Ceram. Soc., 74(5):1036-1044. Dufrane, K.F. (1986), Sliding performance of ceramics for advanced heat engines, in Ceramic Engineering and Science Proceedings, published by Am. Ceram. Soc., 7:1052-1060. Evans, A.G. and Marshall, D.B. (1980), Wear mechanisms in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D. (Ed.), Am. Soc. Metals, Metals Park, OH, 439. Fein, R.S. (1975), AWN — a proposed quantitative measure of wear protection, Lubrication Engineering, 31:581-582. Fischer, T.E., Anderson, M.P., Jahanmir, S., and Salher, R. (1988), Friction and wear of tough and brittle zirconia in nitrogen, air, water, hexadecane, and hexadecane containing stearic acid, Wear, 124:133-142. Gates, R.S., Klaus, E.E., and Hsu, S.M. (1989), Tribochemical mechanism of alumina with water, Tribology Trans., 32(3):357-363. Gates, R.S. and Hsu, S.M. (1991), Effects of selected chemical compounds on the lubrication of silicon nitride, Tribology Trans., 34(3):417-425. Gates, R.S. and Hsu, S.M. (1995a), Silicon nitride boundary lubrication: effects of oxygenates, Tribology Trans., 38(3):607-617. Gates, R.S. and Hsu, S.M. (1995b), Silicon nitride boundary lubrication: lubrication mechanism of alcohols, Tribology Trans., 38(3):645-653. Godet, M. (1988), Modeling of friction and wear phenomena, in Approaches to Modeling of Friction and Wear, Ling, F.F. and Pan, C.H.T. (Eds.), Springer-Verlag, New York, 12. Greenwood, J.A. and Williamson, J.B.P. (1966), Contact of nominally flat surfaces, Proc. R. Soc. A, 295:300-310. Hamilton, G.M. (1983), Explicit equations for the stresses beneath a sliding spherical contact, Proc. Inst. Mech. Engrs., 197C:53-58. He, C., Wang, Y.S., Wallace, J.S., and Hsu, S.M. (1993), The effect of microstructure on the wear transition of zirconia toughened alumina, Wear, 162-164:314-321. He, C. (1995), Microstructural Effects on Wear of ZrO2-Al2O3 Composites, Ph.D. dissertation, University of Maryland, College Park, MD. He, M.Y. and Hutchinson, J.W. (1989), Kinking of a crack out of an interface, J. Appl. Mech., 56:270-278. Hisakado, T. (1986), Wear mechanism of ceramics and surface topography, J. Tribology, 108:9-15. Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in ASME Wear of Materials, Ludema, K.C. (Ed.), 1:1-8. Hsu, S.M., Klaus, E.E., and Cheng, H.S. (1988), A mechano-chemical descriptive model for wear under mixed lubrication conditions, Wear, 128:307-323. Hsu, S.M., Lim, D.S., and Munro, R.G. (1989), Ceramics wear maps. In Proceedings of the 3rd International Symposium, Ceramic Materials and Components for Engines, Tennery, V.J. (Ed.), American Ceramic Society, Columbus, OH, 1236-1245. Hsu, S.M., Lim, D.S., Wang, Y.S., and Munro, R.G. (1991), Ceramic wear maps: concept and method development, Lub. Eng., 47:49-54. Hsu, S.M. (1991), Boundary lubrication of advanced materials, MRS Bulletin, 16(10):54-58.
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Hsu, S.M., Lacey, P.I., Wang, Y.S., and Lee, S.W. (1991), Wear mechanism maps of ceramics, In Advances in Engineering Tribology, Chung, Y.W. and Cheng, H.S. (Eds.), STLE SP-31, Society of Tribologists and Lubrication Engineers, Chicago, 123. Hsu, S.M., Shen, M.C., Ying, T.N., Wang, Y.S., and Lee, S.W. (1994), Tribology of Si-based ceramics, Ceramics Trans., 42:189-205. Hsu, S.M., Nagarajan, V.S., Liu, H.Y., and He, C. (1995), Microstructural design of ceramics for optimum wear resistance, Proceedings of the International Symposium on Advanced Ceramics for Structural and Tribological Applications, Hawthorne, H.M. and Troczynski, T. (Eds.), Canadian Institute of Mining, Metallurgy, and Petroleum, Canada. Kim, S.S., Kato, K., Hokkirigawa, K., and Abe, H., Wear mechanism of ceramic materials in dry rolling friction, ASME J. Tribology, 108:522-526. Kim, S.-S., Kim, S.-W., and Hsu, S.M. (1994), A new parameter for assessment of ceramic wear, Wear, 179:69-73. Komvopoulos, K., Suh, N.P., and Saka, N. (1986), Wear of boundary-lubricated metal surfaces, Wear, 107:107-119. Larsen-Basse, J. (1991), Success and failure of simple models for abrasive wear, in Tribological Modeling for Mechanical Designers, ASTM STP 1105, Ludema, K.C. and Bayer, R.G. (Eds.), American Society for Testing and Materials, Philadelphia, 51. Lee, S.C. and Cheng, H.S. (1992), On the relation of load to average gap in the contact between surfaces with longitudinal roughness, Tribo. Trans., 35:523-532. Lee, S.W., Hsu, S.M., and Munro, R.G. (1990), Ceramic wear maps: SiC whisker reinforced alumina, Tribology of Composite Materials, Rohatgi, P.K., Blau, P.J., and Yust, C.S., pp. 35-41, ASM International, Metals Park, OH. Lee, S.W., Hsu, S.M., and Shen, M.C. (1993), Ceramic wear maps: zirconia, J. Am. Ceram. Soc., 76(8):1937-1947. Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metall., 35(1):1-15. Ling, F.F. and Pan, C.H.T. (1988), Approaches to Modeling of Friction and Wear, Springer-Verlag, New York. Liu, H. and Hsu, S.M. (1996), Modeling of micro-fracture-induced wear and wear transition of polycrystalline alumina under sliding, Wear, 195:169-177. Ludema, K.C. and Bayer, R.G. (1991), Cultural impediments for practical modeling of wear rates, in Tribological Modeling for Mechanical Designers, ASTM STP 1105, American Society for Testing and Materials, Philadelphia, 180. Meng, H.C. and Ludema, K.C. (1995), Wear models and predictive equations: their form and content, Wear, 181-183:443-457. Michalske, T.A., Bunker, B.C., and Freiman, S.W. (1986), Stress corrosion of ionic and mixed ionic/covalent solids, J. Am. Ceram. Soc., 69(10):721-724. Mizuhara, K. and Hsu, S.M. (1992), Tribochemical reaction of oxygen and water on silicon surfaces, in Wear Particles, Dowson, D. et al. (Eds.), Elsevier Science Publishers B. V., 323. Munro, R.G. and Hsu, S.M. (1988), Advanced ceramics: a critical assessment of wear and lubrication, NISTIR 88-3722, National Technical Information Service, Springfield, VA. Nakayama, K. and Hashimoto, H. (1991), Triboemission from various materials in atmosphere, Wear, 147:335-343. Rabinowicz, E. (1965), Friction and Wear of Materials, John Wiley & Sons, New York, 165. Rühle, M., Claussen, N., and Heuer, A.H. (1984), Microstructural studies of Y2O3-containing tetragonal ZrO2 polycrystals (Y-TZP), in Advances in Ceramics, Vol. 12, Science and Technology of Zirconia II, Claussen, N., Rühle, M., and Heuer, A.H. (Eds.), American Ceramic Society, Columbus, OH. Sasaki, S. (1989), The effects of surrounding atmosphere on the friction and wear of alumina, zirconia, silicon carbide, and silicon nitride, Wear of Materials, 2, 409-417. Shen, M.C. and Hsu, S.M. (1996), Wear modeling of Si-based ceramics, in Proceedings of International Tribology Conference, Yokohama, Japan, 403.
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Sibley, L.B. and Allen, C.M. (1962), Friction and wear behavior of refractory materials at high sliding velocities and temperatures, Wear, 5:312-321. Ting, B.Y. (1988), A Thermomechanical Wear Theory, Ph.D. dissertation, Georgia Institute of Technology, Atlanta, Georgia. Tomizawa, H. and Fischer, T.E. (1987), Friction and wear of silicon nitride and silicon carbide in water, ASLE Trans., 30(1):41-52. Wang, F.X., Lacey, P.I., Gates, R.S., and Hsu, S.M. (1991), Study of relative surface conformity between two surfaces in sliding contact, ASME, J. Tribology, 113:755-762. Wang, Y.S., Hsu, S.M., and Munro, R.G. (1991), Ceramic wear maps: alumina, Lub. Eng., 47:63-69. Wang, Y.S., He, C., Hockey, B.J., Lacey, P.I., and Hsu, S.M. (1995), Wear transitions in monolithic alumina and zirconia-alumina composites, Wear, 181-183:156-164. Wang, Y.S. and Hsu, S.M. (1996a), Wear and wear transition modeling of ceramics, Wear, 195:35-46. Wang, Y.S. and Hsu, S.M. (1996b), The effects of operating parameters and environment on the wear and wear transition of alumina, Wear, 195:90-99. Wang, Y.S. and Hsu, S.M. (1996c), Wear and wear transition mechanisms of ceramics, Wear, 195:112-122. Ying, T.-N. (1996), Wear Mechanisms for Ductile and Brittle Materials in a Micro-Contact. Ph.D. dissertation, University of Maryland, College Park, Maryland. Ying, T.-N., Shen, M.C., Wang, Y.S., and Hsu, S.M. (1997), Tribology of Si-based ceramics — wear mechanisms, Tribology Trans., 40:685-693. Zutshi, A., Haber, R.A., Niesz, D.E., Adams, J.W., Wachtman, J.B., Ferber, M.K., and Hsu, S.M. (1994), Processing, microstructure, and wear behavior of silicon nitride hot-pressed with alumina and yttria, J. Am. Ceram. Soc., 77(4):883-890.
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10 Liquid Lubricants and Lubrication Lois J. Gschwender
10.1 10.2
Operating Environment • Viscosity and Fluid-Film Lubrication • Boundary Lubrication Performance • Stability • Fire Resistance • Compatibility • Biodegradability and Toxicity • Additive Susceptibility
Air Force Research Laboratory
David C. Kramer Chevron Global Lubricants
Brent K. Lok
10.3
Chevron Global Lubricants
Shashi K. Sharma Carl E. Snyder, Jr. Air Force Research Laboratory
10.4
Chevron Global Lubricants
10.1
Conventional Lubricants — The Evolution of Base Oil Technology ................................................................. 366 Early Base Oil Processing • Solvent Refining • Additives Improve Performance • Hydrotreating • Hydrocracking • Catalytic Dewaxing and Hydroisomerization • Group II — Modern Conventional Base Oils • Group III — Unconventional Base Oils • Group IV — Traditional “Synthetic Hydrocarbon” Base Oils (PAO) • Group III vs. PAO Performance • Future Evolution
Air Force Research Laboratory
Mark L. Sztenderowicz
Introduction ..................................................................... 361 Lubricant Selection Criteria ............................................ 361
Synthetic Lubricants ........................................................ 373 Reasons For Use
Introduction
Liquid lubricants have been around for a long time and have evolved from the conventional mineral-oil based to the more exotic synthetics. In this chapter, a systematic approach to the selection of a lubricant will be addressed. The evolution of the base oil technology for the conventional lubricants will be discussed in detail. Different classes of the synthetic-based specialty and high-temperature lubricants and their key features will also be addressed.
10.2
Lubricant Selection Criteria
Although this chapter is primarily about liquid lubricants, it is worthwhile to spend a little time discussing some of the other popular lubricant types, i.e., greases and solid lubricants and hard coatings, to get a better idea of why liquid lubricants are selected most often. Also, the primary lubricant in grease is a liquid lubricant, so greases will be discussed to a minor extent throughout this section.
10.2.1 Operating Environment When selecting a lubricant for a specific application, a number of factors must be considered. First, and most important, is the environment in which the lubricant must function; generally, that is the temperature range of the application. However, there are sometimes other environmental considerations, e.g.,
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outer space, liquid oxygen, or other reactive medium. After the above factors have been considered, one must decide which type of lubricant is required for the application. For some applications, greases can be selected which provide a simple design for the lubrication system, i.e., pack the bearing or mechanism with the appropriate grease. For other applications, solid lubricants or hard coatings are preferred. Again, they provide a simple lubrication system, although they frequently require some kind of relubrication process to provide long-time service. Finally we come to the most widely used form of lubricant, the liquids. Besides providing for lubrication of the mechanisms, they also provide damping and cooling. Cooling occurs by removing either the heat from the environment, e.g., a turbine engine bearing compartment, or the heat generated by the friction in the mechanism. By appropriate designing of the lubrication system, a liquid lubricant can control the temperature of a mechanical assembly within a very narrow temperature range, if required. For example, as a lubrication system using a pump to distribute the lubricant becomes hotter, the oil becomes less viscous, flow increases, and therefore the oil removes more heat. The liquid and grease lubricants also provide an efficient relubrication mechanism, i.e., if a grease or liquid lubricant film is broken, the grease or liquid flows back into that contact area, once again providing lubrication. For this reason, liquid and grease lubricants are more widely used than solid lubricants or hard coatings, but the solid lubricants and hard coatings are gaining wider acceptance as improvements in performance and lifetime are being achieved.
10.2.2 Viscosity and Fluid-Film Lubrication As previously stated, the operational environment for a liquid or grease lubricant usually imposes some specific property requirements on the lubricant and guides its selection. These property requirements are both physical and chemical. Perhaps the most used physical property is the viscosity–temperature relationship. The low temperature operational capability of a liquid lubricant is defined by the maximum viscosity at which the lubricant can be pumped; for a grease it is defined by the maximum thickness at which the mechanical assembly or bearing can operate. The high-temperature operating capability of a liquid lubricant may be defined by the minimum viscosity that can provide fluid-film lubrication. The lubricant has to be effective in both the fluid-film lubrication and the boundary lubrication regimes. In fluid-film lubrication, a fluid film separates the interacting surfaces. In boundary lubrication the interacting surfaces react with the lubricant components to form protective physisorbed, chemisorbed, or reaction films. Fluid-film lubrication can be further divided into two broad categories — hydrodynamic lubrication and elastohydrodynamic lubrication. In fluid-film lubrication, the physical properties of the lubricant, such as viscosity, pressure–viscosity, and traction, determine the performance of the lubricated contact. While fluid-film lubrication is the desired mode of operation, the boundary lubrication regime cannot be avoided. Even in fluid-film lubrication, boundary lubrication occurs during start-up and stopping, and during occasional asperity interaction during operation. Therefore, the material (both the surfaces and the lubricant) properties that are important for the boundary lubrication regime are equally important for fluid-film lubrication. For thicker fluid films, a combination of higher viscosity and higher pressure–viscosity coefficient are needed (Hamrock, 1994). Both these properties are affected by the molecular structure of the lubricant. Linear and flexible structures provide better viscosity–temperature characteristics compared to the branched and rigid structures. On the other hand, the branched and rigid structures have higher pressure–viscosity coefficients at a given temperature. The pressure–viscosity coefficient for the branched and rigid structures decreases more sharply with temperature increase than that for the linear and flexible structures (Sharma et al., 1995). The lubricant selected should be able to maintain adequate film thickness throughout the operating temperature range. Lubricant traction coefficient (rolling/sliding friction coefficient) determines the power losses and stability of the rolling-element bearings (Gupta, 1984). For lubricants, a lower traction coefficient is desired for lower power loss and lower heat generation, whereas a higher traction coefficient is desired for the traction-fluids. The molecular structures that result in higher film thicknesses also provide higher
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16
Viscosity @ 40 oC, cSt
14
MIL-PRF-83282 (No VI-improver)
12 10 8 MIL-H-5606 (contains VI-improver) 6 4 0
500
1000
1500
Test Hours
FIGURE 10.1
Viscosity of fluid samples from pump tests.
traction coefficients. Thus, the branched and rigid structures result in higher traction coefficients compared to the linear and flexible molecules (Hentschel, 1985). When selecting a lubricant, a balance must be achieved between the film-thickness and the traction properties. In the lubricant industry, the temperature response of viscosity is expressed as viscosity index (VI). The less the oil viscosity changes with temperature, the better its lubricating performance at high and low temperatures and the higher its VI. Generally, higher VI is preferred for lubricants. To increase the viscosity index of a lubricant, high-molecular-weight VI-improving additives are sometimes added to the lubricant. These additives increase the lubricant’s viscosity at the higher temperatures as well as at the lower temperatures (to a lesser degree), thereby increasing the viscosity index of the lubricant. The VI-improvers have been extensively used in automotive lubricants to formulate the multigrade oils. The viscosity measurements under low shear rates do not directly translate into effective viscosity or film thickness in the lubricated contact for the VI-improved fluids. Under the high-stress and shear conditions, the VI-improved fluids do not contribute to the film thickness and traction to the predicted levels (Palacios and Bajon, 1983; Sharma et al., 1993a). In aircraft hydraulic pump tests, the fluid viscosity dropped sharply during the tests for the VI-improved fluid, whereas there was no viscosity loss for the non-VIimproved fluids, as shown in Figure 10.1 (Sharma et al., 1998; 1999). It is interesting to note that the sheared, reduced viscosity fluid did not adversely affect the pump performance, and perhaps an even lower viscosity fluid would have worked equally well. Equivalent performance was shown in pump tests with a lower viscosity (8 cSt @ 40°C) non-VI-improved fluid (Gschwender et al., 1988), and no viscosity loss was observed. In selecting the lubricant viscosity for an application, one should not look just at the low-shear viscosity, but also the effective viscosity in the contact inlet.
10.2.3 Boundary Lubrication Performance When metal-to-metal contact occurs between two surfaces in a lubricated contact, the asperities on the surfaces shear, thereby exposing a fresh metal surface. The appropriate lubricant reacts with the exposed fresh metal to form protective surface films. The surface films thus formed are generally low-friction and wear-resistant, and protect the surfaces from early failure/wear. During operation, these surface films can wear and regenerate. Antiwear or lubricity additives are generally added to the base oil to enhance the formation of the protective surface films during boundary lubrication. Thus, in boundary lubrication, the chemistry of the lubricant along with the material properties of the interacting surfaces determines the performance of the lubricated contact. Some metals perform better in boundary lubrication than others. Surface coatings (Rai et al., 1999) can also enhance boundary lubrication performance. Therefore, when selecting a lubricant, the lubricated surfaces should be given proper consideration. While full-scale system/component testing is the best way to evaluate a lubricant’s performance, more economical tests, such as the four-ball wear test (e.g., ASTM D4172) and Cameron–Plint reciprocating
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tribometer (e.g. Helmick et al., 1997), are available to measure the boundary lubrication performance of a lubricant/formulation. The full-scale component tests are preferred because sometimes the laboratory tests do not correlate with the lubricant’s performance in the application.
10.2.4 Stability If the upper operating temperature limit for a liquid lubricant is not defined by the viscosity temperature properties, it is generally defined by the stability of the lubricant. For greases, the viscosity at elevated temperature is not generally the critical property. For greases, the upper operating temperature limit is generally defined either by stability or volatility. A lubricant must be stable in the environment in which it is being used so that it provides adequate lubrication for a finite lifetime. Some mechanisms are “lubricated for life,” whereas other mechanisms operate in such a severe environment that the lubricant must be changed on a regular basis. For example, most automobiles require that the engine lubricant be changed every 3000 or 5000 miles, whereas most small electric motor bearings do not require relubrication for their useful life. There are typically three different stabilities to consider that are inherent properties of the base fluid when a class of lubricants is selected for a specific application. They are thermal, thermal–oxidative, and hydrolytic. (For greases, a fourth stability is the ability of the grease to remain a grease and not separate into the base fluid and the thickener.) We must carefully analyze the environment in which the lubricant must operate to determine what kind of stability is required. In an aircraft hydraulic system, for example, the lubricant, or in this case the hydraulic fluid, is not exposed to much air or moisture since the aircraft hydraulic systems are generally closed. Therefore, thermal stability is the most important stability for aircraft hydraulic fluids. On the other hand, if a shipboard hydraulic system is the intended application, hydrolytic stability also becomes very important since the lubricant will be operating in a wet environment. Thermal–oxidative stability becomes important in air breathing systems, such as automotive engines, aircraft engines, etc., where the lubricant will be exposed to both high temperatures and oxygen. This puts another very severe limitation on the selection of the lubricant since many classes of lubricants have limited thermal–oxidative stability. In applications where oxidative stability is of paramount importance, e.g., lubrication of valves coming in contact with liquid oxygen, liquid lubricants must not contain any hydrogen atoms and must be totally halogenated, e.g., chlorofluorocarbons or perfluorinated lubricants. The various classes of liquid lubricants and their thermal, hydrolytic, and oxidative stabilities will be discussed later in this chapter.
10.2.5 Fire Resistance Another important property to consider when a liquid lubricant is selected is fire resistance. Liquid lubricants can range from extremely flammable to nonflammable. Fire resistance is extremely important in hydraulic fluids. Three different aerospace hydraulic fluids have been developed and are in use today strictly to reduce the fire hazards in aircraft hydraulic systems. They are hydraulic fluids based on phosphate esters, specifically AS1241, and synthetic hydrocarbons, MIL-PRF-83282 and MIL-PRF-87257. Fire resistance is especially important for hydraulic fluids since they are used at high pressures (up to 5000 psi), which significantly enhances their potential ignition if the fluid is in the form of a spray. Hatton described the many hazards involved with hydraulic fluids and some of the more widely used methods to determine fire resistance, but even in his book, he failed to recognize one of the most important fireresistance characteristics, flame propagation (Hatton, 1966; Snyder et al., 1981). Most flammability test methods concentrate on a fluid’s ignition characteristics, and, while that indeed is an important property, they fail to assess the potential damage from a fire once ignited. The AS1241 and both MIL-PRF fluids are ignitable, but they have extremely low flame propagation characteristics, making them significantly safer to use (Snyder et al., 1981). Although nonflammable hydraulic fluids have been developed, e.g., MIL-H-53119, a moderate-molecular-weight chlorofluorocarbon, they have not found their way into applications as yet. This has been
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primarily due to the need to develop hydraulic systems around their unique properties, e.g., high density, specific seal compatibility, etc., and the fact that no one is willing to accept the high risk associated with being the first to use a new lubricant. Nonflammable lubricants are currently used only in small-volume applications.
10.2.6 Compatibility For a lubricant to be acceptable for a specific application, it must be compatible with all of the materials with which it will come into contact. This is especially true when trying to replace an existing lubricant with a new one. For this case, it is also important that the new lubricant be compatible and miscible with the former one to facilitate the changeover process from the old to the new lubricant. Significant costs could be experienced if parts of the system, e.g., O-rings, gaskets, and other seals, had to be replaced in order to realize the benefits the new lubricant would bring to that application. Since it is difficult to ensure that the new lubricant will not leak out of the system and get on other materials in the vicinity, e.g., paint, wiring insulation, composites, etc., the new lubricant will need to demonstrate compatibility similar to the old lubricant it is scheduled to replace. That has caused frustration over the years for operators of hydraulic equipment who would like to take advantage of the greater safety afforded by the fire-resistant hydraulic fluids based on phosphate esters. If this equipment was originally designed for use with mineral oil or other hydrocarbon-based hydraulic fluids, many of the materials contained therein will not be compatible with phosphate esters and would have to be changed if phosphate esters were to be used. This has caused many of these operators to stay with the rather flammable hydraulic fluid they have been using instead of exploring other options. In a number of cases, it has been possible to gain a significant increase in fire resistance by converting to a synthetic hydrocarbon- or ester-based hydraulic fluid that is compatible with all the materials of their systems. In addition, the compatibility of these fluids with the previous fluid has made the conversion to the new fluid simple and cost effective.
10.2.7 Biodegradability and Toxicity Biodegradability and toxicity have been combined because they both pertain to similar characteristics of lubricants. The degree of biodegradability of a lubricant relates to the environmental friendliness of a lubricant, whereas the toxicity of a lubricant relates to the friendliness of the lubricant to the user. Biodegradability is becoming a more important property as environmental regulations become more restrictive with regard to protecting the integrity of water supplies and the environment in general. Toxicity has been an important issue for quite some time, and safety to the user will continue to gain attention. So far, the most important aspect of a lubricant for a specific application is that it work well, and the environmental friendliness is secondary. In the future, it could be that the environmental aspects of the lubricant will take precedence over performance.
10.2.8 Additive Susceptibility In order for a lubricant to perform its required function, it is typically necessary to formulate the base oil with performance-improving additives. Some of these additives are typically oxidation inhibitors, lubricity additives (both antiwear and friction modifying), rust inhibitors, antifoam additives, and, in the case of greases, thickeners. It is critical that additives be effective in the base oils for a lubricant to provide satisfactory performance. In the case of liquid lubricants, the additives must also be soluble. For the majority of the hydrocarbon-based lubricants, this is not a problem. They have been in use long enough for effective, soluble additives to have been developed. However, for some of the newer fluids, e.g., the perfluoropolyalkylethers (PFPAE), the traditional additives are not soluble. Therefore, soluble, effective additives have had to be developed. The lack of effective, soluble additives for the PFPAEs has significantly delayed their introduction into the industry (Snyder and Gschwender, 1991). However, their limited introduction speaks well for their unique properties, which will be discussed later in this chapter. There can be cases where additive solubility is not an issue, but effectiveness is. This is the case for the
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polydimethylsiloxane fluids, a.k.a. silicones. Although typical antiwear additives like aromatic phosphates dissolve in silicone fluids, they do not provide improved lubricity for metal-to-metal contacts. This has prevented their widespread use as lubricants for wide-temperature-range applications for which they would be ideal candidates due to their excellent viscosity–temperature properties. Additive susceptibility is an important property to consider when selecting a class of lubricants for specific applications.
10.3
Conventional Lubricants — The Evolution of Base Oil Technology
In this section, we cover some of the major milestones in the evolution of base oil technology used to make “conventional” lubricants. Conventional lubricants are defined here as those that have historically been formulated with mineral oils derived from crude oil. But we will see that as base oil technology continues to evolve, the performance gap continues to close between conventional mineral-based oils and the traditional “synthetic hydrocarbon” oils described later in the chapter.
10.3.1 Early Base Oil Processing From its humble beginnings over 3000 years ago, base oil technology has seen many phases of evolution. In the first phase, animal fats were used as lubricants. Ancient inscriptions dating back to 1400 BC show beef and mutton fat (tallow) being applied to chariot axles. Very little changed over the ages except that the oils sometimes came from more exotic animals such as whales. In 1852 petroleum-based oils first became available. They were not widely accepted at first because they did not perform as well as many of the animal-based products. Raw crude did not make very good lubricant. The base oil industry was on the very steep part of the learning curve. But demand grew with the appearance of the automobile. Soon lubricant manufacturers learned which crudes made the best lubricants. Further improvements were made by refining the crude into narrow distillation cuts with varying viscosity. By 1923 the Society of Automotive Engineers classified engine oils by viscosity; light, medium, and heavy. Engine oils contained no additives and had to be replaced every 800 to 1000 miles. In the 1920s more lubrication manufacturers started “processing” their base oils to improve their performance. There were three popular processing routes. 10.3.1.1 Clay Treating Clay was used to soak up and remove some of the worst components in the petroleum base oil. These compounds were usually aromatic compounds and highly polar compounds containing sulfur and nitrogen. 10.3.1.2 Acid Treating Concentrated sulfuric acid was used to react with the worst components in the base oil and convert them into a sludge that could be removed. This process effectively cleaned up the oil, but it was expensive. This technology has virtually disappeared from North America due to environmental concerns about the acid and sludge (National Petroleum Refiners Association, 1999). 10.3.1.3 SO2 Treating This was a primitive extraction process to remove the worst components in the lube oil by using a recyclable solvent. Unfortunately, the solvent was highly toxic. Although it also has been virtually phased out (National Petroleum Refiners Association, 1999), it was a useful stepping stone to conventional solvent extraction.
10.3.2 Solvent Refining By about 1930 solvent processing emerged as a viable technology for improving base oil performance using a fairly safe, recyclable solvent. Most base oils in the world today still use this process. Solvent refining for base oil manufacturing was pioneered mostly by Texaco and Exxon under trade names such
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TABLE 10.1
API Base Stock Categories
Group
Sulfur, Wt %
I II III IV V
>0.03 <0.03 <0.03
Saturates
V.I.
and/or <90 80–119 and >90 80–119 and >90 ≥120 All Polyalphaolefins (PAOs) All Stocks Not Included in Groups I-IV (Pale Oils and Non-PAO Synthetics)
as “Texaco MP,” “Duo Sol,” “DILCHILL,” and “EXOL.” About two thirds of the base oils in North America are currently manufactured using this route. Solvent-refined base oils are commonly called Group I base oils. Group I base oils are those having less than 90% saturates (>10% aromatics) and more than 300 ppm sulfur. Table 10.1 shows all the base oil groups as defined by the American Petroleum Institute (API). Solvents and hardware have evolved over time, but the basic strategy has not changed since 1930. Solvent refining is still the most widely used route for making base oil. Aromatics are removed by solvent extraction to improve the lubricating quality of the oil. Aromatics make good solvent but they make poor-quality base oil. Aromatics are among the most reactive components in the natural lube boiling range. Oxidation of aromatics can start a chain reaction that can dramatically shorten the useful life of a base oil. The viscosity of the aromatic components also responds poorly to changes in temperature (low VI). Aromatics are removed by feeding the raw lube distillate (vacuum gas oil) into a solvent extractor where it is contacted counter-currently with a solvent. Popular choices of solvent are furfural, NMP (Nmethylpyrrolidone), and a mixture of toluene and MEK (methylethyl ketone). Phenol is very rarely used due to environmental concerns. Solvent extraction typically removes 50 to 80% of the impurities (aromatics, polars, sulfur, and nitrogen-containing species). The resulting product of solvent extraction is usually referred to as a raffinate. The second step is solvent dewaxing. Wax is removed from the oil to keep it from freezing in the sump or crankcase at low temperatures. Wax is removed by diluting the raffinate with a solvent. This is done to thin the oil and enhance the dewaxing rate. Popular dewaxing solvents are MEK/toluene, MEK/MIBK(methylisobutyl ketone), or (rarely) propane. The diluted oil is then chilled to –10 to –20°C. Wax crystals form, precipitate, and are removed by filtration.
10.3.3 Additives Improve Performance Over the next several decades, the solvent refining process did not change very much. Improvements in finished oil quality came mainly from the appearance of additives. Additives began to be widely used in 1947 when the API began to categorize engine oils by severity of service: regular, premium, and heavy duty. Additives were used to extend the life only in premium and heavy-duty oils. In 1950, multigrade oils were introduced which were formulated with polymers to enhance the hot and cold performance of the oil. The additives changed the VI of the oil. This trend continued for several more decades. Lubricant quality improved significantly only when the additive chemistry improved. This was the only viable strategy for progress until a significant improvement in base oil quality was available.
10.3.4 Hydrotreating Hydrotreating was developed in the 1950s and first used in base oil manufacturing in the 1960s by Amoco and others. It was used as an additional “cleanup” step added to the end of a conventional solvent refining process. Hydrotreating added hydrogen to the base oil at elevated temperatures in the presence of catalyst to stabilize the most reactive components in the base oil, improve color, and increase the useful life of the base oil. This process removed some of the nitrogen and sulfur-containing molecules but was not severe enough to remove a significant amount of aromatics. This was a small improvement in base oil technology that would become more important later.
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10.3.5 Hydrocracking Hydrocracking is a more severe form of hydroprocessing. It is done by adding hydrogen at even higher temperatures and pressures than simple hydrotreating. Molecules are reshaped and often cracked into smaller molecules. A great majority of the sulfur, nitrogen, and aromatics are removed. Molecular reshaping of remaining saturated species occurs as rings are opened and paraffin isomers are redistributed, driven by thermodynamics with reaction rates facilitated by catalysts. Clean fuels are by-products of this process. A primitive version of the hydrocracking process was attempted for lube oil manufacturing in the 1930s but was soon abandoned for economic reasons when solvent refining appeared (Sequeira, 1994). After WWII, more modern hydrocracking catalyst technology was imported from Germany. This technology was commercialized for fuel production in the late 1950s by Chevron (Stormont,1959). In 1969 the first hydrocracker for base oil manufacturing was commercialized in Idemitsu Kosan Company’s Chiba refinery using technology licensed by Gulf (Anonymous, 1972). This was followed by Sun Oil Company’s Yabucoa refinery in Puerto Rico in 1971, also using Gulf technology (Sequeira, 1994).
10.3.6 Catalytic Dewaxing and Hydroisomerization Then came first-generation catalytic dewaxing and hydroisomerization in the 1970s. BP, Shell, and others used hydroisomerization technology coupled with solvent extraction to manufacture very high-VI base oils in Europe. In the U.S., Mobil used catalytic dewaxing in place of solvent dewaxing, but still coupled it with solvent extraction to manufacture conventional neutral oils. Catalytic dewaxing was a desirable alternative to solvent dewaxing, especially for waxy high-VI oils. This process removed n-paraffins and waxy side chains from other molecules by catalytically cracking them into smaller molecules. This lowered the pour point of the base oil so that it flowed at low temperatures like a solvent dewaxed oil. In the case of hydroisomerization, the majority of remaining aromatics were saturated, and the majority of remaining sulfur and nitrogen species were also removed. Chevron was the first to combine catalytic dewaxing with hydrocracking and hydrofinishing in its Richmond, California, base oil plant in 1984 (Zakarian et al., 1987). This was the first commercial demonstration of an all-hydroprocessing route for lube manufacturing. In 1994, the first modern wax hydroisomerization process was commercialized by Chevron in the same plant. This was an improvement over earlier catalytic dewaxing because it lowered the pour point of the base oil by isomerizing (reshaping) the n-paraffins and other molecules with waxy side chains into very desirable branched compounds with superior lubricating qualities rather than cracking away the n-paraffins. By combining three catalytic hydroprocessing steps (hydrocracking, hydroisomerization, hydrotreating), molecules with poor lubricating qualities are transformed and reshaped into higher-quality base oil molecules. Pour point, VI, and oxidation stability could be independently controlled. This was fundamentally different than the previous approaches that relied solely on subtraction. Among the many benefits of this combination of processes is greater crude oil flexibility; that is, less reliance on a narrow range of crude oils from which to make high-quality base oils. In addition, the base oil performance is substantially independent of crude source, unlike solvent-refined base oil.
10.3.7 Group II — Modern Conventional Base Oils The modern hydroisomerization process licensed by Chevron under the name ISODEWAXING gained acceptance rapidly in the 1990s. In fact, about one third of all base oils manufactured in North America are now manufactured using this process (Figure 10.2). ISODEWAXING technology is also moving through Asia as well. Rapid growth of this technology in the U.S. prompted the API in 1991 to categorize base oils by composition (API publication 1509), as shown in Table 10.1. Most of the base oils made using modern hydroisomerization are categorized as Group II. Table 10.1 shows that they are differentiated from Group I base oils because they contain significantly lower levels of impurities (<10% aromatics, <300 ppm sulfur). They also look different because Group II oils are normally very clear, almost water-white. From a performance standpoint, improved purity means that the base oil and the additives in the finished product can last much longer. This technology, along with
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35 30 Percent
25 20 15
% Base Oil in North America
10 5 0 1995
FIGURE 10.2
1996
1997
1998
1999
ISODEWAXING trend in North America.
specially designed additives, has already had a tremendous impact on finished oil performance. In some applications, lubricating oils formulated with Group II base oils outperform expensive traditional “synthetic hydrocarbon” oils made from PAO.
10.3.8 Group III — Unconventional Base Oils The difference between Group II and III base oils is simply viscosity index (VI). Base oils with a “conventional” VI (80 to 119) are Group II. Base oils with an “unconventional” VI (120+) are Group III. They are also sometimes called unconventional base oils or UCBOs. Still another commonly used name for these oils is VHVI, or very high VI base oils. Group III base oils were not widely available in North America until a few years ago. Earlier generations of Group III base oils (Min, 1998) were produced in Europe, primarily by Shell and BP, but were not produced using the now commonly accepted all-hydroprocessing route. Consequently, they do not have the exceptional stability and low temperature performance of these modern Group III oils. Fortunately for North American consumers, those older-generation stocks are made and sold in different markets. Many of these plants are being upgraded to modern technologies that will enable them to make the modern Group III oils (Howell, 2000). Modern Group III base oils perform at a level that is significantly higher than “conventional” base oils, both Group I and Group II, and nearly match existing levels of performance in finished lube applications already established by their traditional “synthetic hydrocarbon” counterparts. The most notable exception, arctic oils, have very small market presence. From a processing standpoint, the higher VI in modern Group III base oils is achieved by increasing the temperature or time in the hydrocracker. This is sometimes collectively referred to as the “severity.” Alternatively, the product VI could be increased simply by increasing the feed VI, which is typically done by selecting the appropriate crude. Group III base oils are now widely available in North America because they can be manufactured by most of the companies that currently make Group II oils. Many companies have started adding them to their “synthetic hydrocarbon” product lines.
10.3.9 Group IV — Traditional “Synthetic Hydrocarbon” Base Oils (PAO) Synthetic lubricants will be discussed in detail later in the chapter. However, we thought it would be appropriate to say a few words about “synthetic hydrocarbon” base oils here because they are directly influencing the future direction of mineral-based base oil technology. The hydrogenated polyalphaolefin (PAO) commercial market can be traced as far back as the early 1970s when specialized products were formulated from PAOs (Bui, 1999). PAOs became a major consumer-sought lubricant product when Mobil Oil commercially marketed its Mobil 1™ product 25 years ago. However, Mobil’s involvement with “synthetic hydrocarbons” can be traced back to the 1960s when the oil company resolved a problem plaguing military planes based on aircraft carriers. Mobilgrease 28 was developed to protect against wheel bearing failure caused by atmospheric cold temperatures. Mobil’s SAE 5W-20 engine oil is derived from this base fluid technology. Since then, the PAO market has traveled
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a long and winding road battling a slow, steady growth and criticisms of the higher cost compared to conventional oils. In the last 10 years, the PAO market significantly took off, first in Europe and then in North America, experiencing as much as a double-digit growth. In part, the growth might be attributed to the stricter lubricant specifications in Europe that created a market niche for synthetic hydrocarbons and semisynthetic hydrocarbon products. The demand has since extended to North America and other continents. The use of the word “synthetic” in the lubricant industry has historically been synonymous with polymerized base oils, such as PAOs, and other synthetics, such as esters, polyphenylethers, etc., which are made from smaller molecules. Primarily this use evolved because these types of base oil were the only components available for high-performance lubricants. That changed a number of years ago when some lubricant manufacturers, primarily in Europe, began replacing PAOs with newly available Group III base oils, which are made from feed molecules of substantially the same size as the final product. With the recent availability of modern Group III base oils in North America, this practice is now spreading to North America. This is currently causing a controversy in the lubricant industry, as some synthetic hydrocarbon base oil producers and lubricant manufacturers see only polymerized base oils or other oils made by combining smaller molecules as the true and only synthetic hydrocarbons. PAOs have historically had superior lubricating performance characteristics, such as viscosity index, pour point, volatility, and oxidation stability, that could not be achieved with conventional mineral oils. Now, in modern base oil manufacturing, viscosity index, pour point, volatility, and oxidation stability can be independently controlled. Modern Group III oils today can be designed and manufactured so that their performance closely matches that of PAOs in most commercially significant finished lube applications.
10.3.10 Group III vs. PAO Performance As well-designed Group III base oils become abundant in the market place, the performance gap between Group III and PAO (Group IV) is closing. Here are some key examples: Pour Point — Pour point is the one place where Group III oils allegedly fall short of PAOs. While it is certainly true that the pour point of the neat VHVI base oil is substantially higher than that of a PAO of comparable viscosity, it is important to understand that what matters is the pour point of formulated lubricants, which are comprised of both base oils and additives. Fully formulated Group III-based lubricants are very responsive to pour point depressant additives, and where pour point depressants may be used, these lubricants can demonstrate pour points of –50°C or below when they are manufactured with modern isomerization catalysts. Products such as motor oils made with the lighter-grade PAOs, on the other hand, typically have higher pour points than the base fluid, so the gap in final product pour point between PAO-based and UCBO-based lubricants is smaller than in the base fluids themselves. Moreover, it is entirely possible with modern Group III manufacturing technology to produce base oils of even lower pour point, although this is not currently common practice in the industry precisely because there is very little customer demand or specifications for pour performance below –50°C. Cold Crank Simulator — Viscosity in engine journal bearings during cold temperature startup is a key factor in determining the lowest temperature at which an engine will start. Cold Cranking Simulator (CCS) viscosity, as measured by ASTM D5293, is determined under conditions similar to those experienced in engine bearings during starting. For base oils, this viscosity is determined almost entirely by viscosity and viscosity index. Since VHVI stocks have a VI comparable to that of 4 cSt PAO, one would expect comparable CCS performance. This is demonstrated in Figure 10.3, where it can be seen that a 4 cSt Group III base oil with a kinematic viscosity of 4.2 cSt @ 100°C and a VI of 129, and PAO 4, with a viscosity of 3.9 cSt and VI of 123, have similar CCS values, both about half that of a 4 cSt Group II base stock of about 100 VI. This performance makes the UCBO very effective for formulating fuel-efficient multiviscosity engine oils in the 0W-20 to 0W-50 range, one that has historically been achieved only with PAO-based product.
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FIGURE 10.3
Cold cranking performance of mineral oils and PAO.
FIGURE 10.4
Noack volatility of mineral oils and PAO.
371
Noack Volatility — Noack volatility of an engine oil, as measured by ASTM D 5800 and similar methods, has been found to correlate with oil consumption in passenger car engines. Strict requirements for low volatility are important aspects of several recent and upcoming engine oil specifications, such as ACEA A-3 and B-3 in Europe and ILSAC GF-3 in North America. Figure 10.4 shows that from a blender’s perspective, Group III base oils are similarly effective as PAOs for achieving these low volatility requirements in engine oil applications. The viscosity index of modern Group III oils typically matches or exceeds that of PAO so they can match the volatility of PAOs at a reasonable distillation cut width. Oxidation Stability — Oxidation and thermal stability are among the most important advantages that “synthetic hydrocarbons” bring to the table. Better base oil stability means better additive stability and longer life. High stability is the key to making the premium-quality finished oils of the future with longer drain intervals. Here Group III oils routinely challenge PAO performance. The stability of modern Group III stocks depends mostly on their viscosity index, because VI is an indication of the fraction of highly stable isoparaffinic structures in the base oil (Kramer et al., 1999). However, because modern Group III stocks also undergo additional severe hydrofinishing after hydrocracking and hydroisomerization, they achieve an additional boost in stability because only trace amounts of aromatics and other impurities remain in the finished stocks. The benefit of all-hydroprocessed Group III base oils in oxidation stability is illustrated in Figure 10.5, for hydraulic oils formulated by using the same additive system in four different base oils. Here, the time required to reach an acid number of 2.0 (defined by neutralization of 2.0 mg of KOH/g of oil) in the Universal Oxidation Test (ASTM D4871), a common measure of oil oxidation, was substantially longer for the Group III formulation than for either the Group I or II products. Moreover, the performance of the Group III product was essentially the same as that for the oil formulated with PAO. Table 10.2 lists a variety of North American lubricants of which the authors are aware which are based upon allhydroprocessed Group III base stocks. These products include engine oils, industrial oils, and driveline fluids like automatic transmission fluid, and are targeted at the same performance levels achieved by traditional synthetic hydrocarbon formulations.
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FIGURE 10.5
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Oxidation stability, acid number of hydraulic oils. TABLE 10.2 Synthetic Quality Products Utilizing All-Hydroprocessed Group III Base Stocks Available Now Semi and full synthetic PCMO Semisynthetic HDMO DaimlerChrysler ATF+4® Ford Mercon® V ATF Compressor oil
Upcoming GF-3 PCMO (semi and full synthetic) Extended drain gear oil High performance automotive (racing) oils Motor oils Gear and transmission oils
10.3.11 Future Evolution Looking to the future, the trend is toward base oils with even higher purity, higher VI, lower volatility, and longer life. The base oils will probably look even more like PAO as they become more concentrated in isoparaffins, the most stable component in the base oil. It is likely that as base oil technology continues to evolve, the base oils of the future will surpass current benchmarks such as PAO in the critical performance areas such as oxidation stability and VI. There are many possible routes for improving base oil quality. Continued evolution of the all-hydroprocessing route is one likely possibility. Selectivity toward desired molecular compositions could be improved by improving the catalysts and the processing technology. Improving the feedstock can also improve the product. Very paraffinic (waxy) feedstocks such as Fischer Tropsch wax from natural gasto-liquids plants can potentially be further processed into high-quality base oils. Volumes and applications are expected to grow, as more ultra-waxy feedstocks become more widely available. Other competing technologies are likely to emerge. New routes for manufacturing PAOs have been proposed that use cheaper feedstocks such as ethylene and propylene rather than 1-decene (Heilman et al., 1999). In summary, the conventional base oil technology evolved slowly from ancient times until the middle of the 20th century. Then solvent refining brought base oil performance to a new level. Starting in the 1960s, hydroprocessing technologies were applied and combined to improve base oil purity and performance. Group II base oils were born. An all-hydroprocessing route for Group II base oil manufacturing was commercialized. Modern hydroisomerization technologies, such as ISODEWAXING became widely accepted and have grown exponentially since 1995. They are now used to make one third of all base oils in North America. The next wave appears to be Group III base oils. They offer most of the performance advantages of traditional PAO-based “synthetic hydrocarbon” oils at a fraction of the price. Most of the manufacturers that make Group II base oils can make Group III base oils. As base oil technology and additive technology continue to improve, mineral-based oils will continue to close the performance gap with traditional “synthetic hydrocarbons.” Traditional “synthetic hydrocarbon” oils such as PAO should continue to coexist with Group III oils as they have for years in Europe, but the widespread availability of highquality Group II and III mineral oils is accelerating the rate of change in the finished oil markets. New improved base oils are helping the engine and equipment manufacturers meet increasing demands for better, cleaner lubricants.
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10.4
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10.4.1 Reasons For Use In this section we will present an overview of synthetic fluids with unique properties. Synthetic fluids are selected because a mineral oil is deficient in some respect for a particular application. The U.S. military has often led research and development into new synthetics because of military requirements for high performance. Because of this and the authors’ backgrounds, many examples will be based on military lubricants. Driving the use of these synthetics are cost, availability, performance, and safety. 10.4.1.1 Cost Synthetic fluids are, as a rule, more expensive than mineral oils. An exception was a super-refined, deep dewaxed paraffinic mineral oil, used as the base stock for the SR-71 aircraft hydraulic fluid, MIL-H27601A. MIL-H-27601A cost over $100 per gallon, when a less expensive hydrogenated polyalphaolefinbased replacement was found. In cost analysis, an engineer must not only consider the initial acquisition cost of the lubricant, but also the life cycle cost. In life cycle cost analyses, the synthetic lubricants are often superior because equipment needs fewer repairs with synthetics, which are better inherent lubricants. Often equipment can be lubricated for life, never needing further lubrication, or at least extending maintenance intervals and thereby reducing down time. 10.4.1.2 Availability Synthetic fluids are generally more available in good quality than even the more stable of the mineral oils because the mineral oils come from various wells that may not be the same. Gradually as the better crude oils are depleted, less stable crude oils are used. In several cases in the military, mineral oil products no longer met the specifications that had been written around the original products. Synthetics, on the other hand, can be made consistently, as long as the starting materials are the same. 10.4.1.3 Performance Synthetic lubricants can be adjusted in the synthetic process to optimize property performance to a particular application. With mineral oils, the refiners have some, but much less latitude to adjust properties. High-temperature thermal and oxidative stability of synthetics exceeds those of mineral oils. Also viscosity–temperature range and low-temperature flow can be improved and controlled in synthetics by controlling branching and chain length, for example. The upper limit may be from a thermal stability limit or from a viscosity limit. (A fluid’s lowest useful viscosity depends on the application, but is generally considered to be 0.5 to 1.0 cSt for adequate lubrication film formation in a bearing or other wear surface.) The lower temperature limit may be either from limiting viscosity or from pour point, two distinct properties of a fluid. The low-temperature viscosity depends on the application, e.g., size of fluid pumps, length of tubing lines, and other impediments to flow. For gas turbine engine oils, for example, 19,000 cP is considered the highest usable viscosity, while for hydraulic fluids in aircraft, 2100 cP is considered the highest usable viscosity. Most often, any fluid class is available in a number of viscosity grades. The commercial literature is often the best place to find current information to aid in selecting the proper grade of a fluid. Selecting the proper fluid class, however, is not so simple and requires research to weigh the pros and cons of the available fluid classes. 10.4.1.4 Safety Flammability of lubricants is often a major consideration in the design of equipment, and even in determining if a particular fluid should be used. Mineral oils are a distillation cut of a crude oil and so the final oil’s flash point will be that of the most volatile part of the mixture. Synthetics, on the other hand, can be more closely controlled to be essentially the same molecular weight throughout. This means the flash point of synthetic oil will be higher for a certain viscosity of oil than it would be for a mineral oil of the same viscosity. For a phosphate ester fluid, fire resistance is even greater because the phosphorous atom acts as a fire suppressant.
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FIGURE 10.6
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Polyalphaolefin — general formula.
Flammability testing is a science unto itself (Snyder et al., 1981). The potential threat of an application must be considered, including ignition source, amount of oxygen present, air flow, temperature of the surroundings, and materials present, to name a few. 10.4.1.5 Fluid Classes 10.4.1.5.1 Synthetic Hydrocarbons Synthetic hydrocarbons have gone from the laboratory to a major industrial product. Hydrogenated polyalphaolefin (PAO), Figure 10.6, is the most widely used synthetic hydrocarbon. It is most often synthesized from C10 alpha unsaturated olefins using BF3 catalyst to make C20 , C30 , C40 , etc., finished base oils. The synthesis conditions are adjusted to favor a certain molecular weight product, optimum viscosity–temperature properties and low-temperature flow characteristics. The fluid is hydrogenated to remove residual olefins and fully saturate the molecules. PAOs have many of the advantages of highly refined paraffinic mineral oils such as those from now mostly depleted Pennsylvania crude oils. In fact, PAOs resemble paraffinic oils chemically, as they are largely straight chains, giving them high thermal stability and good viscosity–temperature index. Some branching exists in PAOs, which prevents them from freezing (waxing) at cold temperatures. Mineral oils must be dewaxed to remove the totally linear molecules to prevent low-temperature freezing (waxing). PAOs are synthesized to avoid waxes. Ideal properties for a PAO are a careful balance of branch vs. linear structure. PAOs in general have better lubricating ability than comparable mineral oils because there are no other atoms besides carbon and hydrogen. The thermal stability of PAOs, when oxygen is excluded, is quite high, as shown by the MIL-PRF-27601C fluid upper bulk oil temperature, 288°C. (The MIL-H27601A specification changed from a mineral oil to a PAO-based fluid when it became MIL-H-27601B, as it is in the later revision MIL-PRF-27601C.) Also, PAOs respond to additives very similarly to mineral oils except that additives tend to be less soluble in PAOs (especially the higher-molecular-weight oils) than in mineral oils. PAOs cost less compared to other synthetic fluids. The first major use of PAOs was in military hydraulic fluid, MIL-H-83282 (now MIL-PRF-83282) (–40°C to 200°C), based on decene trimer PAO (Gschwender and Snyder, 1999). This was developed as a fire-resistant fluid to counter the loss of military aircraft and lives from fires resulting from the use of a highly flammable mineral oil-based hydraulic fluid, MIL-H-5606. Aircraft damage directly attributable to hydraulic fluid fires went from over $10 million a year to fewer than $1 million a year with the conversion of the majority of Air Force aircraft to MIL-PRF-83282. MIL-PRF-83282 is now the primary hydraulic fluid for military aircraft in the U.S., Australia, and Israel, and is gradually going into European military aircraft. Other PAO uses in the military are MIL-PRF-87257 (–54°C to 135°C), a fire-resistant hydraulic fluid for cold climate operation; MIL-H-46170, similar to MIL-PRF-83282 but with a rust inhibitor; MIL-PRF-27601 (–40°C to 288°C), the high-temperature hydraulic fluid mentioned earlier. The C20, PAO decene dimer is widely used as a dielectric and cold plate coolant for military radar systems (Flanagan et al., 1991), commercially as a solar heat transfer fluid and as a large computer coolant, and as a shock absorber for higher priced automobiles. PAOs are also used in moisture-resistant, widetemperature greases, e.g., MIL-PRF-32014, and instrument oils. A small but critical higher-molecularweight PAO application is as oil or as grease for spacecraft (Jones et al., 1998). An important advantage of the lower-molecular-weight PAOs is that they are readily biodegradable. MIL-PRF-87257 is a class 1 (the best) and MIL-PRF-83282 is a class 2 (second best) in the ASTM D5864 biodegradability test.
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Decene trimer PAOs are often formulated as a major component of synthetic automobile engine oils, although they are more popular in Europe than in the U.S. Because they are inherently good lubricants, lower viscosity motor oils can be safely used, reducing viscous drag and engine wear. Often automobile operators using synthetic motor oils extend the oil change intervals as well as engine life, greatly offsetting the higher cost of the synthetic oil. Another synthetic hydrocarbon fluid type, with a small but unique niche, is multiply alkylated cyclopentanes (MACs) (Figure 10.7). In most applications, these fluids are too expensive to be commercially viable, but in spacecraft applications, they are being used more and more. Advantages include low volatility and vapor pressure, low pour point, good antiwear properties, and good additive response. The cyclopentane ring acts as an anchor to which alkyl groups can be attached to produce lubricants with good viscosity temperature properties and low pour points. The market FIGURE 10.7 Multiply alkyfor these fluids with unique properties will likely grow. lated cyclopentanes. 10.4.1.5.2 Esters Hermann Zorn in Germany first researched ester lubricants in the 1930s as a replacement for aircraft engine castor oil lubricants, notorious for sludge formation in higher temperature engines. In the U.S., the Naval Research Laboratory also experimented with esters in the 1940s. MIL-L-7808 first defined the ester gas turbine oil requirements in 1951. Revisions of MIL-L-7808 have led to MIL-PRF-7808 K, with Grade 3, a –54°C to 177°C (temperature given refers to the bulk oil temperature) fluid, and Grade 4, a –51°C to 204°C fluid. The U.S. Navy, having less severe low temperature needs, has its own specification, MIL-PRF-23699, with a standard STD type, a –40°C to 177°C oil, and a high temperature HTS type, a –40°C to 204°C oil. Commercial aircraft also use this product as gas turbine engine oil. The first ester lubricants were diesters and, as the temperature demands increased, esters became more complicated, for example, trimethylolpropane, pentaerythritol, and dipentaerythritol esters, as shown in Figure 10.8. Diesters are the least expensive, often similar in price to PAO fluids. As the ester functionality increases, the costs also increase. Diesters have the best viscosity–temperature properties compared to the more complicated esters. The pentaerythritol ester has very high autogenous ignition temperature for a specific viscosity, a property very important in gas turbine engine applications where engine nacelles are extremely hot and fires are disastrous. All esters are considered fire resistant compared to mineral oils of comparable viscosities. Ester lubricants have excellent oxidative stability and can be tailored to new applications. A wide variety of esters are commercially available. Esters are generally readily biodegradable because they react with water as the first step in degradation. One problem with esters in application however, is unwanted hydrolysis, although beta blocking (having an alkyl branch on the second carbon from the oxygen in the acid portion of the ester chain) does stabilize the molecule, both hydrolytically and oxidatively. Esters have many uses besides aircraft engines. Diesters are the base fluids for low temperature greases, e.g., MIL-PRF-23827, gear oils, and instrument oils. Many of the synthetic automotive motor oils are partially ester oils. O
O
R-O-C(CH2)xC-O-R
O CH3CH2CH2-C-[CH2-O-C-R'] 3 Trimethyol Propane Ester
Diester
O
FIGURE 10.8
O
C-[CH2-O-C-R"] 4
O-[CH2 -C-(CH2OC-R") 3]2
Pentaerythritol Ester
Dipentaerythritol Ester
Gas turbine oil esters.
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The U.S. Air Force is now developing the best possible thermally and oxidatively stable (–40°C to 232°C) ester for advanced engines (Gschwender et al., 2000). Improved and new higher-temperature fuels and structural engine materials, and a desire for improved fuel efficiency are leading the way for highertemperature gas turbine engine oils. Problems in development programs with high-temperature perfluoropolyalkylether candidate gas turbine engine oils, as will be discussed later, reinforced the need to develop the best ester-based gas turbine engine oil possible. A recent advancement in esters is the polymer ester, a copolymer of alphaolefins and unsaturated diesters. While they are more expensive than diesters, they have shown high benefit as antiwear blending fluids in about 20 to 30% concentration with other base fluids. The unpaired electrons on the oxygen in the ester are believed to bond to metal surfaces. Because the polymer esters often replace chlorinated cutting fluids, they offer environmentally safer fluids with good antiwear and viscosity–temperature properties. 10.4.1.5.3 Phosphate Esters Phosphate esters are widely used as excellent fire-resistant lubricants. In most flammability tests they are superior to other fireresistant fluids unless significant amounts of halogens (chlorine, fluorine, or bromine) replace the hydrogen in the molecules. The " general structure is shown in Figure 10.9, although the triaryl phosphates are also used as fire-resistant fluids. FIGURE 10.9 Phosphate ester — general formula. Advantages of phosphate ester fluids, besides their fire resistance, include excellent lubricity and bulk modulus. Phosphate esters must be closely monitored in the application to control hydrolysis (reaction with water) to form phosphoric acid on one or more of the P–O–R sites. When properly monitored, they are used with great success. Phosphate ester thermal and oxidative stability is fair, with improvements being made as described below. Another issue in using phosphate esters is compatibility of paints, wiring, and elastomeric seals. These materials must be carefully selected, excluding most materials typically used with mineral oils. For this reason, equipment maintainers must use extreme care not to cross-contaminate phosphate ester fluid with mineral oil, or other hydrocarbon fluids, and vice versa, as disastrous consequences will result. In the U.S. Air Force, for example, any aircraft using phosphate ester fluids is maintained in a separate area from aircraft using hydrocarbon-based fluids. Of synthetics, phosphate ester fluids are more expensive than all except the highly halogenated oils and polyphenylethers. Phosphate ester hydraulic fluids were introduced into commercial aircraft in the late 1950s and have gone through many “type” improvements since then. The fluid is described in the Society of Automotive Engineers document AS 1241. Currently Type IV, –54°C to 107°C, is used with low- and high-density versions, Classes 1 and 2 respectively. Type V is a higher thermal stability version for use in newer, highertemperature commercial aircraft and is currently used in some aircraft. Other uses of phosphate ester fluids are as lubricants, compressor fluids, coolants, brake fluids, and greases. When the user properly maintains the fluid, phosphate ester fluids provide excellent fire resistance in applications for which hydrocarbons are too flammable. Lower fire insurance rates may offset the extra expense of phosphate ester initial cost and monitoring. The excellent antiwear properties of phosphate esters, especially compared to water-based fluids, save on component replacement costs. 10.4.1.5.4 Silicon-Containing Fluids Silicate ester and silicone fluids are illustrated by the formula in Figure 10.10. Both contain Si–O bonds that impart unique properties to these fluids, namely very high viscosity–temperature index, low bulk modulus, and low surface tension. Many authors attribute these properties to flexibility of the molecule around the Si–O bond. These fluids are low volatility and have good fire resistance. The low surface tension of the silicone and silicate ester fluids is generally undesirable in a lubricating application because the oil tends to seep past seals to contaminate other surfaces. A third silicon-containing fluid is the silahydrocarbon, a tetralkylsilane (Figure 10.11). This fluid has the advantages of the other siliconcontaining fluids, while their negative properties are minimized. While silahydrocarbons are not used commercially as yet, they are promising for specialty applications.
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FIGURE 10.10
Silicon-containing fluids.
FIGURE 10.11
Silahydrocarbons.
377
10.4.1.5.5 Silicate Esters The silicate esters, MIL-C-47220, were once widely used as dielectric and plate coolants in many military radar systems, and as a high-temperature, –54°C to 177°C, hydraulic fluid, MIL-H-8446, in the B-58 aircraft. Silicate esters have excellent thermal stability and wide temperature range, but are very expensive. A disiloxane silicate ester hydraulic fluid is still used in the supersonic Concorde commercial aircraft. Both military specifications are now canceled. The silicate ester coolants have been largely replaced with C20 PAO-based fluids (MIL-PRF-87252) in the radar cooling application. One major drawback to silicate ester fluids is the hydrolysis of the Si–O–R bond to form a flammable alcohol and a gel. The alcohol is a safety hazard and the gel is responsible for clogging system filters and, in dielectric applications where the electronics are actually immersed in the coolant, the gel acts as a pathway for electrical arcing, disabling the electronic system. The resulting black strings of decomposed fluid are known in the industry as “black plague.” Most silicates are beta-blocked, that is, they have an ethyl group on the second carbon from the O atom. This interferes with the hydrolysis reaction, but does not totally stop it. The replacement, hydrolytically stable PAO-based fluids are also considerably less expensive than the silicate esters. While PAOs are not as good in viscosity–temperature properties as silicate esters, they are miscible and compatible and have worked well as drain-and-fill replacements wherever tried. 10.4.1.5.6 Silicones The R groups in the silicone fluids (Figure 10.10) can be methyl or other alkyl, phenyl, or alkyl, with some of the hydrogen substituted with either chlorine or fluorine. The greater the ratio of Si and O to hydrocarbon in the molecule, the higher the viscosity index, and the lower the thermal stability and surface tension, and vice versa. When these fluids decompose thermally they create an undesirable gel, similar to the gel from the hydrolytic decomposition of silicate esters. The chlorine or fluorine in some silicone fluids improves their thermal stability and also their antiwear characteristics. Silicone fluids have rather poor performance in wear properties of the base fluid by itself, and few additives are soluble or effective for antiwear benefit. Silicone fluids are now primarily used in greases.
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The greases are useful as wide temperature range products because of their excellent viscosity–temperature properties and good high-temperature performance. Currently, MIL-PRF-83261 is an alkyl substituted silicone-fluid grease, and MIL-PRF-83363 is a fluoroalkyl dimethyl copolymer-substituted silicone fluid grease. Solubility of additives is less of an issue for greases, as partially soluble or even insoluble additives can be used. Since much less grease is usually used, the higher cost of silicone greases is less of an issue than when a liquid lubricant is used. Other applications of silicone fluids are in synchronous motors, in precision equipment, with plastic and rubber parts of refrigerators and recording tape, as dielectric coolants, as brake fluids, and as damping fluids. 10.4.1.5.7 Silahydrocarbons Silahydrocarbon fluids (Figure 10.11) were first synthesized and characterized in the 1950s (Rosenberg et al., 1960). Their excellent, unique viscosity–temperature range and thermal stability were recognized, but these fluids froze at rather high temperatures. In the 1970s, silahydrocarbons were synthesized with good low-temperature properties by using various alkyl group lengths in the starting materials, allowing a –54°C to 316°C missile hydraulic fluid to be developed (Gschwender et al., 1981; Snyder et al., 1982). The fluid was never used, however, because the missile program was canceled. These fluids had one silicon atom that acted as an anchor for the hydrocarbon chains, giving the fluids good viscosity–temperature properties and low pour points. In the 1990s, University of Dayton Research Institute under contract to Wright-Patterson Air Force Base first synthesized high-molecular-weight silahydrocarbon spacecraft fluids with three or four silicon atoms. The result was the first candidate space fluid that was unimolecular. These fluids have volatility lower than any other space lubricant, except those based on Fomblin Z® perfluoropolyalkylether fluid. In addition, they have lower torque in wear applications than PAOs or multiply alkylated cyclopentane fluids, the newest synthetic space lubricants currently in spacecraft (Sharma et al., 1993b). Other variations of space silahydrocarbons have been synthesized under Air Force sponsorship. Recently NASA Glenn Research Center conducted vacuum wear tests, finding silahydrocarbon space fluids to perform extremely well (Jones et al., 1999). Other advantages of silahydrocarbons are: 1. They are fire resistant. 2. The properties can be tailored to new applications by making them higher or lower molecular weight. 3. They are compatible with other hydrocarbon fluids, an advantage in easy fluid conversion. 4. They have good bulk modulus; not quite as good as PAOs, but much better than other siliconcontaining fluids. 5. They have low traction properties, which means bearings operate with low internal friction. The major disadvantages are they are not commercially available as of this writing and are more expensive than other hydrocarbon synthetics. Potential silahydrocarbon fluid applications include fire-resistant, wide-temperature-range hydraulic fluids, space lubricants, and in niche commercial lubricants especially in precision bearings. Figure 10.12 shows the typical ASTM D92 flash points of hydraulic fluids. Three fluids with different base fluid chemical classes, all have –54°C viscosities of less than 2500 cSt. The flash point of the fourth fluid (MILPRF-83282), which has a –40°C viscosity of 2500 cSt, is also shown for comparison. The silahydrocarbon has the highest flash point or the greatest safety margin, compared to the mineral oil (MIL-H-5606) and PAO (MIL-PRF-87257) fluids (all –54°C operational fluids). Also, several commercially available additives have been found to be both soluble and effective antiwear additives for silahydrocarbons. 10.4.1.5.8 Chlorotrifluoroethylene Polymers Chlorotrifluoroethylene fluids (CTFEs) were developed in the 1940s for the Manhattan Project and have enjoyed a niche market since then. They are represented by the formula Cl(CClFCCl2)nF. They are nonflammable by any practical definition and can be used in contact with liquid oxygen and other aggressive
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FIGURE 10.12
379
Comparative ASTM D92 flash point of mineral oil, PAO, and SiHC.
materials totally unsuitable for hydrocarbon lubricant contact. CTFEs are more expensive than synthetic hydrocarbon fluids but are a less expensive alternative to perfluoropolyalkylethers (PFPAEs) for demanding applications. CTFEs have good stability (up to 177°C) and excellent viscosity–temperature range. They have bulk moduli almost as good as that of hydrocarbon fluids and much better than that of the PFPAEs. Another advantage is they solubilize many of the commercially available hydrocarbon additives, although many of those additives are ineffective in CTFE (Gschwender et al., 1992). A major disadvantage of CTFE fluids is their high density, approximately double that of hydrocarbon fluids. Also, they react with copper and low chrome steels, which should be avoided in components. Also, as mentioned earlier, their cost is considerably higher than many people expect to pay for oil. In the 1970s the U.S. Air Force selected a CTFE oligomer as the base fluid for a –54°C to 177°C nonflammable hydraulic fluid, MIL-H-53119. Considerable research and development advanced the knowledge of both the fluid and components designed for use with it. In the end, it was not selected for aircraft application beyond test aircraft because it was considered too high a risk. MIL-H-53119 contains an additive package with both an antiwear additive and an antirust additive to make it a usable, effective, nonflammable hydraulic fluid. Extensive testing by the U.S. Air Force and others allayed concerns about the potential toxicity and ozone depletion effects of CTFE. Current commercial applications of higher-molecular-weight CTFE fluids are as gyroscope flotation fluids, vacuum pump oils, and metal-working lubricants. 10.4.1.5.9 Polyphenylethers Polyphenylethers (PPEs) (Figure 10.13) were first developed as the gas turbine engine oil for the SR-71 reconnaissance aircraft in the 1960s. MIL-L-87100 was written to describe these fluids. PPEs have excellent high-temperature oxidative stability, excellent bulk modulus, low volatility, and good fire resistance. Their major disadvantages are poor low-temperature flow, which is partially improved by isomer mixtures of meta and para linkage of the benzene rings by the oxygen atom, and poor lubricity. The five phenylether with isomer mixture has a pour point of –4°C. In the SR-71, one scheme to keep the PPE liquid at lower temperatures was to dilute it with solvent. After the engine heated from operation, the solvent would boil out, leaving the PPE engine oil. Needless to say, today, such a plan would not be environmentally acceptable. PPEs have poor inherent lubricating ability, and antiwear additives have not been highly successful. Besides these problems, PPEs are quite expensive because of the many synthesis steps required
FIGURE 10.13
Polyphenylethers.
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FIGURE 10.14
Modern Tribology Handbook
Perfluoropolyalkylethers.
to produce them. Since the SR-71 aircraft was inactivated in the 1980s (except for a few test aircraft used by NASA) PPEs, the 5- and 6-ring fluids, now have only a small market as electronic contact lubricants and as vacuum pump oils. 10.4.1.5.10 Perfluorinated Fluids Perfluoropolyalkylether (PFPAE) fluids were introduced in the 1960s and have been intensely studied ever since, owing to their unique thermal and oxidative stability, nonflammability, and inertness to highly reactive materials. Four classes are generally recognized, as shown in Figure 10.14. The physical properties and stability of PFPAE fluids depend primarily on the carbon-to-oxygen ratio of the fluid and to a lesser, but significant, extent on the amount of branching and the presence of less stable OCF2O linkage. Major limitations of PFPAE fluids are high cost, corrosive wear in the presence of some metals, especially steel and aluminum, and autocatalytic degradation in the presence of metal oxides/Lewis acids. Companies that produce PFPAEs, the U.S. Air Force, NASA Glenn Research Center, and, more recently, the recording media industry have led the research on PFPAE fluids. To briefly summarize the experience in the authors’ laboratory on the types of PFPAE fluids, the K fluids have the highest thermal and oxidative stability, but the poorest viscosity–temperature properties and highest volatility. The Y fluids have viscosity–temperature and stability properties similar to the K fluids. The Z fluids have exceptional viscosity–temperature properties and volatility, but the highest cost and the poorest thermal and oxidative stability of the PFPAE fluids. Z fluids are also the most reactive to metals. M fluids are similar to Z fluids, but cost less and have somewhat higher volatility. The D fluids, the newest commercially available materials, have good viscosity–temperature properties and excellent thermal and oxidative stability, almost as good as the K fluids. A further advantage of the D fluids is their lower cost compared to the other three fluids. PFPAEs with functional end groups are used successfully for niche applications, such as by the recording media industry as monolayer surface modifiers to reduce friction and stiction. Soluble additives for PFPAE fluids were first synthesized by the U.S. Air Force (Tamborski and Snyder, 1977). Since then the PFPAE fluid producers and some other groups have expanded the list of additives to combat corrosive wear and catalytic degradation (Srinivasan et al., 1993; Gschwender et al., 1993). PFPAEs are used in contact with reactive materials in wide-temperature-range applications and where a small amount of lubricant is sufficient. Greases based on PFPAE fluids, MIL-PRF-27617, are used in aircraft high-temperature applications and in many commercial applications.
References Anonymous (1972), First lubricant-oil cracker has trouble-free record, Oil Gas J., 70, 94-97. Bui, K. (1999), A defining moment for synthetics — part 2, Lubr. World, 9, 35-37. Flanagan, S.R., Gschwender, L.J., Pekarek, B., Cupples, B., Maeder, A., Bavani, S., Tacco, D., Strong, R., and Letton, G., (1991), PAO coolant conversion workshop proceedings, WL-TR-91-4108, accession number B159981. Available from DODSOP Subn. Serv. Desk, 700 Robbins Ave., Philadelphia, PA 19111.
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381
Gschwender, L.J., Anderson, D.R., and Chen, G. (1981), Development of high temperature –54° to 316°C hydraulic fluids for Advanced Strategic Air Launched Missile (ASALM) application, AFWAL-TR81-4163. Gschwender, L. J., Snyder, C.E., Jr., and Sharma S.K. (1988), Pump evaluation of hydrogenated polyalphaolefin candidates for a –54°C to 135°C fire-resistant Air Force aircraft hydraulic fluid, Lubr. Eng., 44, 324-329. Gschwender, L.J., Snyder, C.E., Jr., VanBrocklin, C.H., and Warner, W.M. (1992), Chlorotrifluoroethylene oligomer based nonflammable hydraulic fluid, I. fluid, additive and elastomer development, J. Syn. Lubr., 9, 188-203. Gschwender, L.J., Snyder, C.E., Jr., and Fultz, G.F., (1993) Soluble additives for perfluoropolyalkylether liquid lubricants, Lubr. Eng., 49, 702-708. Gschwender, L.J. and Snyder, C.E., Jr. (1999), Advances in U.S. Air Force hydraulic fluids, J. Syn. Lubr., 16, 35-50. Gschwender, L.J., Snyder, C.E., Jr., Nelson, L., Carswell, L., Fultz, G.W., and Saba, C. (2000), Research and development of advanced high-temperature Air Force turbine engine oil, Lubr. Eng., 55. Gupta, P.K. (1984), Advanced Dynamics of Rolling Elements, Springer-Verlag, New York. Hamrock, B.J. (1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. Hatton, R. (1966), Fire Resistance of Hydraulic Fluids, ASTM Special Publication 406, American Society for Testing and Materials, Philadelphia. Heilman, W. J., Chiu, I.C., and Chien, J.C.W. (1999), New polyalphaolefin base oils, Amer. Chem. Soc., Div. of Petrol. Chem., PREPRINTS, 44, 248-250. Helmick, L.S., Gschwender, L.J., Sharma, S.K., Snyder, C.E., Jr., Liang, J.C., and G.W. Fultz (1997), The effect of humidity on the wear behavior of bearing steels with RfO(n-C3F6O)xRf perfluoropolyalkylether fluids and formulations, Trib. Trans., 40, 3, 393-402. Hentschel, K.H. (1985), The influence of molecular structure on the frictional behavior of lubricating fluids, J. Syn. Lubr., 2, 2, 143-165. Howell, R.L. (2000), Hydroprocessing routes to improved base oil quality and refining economics, 6th Annual Fuels and Lubes Conference, Singapore, Fuels & Lubes Asia Publications, Manila. Jones, W.R., Jr., Shogrin, B.A., and Jansen, M.J. (1998), Research on liquid lubricants for space mechanisms, Proceedings from the 32nd Aerospace Mechanism Symposium, NASA, Washington, D.C., 299-310. Jones, W.R., Jr., Poslowski, A.G., Shogrin, B.A., Herrera-Fierro, P., and Jansen, M.J. (1999), Evaluation of several space lubricants using a vacuum four-ball tribometer, Trib. Trans., 42, 317-323. Kramer, D.C., Ziemer, J.N., Cheng, M.T., Fry, C.E., Reynolds, R.N., Lok, B.K., Krug, R.R., and Sztenderowicz, M.L. (1999), Influence of group II and III base oil composition on VI and oxidation stability, AIChE Spring Meeting Paper 46a. Min, P.Y. (1998), VHVI base oils: supply and demand, 4th Annual Fuels and Lubes Conference, Singapore, Paper 30, Fuels & Lubes Asia Publications, Manila, 30-1. National Petroleum Refiners Association (1999), 1999 Lubricating Oil and Wax Capacities of Refiners and Re-Refiners in the Western Hemisphere, NPRA, Washington, D.C. Palacios, J.M. and Bajon, M.L. (February 1983), Effective viscosity of oils containing VI improvers and its relation to wear, Trib. Intl., 27-31. Rai, A.K., Massey, M., Gschwender, L., Snyder, C., Zabinski, J., and Sharma, S. (1999), Performance evaluation of some Pennzane-based greases for space applications, 33rd Aerospace Mechanisms Symposium Proceedings, NASA/CP-1999-209259, 213-220. Rosenberg, H., Groves, J.D. and Tamborski, C. (1960), Organosilicon compounds: I. Synthesis of some long-chain tetraalkylsilanes, J. Org. Chem., 25, 243-246. Sequeira, A., Jr. (1994), Lubricant Base Oil and Wax Processing, Chemical Industries Series, Vol. 60, Marcel Dekker, New York. Sharma, S.K., Forster, N.H., and Gschwender, L.J. (1993a), Effect of viscosity index improvers on the elastohydrodynamic lubrication characteristics of a chlorotrifluoroethylene and a polyalphaolefin fluid, Trib. Trans., 36, 3, 555-564.
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Sharma, S.K., Snyder, C.E., Jr., and Gschwender, L.J. (1993b), Tribological behavior of some candidate advanced space lubricants, Trib. Trans., 36, 321-325. Sharma, S.K., Höglund, E., Hamrock, B.J., and Rosado, L. (1995), Rheology of perfluoropolyalkylether fluids in elastohydrodynamic lubrication, Trib. Trans., 38, 4, 769-780. Sharma S.K., Snyder, C.E., Jr., Gschwender, L.J., Cecere, G.J., and Jenney, T.A. (1998), Endurance pump tests with fresh and purified MIL-H-5606 hydraulic fluid, AFRL-ML-WP-TR-1998-4211. Sharma S.K., Snyder, C.E., Jr., Gschwender, L.J., Cecere, G.J., and Jenney, T.A. (1999), Endurance pump tests with fresh and purified MIL-PRF-83282 hydraulic fluid, AFRL-ML-WP-TR-1999-4185. Snyder, C.E., Jr., Krawetz, A.A. and Tovrog, T. (1981), Determination of the flammability characteristics of aerospace hydraulic fluids, Lubr. Eng., 37, 705-714. Snyder, C. E., Jr., Gschwender, L.J., Tamborski, C., Chen, G.J. and Anderson, D.R., (1982), Synthesis and characterization of silahydrocarbons — a class of thermally stable wide-liquid-range functional fluids, ASLE Trans., 9, 299-308. Snyder, C.E., Jr. and Gschwender, L.J. (1991), Perfluoropolyalkylethers — liquid lubricants of the future?, Advances in Engineering Tribology, Chung, Y.P. and Cheng, H.S. (Eds.), STLE, Park Ridge, IL, SP-31, 216. Srinivasan, P., Corti. C., Montagna, L. and Salvelli, P. (1993), Soluble additives for perfluorinated lubricants, J. Syn. Lubr., 10, 143-164. Stormont, D.H. (1959), New process has big possibilities, Oil Gas J., 57, 44, 48-49. Tamborski C. and Snyder, C.E., Jr. (1977), U.S. Patent 4,011,267, Perfluoroalkylether substituted aryl phosphines and their synthesis. Zakarian, J.A., Robson, R.J. and Farrell, T.R. (1987), All-hydroprocessing route for high-viscosity index lubes, Energy Progress, 7, 59-64.
For Further Information An excellent book on lubricant classes and properties is Synthetic Lubricants edited by Reigh C. Gunderson and Andrew W. Hart. The book is out of print, but if you are lucky enough to find one, it is a real treasure. A newer, also excellent book, is Synthetic Lubricants and High-Performance Functional Fluids, edited by Lester R. Rudnick and Ronald L. Shubkin. The military technical reports (containing–TR–designations) referred to in this chapter are available from DTIC (Defense Technical Information Center), 8725 John J. Kingman Road, Ste. 0944, Ft Belvoir, VA 22060-6218. The military specifications referred to in this chapter are available from Standardization Document Order Desk, Bldg. 4D, 700 Robbins Ave., Philadelphia PA 19111-5094. Aerospace Standards AS1241, “Fire Resistant Phosphate Ester Hydraulic Fluid for Aircraft,” and AIR1362, “Aerospace Hydraulic Fluid Physical Properties,” are available from SAE, 400 Commonwealth Dr., Warrendale PA 15096. Factory Mutual Research in Norwood, MA, is the most well-known organization for the testing and certification of fire-resistant fluids and can be accessed at www.fmglobal.com.
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11 Hydrodynamic and Elastohydrodynamic Lubrication 11.1 Basic Equations .................................................................. 384 Lubrication Approximation • The Reynolds Equation • The Energy Equation
11.2 Externally Pressurized Bearings ........................................ 391 Annular Thrust Pad • Optimization • Operation with Capillary Restrictor
11.3 Hydrodynamic Lubrication ............................................... 398 Journal Bearings • Thrust Bearings
11.4 Dynamic Properties of Lubricant Films........................... 422 Linearized Spring and Damping Coefficients • Stability of a Flexible Rotor
11.5 Elastohydrodynamic Lubrication ...................................... 438
Andras Z. Szeri University of Delaware
Contact Mechanics • Dimensional Analysis • FilmThickness Design Formulas • Minimum Film Thickness Calculations
The friction force generated when two bodies rub against each other can be drastically decreased, and the subsequent wear almost entirely eliminated, if a lubricant is interposed between the surfaces in contact. Lubricants are generally considered to be oils, particularly petroleum oils because we have so much experience with them. However, almost any material can be a lubricant. As da Vinci observed 400 years ago, “All things and anything whatsoever, however thin it be, which is interposed in the middle between objects that rub together lighten the difficulty of this friction.” Nevertheless, in this chapter lubrication with fluids, in particular incompressible fluids, is the only type of lubrication that will be discussed. The equations that describe lubrication with continuous fluid films are derived from the basic equations of fluid dynamics through specialization to the particular geometry of the typical lubricant film; lubricant films are distinguished by their small thickness relative to their lateral extent. If Ly and Lxz denote the characteristic dimensions across the film thickness and the ‘plane’ of the film, respectively, as indicated in Figure 11.1, then typical industrial bearings are characterized by (Ly /Lxz) = O(10–3). This fact alone, and the assumption of laminar flow, allows us to combine the equations of motion and continuity into a single equation in lubricant pressure, the so called the Reynolds equation. The theory of lubrication is concerned with the solution of the Reynolds equation, sometimes in combination with the equation of energy, under various lubricating conditions. When the surfaces are deformable, as in rolling contact bearings or human and animal joints, the equations of elasticity and the pressure dependence of lubricant viscosity must also be included in the solution of the problem.
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FIGURE 11.1
11.1
Schematic of lubricant film.
Basic Equations
The flow of an incompressible, constant viscosity fluid is governed by the equations of motion, the socalled Navier–Stokes equation (Szeri, 1998),
∂v ρ + v ⋅∇v = −∇p + µ∇ 2 v + ρf ∂t
(11.1)
div v = 0
(11.2)
(
)
and the equation of continuity
We render these equations dimensionless by normalizing the orthogonal Cartesian coordinates (x,y,z) with the corresponding length scales and the velocities with the velocity scales, U* in the in the x-z plane and V* perpendicular to it
x = L xz x , y = L y y , z = L xz z
(11.3a)
u = U ∗u , v = V∗v , w = U∗w
(11.3b)
We note that the characteristic velocity in the y direction, V*, cannot be chosen independent of U*, as the terms in the equation of continuity must balance. Substitution of Equation 11.3 into Equation 11.2 yields
∂u V∗L xz ∂v ∂w + + =0 ∂x U∗L y ∂y ∂z
(11.4)
indicating that the terms of the continuity equations will balance provided that
()
V∗L xz =O 1 U∗L y
or
L V∗ = y U∗ L xz
(11.5)
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This establishes the velocity scale in the y direction. To nondimensionalize pressure and time we choose
p = re
p , ρU ∗2
t = Ωt
(11.6)
– The reduced Reynolds number, re, and the nondimensional frequency, Ω, have the definition
L LU re = y y ∗ L xz ν
(
L L y L xz Ω and Ω = y ν L xz
)
where Ω is the characteristic frequency of the system. For journal bearings, the characteristic frequency is related to the rotational velocity of the journal. Taking the shaft surface speed as the characteristic velocity, U* = Rω, and the journal radius as the characteristic length in the “plane” of the bearing, Lxz = – R, we have re ≈ Ω. Making use of this approximation, we write the equations of motion and continuity in terms of the normalized quantities as 2
∂u ∂u ∂u ∂u ∂p ∂2u L y ∂2u ∂2u re +u +v +w = − + + + ∂x ∂y ∂z ∂x ∂y 2 L xz ∂x 2 ∂z 2 ∂t Ly L xz
2
2 2 2 2 r ∂v + u ∂v + v ∂v + w ∂v − ∂ v − L y ∂ v + ∂ v = − ∂p e ∂t ∂x ∂y ∂z ∂y 2 L xz ∂x 2 ∂z 2 ∂y
(11.7a)
(11.7b)
2
∂w ∂w ∂w ∂w ∂p ∂2w L y ∂2w ∂2w re +u +v +w = − + + + ∂x ∂y ∂z ∂z ∂y 2 L xz ∂x 2 ∂z 2 ∂t
(11.7c)
∂u ∂v ∂w + + =0 ∂x ∂y ∂z
(11.8)
11.1.1 Lubrication Approximation Resulting from the normalization in Equations 11.3 and 11.6, we anticipate that each of the variable terms in Equations 11.7 and 11.8 are of the same order, say O(1). But then the relative importance of the variable terms is decided only by the magnitude of the dimensionless parameters (Ly /Lxz) and re that multiply them. Under normal conditions lubricant films are thin relative to their lateral extent. For liquid lubricated bearings (Ly /Lxz) = O(10–3). For gas bearings a film thickness of h ≈ 2.5 µm is not uncommon. The socalled lubrication approximation of Reynolds is developed under the assumptions that (Ly /Lxz) → 0 and re → 0. Under these conditions Equations 11.7 indicates that
( )
∂p = O 10 −6 ∂y and Equations 11.7 and 11.8 reduce to
while
∂p ∂p ≈ =O 1 ∂x ∂z
()
(11.9)
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∂p ∂ 2u =µ 2, ∂x ∂y
∂p = 0, ∂y
∂p ∂ 2w =µ 2 ∂z ∂y
(11.10)
∂u ∂v ∂w + + =0 ∂x ∂y ∂z
(11.11)
written now in terms of the primitive variables.
11.1.2 The Reynolds Equation The second part of Equation 11.10 asserts that to the order of approximation employed here, the pressure is invariant in the y direction, i.e., across the film. But then the first and last parts of Equation 11.10 can be integrated to obtain
u=
1 ∂p 2 y + Ay + B 2µ ∂x
(11.12a)
w=
1 ∂p 2 y + Cy + D 2µ ∂z
(11.12b)
The integration constants A, B, C, D are evaluated with the aid of the boundary conditions on velocity (Figure 11.1),
u = U1, w = 0 at y = 0
(11.13)
u = U 2 , w = 0 at y = h to obtain the velocity components in the plane of the bearing
u=
y 1 ∂p 2 y y − yh + 1 − U1 + U 2 2µ ∂x h h
(
)
(
1 ∂p 2 w= y − yh 2µ ∂z
(11.14)
)
The pressure distribution appearing in Equation 11.14 is not arbitrary but must be such that the equation of continuity is satisfied. For this, we substitute Equation 11.14 into the averaged (across the film) equation of continuity, which, upon interchanging the indicated differentiation and integration, becomes
[v] (
h x,t 0
)
=− −
∂ 1 ∂p ∂x 2µ ∂x ∂ ∂x
∫
( )
∂ 1 ∂p ∫ ( y − yh)dy − ∂z 2µ ∂z ∫ ( y − yh)dy 2
0
h x,t
2
0
( )
h x,t
0
( )
h x,t
y ∂h y 1 − U1 + U 2 dy + U 2 h ∂x h
(11.15)
Recognizing that
[v] (
h x,t y =0
)
(
)
= − V1 − V2 =
dh dt
(11.16)
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where V1, V2 are the normal, i.e., approach, velocities of the bearing surfaces, we obtain the Reynolds equation that governs the pressure distribution in a lubricant film (Szeri, 1998)
(
)
∂ U1 + U 2 ∂ h 3 ∂p ∂ h 3 ∂p ∂h + 12 V2 − V1 + + 6h = 6 U1 − U 2 ∂x ∂x µ ∂x ∂z µ ∂z ∂x
(
)
(
)
(11.17)
If the relative motion between the surfaces in contact is pure translation, as is in conventional thrust bearings, Equation 11.17 can be cast in the form
∂ h 3 ∂p ∂ h 3 ∂p ∂h + = 6U 0 + 12V0 ∂x µ ∂x ∂z µ ∂z ∂x
(11.18)
where
U 0 = U1 − U 2 ,
V0 = V2 − V1
and we assume that ∂(U1 + U2)/∂x = 0. If, however, relative rotation of the surfaces is encountered, as in journal bearings, then a component of the rotational velocity will augment the relative motion in the tangential direction (see Figure 11.10) as the surfaces are not parallel. Equation 11.17 now takes the form
∂ h 3 ∂p ∂ h 3 ∂p ∂h + = 6U 0 + 12V0 ∂x µ ∂x ∂z µ ∂z ∂x
(11.19)
Here U0 = U1 + U2 and V0 = V2 – V1. Thus while in thrust bearings it is the difference in tangential velocities that creates pressure, in journal bearings it is their sum; if journal and bearing rotate in opposite directions but with the same speed, there is no pressure generated. However, for both journal and thrust bearings positive pressures are generated only when the film is convergent, both in space and time.
U0
∂h ∂h < 0, <0 ∂x ∂t
(11.20)
11.1.2.1 Turbulent Flow For turbulent flow of the lubricant, most theories currently in use yield a formally similar Reynolds equation, but now the film thickness is weighted by the functions kx1/3 and kz1/3, respectively, in the direction of relative motion and perpendicular to it (Szeri, 1998). For a journal bearing, the turbulent Reynolds equation takes the form
∂ h 3 ∂P ∂ h 3 ∂P 1 ∂h + = U ∂x µk x ∂x ∂z µkz ∂z 2 0 ∂x
(11.21a)
–
where P is the average value of p. The weighting functions are related (in Constantinescu’s model) to the local Reynolds number as
(
k x = 12 + 0.53 k 2 Re h
)
0.725
(11.21b)
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(
kz = 12 + 0.296 k 2 Re h
)
0.65
(11.21c)
and the local Reynolds number, Reh = Rωh/v, is calculated from the reduced Reynolds number through Reh = re(h/C)(R/C). 11.1.2.2 Surface Roughness Surface roughness should be taken into account if it is excessive. This can be done by applying the Patir–Cheng flow factors (Patir and Cheng, 1978), obtained by numerically solving the Reynolds equation – for microbearings possessing real, rough, surfaces (Figure 11.2). To calculate the pressure flow factors φx – and φz, the microbearing is subjected to mean pressure gradients (p1 – p2)/(x2 – x1) and (p1 – p2)/(z2 – z1), respectively, where (x2 – x1)(z2 – z1) is the projected area of the microbearing. The pressure flow factor φx, for example, is calculated from
∂p φx = h ∂x
( (
p −p h 3 2 1 x2 − x1
) )
where the overscore bar indicates statistical averaging. In the next step, the flow factors themselves are averaged, having been calculated for a large number of statistically identical microbearings. The Reynolds equation for rough surfaces now takes the form
∂ h 3 ∂p ∂ h 3 ∂p U1 + U 2 ∂h U1 − U 2 ∂φs ∂h φx φ σ + = + + 2 2 ∂x 12µ ∂x ∂z z 12µ ∂z ∂x ∂x ∂t
(11.22)
where σ is the standard deviation of the surface roughness.
11.1.3 The Energy Equation It is well to remember that bearings rarely operate in the isothermal mode. In almost all cases of practical bearing operations, sufficient heat is generated by dissipation to invalidate the isothermal assumption. Some of the generated heat is conducted away, predominantly by the bearing pad, but the remainder is used to increase the temperature of the lubricant. Increasing the temperature of the lubricant changes its viscosity, and as the rate of heat generation in the film is nonuniform, so will be the viscosity distribution. Under conditions of light load, low speed, and large bearing-thermal capacity, bearing performance can be adequately predicted when using an average or operating viscosity, obtained by iteration between the bearing performance charts and the viscosity–temperature chart (Szeri, 1998). In other, more general cases, the actual point by point variation of the lubricant’s viscosity must be taken into account; thus the fluid equations and the energy equations must be solved simultaneously (Suganami and Szeri, 1979). The equation of energy for a heat-conducting Newtonian fluid is
ρ
( ) = − pdiv v + µΦ + div (k gradT )
d c vT dt
(11.23)
If the fluid is incompressible cv = cp = c and –pdivv = 0 by Equation 11.2. Assuming further that the heat conductivity is constant, Equation 11.23 becomes
∂2T ∂2T ∂2T ∂T ∂T ∂T ∂T = ρc +u +v +w k ∂x 2 + ∂y 2 + ∂z 2 + µΦ ∂x ∂y ∂z ∂t
(11.24a)
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FIGURE 11.2 Flow factors for rough surfaces, (a) pressure flow factor, (b) shear flow factor. (From Patir, N. and Cheng, H.S. (1979), Application of average flow model to lubrication between rough sliding surfaces, ASME J. Lub. Tech., 101, 220-30. With permission.)
In orthogonal Cartesian coordinates the dissipation function is
∂u 2 ∂v 2 ∂w 2 ∂u ∂v 2 ∂v ∂w 2 ∂w ∂u 2 + Φ = 2 + + + + + + + ∂x ∂y ∂z ∂y ∂x ∂z ∂y ∂x ∂z
(11.24b)
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Applying the lubrication approximation, Equations 11.3 and 11.6, we obtain
u
∂u 2 ∂w 2 1 ∂2T ∂T ∂T ∂T + +v +w = + Λ µ ∂x ∂y ∂z Pe ∂y 2 ∂y ∂y
(11.25)
where the Peclet number and the dissipation number have the definition, respectively,
µ ωL Λ = ∗ xz ρcT∗ L y
cµ Pe = ∗ re , k
2
– the starred quantities are evaluate in the reference state, and T = UT/T*, µ– = µ/µ*. The thermohydrodynamic (THD) theory of fluid film lubrication accounts for pointwise variation of lubricant viscosity and relies on the simultaneous solution of Equation 11.25, the equation of heat conduction in the bearing, and the extended form of the Reynolds equation that is written for variable viscosity (Suganami and Szeri, 1979)
( (
) )
ξ2 x , h, z ∂ Γh 3 ∂P ∂ Γh 3 ∂P ∂ + = − U h + V0 0 ∂x µ∗ ∂x ∂z µ∗ ∂z ∂x ξ1 x , h, z
(11.26)
for journal bearings and
( (
) )
∂ Γh 3 ∂P ∂ Γh 3 ∂P ∂ ξ2 x , h, z + V0 + = U0 ∂x µ∗ ∂x ∂z µ∗ ∂z ∂x ξ1 x , h, z
(11.27)
for slider bearings. Here we employed the notation
) ((
) ( )
ξ2 x , h, z Γ x , z = − ξ 2 x , y , z − ξ1 x , y , z ξ1 x , h, z 0 1
( ) ∫ ( (
η
) ∫ µ( x , y , z ) ,
ξ1 x , η, z =
0
dy
(
) dy
η
) ∫ µ(xydy, y, z )
ξ2 x , η, z =
0
11.1.3.1 Effective Viscosity In numerous applications, the temperature rise in the lubricant remains relatively small and uniform throughout the film. In these cases the isothermal theory will provide useful approximations to actual bearing performance, provided that an average or effective viscosity value that is compatible with the bearing temperature rise is used in the computations (Kaufman et al., 1978). This calculation might be based on the assumptions that: 1. All heat, H, generated in the film by viscous dissipation is removed from the bearing by the lubricant. 2. The lubricant that exits the bearing by its sides has an average temperature Ts = (Ti + ∆T/2), where ∆T = To – Ti is the average temperature rise across the bearing.
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This average temperature rise, ∆T, can be calculated from a simple energy balance
[ (
)]
∆t = H ρc Q − Qs 2
(11.28)
For typical petroleum oils ρc ≈ 1.39 MPa/C and ρc = 4.06 MPa/C for water.
11.2
Externally Pressurized Bearings
The operation of externally pressurized bearings is simple in principle. Figure 11.3a shows a hydrostatic pad with the runner covering the recess and resting on the land, sealing the pressurized lubricant in the recess. As there is no flow, the recess pressure equals the supply pressure. Increasing the supply pressure to the point that the pressure force on the runner equals the external load, the runner lifts off the land and flow out of the recess commences, as indicated in Figure 11.3b. As now there is flow, the pressure force over the recess becomes somewhat smaller than before, but this decrease is compensated by the pressure force developed over the land, and the total pressure force still equals the external load. Increasing (decreasing) the supply pressure ps, the recess pressure pr will simply adjust itself through increasing (decreasing) the film thickness so that the generated pressure force always balances the external load. To deal with unsymmetrical load distribution, two or more hydrostatic pads are applied in conjunction with flow restrictors (compensated hydrostatic bearing). Flow restrictors are simple devices, such as capillaries, orifices, or flow-control valves, for which a small change in flow rate results in a large pressure drop across the device. Figure 11.4 is a schematic of a two-pad hydrostatic bearing, equipped with flow restrictors. The two recesses are fed from a common pressurized manifold. When the load is distributed symmetrically, the film thickness over the two pads has the same value, leading to equal recess pressures (Position I). If now the external load vector is disturbed so that the film thickness decreases over pad A (Position II), the flow rate across the flow-control device in that same pad is decreased. As there is now less pressure drop across the restrictor due to the decreased flow rate, the recess pressure in pad A will increase and yield a righting moment. Ordinarily, hydrostatic bearings are characterized by constant film thickness h = 0. Then the Reynolds equation valid for simple relative translation of the bearing surfaces, Equation 11.18, reduces to
∂2 p ∂2 p + =0 ∂x 2 ∂z 2
(11.29)
FIGURE 11.3 Hydrostatic bearing schematics (a) before and (b) after lift-off. (From Szeri, A.Z. (1998). Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
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FIGURE 11.4 Schematic of a two-pad compensated hydrostatic bearing, (I) symmetrical, (II) unsymmetrical load distribution. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
The boundary conditions that accompany Equation 11.29 are
p = pr on Γ1 p = pa on Γ2
(11.30)
where Γ1 and Γ2 represent inside (recess) and outside contours, respectively, of the pad. Equation 11.29, subject to boundary conditions Equation 11.30, is easily solved in any of several orthogonal curvilinear coordinate systems where Laplace’s equation separates, provided that Γ1, Γ2 are composed of coordinate lines. Otherwise, though the solution is still elementary, it must be performed on the computer. Irrespective of the method of solution, i.e., analytical or numerical, and the geometry and size of the bearing pad, the performance of hydrostatic bearings can be written in terms of a set of dimensionless parameters: the load factor af , the flow factor qf , and the loss factor hf . If W, Q, Hp , Hf represent the external load, the lubricant flow, the pressure power loss, and the frictional power loss, respectively, then we can write
W = a f Apr
(11.31a)
h3 p µ r
(11.31b)
H p = qf
h3 p p µ r s
(11.31c)
H f = hf
µU M2 A h
(11.31d)
Q = qf
Here A is the combined area of pad and recess, ps is the supply pressure, pr is the recess pressure, and UM is the maximum relative velocity between pad and runner.
11.2.1 Annular Thrust Pad We illustrate the evaluation of the load, flow, and friction factors on the analytically simplest of hydrostatic pads, the annular thrust pad. The geometry is characterized by the inner (recess) radius R1 and the outer (pad) radius R2 > R1. We use the pad radius and the recess pressure to normalize Equations 11.29 and 11.30
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p = pr p,
r = R2r
(11.32)
and obtain
d dp r = 0 dr dr
(11.33a)
in place of Equation 11.29, while the boundary conditions take the form
R1 , R2
p = 1 at r =
p = 0 at r = 1
(11.33b)
Integrating of Equation 11.33a and enforcing the boundary conditions, Equation 11.33b, lead to
ln r ln R1 R2
p=
(
(11.34)
)
Having found the pressure distribution, we are ready to evaluate the performance of the pad. Load capacity: 2 R1 2 W = πR pr + 2π rpdr = πR pr + R2 ln R1 R2 R1 R2
∫
2 1
=
2 2
(
( ) Ap 2 ln( R R )
1
r ln rdr R2
) ∫ R1
(11.35a)
2
1 − R1 R2
r
2
1
Flow rate: h
∫
Q = 2πrur dy =
h 3 pr π 6 ln R2 R1 µ
)
(11.35b)
h 3 ps pr π µ 6 ln R2 R1
(11.35c)
0
(
where
ur =
(
1 dp y y −h 2µ dr
)
is the (radial) flow velocity, obtained as in Equation 11.14. Pumping power:
H p = psQ =
(
)
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Frictional power loss:
Hf =
∫
R2
rωτdA =
(
1 − R1 R2
)
4
2
R1
µU M2 A h
(11.35d)
where τ = µdur /dr is the shear stress on the runner. A comparison of Equations 11.31 to 11.35 yields
af
( ) = 2 ln( R R )
(11.36a)
π 6 ln R2 R1
(11.36b)
2
qf =
hf =
2
1 − R1 R2
1
(
)
(
)
1 − R1 R2
4
(11.36c)
2
The total power loss is the sum of frictional loss and pumping power
HT = H p + H f = q f
µU M2 A h3 pr ps + h f µ h
(11.37)
11.2.2 Optimization The curves of Figure 11.5 indicate the existence of optimum values hopt , µopt of the film thickness and the viscosity, respectively, defined by the conditions
∂H T = 0, ∂h
∂H T =0 ∂µ
(11.38)
Substitution of HT from Equation 11.37 into Equation 11.38 yields the optimum film thickness at constant viscosity and the optimum viscosity at constant film thickness, respectively (Szeri, 1998) 14
hopt
h µ 2U M2 A = f , 3q f pr ps
µ opt
q h4 p p = f 2r s hf U M A
12
(11.39a,b)
Substituting Equation 11.39a into Equations 11.31c and 11.31d, we find that at constant viscosity the total power loss is minimum when Hf /Hp = 3 and the total power consumption of the bearing is
H T ,hopt =
4 3
34
(q h p p µ U A ) f
3 f r
2
s
6 M
3
14
(11.40a)
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FIGURE 11.5 Power loss for an annular hydrostatic bearing as function of (a) the dimensionless film thickness and (b) the dimensionless velocity. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
When Equation 11.39b is used, we find that Hf /Hp = 1 and the minimum power at constant film thickness is
H T ,µopt = 2 q f h f Apr ps hU M
(11.40b)
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Obviously, the conditions Hf /Hp = 1 and Hf /Hp = 3 cannot be satisfied simultaneously. However, by calculating the variation of HT when the ratio Hf /Hp is in the interval 1 ≤ Hf /Hp ≤ 3 we find
≤ 1.1398 H T , hopt Hf ≥1 for 3 ≥ HT , µ Hp 1.1547 ≥ ≥1 H T , µopt 1≤
HT ,h
(11.41)
Equation 11.41 shows that as long as we keep 1 ≤ Hf /Hp ≤ 3, the total power will not exceed its optimal value by more than 16%. But this is not the full story, as we should also keep in mind the temperature rise as the result of dissipation. Assuming that all heat generated is used for increasing the temperature of the lubricant and that none is conducted away, a simple energy balance yields
∆T =
1 h f µ 2U M2 A + ps 4 ρc q f h pr
(11.42)
Assuming, for the sake of simplicity, that ps /pr = const., the condition ∂∆T/∂ps = 0 assures us that the temperature rise is a minimum when Hf /Hp = 1, thus we do well to design for this condition.
11.2.3 Operation with Capillary Restrictor The recess pressure is related to the supply pressure through pr(RC + RB) = psRB where RB is the resistance to flow over the land and RC is the resistance in the capillary. The capillary flow Qc , on the other hand, is determined by the pressure drop ∆p and can be calculated from the Hagen–Poisseuille law Qc = ∆p/RC. We can also relate the external load to the supply pressure
W = a f Aps
RB , RC + RB
RB = µ q f h 3 , RC =
128µlC2 πdC4
(11.43)
where lC is the length of the capillary and dC is its diameter. Let W0 be the load at the reference film thickness h0, then the ratio of load to reference load is
W 1+ ξ = W0 1 + ξX 3
(11.44)
where
ξ=
RC RBo
and X =
h h0
and the ratio of supply pressure to recess pressure is given by ps /pr = 1+ ξ. The dimensionless bearing stiffness is obtained by differentiating W/W0 with respect to h/h0
λ≡−
(
∂ W W0
) = 3ξ(1 + ξ)X
( ) (1 + ξX )
∂ h h0
3
2
2
(11.45)
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FIGURE 11.6 Operation with capillary restrictor: dimensionless bearing stiffness vs. film thickness. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
Figure 11.6 shows the variation of λ/(1 + ξ) with X. (i) Operation without regulator. Single bearing: If there are no flow regulators installed so that the recess is fed directly by the pump, then the flow in the recess is defined by the pump flow-pressure characteristics. The applied load and the geometry specifies the recess pressure pr(1) = W(1)/af A. The pump will supply flow Q(1) = qf h(1)3/µpr , and we may find h(1) for a given µ, or µ at given h(1). If the load were to be increased to W (2) > W(1), we would obtain pr(2) > pr(1), h(2) < h(1), and Q(2) < Q(1). Two bearings: Let us assume, for simplicity, that the two bearings, which operate from a single manifold without flow regulators, are geometrically identical but carry loads W (1) and W (2) > W (1), respectively. The required recess pressures are
(1)
pr =
(1)
(2 )
W W (2 ) < = pr af A af A
At the start of operation the pump delivery pressure is increased from zero and reaches the lower of the lift-off pressures pL(1) = W(1)/Ar, where Ar is the area of the recess. Now that the passage is open for the lubricant, the delivery pressure will drop back to pr(1) and there it will stay. There is no way for the pump to reach pL(2) = W(2)/Ar > pL(1) > pr1, the lift required by pad no. 2, i.e., pad no. 2 will not come into operation at all. (ii) Operation with capillary restrictor. The size of the restrictor to be installed in bearing no. 1 of the previous example must be such that ∆p (1) + pr(1) > pL(2) at the required flowrate Q(1).
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TABLE 11.1 Capillary Restrictors for Hydrostatic Pad dC (cm)
lC (cm)
lC/dC
0.38 0.27 0.18 0.12 0.084 0.069 0.051
1184 302 60 12 2.8 1.3 0.38
3120 1100 333 96 18 17 7.4
Example 1. Hydrostatic Pad Design an annular hydrostatic pad with the following requirements:
W = 44, 500 N , R1 = 6.35 cm, R2 = 12.7 cm, h ≥ 50.8 µm, µ = 3.03 × 10 −2 Pa ⋅ s For this geometry Equation 11.36 yields af = 0.54 and qf = 0.755, so that
pr =
44500 = 1.626 MPa 0.54 × 0.1272 π
(5.08 × 10 ) 1.627 × 10 = 5.3115 × 10 Q = 0.755 −6
3
6
3.03 × 10−2
−6
m3 s
We select a pump that delivers 6.309 cm3/sec. At this flowrate the film thickness is an acceptable
6.309 × 10−6 × 3.03 × 10−2 h= 6 0.755 × 1.626 × 10
13
= 53.80 µm > 50.8 µm
We thus need a pump that delivers pL = 44,500/(0.0635)2 π = 3.5129 MPa at zero flow and 1.626 MPa at Q = 6.31 cm3/s. Assume a supply pressure ps = 2.0684 MPa at Q = 6.309 cm3/s, then from the Hagen–Poisseuille law
( )
lC cm =
(
)
π 2.0684 − 1.626 × 106 −2
128 × 3.03 × 10 × 6.309 × 10
−6
( )
dC4 = 5.68 × 104 × dC4 cm
Using this last equation, for standard capillary inside diameters we construct Table 11.1. Only capillaries with 0.084 < dC < 0.18 are satisfactory, and we choose dC = 0.12 cm and lC = 12.0 cm: as lC/dC > 20, the required length is practical, and dC > 0.0635 cm (clogging). The choice of flow restrictors will influence bearing performance under dynamic conditions. Table 11.2 lists advantages and disadvantages of flow restrictors (rating 1 is best or most desirable).
11.3
Hydrodynamic Lubrication
Hydrodynamic lubrication relies on the relative motion of nonparallel bearing surfaces. To generate positive, i.e., load-carrying, pressure, the film must be convergent in the direction of relative motion
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TABLE 11.2
Advantages/Disadvantages of Flow Restrictors
Compensating Elements
Capillary
Orifice
Valve
Initial cost Cost to fabricate, install Space requirement Reliability Useful life Availability Tendency to clog Serviceability Adjustability
2 2 2 1 1 2 1 2 3
1 3 1 2 2 3 2 1 2
3 1 3 3 3 1 3 3 1
(Figure 11.1). No outside agency is required to create and maintain a load-carrying film, provided that adequate lubricant is made available. Hydrodynamic films are easy to obtain; in fact they often occur even when their presence is deemed undesirable, e.g., in hydroplaning of automobile tires on wet pavement. Prototypes of conformal hydrodynamic bearings are journal bearings and thrust bearings; these bearings might also be called “thick film” bearings. A journal bearing at load per projected bearing area of 1.36 MPa, speed 60 rps, and lubricated with an ASTM Grade 315 oil at 52°C would have a minimum film thickness of the order of 88.4 µm. This film is thick in comparison to film found in counterformal bearings, such as ball and roller bearings. Journal bearings are designed to support radial loads on rotating shafts, while thrust bearings, as their name implies, support axial or thrust loads. Although the mode of lubrication is identical in these two bearing types, their geometry is sufficiently distinct for us to discuss them under separate headings; in journal bearings, in general, the clearance geometry is convergent–divergent, and film rupture occurs in the divergent part. Conventional thrust bearings, on the other hand, are purely convergent and their film remains continuous throughout the clearance. The third main heading of this section introduces the idea of lubricant film instability in the dynamic sense; in most cases of application, the thermomechanical load on the bearing varies with time and, as a result, the bearing surfaces undergo cyclic oscillation that can lead to catastrophic film failure.
11.3.1 Journal Bearings In its most elementary form, a journal bearing is a short, rigid, metal cylinder that surrounds and supports the rotating shaft, as in Figure 11.7. The clearance space between bearing and shaft is filled with a lubricant, usually a petroleum oil. Under zero load and negligible body weight, the rotating journal is concentric with its bearing, but as the external load on the journal is increased, the shaft center sinks below the center of the bearing. For
FIGURE 11.7 Schematic of a full journal bearing. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
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FIGURE 11.8 Shaft trajectory during static loading. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
isothermal operations, somewhat of a rarity in practice, the loading conditions on the shaft can be characterized by a single dimensionless group, the Sommerfeld number S, defined by
S=
µN R P C
2
where N is the rotation and R is the radius of the shaft, C is the radial clearance between bearing and shaft, µ is the viscosity of the fluid, and P is the specific load. The specific load has the definition P = W/LD, where L is the length and D is the diameter of the bearing; note that this definition of P is used even for partial arc bearings, for which the projected bearing area might be less than LD. For an unloaded bearing P → 0 and S → ∞, a weightless shaft runs concentric with its bearing. On increasing the external load or decreasing the speed, i.e., on decreasing S, the journal will move away from its concentric position, the journal trajectory approximating a semicircular arc (Figure 11.8). Under extreme load or vanishing speed, S → 0, metal-to-metal contact occurs at the point where the load line cuts the bearing. In most applications there is considerable heat generation, and the viscosity of the lubricant does not remain uniform throughout the film. In such cases we need more than a single dimensionless group to characterize journal bearing operations. In fact, under nonisothermal conditions the number of characterizing parameters is so large that tabulation of bearing performance becomes impractical. Denote the radial clearance, i.e., the difference in radii between cylinder and shaft, by C as before, the radius of the shaft by Rs and the radius of the cylinder by Rb , so that C = Rb – Rs , then in normal design practice (C/R) = O(10–3). This signifies that the lubrication approximation to Equations 11.1 and 11.2 is valid, and we can employ the Reynolds equation for evaluating bearing performance. The small value of C/R further signifies that the curvature of the film can be neglected to the same order, thus the analysis may be performed in an orthogonal Cartesian coordinate system. The (x,z) plane of this coordinate system lies in the surface of the bearing, so that x is the “circumferential” coordinate and z is parallel to the axis of the shaft. The y coordinate is normal to the “plane” of the bearing, i.e., it points toward the center of the bearing arc, yet to the approximation involved here the y arrays appear parallel to one
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another. Because of the smallness of the clearance, it makes no difference whether we put R = Rs or R = Rb in the definition of the Sommerfeld number. Using plane trigonometry and the binomial expansion (Szeri, 1998), it can be shown that the film thickness between eccentric cylinders is well approximated by the formula
(
h = C + e cos θ = C 1 + ε cos θ
)
(11.46)
where e is the eccentricity, h the film thickness, and θ the angle measured from the line of centers in the direction of shaft rotation. When the load-line, and therefore the line of centers, is not fixed but oscillating, as when there is a rotating out of balance force on the shaft, the film thickness relates to the fixed position through the formula
[ (
h = C + e cos Ξ − φ + ψ
)]
(11.47)
Here φ is the angle between load-line and line of centers, the so-called attitude angle, and ψ defines the load-line relative to the fixed position = 0. Equation 11.47 can be used to evaluate the right-hand side of the Reynolds equation, Equation 11.19, to obtain (Szeri, 1998)
∂ h 3 ∂p ∂ h 3 ∂p ∂h + = 6 Rω + 12 e˙ cos θ + e φ˙ + ω W sin θ ∂x µ ∂x ∂z µ ∂z ∂x
[
(
)
]
(11.48)
Here ω and ωW = dψ/dt are the angular frequencies of the shaft and the load vector, respectively. Equation 11.48 is only an approximation to the governing equations of lubricant flow, good to order C/R · · φ, provided that e, and ωW are of the same order of magnitude as ω or smaller. Though Equation 11.48 was arrived at through simplification of the full nonlinear equations, Equations 11.1 and 11.2, its solution is still difficult to obtain except in numerical form. For this reason, before the advent of high-speed computing Equation 11.48 was further simplified to make it amenable to analytical solutions. These simplifications, known as the short-bearing and the long-bearing approximations to the Reynolds equation, must be used with great caution, however, as they may yield incorrect performance parameter values. Before discussing these approximations to Equation 11.49 we shall make the equation nondimensional. The Reynolds equation is nondimensionalized via the substitutions 2
R L x = Rθ, z = z , h = CH = C 1 + ε cos θ , p = µN p 2 C
(
)
(11.49)
· Assuming that e· = φ = ωW = 0 in Equation 11.48, the nondimensional form of the Reynolds equation, valid for journal bearings under static loading, is 2
∂ 3 ∂p D ∂ 3 ∂p ∂H H + H = 12π ∂θ ∂θ L ∂z ∂z ∂θ The individual terms on the left-hand side of Equation 11.50 2
D ∂ 3 ∂p ∂ 3 ∂p H and H ∂θ ∂θ ∂z L ∂z
(11.50)
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represent the rate of average (across the film thickness) pressure flow in the circumferential and axial directions respectively, the sum of which is balanced by the shear flow
12π
∂H ∂θ
By the normalizing transformation, Equation 11.49, each of the variable terms of Equation 11.50 are of the same order of magnitude; thus for long-bearings for which (D/L)2 → 0 the following approximation is acceptable
d 3 d p dH = 12π H dθ dθ ∂θ
(11.51)
whereas for short-bearings (L/D)2 → 0, and we may approximate Equation 11.50 in the form 2
L ∂H ∂ 3 ∂p H = 12π ∂z ∂z D ∂θ
(11.52)
When solved with zero pressure boundary conditions, the pressure distributions specified by Equation 11.50 or its approximations, Equations 11.51 and 11.52, are 2π-periodic functions, antisymmetric with respect to the position of minimum film thickness, θ = π. They yield negative pressures of the same magnitude as positive pressures. However, unless special care is taken to remove all impurities, liquids cannot withstand large negative pressures and the lubricant film will rupture within a short distance downstream from the position of the minimum film thickness. Though the cavitation zone might be preceded by a short range of subambient pressures, in most performance calculations this region of subambient pressures is disregarded. The boundary condition at film-cavity interface is complicated, particularly when dynamic loading conditions prevail, and is still under investigation. Most computer calculations are based on the so-called Swift–Stieber boundary conditions
p=
∂p = 0, at θ = θcav ∂θ
(11.53)
– that preserve flow continuity at the film-cavity interface. Here θcav = θcav (z) denotes the angular position – of the film-cavity interface. Equation 11.50 also implies that p ≥ 0 everywhere in the film. The Swift–Stieber boundary condition cannot be implemented in the short-bearing approximation, – and only with some difficulty in the long-bearing as the latter is governed by a differential equation in z, approximation. The closest we can come to Equation 11.53 when using the short-bearing approximation is to disregard negative (below ambient) pressures in calculating bearing performance, i.e., assume the film to cavitate at the position of minimum film thickness. The conditions
() p(θ) = 0, p θ ≥ 0,
0≤θ≤π π ≤ θ ≤ 2π
(11.54)
are used extensively for performance calculations in both short-bearing and long-bearing approximations and are known as the Gümbel boundary conditions. We will evaluate bearing performance, for both shortbearing and long-bearing approximations, under the conditions specified in Equation 11.54, but for finite bearings we use the Swift–Stieber conditions, Equation 11.35. Figure 11.9 displays pressure distribution under Sommerfeld, Gümbel, and Swift–Stieber boundary conditions.
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FIGURE 11.9 Journal bearing pressure distribution under (a) Sommerfeld, Gümbel, and (b) Swift–Stieber boundary conditions. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
Bearing performance is calculated from the pressure distribution by substitution into the following formulas Load capacity: The force balance (Figure 11.10)
W cos φ + FR = 0
(11.55)
−W sin φ + FT = 0
where FR and FT are the components of the pressure force along the line of centers and normal to it, respectively, and W is the external load on the shaft, yield
( ) ∫ ∫
Rθcav
( ) ∫ ∫
Rθcav
2
FR ≡ f R LDµN R C = 2
FT ≡ fT LDµN R C =
L 2
−L 2 0 L 2
−L 2 0
p cosθdxdz
(11.56a)
p sinθdxdz
(11.56b)
Equations 11.56 define the he nondimensional force components fR , fT . The Sommerfeld number reemerges here as the inverse of the nondimensional pressure force
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FIGURE 11.10 Journal bearing nomenclature. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.) 2
µN R 2 2 S≡ = f R + fT P C
(
)
−1 2
(11.57)
Attitude angle: The attitude angle, i.e., the angle between the load vector and the line of centers is given by
fT fR
φ = arctan
(11.58)
Friction variable: The friction force exerted on the shaft is found from
C Fµ ≡ c µ W = R
L
∫∫ 0
2 πR
0
τ xy h ( x ) dxdz
(11.59)
where τxyh(x) is the shear stress on the shaft and cµ is the friction variable, which is the conventional friction coefficient scaled with (C/R) to numerically convenient values. Lubricant flow: The rate of inflow can be calculated from
Qi ≡ qi NRLC = 2
()
∫ ∫ u(0, y, z )dydz 2 πR
0
h x
0
where u is given by Equation 11.14 and qi is the dimensionless inflow variable.
(11.60)
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TABLE 11.3
Performance of Short- and Long-Bearings Short-Bearing Approximation (Gümbel condition) 2
Long-Bearing Approximation (Gümbel condition)
Equation for pressure, p
∂p 3 dp L ∂H H = 12π D ∂θ ∂z dz
∂ 3 dp ∂H H = 12π ∂θ dθ ∂θ
Boundary condition
p = pa at z = ±1
p(0) = p(2π) = pi
–
2
Pressure, p
L 1 ∂H 2 6 π z − 1 + pa D H 3 ∂θ
Radial force, fR
L 4πε 2 − D 1− ε 2
Tangential force, fT
π 2ε L D (1 − ε )3 2 2
Attitude angle, φ
π 1 − ε2 arctan 4ε
Sommerfeld number, S
1− ε D L πε π 2 1 − ε 2 + 16ε 2
–
(
)
12πε sin θ(2 + ε cos θ)
(2 + ε )(1 + ε cos θ) 2
2
(
)
−
2
( (
Friction variable, cµ Flow variable, qi
2 π 2S
(1 − ε ) 2
2πε
+ pi
12πε 2
(2 + ε )(1 − ε ) 2
2
6π 2ε
2
2
2
(2 + ε )(1 − ε ) 2
2
12
π 1 − ε2 arctan 2ε 2
) )
2
(2 + ε )(1 − ε ) 6πε 4ε + π (1 − ε ) 2
2
ε sin φ +
2
2
2
4π 2 S 1 − ε2
—
Table 11.3 lists the performance characteristics for both short- and long-bearings. These calculations are based on the Gümbel conditions, Equation 11.54. As the cavitated film does not contribute to load capacity but only to unwanted friction, it serves no useful purpose. This leads to the idea of employing partial arc pads instead of 360°, or full, bearings to support the shaft. Different types of fixed pad partial journal bearings, each of arc β, are shown schematically in Figure 11.11.
FIGURE 11.11 Fixed type journal bearings: (a) full 360° bearing, (b) centrally loaded partial bearing, (c) offset loaded partial bearing (offset parameter α/β). (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R., (Ed.), CRC Press, Boca Raton, FL. With permission.)
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11.3.1.1 Finite Journal Bearings The pressure distribution in a finite journal bearing of length L, diameter D and angular extent β, is governed by the Reynolds equation 2
∂ 3 ∂p D ∂ 3 ∂p ∂H H + H = 12π ∂θ ∂θ L ∂z ∂z ∂θ
(11.61)
–
and the boundary conditions (considering p as gauge pressure)
p = 0 at z = ±1
(11.62a)
p = 0 at θ = θ1, θ1 + β
(11.62b)
If (θ1 + β) > π, Equation 11.61 yields both positive and negative pressures, leading to film rupture as previously discussed. At the film-cavity interface the Swift–Stieber conditions, Equation 11.35, are usually applied. Equation 11.61 and its boundary conditions, Equation 11.62, contain three parameters, (L/D), θ1, and β. The only additional parameter of the problem, ε, appears in the definition of the lubricant film geometry
x H = 1 + ε cos θ = 1 + ε cos θ1 + , θ1 ≤ θ ≤ β R
(11.63)
Thus the journal bearing problem is uniquely characterized by the parameter set
{L D, β, ε, θ } 1
(11.64)
The first two parameters of this set define bearing geometry, while the last two characterize the geometry of the film. Having selected parameter set (11.64), we can find the pressure by solving the system consisting of Equations 11.61, 11.62, and 11.63. The nondimensional lubricant force components are obtained from (note the limits of integration on z)
fR =
1 2
∫∫
θcav
fT =
1 2
1
θcav
1
θ1
0
∫∫ 0
θ1
p cosθdθdz
(11.65a)
p sinθdθdz
(11.65b)
and the attitude angle from
φ = arctan
fT fR
(11.66)
Knowledge of the force components {fR, fT } thus enables us to determine both the magnitude, f =
f R + f T , and the direction, φ, of the load the lubricant film will support under the specified conditions. 2
2
Instead of characterizing the oil-film force this way, however, it has been customary to employ an alternate representation of the Sommerfeld number
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S =1 f
(11.67)
and the offset parameter (α/β)
[ (
α 1 = π − θ1 + φ β β
)]
(11.68)
where α is the position of the load-line relative to the leading edge of the pad (Figure 11.11). As shown above, under isothermal conditions the computational problem is defined by the “design parameters” {L/D, β, ε, θ1}, while the computations yield the “performance, parameters” {L/D, β, S, α/β}. The designer, however, must proceed in an inverse manner, so to speak. (In the following, we drop the parameters L/D and β from the list.) What is known at the design stage are the pad geometry and the performance requirements, i.e., the magnitude and direction of the external load, the shaft speed and the viscosity of the lubricant, and it is easy for the designer to define the couple {S, α/β}; but the designer has no way of determining the couple {ε, θ1} that is required in order to compute the minimum film thickness, often the controlling parameter. Let Ω(ε, θ1) and Ψ(ε, θ1) represent the Sommerfeld number and the offset parameter, respectively, obtained by the analyst at some given {ε, θ1}, and let S and α/β be the values that are requested by the designer. The task for the analyst is then to find that particular {ε, θ1} that yields
( )
S − Ω ε, θ1 = 0
(11.69a)
α − Ψ ε, θ1 = 0 β
(11.69b)
(
)
We can solve this pair of nonlinear equations for the unknowns {ε, θ1} by iteration, e.g., using Newton’s method
∂Ω ∂ε ∂Ψ ∂ε
∂Ω n n −1 ∂θ1 ε( ) − ε( ) Ω − S α , n = 1, 2, 3, … (n ) (n−1) = ∂Ψ θ − θ Ψ − 1 1 β ∂θ1
(11.70)
The performance curves in Figure 11.12, taken from Raimondi and Szeri (1984), are for centrally loaded fixed-pad partial bearings of L/D = 1, β = 160° and various values of the Reynolds number. The turbulent data were obtained from Equation 11.21. Example 2. Journal Bearing Calculate the performance of a centrally loaded partial arc journal bearing given the following data
(
)
β = 2.79rad 160° −3
C R = 2 × 10 D = L = 0.508 m
(
N = 40 sec, ω = 251rad sec ISO VG 32, ρ = 831kg m W = 355.84 kN
3
To start the design process, we assume an effective viscosity
µ = 3.447 × 10−2 Pa ⋅ s ;
ν = 0.4148 cm2 s
)
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FIGURE 11.12 Performance of an (L/D) = 1, β = 160° partial journal bearing: (a) minimum film thickness, (b) position of minimum film thickness, (c) power loss, (d) lubricant inflow, (e) lubricant side flow. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R., (Ed.), CRC Press, Boca Raton, FL. With permission.)
For Reynolds and Sommerfeld numbers, respectively, we obtain
Re = S=
25.4 × 251 × 0.0508 = 781 < 1000, the flow is laminar 0.4148
3.447 × 10−2 × 40 1.3789 × 10
6
(500) = 0.25 2
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FIGURE 11.12 (continued)
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FIGURE 11.12 (continued)
Entering Figure 11.12c, d, and e in succession we find
H = 3.05 × 2π × 355.84 × 103 × 40 × 5.08 × 10−4 = 0.1386 MW Q = 3.2 × 0.254 × 5.08 × 10−4 × 40 × 0.508 = 8.39 × 10−3 m 3 s Qs = 1.32 × 2.6219 × 10−3 = 3.46 × 10−3 m 3 s The temperature rise across the bearing is calculated from a simple heat balance, Equation 11.28,
∆T =
1.386 × 105
(
)
1.39 × 106 8.39 − 3.46 2 × 10−3
= 14.97 C
and, assuming an inlet temperature of Ti = 45 C, yields the operating temperature
Ts = Ti + 0.5 × ∆T = 52.5C On Figure 11.13 plot the point A(52.5, 34.47). Note that 1 Pa · s = 1000 cP. Assume another effective viscosity: µ = 6.8948 × 10–3 Pa · s, v = 0.083 cm2/s. The corresponding performance parameters are
Re = 3904 > 1000, turbulent flow S = 0.05 Q = 8.39 × 10−3 m 3 s
)
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411
FIGURE 11.13 ISO viscosity grade for lubricating oils. Points A, B, and the line drawn through them, refer to Example 2. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Q s = 4.93 × 10−3 m 3 s H = 0.123 MW ∆T = 14.94 C The operating temperature is Ts = 45 + 14.94/2 = 52.47 C, and we plot point B(52.5, 6.9) in Figure 11.13. The line drawn from A to B intersects the ISO VG 32 line at
Ts = 52.5 C and µ s = 1.7 × 10−2 Pa ⋅ s giving the effective temperature and effective viscosity that is consistent with the operating conditions of the bearing under the assumption that a single viscosity can portray bearing performance. The final Reynolds number, Sommerfeld number, and minimum film thickness are
Re = 1583, S = 0.123, hn = 0.4 × 0.0508 = 0.0203 cm 11.3.1.2 Pivoted-Pad Journal Bearings In many applications the bearings are constructed of several identical pads. Multipad bearings, in general, dissipate less energy than full bearings. However, they too are unable to damp out unwanted rotor vibrations. This becomes a problem especially when attempting to operate the rotor in the neighborhood of a system critical speed. For this reason the pads are often pivoted in one point or along a line. Pivoted
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FIGURE 11.14 Preloading of a pad: (1) as machined, (2) preloaded (Ob , Oj , Op , bearing, journal, pad center; rb , rp , R, bearing, pad, journal radius). (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
pads are free to swivel and follow the motion of the rotor, maintaining, at all times of normal operation, a load-carrying lubricant film between rotor and pad. Other advantages of pivoted-pad bearings are that the clearance can be closely controlled by making the pivots adjust radially, thus enabling operation with smaller clearances than considered appropriate for a plain journal bearing, and the pads can be preloaded to achieve relatively high stiffness (important with a vertical rotor). Figure 11.14 shows a pad machined to radius R + C (position 1). Assuming the pad does not tilt, the film thickness is uniform and equal to C, and the pad develops no hydrodynamic force. If the pad is now moved inward the distance (C – C′) into position 2, the film thickness will no longer be uniform; the resulting hydrodynamic force preloads the pad. The degree of preload is indicated by the preload coefficient m = (C – C′)/C, the value of which varies between m = 0 for no preload, to m = 1, for metal-to-metal contact between pad and shaft. Figure 11.15 is a schematic of the geometrical relationships in a pivoted-pad journal bearing. The symbols OB and OJ mark the positions of the bearing center and the instantaneous position of the shaft center. The center of the pad is at Ono when the pad is unloaded and moves to On when it is loaded. The pivot point P is located at angle ψ relative to the vertical load line WB . The eccentricity of the journal relative to the bearing center, OB , is e0 = C′ε0 and its attitude angle φ0. Relative to the instantaneous pad center, OJ , the journal eccentricity is e = Cε and the attitude angle φ, the latter measured from the load line that, by necessity, intersects the pivot P. The radii of journal, pad, and pivot circle are R, O n P , and O B P , respectively. From geometric consideration we have (Lund, 1964)
ε n cos φn = 1 −
C′ − ε 0 cos ψ n − φ0 = m − ε 0 cos ψ n − φ0 C
(
)
(
)
(11.71)
where m is the preload coefficient defined earlier, and the index n refers to the nth pad. Once the position of the journal relative to the bearing is specified, i.e., (ε0,φ0) is given, Equation 11.71 together with the constraint that the load must pass through the pivot are sufficient to determine (εn,φn), the position of the nth pad, n = 1,…,N, relative to the journal. Knowing (εn,φn) makes it possible to calculate individual pad performance that can then be summed to yield the performance characteristics of the bearing. Unfortunately (ε0,φ0) is not known at the design stage, and the best the designer can do is assume ε0 and use the condition that WB is purely vertical to calculate the corresponding φ0. This procedure is, at least, tedious. If, however, the pivots are arranged symmetrically with respect to the loadline, the pads are centrally pivoted and are identical, the journal will move along the load line WB and
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FIGURE 11.15 Geometry of a pivoted-pad journal bearing. (From Lund, J.W. (1964), Spring and damping coefficients for the tilting pad journal bearing, ASLE Trans., 7, 342. With permission.)
φ0 ≡ 0. Figure 11.16 plots performance data for a five-pad pivoted-pad journal bearing (ε′0 = ε0/max(ε0), and for the five-pad bearing max(ε0) from geometry). Example 3 Find the performance for a five-pad tilting-pad bearing for a horizontal rotor, given the following data
( )
β = 1.05 rad 60°
W = 11.12 kN
D = 12.7 cm L = 6.35 cm C = C ′ = 0.0127 cm
µ = 1.379 × 10 −2 Pa ⋅ s v = 0.1658 cm2 s N = 60 r sec
Bearing performance is calculated as follows:
Re =
6.35 × 2π × 60 × 0.0127 = 183 < 1000 laminar 0.1658
(
)
2
S=
1.379 × 10 −2 × 60 6.35 = 0.15 1.3789 × 106 0.0127
hn = 0.26 × 0.127 = 0.0033 cm, from Figure 11.16a H = 3.9 × 2π × 11.12 × 10 3 × 60 × 1.27 × 10 −4 = 2.08 kW , from Figure 11.16b ε ′0 = 0.67, from Figure 11.16c The normalized bearing eccentricity ratio ε′0 = ε0/1.236 will be used to obtain stiffness and damping coefficients.
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FIGURE 11.16 Performance of a five-pad pivoted-pad journal bearing (L/D) = 1, β = 160°: (a) minimum film thickness, (b) power loss, (c) normalized bearing eccentricity ratio. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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415
FIGURE 11.16 (continued)
FIGURE 11.17 Schematic of a plain slider. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
11.3.2 Thrust Bearings Thrust bearings in their most elementary form consist of two inclined plane surfaces in relative motion to one another. The geometry of the bearing surfaces is commonly rectangular, to accommodate a linear motion, or sector shaped, to support a rotation, but other geometries are possible. 11.3.2.1 The Plane Slider A schematic of a fixed plane slider is shown in Figure 11.17. The gradient of the pad surface m = (h2 – h1)/B is used to scale Equation 11.18 and its boundary conditions 2
∂ 3 ∂p B ∂ 3 ∂p x = −1 x + 4 ∂x ∂x L ∂z ∂z
(11.72a)
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TABLE 11.4a –
Nondimensional Oil-Film Force: f = Fh12/µULB 2
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
0.0458 0.0700 0.0825 0.1155 0.1205 0.1238 0.1225 0.1179 0.1081 0.1005 0.0901 0.0676 0.0577 0.0330
0.0424 — 0.0755 0.1047 — — 0.1110 — — 0.0903 — 0.0607 0.0518 0.0296
0.0360 — 0.0623 0.0845 — — 0.0879 — — 0.0715 — 0.0479 0.0409 0.0234
0.0303 0.0441 0.0509 0.0675 0.0697 — 0.0692 0.0662 0.0604 0.0559 0.0500 0.0374 0.0319 0.0182
0.0216 0.0303 0.0344 0.0337 0.0447 0.0448 0.0437 0.0415 0.0377 0.0348 0.0311 0.0232 0.0198 0.0113
0.0161 0.0218 0.0243 0.0298 0.0303 0.0301 0.0291 0.0276 0.0249 0.0230 0.0205 0.0153 0.0130 0.074
0.0099 0.0127 0.0139 — 0.0162 0.0159 0.0152 0.0144 0.0129 0.0119 0.0106 0.0078 0.0067 0.0038
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F., 92, 466-72.
(
)
p x, ±1 = 0
( ) (
(11.72b)
)
p x1, z = p x2 , z = 0
(11.72c)
Here
x = Bx , y = mBy , z =
6µU L z, p = p 2 Bm2
(11.72d)
The nondimensional force f is calculated from
f≡
Fh12 = 6 x12 µULB2
1
∫∫ 0
x1 +1
( )
p x , z dxdz x1
(11.73)
Its values at various values of x– 1 and aspect ratio (L/B) are displayed in Table 11.4a. The center of pressure, xp, is calculated from
Fx p = –
∫ ∫ xp(x, z )dxdz L 2
x2
− L 2 x1
(11.74)
–
Let xp = x1 + δ represent the dimensionless coordinate of the center of pressure, i.e., the location of the pivot for a pivoted pad, then δ, the dimensionless distance between pad leading edge and pivot, is given by
δ = − x1 +
6 x12 f
1
∫∫ 0
x1 +1 x1
( )
xp x , z dx dz
(11.75)
Table 11.4b lists pivot position δ at various values of x– 1 and aspect ratio (L/B). The nondimensional flow variable at inlet, x2, is listed in Table 11.4c.
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TABLE 11.4b –
Optimum Pivot Position: δ = (x– p – x–1)
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
0.2900 0.3236 0.3397 0.3876 0.3992 0.4161 0.4281 0.4388 0.4510 0.4576 0.4649 0.4568 0.4811 0.4883
0.2858 — 0.3363 0.3851 — — 0.4264 — — 0.4567 — 0.4763 0.4806 0.4878
0.2766 — 0.3286 0.3793 — — 0.4226 — — 0.4544 — 0.4750 0.4796 0.4868
0.2663 0.3021 0.3196 0.3725 0.3854 — 0.4180 0.4302 0.4440 0.4516 0.4599 0.4736 0.4784 0.4854
0.2452 0.2825 0.3009 0.3579 0.3721 0.3931 0.4081 0.4217 0.4372 0.4456 0.4549 0.4704 0.4758 0.4820
0.2268 0.2649 0.2841 0.3444 0.3597 0.3825 0.3988 0.4137 0.4307 0.4399 0.4503 0.4674 0.4735 0.4780
0.2000 0.2388 0.2588 — 0.3408 0.3662 0.3844 0.4013 0.4207 0.4311 0.4431 0.4631 0.4701 —
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution. ASME Trans., Ser. F, 92, 466-72.
TABLE 11.4c –
Nondimensional Flow at Inlet: qi = Qx=β /ULh1
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
1.6990 1.3390 1.2059 0.9168 0.8621 0.7879 0.7396 0.6990 0.6550 0.6322 0.6083 0.5702 0.5569 0.5293
1.9662 — 1.3318 0.9717 — — 0.7638 — — 0.6427 — 0.5750 0.5607 0.5310
2.4632 — 1.5588 1.0735 — — 0.8078 — — 0.6621 — 0.5838 0.5676 0.5343
2.8866 2.0402 1.7544 1.1584 1.0558 — 0.8449 0.7791 0.7123 0.6783 0.6439 0.5912 0.5733 0.5370
3.4626 2.3825 2.0156 1.2728 1.1485 0.9905 0.8948 0.8176 0.7393 0.7004 0.6611 0.6014 0.5813 0.5409
3.7744 2.5670 2.1584 1.3360 1.1997 1.0270 0.9229 0.8393 0.7549 0.7130 0.6709 0.6072 0.5859 0.5431
4.0710 2.7362 2.2904 — 1.2789 1.0625 0.9505 0.8608 0.7704 0.7260 0.6809 0.6132 0.5906 0.5454
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F, 92, 466-72.
Example 4. Plane Slider Calculate the performance of a fixed-pad slider bearing if the following data are specified
W = 16.013 kN ,
L = 20.32 cm,
U = 30.5 m s ,
µ = 0.04137 Pa ⋅ s
B = 7.62 cm,
From Equation 11.73 we obtain the relationship between the external load and the dimensionless lubricant force
f=
16.013 × 10 3 × h12 = 1.0756 × 107 h12 m 0.04137 × 30.5 × 0.2032 × 0.07622
( )
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For (L/B) = 8/3, the dimensionless force has its maximum value of f = 0.1238 at x– 1 = 0.8, yielding the largest value of the exit film thickness at which this bearing can carry the assigned load.
0.1238 h1 = 7 1.0756 × 10
12
= 1.073 × 10 −4 m
The corresponding surface slope is calculated from
m=
1.073 × 10 −4 = 0.00176 0.8 × 7.62 × 10 −2
The film thickness at inlet is h2 = 0.01073 + 0.00176 × 7.62 = 0.024 cm. The lubricant flow-rate at inlet is Q = 0.7879 × 30.5 × 0.2032 × 1.073 × 10–4 = 524 × 10–6 m3/s and the optimum pivot position is xp – x1 = 0.4161 × 7.62 = 3.12 cm from the trailing edge. 11.3.2.2 Annular Thrust Bearing The fixed-pad slider bearing is the most basic configuration. If the pads are arranged in an annular configuration with radial oil distribution grooves, a complete thrust bearing (Figure 11.18a) is achieved.
FIGURE 11.18 Fixed-pad thrust bearing: (a) arrangement of pads, (b) pad geometry. (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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FIGURE 11.19 Pivoted-pad thrust bearing. Source: Raimondi, A. A. and Szeri, A. Z. 1984. Journal and thrust bearings. (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Approximate performance calculations of this bearing can be made by relating the rectangular slider bearing (width B, length L) to the sector configuration (Figure 11.18b). The pads of pivoted-pad thrust bearings are supported on pivots (Figure 11.19). As the location of the pivot fixes the location of the center of pressure, on loading a pad will swivel until it occupies a position that places the center of pressure over the pivot. While performance of a pivoted pad is identical to that of a fixed pad designed with the same surface slope, the pivoted-type bearing has the advantages of (a) being self-aligning, (b) automatically adjusting pad inclination to optimally match the needs of varying speed and load, and (c) having the capability of operating in either direction of rotation. Theoretically, the pivoted pad can be optimized for all speeds and loads by judicious pivot positioning, whereas the fixedpad bearing can have optimum performance only for one operating condition. Although pivoted-pad bearings involve somewhat greater complexity, standard designs are readily available for large machines. The Reynolds equation, Equation 11.19, in cylindrical coordinates (r,θ) takes the form
∂ 3 ∂p 1 ∂ 3 ∂p ∂h rh + h = 6µωr ∂r ∂r r ∂θ ∂θ ∂θ
(11.76)
This equation can be solved numerically. The resulting performance charts (Figures 11.20a to 11.20f) are conveniently entered on a trial basis with an assumed tangential slope parameter mθ and radial slope parameter mr . Load capacity, minimum film thickness, power loss, flow and pivot location (if pivotedpad type) are then determined and the procedure, if necessary, repeated to find an optimum design. Figures 11.20e and 11.20f provide pivot locations for tilting pad sectors. The thrust bearing charts were prepared for a ratio of outside radius to inside radius of 2 and a sector angular length of 40°. While this angle corresponds to seven sectors to form a full thrust bearing, the results should generally give a preliminary indication of performance of other geometries with the same surface area and mean radius. For other pad geometries see Pinkus and Sternlicht (1961). Example 5. Sector Thrust Pad Calculate thrust pad sector performance when given the following:
(
β = 40°
γ r = 0 no radial tilt
R2 = 13.97 cm
γ θ = 5.82 × 10−4 rad
)
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FIGURE 11.20 Performance charts for fixed or tilting pad sector: (a) load capacity, (b) minimum film thickness, (c) power loss, (d) flow, (e) center of pressure (tangential location), and (f) center of pressure (radial location). (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
R1 = 6.985 cm
µ = 1.379 × 10−2 Pa ⋅ s
hc = 50.8 µm, pad center
N = 50 r sec ω = 314 rad sec
(
)
Calculating first
(
mθ = R1 hc
)
(
)
γ θ = 6.985 × 10 −2 50.8 × 10 −6 × 5.82 × 10 −4 = 0.80
Enter Figures 11.20a to 11.20d with mθ = 0.8 and mr = 0.0
(
) (50.8 × 10 )
W = 0.058 × 6 × 1.379 × 10 −2 × 314 × 0.1397 − 0.06985 hmin = 0.45 × 50.8 × 10 −6 = 22.86 µm
4
−6
2
= 13.9 kN
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FIGURE 11.20 (continued)
(
)
H = 3.04 × 1.379 × 10 −2 × 3142 × 0.1397 − 0.06985
(
)
(
)
2
Qin = 0.86 × 50.8 × 10 −6 × 314 × 0.1397 − 0.06985
4
50.8 × 10 −6 = 1.94 kW 6.6931 × 10 −5 m 3 s
2
Qs = 0.35 × 50.8 × 10 −6 × 314 × 0.1397 − 0.06985 = 2.723 × 10 −5 m 3 s Temperature rise can be calculated from Equation 11.28
∆T =
1.94 × 103
(
)
1.39 × 106 × 66.93 − 27.23 2 × 106
= 26.18 C
This temperature rise implies an inlet temperature of Ti = 57 – 26/2 = 44 C. If this did not match the actual oil inlet temperature, a new effective viscosity would be assumed and the steps repeated. From Figures 11.20e and 11.20f, the pivot must be placed at θp /β = 0.39 and (rp – R1)/(R2 – R1) = 0.56, to achieve the above calculated performance. This performance is also achieved with a fixed-type bearing machined to slopes γθ = 0.0333°, γr = 0.0.
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FIGURE 11.20 (continued)
11.4
Dynamic Properties of Lubricant Films
Assuming rigid supports, rotor response to small excitation, say a force imbalance, will be as shown in Figure 11.21a. (The same curve applies with rolling element bearings.) Such rotors cannot be operated at system critical speeds and become “hung” on a critical speed when attempting to drive through. When
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FIGURE 11.20 (continued)
hydrodynamic bearings are used, the lubricant film adds spring, in addition to the shaft spring in bending, and considerable damping to the system. Two effects may be noticed in the rotor response curve on introducing a hydrodynamic film: (1) the critical speed is lowered, and (2) the vibration amplitude is reduced. The rotor-shaft configuration is reduced to a simple dynamical system of springs and dashpots in Figure 11.21b. The four spring coefficients Kxx , Kxy , Kyx , Kyy and the four damping coefficients Cxx , Cxy , Cyx , Cyy (only some shown in Figure 11.21b) enable linear representation of the incremental oil film force when departure from equilibrium is small.
dFx K xx dF = − K y yx
K xy x C xx − K yy y C yx
C xy x˙ C yy y˙
(11.77)
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FIGURE 11.21 Dynamic properties of lubricant films: (a) effect of oil-film on shaft response, (b) Oil film as a simple dynamic system. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 11.22 Force decomposition in journal bearings, a schematic. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
When departure from equilibrium is “large,” lubricant film behavior is highly nonlinear and the representation depicted in Figure 11.21b and Equation 11.77 becomes inaccurate. With the aid of Equation 11.77, the equations of motion of the journal of mass m with periodic excitation Ω can be written as
mx˙˙ + C xx x˙ + C xy y˙ + K xx x + K xy y = F cos Ωt
my˙˙ + C yy y˙ + C yx x˙ + K yy y + K yx x = F sin Ωt
(11.78)
11.4.1 Linearized Spring and Damping Coefficients In the following we illustrate how the element of the stiffness, K, and damping, D, matrices can be calculated under specified loading conditions (Szeri, 1998). For this, we refer to Figure 11.22, which shows a journal in its equilibrium position, OJs, and displaced from it, OJ , and the nomenclature we shall be using. For small values of ∆φ we refer the instantaneous force components Fr , Ft to the line of centers, R, and perpendicular to it, T, in the journal equilibrium position OJs , thus
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FR = Fr − ∆φFt
(11.79)
FT = ∆φFr + Ft The force increments, when referred to the (R,T) axes, are
( )
∆FR = Fr − FR − ∆φFt 0
(11.80)
( )
∆FT = ∆φFr + Ft − FT
0
The instantaneous force component Fr is a perturbation of (FR)0, its magnitude in equilibrium, and thus can be obtained from a (first-order) Taylor expansion centered at equilibrium
∂F ∂F ∂F ∂F Fr = FR + R de + R dφ + R de˙ + R dφ˙ , 0 ∂e 0 ∂φ 0 ∂e˙ 0 ∂φ˙ 0
( )
(11.81)
Substitution of Equation 11.81, and a similar equation for Ft , into Equation 11.80 yields an equation similar to Equation 11.77, but written with reference to the (R,T) coordinate system defined by the shaft equilibrium position
∂FR dFR ∂ε dF = ∂F T T ∂ε
∂FR ∂FR − FT ∂ε˙ d ε ∂φ + ∂FT ∂F dφ + FR T ∂φ ∂ε˙
∂FR ∂φ˙ dε˙ ∂FT dφ˙ ∂φ˙
(11.82)
The elements of the stiffness and damping matrices in Equation 11.82 will be calculated with the aid of the Reynolds equation, Equation 11.48, but for this we write the latter in terms of the “dynamic” · – – – · pressure pˆ = p/(1 – 2φ/ω), rather than the “static” pressure p (note that pˆ as p φ → 0), 2
∂ 3 ∂pˆ D ∂ 3 ∂pˆ ε˙ ω cos θ H + H = −12πε sin θ + 24 π ∂θ ∂θ L ∂z ∂z φ˙ 1 − 2 ω
(11.83)
Employing the notation, (Equation 11.56)
fR =
1 2
θ1
1
∫∫ 0
0
1 pˆ cos θdθdz , fT = 2
θ1
1
∫∫ 0
pˆ sin θdθdz
0
we write the nondimensionalized force components symbolically as
FR ≡
FT ≡
FR LD
( )
µN R C
2
FT LD
( )
µN R C
2
φ˙ ε˙ ω = 1 − 2 f R ε, φ, ω 1 − 2φ˙ ω
(
φ˙ ε˙ ω = 1 − 2 fT ε, φ, ω 1 − 2φ˙ ω
(
)
(11.84a)
)
(11.84b)
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We are now ready to evaluate the force derivatives required in Equation 11.82
∂f R dFR ∂ε = dFT ∂fT ∂ε
∂f R − ε∂φ ∂fT + ε∂φ
∂f R fT ∂ ε˙ ω ε dε + f R εdφ ∂fT ˙ ε ∂ε ω
2 fR ε d ε˙ ω 2 fT εd φ˙ ω − ε
( ) ( )
−
(11.85)
· The derivatives are evaluated in the static equilibrium position, ε = ε0, φ = φ0, ε· = 0, φ = 0. The nondimensional stiffness and damping matrices are defined, respectively, by
∂f R ∂ε k ≡ ∂fT ∂ε
∂f R − ε∂φ ∂fT + ε∂φ
∂f R ∂ε˙ ω c ≡ ∂fT ˙ ∂ε ω
fT ε fR ε
2 fR ε 2f − T ε
(11.86)
c
(11.87)
−
and are related to their dimensional counterparts through
k=
C R LDµN C
c=
k
2
C R LDµN C
2
Table 11.5 contains the analytic stiffness and damping coefficients for both the long-bearing and the short-bearing approximations, calculated under Gümbel conditions from Long-bearing:
1 1 ε sin θ 2 + ε cos θ pˆ = 12π + 2 2 ε 2 + ε 1 + ε cos θ 1 + ε cos θ
( )(
(
fR = −
) )
12πε 2
(
12π
−
(2 + ε )(1 − ε ) (1 − ε ) 2
fT =
2
2
6π2ε
+
32
(2 + ε )(1 − ε ) ( 2
2
12
−
ε˙ ω 2 ˙ 1 + ε 1 − 2φ ω 1
) ( ) ( 2
˙ 8 π − ε ω 2 2 π 2 + ε 1 − 2φ˙ ω
(
24 πε
)(
2 + ε2 1 − ε2
)(
ε˙ ω 1 − 2φ˙ ω
)(
)
)
)
(11.88a)
(11.88b)
(11.88c)
Short-bearing:
(
)
2 1− z2 D ε˙ ω ε sin θ − 2 cos θ p = 6π L 1 + ε cos θ 1 − 2φ˙ ω
(
(
)
(
)
)
2 2π2 1 + 2ε 2 D 4 πε 2 ε˙ ω = − − f R 2 52 2 2 L 1 − 2φ˙ ω 1− ε 1− ε
(
) (
) (
)
(11.89a)
(11.89b)
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TABLE 11.5 Analytical Stiffness and Damping Coefficients (Gümbel conditions) Long-Bearing
k RR
) (2 + ε ) (1 − ε )
(
−24πε 2 + ε 4 2
2
k RT
2
2
2
(1 − ε ) 2
c RT
c TR
c TT
3 2
3 2
)
2
2
2
8πε
(1 − ε )
2
2
24πε
2
8πε
(1 + ε) (1 − ε )
(1 − ε )
2
2
−12π 2
−
1 2
2
L D
2
L D
2
2π 2
(1 − ε ) 2
2
5 2
2
(2 + ε ) (1 − ε )
2
5 2
) 2π (1 + 2ε ) L − (1 − ε ) D
24πε
2
2
(
(
(2 + ε ) (1 − ε )
2
2
−4πε L 2 D 1− ε 2
8 π − 2 π 2 + ε2
2
L D
3 2
2
2
12π
)
2
(2 + ε ) (1 − ε ) 2
(
2
−12πε 2
)
(1 − ε ) π (1 + 2ε ) L (1 − ε ) D
4
2
(
8πε 1 + ε 2 L 2 3 D 1− ε 2 −π 2
1 2
2
2
c RR
2
(2 + ε ) (1 − ε ) 6 π ( 2 − ε + 2ε ) (2 + ε ) (1 − ε ) 2
k TT
−
−6π 2
2
k TR
Short-Bearing
3 2
L D
2
Source: Szeri, A. Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.
2
D π2ε 8πε + fT = 32 L 1 − ε2 1 − ε2
(
)
(
ε˙ ω 1 − 2φ˙ ω
)( 2
–
(11.89c)
)
–
The stiffness and damping matrices will now be referred to the (ξ, η) coordinate system (Figure 11.22)
dFξ ˙ T ξ T ξ = + QkQ QcQ ˙ η η dFη –
cos φ0 Q= sin φ0
− sin φ0 cos φ0
(11.90)
–
where φ0 is measured– from ξ to e0, and ξ = ξ/C, η = η/C. Denoting the stiffness and damping matrices — – – relative to the new (ξ, η) coordinate system by K and C, respectively, we see from Equation 11.90 that
K = −QkQ T , C = −QcQ T
(11.91)
– – Equation 11.91 proves that the stiffness K and damping C are second-order Cartesian tensors. The – – components relative to (ξ, η) are (Lund, 1964):
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K ξξ = −
∂f ∂f R ∂f ∂f sin 2φ f η cos2 φ − T sin2 φ + T + R − sin φ ∂ε ε∂φ ∂ ε ε ∂φ 2 ε
K ξη = −
∂f ∂f R ∂f ∂f sin 2φ f η cos2 φ + T sin2 φ + T − R + cos φ ∂ε ε∂φ ε ε∂φ ∂ε 2
K ηξ = −
∂f ∂f sin 2φ fξ ∂fT ∂f + cos φ cos2 φ + R sin2 φ + T − R ε∂φ ε ∂ε ε∂φ ∂ε 2
K ηη = −
∂f ∂fT ∂f ∂f sin 2φ fξ cos2 φ − R sin2 φ − R + T − cos φ ε∂φ ∂ε ε ε∂φ ∂ε 2
Cξξ = − Cξη =
(11.92)
∂f R ∂f sin 2φ 2 fξ cos2 φ + T − sin φ ∂ε˙ ω ∂ε˙ ω 2 ε
∂fT ∂f sin 2φ 2 fξ + cos φ sin2 φ − R ε ∂ε˙ ω ∂ε˙ ω 2
Cηξ = −
∂fT ∂f sin 2φ 2 f η cos2 φ − R − sin φ ∂ε˙ ω ∂ε˙ ω 2 ε
Cηη = −
∂f R ∂f sin 2φ 2 f η cos φ sin2 φ − T + ˙ ε ∂ε ω ∂ε˙ ω 2
Here we employed the notation:
fξ fR f = Q f T η Example 6. Linearized Force Coefficients The stiffness and damping properties of the bearing in Example 2 are obtained from Figure 11.23a and 11.23b, respectively, with the eccentricity ratio ε = 1 – hn /C = 0.6.
K xx = 3.0 × 355.84 × 10 3 5.08 × 10 −2 = 21.0 MN cm K xy = 3.0 × 355.84 × 10 3 5.08 × 10 −2 = 21.0 MN cm K yx = −0.38 × 355.84 × 10 3 5.08 × 10 −2 = −2.66 MN cm K yy = 1.5 × 355.84 × 10 3 5.08 × 10 −2 = 10.5 MN cm
( (5.08 × 10 (5.08 × 10 (5.08 × 10
) × 251) = 47.4 kN ⋅ s cm × 251) = 47.4 kN ⋅ s cm × 251) = 50.2 kN ⋅ s cm
C xx = 7.0 × 355.84 84 × 10 3 5.08 × 10 −2 × 251 = 195.4 kN ⋅ s cm C xy = 1.7 × 355.84 × 10 3 C yx = 1.7 × 355.84 × 10 3 C yy = 1.8 × 355.84 × 10 3
−2
−2
−2
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FIGURE 11.23 Linearized force coefficients of a partial arc bearing: (a) stiffness, (b) damping. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
11.4.2 Stability of a Flexible Rotor If a rotor-bearing system is undisturbed, the rotor center will remain in its static equilibrium position. It will move out of that position, however, if disturbed. After the disturbance dies out, the rotor center may return to its static equilibrium position, in which case we have a stable system. If the disturbance does not die out, the rotor center will either orbit around its equilibrium position (limit cycle) or spiral outward until metal-to-metal contact occurs. It is of great practical importance to establish the stability boundaries of a given rotor-bearing system. Figure 11.24 illustrates a weightless shaft supporting a disk of mass M at its mid-span. The shaft, in its turn, is supported by identical, single-pad, journal bearings. The geometric center of the bearing is designated by Ob . Under the static load W = Mg the journal center occupies the position OJs while the mass center moves to OM. The equations of motion are: Rotor:
( −k ( y
) − y ) = My˙˙
−k x2 − x1 = Mx˙˙2 2
1
where k is the stiffness of the flexible rotor (both sides).
2
(11.93)
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FIGURE 11.23 (continued)
Modern Tribology Handbook
Note that the symbol Bxx is used here in place of Cxx to represent damping.
FIGURE 11.24 Schematic of rotor-bearing system. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
Bearing:
( + k( y
) −y )=0
2dFx + k x2 − x1 = 0 2dFy
2
1
(11.94)
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To solve Equations 11.93 and 11.94 assume that the centers of both journal and disk undergo harmonic motion according to
x1 X1 υt x2 X 2 υt y = Y e , y = Y e 1 1 2 2
(11.95)
The exponent υ is a complex quantity, υ = R(υ) + iI(υ), and we have
e υt = e
[ ()
( )]
( ) cos I υ t + i sin I υ t
R υ t
The real part of υ is the damping exponent. Stable motion, R(υ) < 0, is separated from unstable motion, R(υ) > 0, by the neutral state of stability, R(υ) = 0. The imaginary part of υ is the orbiting frequency. Substituting Equation 11.95 into the equations of motion, Equations 11.93 and 11.94, and eliminating the amplitude of rotor motion (X2, Y2), we obtain
α + 2K xx + 2 υC xx 2K yx + 2 υC yx
2K xy + 2 υC xy X1 0 = α + 2K yy + 2 υC yy Y1 0
(11.96)
Here we used the nondimensionalization
( ) {K ,C , k }, C
LDµN R C
{K , ωC , k} = {X ,Y } = C{x , y }, ij
1
ij
1
1
1
2
ij
ij
(11.97)
υ = ωυ, ω = ω N ω ,
and the abbreviation
α=
k υ 2ω 2 υ 2ω 2 + 1
(a real number)
For Equation 11.96 to have nontrivial solutions, the system determinants must vanish. Separating the real and imaginary parts of the determinant we have
α + 2K xx 2K yx
2K xy 2C + υ 2 xx α + 2K yy 2C xy
2C xx
2K xy
2C yx
α + 2K yy
υ+
2C yx =0 2C yy
α + 2K xx
2C xy
2K yx
2C yy
(11.98a)
υ=0
(11.98b)
)
(11.99)
On expansion, Equation 11.98a yields
α=
while Equation 11.98b results in
(
2 K xyC yx + K yxC xy − K yyC xx − K xxC yy
(C
xx
+ C yy
)
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FIGURE 11.25 Stability of a single mass rotor supported by full journal bearings. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
υ =− 2
(
)
(
α 2 + 2 K xx + K yy α + 4 K xx K yy − K xy K yx
(
4 C xxC yy − C yxC xy
)
)
(11.100)
Using the definition for α, we find the instability threshold value of the normalized frequency as
ωc2 =
α υ k −α 2
(
)
(11.101)
In the state of neutral stability, υ is purely imaginary, thus the whirl ratio υwhirl /ω is given by
υ whirl = − υ2 ω
(11.102)
– Figure 11.25 plots the stability parameter M = CMω2/W against the Sommerfeld number S. (Note that both ωc and υ are functions of the stiffness and damping evaluated in the static equilibrium position, which, in turn, is characterized by the Sommerfeld number alone.) Example 7. Rotor-Bearing Stability Determine the bearing-rotor stability for the following conditions:
D = 12.7 cm
µ = 1.38 × 10−2 Pa ⋅ s
L = 6.35 cm
K s ≡ k = 8.76 MN cm
C = 0.0127 cm
2W = 22.24 kN
N = 90 r s
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Calculate
P=
11.12 × 103 = 1.38 MPa 0.127 × 0.0635
S=
1.38 × 10−2 × 90 5002 = 0.225 1.38 × 106 2
L S = 0.0563 D C 1.27 × 10−4 8.76 × 108 = 10 Ks = W 11.12 × 103 1.27 × 10−4 22.24 × 103 2 C 2 × × 2π × 90 = 8.28 Mω = 3 . 9 807 W 11.12 × 10
(
)
Since the point (0.0563, 8.28) lies below the curve for (C/W)Ks = 10, the rotor is free of oil-whip instability. 11.4.2.1 Pivoted-Pad Bearings Calculating linearized force coefficients and stability characteristics of tilting-pad bearings is made difficult by having to take into account the motion of the pads as well as the rotor. The pad assembly method (Shapiro and Colsher, 1977) calculates the stiffness and damping coefficients associated with all degrees of freedom of a single pad over the whole range of eccentricities and stores them according to pivot film thickness. The performance characteristics of the tilting-pad bearing are then calculated in the following steps (viz., Figure 11.15): 1. Calculate individual pad performance data for a wide range of eccentricities and store according to pivot film thickness. 2. Fix position of journal (ψ = 0 for symmetric arrangement of identical, centrally pivoted pads). 3. Calculate film thickness over each pivot from bearing geometry and interpolate from previously stored pad data to obtain pad characteristics at operating conditions. 4. Form vectorial sum of individual pad characteristics to obtain bearing characteristics. Excitation frequency and pad inertia enter the analysis of the rotor-bearing system only when specific pad motion, necessary for the reduction of the results of the pad assembly method to “standard” 4 × 4 stiffness and damping matrices, is postulated. For this illustration of the pad assembly method the rotor is assumed rigid (2 degrees of freedom) and the bearings comprise N pads, each pad assuming its own orientation δi , i = 1, …, N (1 degree of freedom each). The equations of motion are as follows Rotor: N
Mx˙˙ + K xx x + K xy y + C xx x˙ + C xy y˙ +
∑ (K i =1
N
My˙˙ + K yx x + K yy y + C yx x˙ + C yy y˙ +
∑ (K i =1
)
(11.103a)
)
(11.103b)
δ + C xδi δ˙ i = 0
xδi i
δ + C yδi δ˙ i = 0
yδi i
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TABLE 11.6
–∆Fx –∆Fy –∆M1 –∆M2 –∆M3 –∆M4 –∆M5
Stiffness Matrix for a Five-Pad Bearing
∆x
∆y
∆δ1
∆δ2
∆δ3
∆δ4
∆δ5
Kxx Kyx Kδ1x Kδ2x Kδ3x Kδ4x Kδ5x
Kxy Kyy Kδ1y Kδ2y Kδ3y Kδ4y Kδ5y
Kxδ1 Kyδ1 Kδ1δ1 0 0 0 0
Kxδ2 Kyδ2 0 Kδ2δ2
Kxδ3 Kyδ3 0 0 Kδ3δ3 0 0
Kxδ4 Kyδ4 0 0 0 Kδ4δ4 0
Kxδ5 Kyδ5 0 0 0 0 Kδ5δ5
0 0 0
ith pad, i = 1, …, N:
I pδ˙˙ i + K δiδi δ i + Cδiδi δ˙ i + K δi x x + K δi y y + Cδi x x˙ + Cδi y y˙ = 0
(11.104)
The stiffness and damping terms in Equations 11.104 have the definitions
K xx = −
∆Fx ∆F ∆F ∆F ,…, C xx = − x ,…, K xδi = − x ,…, C xδi = − ˙ x ,… ∆x ∆x˙ ∆δ i ∆δ i
K δiδi = −
∆M i ∆M ∆M i ∆M i ,…, Cδiδi = − ˙ i ,…, K δi x = − ,…, Cδi x = − ,… ∆δ i ∆δ i ∆x ∆x˙
The coefficients Kxx,…,CδN y are calculated by perturbing the equilibrium of the shaft while keeping the pads in their respective position of static equilibrium. The coefficients Kxδ1,…,CδNδN, on the other hand, result from constraining the shaft to static equilibrium and perturbing the pitch angle or the angular velocity of the ith pad, i = 1,…,N. Table 11.6 displays the full stiffness matrix for a five-pad bearing. A pad supported on a rigid pivot will track journal vibration by rocking (pitching) about the pivot. However, the influence of pad inertia on dynamic spring and damping coefficients is negligible except when approaching pad resonance, which is characterized by the rotor motion and pad motion being 90° out of phase. Onset of pad resonance can be determined from the critical pad mass parameter, and requires calculation of the pad moment of inertia, Ip , about the pivot. Figures 11.26a through 11.26e plot the performance characteristics for a five-pad journal bearing. The pads are centrally loaded, the preload is zero, and shaft excitation occurs at the running speed. Critical pad mass is calculated from 2
CK ηη CωCηη + CWB M CRIT 1 WB WB = 2 CK ηη 4 πS 2 2 R µDL C WB
2
and is plotted in Figure 11.26e. Example 8. Pivoted-Pad Bearing Performance Find the performance of the five-pad journal bearing, given the following:
(11.105)
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FIGURE 11.26 Performance of five-pad tilting-pad bearing: (a) vertical stiffness, (b) horizontal stiffness, (c) damping (here, B), (d) critical pad–mass parameter. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
( )
β = 1.05 rad 60°
W = 11.12 kN
D = 12.7 cm
µ = 0.0138 Pa ⋅ s
L = 6.35 cm
ρ = 832.3 kg m 3
N = 60 r s
v = 0.1658 cm2 s
C = C ′ = 0.0127 cm
m = 0.0
The Sommerfeld and Reynolds numbers are calculated as
S=
0.0138 × 60 1.3789 × 106
Re =
× 5002 = 0.15
0.0635 × 2π × 60 × 1.27 × 10−4 1.658 × 10−5
(
= 183 < 1000 laminar
)
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FIGURE 11.26 (continued)
Entering Figure 11.16a at S = 0.15 we find hn /C = 0.26. The power loss is obtained from Figure 11.16b, H/(2πWNC) = 3.9, and the normalized bearing eccentricity, ε′ = ε0 /1.2361 = 0.67, from Figure 11.16c. To obtain the linearized force coefficients enter Figures 11.25a through 11.25c at ε′ = 0.67
)
hn = 0.0033 cm
H = 2.08 kW
K xx = 4.4 MN cm
K yy = 2.1 MN cm
C xx = 8.4 kN ⋅ s cm
C yy = 4.7 kN ⋅ s cm
The critical pad mass can be estimated from Figure 11.25d
M crit =
[
0.45 × 0.0138 × 0.127 × 0.0635 × 5002 1.27 × 10−4 × 11.12 × 103
]
2
= 246.7 kg
and the critical pad polar moment of inertia is (Ip)crit = 246.7 × 0.06352 = 0.9946 kg · m2.
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FIGURE 11.26 (continued)
If t is the thickness of the pad, rp + t1 is the radius of the pivot circle, i.e., distance between pivot point and center of pad, and α1, α2 represent the angular distance of pivot from the edges of the bearing. The polar moment of inertia of the pad can be obtained from
(
)
sin α + sin α 1 2 I p = 2rp2 M p 1 + f1 − f2 β
(11.106)
where 2 2 t1 1 t1 1 t 1 t f1 = + + + 2 rp 2 rp 4 rp r p 2 t t 1 t 1 f2 = 1 + 1 + + 2 rp r rp p
1 t 1 + 2 rp
For α1 = α2 = 30° and t = t1 = 0.0 we have rp = D/2 and (Ip)actual = 2rp2 M [1 – 2 sin 30°/1.05] = 3.84 × 10–4M. If the actual pad mass is less than 0.9946/3.84 × 10–4 = 2590 kg, there is no danger of pad resonance.
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FIGURE 11.26 (continued)
11.5
Elastohydrodynamic Lubrication
Elastohydrodynamic lubrication (EHL) is the name given to hydrodynamic lubrication when applied to solid surfaces of low geometric conformity that deform elastically. In bearings utilizing this mode of lubrication, the pressure and film thickness are of order 1 GP and 1 µm, respectively — under such conditions, conventional lubricants exhibit material behavior distinctly different from their bulk properties at normal pressure. In fact, without taking into account the viscosity–pressure characteristics of the liquid lubricant and the elastic deformation of the bounding solids, hydrodynamic theory is incapable of explaining the existence of continuous lubricant films in highly loaded gears and rolling contact bearings. The principal features of EHL contacts are: (1) the film thickness is nearly uniform over the contact zone, but displays a sudden decrease just upstream of the trailing edge, (2) the pressure distribution curve follows the Hertzian ellipse over most of the contact zone, but a sharp second pressure maximum manifests itself at high speeds and light loads (Figures 11.27 and 11.28). The principal variable of interest in EHL lubrication is the minimum film thickness, but to estimate this we need simultaneous solutions of the Reynolds equation, the equations of elasticity, and the viscosity–pressure relationship of the lubricant. Contact mechanics has been discussed in detail elsewhere in this handbook; here we list only formulas required in our sample calculations of minimum film thickness.
11.5.1 Contact Mechanics When two convex, elastic bodies come into contact under zero load, they touch along a line (e.g., cylinder on a plane) or in a point (e.g., two spheres). However, on increasing the normal contact load, the bodies
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FIGURE 11.27 Pressure and film thickness in EHL contact for (a) steel and mineral oil and (b) bronze and mineral – oil under high load, p = p/E′, H = h/R. (From Dowson, D. and Higginson, G.R. 1960. Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Reprinted by permission of the Council of the Institution of Mechanical Engineers.)
deform to yield small, though finite, areas of contact, ensuring finiteness of the surface stresses. The shape of this finite contact zone is an infinite strip for nominal line contact, and an ellipse for nominal point contact. To facilitate further discussion, we replace our bodies in the neighborhood of the point of contact by ellipsoids that have the same principal curvatures, r1x, r1y , and, r2x, r2y , as bodies 1 and 2, respectively. The principal relative radii of curvature, Rx, Ry , are specified by
1 1 1 = + , Rx r1 x r2 x
1 1 1 = + Ry r1 y r2 y
The contours of constant gap h between the undeformed surfaces are the ellipses
x2 2hR x
2
+
y2 2hR y
2
=1
(11.107)
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FIGURE 11.28 Pressure and film thickness in EHL contact for (a) steel-mineral oil and (b) bronze-mineral oil – under low load, p = p/E′, H = h/R. (From Dowson, D. and Higginson, G.R. 1960. Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Reprinted by permission of the Council of the Institution of Mechanical Engineers.)
the ratio of whose axes are given by (Ry /Rx)1/2. When pressed together, the bodies deform in the neighborhood of the point of their first contact, and touch over a finite area. Though the contact area also has the shape of an ellipse, the ratio of whose semi axes, κ = b/a, depends on (Ry /Rx)1/2 alone, κ = (Ry /Rx)1/2 only in the limit (Ry /Rx) → 1. The ratio of the semi axes, κ, is called the ellipticity parameter; it can be calculated from the approximate formula
R κ ≈ α r2 π , α r = y Rx
(11.108a)
The elastic deflection of the surfaces δ is given by (Harris, 1991) 2 9 w δ = F 2ER πκE ′
1 3
where the composite modulus, E′, and the composite radius of curvature, R, are defined by
(11.108b)
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TABLE 11.7 Parameters Employed in EHL Design Formulas Type of Contact
Parameter Film Thickness, H Load, W Speed, U Materials, G Ellipticity, κ
Point
Line
h/Rx w/Rx2 E′ µoV/E′Rx αE′ b/a
h/Rx w/RxLE′ ˜ ′R x µ0u/E αE′ —
u˜ = (u1 + u2)/2, V = (u2 + v2)1/2
1 1 1 − v12 1 − v22 = + , E ′ 2 E1 E2
1 1 1 = + R Rx Ry
The functions F and E are elliptic functions of αr that can be conveniently approximated by the formulas
π E ≈ 1 + − 1 α r , 2
F≈
π π + − 1 ln α r 2 2
11.5.2 Dimensional Analysis The EHL problem is characterized by such a multitude of independent parameters that tabulation of EHL solutions is impractical. The number of these parameters can, however, be significantly reduced through an application of dimensional analysis. Assuming pressure dependence of lubricant viscosity in the form µ = µo exp(αp), dimensional analysis of the EHL problem yields
(
)
Φ H , U , W , G, κ = 0
(11.109)
For the two types of contacts, viz., nominal line and nominal point, the parameters in Equation 11.109 have somewhat differing definitions, as shown in Table 11.7. We also note that the ellipticity parameter κ does not appear in Equation 11.109 when application is to line contacts (Arnell et al., 1991; Hamrock and Dowson, 1981). Although we have reduced the number of independent variables through application of dimensional analysis, the film thickness variable H is still dependent on four nondimensional groups U, W, G, and κ, and tabulation of H is still a formidable task. However, with little sacrifice to accuracy of representation, the number of nondimensional groups involved in determining the film thickness can be further reduced by employing another set of nondimensional groups, constructed by combining the elements of the sets in Table 11.7. The new parameters, gH , gE , gV , and κ have the added advantage that they are easily identified with the main characteristics of EHL: they represent film thickness, deviation from isoviscosity, deviation from rigidity, and the geometry of the contact: 1. gV = 0, gE = 0, Rigid – Isoviscous Regime: The pressure is low enough to leave the viscosity unaltered; neither does it cause significant elastic deformation of the surfaces. This is the condition encountered in hydrodynamic journal and thrust bearings and in lightly loaded counterformal contacts. 2. gV ≠ 0, gE = 0, Rigid — Piezoviscous Regime: The pressure is high enough to effectively change the lubricant’s viscosity (for certain types of lubricants) from its inlet value, yet not as high as to initiate significant elastic deformation in the bearing material.
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3. gE ≠ 0, gV = 0, Elastic — Isoviscous Regime: Characterized by significant elastic deformation but the pressure is not high enough to affect the viscosity of the particular lubricant employed (also, soft EHL). 4. gE ≠ 0, gV ≠ 0, Elastic — Piezoviscous Regime: The elastic deformation of the surfaces can be orders of magnitude larger than the thickness of the film and the lubricant viscosity orders of magnitude higher than its bulk value (also, hard EHL). The dimensionless groups gH , gE, gV , and κ are not formed identically for line and point contacts and will be listed separately. 2
W gH = H U GW 3 gV = 2 U W gH = H U W 3 2G gV = 1 2 U
0.636 R κ = 1.0339 y Rx g E = W 8 3U 2
gE =
nominal point contact
(11.110)
nominal line contact
(11.111)
W U1 2
We now have the relationship
(
g H = Ψ g V , g E ,κ
)
(11.112)
in place of Equation 11.109, and the task is to find the function Ψ(gV , gE , κ) over practical ranges of its arguments (in nominal line contact, drop κ from the list). This is accomplished by solving the EHL problem for a number of inputs (gV , gE , κ) and then curve fitting to the surface gH = Ψ(gV , gE , κ) in fourdimensional parameter space. For a nominal line contact, for example, the EHL problem is defined by a system composed of the following equations and boundary conditions: 1. Reynolds equation and its boundary condition:
h−h dp = 12µu˜ 3 o dx h p = 0 at x = xi p = 0,
dp = 0 at x = xo dx
2. Viscosity–pressure correlation of Roeland (z is a material parameter):
µ = exp ln µ 0 + 9.67
(
)−1 + (1 + 5.1 × 10 p) −9
z
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3. Lubricant density–pressure correlation of Dowson and Higginson (p in MPa):
0.6 × 10−3 p ρ = ρo 1 + −3 1 + 1.7 × 10 p 4. Elastic deformation:
()
h x = hw +
x2 2 − 2Rx πE ′
∫ () ( ) x0
2
p s ln x − s ds
xi
5. Force balance (w′ is the external load)
∫ p(x )dx x0
w′ =
xi
The various lubrication regimes are depicted in Figures 11.29 and 11.30.
11.5.3 Film-Thickness Design Formulas Nominal Line Contact (Arnell et al., 1991) 1. Rigid-Isoviscous regime: gH = 2.45 2. Rigid-Piezoviscous regime: gH = 1.05 gV2/3 3. Elastic-Isoviscous regime: gH = 2.45 gE0.8 4. Full EHL regime: gH = 1.654 gV0.54 gE0.06
(11.113)
Nominal Point Contact (Hamrock and Dowson, 1981) 2
α 1. Rigid-Isoviscous regime: g H = 128α r λ2b 0.131 tan −1 r + 1.683 , λ b = 1 + 2 3α r 2
[
2. Rigid-Piezoviscous regime: g H = 141g V0.375 1 − e −0.0387α r
[
] ]
(
)
−1
(11.114)
3. Elastic-Isoviscous regime: g H = 8.70 g E0.67 1 − 0.85e −0.31κ
[
4. Full EHL regime: g H = 3.42 g V0.49 g E0.17 1 − e −0.68κ
]
11.5.4 Minimum Film Thickness Calculations Example 9. Nominal Line Contact (Table 11.8) Cylindrical roller bearing geometry is depicted in Figure 11.31. Stribeck’s formula calculates the load on the most heavily loaded roller as
wmax =
4w = 4.8kN n
The radii of curvature at contact on the inner and outer race, respectively, are
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10000
gh = 500 gh = 300 gh = 200
1000
gh = 100 gh = 70
Rigid piezoviscous u ti c c o a s is El zov e pi
Viscosity parameter gv
gh = 50 gh = 30
100
s
gh = 20 gh = 10 10
gh = 7
gh = 5
a El
st
ic
i
us co is v so
1.0 Rigid isoviscous
gh = 4.9 0.1 0.1
1.0
10
100
10,000
Elasticity parameter ge
FIGURE 11.29 Map of lubrication regimes for nominal line contact. (From Arnell, R.D., Davies, P.B., Halling, J., and Whomes, T.L. (1991), Tribology Principles and Design Applications, Springer Verlag. With permission.)
1 1 1 5 = + = Rx , i 0.08 0.032 0.032
1 1 1 5 = − = Rx , o 0.08 0.048 0.048
yielding Rx,i = 0.0064 m, and Rx,o = 0.0096 m. The effective modulus E′ and the pitch diameter de are
E′ =
2 1− v 1− v + E1 E2 2 1
2 2
= 228 GPa,
de =
d0 + di = 0.08 m 2
Assuming pure rolling, the surface velocity for cylindrical rollers is calculated from (Hamrock, 1991)
u˜ =
ω i + ω 0 × de2 − d 2 4de
= 10.061 m s
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FIGURE 11.30 Map of lubrication regimes for nominal point contact, (a) κ = 1, (b) κ = 3, (c) κ = 6. (From Hamrock, B.J. and Dowson, D. (1981), Ball Bearing Lubrication, John Wiley & Sons. With permission.)
Calculation will be performed for the inner-race contact alone. The relevant parameters are
U=
µ 0u˜ 0.01 × 10.061 = 6.895 × 10−11 = 11 E ′Rx , i 2.28 × 10 × 0.0064
W=
wmax 4800 = = 2.0559 × 10−4 11 E ′LRx , i 2.28 × 10 × 0.016 × 0.0064
G = αE ′ = 2.2 × 10−8 × 2.28 × 1011 = 5.016 × 103 The effects of viscosity change and elastic deformation are indicated by the parameters
gV =
W 2 3G = 1.7804 × 103 , U1 2
gE =
W = 24.759 U1 2
The point (gV , gE) characterizing conditions at the inner contact can be plotted in Figure 11.29, showing that full EHL conditions apply. Thus the minimum film thickness calculations are
g H = 1.6549 g V0.54 g 0E.06 = 114.15
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FIGURE 11.30 (continued)
U H min = g H = 3.8284 × 10−5 W hmin = Rx , i H min = 0.245 µm Example 10. Nominal Point Contact (Table 11.9) Spherical roller bearing geometry is depicted in Figure 11.32. The inner-race contact calculations are as follows. The pitch diameter is
de =
(d + d ) = 0.065 m o
e
2
and the equivalent radii and curvature are
Rx = Ry =
(
d de − d cos β 2de
) = 0.00511 m
rd i = 0.165 m 2ri − d
1 1 1 = + = 201.76 R Rx Ry
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FIGURE 11.30 (continued)
TABLE 11.8 Problem
Data for Nominal Line Contact
Inner-race diameter Outer-race diameter Roller diameter Roller axial length No. Rollers per bearing Radial load per roller Inner-race angular velocity Outer-race angular velocity Absolute viscosity Viscosity–pressure coefficient Elastic modulus (rollers, races) Poisson’s ratio
di = 0.064 m do = 0.096 m d = 0.016 m l = 0.016 m n=9 w = 10.8 kN ωi = 524 rad/s ωi = 0 µ0 = 0.001 Pa · s α = 2.2 × 10–8 Pa–1 E = 207.5 GPa v = 0.3
yielding R = 4.956 × 10–3 m, αR = RY/Rx = 32.29, and an ellipticity parameter
κ = α r2 3 = 9.1348
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FIGURE 11.31 Schematic of a cylindrical roller bearing. (From Szeri, A.Z. (1998) Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
TABLE 11.9 Problem
Date for Nominal Point Contact
Inner-race diameter Outer-race diameter Ball diameter No. of balls per bearing Inner-groove radius Outer-groove radius Contact angle Radial load Inner-race angular velocity Outer-race angular velocity Absolute viscosity Viscosity–pressure coefficient Modulus of elasticity Poisson’s ratio
di = 0.052291 m do = 0.077706 m d = 0.012700 m n=9 ri = 0.006604 m ro = 0.006604 m β=0 wz = 8.9 kN ωi = 400 rad/s ωo = 0 µ0 = 0.04 Pa · s α = 2.3 × 10–8 Pa–1 E = 200 GPa v = 0.3
The approximate formulae for the elliptic integrals give
π E = 1 + − 1 α r = 1.0177 2 F=
π π + − 1 ln α r = 3.5542 2 2
Using E′ = 219.8 MPa for effective modulus and Stribeck’s estimate for the maximum load
wmax = the deformation is estimated from
5w z = 4.944 kN n
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FIGURE 11.32 Schematics of a ball bearing. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
2 9 wmax δ=F 2ER πκE ′
13
= 29.087 µm
Assuming pure rolling, the surface velocity is calculated from (Hamrock, 1991)
u˜ =
wo − wi de2 − d 2 4de
= 6.252 m s
and the design parameters are
U=
µ 0u˜ 0.04 × 6.252 = 2.227 × 10−10 = E ′Rx 2.198 × 1011 × 5.11 × 10−3
G = αE ′ = 2.3 × 10−8 × 2.198 × 1011 = 5.055 × 103 W=
wmax E ′Rx2
=
4944.0
(
2.198 × 10 × 5.11 × 10 11
−3
)
2
= 8.6141 × 10−4
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The minimum film thickness variable is
[
g H = 3.42 g V0.49 g E0.17 1 − e −0.68κ
]
(11.115)
Substituting
GW 3 g V = 2 = 6.5149 × 1013 U g E = W 8 3U 2 = 1.3545 × 1011 into Equation 11.115 we find
g H = 1.5645 × 109 U2 H = g H = 1.0457 × 10−4 W and
hmin = rx H = 0.00511 × 1.0457 × 10−4 = 0.5345 µm
References Arnell, R.D., Davies, P.B., Halling, J., and Whomes, T.L. (1991), Tribology Principles and Design Applications, Springer-Verlag, New York. Dowson, D. and Higginson, G.R. (1960), Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Hamrock, B.J. (1991), Fundamentals of Fluid Film Lubrication, NASA Reference Publication 1255. Hamrock, B.J. and Dowson, D. (1981), Ball Bearing Lubrication, John Wiley & Sons, New York. Harris, T.A. (1991), Rolling Bearing Analysis, John Wiley & Sons, New York. Kaufman, H.N., Szeri, A.Z., and Raimondi, A.A. (1978), Performance of a centrifugal disk-lubricated bearing, Trans. ASLE, 21, 314-22. Lund, J.W. (1964), Spring and damping coefficients for the tilting pad journal bearing, ASLE Trans., 7, 342. Patir, N. and Cheng, H.S. (1978), An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, ASME J. Lub. Tech., 100, 12-7. Patir, N. and Cheng, H.S. (1979), Application of average flow model to lubrication between rough sliding surfaces, ASME J. Lub. Tech., 101, 220-30. Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. Shapiro, W. and Colsher, R. (1977), Dynamic characteristics of fluid-film bearings, Proc. 6th Turbomachinery Symp., Texas A&M University, 39-54. Suganami, T. and Szeri, A.Z. (1979a), A thermohydrodynamic analysis of journal bearings, ASME J. Lub. Tech., 101, 21-7. Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press, Cambridge. Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F., 92, 466-72.
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451
Recommendations for Further Reading The treatment of fluid film bearings in this chapter essentially follows that in Szeri, A.Z.: Fluid Film Bearings, Theory and Design, Cambridge University Press, 1998. However, while results are often only quoted here without derivation, they are rigorously derived in the book. For the other than casual reader, we strongly recommend the above-cited book by Szeri. Extensive treatment of the elastohydrodynamic problem can be found in Hamrock, B.J. and Dowson, D.: Ball Bearing Lubrication, John Wiley & Sons, 1981; Hamrock, B. J.: Fundamentals of Fluid Film Lubrication, NASA, 1991, and in the series of papers by these two authors that appeared in the ASME Journal of Lubrication Technology (now, Journal of Tribology) during the 1970s. For a thorough treatment of rolling element bearings we recommend Harris, T.A.: Contact Bearing Analysis, John Wiley & Sons, 1991. This book discusses not only the more practical aspects of rolling element bearings, but also gives a lucid exposition of the underlying contact mechanics. For readers interested in the thermal aspects of fluid film lubrication, the French language book Lubrification Hydrodynamique by Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. is recommended. Another extensive treatment of THD lubrication can be found in Pinkus, O.: Thermal Aspects of Fluid Film Tribology, ASME Press, 1990.
Nomenclature A B C C′ Cxx ,…,Cyy Cξξ ,…,Cηη D E′ F, FR, FT Fµ G H Hp , Hf , HT Kxx ,…,Kyy Kξξ ,…,Kηη L Mcrit N P Q Qs R, I RB, RJ RP R1, R2 RB, RC Rx, Ry S
area of hydrostatic pad slider dimension (in direction of motion) radial clearance pivot circle clearance bearing damping coefficients fixed pad damping coefficients bearing diameter effective elastic modulus oil film force, radial and tangential components friction force material parameter film thickness parameter, dimensionless film thickness pumping power, shear power, total power bearing spring coefficients fixed pad spring coefficients bearing length critical pad mass shaft speed lubricant force per projected bearing area rate of flow side leakage real, imaginary part radius of bearing, journal radius of pivot circle hydrostatic pad inner and outer radii resistance resulting from bearing, capillary relative principal radii of curvature Sommerfeld number
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T U U, V UM V0 W af a, b gE mr , mθ h, hc , h1, h2 hf gH gV pH rix, riy c cµ dc f, fR, fT lc m p, pc pr, pa, ps pi qi qf t ui (u, v, w) u˜ v xi (x, y, z) xp Γ1, Γ2 α β δ ε θ θ1, θ2 λ µ ρ σ τ φ ω ωw ε0 ξ, η φ0
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temperature velocity parameter surface velocity components maximum surface velocity squeeze velocity external load, load parameter area factor semi-axes of elliptical contact elasticity parameter radial, azimuthal tilt parameter film thickness, at pad center, minimum, maximum friction factor film parameter viscosity parameter maximum Hertzian pressure principal radii of curvature specific heat coefficient of friction diameter of capillary restrictor dimensionless lubricant force, radial and tangential components length of capillary restrictor slope of bearing surfaces, preload parameter pressure, center line pressure recess, ambient, supply pressures inlet pressures inflow variable flow factor time lubricant velocity components effective velocity lubricant velocity vector orthogonal Cartesian coordinates pivot position recess boundary, pad external boundary angular coordinate position of load relative to pad leading edge, pressure-viscosity coefficient pad angle dimensionless pivot position, surface deflection eccentricity ratio angular coordinate measured from line of centers angular coordinates of pad leading edge, trailing edge dimensionless bearing stiffness lubricant viscosity lubricant density standard deviation shear stress attitude angle shaft angular velocity angular frequency of applied load eccentricity ratio with respect to the bearing center coordinates of journal center with respect to the pad attitude angle with respect to the bearing load line
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ψn αr κ ( )
( )cav
angle from vertical (negative x-axis) to pad pivot point ratio Ry /Rx ellipticity parameter dimensionless quantity evaluated at fluid-cavity interface
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12 Boundary Lubrication and Boundary Lubricating Films 12.1
Introduction ..................................................................... 455 Definitions
12.2
The Nature of Surfaces .................................................... 457 Surface Structures and Compositions • Surface Energy and Reactivity • Surface Emission under Stress • Surface Roughness and Relative Conformity
12.3
Lubricants and Their Reactions ...................................... 459 Lubricant Basestocks and Additives • Relationship Between Oxidation Reactions and Film Formation • Organometallic Chemistry and Tribochemistry
12.4
Physical and Chemical Properties • The Detection of Organometallic Compounds in Films • Mechanical Properties of Boundary Lubricating Films • Advances in Measurement Techniques
Stephen M. Hsu National Institute of Standards and Technology
12.5
Richard S. Gates National Institute of Standards and Technology
12.1
Boundary Lubricating Films ........................................... 468
Boundary Lubrication Modeling .................................... 479 Wear • Flash Temperatures • Asperity-Asperity Understanding • Molecular Dynamics Modeling
12.6
Concluding Remarks ....................................................... 486
Introduction
Lubrication may be defined as any means capable of controlling friction and wear of interacting surfaces in relative motion under load. Gases, liquids, and solids have been used successfully as lubricants. Boundary lubrication usually occurs under high load and low speed conditions in bearings, gears, cam and tappet interfaces, piston rings and liner interfaces, pumps, transmissions, etc. In many cases, it is the critical lubrication regime that governs the life of the components subject to wear. Because of its industrial significance, many studies have been conducted in the past. The most comprehensive was the 1969 assessment by the American Society of Mechanical Engineers (ASME) Research Committee on Lubrication (Ling et al., 1969). The study included critical reviews on surface physics, chemistry, fluid mechanics, contact mechanics, and materials science. The major conclusion in that review was that more research was needed to understand the complex chemical, physical, and material interactions. Since then, topical symposia have been organized by different researchers on lubricant chemistry, contact mechanics, microelastohydrodynamic lubrication (µ-EHL), analytical techniques, boundary films, and molecular dynamics simulations. Cross communication and integration of the significant advances in analytical chemistry, surface analysis, materials sciences, and molecular modeling, however, have seldom been made. This chapter attempts to provide a bird’s eye view across these disciplines. 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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12.1.1 Definitions When the contact geometry and the operating conditions are such that the load is fully supported by a fluid film, the surfaces are completely separated. This is generally referred to as the hydrodynamic lubrication. Theory for fluid film design is well developed based on Reynolds’ equations and continuum mechanics (Reynolds, 1886). When the load is high and/or the speed is low, the hydrodynamic or hydrostatic pressure may not be sufficient to fully support the load, and the surfaces come into contact. The contact occurs at the peaks and hills of the surfaces, and these are referred to as asperities. The amount and the extent of the asperity contact depend on many factors: surface roughness, fluid film pressure, normal load, hardness, and elasticity of the asperities, etc. Many of the asperities undergo elastic deformation under the contacting conditions, and the normal load is supported by the asperities and the thin fluid film. This condition is generally referred to as the elastohydrodynamic lubrication (EHL) (Dowson and Higginson, 1959). The EHL theories are reasonably well developed and are capable of describing the surface temperatures, fluid film thickness, and the fluid film pressures supporting the load. The theory assumes continuum mechanics and does not take into account the effects of wear and the presence of a third body (wear debris). No chemical effect between the asperity and the lubricant is taken into account. Further increase in the contact pressure beyond the EHL conditions causes the contacting asperities to deform plastically and the number of contacts to increase as well as for the fluid film thickness to decrease. When the average fluid film thickness falls below the average relative surface roughness, surface contact becomes a major part of the load supporting system. Mechanical interactions of these contacts produce wear, deformation, abrasion, adhesion, and fatigue under dry sliding conditions. Chemical reactions between the lubricant molecules and the asperity surface, due to frictional heating, often produce a boundary chemical film which can be either beneficial or detrimental in terms of wear. The combination of the load sharing by the asperities and the occurrence of chemical reactions constitutes the lubrication regime commonly referred to as the boundary lubrication (BL) regime. Figure 12.1 shows an approximation of the relationship for these regimes as they relate to coefficient of friction and contact severity. Under boundary lubrication conditions, interactions between the two surfaces take place in the form of asperities colliding with each other. These collisions produce a wide range of consequences at the asperity level, from elastic deformation to plastic deformation to fracture. These collisions produce friction, heat, and sometimes wear. Chemical reactions between lubricant molecules and surfaces usually accompany such collisions producing organic and inorganic surface films. It has long been thought that surface films protect against wear. Closer examination (Hsu, 1991) suggests that some films are protective (antiwear), some films are benign, and some films are detrimental (prowear). A theory for a comprehensive view on boundary lubrication is currently lacking; however, models on lubricant chemistry and contact mechanics do exist (Klaus et al., 1991; Blencoe et al., 1998; Yang et al., 1996; Cheng and Lee, 1989). Recently, molecular dynamics models have been developed to describe atomic interactions under simplified boundary lubricated conditions (Stuart and Harrison, 1999). The detailed physical and chemical processes occurring in the contact zone are still not well understood. Where does EHL end and BL begin? Since the surfaces have a range of asperity height distributions, two surfaces in contact produce a range of distribution of stresses within the contact zone. Therefore, in practical systems there is often no pure EHL or BL lubrication regime, and a mixed lubrication regime exists. Some asperities are in the hydrodynamic mode, some asperities in EHL, and some asperities in BL mode. As wear occurs, surface topography also changes. Depending on the nature and extent of chemical reactions, conformity of surfaces can either develop or disappear. This changes the real area of contact and, hence, the asperity stress distribution. The following sections will attempt to present the current view of boundary lubrication and address some of the important issues. We will discuss the following topics: the nature of surfaces, lubricants and their reactions, boundary lubricating film formation, and modeling and prediction of boundary lubrication.
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FIGURE 12.1
12.2
457
Comparison of lubrication regimes encountered under different contact severities.
The Nature of Surfaces
12.2.1 Surface Structures and Compositions Engineering materials usually go through a series of manufacturing/fabrication and machining/polishing steps to become load-bearing components in machinery. These steps invariably change the surface structure and sometimes the chemical composition. For most engineering surfaces, the surface is covered with oxides. In the case of iron-based alloys, for example, the surface is covered with oxides of iron such as FeO, Fe3O4 , and Fe2O3. The subsurface beneath the oxide is often a deformed or case-hardened layer, often called the Beilby layer, which is the result of the machining and polishing steps and/or heat treatment the material has undergone during the manufacturing process. The microstructure of this layer generally is a microcrystalline phase dispersed in an amorphous phase for most steels. Specific compositions depend on the particular alloying elements present.
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Contaminants in the alloying elements often diffuse to the surface during the manufacturing process, resulting in higher concentrations of the minor elements near the surface than the bulk material. The atoms in solids are bonded together by different forces. They are: covalent, ionic, metallic, hydrogen and van der Waals. Covalent bonds are strong bonds that are formed when electrons are shared between atoms of similar electronegativity. They have an intrinsic directional nature. Ionic bonds result when complete electron transfer takes place between atoms of different electronegativity. Coulombic attraction between the resulting charged ions results in strong bonds. Metallic bonds are the result of attractive coulombic forces between positive metallic atoms with commonly shared free negative electrons resulting in high electrical and thermal conductivity. Hydrogen bonds refer to when hydrogen acts as a bridge between its primary bond to an electronegative atom and another electronegative atom. van der Waals forces are weaker long-range forces that result from dipole–dipole interactions between atoms; they influence bonding strengths in some solids. These bonds have different strengths and require different amounts of energy to break them. Additionally, in a solid, complex atomic and molecular units must fit together with a periodicity that minimizes electrostatic repulsive forces. When different bonds are broken (by mechanical or chemical means), the resulting surface energy and reactivity are different. For single crystalline solids, different crystalline planes often exhibit different physical, mechanical, and chemical properties. Frictional studies have shown that different crystalline phases produce different frictional resistance to sliding when subjected to the same conditions (Buckley, D.H., 1981). Thus, polycrystalline solids as well as polymeric solids often have anisotropic properties. This adds to the complexity of the surface structure/properties relationships. Under boundary lubricated conditions, different crystalline phases also exhibit different reactivity to lubricants, moisture, oxidation, and surface contaminants under sliding conditions.
12.2.2 Surface Energy and Reactivity Surface energy for most engineering surfaces is difficult to determine. Rabinowicz (Rabinowicz, 1965) has suggested that the surface energy of a solid can be approximated by using the surface energy of the liquid at the melting point of the material. The agreement between this approximation and experimentally determined value for simple pure materials is surprisingly good. It was further shown that the ratio of the surface energy to penetration hardness could be correlated to friction, i.e., lower the ratio, lower the friction. Thermodynamically, the higher the surface energy, the more reactive the surface will be. Therefore knowing the surface energy will give an indication of the potential chemical reactivity toward oxygen, water, and lubricants. Unfortunately, as has been discussed before, the surface is covered with oxides, other impurities, and mechanically altered layers. When the surface roughness is superimposed on it, the energy of the engineering surface is very difficult to estimate. Additionally, as with any solids, there are defects. Atomic misalignment, lattice mismatch defects, dislocations, voids, and phase segregations abound in solids. When these defects are on the surface, including steps, twists, kinks for crystalline solids, they provide high-energy sites at which chemical reactions, adsorption, and catalysis take place preferentially (Yates et al., 1996). Experimentally, contact angle measurements with a series of well-known liquids have been used to estimate “surface energy” of a smooth solid surface. Results are useful to understand wettability and spreading of liquids on that solid surface, but caution must be used in generalizing to other surfaces.
12.2.3 Surface Emission under Stress When atomic bonds are broken at the surface by mechanical processes, energy is both consumed and released. This often changes the surface energy state. When all the oxides and other mechanically deformed layers are broken through by scratches, nascent surface emerges. The energy state of such nascent surfaces is high compared with the “normal” surfaces.
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Simoi et al. (1968) suggested that the rubbing of metal surfaces produced highly localized electron clouds, referred to as the “exo-electrons.” The presence of these electrons had also been detected by others (Ramsey, 1967; Rosenblum et al., 1977). How this electron cloud could induce reactions that otherwise would not occur remained to be proven. Lenahan (1990) reported the measurement of dangling bonds on silicon nitride, suggesting that rubbing might produce dangling bonds on crystalline surfaces, and these dangling bonds were highly energetic and reactive. Nakayama (1991) detected the emissions of charged particles, electrons, and photons from scratched silicon-based ceramics. Dickinson et al. (1993) observed the emission of particles and electrons from fracture of crystalline surfaces. In repeated single-pass experiments, Ying (1994) observed the surface to be highly strained and ordered for various metals. Strain-induced fracture and deformation appeared to be the dominant mechanisms under lubricated conditions for metals. Would this highly strained state upon fracture produce electrons and charged particles?
12.2.4 Surface Roughness and Relative Conformity Surfaces have microscopic roughnesses which are often random in nature. Under concentrated contact, these asperities are deformed either elastically or plastically to form the interface. So the initial interface depends on the relative hardness and the relative roughness of the two surfaces in contact. If the two surfaces conform perfectly to each other and all the asperities are deformed 100%, then the real contact area is equal to the apparent contact area. Of course, this is not the case for most engineering contacts. For highly loaded steel bearing surfaces under sliding conditions, the real area of contact may be only 15 to 25% of the apparent area of contact (Wang et al., 1991) depending on other parameters, such as relative surface roughness and the relative surface hardness. If the normal force acting on the surface is very high, then some plastic deformation will also occur. Greenwood and Williamson and others have studied this topic extensively (Greenwood and Williamson, 1966; McCool, 1986). On each asperity, there are subasperities which are smaller in scale. On each subasperity, there are sub-subasperities, and so on. If the distribution of asperity heights is Gaussian in nature, such as in the case of ball bearings, the typical surface roughness parameters such as average roughness (Ra), root mean square roughness (RMS), skewness, and kurtosis, will be adequate in describing the surface roughness. However, if the asperity height distribution is not Gaussian, as for example, when two or three major peaks have many smaller-scale subasperities, then the multimodal characteristics of the load-bearing asperities become important. In lubrication, the surface roughness is an important indicator as well as a significant parameter in the calculation of oil film thickness. Wang et al. (1991) suggested that in a lubricated case, even though the surfaces may be rough, if they conform to each other under plastic yielding, then the relative surface roughness may be quite small. Oil film calculations based on elastohydrodynamics may yield significantly smaller film thickness than is actually present. Conformity has been demonstrated to change with time, materials, chemical additives, and wear modes (Wang et al., 1991).
12.3
Lubricants and Their Reactions
In lubricated systems, liquid lubricants are commonly used. When liquid lubricants are used in engines and machineries, they serve multiple functions. They control friction and wear, cool the surfaces, remove debris and contaminants, generate hydrodynamic pressures to support load, and redistribute stresses over the surface. Since most of the liquid lubricants are hydrocarbons, they tend to oxidize, thermally decompose, and polymerize. These reactions produce high-molecular-weight reaction products which lead to the formation of “friction polymers.” To understand the interplay between these reactions and wear, we need to understand the chemical reactions that take place as well as the chemical composition of the lubricants.
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12.3.1 Lubricant Basestocks and Additives Modern liquid lubricants are compounded from lubricating basestocks and chemical additives. Selective combination of the two produces a myriad of special lubricants designed for different applications. There are two major classes of basestocks: (a) petroleum or mineral-oil derived; and (b) specially synthesized basestocks. 12.3.1.1 Petroleum Basestocks Petroleum basestocks are selected hydrocarbon fractions derived from crude oils. They generally consist of molecules containing 18 to 40 carbon atoms in three basic hydrocarbon types: (a) paraffins, (b) aromatics, and (c) naphthenes (cycloparaffins). Most of the molecules are of the mixed type containing two or more basic hydrocarbon structures. These basestocks also contain a small percentage of compounds containing heteroatoms, such as sulfur, nitrogen, or oxygen, substituted into the various hydrocarbon structures. Typical molecular structures are illustrated in Figure 12.2. Stereochemical possibilities provide an astronomical number of structural variations in such molecules. This is one of the reasons why the effects of molecular structure on lubrication are not well understood today. In typical basestocks, the mass fraction of aromatics usually ranges from 5 to 40% with the average about 20%; straight chain paraffins usually range from 10 to 20%; and cycloparaffins make up the difference. Molecules containing heteroatoms (N, S, O) usually range from 0.5 to 4% depending on crude source, processing technology, and viscosity grade. Although the heteroatoms are a small fraction of the basestock mixture, they have a significant influence on basestock stability and friction. The aromatics provide solvency for additives and oxidized products, but they tend to react to form oil insoluble products.
FIGURE 12.2
Base oil molecular structures.
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12.3.1.2 Synthetic Basestocks Synthetic basestocks are mostly long-chain molecules produced by chemical reactions in order to obtain specific characteristics. They are made from petrochemicals, animal and vegetable oils, and coal-derived feed stocks. There are five major classes of synthetic basestocks: synthesized hydrocarbons, esters, ethers, halogenated compounds and silicone polymers. Others include sodium–potassium eutectics, and inorganic polymers of boron, phosphorus, and nitrogen, for highly specialized applications. More comprehensive descriptions of synthetic lubricants are available in the literature (Gunderson and Hart, 1962; Shubkin, 1993). a. Synthesized Hydrocarbons Synthesized hydrocarbons include alkylbenzenes, cycloaliphatics, poly-α-olefins, and polybutenes. Alkylbenzenes are mainly used in low-temperature applications as hydraulic oils, greases, and sometimes engine oils. Poly-α-olefins have found increasing acceptance due to their similarity to and compatibility with petroleum base oils, good thermal stability, and excellent viscosity–temperature relationship. b. Esters Esters are by far the most common synthetic basestock. Large quantities of materials with various structures are readily available from chemical manufacturers. They consist of monoesters, dibasic acid esters (adipates, azelates, dodecanedioates), polyol esters (neopentyl esters), polyesters, phosphate esters, and silicate esters. Most of these exhibit high boiling points, excellent viscosity–volatility characteristics, and high-temperature stability. Esters generally exhibit good solvency and have good friction and wear characteristics. They tend to react to form acidic species (acid esters and half acid esters) faster than paraffins. c. Polyethers Among polyethers, polyglycol ethers provide a variety of viscosity and molecular-weight grades. They are used mostly in water-based fire retardant hydraulic fluids, brake fluids, and rubber molding lubricants. They are available in water-soluble and oil-soluble forms. They have low pour points, good compatibility with rubber, and good sludge and varnish resistance. The volatility and oxidation stability of the polyethers are generally similar to those of petroleum basestocks. They have a unique property in that their decomposition products are low-molecular-weight compounds similar in physical properties to the original starting material. Polyphenyl ethers represent a thermally stable class of aromatic compounds containing no paraffinic side chains. These materials exhibit relatively poor viscosity–temperature and low-temperature fluidity properties. d. Halogenated Compounds In halogenated compounds the hydrogen is replaced by chlorine, fluorine, or bromine. This generally results in reduced flammability. Nonflammability may be achieved by incorporating more than 60% of halogen into the molecule. Toxicity has placed severe limitations on the use of chlorinated and brominated compounds. Perfluoropolyethers are examples of halocarbons that are in current use as lubricants. These materials show excellent oxidation stability and good viscosity and volatility properties. The very high cost of these materials has limited their use in commercial applications. e. Silicone Polymers Silicone polymers were one of the earliest compound types investigated for lubricant applications. They are mainly dimethyl silicone polymers and methylphenyl silicone polymers with various chain lengths. Methyl silicones were developed in the 1940s as the liquids with the best physical properties (viscosity–temperature) for lubricant application. Since then a series of modified structures, including phenyl, phenyl methyl, chlorophenyl methyl, fluoromethyl, and alkyl (C4-C5) silicones have been developed to overcome the major problems of the silicones, which is the lack of boundary lubricity on ferrous bearing
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systems. Silicones have excellent fluid properties and have been used as lubricants in systems designed to run under hydrodynamic and elastohydrodynamic conditions where the bearing systems are nonferrous. They have probably the best viscosity–temperature characteristics of any synthetics, with very low volatility and excellent oxidative and thermal stability. However, their solvency is poor and they are not miscible with petroleum oils. 12.3.1.3 Additives Most lubricants contain special chemical additives to impart specific properties to the basestocks to enhance performance and inhibit degradation. A wide variety of additive chemicals has been developed. There are 10 major classes of additions, categorized according to their functions: antiwear additives; friction modifiers; extreme-pressure additives; detergents; dispersants; antioxidants; corrosion inhibitors; pour-point depressants; defoamants; and viscosity-index improvers. There are also other additives such as tackiness agents, fatty oils, thickening agents, and color stabilizers. Smalheer and Smith (1967) describe many chemical types in each class. For additional information, see Booser (1984). Recent advances in the additive area are available through patent summaries published periodically (for example, Ranney, 1980; Satriana, 1982). a. Antiwear Additives Additives are used to reduce wear under elastohydrodynamic and boundary lubrication conditions. The most widely used are zinc dithiophosphates and tricresyl phosphate. Each of these additives has a family of derivatives modified for different temperature and stability requirements. Other additives used for wear control are acid phosphates, phosphites, sulfurized terpenes, sulfurized sperm oils, metal dithiocarbamates, and occasionally some sulfides. The antiwear additives generally function by adsorbing on or reacting with metal surfaces to form a protective film that is easily shearable. Since direct reactions or interactions are sometimes involved, additive–metal compatibility is important. One lubricant with an antiwear additive may function very well for one material pair but may fail in another material combination. b. Friction Modifiers Additives are also used to modify the frictional characteristics of the material under boundary lubrication contact. Fatty oils are sometimes used, such as lard oil, tallow, sperm whale oil, porpoise-jaw oil, and blown rapeseed oil. Recent research on friction modifiers has centered on glycerides, oil-soluble molybdenum compounds, finely dispersed graphite in oil, and synthetic esters of various fatty acids. c. Extreme-Pressure Additives Extreme-pressure (EP) additives are used under highly loaded conditions to prevent seizure, scoring, and welding. In metal forming and cutting applications, wear of one contacting surface is acceptable. The additives therefore are chemically active compounds containing chlorine, phosphorus, and/or sulfur. Examples are chlorinated wax, sulfurized fatty oils, sulfurized mineral oil, chlorinated mineral oil, phosphosulfurized fatty oils, benzyl and chlorobenzyl disulfides, and some phosphites. d. Detergent/Dispersant Additives Detergent/dispersant additives may be separated into two classes of compounds: metal-containing (ashcontaining) high-temperature detergents and ashless low-temperature dispersants. Their common function is to prevent deposits from forming on metal surfaces due to oil oxidation, contamination, or polymerization. The detergents function as surfactants that tend to adsorb on surfaces forming micelles around the insoluble material from the degradation of the oil. A stable microemulsion results from this process. Modern automotive and diesel engine lubricants contain some “overbasing” associated with the detergents. Calcium carbonate is added in the form of micelles to the detergent. This form of overbase can thus neutralize acidic components from either the environment or oxidation of the lubricant. There are many classes of detergents: metal sulfonates, metal phenates, metal salicylates, and metal phosphonates and thiophosphonates. Most of these can be overbased to varying degrees. Metals commonly used in detergents are calcium, magnesium, barium, and zinc.
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Dispersants are primarily additives used to disperse oxidized oil-insoluble products, water, fuel, or other contaminants at relatively low temperatures (100°C or below). Because they do not contain metal, they sometimes are referred to as ashless dispersants. There are two main families: Mannich reaction products and succinimides. Mannich reaction products are reaction products from polybutene and phenol; they are treated with amines and boric acid. Succinimides are usually n-substituted long-chain alkenyl succinimides. The detailed mechanism of the dispersion is not well understood, but most researchers agree that they adsorb on the oil-insoluble submicrometer particles and keep them finely dispersed in oil without further aggregation. e. Antioxidants There are numerous antioxidants available for lubricant use. The limiting factor sometimes is oil solubility. The important classes are hindered phenols, amines, and sulfur and phosphorus compounds. Hindered phenols are phenols in which the hydroxyl group is sterically blocked or hindered, such as 2,6di-tert-butyl-4-methylphenol. They act as peroxide-radical traps to interrupt the oxidation chain reaction. Amines such as N-phenyl α-naphthylamine are also widely used. Sulfur and phosphorus compounds are usually used at high temperatures in the presence of metals, which often catalyze oxidation of hydrocarbons. Some researchers speculate that sulfur and phosphorus compounds inhibit oxidation by passivating the metal surface with a protective film. Some phosphorus compounds, such as zinc dialkyldithiophosphate, also act as peroxide-radical traps to stop the oxidation chain reaction. Johnson (1975) lists over 100 antioxidants used in lubricants. f. Corrosion Inhibitors Corrosion inhibitors are additives that protect metal components used in engines and bearings against attack from acidic contaminants in the lubricant. Rust inhibitors are a subset of corrosion inhibitors designed specifically to protect ferrous materials against attack. Corrosion inhibitors function by forming a tight passive film on the metal surfaces to withstand the detergent or dispersant often present in the same lubricant. The most common corrosion inhibitors are zinc dithiophosphate, zinc dithiocarbamate, sulfurized terpenes, and phosphosulfurized terpenes. Common rust inhibitors are alkenyl succinic acids, alkyl thioacetic acids and their derivatives, imidazolines, amine phosphates, and acid phosphate esters. In high-temperature applications such as the internal-combustion engine, calcium or magnesium sulfonates are usually used. g. Viscosity-Index Improvers Viscosity-index (VI) improvers are polymers with molecular weights on the order of 100,000 or more, which thicken the oil at high temperatures. There are numerous variants of these additives, but the most widely used include three types: polymethacrylates, olefin copolymers, and polyisobutenes. These VI improvers are currently used in automotive crankcase oils, automatic transmission fluids, hypoid gear oils, and hydraulic fluids. The polymers tend to break down permanently with use and the viscosity of the polymer solution is decreased irreversibly at high shear rates. The stability requirements for the various areas of application are met by careful control of the molecular weight and concentration of the polymer used. In order to change the viscosity–temperature relationship sufficiently, relatively large dosage is required (5 to 10% neat polymer). 12.3.1.4 Lubricant Formulation Technology The large array of available petroleum basestocks, synthetics, and various chemical additives makes numerous combinations possible. Lubricant formulators, when confronted with a particular lubrication problem, select a certain basestock to satisfy the viscosity–temperature requirements and a particular set of additives to give different characteristics. However, additives often interact with the basestocks as well as with other additives in ways that are not understood. Therefore, most lubricants are developed by actual equipment testing through trial and error. O’Connor (1968) lists over 30 major types of lubricants and their requirements and some typical additives used in each application.
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12.3.2 Relationship Between Oxidation Reactions and Film Formation The relationship between lubricant reactions and wear has long been observed in engines. Historically, however, the link between the two technical areas is very weak. This is because the studies are largely conducted by two separate communities. One group focuses on the oxidation mechanism and bench test development; the other emphasizes the boundary lubrication mechanisms. 12.3.2.1 Chemical Reactions The chemistry in the contact is complex and abundant. There are oxidation and thermal reactions of hydrocarbons, polymerization to form high-molecular-weight products, adsorption and corrosion reactions, and catalysis by metal surfaces. In addition, tribochemistry, tribomechanical reactions, surface oxide reactions, phase transitions, and mechanochemical effects also come into play. For semiconductors, double-layer surface charges complicate the matter by introducing potential electrochemical reactions. 12.3.2.2 Oxidation and Thermal Reactions It is well known that hydrocarbons oxidize via a free radical mechanism. The basic reaction mechanisms are simple in principle but complex in reality. It follows primarily four steps: initiation, propagation, branching, and termination (Hucknell, 1974): RH → R• + H
1. Initiation 2. Propagation
R• + O2 → ROO• ROO• + RH → ROOH + R• ROOH → RO• + HO• RO• + RH → ROH + R• HO• + RH → H2O + R•
3. Branching
4. Termination
alcohols R• +R• aldehydes R• +ROO• ⇒ ROO• +ROO• ketones acids RO• +R•
12.3.2.3 Metal Catalyzed Oxidation Reactions Many metals, such as iron, chromium, copper, and nickel, have known catalytic activities with hydrocarbons. In lubricant oxidation studies, metal coupons are routinely used to simulate the catalytic reactions encountered in actual applications. Studies reveal that the hydrocarbons react with oxygen and form polar species such as carboxylic acids which adsorb onto the metal surface and react with the metal forming metal complexes (Hsu et al., 1988). These metal complexes are soluble in oil, and both homogeneous and heterogeneous catalytic reactions take place. Such reactions generally follow the reaction mechanism (Hucknell, 1974): Initiation: Propagation:
Termination:
Rn M + RH → R• + RH + Rn–1 M R• + O2 → ROO• RO• + RH → ROOH + R• Rn–1MH + ROOH → ROO• + Rn–1MH Rn–1MH + ROOH → RO• + Rn–1M + H2O Rn–1MH + ROH → R• + Rn–1M + H2O Rn–1M + C – O/C = O → RC•O + Rn–1M + H2O R• + Rn–1MH → Rn–1M + ROH and further oxidation products R• + RnM → R – R + Rn–2M ROO• + Rn–1M → Rn–1M – ROO
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FIGURE 12.3
465
Catalytic effect of different metals on oxidation rate.
The role of metal catalysis on lubricant oxidation is a complex one. Since the molecular species in a lubricant are numerous, the possible reaction pathways and the number of isomers are astronomical. Because the fundamental reaction mechanisms are functions of the molecular structures, the mechanism described above can only serve as an illustration of the general directions of the reaction steps. Detailed understanding of the catalysis mechanism is currently not available. Different metals exhibit different degrees of catalytic activities on lubricant oxidation. Figure 12.3 illustrates the effects of different metal surfaces on the rate of oxidation (Lahijani et al., 1981). Low carbon steel has the highest “catalytic” effect in terms of causing the lubricant to oxidize. 12.3.2.4 Polymerization Reactions Lubricant molecules upon oxidation always tend to go in two different directions: smaller molecules through beta carbon scission and/or decomposition; high-molecular-weight “polymers” through condensation reactions. Because of the myriad molecular species present in the lubricant molecular mixtures, there is a statistical averaging effect in terms of product mix and distribution among all lubricants. A typical aldol condensation reaction is shown below:
O O OH | CH3–C–CH3 + CH3–C–CH3 → CH3–C–CH3 → CH3–C–CH3 + H2O | CH2 CH | | CO CO CH3 CH3 The conjugated double bonds of the products are characteristic of the condensation reactions. They have been experimentally detected by NMR on surface films produced under base oil lubricated contacts (Naidu et al., 1984). These conjugated double bonds then provide the impetus for further polymerization to higher-molecular-weight products. Naidu et al. (1984) demonstrated that the chemistry proceeds in the following sequence: primary oxidation step; formation of organic acids; aldol condensation reactions to form high-molecular-weight compounds. When the molecular weight reaches the solubility limit (about 100,000), the reaction products become insoluble and deposit on the surface. Figure 12.4 shows the molecular weight increase as a function of oxidation time. The lubricant is subjected to thin film oxidation at temperatures of 225 and
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FIGURE 12.4
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Effect of oxidation on high-molecular-weight reaction product formation.
275°C for different oxidation durations. The surface reaction products are dissolved in a polar solvent, typically tetrahydrofuran (THF), and analyzed by passing through a gel permeation column for molecular size separation. The detailed procedure is described elsewhere (Cho and Klaus, 1983). As shown in Figure 12.4 (Cho and Klaus, 1983), the original lubricant has an average molecular weight of about 400, which is indicated by the solid zero minute line. As the oxidation continues, the highermolecular-weight fraction increases in magnitude. At a higher temperature of 275°C, the increase in molecular weight is much faster, but the trend is the same. Similar behavior has been observed under dynamic wearing conditions, as will be discussed in a later section on organometallic compounds. As one can see, oxidation reactions are complex, and they are necessary to form the polar species, which in turn react with the metal surfaces, forming polymers which lubricate the surface. The linkage between oxidation and wear has long been suspected, but the detailed mechanistic explanation is lacking. It has long been postulated by the lubricant researchers’ community that more oxidation-resistant oils are intrinsically more wear resistant. But as we shall demonstrate, the relationship between oxidation
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FIGURE 12.5
467
Effect of oxidation on wear for IIID reference oils.
reactions and film formation tendencies is complex. Figure 12.5 shows the relationship between oxidation and wear for a set of five reference oils (ASTM sequence III engine dynamometer test for oxidation and wear; high wear reference oils produce higher wear in the engine dynamometer tests, low wear reference oils produce lower wear). Four-ball wear test results are measured before and after oil thickening tests (OTT) on the lubricants (oil thickening tests conditions: 60 mL/min air flow rate, 171°C, 5% drain oil as catalyst). As can be seen, the high wear reference oils (77B and 77C) have a much higher response to oxidation than the low wear reference oils.
12.3.3 Organometallic Chemistry and Tribochemistry In examining the nature of chemical reactions occurring in a contact, the direct reaction between the surface and lubricant molecules has been alluded to. In this section, we will discuss the role of chemical reactions induced by mechanical rubbing (tribochemistry). 12.3.3.1 Direct Reactions with Metals Buckley (1974) has suggested that the nascent surfaces of metals behave differently than oxide-covered surfaces. Morecroft (1971) performed high-vacuum experiments to show chemical reactions occurred on freshly exposed metal surfaces. Exoelectrons have been measured and used to explain the enhance reactivity of the freshly exposed metal surfaces. These early works sparked research into the effects of nascent surfaces on chemical reactivity. In general, it was found that nascent surfaces under high-vacuum conditions, readily reacted with any hydrocarbon, decomposing the molecules into fragments. No polymerization reactions have been reported. A conclusion may be that freshly exposed metal surfaces will readily react, form oxides, and decompose hydrocarbons. In reality, engineering surfaces are almost always oxide covered. How this observation fits into lubrication theory is not certain. Hsu and Klaus (1978) used chemical reaction kinetics to back-calculate the reaction temperatures necessary to generate the observed amount of products from the wear processes and the thermally induced simulations. The reaction temperatures determined for steel systems are very similar, 379 ± 28°C for the static case (oxide-covered surfaces) and 349 ± 8°C for the dynamic rubbing case (fresh metal surfaces exposed). Hsu concluded that, based on these results, the nascent surface effects on reaction rates under atmospheric conditions are minimal. Thermal effect is the dominant factor for controlling the boundary chemical reactions for steels.
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FIGURE 12.6
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Comparison of antiwear effectiveness of different additives with SiC and Si3N4 .
12.3.3.2 Tribochemistry Observed for Ceramics For ceramics, such as aluminas, silicon nitrides, and silicon carbides, the situation turns out to be different. Fundamentally, these are polycrystalline solids with very well-defined crystalline structures and bonding energies. When the surfaces are disrupted, dangling bonds are created. Since these bonds are atom specific, they are not only more reactive but also tend to be more reaction specific than thermally controlled reactions. Hydroxide formation was first reported by Gates et al. (1989) for aluminas, and subsequently, hydration reactions were reported in wearing systems as well as in static systems for other ceramics (Tomizawa and Fischer, 1986; Mizuhara and Hsu, 1992). Gates and Hsu (1995), in studying alcohols lubricating silicon nitrides, discovered that the alkoxide reactions dominated the tribochemistry, and these reactions cannot be simulated by thermal conditions. In studying the surface reactions, Deckman (1995) compared the reactions of silicon nitride with silicon carbide under identical conditions. Even though the surface species are predominantly the same, namely silicon oxides and oxynitrides, the response to different chemistry under rubbing experiments is totally different. Figure 12.6 illustrates the lack of correlation between the two materials responding to the same chemical compounds under the same conditions. While these results are puzzling, they point to the importance of tribochemistry. In metal systems the thermal reactions dominate and the nascent surface effects are minor. For crystalline materials, not only is the reactivity different, but the nature of the reaction pathways is different. The cause for this difference may be suggested by some recent results reported by Nakayama and Hashimoto (1991) and Dickinson et al. (1993). They independently studied the charged particle emission from crystalline surfaces and found under deformation and fracture conditions, different materials emit different amounts of particles (electrons, molecules, charged particles). Figure 12.7 shows that different materials under rubbing conditions emit different amounts of charged particles. The amount of emission for silicon carbide is much lower than silicon nitride. This observation may not explain directly the difference in reactivity observed for the two materials, but it does point to a direction for some future research to resolve this issue.
12.4 Boundary Lubricating Films As early as 1958, Hermance and Egan (1958) noted that the lubrication of metallic surfaces was often accompanied by opaque organic deposits on and around the contact surfaces. Analysis revealed that these were high-molecular-weight “polymeric” materials. Over the years, the term “friction polymers” was coined over the objections of polymer chemists. The early perception is that this film is responsible for successful lubrication of the surface, and its formation is controlled by the chemical additives in the lubricants. Therefore, many research efforts have been focused on the mechanical properties of these films, the nature of them, and in their information mechanisms.
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FIGURE 12.7 Charged particle emission of different surfaces under rubbing conditions. (From Nakayama, K. and Hashimoto, H. (1991), Triboemission from Various Materials in Atmosphere, Wear, 147 (2):335-343. With permission.)
Recent data suggest that not all films are protective (Hsu, 1991). Depending on the nature of the solid surfaces, many films can be formed. Some of them are protective, some of them are corrosive, and some are simply the reaction product residue, which does not affect the friction and wear.
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Direct visual observation of formation of ZDP films in a contact during rubbing has provided additional insight into the complex dynamic nature of the process (Sheasby et al., 1991). Similarly, in an elastohydrodynamic regime, Gunsel and Spikes measured ZDP film thickness as a function of test duration and temperature (Gunsel et al., 1993; Spikes, 1996).
12.4.1 Physical and Chemical Properties There have been many studies conducted to analyze the physical and chemical properties of boundary lubricating films (Belin et al., 1989; Briscoe et al., 1992; Gates et al., 1989; Godfrey, 1962; Hsu and Klaus, 1979; Klaus et al., 1987; Klaus et al., 1985; Lindsay et al., 1993; Martin et al., 1986; Morecroft, 1971; Mori and Imaizumi, 1988; Tonck et al., 1986). Results of these studies suggest that the chemical compositions of the films are mainly micron- and submicron-sized particles of iron and iron oxides intertwined with high-molecular-weight organometallic compounds of 3000 to 100,000 MW (Gates et al., 1989). If antiwear additives such as zinc dialkyldithiophosphate or tricresylphosphate are present in the lubricants, iron phosphates and phosphate glasses can be formed and become part of the boundary film (Belin et al., 1989; Martin et al., 1986). The appearance and morphology of the films can be patchy, continuous, or discrete, and have different colors, from green to brown to black (Lindsay et al., 1993; Klaus et al., 1987). This is probably due to the different chemical compositions as well as the thickness of the films. Different thicknesses reflect and refract part of the light spectrum resulting in different colors being observed (Choa et al., 1994). Overall, there is no general correlation between the appearance and morphology of the films to effective boundary lubrication. Several boundary lubricating films are illustrated in Figure 12.8. These are photomicrographs taken of the wear scars from ball-on-three-flat tests conducted on silicon nitride at 2 GPa mean pressures (Gates and Hsu, 1995). The films range from fluid-like, observed for 2-ethyl hexyl ZDP (Figure 12.8a) and calcium phenate (Figure 12.8b), to the more solid-like films of tricresyl phosphate (Figure 12.8c) and magnesium sulfonate (Figure 12.8d). The film formed from ZDP appears to be flexible, as shown by Figure 12.9. There are several mechanisms by which boundary lubricating films function: sacrificial layer, low shear interlayer, friction modifying layer, shear resistant layer, and load bearing glasses. The sacrificial layer is based on the fact that the reaction product layer is weakly bound and easily removable; thereby providing a low shear interfacial layer against the rubbing. So instead of the surfaces being worn by the shear stresses, this layer is removed instead. For such films to be effective, the rate of film formation has to be higher than the rate of film removal to protect the surface. An example is the oxide layer in the case of steels (Quinn et al., 1984). The oxide layer forms rapidly and is easily removed, thus protecting the steel surfaces. The low shear interlayer mechanism can best be illustrated by the use of solid lubricant molecules. The solid lubricant molecules have weak interlattice attraction between shear planes; therefore, the lubricating film can slide easily along the low shear planes within the film, thus accommodating the motion and shear. Another mechanism is that the molecules or reaction products form an ordered structure at the interface, and the sliding of the two surfaces is accomplished between the two weakly bonded absorbed layers in the ordered structure. This is how friction modifiers such as fatty acids function. Of course, the other alternative mechanism is to have a strongly adhered bonded layer which is shear resistant by itself. Under certain conditions, the lubricant layer will behave like a solid exhibiting limiting shear and shear band fracture (Bair et al., 1993). These mechanisms operate in different regimes controlled by the environment and operating conditions. What works for one system may not work for another. Within the same system, what works within one set of operating conditions may not work when the operating conditions change significantly. Figures 12.10 and 12.11 illustrate different film morphologies and appearances for two different materials. Figure 12.10 shows very thin dense films that work for silicon nitride. These films are similar in appearances and textures to the steel-on-steel systems. Figure 12.11 shows effective films for the silicon carbide system. The same chemicals in Figure 12.10 do not work for silicon carbide. Because of the brittleness of silicon carbide, thicker films are needed to protect the system.
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FIGURE 12.8 Optical micrographs of wear scars from wear tests on silicon nitride using paraffin oil containing (A) 1% 2-ethylhexyl ZDP; (B) 1% Ca phenate. Optical micrographs of wear scars from wear tests on silicon nitride using paraffin oil containing (C) 1% tricresyl phosphate; (D) 1% Mg sulfonate.
FIGURE 12.9 SEM micrographs of film from wear tests on silicon nitride using paraffin oil containing 1% 2-ethylhexyl ZDP.
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FIGURE 12.10 SEM photomicrographs of wear scars from wear tests on silicon nitride using paraffin oil containing 1% 2-ethylhexyl ZDP.
12.4.2
The Detection of Organometallic Compounds in Films
Oil-soluble metal-containing compounds were first identified as being generated in lubricants under oxidizing conditions (Klaus and Tewksbury, 1973). These compounds were later identified to be highmolecular-weight organometallic compounds using gel permeation chromatography coupled with atomic absorption spectroscopy (Gates et al., 1989). Figures 12.12 through 12.15 show the results for two cases: static oxidation test conditions and dynamic wear test conditions. Under static oxidation test conditions, a thin oil film about 40 µm thick was deposited on a steel disk and oxidized at a temperature of 225°C for 20 to 30 minutes. Afterwards, the surface reaction products were dissolved by a solvent (tetrahydrofuran). The solution was then injected into the GPC columns for molecular size separation. The effluent flowed through two detectors, refractive index and ultraviolet detector. After the detectors, the effluent stream was collected in a autosampler vial for the determination of metal content in the effluent stream by atomic absorption spectroscopy analysis. The same procedures were followed to examine the films formed on worn surfaces after wear experiments. Figure 12.12 shows that organometallic compounds are formed when lubricants are reacted with the metal surfaces under static oxidation conditions. The top curves denote the molecular weight distributions of the lubricant (a 150 N paraffinic base oil) after 30 minutes of reaction time at 225°C on steel and copper surfaces. The original molecular weight distribution centers around 300 (similar to the molecular weight distribution curve for the copper surface). The lower two curves are the results of the atomic absorption signals as a function of the discrete volumetric increments of the effluent from the
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FIGURE 12.11 SEM photomicrographs of wear scars from wear tests on silicon carbide using paraffin oil containing 1% benzyl phenyl sulfide.
gel permeation column. So these signals indicate the amount of organometallic compounds as a function of molecular weight. In these two cases, one can see that the steel surface, under identical reaction conditions, forms a larger quantity of high-molecular-weight products and produces a large quantity of organo-iron compounds. The copper surface, on the other hand, produces a much smaller amount of organo-copper compounds (note the scale difference between steel and copper) even though the molecular weights of the organometallic compounds are about the same. The molecular weight distribution curves also suggest that copper did not cause the original molecular weight distribution to change substantially, i.e., the lubricant is not significantly oxidized. Figure 12.13 shows the formation of organo-iron compounds as a function of time under static oxidizing conditions. As one can see, the iron peak intensity increases with time. This indicates that the amount of organo-iron compounds are increasing as a function of time. The data also indicate that there is an induction time under static oxidation conditions for the organo-iron compounds to form. The analytical procedures used here are sensitive to ppm level of iron, and the amount of organometallic compounds detected depends on the solvent and the extraction procedure. Figure 12.14 shows the result when the same procedure is applied to the dynamic wear case for a superrefined mineral oil base stock in a four-ball wear tester. The wear procedure used is a modified procedure in that only 6 µL of lubricant is available to the contacts. This way, the reaction products and the reaction sequence are concentrated for ease of analysis. A broad spectrum of organo-iron compounds of various molecular weights is found, with molecular weights ranging up to about 100,000. Higher-molecularweight compounds are not detected, suggesting that the solubility limit has been reached Figure 12.15 shows the results for a fully formulated lubricant (containing antiwear additives, detergents, dispersants, etc.) as a function of time. In this case, the amount of organo-iron compounds is much less, but the presence of organo-iron compounds can be detected very rapidly. Optical pictures reveal that the boundary
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FIGURE 12.12 Molecular weight distribution of organometallic compounds from oxidation tests conducted on iron and copper surfaces.
lubricating film is fully formed after only 1 minute of wearing contact. There seems to be a shearing action reducing the molecular weight of the products and shifting the maximum amount of organo-iron to a molecular weight of about 3000. These organometallic compounds are also found on cam and tappet parts in an ASTM engine dynamometer test, the sequence III oxidation wear test. Cam and tappet parts were taken from ASTM test stand calibration runs and analyzed for surface reaction products. Similar patterns were observed. This suggests that organometallic compounds play an important role in the formation of the boundary lubricating films.
12.4.3 Mechanical Properties of Boundary Lubricating Films Let us hypothesize that these high-molecular-weight organometallic compounds form the glue to provide cohesive strength with dispersed fine particles of iron and iron oxides. The bonding via the iron organometallic bonds provides the adhesive strength. Then once the film is formed, one should be able to measure the shear strength of these films. In the last few decades, many researchers have attempted to measure the film strength. There have been some limited successes. Briscoe et al. (1973) studied the shear strength of thin films under a range of high pressure (MPa to GPa). They found that at these pressures shear strengths increased with increasing pressure for calcium and copper stearate and polyethylene films. Increasing temperature reduced shear strength. Researchers at École Centrale de Lyon have devised clever ways to measure the shear strength of thin films by a microslip method (Tonck et al., 1986). These strengths are tabulated in Table 12.1. Generally, the film strength increases with load for base fluids, zinc dithiophosphates, and
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FIGURE 12.13 at 250°C.
475
Molecular weight distribution of organometallic compounds from static oxidation tests conducted
calcium sulfonates but decreases with load in the case of a friction modifier. This is reasonable since friction modifiers depend on multilayer adsorption and easily sheared planes between the molecular layers. As load increases, the film thickness will decrease. Monomolecular film studies have also been done (Briscoe and Evans, 1982). The measured shear strength for stearic acid was found to be on the order of about 10 MPa on a steel surface. Comparison of these two results is difficult because of the differences in measurement techniques, film chemistry, and film thickness. Yet in terms of an order of magnitude comparison, it is instructive to note that a monolayer is relatively weak and the complex films generated by lubricants are relatively strong. Another observation is that not all films lubricate (Deckman, 1995). Hsu (1991) suggested that there is an optimum reactivity for a film to lubricate the surfaces based on the commonly observed constant renewal, sacrificial lubrication mechanisms. The ability of the film to lubricate the surfaces depends on the adhesive and cohesive strengths of the film with respect to the surface. Warren et al. (1998) used scanning force microscopy to determine nanomechanical properties of ZDP films from both static (heating) and wear tests. They found that films generated in the highly loaded regions of the wear test were markedly different in nanomechanical response than films from a lightly loaded region and films from a static test. We have attempted to show the linkage among the oxidation reactions, polymerization reactions, and the effects of different materials in effecting lubrication. The picture that is emerging is complex but traceable to molecular phenomena on the surface. The surface is an integral part of the reacting system. Since surfaces depend on many variables including machining, defects, crystalline configurations, oxide layers, hydride layers, etc., the resulting reaction pathways sometimes are difficult to predict. But knowing
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Intensity, arb. units
Apparatus: 4-ball wear tester Speed: 600 rpm Load: 40 kg Atmosphere: 0.25 l/min dry air Lubricant: 6ml superrefined mineral oil Duration: 30 minutes Material: 52100 steel
Molecular weight distribution (refractive index detector)
Fe peak intensities
106
105
104
103
102
101
100
Molecular Weight
FIGURE 12.14
Molecular weight distribution of organometallic compounds from dynamic wear tests.
the surface layer composition precisely, and the operating conditions, the future of predicting boundary lubrication is foreseeable, albeit with the existence of many formidable obstacles. With the many studies on boundary film formation, some generalizations can also be made. Figure 12.16 shows the general diagram for the formation of boundary films. The area of tribochemistry needs many more studies to understand the intricate interactions between surfaces and molecules under rubbing conditions. The role of surface defects as well as dangling bonds (Lenahan and Curry, 1990) needs to be identified and characterized in order to gain important insights into surface reactions which have wide implications for other areas of research as well.
12.4.4 Advances in Measurement Techniques There are several new techniques that have been applied to boundary lubrication issues, ranging from new wear and property measurement to specialized surface and film analysis. In general, these new techniques have followed a trend toward smaller-scale as well as more specific property measurement. At the small end of the scale — atomic-level property measurement — the surface forces apparatus (SFA), pioneered by Israelachvili (Israelachvili, 1986), is being used to probe the properties of the first monolayer of molecules on surfaces. Significant progress has been made on the properties of confined films, even though the technique is limited to transparent, atomically smooth, materials like mica. Scanning probe microscopy (SPM), first introduced as a technique for looking at the topography of surfaces at the nanometer level, is also now being used essentially as a “nanotribometer.” Many different forms of the nanotribometer SPM have been used to measure friction, adhesion, and wear at this ultrasmall scale (Mate, 1995; Feldman et al., 1998; Bhushan et al., 1995). At this scale however, issues of calibration and control are critical and continuously evolving, with recent designs for instruments such as the NIST “calibrated” atomic force microscope (Schneir et al., 1994) as well as commercial “metrology” instruments making their way into use. The issue of cantilever calibration, so critical to obtaining accurate absolute values for forces is being approached from several angles such as finite element analysis (Hazel
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FIGURE 12.15
Molecular weight distribution of organometallic compounds from wear tests of different duration. TABLE 12.1 Mechanical Properties of Surface Films Measured by Microslip Technique: Cast Iron on 52100 Steel Measure Shear Moduli at Selected Normal Load (GPa) Film
1N
2N
5N
10N
Film A, 120 nm dodecane Film b, 60 nm ZDP Film C, 60 nm Ca sulfonate 5% Film D, FM complex ester 1%
3 3.5 1.9 3.4
3.3 3.8 2.1 2.9
3.6 4.7 3.1 2.5
4.3 4.2 3.2 1.8
Data from Tonck, A., Kapsa, Ph., and Sabot, J. (1986), Mechanical behavior of tribochemical films under a cyclic tangential load in a ball flat contact, J. Tribology, Vol. 108, 117.
and Tsukruk, 1998), resonance methods (Cleveland et al., 1993), and reference cantilevers (Gibson et al., 1996). A simple, accurate, calibration for both normal and tangential forces is still elusive. The issue of relevance of these nanoscale measurements to larger “real world” devices is still being debated. Interestingly enough, the relevance issue is being bridged by the fact that actual devices are now shrinking down to the scale of measurement — as in the rapidly developing fields of micromachines and microelectromechanical systems (MEMS). Some very interesting contributions are being made on slightly larger scales with modified SFA and SPM apparatus. These tribometers and indenters make very small-scale measurements of surfaces and films in the nanometer and micrometer scale contact regime. One of the simplest SPM modifications,
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FIGURE 12.16
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Overall framework for boundary lubricating film formation.
first made by Ducker (Ducker et al., 1991), was the attachment of very small spheres to the end of an SPM cantilever. Instead of a contact with 10 nm radius of contact that might just push a film aside, the contact could be enlarged to micrometer dimensions. In another approach, the research group at L’École Central (Bec et al., 1996; Tonck et al., 1986; Georges et al., 1998) have developed an apparatus that utilizes a variety of diamond and sphere tips to apply controlled forces to surfaces and measure their effects. They have made considerable progress in probing the properties of important boundary lubricating thin films such as ZDP on surfaces. In boundary lubrication research, the key has always been unlocking the understanding of the underlying chemistry taking place during lubrication. In many cases this means using the combination of wear testing and key analytical instrumentation designed to elucidate the chemical mechanism responsible for lubrication. In the area of analytical measurements of surface films, the workhorse techniques of FTIR, Raman, XPS, and Auger are being augmented with highly sensitive and specific techniques such as near edge X-ray absorption fine structure (NEXAFS) spectroscopy, which utilizes a synchrotron radiation source to generate soft X-ray beams to measure the presence and orientation of molecularly thin films on surfaces. This technique was first applied to stearic acid on copper and was able to provide a detailed understanding of the surface bonding under both static and dynamic rubbing conditions (Fischer et al., 1997a,b). The technique was also recently applied to nanometer-thin layers of perfluoropolyether
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containing phosphazene on magnetic hard disks to show the presence of unsaturated carbon bonds at the interface (Kang et al., 1999). Time of flight secondary ion mass spectrometry (TOF SIMS) has been used to probe the chemical composition of relatively high-molecular-weight films formed from silicon nitride lubricated by a monoalcohol (Gates and Hsu, 1995). The technique showed unambiguously that silicon alkoxides were being produced by tribochemical reactions during rubbing and helped to define the tribochemical mechanism of boundary lubrication of silicon nitride by alcohols. Other techniques such as microellipsometry and surface reflectivity are being utilized in direct response to specific industrial needs. In the case of the hard disk industry, surface reflectivity techniques are being refined in such a way that depletion of the nanometer-thin lubricant film and wear of the protective carbon overcoat layer can be measured in situ during component testing (Meeks et al., 1995).
12.5 Boundary Lubrication Modeling Boundary lubrication effectiveness has long been considered to be essential in modern machine designs for proper operation. As the demands for better energy efficiency, tighter tolerances, and the availability of new materials, the need to predict lubrication effectiveness in this regime increases. What do we mean by effective predictive models? Given the materials pair, speed, load, surface roughness, lubricant type (viscosity, additive chemistry), and duty cycles, can we predict length of service, amount of wear, time to scuffing, seizure? According to this definition, we currently do not have any such model. At the same time, we can describe fairly well average film thickness, elastohydrodynamic support, and even some wear. It is instructive, therefore, to examine the current predictive ability on some of these parameters: wear, flash temperatures at the tips of the asperities, lubrication transition temperatures, and some discussion on the subject of molecular dynamic simulation.
12.5.1 Wear Wear is a system function. It depends on the system, which includes the materials, surface roughness, lubricants, environment, operating conditions, temperatures, etc. To predict wear a priori, i.e., without experimental fitting constants, is very difficult. Yet wear is such an important parameter, so studies abound to describe the wear processes (Choa et al., 1994). Under boundary lubrication regime, one of the most critical initial system parameters is the real area of contact. This parameter controls the real load the asperities are under and the subsequent stress/strain relationship beneath the contact. As discussed in the chapter titled, “Wear Maps,” the fundamental wear process for most metals is controlled by the accumulation of strain. Greenwood and Williamson (1966) proposed several models to describe the initial real area of contact, which is usually a small fraction of the apparent area of contact between two engineering surfaces. One version, which assumes a distribution of peak heights can be written as:
()
A = π ηβσ F1 h
where η = number of asperities β = asperity radius σ = standard deviation of the peak height distributions and ∞
( ) ∫ (s − h) φ * (s)ds
Fm h =
h
where φ* (s) is a probability density.
m
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However, once the sliding takes place, the real area of contact changes with wear. Under steady-state mild wear condition the real contact area could be quite high when the two surfaces conform to one another. The next step is to model the lubricant rheology in the contact. Under boundary lubrication conditions, traditionally, bulk fluid viscosity does not play a role since the asperities are bearing the load. However, recent studies of fluid molecules under confined space exhibit radically different mechanical and flow properties as compared to those in the bulk (Coy, 1998; Granick, 1991a,b; Granick, 1999; Israelachvili, 1993, 1986; Israelachvili et al., 1988). The viscosity near the wall (nanometers) is much higher than those of the bulk. This also implies that viscosity of the fluid trapped inside the contact among the asperities under sliding conditions may be higher, hence giving rise to the elastohydrodynamic life at the local level. Some of this viscosity and polymer solution behavior near the wall can be simulated by dissipative particle dynamics (DPD) (Hoogerbrugge and Koelman Jmva, 1992; Kong et al., 1997), which is an accelerated molecules dynamics method. Once the rheology is defined, fluid film thickness can be estimated by Dowson and Higginson’s (Dowson and Higginson, 1959) equation:
η0.7 α 0.54 V 0.7 R0.43 h = 1.63 0 00.13 L E ′ 0.03 There are several computer programs available to calculate the contact stresses, fluid flow, temperatures, and elastohydrodynamic lifts (Lee and Cheng, 1992), but to link these calculations to wear is a big step. Bell (Bell and Colgan, 1991; Bell and Willemse, 1998) used component cam-follower wear data to correlate with oil film thickness and calculate the oil film thickness using a finite element program. The wear contours and approximate amount of wear of the cam-follower contact in an engine was successfully simulated. Chemical film formation as a function of additive concentrations and temperatures was not taken into account but simulated by the bench tests.
12.5.2 Flash Temperatures Engineering surfaces are not atomically smooth. Under contact conditions, the hills (asperities) of each surface bump into the hills of the other surface. When they move relative to one another, frictional energy producers heat, and the transient temperatures at the tips of asperities are called flash temperatures. They are a microsecond in duration and highly localized (Furey, 1964). When one surface begins to move over another surface, the contact phenomena are controlled by asperity interactions and the interfacial layer (liquid lubricant or oxide). At very light loads, the friction is controlled by the surface forces which include van der Waals forces, hydration force, electrostatic or double layer forces (depending on the materials), and elastic contacts of the asperities and the viscous drag of the oil film. The elastic contacts will sometimes produce chatter, or stick slip phenomena as observed by frictional force traces. Under high load, the asperity contacts result in plastic deformation of the asperities. This changes the surface features of the interface. The asperity–asperity contacts lead to deformation of the asperities, and this process provides the majority of the frictional resistance. Other processes contributing to friction and heat release are adhesion, plowing, and abrasion. In boundary lubrication, chemical films are produced to provide surface protection. The films for steel systems are produced mostly by frictional heating. Therefore, if one is able to predict the asperity temperatures in the contact one can calculate the chemical reaction rate to generate the films. Historically, two approaches have been used to estimate the flash temperature. One is chemical; the total amount of reaction products is measured and compared to constant temperature reaction rates at different temperatures. Given the time and temperatures, from the total reaction products, the average surface reaction temperatures can be estimated. The other approach is mechanical; asperity contacts are
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modeled to take into account the elasticity, frictional heating, fluid flow, heat transfer characteristics as a function of load, speed, surface roughness, and materials properties. To compare these two approaches, Hsu, Klaus, and Cheng (1988) used a simple experiment on a fourball wear tester. The chemistry of the lubricant was kept simple by using a purified paraffinic base oil. A microsample test procedure was used to allow maximum lubricant degradation. The composition of the lubricant during and after the test was analyzed to show molecular weight changes. The total amount of reaction products generated during the wear test was measured. Knowing the kinetics of the reaction, the temperatures in the contact were calculated. The temperatures were also determined by using a mechanical contact model given the surface roughness, material properties, and physical properties of the lubricant. These two temperatures were then compared. Klaus et al. (1980) demonstrated that conditions within a thin-film micro-oxidation test closely resemble those within a sliding contact. The test used a thin lubricant film on a metal catalyst cup in a nitrogen–oxygen mixture, thus both temperature and oxygen availability may be controlled. Subsequent work (Clark et al., 1985; Klaus et al., 1982) demonstrated that the oxidation reactions followed the Arrhenius relationship. The equation has the form:
k = m e − E RT where T = temperature m = a fitting coefficient E = the activation energy (cal/mode) R = gas constant Naidu et al. (1986) described a global rate model based on the consumption of lubricant within a microoxidation test, subjected to conditions similar to those encountered in a sliding contact. The model describes the primary oxidation step as well as the subsequent condensation polymerization step, which results in lubricant viscosity increase and insoluble sludge formation. These reactions can be described as follows:
where A E B F P D k
= original oil = evaporated original oil = low-molecular-weight oxidation products = evaporated low-molecular-weight products = high-molecular-weight liquid polymerization products = insoluble deposits = reaction rate constants
The estimated contact temperature required to produce polymerization in 10% of the total lubricant volume is shown in Figure 12.17, as a function of film thickness. As the mean separation between the opposing surfaces decreases, the theoretical oil temperature increases exponentially, as less oil is able to enter the contact junction. The mean boundary film thickness between the opposing surfaces is approximately 0.06 µm (600 Å), as calculated from the asperity contact model detailed in the following section. The required film temperature at this separation is 375°C. Figure 12.18 shows the calculated lubricant life at this temperature
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Film Thickness, µm
FIGURE 12.17
Estimated lubricant temperature as a function of film thickness.
400
Time to Failure, minutes
600 rpm 40 kg 300
3 75
200
°C
100
0 0
1
2
3
4
5
Lubricant Volume, µl
FIGURE 12.18 Calculated oil film temperature required to provide the lubricant oxidation measured during microsample wear tests with different volumes of lubricant.
as a function of lubricant volume, along with experimentally determined values for comparison. As may be seen, the predicted values are in general agreement with the experimental data. The asperity temperatures within the contact zone of two rough surfaces were calculated using the model developed by Lee and Cheng (1992). The input data include two groups: (1) experimental conditions such as sample geometries, load, speed, the material’s elastic constants, and lubricant properties, and (2) measured data such as friction and surface roughness profiles of the worn samples. Given roughness profiles of the opposing surfaces, the calculations include three sequential steps: (1) contact modeling to determine the relationship between average contact pressure and the average distance (gap) between the two surfaces, (2) rough-EHD analysis to calculate the average film thickness and the load distribution between hydrodynamic film support and asperity contacts, and (3) temperature calculation to determine the asperity temperature distribution within the contact zone.
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Surface Roughness Top Ball (inverted)
RMS: 0.19
Lower Ball
RMS: 0.31 Calculation Region
Relative
RMS: 0.23
Test: 2160R Load: 40kg Scale, µm Speed: 600rpm Time: 60 minutes 1 Lubricant: Paraffin Oil Material: 52100 steel 100 Measurements taken perpendicular to direction of sliding
FIGURE 12.19
Profiles taken from opposing worn surfaces.
To model two surfaces in contact, one has to describe the surface roughness and simulate the contact geometry under static load mathematically. The contact model used assumes that both surfaces have longitudinal roughness. The validity of this assumption has been demonstrated (Sugimura and Kimura, 1984; Wang et al., 1991) for wear scars formed after a four-ball wear test. Figure 12.19 shows the surface roughness profiles taken from the top ball (inverted) and the lower balls after the prewear test. These profiles were measured perpendicular to the sliding direction. To ensure accurate representation of the wear scar on the top ball, its roughness trace was determined by averaging digitized profiles in three angular directions (θ = 0°, θ = 120°, θ = 240°). An average trace for the lower balls was similarly determined, one profile being taken from each of the lower balls. Subsequently, the profiles from the top ball and the lower balls were derived, by subtraction, to form a composite profile, denoted as “relative” trace in Figure 12.19. The contact between the top ball and the lower balls was then simulated by analyzing the contact between the composite profile and a rigid plane. Taking into account the elastic deformation, the local high spots (asperities) of the composite profile would deform and become flattened when the profile is pressed against the rigid plane. The distance measured from the rigid plane to the mean line (plane) of the deformed composite profile defines the average gap between the mean lines (planes) of the two rough surfaces under the same load. Meanwhile, the average pressure of those deformed asperities defines the average contact pressure. By increasing the severity of loading, the average gap becomes smaller, while the contact pressures of the individual asperities increase. Depending on the local geometries, some of the asperities may yield as the contact severity increases. When this happens, the model assumes that the contact pressure stays at the yield pressure and does not increase further. If one varies the loading mathematically, one could determine the relationship between the average contact pressure and the average gap, as illustrated in Figure 12.20. For this particular simulation, since the balls are preworn, the maximum Hertzian pressure under an applied load of 40 kg is estimated to be 0.847 GPa. The average gap in the central portion of the contact is about 0.06 µm, according to Figure 12.20. The r.m.s. value of the “relative” roughness shown in Figure 12.19 is 0.23 µm. After the relationship between average contact pressure and average gap has been determined, the rough-EHD analysis was then carried out. In the rough-EHD analysis, a line-contact between two rough cylinders is assumed, and only the inlet half of the contact is analyzed (Lee and Cheng, 1992). The pressure along the centerline of the line contact is assumed to be the same as the maximum Hertzian pressure determined by considering the preworn geometry. The film thickness solution of the rough-EHD analysis is based on the average gap. Since the analysis is based on two rough surfaces in contact, the two cylinders are subjected to two types of pressures; one from hydrodynamic lift, the other from asperity contact pressures. The relationship between average contact pressure and average gap determined in the contact simulation previously is therefore utilized
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Average Pressure, GPa
5
4
3
2
1
0 0.0
0.1
0.3
0.2
Average Gap, µm
FIGURE 12.20
Average contact pressure as a function of gap between mean lines of opposing surfaces.
1.0
Fraction of Centerline Pressure
0.8
Asperity Pressure
0.6
0.4
0.2 Hydrodynamic Pressure 0.0 -1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
X/b
FIGURE 12.21
Normal pressure as a function of normalized distance from contact center.
in the calculation of the overall pressure distribution of the contact. Figure 12.21 illustrates the loadsharing characteristics between asperity contact and hydrodynamic lift, as a function of the normalized distance from the center of the contact. The parameter b is the Hertzian contact radius. Clearly, asperity contacts carry most of the normal load, thus, sliding friction between the opposing asperity contacts will be responsible for most of the heat generated. Besides the pressure estimations, the rough-EHD analysis also calculates the average friction coefficient from the asperity contacts based on the measured friction value (Lee and Cheng, 1992). In this case, the measured friction coefficient was 0.11, and the average asperity contact friction was determined to be 0.112. From the rough-EHD calculations, the size and shape of the asperities within the contact zone can be determined. Each asperity contact forms roughly an elongated ellipse, with its major axis orientated in the sliding direction. Also, the pressure distribution on each asperity as a function of distance from the contact centerline can be determined. Before the temperature calculations are performed based on Jaeger’s work (Jaeger, 1942), some further simplifications are taken. Each asperity contact is approximated to be rectangular, and its average contact pressure is used for temperature calculations. Frictional heating is
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Temperature, °C
180
160
140
120
100 0.0
0.1
0.2
0.3
0.4
0.5
Contact Area Ratio
FIGURE 12.22
Cumulative temperature distribution within the Hertzian contact.
considered as the heat source, which includes both the average asperity contact friction and the hydrodynamic film friction. The resulting temperature within each asperity contact is a function of the location measured from the centerline of the nominal contact zone. The maximum temperature of each asperity contact is sought and will be considered as the representative temperature for that asperity. Figure 12.22 shows the cumulative temperature distribution under the conditions included in Figure 12.19. The highest temperature attainable is approximately 220°C covering about 3% of the nominal area. These results also reveal that the asperity contacts cover approximately 45% of the nominal area, and the bulk temperature is ~150°C. The results of the temperature analysis show that the temperatures within the contact zone are in the range of 150 to 220°C. This is in general agreement with other continuum models (Francis, 1970; Fein, 1960) which, for the present test conditions, predict the maximum contact temperature to be 157 and 160°C, respectively. By using the current model, the considerations of asperity contacts, thus local high contact pressures, and a slightly higher average friction than the measured overall friction appear to have already increased the temperature estimates. However, the reaction kinetics model estimates an average temperature of 375°C in the lubricant film is necessary to degrade 10% of the total lubricant. Also, measurements carried out by Bos (Bos, 1975) under slightly more severe conditions using a subsurface thermocouple, demonstrated that the true surface temperatures during a four-ball wear test are in excess of 300°C. Clearly, the predicted contact temperatures based on the current mechanical model are considerably lower than that required by the chemical reaction model. The discrepancy is large enough to be significant. For a more detailed discussion on the subject, see reference Hsu et al., 1994.
12.5.3 Asperity-Asperity Understanding One can effectively argue that most wear events under effective lubrication conditions are occurring at the asperity level. Conversely, lubrication means protecting the asperities. When asperities are touching and sliding over each other, both mechanical events and chemical events occur, but the wear is dominated by the mechanical events in the form of contact pressures, stresses, and strain accumulation rate. If the load is so high that fracture of the asperity is inevitable, lubrication has little impact. For lower loads, the protective mechanisms are: load-bearing interface; easily shearable layer; interfilm shear; and adhesion barrier. Under high pressure, the lubricant or the chemical film behaves like a solid between the contact, enlarging the real area of contact, hence reducing the contact pressure, redistributing the stresses, and therefore reducing the strain buildup rate for metals or the stress intensity for brittle solids. Since wear of brittle solids depends primarily on stress intensity, lowering it minimizes wear. If the film
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is easily shearable and has sufficient thickness, then the magnitude of the tensile stresses imposed by the asperity will be significantly reduced. If the film is thick enough and can allow interfilm shear to take place easily, such as solid lubricating films with weak planar attractive forces, the relative motion can be accommodated by interfilm movement. If the molecules are large, have strong bonding to the surface to resist shear, and cover the asperity surface reasonably well, the presence of such film will prevent nascent surface contact forming cold welding or adhesion. Under current boundary lubrication technology, many of these protective mechanisms are being used to protect the surfaces.
12.5.4 Molecular Dynamics Modeling In the last decade, molecular dynamics modeling of contacts and friction between materials has been used to understand the atomic and molecular origin of friction and wear (Harrison et al., 1995; Perry and Harrison, 1996; Stuart and Harrison, 1999). Concurrently, experimental measurements at the atomic and molecular level have been conducted (Granick, 1991a,b; Granick, 1999; Krim, 1996; Mate, 1995). These results are providing insights into the fundamental processes of friction and wear. 12.5.4.1 The Issue of Scale While the molecular dynamic calculations and the atomic scale measurements are providing valuable insights into the basic processes, the issue of scale emerges. Proponents of atomic scale investigations point out that if we understand the friction at the molecular level, then we can apply this knowledge to the micro- and macroscale events and significantly improve the technology. At this time, this has not taken place. Let us examine the issue from an engineering point of view. On each asperity, there are subasperities, which are smaller in scale. On each subasperity, there are sub-subasperities, and so on. At what scale should the contact of two surfaces be considered? For most engineering applications, the critical scale for friction is at the micron scale. The sub- subasperities need not be considered. Can one describe fully the asperity deformation process from the deformation of subasperities, sub-subasperities … down to the molecular or atomic level? The asperity deformation process is a complex system containing many stress domains, defects, and various dislocation zones. Within each zone, there are many energy levels existing at the molecular level. It is not clear how atomic simulations can reach the proper scale factor to simulate what is happening at the interface. But if a constitutive relationship can be developed from the molecular dynamic models, it may help to explain phenomena difficult to observe experimentally. 12.5.4.2 Molecular Dynamics Models The basic calculation procedure has been laid out (Harrison et al., 1993). Take a collection of atoms or molecules, calculate the interatomic forces, integrate equations of motion within a boundary from an initial position, according to the temperature, pressure, stress, and energy transfer mechanisms specified by the model. Periodic boundaries are used to simulate an extended array of atoms. Reactions and molecular attachment are dictated by energy levels and pairwise potentials (Brenner, 1990). An example of this technique is shown in Figure 12.23 for the simulated tribochemical wear of diamond (Harrison and Brenner, 1994). As the model diamond surfaces pass one another under contact (from a → d), we observe C–C bond formation (adhesion), and subsequent bond breakage resulting in the transfer of atoms from one surface to the other. This area of study is rapidly evolving to handle complex situations more relevant to boundary lubrication; however, the current significance to practical lubrication is not clear at this time.
12.6
Concluding Remarks
Significant progress has been made in the field of boundary lubrication research in the past 20 years. Much of this is focused on understanding the factors that influence lubrication effectiveness. We can identify the effects of tribochemistry, lubrication film formation, and the failure mechanisms of boundary
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FIGURE 12.23 Molecular dynamics model simulation of tribochemical interaction between diamond surfaces. (From Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry — an atomic-scale view of the wear of diamond, Journal of the American Chemical Society, 116 (23):10399-10402. With permission.)
lubrication much better; however, our ability to predict lubrication effectiveness in any given instance for a particular system still needs development.
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Granick, S. (1991b), Molecular tribology, MRS Bulletin., 16 (10):33-35. Granick, S. (1999), Soft matter in a tight spot, Physics Today, 52 (7):26-31. Greenwood, J.A. and Williamson, J.B.P. (1966), Contact of nominally flat rough surfaces, Proc. R. Soc. Lond., Vol. A295, 300-319. Gunderson, R.C. and Hart, A.W. (1962), Synthetic Lubricants, Reinhold, New York. Gunsel, S., Spikes, H.A., and Aderin, M. (1993), In situ measurement of Zddp films in concentrated contacts, Tribology Trans., 36 (2):276-282. Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry — an atomic-scale view of the wear of diamond, Journal of the American Chemical Society, 116 (23):10399- 10402. Harrison, J.A., Colton, R.J., White, C.T., and Brenner, D.W. (1993), Effect of atomic-scale surface-roughness on friction — a molecular-dynamics study of diamond surfaces, Wear, 168 (1-2):127-133. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1995), Investigation of the atomic-scale friction and energy-dissipation in diamond using molecular-dynamics, Thin Solid Films, 260 (2):205-211. Hazel, J.L. and Tsukruk, V.V. (1998), Friction force microscopy measurements: normal and torsional spring constants for V-shaped cantilevers, Journal of Tribology — Transactions of the ASME, 120 (4):814-819. Hermance, H.W. and Egan, T.F. (1958), Organic deposits on precious metal contacts, Bell System Tech. J., Vol. 27, 739-766. Hoogerbrugge, P.J. and Koelman Jmva (1992), Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics, Europhysics Letters, 19 (3):155-160. Hsu, S.M. (1991), Boundary lubrication of advanced materials, Mrs Bulletin., 16 (10):54- 58. Hsu, S.M. and Klaus, E.E. (1978), Estimation of molecular junction temperatures in a four-ball wear contact by chemical reaction rate studies, ASLE Trans., Vol. 21, (3):201. Hsu, S.M. and Klaus, E.E. (1979), Some chemical effects in boundary lubrication part 1: base oil-metal interaction, ASLE Trans., Vol. 22, (2):135-145. Hsu, S.M., Klaus, E.E., and Cheng, H.S. (1988), A mechano-chemical descriptive model for wear under mixed lubrication conditions, Wear, 128 (3):307-323. Hsu, S.M., Shen, M.C., Klaus, E.E., Cheng, H.S., and Lacey, P.I. (1994), Mechanochemical model — reaction temperatures in a concentrated contact, Wear, 175 (1-2):209-218. Hucknell, D.J. (1974), Selective Oxidation of Hydrocarbons, Academic Press, New York. Israelachvili, J. (1993), Dynamic properties of liquids at interfaces, Abstracts of Papers of the American Chemical Society, 206:103-COLL. Israelachvili, J.N. (1986), Measurement of the viscosity of liquids in very thin-films, Journal of Colloid and Interface Science, 110 (1):263-271. Israelachvili, J.N., Mcguiggan, P.M., and Homola, A.M. (1988), Dynamic properties of molecularly thin liquid-films, Science, 240 (4849):189-191. Jaeger, J.D. (1942), Moving sources of heat and the temperature at sliding contacts, Proc. R. Soc. London, N.S.W., Vol. 56, 203. Johnson, J.C., (1975), Antioxidants: Synthesis and Applications, Noyes Data Corp., Park Ridge, N.J. Kang, H.J., Zhao, Q., Talke, F.E., Perettie, D.J., Dekoven, B.M., Morgan, T.A., Fischer, D.A., Hsu, S.M., and Bhatia, S. (1999), The use of cyclic phosphazene additives to enhance the performance of the head/disk interface (C), Lubrication Engineering, 55 (3):22-27. Klaus, E.E., Duda, J.L., and Chao, K.K. (1991), A study of wear chemistry using a micro sample fourball wear test, STLE Tribology Trans., 34 (3):426. Klaus, E.E., Krishnamachar, V., and Dang, H. (1980), Evaluation of basestock and formulated lubes using the Penn State micro-oxidation test, Proceedings of the Conference on Measurements and Standards for Recycled Oil, Vol. 584, 285. Klaus, E.E., Nagarajan, R., Duda, J.L., and Shah, K.M. (1987), The adsorption of tribochemical reaction products at solid surfaces, Proceedings of the Inst. Mech. Engr. International Conference on Friction, Lubrication and Wear, Vol. 1, 379.
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Klaus, E.E., Shah, P., and Krishnamachar, V. (1982), Development and use of the micro-oxidation test with crankcase oils, Proceedings of the Conference on Measurements and Standards for Recycled Oil, National Bureau of Standards, Gaithersburg, MD. Klaus, E.E. and Tewksbury, E.J. (1973), Microcorrosion studies with functional fluids, Lubrication Engineer, Vol. 29, 205. Klaus, E.E., Ugwuzor, D.I., Naidu, S.K., and Duda, J.L. (1985), Lubricant metal interaction under conditions simulating automotive bearing lubrication, Proceedings of the JSLE International Conference, JSLE, 859. Kong, Y., Manke, C.W., Madden, W.G., and Schlijper, A.G. (1997), Effect of solvent quality on the conformation and relaxation of polymers via dissipative particle dynamics, Journal of Chemical Physics, 107 (2):592-602. Krim, J. (1996), Friction at the atomic scale, Scientific American, 275 (4):74-80. Lahijani, J., Lockwood, F.E., and Klaus, E.E. (1981), The influence of metals on sludge formation, ASLE Transactions, 25(1):25-32. Lee, S.C. and Cheng, H.S. (1992), On the relation of load to average gap in the contact between surfaces with longitudinal roughness, Tribology Trans., 35 (3):523-529. Lenahan, P.M. and Curry, S.E. (1990), First observation of the (29) Si hyperfine spectra of silicon dangling bond centers in silicon nitride, Appl. Phys. Lett., Vol. 56, (157):207. Lindsay, N.E., Carter, R.O., Schmitz, P.J., Hack, L.P., Chase, R.E., deVries, J.E., and Willermet, P.A. (1993), Characterization of films formed at a lubricated cam/tappet contact, Spectrochemica Acta, Vol. 49A, 2057. Ling, F.F., Klaus, E.E., Fein, R.S., and Editors (1969), Boundary Lubrication: An Appraisal of World Literature, ASME, New York. Martin, J.M., Belin, M., and Mansot, J.L. (1986), Friction-induced amorphization with ZDDP — an EXAFS study, ASLE Trans., Vol. 49, 523. Mate, C.M. (1995), Force microscopy studies of the molecular origins of friction and lubrication, IBM Journal of Research and Development, 39 (6):617-627. McCool, J.L. (1986), Comparison of models for the contact of rough surfaces, Wear, Vol. 107, 37-60. Meeks, S.W., Weresin, W.E., and Rosen, H.J. (1995), Optical-surface analysis of the head-disk-interface of thin-film disks, Journal of Tribology — Transactions of the ASME, 117 (1):112-118. Mizuhara, K. and Hsu, S.M. (1992), Tribochemical reaction of oxygen and water on silicon surfaces, in Wear Particles, Dowson, D. (Ed.), Elsevier Science Publishers, 323. Morecroft, D.W. (1971), Reaction of octadecane and decoic acid with clean iron surfaces, Wear, 18:333. Mori, S. and Imaizumi, Y. (1988), Adsorption of model compounds of lubricant on nascent surfaces of mild and stainless steels under dynamic conditions, STLE Trans., Vol. 31, 449. Naidu, S.K., Klaus, E.E., and Duda, J.L. (1984), Evaluation of liquid phase oxidation products for ester and mineral oil lubricants, Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, 613. Naidu, S.K., Klaus, E.E., and Duda, J.L. (1986), Kinetic model for high-temperature oxidation of lubricants, Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, 566. Nakayama, K. and Hashimoto, H. (1991), Triboemission from various materials in atmosphere, Wear, 147 (2):335-343. O’Connor, J.J. (1968), Standard Handbook of Lubrication Engineering, McGraw Hill, New York. Perry, M.D. and Harrison, J.A. (1996), Molecular dynamics studies of the frictional properties of hydrocarbon materials, Langmuir, 12 (19):4552-4556. Quinn, T.F.J., Sullivan, J.L., and Rowson, D.M. (1984), Origins and development of oxidational wear at low ambient-temperatures, Wear, 94 (2):175-191. Rabinowicz, E., (1965), Friction and Wear of Materials, John Wiley & Sons: New York. Ramsey, J.A. (1967), The emission of electrons from aluminium abraded in atmosphere of air, oxygen, nitrogen, and water vapour, Surface Science, Vol. 8, 313.
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Ranney, M.W. (1980) Synthetic Oils and Additives for Lubricants: Advances since 1977, Noyes Data Corp., Park Ridge, N.J. Reynolds, O. (1886), On the theory of lubrication and its application to Mr Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil, Phil. Trans. R. Soc., 117:157-234. Rosenblum, F., Braunlich P., and Himmel, L. (1977), Spontaneous emission of charged particles and photons during tensile deformation of oxide-covered metals under ultrahigh vacuum conditions, J. Appl. Phys., Vol. 48, 5262. Satriana, M.J. (1982) Synthetic Oils and Additives: Advances Since 1979, Noyes Data Corp., Park Ridge, N.J. Schneir, J., Mcwaid, T.H., Alexander, J., and Wilfley, B.P. (1994), Design of an atomic-force microscope with interferometric position control, Journal of Vacuum Science & Technology B, 12 (6):3561-3566. Sheasby, J.S., Caughlin, T.A., and Habeeb, J.J. (1991), Observation of the antiwear activity of zinc dialkyldithiophosphate additives, Wear, 150 (1-2):247-257. Shubkin, R.L. (1993), Synthetic Lubricants and High Performance Functional Fluids, Marcel Dekker, New York. Simoi, C., Hrianca, I., and Cracium, P. (1968), Exoemission of electrons without photo-stimulation, Phys. Status Solidi, Vol. 29, 761. Smalheer, C.V. and Smith, R.K. Lubricant Additives, Lezius-Hiles, Cleveland, OH. Spikes, H.A. (1996), Direct observation of boundary layers, Langmuir, 12 (19):4567-4573. Stuart, S.J. and Harrison, J.A. (1999), Molecular dynamics study of lubrication by small hydrocarbons, Abstracts of Papers of the American Chemical Society, 217:U589. Sugimura, J. and Kimura, Y. (1984), Characterization of topographical changes during lubricated wear, Wear, Vol. 98, 101. Tomizawa, H. and Fischer, T. (1986), Friction and wear of silicon nitride and silicon carbide in water: hydrodynamic lubrication at low sliding speed obtained by tribochemical wear, ASLE Trans., Vol. 30, 41. Tonck, A., Kapsa, Ph., and Sabot, J. (1986), Mechanical behavior of tribochemical films under a cyclic tangential load in a ball flat contact, J. Tribology, Vol. 108, 117. Wang, F.X., Lacey, P., Gates, R.S., and Hsu, S.M. (1991), A study of the relative surface conformity between 2 surfaces in sliding contact, Journal of Tribology — Transactions of the ASME, 113 (4):755-761. Warren, O.L., Graham, J.F., Norton, P.R., Houston, J.E., and Michalske, T.A. (1998), Nanomechanical properties of films derived from zinc dialkyldithiophosphate, Tribology Letters, 4:189-198. Yang, Y.Y., Torrance, A.A., and Oxley, P.L.B. (1996), Modelling mechanical wear processes in metallic sliding friction, Journal of Physics D — Applied Physics, 29 (3):600-608. Yates, J.T., Dohnalek, Z., Yang, W., and Choyke, W.J. (1996), Defect site effects on chlorine chemistry on silicon, Abstracts of Papers of the American Chemical Society, 211:18-PHYS. Ying, T.N. (1994), Wear mechanisms for ductile and brittle materials in a microcontact, Ph.D. Thesis, Department of Materials and Nuclear Engineering, University of Maryland, College Park, MD.
For Further Information The reader is directed to the following important resources for further information on the topics discussed in this chapter on boundary lubrication. Boundary Lubrication: An Appraisal of World Literature, F.F. Ling, E.E. Klaus, and R.S. Fein, Editors, ASME, NY [1969]. CRC Handbook of Lubrication, Theory and Practice of Tribology, Volume II: Theory and Design, Richard Booser, Editor, CRC Press, Boca Raton, FL [1984]. Limits of Lubrication, selected papers from the Limits of Lubrication Conference in Williamsburg, VA, April 14-18, 1996. Tribology Letters 3(1) [1997]. Tribochemistry, Heinke, G., Hanser Press, Munich, Germany [1984].
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Defining Terms Additive: Chemical compounds dissolved or dispersed in a base fluid to impart or extend desirable properties to the lubricant. Basestocks: Main fluid component of a lubricant. Can be derived from naturally occurring, or synthetic sources. Boundary Lubrication: Lubrication regime involving contact between asperities in relative motion in which chemical reactions dominate the mechanism of reduction of friction and wear. Dangling Bonds: Highly reactive sites on atoms resulting from inability of the atom to form proper bonds with nearest neighbor atoms. Can occur when bonds in a structure are broken by mechanical forces. Friction Polymer: High-molecular-weight product formed in some contacts under boundary lubricating conditions. Kurtosis: Surface roughness parameter describing the narrowness of the peak height distribution. Nascent Surfaces: Fresh surfaces formed during rubbing. Highly reactive. Organometallic: Chemical compounds consisting of metal atoms bonded to organic molecules. Ra: Surface roughness parameter describing the average surface roughness, also known as centerline average roughness. RMS: Surface roughness parameter describing the root mean square surface roughness. Skewness: Surface roughness parameter describing the asymmetry of the peak height distribution of a surface. Tribochemistry: Chemical reactions that are induced by rubbing, usually referring to reactions that are not observed by purely thermal means.
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13 Friction and Wear Measurement Techniques
Niklas Axén Uppsala University
Sture Hogmark Uppsala University
Staffan Jacobson Uppsala University
13.1
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10
The Importance of Testing in Tribology ........................ 493 Wear or Surface Damage ................................................. 494 Classification of Tribotests .............................................. 497 Tribotest Planning............................................................ 498 Evaluation of Wear Processes.......................................... 500 Tribotests — Selected Examples ..................................... 501 Abrasive Wear................................................................... 502 Erosive Wear ..................................................................... 504 Wear in Sliding and Rolling Contacts ............................ 505 Very Mild Wear ................................................................ 508
The Importance of Testing in Tribology
Friction and wear are caused by complicated and multiplex sets of microscopic interactions between surfaces that are in mechanical contact and slide against each other. These interactions are the result of the materials, the geometrical and topographical characteristics of the surfaces, and the overall conditions under which the surfaces are made to slide against each other, e.g., loading, temperature, atmosphere, type of contact, etc. All mechanical, physical, chemical, and geometrical aspects of the surface contact and of the surrounding atmosphere affect the surface interactions and thereby also the tribological characteristics of the system. Therefore, friction and wear are not simply materials parameters available in handbooks; they are unique characteristics of the tribological system in which they are measured. For most surfaces in relative sliding or rolling contact, the area of real contact is much smaller than the nominal contact area. The applied load is carried by a number of small local asperities making up the area of real contact, and the friction and wear behavior results from the interactions between these local contact asperities. At the regions of these local contacts, the conditions are characterized by very high pressures and shear stresses, often well above the yield stress of the materials, high local (flash) temperatures of short duration, and maybe also very high degrees of deformation and high shear rates. Under such conditions, the local mechanical properties of the materials may be very different from what is found, for example, in normal tensile testing. The importance of oxide layers, small amounts of contaminants, local phase transformations, etc., is also much greater than in large-scale mechanical testing. Consequently, the properties of a material in the real contact areas may be far from those measured in normal mechanical testing procedures, and the coupling between wear and friction properties and traditional mechanical properties, such as elastic modulus and yield strength, is weak. See Zum Gahr (1987) and Hutchings (1992). 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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It also follows from the systems aspect of friction and wear (and the insight into how complicated a surface contact consisting of interacting local asperities, rather than of flats, really may be) that modeling of friction and wear becomes very difficult. Unfortunately, there are very few reliably and reasonably comprehensive models describing the wear or friction processes. This dearth of good models strongly complicates the interpretation of measured wear and friction data. There is also generally no simple correlation between wear and friction; for example, low friction does not automatically imply low wear rates. See Czichos (1987). Still, the effect of system parameters on tribological properties should not be exaggerated. Many materials do produce low friction or high wear resistance in most practical situations, and may therefore very well be referred to as low-friction materials or wear-resistant materials. Diamond or Teflon® (PTFE) produce low friction in most sliding systems, but exceptions can certainly be found. Cemented carbides are wear-resistant materials, but they may wear very quickly in corrosive environments. But, because of the system nature of tribological parameters, tabulated friction or wear values for these or any other materials are only meaningful if test conditions are very carefully documented. Conclusively, because tribological properties are not materials but system parameters, tribotesting has to be an integral part of both the process of developing tribomaterials and in the selection of materials for applications involving friction and wear.
13.2
Wear or Surface Damage
According to DIN 50 320, or similarly in other terminology standards, wear is the progressive removal of material from a surface in sliding or rolling contact against a countersurface. As described in many textbooks, e.g., Zum Gahr (1987) and Hutchings (1992), different types of wear may be separated by referring to the basic material removal mechanisms, the wear mechanisms, that cause the wear on a microscopic level. There are many attempts to classify wear by wear mechanisms, but a commonly accepted first order classification distinguishes between adhesive wear, abrasive wear, wear caused by surface fatigue, and wear due to tribochemical reactions. Over a longer sliding distance, either one mechanism alone, or a combination of several of these wear mechanisms, causes a continuous removal of material from the mating surfaces, and thereby also adds to the friction force that opposes the sliding. Such continuous, steady-state wear and friction conditions may be quantified in terms of wear rates, i.e., removed material mass or volume per sliding distance or time, or its inverse, the wear resistance, and in terms of friction forces or friction coefficients. However, not all types of tribological failures are due to wear in the sense of a continuous material removal from tribosurfaces, and the tribological properties of the materials in a component are not always best described by their wear resistances or friction properties. Instead a broader study of the various types of surface damages that occur may be more meaningful. If for example the lubrication of a piston-cylinder system fails, the result will generally be an increased temperature leading to softening or even melting of the surface asperities, followed by an increasing adhesion, material transfer, and local surface welds between the piston and cylinder surfaces; the engine seizes, as exemplified in Figure 13.1. Or, taking cutting tools as another example, the reason for lost cutting performance may very well not be a continuous wear of the cutting edges. Instead a few sudden, catastrophic and discrete events, such as grain pull-outs, edge fractures, or sudden local overheating causing plastic deformation, may lead to lost edge geometry followed by reduced tolerances, unacceptable surface finish, or increased cutting forces. In both these examples the actual wear rate may be very low and perhaps of no importance for the occurrence of the seizure or the lost cutting edge performance; but still, the effect of the events on the performance of the tribosystems is dramatic. Often, the wear process will undergo several stages as sliding proceeds; at least three stages are commonly identified: The wear starts with what could be called a run-in stage, during which steady-state conditions are building up (Figure 13.2). The running-in may be very important for some sliding systems, as for many types of bearings and gears. During this stage the mating surfaces conform to each other in
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FIGURE 13.1
Seized piston from combustion engine.
FIGURE 13.2
Typical wear stages appearing over longer service times in sliding contacts.
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such a way that the load is more favorably distributed over the surfaces. During the early running-in stages, the wear rates may be relatively high; running-in should, however, be short compared to the whole lifetime of the component. Steady-state conditions with low wear rates and stable friction values should prevail for most of the lifetime of the system, but low steady-state wear rates will eventually alter clearances or surface properties to the extent that components fail, during a brief, final, catastrophic stage during which wear rates are high and severe surface damage occurs. Only wear rates or friction forces measured during the stable, steady-state conditions are useful in characterizing the long-term properties of the system. Damages to a failed component, which occurred just shortly before the failure, are not characteristic of the continuous wear of the materials, and can therefore not explain the series of events leading to failure. Identifying the stage during which a component’s surface damages (or their precursors) did appear, and what their importance is to overall performance of the component, is one of the more difficult parts of analyzing the failure of tribological components, and probably also the point at which many analyses go wrong. To predict the onset of severe wear regimes is a challenge. The variety of surface damage types that may occur is vast. An attempt to provide some organization of all the possible types of surface damages is found in Hogmark et al. (1992). The following classes of surface damage of tribological importance are there described (Figure 13.3):
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FIGURE 13.3
Classification of surface damages and wear.
• Structural changes of the surface, for example phase transformations, formation of diffusion zones or recrystallization. Such surface changes may occur solely because of mechanical deformation of the surface, or be the result of heat generation causing diffusion or chemical reactions. Structural surface changes do not necessarily imply wear, but they may alter the mechanical properties of the outer surface layers and may constitute the initial stages of wear or other types of failures. • Plastic deformation caused by mechanical stresses or by thermal gradients at the surface. Although plastic deformation of surface asperities or of an entire surface zone does not necessarily need to be associated with gradual wear, it is of the utmost importance in the creation of any surface damage that may eventually lead to catastrophic failures. • Cracking in the surface zone may also be caused by exaggerated surface stresses, fatiguing cyclic deformations, or of repeated thermal alterations. Cracking may also be an initial mechanism that eventually leads to large-scale damage without causing any progressive wear during the service stage. • Corrosion or other chemical attacks may represent the main wear mechanism, but more frequently they assist in mechanical wear processes. Frequently, chemical attacks are the cause of lost surface finish and accelerated crack propagation.
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• Wear or surface damage involving continuous material loss due to various types of microscopic material removal mechanisms, causing material to leave the surface as debris. The wear mechanisms may ultimately be both mechanical and chemical. • Gain of material, such as material transfer from the countersurface, resulting from excessive heating of the surfaces, agglomeration of debris such as may appear in seizure, or embedment during erosion. The resulting “third-body” layers are typical of conformal sliding contacts. Very commonly, the damage observed on a tribologically loaded surface is a result of two or more coexisting or interacting surface damage types. Interacting damage types may lead to unproportionally high wear rates, as for example in oxidation-enhanced surface cracking; adhesive wear may however also be suppressed by oxidation. In the selection and design of tribological test systems, and in the choice of test parameters, great care must be taken in considering whether measured wear rates or friction forces are the best characterization parameters for the system. Perhaps the study should focus on the occurring types of surface damage instead. Generally a combination of the two is most rewarding. Likewise, it is important to consider what stages in the life-cycle of a tribosurface a test should evaluate: wear rates or wear mechanisms during steady-state conditions or surface damages responsible for the failure. In many cases microscopy or other surface characterization techniques may be more important than wear rate or friction measurements. As further described below, a selected tribotest always has to reproduce the specific type of wear mechanisms or surface damages that appear in the intended application. An approach to this is also described in Chapter 14.
13.3
Classification of Tribotests
Tribological tests can be performed in an almost endless number of ways. As the outcome of a tribotest is strongly related not only to the characteristics of the materials couple, but also to the whole mechanical system and its environment, the process of selecting the most appropriate test for a specific purpose is fundamental to making meaningful interpretations; it is crucial to plan tribotesting in detail, as shall be further described below. A rational tribotest classification facilitates the tribotest planning. It is convenient to classify tribological test methods according to their degree of realism, i.e., how closely they imitate the conditions of a real application. Generally a high degree of realism is aimed for, but there are also many reasons to evaluate materials in tests far from any application. Consider for example the aspects of cost, test time, and the accurate control of test conditions, or the wish to perform a scientific study of individual, isolated wear mechanisms. For such evaluations, clearly the simulation of an application does not have the highest priority. One of the most accepted ways of classifying tribotests, found for example in the DIN 50 322 German industrial standards or Zum Gahr (1987), identifies five levels of simple tests in addition to the field test of the entire system (Figure 13.4). If for example the wear characteristics of the cylinder–piston system in a car engine are to be investigated, a field test would include the whole vehicle driven under realistic service conditions. The whole vehicle could, however, also be evaluated in a bench test, which to improve the degree of test condition control is performed in a laboratory or other controlled milieu. Serving the purpose of reducing cost, only the important subsystem (which is still a real system and not a model), the engine in this example, may be tested under controlled conditions in a laboratory. To simplify even further, only the important machine components can be evaluated in a component test. Although a wellplanned component test might at first seem similar to any bench or field test, the alterations in the system’s complicated environments are likely to affect the test conditions significantly; heat dissipation, vibrations, conditions of lubrication, etc., will not be entirely identical. To further increase efficiency and the degree of control over the test conditions, a simplified component test or a full-model test may be explored. With a simple model test a large range of materials can be easily, quickly, and cheaply evaluated, under well-controlled test conditions. The degree of realism, however, in the data and the surface damage features, and also the possibility of making reliable conclusions about performance or usability in an application, decreases when we go from the field test to the simpler model test.
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Classification
FIGURE 13.4
Decreasing cost and Increasing control
Increasing test realism
Field test
Bench test Tribocouple test Sub-system test
Component test
Simplified component test
Semi-tribocouple test
Model test
Model test
Classification of tribotests according to the degree of realism.
Any model test may be further classified according to the characteristics of the tribosystem, as illustrated in Figure 13.4. This classification originates from the frequent wish to evaluate new materials or new designs for one or two components in already existing machinery. Because of cost and time schedules, the evaluations should be performed in some kind of simplistic test equipment; the components are real, but the rest of the tribosystem has to be simulated. In such situations one may distinguish between tests with full tribocouples, thus involving the real components in both of the sliding surfaces, or semitribocouple tests in which only one of the surfaces represents an actual component. In a pure model test both tribosurfaces are replaced by simulated components. In addition, tribotests may be classified as open or closed, with respect to the type of tribological contact situation. If one tribosurface continuously follows the same track on the counterbody, the system is closed, whereas the sliding track is continuously renewed in an open system. (Open or closed may also refer to systems with fresh or recycled particles or oil.) One can also distinguish between tests involving unidirectional or reciprocal sliding, or specify whether the contact involves impacts. Sometimes it may be convenient to distinguish between conformal or nonconformal (alternatively counterformal) contacts. For counterformal geometries, the contact area changes (often increases) as wear proceeds, leading to varied contact conditions, as for example, when a sphere is worn against a flat. Further test configurations are outlined in a later section on selected examples of tribotests.
13.4
Tribotest Planning
It follows from the systems aspect of wear and friction, i.e., the insight that tribological properties depend on the whole tribosystem and not merely on the materials, that any tribological testing should be preceded by a thorough evaluation of the characteristics of the system to be evaluated and the purposes of the test;
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FIGURE 13.5
499
Reasons to perform tribotests.
a tribotest should always be designed to meet a defined need (Figure 13.5). One such need to perform a tribotest may be to rank a set of materials in terms of their friction and wear properties in a certain, welldefined system, either with the purpose of selecting a material for an existing piece of machinery, which the tribotest then should imitate, or to select a tribological material for a construction under development, for which field tests or component tests are impossible. Alternatively, the purpose of tribotesting may be to increase the fundamental and general understanding of how a material behaves in tribological applications. For that purpose, the response of that material to each individual type of wear mechanism has to be studied; this includes the exposure of the material to a variety of model tests simulating different mechanisms under systematically varied loading conditions. For each mechanism, the materials are characterized in terms of wear resistance, friction properties and typical types of surface damage — what may be called the tribological profile of the material. This is the scientific procedure to evaluate the tribological properties of new materials, and the purpose may be to recommend tribological applications for a new material. In evaluating materials for specific applications, the tribotest selection procedure becomes critical. Always choose the highest possible level of realism in the tests (i.e., higher test level according to Figure 13.4), considering the aspects of time, cost, and test condition control. As the degree of realism in the test increases, the interpretation of the test results becomes more reliable and can be more safely applied to the application in mind. A lower test level ranking means that more care must be taken to ensure that the friction and wear mechanisms of the service component are indeed simulated in the test, and surface damage analysis thereby becomes an important part of the tribotesting procedure. Also in terms of test parameters, the closest possible resemblance to the application should be aimed for. Imitate the loading situation, the contact pressures, sliding speeds, contact frequencies, ambient temperatures, atmospheres, lubricants, etc. (Hogmark et al., 1991). Consequently, the first step in the tribotest planning process is to study the application carefully in order to simulate the loading conditions as closely as possible. Secondly, the appearing wear mechanisms, specific for the service conditions have to be identified, and as a third step, a tribotest may be selected, possibly following an iterative process of wear mechanism control (Figure 13.6). The most basic and important criterion for ensuring the relevance of a model test is the close reproduction of the wear mechanisms appearing in the application during service conditions. The imitation of the actual wear mechanism is decisive for the friction and wear behavior of the tested materials. The wear mechanism, or set of wear mechanisms that a tested material is exposed to, are determined by the properties of the counterface material together with all test parameters. Temperature in particular may greatly influence wear behavior, even if the mechanism itself is under control. Maintaining the proper temperature may be difficult even if all other conditions are satisfactory, e.g., because the test pieces may be smaller than the actual components, providing a smaller heat capacity, or because heat dissipation from the tribocontact or cooling rates through the atmosphere or lubricant might differ.
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FIGURE 13.6
Recommendations for the planning of a tribotest.
Very often laboratory model tests are deliberately designed to increase, or accelerate, the wear rate of a test in order to speed up the evaluation. This is most generally achieved by exaggerating either contact pressure or sliding speed, or both. Unfortunately, test acceleration by exaggerating the contact pressure and sliding speed often alters the wear type, particularly through changing the temperature conditions, and accelerated tests that do not reproduce the true wear mechanisms are of limited value. For wear types that result from a large number of microevents, the obvious example being erosion by hard particles, the test procedure can be accelerated by increasing the rate at which the events appear, for example by increasing the rate of erodent hits, or the density of grit in an abrasive type of wear. For simulation of tribosystems with intermittent contact, a decrease in the duration of the noncontact phase may be a good way of accelerating a test. Another, often neglected part of tribotesting, also emerging from the system aspect of tribological properties, is the importance of using reference materials. Strictly seen, tribological properties are only comparative parameters, and even in a tribosystem as well characterized as it realistically can be, a wear rate or friction value measured for a sole material shall be used with skepticism. The selection of reference materials may follow different routes. In the ranking procedure for existing machineries, of course materials commonly used in the application are adequate references, but in a general tribological evaluation of an uncharacterized material, reference materials well known for specific behaviors, e.g., ductility, resistance to surface fatigue, low friction, etc., may be selected for comparison purposes. To gain knowledge about the wear mechanisms and to facilitate the overall ranking of materials, it may even pay to include materials which are known to behave poorly in the application.
13.5
Evaluation of Wear Processes
The most commonly used techniques to evaluate wear are weighing and measurement of changes in dimensions. Weighing may often be difficult if the worn volumes are small compared to the weight of the component, as is further discussed in the later section on mild wear. The wear may also be unevenly distributed over a surface, making the measurement of local wear damage more relevant than the total mass loss. Laboratory model tests may allow a continuous recording of the wear, whereas this may be more problematic in the evaluation of actual components, for which estimations of wear scar dimensions with microscopy is more realistic. The identification of wear mechanisms and surface damages is an important part of any tribotesting procedure and should accompany the measuring of wear and friction values. Therefore, the study of worn surfaces, for example with microscopy or surface topography techniques, becomes an integral part of the evaluation procedure. When examining a worn surface it is important to be attentive to the type of surface damage which sets the life time of the component; this may not be the most spectacular feature appearing on the wear scar. In other words, the identification of the most important mechanisms of a
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FIGURE 13.7
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Recommendations for the evaluation of wear processes
wear process is an important part of the evaluation process. For large components, the use of replica techniques may prove fruitful. This identification procedure may be very difficult and there are no universal procedures to follow (Figure 13.7). Be attentive to what has caused the failure and identify the location of the damage on the surface. Consider whether the failure is the result of continuous wear, or of suddenly appearing damage. Also be aware that a worn out or failed detail seldom gives information about the wear mechanism which caused the wear during service, since these may be hidden by damage that occurred during the end phase of the failure. Study components that have not yet failed, and compare worn and unworn components. This helps to differentiate between surface features which appeared during the manufacturing, and those caused by the service conditions. Study the worn surface in cross-section. This provides information about the depth of the damage, crystallographic changes caused by temperature; the lack of surface zones may indicate chemical wear. Study the countersurface. This may provide further hints about the wear process, such as transferred layers of material or embedded hard particles. Try to collect wear debris; its size, shape, and chemical content may provide ideas about wear mechanisms and surface temperatures. Because of the number of parameters influencing friction and wear, and their potential fluctuations and time dependence, scatter of data is one of the prime problems in tribotesting. The influence of both systematic and random deviations has to be taken into account. The causes of scatter may be found far from the materials or the tribometer itself; surface preparations, heat treatments, variations between batches, humidity variations, etc., may all strongly affect the measured values of friction and wear. Therefore the number of tests required to achieve a reliable result is a matter of constant debate among tribologists. It is no understatement that the result of a single measurement should be considered with great prudence. To minimize the number of influencing parameters, it is generally favorable if all tests in an evaluation procedure can be run by the same operator during a limited time period.
13.6
Tribotests — Selected Examples
Large amounts of test equipment for the evaluation of wear and friction properties, often referred to as tribometers, have been designed over the years for a variety of purposes. In this context, only a small number of model tests will be presented; these tests merit particular attention either because of being frequently used, or for representing interesting recent developments in the field of tribotesting. In addition to model tests, a large number of more application-oriented tests are in use, particularly in the industrial sector. As part of the development of materials for cutting and grinding tools, bearings, seals, etc., accelerated application-close trial tests are frequently used. For further examples of tribotests, see Blau (1992) and Normung (1986). The tribotest examples below are organized according to the main wear mechanism they are designed to simulate.
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Abrasive Wear
Among the basic wear mechanisms, pure abrasion, which is grooving by hard particles or hard asperities on a countersurface, is probably the most meticulously studied. Compared to other types of wear, the analytical models developed to describe abrasion are much more reliable and comprehensive, which strongly facilitates the interpretation of test results. For well-characterized materials, rough material rankings are sometimes possible without any testing at all. In pure abrasion there is a linearity between wear volume and sliding distance (as long as the wear of the abrasives is negligible), which is in strong contrast to many sliding contact situations. For relatively ductile materials, including most metals, a proportionality between abrasive wear resistance and indentation hardness is also generally observed, although the dependence on hardness is strongly different for different groups of ductile materials. There are also functional analytical models for the effect of grit shape and size, and for the abrasion properties of materials consisting of several phases (see Zum Gahr [1987] and Axén et al. [1996]). Since the abrasion rate depends very strongly on the shape, size, hardness, and friability of the abrasive particles, the choice of grit is particularly important in the evaluation of abrasion properties. A strong decrease in wear rate occurs when the sample hardness exceeds the grit hardness (Hutchings, 1992). Also, abrasion with loose particles, called three-body abrasion, produces fundamentally different wear types compared to tests with fixed abrasives (two-body abrasion). Three-body abrasion becomes intimately sensitive to the properties, particularly the hardness, of the counterbody. A strong shift in the wear rate has been identified at unity ratio of grit hardness to workpiece hardness (see Figure 13.8 and Axén et al., 1994). Also the degree of freedom of motion of the grit, the compliance of the support, etc., affect the characteristics of an abrasion test. Thus, also for pure abrasion, materials may behave, and also rank differently depending on the details of the test procedure. Most common tests to evaluate the resistance of materials to abrasive wear explore either wearing surfaces with fixed abrasives, e.g., grinding papers or grinding wheels, or use loose abrasives which are fed into the contact between the sample and a countersurface, for example a rotating wheel or disk. The configuration details for abrasion tests vary widely (Figure 13.9). The pin-on-disk (a) or pin-on-drum (c) configurations are very common, the latter forming the basis of a tribometer defined in the German Industrial standards in DIN 53516, and being commonly used for polymers. Rectilinear sliding of pins
Ring Slurry
Specific wear resistance [ mm/(N km) ]
Block 1.5
two-body abrasion-
Ring Block 1.0
0.5 Three-body abrasion
0 0.01
0.1 1 10 100 Hardness of ring/hardness of block
FIGURE 13.8 Wear rate as a function of the hardness ratio of the two sliding surfaces in an abrasion test with initially loose particles, evaluating a tool steel and an aluminum alloy heat treated to different hardnesses.
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FIGURE 13.9
FIGURE 13.10
503
Common abrasive wear test configuration.
Schematics of common crater grinding tests configurations.
over flats is also in use (Figure 13.9b). Figure 13.9d illustrates the frequently applied rubber wheel abrasion test, defined in the U.S. standard ASTM G65. The specimen, in the form of a block is pressed with a constant load against a rotating wheel, the rim of which is covered with a thick layer of replaceable rubber. In tests with fixed particles, the wear rate decreases with the number of passes over the same track due to the degradation of the abrasives. Therefore many apparatuses move the test pins along spiral tracks to make them meet constantly fresh abrasives. The three-body tests avoid this problem to some degree, but becomes more sensitive to the properties of the counterbody providing the grit support. Also more application-close abrasion tests have been developed. One example is the laboratory scale jawcrusher, used to simulate the gouging abrasion which occurs in mining operations. This test has been adopted to the U.S. standard and is described in ASTM G81. In contrast to these fairly coarse abrasion tests, the recent development of a finer type of abrasion test, often referred to as the dimple grinder test or the ball crater test, has attracted much attention. With the help of a rotating wheel or ball, small craters, often less than 1 mm in diameter and with depths of less than 10 microns, are ground on the sample surfaces using grit slurries (Figure 13.10). The tests have proved very practical because of their simplicity of operation, the good control of test conditions, the simplicity of measuring the wear volumes, and because of the fact that the small wear scars make the tests virtually nondestructive. Crater grinding tests have been evaluated on hard coatings, ceramics and metals bulks, thin amorphous metal bands, small ceramic crystallites, and on soft coatings of paint, in most cases with very promising results (Kassman et al., 1991 or Rutherford et al., 1996). A test procedure to evaluate the abrasion properties of multiphase materials consisting of hard phases in a softer matrix is outlined in Axén et al. (1996). This procedure has found industrial use for the evaluation of the wear resistances of the hardphase in grinding tools and multiphase materials with
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Composite wear resistance, Ω
Ωp
r
ea
w al
tim
Op
Minimal wear resistance
Ωm 0
FIGURE 13.11
ce
an
ist
s re
Amount of hardphase
1
Load-specific composite wear resistance as a function of the amount of reinforcement.
superhard reinforcements used in the machining and drilling of rock. The work is based on the concept of load distribution between the phases in a multiphase material, and it clarifies how the load applied to the sliding surfaces may be shared between the different phases of a multiphase material. Generally, a more wear-resistant phase takes a higher load and thereby contributes more to the wear and friction properties of the composite material, as described in detail in Axén et al. (1996). The wear resistant phase may also carry low load shares and contribute very little to the wear resistance of a multiphase material. By identifying the upper and lower limits for how well a hard phase can carry load, the possible load distribution limits, and thereby the optimal and minimal wear resistance of a composite, can be predicted. In practice, measured values of the wear resistance and friction of the individual phases, or extrapolated values measured for materials with very low or high amounts of reinforcements, are used to calculate upper and lower limits for the wear and friction properties of the multiphase material. The contribution of hard reinforcing phases to the properties of the composite is thereafter quantified in terms of load distribution coefficients relating to the possible maximum or minimum values. The procedure is practical in the evaluation of reinforcements because it is based rather on measurable values of load distributions between the phases, and is less dependent on the subjective study of wear mechanisms (Figure 13.11). In the context of abrasion tests, which are basically multiple-tip grooving tests, single-tip scratch tests also merit being mentioned. Equipment to slide a diamond stylus over the sample surface under controlled loading and speed conditions is commercially available and commonly used to evaluate both bulk materials and coatings. Often hardness indentors of the Rockwell C or Vickers types are slid over the sample surface to produce a controlled groove along which failure mechanisms can be studied with microscopy, or by the use of acoustic emission detection units and friction recordings (Axén et al., 1997).
13.8
Erosive Wear
Solid particle erosion is the wear caused by hard particles bombarding a surface. Like abrasion, erosive wear can involve both plastic deformation and brittle fracture, and the details of the appearing wear mechanism depends on both the wearing material, the erodents, and the condition of the impacts, primarily particle mass, velocity, and impingement angle. The erosion behavior of materials is closely linked to the properties of the eroding grit; shape, hardness, toughness, and size all strongly affect the erosion rate of any test material. Deterioration of the erodents during testing has to be taken into account, and testing with recycled particles should be avoided, unless appropriate for the application being
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FIGURE 13.12
505
Basic test configurations for erosive wear.
investigated. The erosion rate increases with the speed of the eroding particles and their mass and tends to fall with the hardness of the wearing material, although the hardness dependence may be weak for certain groups of materials (Söderberg et al., 1981). The effect of impact angle is fundamentally different for materials of different mechanical properties. The erosion rates of brittle materials generally increase continuously with impact angle, from the particles streaming close to parallel to the surfaces, to the case of orthogonal impacts. Ductile materials, however, tend to erode the fastest at an intermediate impact angle, often at around 20 to 30° measured from the eroded surface tangent (Kosel, 1992; Hutchings, 1992). Erosion properties thus also depend on the details of the test configuration, and there is a need to control test conditions accurately. Test methods for laboratory evaluation of erosion can be classified according to the principles for the propulsion of the eroding particles toward the samples. Most commonly the particles are carried either by a fast gas or liquid stream exiting through a nozzle directed toward the test materials; alternatively they are propelled by the rotary motion of a disk or propeller. Figure 13.12 shows different types of testing methods. In the jet impingement or gas-blast method illustrated in Figure 13.12a, particles are accelerated toward the sample by a stream of gas or fluid along a nozzle. Gasblasting methods are standardized in the ASTM G76 and the DIN 50332 industrial standards. Systems exploring a loop through which gas-born particles or slurries are pumped are used to establish wear properties of pipework components (Figure 13.12b), e.g., pneumatic or hydraulic components. The centrifugal techniques, illustrated in Figure 13.12c, or rigs based on whirling arms have the advantage of allowing accurate calculation of particle speeds; in the gas or liquid carrier methods, particle speed has to be measured by separate systems. Centrifugal techniques also facilitate the evaluation of large numbers of samples in each test run. Also there is detonation gun equipment for single particle impacts. Some attempts have been made to use erosion for the evaluation of the durability of coatings. Thick, thermally sprayed coatings can be tested along the same principles as bulk materials. For thin coatings, Shipway (1995) has developed a procedure capable of extracting the erosion resistance of the coating material from deep wear scars involving simultaneous wear of coating and substrate. The technique is based on assumptions about the variation of particle flux along the radius of the circular wear scars produced by a stream of particles leaving a long parallel nozzle. The radius of the area corresponding to the exposed substrate, or the start of the coating, thereby also indicates the mass of particles required just to remove the coating. By following the rate at which this radius widens with the dose of erodents, values for what Shipway called the “erosion durability” can hence be established. The technique has been shown to be sensitive to the adhesion of the coating to the substrate.
13.9
Wear in Sliding and Rolling Contacts
Sliding or rolling wear do not specify any wear mechanisms, but refer to the types of contact between two surfaces in relative motion. Instead numerous types of material removal mechanisms may appear in
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Illustrations of common sliding wear test configuration.
these types of contacts. Surface damages or wear based on adhesion or on surface fatigue are common, but also grooving by surface asperities, i.e., abrasion, tribochemical wear types and other mechanisms are possible. Nevertheless, wear and friction in sliding and rolling contacts are naturally of great interest because of their common occurrence in many machine elements. Therefore, numerous tests for sliding and rolling wear evaluations have been produced. Because of the vast variety of surface interactions and types of surface damages that may occur in sliding contacts, apparently minor alterations in the test conditions can lead to radical and sharp changes in the dominant wear mechanisms and the associated wear and friction values. When choosing model tests for materials ranking, it therefore becomes important to simulate the conditions of the application in detail. Contact stress, thermal conditions, sliding speed, and chemical environment are all vital test parameters in sliding and rolling wear. The interpretation of sliding wear test results is generally much more difficult than for abrasion or erosion. While these types of wear by hard particles are the result of a very large number of microevents, a sliding contact may initiate a variety of interacting phenomena whose character changes as the test proceeds. As a consequence, wear rate is often not proportional to the sliding distance, and correlations to any bulk materials properties, such as hardness, toughness, etc., cannot generally be taken for granted. Sliding wear tests may be performed with a large variety of geometrical configurations (Figure 13.13). It is practical to distinguish between tests where the test bodies are symmetrically or asymmetrically arranged. Figure 13.13a and c illustrate symmetrical versions for which self-mated materials should ideally give identical results. Symmetrical arrangements are not often used in model tests; an example, however, are rings arranged as in Figure 13.13c simulating the symmetrical and conformal contact of axial seals. Asymmetrical configurations, exemplified in Figure 13.13d to f are more common, and because of the noncontinuity of the contact, they produce different results depending on the positioning of the test sample. Probably because of their simplicity and flexibility in terms of test conditions and specimen shape, rigs of the asymmetrical pin-on-disk configuration (Figure 13.13e) have become some of the most popular model tests for evaluating sliding wear. Pin-on-disk rigs with attached heat stages and cover boxes enabling tests in controlled atmospheres are commercially available. Also pin- or block-on-cylinder configurations (Figure 13.13d) are frequently used. The configuration of a stationary pin loaded against
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a sliding block, or vice versa, primarily finds use for friction measurements in monopass tests. Very important for all these configurations is to make the distinction between conformal and nonconformal (counterformal) contacts. The contact may initially be of the point or line type, and then continuously grow as wear proceeds, or the contact may from the start be extended over a large area which remains constant as the test proceeds, as illustrated in Figure 13.14. Several sliding wear test configurations are specified in national standards. Tests based on the block-on-ring (ASTM G77), crossed cylinders (ASTM G83), pin-on-disk (ASTM G99), and sphereon-disk (DIN 50 324) are examples of American and German industrial standards. However, standardizations in tribology only serve the purpose of facilitating comparisons between results from different laboratories; the system aspect of wear and friction is unavoidable, being particularly apparent in sliding wear tests. In one recently developed apparatus to evaluate the sliding behavior of components, the orientation of the test specimens and their motion during testing is arranged in such a way that the contact spot on each specimen moves along a contact path during testing (Jacobson, 1998). In the test two specimens are loaded against each other to form a well defined contact spot on each specimen. The primary novelty of this technique is that, during testing, each contact spot on both specimens only makes contact to one specific spot on the other specimen, and vice versa. The test configuration is typically that of two crossed test bars, cylinders, or similar geometries. During testing the point of contact between the bars is for both bars moving from one end to the other (Figure 13.15 and 13.16). Testing is either performed as a single stroke operation or by reciprocally sliding the specimens across each other under controlled loading conditions. The load can be kept constant or increased gradually or stepwise. Independently of the loading, each point along the contact path of both test rods will only experience a unique load, both if the test is performed as a single stroke or reciprocally.
FIGURE 13.14 Counterformal (a) and conformal (b) contacts.
Contact path
Stationary specimen
Lower, moving specimen
End position
Intermediate position
Start position
FIGURE 13.15 Schematics of equipment loading and sliding two test rods against each other. The contact spot path resulting form the movement of the lower specimen moves along the contact path (full black line) on both specimens.
FIGURE 13.16 Typical friction graph obtained for a metal in the equipment presented in Figure 13.15. The friction shows a sudden increase at the load of seizure.
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Very Mild Wear
In situations of mild wear, such as the wear of most tribological components involving lubricated sliding or rolling contact, the mass loss is often very small in relation to the total mass of the worn component. For many machine elements it can be assumed that the wear appears on an atomistic scale. A precision balance typically has a resolution of 10–6 of the maximum load (e.g., 0.1 mg resolution at 100 g load), which naturally sets a limit to the minimum load possible to quantify in relation to the total weight of the component. Often this excludes the weighing of components before and after wear testing as a method of quantifying wear. Further, weighing gives no information about the distribution of the wear over the worn surface. In most cases this is a serious disadvantage, since the service life is often limited by the maximum wear at some critical location, rather than by the total wear. For further information, Ruff (1992) has given an overview of wear measurement techniques. As discussed above, acceleration of the wear situation may lead to changes of the wear mechanisms, and so provide unreliable results, and tests involving normal wear rates may require unrealistically long test times. In such situations modern topographical methods may be the best way to evaluate the wear. With the introduction of high-resolution instruments such as the atomic force microscope (AFM) and optical interferometry, techniques capable of determining height differences in the subnanometer range (with lateral resolutions of about 1 nm and 1 µm, respectively) and storing the obtained topographical data digitally, it is now possible to measure the volume of topographical features in the sub µm3 range. (The mass of 1 µm3 of steel equals ca. 10–11 g) Another benefit of this kind of instrument is that the topographical data are used directly to render images of the surface, including shading and color-coded heights. Recently a new method to map and quantify wear was presented by Gåhlin and Jacobson (1998). They used the technique, called the topographical difference method, to evaluate the very minute initial wear of a hydraulic motor cam roller (Gåhlin et al., 1998). The topographical difference method for evaluation of wear comprises two techniques: topographic image subtraction for wear distribution mapping, and bearing volume subtraction for local wear volume determination. Topographical image subtraction is suitable mainly for qualitative presentation of the distribution of wear over the surface and to indicate the magnitude of the individual wear events. This information is obtained by taking the topographical image of a worn surface and subtracting the previously recorded unworn (or less worn) topographical image of the same surface. This procedure effectively eliminates all unaltered surface features, leaving corresponding areas flat, and exhibits lost material as elevations over this flat surface and gained (plastically displaced) material as depressions. To get a good mapping, the lateral matching of the two images has to be very precise. On the other hand, the technique does not require a height reference, but only the existence of unaltered parts of the surface that become flat after subtraction and thus indicate the “zero wear” level. Bearing volume subtraction is used to quantitatively determine the volume loss over the local studied area. This is achieved by using bearing histograms to calculate the volume of material left above a common fixed surface level (Figure 13.17). The more the surfaces are worn, the less material is left above this reference level. To obtain the bearing volumes from the topographical data, each measured point (surface element) of the specified surface area is multiplied by its height over the reference level. The accumulated wear volume is then calculated by subtracting this bearing volume by the corresponding volume obtained after the wear test. In contrast to topographical image subtraction, bearing volume subtraction involves no point-to-point comparison and thus does not depend on a precise lateral matching of the two images. The first application of this method to actual components involved wear evaluation of a hydraulic motor. The wear of the cam rollers was successfully mapped and measured (Figure 13.18), using a standalone-type AFM. For this application typical average wear depths of 30 nm were registered after a sliding distance of about 15 km (2165 h test time), corresponding to a total wear of about 1 mg of the 600 g roller. The wear distribution map revealed that this minute wear was localized at the uppermost parts of the grinding ridges (Figure 13.19). These results were obtained on rollers, where the curved geometry put extra demands on the experimental technique. This clearly demonstrates that the topographical difference method is not restricted to simplified laboratory tests.
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FIGURE 13.17 A computer-generated two-dimensional profile of a surface showing the effect of wear with and without plastic deformation. The wear distribution maps produced by subtracting profiles and the changes of corresponding bearing histograms are shown. The magnitude of the initial bearing volume and the two bearing volume differences are also indicated.
FIGURE 13.18 Topography and corresponding bearing histograms of a chromium steel roller before and after sliding against silicon nitride in a full-scale hydraulic motor test. The average wear depth is about 40 nm, corresponding to a mass loss of 10–9 g. (10× larger magnification in the height direction.) (a) Initial and (b) worn 2165 h.
FIGURE 13.19 Wear distribution map of the roller obtained by subtracting the initial surface by the worn surface. (10× larger magnification in the height direction.)
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In conclusion, extremely high resolution methods such as the one described above, promise to improve tribological testing of real machine elements by reducing the need for excessively accelerated tests or extremely long test times.
References Axén, N., Kahlman, L., and Hutchings, I.M. (1997), Correlations between tangential force and failure mechanisms in scratch testing of ceramics, Tribol. Int., 30, 7, 467-474. Axén, N. and Hutchings, I.M. (1996), Analysis of the abrasive wear and friction behaviour of composites, Mater. Sci. Technol., 12, 757-765. Axén, N., Jacobson, S., and Hogmark, S. (1994), Influence of hardness of the counterbody in three-body abrasive wear — an overlooked hardness effect, Tribol. Int., 27, 4, 233-236. Blau, P. (Ed.) (1992), ASM Handbook on Friction, Lubrication and Wear Technology Technology, ASM International, vol. 18, 362. Czichos, H. (1987), Tribology — A System Approach to the Science and Technology of Friction, Lubrication and Wear, Elsevier, Amsterdam, 351. Gåhlin, R. and Jacobson, S. (1998), A novel method to map and quantify wear on a micro-scale, Wear, 222, 93–102. Gåhlin, R., Larker, R., and Jacobson, S. (1998), Wear volume and wear distribution of hydraulic motor cam rollers studied by a novel AFM technique, Wear, 220, 1–8. Hogmark, S., Jacobson, S., and Vingsbo, O. (1992), ASM Handbook on Friction, Lubrication and Wear Technology, Blau, P. (Ed.), 18, 176-183. Hogmark, S. and Jacobson, S. (1991), Hints and guidelines for tribotesting and evaluation, Journal of the Society of Tribologists and Lubrication Engineers, 48, 5, 401-409 Hutchings, I.M. (1992), Tribology — Friction and Wear of Engineering Materials, Edward Arnold, London. Hutchings, I.M. (1998) Abrasive and erosive wear tests for thin coatings: a unified approach, Proceedings of the World Tribology Congress, London, 269-278. Jacobson, S. and Hogmark, S. (1998), Swedish Patent no. 9802017-6. Kassman, Å., Jacobson, S., Erickson, L., Hedenqvist, P., and Olsson, M. (1991), A new test method for intrinsic abrasion resistance of thin coatings, Surf. Coat. Technol., 50, 75-84. Kosel, T.H. (1992), Solid particle erosion, in ASM Handbook on Friction, Lubrication and Wear Technology, Blau, P. (Ed.), 18, 199. Normung, D.I. (1986), Wear Testing Categories, Beuth Verlag, Berlin. Ruff, A.W. (1992), Friction, Lubrication and Wear Technology, ASM International, Blau, P. (Ed.), Vol. 18, ASM Handbook, 362. Rutherford, K.L. and Hutchings, I.M. (1996), A micro-abrasive wear test, with particular application to coated systems, Surf. Coat. Technol., 79, 231-239. Shipway, P.H. and Hutchings, I.M. (1995), Measurement of coating durability by solid particle erosion, Thin Solid Films, 137, 65-77. Söderberg, S., Hogmark, S., Engman, U., and Swahn, H. (1981), Erosion classification of materials using a centrifugal erosion tester, Tribology International, 14, 6, 333-343. Zum Gahr, K.-H. (1987), Microstructure and Wear of Materials, Tribology Series 10, Elsevier, Amsterdam.
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14 Simulative Friction and Wear Testing 14.1 14.2 14.3
Introduction ..................................................................... 511 Defining the Problem ...................................................... 512 Selecting a Scale of Simulation ....................................... 514
14.4 14.5 14.6
Defining Field-Compatible Metrics................................ 516 Selecting or Constructing the Test Apparatus ............... 517 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed ....................... 517 Case Studies...................................................................... 518
Levels of Tribosimulation
14.7
An Oil Pump Gear Set with Several Wear Modes • Wear of Gravure Rollers on Doctor Blades • Scoring of Spur Gears • Wear of Plastic Parts in an Optical Disk Drive • Wear of Rotary Slitter Knife Blades • Erosive Wear of Piping
Peter J. Blau Tribomaterials Investigative Systems
14.8
Conclusions ...................................................................... 522
14.1 Introduction The selection of lubricants, materials, or surface treatments for friction and wear-critical applications often involves validation or screening tests before final decisions are made. Testing is particularly valuable during the development of new machines for which operating conditions are much different than existing designs. An example of the latter might be a new design that cannot use off-the-shelf bearings or gears because the temperatures are too high or the surrounding environments are too corrosive. The steps involved in developing tribosimulations of current or newly designed systems are, with only one significant exception, essentially the same. The exception is that for an existing friction of wear problem, there is prior experience in the response of the materials and lubricants to the operating conditions. In a new design, however, there may be no direct prior experience in the behavior of candidate materials, although there may be some relevant experience from machinery of a similar kind. There are two types of tribosimulations: computer simulations and physical simulations. The computer simulation uses a virtual mechanical assembly that consists of several components defined in terms of a set of properties, spatial relationships, and assumed rules of interaction. Known or estimated properties of the materials and/or lubricants are provided to the model, and the expected responses of the virtual tribosystem to such variables as load cycles, deflections, temperature excursions, etc., are calculated. Such programs have been prepared by both academic researchers and industry engineers for tribological components like bearings, face seals, brakes, and gears. Component designers have also developed sophisticated design tools for automotive valve trains, engines, and pumping systems as well. The second type of tribosimulation is the physical simulation. Here, materials and lubricants are screened in an apparatus that is intended to provide the essential operating characteristics of the intended
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511
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application. An additional use of virtual and physical simulations is to observe how a certain material or lubricant might react in a situation when the opportunity to observe the material or lubricant is not practical. For example, bearings for use in unmanned orbiting satellites might be observed in an ultrahigh vacuum, space-like environmental chamber created in the laboratory for that purpose. This article focuses on the development and use of physical tribosimulations. It describes the process involved in developing and validating laboratory bench-scale simulations for friction and wear-critical machine components. The steps in developing a physical tribosimulation are similar in some respects to those used to set up a computer simulation. They are: 1. 2. 3. 4. 5. 6. 7.
Define the nature of the friction or wear problem to be investigated Select a scale of simulation Define field-compatible metrics to use to assess the results of the simulation Select or build the apparatus (the model, in the case of the computer simulation) Conduct baseline tests to establish the repeatability and characteristics of the method Analyze baseline test results using the established metrics Refine as needed to achieve an acceptable engineering confidence level
14.2 Defining the Problem Defining the nature of the friction or wear problem is critical before any test method can be selected, developed, or successfully employed. Rushing ahead to testing without proper analysis of the problem is akin to sitting down at a table to play cards without knowing what game is to be played and what its rules are. At the first level of problem definition, one answers the following questions: 1. 2. 3. 4.
What are the physical attributes of the tribosystem? Is it an open or closed tribosystem? What form or forms of friction or wear are likely to be involved? What quantitative measures, if any, are there to describe the behavior of the materials in the situation of interest? 5. What materials or lubricants are currently under consideration for this application? 6. What time and resources are available to use to solve the current problem? By defining the physical limits of the tribosystem, we are forced to make the first judgment. At what distance from the tribological interface will the surroundings still affect the tribological function? For example, if we limit our focus to a pair of wearing gears in isolation from their surroundings, we might inadvertently neglect externally produced mechanical vibrations, sources of abrasive debris, or temperature excursions from surrounding components as potential contributions to the gears’ wear environment. Thus our simulation could omit critical, wear life-limiting elements which come from the surroundings, elements which might in fact be just as important to include in the simulation as the imposed load on the gear teeth or the speed of relative rotation. Closed tribosystems involve, for example, recirculating lubricants or contact environments which are contained within a certain portion of the machine. Open tribosystems are more complicated and difficult to simulate because materials of unforeseen origin might enter the area of contact from sources external to the machine and cause strong friction or wear responses. An example of an open tribosystem is the bucket teeth on construction equipment that must dig through all kinds of dirt, soil, and rock under wet and dry, hot and cold conditions. The forms of friction or wear must be defined early. It is common to observe more than one type of wear or mechanical surface damage in different locations, even on the same part. Therefore, the locations and wear types most damaging to the satisfactory operation of the component must be identified and prioritized. It is possible that more than one type of test will be required to ensure that the proposed materials or lubricants will respond suitably to all the critical contact conditions on various surfaces of the component. For example, the side of a pump gear may slide against its case while the teeth of the same gear may experience contact fatigue worsened by a small amount of tangential slip.
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TABLE 14.1
Elements of a TriboSystem Analysis (TSA)
Element Tribosystem — open or closed? Macro contact and conformity Microcontact and surface finish Type of relative motion Speed of relative motion Contact load and pressure Temperature Contact environment and lubrication
Third bodies Type(s) of wear Performance degradation Experience Metrics
Description Is the system open to the environment, like the teeth of earthmoving equipment, or closed, like a sealed recirculation system? To what degree do the shapes of the contacting bodies conform to one another? How can the geometry be described: convex curve-on-convex curve, flat-on-flat, particles-on-flat, etc.? Is the contact open on the edges or closed so as to confine wear debris? Surface texture of the interacting bodies — roughness, waviness, and lay. How long does the initial finish persist in service? Is the motion unidirectional, reciprocating, intermittent, or continuous? What is the characteristic constant distance (stroke length, etc.)? Fretting or long-distance sliding? Sliding velocity or impingement velocity, if particles are involved. How is the load distributed on the surfaces? What is the magnitude of the normal force? How does it vary? Does the temperature change during operation or remain constant? Is frictional heating an issue? What chemical environment does the contact area experience? Is there a lubricant? What lubricant regime is present (dry, starved, boundary, mixed, hydrodynamic)? What are the lubricant characteristics? Are there contaminants in the lubricant? Is the lubricant agitated so as to entrain air? Are there vibrations or other mechanical contributions to negative performance? Are there particles involved in the wear, and if so, what are their characteristics? Are particles generated by wear or externally to the contact area? Using surface analysis and microscopy, what is/are the dominant form(s) of wear? To solve the problem, the negative manner in which wear or friction affect the operation must be defined. What are the current materials and lubricants, and which others have been tried? What quantitative measures are used to described the wear or friction of the subject component?
In existing applications, identifying the type of wear involves examining field-worn parts which have been protected from the environment after having been removed from the machine. Surfaces of worn parts which have stood unprotected for some time may be corroded and difficult to analyze. Other complications include removing surface deposits of degraded or heat-altered lubricants without destroying the most telling clues as to the dominant mode of wear damage. In new designs, the engineer is placed in a position of speculating what the environment of the tribosystem will be, and adjusting the simulation appropriately. Some guidance can, however, be obtained by analyzing existing systems with similar mechanical, thermal, and chemical aspects in the key areas of tribocontact. TriboSystem Analysis (TSA) [3] is a means to define the operating conditions of a system to be simulated. It involves a systematic analysis, aspect-by-aspect, of the operating environment of the subject component(s). Table 14.1 lists key elements for analyzing a tribosystem. Often, not all of the operating parameters are known. Therefore it is doubly important to understand the characteristic wear features or other key aspects of the tribosystem that will help to define metrics for the simulation (see Section 14.4). Understanding the properties and behavior of the currently used materials, or those used in an application which has key operating aspects in common with the component of interest, is important. Knowing what materials have and have not worked in the given application is equally valuable because it could save a great deal of time and effort. Simply asking the questions embodied in a thorough tribosystem analysis can go a long way toward solving the problem. Verifying the answers to those questions with a second opinion or a measurement can also be helpful. Sometimes people incorrectly assume that certain operating conditions exist. Tribosimulations sometimes need to be sensitive enough to distinguish between different variants of the same material. For example, there are many ways to heat-treat steels. A wear problem may occur if a component supplier changes the heat treatment, perhaps for reasons of economy, or changes the material supplier without notifying the customer (see the later example of gear scoring). The simulation in that case must be sensitive enough to detect the differences due to different heat treatments. Detecting
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small variations in friction or wear using short-term laboratory tests can be challenging, but it can be facilitated through the use of statistical methods for data analysis. Therefore, multiple tests of each material or lubricant combination are needed to establish the characteristics of the laboratory test method; particularly, if the test method is new and has no historical record of performance. Using ASTM and other standardized tests offers the benefit of having previous data available from tests conducted in the same manner.
14.3 Selecting a Scale of Simulation Field-trials evaluate materials and lubricants under actual operating environments. Sometime field trials involve monitoring components as they are used in normal service. These instrumented components can be subjected to certain prescribed patterns of use. For example, some automotive companies have instrumented the brakes of test vehicles and returned those vehicles to their owners for a period of time, treating the driver’s behavior as a variable. In other cases, instrumented vehicles have been run in several cities, but over carefully prescribed driving routes. Both types of field tests provide valuable information, but interpreting the wealth of data that obtains in these situations is difficult and complicated due to the many uncontrolled variables present in the field. For example, test drivers on city routes might be forced to break rapidly to avoid hitting a child or a dog. They could wind up behind a slow moving vehicle. In truth, the more “channels of information” that are collected, the more challenging is the task of interpreting the results and determining the underlying relationships in material and lubricant behavior. Like the automotive and truck brakes in the foregoing example, a great many tribological components are not operated under steady-state conditions. Some machine parts may experience short start-up and slow-down intervals but spend most of their lives under constant conditions. A classic example is the piston ring in an internal combustion engine that experiences hydrodynamic fluid film breakdown at the ends of the stroke. Other interfaces may be in a constant state of change and never reach what might be termed steady-state. Perhaps the contact pressure is not constant, the contact velocity is not constant, the temperature is not constant, and the direction of relative motion is not constant. In addition, tribosystems tend to age. Lubricants change properties as their additives degrade on exposure to high temperatures, react with the surfaces and other chemical species in the environment, and become contaminated with wear particles. The degree to which these factors affect the validity of a tribosimulation’s results is not easy to determine a priori, but they can be taken into account to some degree in a well-designed tribosimulation.
14.3.1 Levels of Tribosimulation For the purposes of this chapter, we shall consider four levels of tribosimulation. Figure 14.1 shows these levels, indicating the parallels between physical and computer tribosimulations. Generally, the more realistic the simulation, the more costly and complicated it becomes. Level 1 tribosimulations use full-scale machines, such as entire automobiles, trucks, aircraft, ships, manufacturing machinery, and consumer products. These machines may be instrumented to measure loads, temperatures, strains, power demands on motors, and vibrations. In physical simulations, fullscale machines are operated under controlled conditions, such as on a test stand or inside an environmental chamber. For example, an entire communications satellite might be placed in a high-vacuum chamber and its antennas caused to rotate to determine whether the bearing lubricants will perform effectively in space. A truck might be rolled onto a chassis dynamometer and its wheels subjected to various braking loads and cycles. However, even the high-level simulations of Level 1 might omit certain factors present in the field. For example, the effects of zero-gravity on the aforementioned satellite cannot be completely simulated in a vacuum chamber on Earth. The effects of random potholes, loose gravel, and uneven road surfaces cannot easily be simulated on a test stand, but recent developments in computercontrolled test stands are making such simulations increasingly realistic.
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FIGURE 14.1
515
The levels of tribosimulation.
Level 2 tribosimulations use subassemblies which are subjected to near-operating conditions. Examples include brake pads and rotor combinations on dynamometers, fluid pumps in closed-loop pump test rigs, and jet engines in engine test cells. Nearly as expensive as Level 1 tests, Level 2 tests offer additional control of the externally applied test parameters. At the same time, fewer of the field-associated effects on performance are faithfully simulated. For example, the effects of road-induced vibrations on piston motions, the vehicle-specific flow of air past brake components, and the introduction of environmental contaminants into wheel bearing grease may be omitted in subassembly tests. In dynamometer tests of break component materials it is common to apply a series of test stages in an attempt to simulate specific types of frictional phenomena, like fade effects at elevated temperatures. Even staged Level 2 tests as complex as these cannot totally simulate the full range of habits of individual drivers and driving conditions. In some cases, however, Level 2 tribosimulations can be very effective in screening materials or lubricants because the operating conditions of the system are more clearly known. For example, loopby-loop ballpoint pen testers can show how long the products will continue to write effectively and establish failure statistics for the entire pen, whose satisfactory performance depends on the ability of the point to deliver a clear, uniform line of writing fluid to the paper. One tribosimulation area of particular medical interest is that of computerized hip and knee joint testing. Attention here is given to mimicking the forces, types of motion, and impact loads to which bioimplants are subjected. This subject area can make effective use of both physical and virtual component Level 2 simulations. The selection of the fluids to simulate synovial fluid and to correlate with clinical results is an important issue. Material swelling in situ, in the case of polymeric materials, and the role of debris particles as they interact with the soft tissues surrounding the joints, are also of interest. Level 3 tribosimulations involve test rigs designed to test specific components, like bearings and gears. For example, bearing test rigs have been successful in developing empirical design and selection guidelines for rolling element bearings of many kinds. Multiple-station rigs, automated to take data or to ascertain critical failure conditions, like excessive heat or vibration, can be run unattended, enabling the compilation of lifetime statistics and related performance data for consumer products or machine components. Level 4 tribosimulations involve test coupons of simple shapes. Examples include pin-on-disk tests, block-on-ring tests, four-ball lubricant tests, dry-sand-rubber-wheel abrasion tests, and vibratory cavitation tests. These tests are described elsewhere in this volume and in the wear testing literature [e.g., ASM (1992, 1997)]. Their usefulness is based on their ability to simulate the key contact conditions of the components of interest. For example, a cam roller follower in the engine of a certain diesel engine might be simulated by two disks turning at different speeds to impart a desired degree of slip to the
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TABLE 14.2
Modern Tribology Handbook
Common Metrics for Assessing Friction and Wear Situations
Situation Field component
Tribological Problem High friction
Surface damage Wear
Laboratory specimen
High friction Surface damage Wear
Typical Metrics Seizure; galling or scuffing marks; power draw of a motor; overheating of bearings or slideways; irregular motions; excessive wear of bearing or sealing surfaces; unusual noises or vibrations; marring of a formed product’s surface, as in metalworking; irregular speed fluctuations in a bearing Scuffing marks; galling and other visual indications Fluid leakage in a seal; loss of compression in a piston; erosive perforation of a pipe elbow; presence of wear particles in a lubricant; loss of fit between parts; excessive or unusual noise from gears or bearings; excessive or unusual vibrations; changes in the appearance of contact surfaces (abrasive grooves, scuff marks, etc.); signal drop-out in electrical contacts; loss of cutting performance of a tooling insert. Friction force or torque measurements Visual inspection or profilometric measurements Weight loss; displacement relative to another specimen or reference plane, wear scar size; wear depth; wear volume calculated by surface measurements or by weight change; visual examination; changes in friction force, surface temperature, or vibrations as detected by sensors; surface reflection characteristics measured by sensors
contact. Furthermore, the test disks could be supplied with a lubricant and heated to simulate engine conditions. The linkage between tribosimulation levels can be important to establish the validation of Level 3 and 4 tests as effective screening methods. For example, if a set of Level 4 rankings agrees with relative rankings of the same set of materials or lubricants in Level 3 tests, and the validity of Level 3 tests in a certain application has been confirmed, then the usefulness of Level 4 tests will be greatly extended.
14.4 Defining Field-Compatible Metrics A metric is a measurable quantity or unique observational feature that can be used to rank or otherwise distinguish the performance of a material or lubricant in a tribosystem. Table 14.2 lists a few metrics commonly used in the field and in tribology laboratories. Wear and friction measurement methods are described in more detail elsewhere in this volume and in ASM publications (ASM, 1992, 1997). Ideally, metrics for assessing friction or wear problems should be quantitative, accurate, straightforward to measure, and not subject to the investigator’s judgment. In practice, however, some or all of the foregoing criteria cannot be met. Furthermore, as Table 14.2 shows, there is often a significant difference between the parameters or observations that can be made in the field and those that can be made in the laboratory. Therefore, an important issue in assessing the usefulness and validity of simulations involves arriving at a set of common metrics which laboratory investigators and field engineers can agree on. There is no point in developing a laboratory test if field engineers refuse to believe that the results of the tests are relevant or cannot relate the test results to what they observe. Some key wear and surface damage metrics, in order of preference, follow: 1. Quantitative measures, like weight loss or dimensional changes, that can be measured both in the field and in the laboratory 2. A series of reference materials that rank in similar order of merit in the field and laboratory tests. 3. Visual wear features that appear similar in field-worn and laboratory-generated surfaces. 4. Wear debris that looks similar in field and laboratory-collected samples.
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14.5 Selecting or Constructing the Test Apparatus Well-equipped tribology laboratories usually contain a variety of testing machines, capable of testing for a range of tribological behavior. One or more of these machines might be suitable for conducting the given tribosimulation. Commercially manufactured wear testing machines may be a cost-effective alternatives to designing and building new, special-purpose machines for the problem at hand. But commercial machines should be used only if they serve the required purposes, including simulating specific wear of friction conditions. It may also be possible to modify an existing machine to perform the requisite simulation. It is beyond the scope of this chapter to provide guidance on the design and construction of friction and wear testing machines because there is an enormous number of alternative designs. Well-equipped tribology laboratories also contain auxiliary equipment for measuring and characterizing wear, such as precision microbalances, profiling instruments, hardness testers, and microscopes of various types. Special techniques and highly trained personnel experienced in cross-sectioning wear surfaces or performing surface chemical analysis populate a well-equipped tribology laboratory. When selecting or designing a friction or wear testing apparatus for a specific purpose, it is important that the reason for testing, and the metrics selected for validating the results, are firmly in mind. For example, if weight loss is a metric, specimen fixturing and handling procedures should be designed to avoid sources of error in mounting specimens, treating them after exposure to wear, and transferring them to the weighing system. If surface appearance is a metric, protection of wear features from demounting and handling artifacts must be a part of the procedure.
14.6 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed Baseline tests with the materials and lubricants in current use, or believed to be the leading candidates for a new application, are helpful in establishing the repeatability and characteristics of the test method itself. It is worthwhile to conduct a series of replicated tests to establish the repeatability of the baseline conditions. Knowing this, the performance of other materials or lubricants can be analyzed to determine if it is statistically different from the normal scatter in the test results. One test per materials couple or set of test conditions does not provide very strong evidence on which to make engineering decisions. If wear is measured quantitatively, then the wear factors or other metrics from baseline tests can be used in the denominator of a figure of merit. For example, the lifetime of a baseline cutting tool material, expressed as the number of workpieces produced before tool replacement is required, is divided into the lifetime of another candidate tool material to give the relative lifetime of the candidate. The higher the number is above 1.0, the greater the wear benefits of substitution, other factors being equal. An alternative engineering metric might be the tooling cost per unit part machined. Sometimes suitable quantitative metrics cannot be found. It may then be possible to compare the appearance of the test specimen to a worn part to establish the success of the simulation. An example is given in 14.7.1. It is likely that laboratory simulations will not be able to reproduce every aspect of the part operating conditions. Therefore, it is, in general, unreasonable to expect that precisely the same wear rates or metrics will be obtained in the laboratory and in the field. From the standpoint of screening, however, it is very important that candidate materials rank in very much the same order in the field and in the laboratory. Since there are many ways to measure wear in the laboratory (weight loss, wear profile, wear scar dimensions, etc.), there may be one metric that correlates better with the field wear results than another. Therefore if one method of laboratory wear measurement does not correlate well with field results, another may work better. The following section describes several laboratory simulations that used different kinds of metrics and testing procedures depending on the nature of the parts being simulated.
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14.7 Case Studies Six case studies on the selection and use of simulative friction and wear tests are provided below. The first case, which is described by Blau (1998), involves an automotive application in which new simulative test fixtures and procedures were developed. In the latter five case studies, summarized from an article by Blau and Budinski (1999), existing or slightly modified ASTM test methods were used to solve industrial plant wear issues and product-related wear problems.
14.7.1 An Oil Pump Gear Set with Several Wear Modes An initiative was undertaken to replace certain steel fluid pump gears with a lighter-weight, aluminumbased alloy. One criterion for the acceptability of the new gear material was that it possess acceptable wear characteristics when substituted for the current steel. The gears were of a gerotor type in which a wedge of fluid is trapped between the teeth of eccentrically mounted inner and outer gears. As the gears turn, the fluid is forced between them, pressurized, and then out of a pocket in the pump housing. This type of pump is typical of automotive oil pumps and automatic transmission fluid pumps. Based on the results of a TSA, described in Section 14.2, and with input from both pump part makers and pump users, the two wear-critical areas were determined to be the teeth contact points and the flat gerotor gear faces which can rub intermittently against the inside faces of the housing. In the latter case, little or nothing was known about the surface contact pressures or loads. In addition, specimens of gears run in actual service and in full-sized gear pump test rigs were carefully examined by optical microscopy and cross-sectioned for subsurface study. Based on the relatively small quantities of candidate materials available for use in the material selection process, it was necessary to devise a simulative test method which used small, round disks, about 20 mm in diameter and 10 mm thick. These were about 1/4 the diameter of the actual gear disks. To simplify the testing process and make the best use of limited materials, it was decided to use the same specimen dimensions for tests of both tooth wear and the flat face-on-casing wear. It was desired to use quantitative metrics to screen the various candidate materials, but as described later, some of the wear metrics turned out to be only semiquantitative. Several testing configurations were developed. Eventually, the wear simulation evolved into a configuration that emphasized tooth-to-tooth slip which resulted in combined adhesive and three-body abrasive wear and subsequent loss of the gear tooth profile. One disk was rigidly held vertically with its curved outer diameter, simulating the curvature of the tooth face. It was oscillated against the flat face of a second disk of the same material (Figure 14.2). Hot, lubricated tests were performed at temperatures similar to that of the application. The length of the test was determined by the time needed to produce wear features similar to those seen in actual gears. The width of the wear scar on the curved disk’s outer diameter was measured and converted to a wear volume. This wear volume was normalized by dividing by the product of the applied load and the number of cycles to obtain a wear rate (mm3/N-cycle). The gear face-on-casing sliding wear mode was simulated by placing the flat faces of two disk specimens together in a thrust-washer-type geometry (Figure 14.3). Circular insets were machined into one or both disk specimens to produce an annular contact. The upper specimen was held fixed in a spring-loaded arrangement to assure good flat-on-flat seating with the lower rotating disk. The rotating disk was made of the candidate lightweight gear material and the upper was made of typical casting alloy. Tests were run with oil-coated surfaces. Each test consisted of four segments in which the test was stopped and oil was replenished on the contact surfaces. Weight losses and dimensional changes were unsatisfactory quantities for measuring the small amount of wear produced in this type of flat-on-flat test. Therefore, a semiquantitative method for determining the wear severity was used. This involved cataloging the types of wear damage, such as scuffing, abrasion, gouging, etc., and assigning several severity levels to each. Table 14.3 shows the wear damage rating scale. Each level was defined sufficiently well so that two people independently obtained the same numerical rankings on the same test specimens. The wear damage ratings for each disk specimen were determined,
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FIGURE 14.2
Curve-on-flat geometry used to simulate tooth-on-tooth rubbing contact.
FIGURE 14.3
Flat-on-flat geometry used to simulate gear-on-casing sliding.
519
and then a composite rating for each couple was determined (the sum of the two specimen ratings). Each test was duplicated to establish the repeatability of the results, and to enhance the investigators’ confidence in the differences between the wear ratings of different material couples. Figure 14.4 compares the wear seen on an actual part with that produced in laboratory experiments of several candidate alloys. Results from these two kinds of simulative tests, coupled with full-scale pump rig tests at a manufacturer’s facility, cost modeling, and alloy processing trials, were used to select the leading alloy and surface treatment for this application.
14.7.2 Wear of Gravure Rollers on Doctor Blades In a certain industrial coating process, dimpled cylinders (gravure rollers) are used to pick up and deliver a solution to another surface. These cylinders are cyclically wiped by steel doctor blades to remove the
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TABLE 14.3
Modern Tribology Handbook
Wear Damage Rating (WDR) Scale Used to Assess Flat-on-Flat Wear
Factor
Severity
Description
Light abrasion
1.0
Moderate abrasion Severe abrasion
4.0 6.0
Light scuffing
1.5
Moderate scuffing Scoring
3.0 5.0
Pull-out
5.0
Delamination
5.0
Burning Severe metallic wear Microwelding Major transfer
5.0 6.0
Faint, widely spaced grooves aligned parallel to the sliding direction. Grooves may not be continuous around the track and are similar in depth to the original grinding marks. Multiple, parallel wear grooves extending across a substantial portion of the contact area. Some of the original surface finish visible between the abrasion grooves. Deep abrasive wear grooves across the entire contact face. Little or no trace of the original surface finish. Polished-looking areas with little or no original surface finish within their boundaries. Scuffed area < 25% of the nominal contact area. Scuffed area 25 to 75% of the nominal contact area. Localized, relatively deep grooves ( depth of original machining marks), suggesting plowing by large hard particles. Removal of particles or entire grains from the surface. Regions of pull-out may be associated with scoring by the removal material. Detachment of thin, flat platelets; typically associated with fatigue crack growth parallel to the free surface. Production of dark oxides or tarnishes suggestive of exposure to excessive frictional heating. Significant plastic deformation accompanied by deep grooving. No traces of the original surface finish. Often accompanied by shiny flake-like wear particles. Presence of tiny flecks of highly adherent, transferred material from the opposing surface. Presence of relatively large particles or patches of highly adherent material from the opposing surface.
1.0 2.0
excess coating material, and were experiencing unacceptable wear as a result. It was decided to try ionimplanting the surfaces of the rollers to improve their wear. ASTM standards G-99 (pin-on-disk test) was used to compare the implanted and unimplanted (current) materials. While the wear of the roller material was markedly improved, the wear of the doctor blade material increased to an unacceptable level. Therefore, it was decided that ion implantation would not be an acceptable solution in this case. While the pin-on-disk method was not an exact simulation of the doctor blade operating conditions, it was felt to be adequate to evaluate one potential solution for this wear problem, and to determine that alternative methods of surface engineering or materials substitution would be required.
14.7.3 Scoring of Spur Gears An expensive steel gear set in production equipment began to exhibit signs of significant scoring. It was learned that the supplier had modified his processing and that the hardness of the new gears varied from that of the previous sets. ASTM standard G-98 (the button-on-block galling test) was used to determine the critical level of Rockwell hardness to avoid the onset of galling. This ASTM test method is based on using visual observations to obtain a numerical metric; namely, the threshold stress for galling. Using observations of test coupon surfaces subjected to increasing levels of normal force, one assesses the normal pressure at which galling begins. It turned out that a difference of only 1 or 2 units on the Rockwell C hardness scale made the difference between steel gears that ran acceptably and those that did not. Costly future failures were therefore avoided by tightening the hardness specifications on the gear steels. Increasing the hardness of a material to improve its surface durability and wear resistance is a longstanding, intuitive notion that is not always substantiated by testing. That is because other factors, such as the type of wear being experienced, the material’s fracture toughness, fatigue resistance, and chemical reactivity with the environment can also affect the surface response to contact conditions. In the present fortuitous example, the suitability of the steels for use as gear teeth could be directly correlated to their Rockwell hardness numbers with the help of a standardized test method that captured the essential elements of surface contact in the application.
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FIGURE 14.4 (a) Wear features on a gear side face tested in a commercial producers’ testing facility under severe operating conditions. (b–d) Different levels of wear damage observed on laboratory test specimens in the flat-onflat simulator test shown in Figure 14.3.
14.7.4 Wear of Plastic Parts in an Optical Disk Drive Not only wear, but the presence of wear products (debris particles) can seriously affect the performance of imaging and computer equipment. This was the case for contacting plastic parts in an optical disk drive. The ASTM G-133 reciprocating pin-on-flat test was used to screen plastic pairs for those which not only had the best material-to-material compatibility, but also produced the least harmful debris insofar as the surrounding machinery was concerned. Therefore, an additional metric was an observationally bases scale of the distribution of wear debris in the vicinity of the contact area on the pin and flat specimens.
14.7.5 Wear of Rotary Slitter Knife Blades Rotary slitter knives were used to cut plastic sheeting to size. The edges of the knives slid against one another repeatedly as they worked. Excessive wear led to unsatisfactory performance, costly equipment shutdowns, and product damage. In this case, the development of acceptable metrics for laboratory screening was complicated by the lack of a clear definition for the blade “sharpness.” A decrease in product cut-edge quality is the result of worn blades, but edge quality is difficult to quantify in a way that can be used in cost-effective laboratory tests. The ASTM G-83 crossed cylinders wear test was eventually selected to screen materials for knife blade applications. This test produces a concentrated contact at the intersection of two orthogonal cylindrical
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specimens. While not exhibiting the exact geometry of the application, the small, highly-loaded contact between test specimens contained enough of the essential elements of rotary slitter knife interactions to produce a useful screening test. Wear volume is used as the metric and is computed from the test materials’ densities and their weight losses. By examining a great deal of crossed-cylinders laboratory wear test data that would have been impractical to obtain on the production floor, it was discovered that at least one of the blades had to be composed of carbide material in order for the slitter knives to perform satisfactorily. Since more than one material combination with satisfactory wear rates was identified in the course of the testing campaign, it was possible to select the most affordable solution to the problem from among several alternatives.
14.7.6 Erosive Wear of Piping During the process of designing a new plant involving the piping of dicalcium phosphate, it was necessary to know what material would be the best choice for the piping. Issues were not only erosion resistance, but corrosion resistance as well. The G-32 solid particle impingement erosion test was selected. Several candidate materials were exposed to dicalcium phosphate and other erodants using a pressurized air jet apparatus, such as that prescribed in the standard. It was determined that a soft stainless steel would work adequately in this application, and the decision was made to use that material for construction. Significantly, higher hardness did not ensure wear resistance, as it did in the case described in Section 14.7.3. Therefore, the selection of materials for wear applications based on properties like hardness depends on the type of wear involved and on other performance requirements.
14.8 Conclusions The development of simulative friction and wear tests requires an interdisciplinary approach, beginning with a tribosystem analysis to define the problem and to establish key metrics that can be used to test the validity of simulations. Laboratory simulations using either custom-designed apparatus or standard test methods can be successfully applied to save time and money in solving friction and wear problems. No single test method will solve all problems, and proper test selection is critical for success. Sometimes, more than one test method will be needed to establish an engineering solution; especially, if more than one form of wear or surface damage is present in the application of interest.
References ASM Handbook (1992), Friction Lubrication and Wear Technology, 18, ASM International Materials Park, OH. ASM (1997), Source Book on Friction and Wear Testing, ASM International, Materials Park, OH. Blau, P.J. (1998), Development of bench-scale test methods for screening P/M aluminum alloys for wear resistance, in Powder Metallurgy Aluminum and Light Alloys for Automotive Applications, Jandeska, Jr., W.F. and Chernenkoff, R.A. (Eds.), Metal Powder Industries Federation, Princeton, NJ, 97. Blau, P.J. and Budinski, K.G. (1999), Use of ASTM standard wear tests for solving practical industrial wear problems, Wear, 225-229, 1159.
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15 Friction and Wear Data Bank 15.1 15.2 15.3
Introduction ..................................................................... 523 Sources of Data ................................................................ 523 Materials Found in Data Bank........................................ 527 Metals for Fluid (Oil) Film Bearings • Porous Metals • Plastics • Carbon–Graphites • Miscellaneous Nonmetallic Materials • Materials under Abrasive Wear
A. William Ruff Consultant
15.1
15.4
Data Bank Format............................................................ 529 Material Data • Tribological Data • Data Field Definitions
Introduction
Tribology is a critical science that has a key role in U.S. technology and competitiveness. Increased knowledge in tribology attained through research, both fundamental and applied, can lead to improved system reliability and durability, as well as decreased energy and material losses, throughout industrial technology. Transfer of tribology research results into general engineering practice is essential and can be assisted through the dissemination and use of critical tribological data. Tribology encompasses crossdisciplinary research and practice in materials, lubricants, and design (Zum Gahr, 1987). As a result, tribology research results are published in a number of specialized journals. This fact coupled with the diversity of tribology conditions of interest makes it difficult for researchers and engineers who work in different fields to locate pertinent information. As a result, advances in tribology have sometimes only slowly been incorporated into engineering practice. One approach to reduce this problem is the creation of tribological data and information banks. Many equipment manufacturing companies have taken steps to create proprietary data banks for their own use in design and material selection. In the public sector, the National Institute of Standards and Technology began in 1985 to develop a computerized tribology information system that would be widely available (Jahanmir et al., 1988). That system, termed ACTIS, was planned in accordance with recommendations from the international tribology community. The system was constructed to be computer-based and suitable for PCs generally available at that time. Within the limits of available funding, a total of 11 individual modules of code and data were developed and marketed. Recently, seven modules of the system, including databases and design codes, have been made available to the public without charge (see Further Information). The data included in this publication are drawn from those databases.
15.2
Sources of Data
Data generation in tribology involves a wide variety of experimental systems. In a compilation of 157 different wear test systems used to report data at the ASME Wear of Materials Conferences over the
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SLIDING VELOCITY v (m/s) 10-4 2.0
10-2
1
102
STEEL
COEFFICIENT OF FRICTION µ
COEFFICIENT OF FRICTION µ
The range of possible values for roughened disks
1.0
roughened disks
Mirror-smooth disks
0 FIGURE 15.1 Variation in coefficient of friction with sliding velocity for unlubricated steel–steel combinations.
period 1977 to 1985 (Glaeser et al., 1986) found that predominant systems were pin/disk (32%), pin/flat (29%), and block/ring (17%). Since each of these test geometries has different mechanical and thermal contact characteristics, it should be expected that measured tribological data will reflect those differences. Interlaboratory comparisons in fact show significant differences in wear results using basically similar pin/disk systems (Czichos et al., 1987) and even larger differences using dissimilar pin/disk systems (Almond et al., 1987). There is not yet any known way to adjust data from any test geometry to some reference measurement condition. Since results from laboratory tribology measurements are determined by the properties and conditions of the specific test system (Czichos, 1978), it is essential that the conditions used are appropriate to the final application intended. This requirement has been well stated (Barwell et al., 1983): “For … experiment to have meaning, it must reproduce the circumstances surrounding the occurrence of the phenomena under study. Otherwise the results … will be irrelevant to the purpose of the investigation.” Ashby and co-workers (Lim et al., 1987) have gathered friction data and wear rate data from the literature pertaining to pin/disk test systems involving steel/steel contacts. The results for system friction are shown in Figure 15.1, plotted vs. sliding velocity. Clearly there is a significant spread of friction values at any velocity. A simple functional relationship is difficult to justify using these data, and it is impossible to determine a single representative friction value. The authors discuss possible reasons for the wide variation. Similar difficulties were found in handling wear data collected from the literature. The scatter inherent in tribology data has been noted by many authors (Rabinowicz, 1981; Ruff, 1989). Figure 15.2 summarizes findings reported from a laboratory study of sliding UHMW polyethylene against stainless steel (Walbridge et al., 1987). By repeatedly interrupting a long-term test, the investigators were able to follow the progression of the wear coefficient as a function of time. The statistical distribution of those wear
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FIGURE 15.2 The distribution of calculated wear coefficient values of measured wear loss for UHMW polyethylene sliding against type 316L stainless steel.
coefficients was found to be a lognormal distribution. In most of the cases, there was significant difference between the most frequent value and the mean value. That suggests that descriptions of wear data by mean value and standard deviation analysis, while customary, may not always be suitable. This particular point needs to be more widely examined as tribological data are evaluated and added to data banks. Two specific examples of data gathering and evaluation for quite different tribological situations will be discussed. Two different modes of wear, mild and severe, are involved. Example 1. Mild Sliding Wear Mild wear situations are commonly experienced in service. This mode of damage might be considered as an extreme upper limit to tolerable behavior in many tribological systems. Ashby and co-workers have published wear rate results gathered from the literature on selected material combinations. Figure 15.3 shows their findings for pin/disk unlubricated sliding wear of low carbon steel against itself (Lim et al., 1987). In order to simplify the figure, contour lines have been drawn here guided by the actual data values that were in the original plot. In this graph the variables, normalized pressure and normalized velocity, cover a wide range of 4 decades and 6 decades, respectively, while the wear rates cover 6 decades. This clearly represents a physical situation of extremely large range in design and use conditions. For example, in certain regions of the plot, a change by a factor of 2 in pressure or velocity can produce a change by a factor of 10 in wear rate. This may be due to changes in the controlling wear mechanisms, or due to inherent sensitivity of wear to conditions in that region. In order to examine data from a more systematic, controlled perspective, consider two carefully controlled interlaboratory studies that have been reported. The VAMAS studies (Czichos et al., 1987) reported the wear constant for steel sliding against steel, as summarized in Figure 15.4. Results for six U.S. laboratories are individually indicated along with, separately, the average for the U.S. and for the world laboratories. The individual number of measurements is indicated in each case. It is seen that while the average values for the U.S. and world groups agree very well, there is considerable variation among the individual U.S. labs, up to a factor of 6 times in the average values reported. A similar situation is seen in a second set of interlaboratory data developed by a U.K. effort (Almond et al., 1987) and summarized in Figure 15.5. Both single-pin/disk tests, carried out with conditions similar to the VAMAS tests, and tri-pin/disk tests were done. Looking at the single- pin test results, one sees a large difference in average wear constant value among the individual labs, up to a factor of 4 times. The comparison between the single-pin test average and the tri-pin test average disagrees by a factor of about 2 times. The large individual differences in average wear constant shown, in spite of the care taken to control test specimen and test condition uniformity, suggest that both bias and precision of the data must be substantial concerns in any effort to construct data banks.
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Modern Tribology Handbook
SLIDING VELOCITY v (m/s) 10
10
-4
10
-2
1
10
2
LOW CARBON STEEL
~ NORMALIZED PRESSURE F
WEAR-RATE DATA-MAP
-4 10
-1
-5 -6
-4
-7
-5 10
-3
-6
-8
-7 -9 -6
-6 -7 -8 10
-9
-10
-5
FIGURE 15.3 Contours of constant wear rate order-of-magnitude values (mm3/m) for steel–steel unlubricated sliding conditions vs. normalized pressure and velocity. (Adapted from Lim, S.C. and Ashby, M.F. (1987), Wearmechanism maps, Acta Metallurgica, 35, 1-24.)
FIGURE 15.4 Wear constant results from VAMAS interlaboratory measurements of steel–steel combinations in unlubricated sliding. Each bar is a mean value topped by one standard deviation. The number of individual measurements is shown above each bar.
Example 2. Severe Abrasive Wear The second example involves a comparison of laboratory abrasive wear data obtained using two different test methods. Figure 15.6 shows a comparison (Moore et al., 1983) between two laboratory methods, pin/abrasive disk sliding, and dry sand abrasion, for a high hardness steel. The data for the rounded Ottawa sand follow a 1:1 relation comparing measurements from the two tests. However, the results using crushed quartz abrasive deviate significantly from that relationship, up to about 50%. The authors interpreted this spread to show the significance of different abrasive shape and composition characteristics on wear.
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FIGURE 15.5 Wear constant results from U.K. interlaboratory measurements of steel–steel combinations in unlubricated sliding. Each bar is a mean value topped by one standard deviation. The number of individual measurements is shown above each bar.
FIGURE 15.6 Comparison of relative wear resistances between two abrasion test methods using two types of abrasive.
One can conclude from these and other examples that extreme care must be used in selecting test results for data bank construction, so that substantial bias and variability are not introduced into the data collection.
15.3
Materials Found in Data Bank
A brief discussion of the material types found in the database, Table 15.1, is in order.
15.3.1 Metals for Fluid (Oil) Film Bearings This group of metals is primarily composed of alloys with a high content of lead, tin, copper, silver, cadmium, indium, aluminum, or zinc. They are compatible against steel journals and thrust surfaces. Friction and wear data are for dry operation with carbon steel. For dynamic lubricated operation with
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the load supported on a full oil film, the coefficient of friction commonly lies in the 0.001 range and is determined by characteristics of the oil film rather than by the bearing material. With a boundary film, both dynamic friction and wear rates will attain intermediate levels between dry and full oil film values. The softest material capable of meeting the load and temperature requirements is the common choice for optimum embedding of foreign particles and tolerating misalignment. Even where fatigue load capacity is inadequate with a soft material such as babbitt, the material can be used when it is applied as a thin layer on a backing of either steel or a stronger bearing material. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions.
15.3.2 Porous Metals These materials are employed extensively in boundary lubricated service for operation within the tabulated load, speed, and temperature limits while using the oil supply self-contained within the pores. While a PV limit of 1.75 MPa m/s (50,000 psi ft/min) is commonly quoted for use of porous metals, conservative values should again be held to 10 to 20% of that limit for long-time service. A PV limit of 0.35 MPa m/s (10,000 psi ft/min) is usually suggested for application of porous metals in thrust bearing applications. Operating life at the 135°C (275°F) temperature limit given for porous bearing materials will reflect primarily the oxidation life of the oil impregnating the pores. Much longer life is possible in the 82°C (180°F) range and at even lower temperatures. With continuous feed of oil, porous metals can be used as fluid (oil) film bearing materials in a wide variety of higher speed and higher load applications. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions.
15.3.3 Plastics Plastic materials are used for dry (unlubricated) or boundary lubricated, slow speed sliding and intermittent operation within the tabulated limits of temperature, P, V, and PV values, where P is unit loading on the projected bearing area in N/m2, V is surface velocity in m/s, and their product PV gives some measure of the temperature rise and wear severity for the contact. For acceptable wear performance in long-term operation, PV values should be held to about 10 to 20% of the maximum PV value listed, which is for short-time running under a most severe condition. The limiting PV given here was usually determined at approximately V = 0.5 m/s (100 ft./min.) in a short-time laboratory bench test. Tabulated P, V, and PV limits are either for dry operation on steel or for operation with the lubricants originally incorporated (where possible) in the plastic. With a supplementary supply of lubrication, much more demanding requirements may be accommodated. Friction and wear data for the plastics are for sliding against carbon steel surfaces. Manufacturers can often supply further guidelines for running against aluminum or various plastics. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
15.3.4 Carbon–Graphites These materials are widely used for dry operation at high temperature, and also for bearings and seals running with low-viscosity fluids such as water, solvents, and fuels; such fluids are inadequate for lubrication of fluid (oil) film bearing metals. These hard and brittle carbon–graphites require hardened mating surfaces and tolerate dirt contamination poorly. P, V, and PV data are given for application of carbon–graphites in dry operation. When used with water, fuels, solvents, and many process fluids, the carbon–graphites are excellent fluid-film bearing materials. In such cases, operating limits are commonly much higher than those given here, and performance characteristics depend largely on the nature of the fluid film involved in the bearing. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
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15.3.5 Miscellaneous Nonmetallic Materials Almost all materials used in the construction of mechanical systems have been employed at some time as bearing surfaces. Included are examples of the growing group of ceramics and composites which find use in special applications and as high temperature sliding surfaces. Also included in this group are rubber and wood, which find use with water, slurries, and a variety of low-viscosity liquids. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions, particularly test pressure and load values for ceramics.
15.3.6 Materials under Abrasive Wear Abrasive wear data were obtained from laboratory tests using the dry sand/rubber wheel abrasion test as described in ASTM standard G-65. The tests involved abrading a specimen with rounded silica sand of controlled size. The abrasive was introduced between the specimen and a rotating wheel with a rubber rim of specified material. The specimen was pressed against the rotating wheel by a specified normal force. A controlled stream of abrasive was fed by gravity into the contact region. The wear mode is usually referred to in the literature as low stress, scratching, three-body abrasion. The data were obtained in a series of interlaboratory tests using the particular conditions given. The test conditions used were carefully chosen to provide uniform and reproducible wear. The test method has been used to provide relative rankings of materials to wear. In some reported cases a good correlation has been found between actual abrasive wear performance in service and that measured using this test. However, the severity of abrasive wear will depend on the particulars of abrasive size and shape, and on the system parameters of load and environment. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
15.4
Data Bank Format
The database, Table 15.1, contains data records of two types: materials data and tribological data.
15.4.1 Material Data These records contain properties data (composition, processing, physical, mechanical) on a group of materials frequently used in tribological applications. Since the materials are used in a variety of different tribological applications, specific tribological performance data are not given for records of this type.
15.4.2 Tribological Data These records contain critically evaluated tribological data for a group of materials measured under specific tribological use or test conditions. The counterface material, the contact environment, and other parameters associated with the data are specified to the extent that such information was available in the original report. Blank spaces in the data records indicate data not available. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions. Note that the materials data in records of this type may not be complete in all cases because they depend on the original source.
15.4.3 Data Field Definitions The definitions, given here in alphabetical order, in most cases follow ASTM definitions. Class: Common name: Component name: Component weight percent:
A major material class, e.g., metal, ceramic, polymer, etc. A name frequently given to a particular material, e.g., nylon. The set of components (elements) present, in order present. The weight percent of each component (element) in order.
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Contact environment: Contact geometry: Counterface description: Counterface material: Data source: Density: Distance: Expansion coefficient: Form: Fracture toughness (Mode I, plane strain): Friction coefficient: Grade: Hardness: Heat capacity: Load: Maximum operating temperature: Maximum pressure: Maximum velocity: Melting point: P(ressure) V(elocity) limit: Principal component: Processing conditions: Processing and treatment: Resistivity: Second component: Specification: Specimen shape: Standard test: Sub-class: Temperature: Tensile strength: Thermal conductivity: Velocity: Wear coefficient: Wear constant: Wear rate:
Modern Tribology Handbook
Terms describing the local environment at the contact, e.g., atmosphere, lubricant, abrasive, etc. Terms describing the geometry such as pin/disk, etc. Further identification of the counterface. Identification of the opposing surface material, e.g., rubber, steel. Source of data for this record (consult data sources at end of table). Mass per unit volume, in kilograms per cubic meter. Sliding distance used in the test, in meters. Increase in dimensions of a body due to change in temperature, in micrometers per meter per degree C. The material form, e.g., rod, sheet, cast, etc. Resistance to extension of a crack, given here by KIC, the critical stress intensity factor for plane strain, linear–elastic conditions, in MPa m1/2. Dimensionless ratio of the force resisting motion to the normal force pressing two moving bodies together. Designation given a material by a manufacturer. Resistance of a material to indentation. The usual methods for hardness determinations include Rockwell C, Vickers, etc. Amount of heat necessary to change the temperature of unit mass by one degree, in kilojoules per kilogram per degree C. Normal contact load used in the test, in Newtons. Maximum permitted contact temperature, in degrees C. Maximum permitted contact pressure, in MPa. The maximum permitted sliding velocity, in m/s. Temperature at which a solid changes to liquid state at one standard atmosphere, in degrees C. Maximum permitted value of the product contact pressure times sliding velocity, in MPa m/s. The principal component (element) designation. Specific process conditions used, e.g., 200°C temperature. A descriptive phrase on the process method, e.g., cast. Electrical resistance measured between opposite faces of a centimeter cube of material, in units of micro-ohm cm. The second component (element) present. A precise statement of a set of requirements to be satisfied by a material, promulgated by an organization, e.g., ASTM-###, SAE-###, etc. The shape of the test specimen, e.g., block, pin. Test designation, i.e., ASTM, SAE, etc. Subdivisions of a class, e.g., ferrous, boride, etc. Test temperature, in degrees C. Maximum amount of tensile load per unit original cross-section area that a material attains when tested to rupture, in MPa. Time rate of steady heat flow through unit area per unit temperature gradient, in watts per meter per degree C. Relative speed of motion between the two contacting surfaces, in m/s. Dimensionless coefficient calculated by the relationship: (wear volume)∗(hardness)/(load)/(sliding distance). Volume rate of material removal per unit sliding distance per unit load, in cubic millimeters per Newton-millimeter. Volume rate of material removal per unit sliding distance, in cubic millimeters per meter.
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Wear type:
Young’s modulus:
531
Five possible types are considered: abrasive, adhesive, fatigue, fretting, or lubricated, defined as: (1) abrasive — wear being caused by the action of hard particles or protuberances between the contacting surfaces; (2) adhesive — wear caused by surface interactions usually involving deformation; (3) fatigue — wear due to time-dependent, accumulative fatigue processes at or beneath the contacting surfaces; (4) fretting — wear under oscillating conditions at small sliding amplitudes; (5) lubricated — wear under conditions in which a lubricant is present. Ratio of tensile or compressive stress to corresponding strain below the proportional limit of the material, in MPa.
References Almond, E.A. and Gee, M.G. (1987), Results from a U.K. interlaboratory project on dry sliding wear, Wear, 120, 101-116. Barwell, F.T. and Jones, M.H. (1983), Role of laboratory test machines, in Industrial Tribology, Jones, M.H. and Scott, D. (Eds.), Elsevier, NY. Czichos, H. (1978), Tribology: A Systems Approach to the Science and Technology of Friction, Lubrication, and Wear, Elsevier, NY. Czichos, H., Becker, S., and Lexow, J. (1987), Multilaboratory tribotesting: results from the VAMAS program on wear test methods, Wear, 114, 109-130. Glaeser, W. and Ruff, A.W. (1986), private communication. Jahanmir, S., Ruff, A.W., and Hsu, S.M. (1988), A computerized tribology information system, in Proceedings ASM Conference on Engineered Materials for Advanced Friction and Wear Applications, ASM International, OH, 243-247. Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metallurgica, 35, 1-24. Moore, M.A. and Swanson, P.A. (1983), The effect of particle shape on abrasive wear: a comparison of theory and experiment, in Proceedings of Wear of Materials Conference — 1983, American Society of Mechanical Engineers, NY, 1-11. Peterson, M.B. and Winer, W.O. (1980) (Eds.), Wear Control Handbook, American Society of Mechanical Engineers, NY. Rabinowicz, E. (1981), The wear coefficient — magnitude, scatter, uses, Transactions of the American Society of Mechanical Engineers, 103, 188-194. Ruff, A.W. (1989), Comparison of standard test methods for non-lubricated sliding wear, in Proceedings of Wear of Materials Conference — 1989, American Society of Mechanical Engineers, NY, 717-721. Walbridge, N.C. and Dowson, D. (1987), Distribution of wear rate data and a statistical approach to sliding wear theory, in Proceedings of Wear of Materials Conference — 1987, American Society of Mechanical Engineers, NY, 101-110. Zum Gahr, K.-H. (1987), Microstructure and Wear of Materials, Elsevier, NY.
For Further Information Free copies of the PC-based code and database modules developed for the ACTIS system are available by contacting: NIST Office of Standard Reference Data, North Building, Gaithersburg, MD 20899. A thorough description of the development process that led to the ACTIS system is found in the reference of Jahanmir et al., 1988. Good, accessible sources of tribological data include Wear Control Handbook (Peterson, M. B. and Winer, W. O. (1980), Eds., American Society of Mechanical Engineers, NY); ASM Handbook — Friction, Lubrication, and Wear Technology, Vol. 18, (Blau, P. J. (1998), Ed., ASM International), and Wear of Materials Conference Proceedings, 1977–1999 (published biannually by ASME, NY, and Elsevier, NY).
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TABLE 15.1 NUMBER
Modern Tribology Handbook
Tribo-Materials Database (Part A) COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
1 2 3 4 5 6 7 8 9 10
TITANIUM DIBORIDE BORON CARBIDE CHROMIUM CARBIDE SILICON CARBIDE TITANIUM CARBIDE TITANUM CARBIDE TUNGSTEN CARBIDE TUNGSTEN CARBIDE CARBON CARBON
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
BORIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBON CARBON
TIB2 B4C CR3C2 SIC TIC TIC WC WC C C
11 12 13 14 15 16 17 18 19 20
CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON GRAPHITE CARBON GRAPHITE-BABBITT CARBON GRAPHITE-COPPER
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON
C C C C C C C C C C
21 22 23 24 25 26 27 28 29 30
CARBON GRAPHITE-GLASS CARBON GRAPHITE-LITHIUM FLUORIDE CARBON GRAPHITE-RESIN CARBON GRAPHITE-SILVER GRAPHITE QUARTZ GLASS SODA GLASS SILICON NITRIDE TITANIUM NITRIDE ALUMINUM OXIDE
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
CARBON CARBON CARBON CARBON CARBON GLASS GLASS NITRIDE NITRIDE OXIDE
C C C C C SIO2 SIO2 SI3N4 TIN AL2O3
SIO2 LIF
31 32 33 34 35 36 37 38 39 40
ALUMINUM OXIDE – TITANIUM OXIDE BERYLLIUM OXIDE PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA SILICON DIOXIDE TITANIUM DIOXIDE WOOD/OIL IMPREGNATED
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC COMPOSITE
OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE CELLULOSE
AL2O3 BEO ZRO2 ZRO2 ZRO2 ZRO2 ZRO2 SIO2 TIO2 WOOD
TIO2
SPK SN80
Y2O3
TZ3Y 1027 MS 2016 Z191
41 42 43 44 45 46 47 48 49 50
MOLYBDENUM DISULFIDE COMPOSITE DU (BRONZE/PTFE) STEEL/TiC TUNGSTEN CARBIDE – COBALT TUNGSTEN CARBIDE – COBALT CAST IRON CAST IRON CAST IRON CAST IRON CAST IRON
COMPOSITE COMPOSITE COMPOSITE COMPOSITE COMPOSITE METAL METAL METAL METAL METAL
COMPOSITE METAL MATRIX METAL MATRIX METAL MATRIX METAL MATRIX FERROUS FERROUS FERROUS FERROUS FERROUS
MOS2 CU FE WC WC FE FE FE FE FE
TA PTFE TiC CO CO NI CR SI NI CR
51 52 53 54 55 56 57 58 59 60
CAST IRON CAST IRON, OIL-FILLED IRON IRON-COPPER, OIL-FILLED IRON-COPPER, OIL-FILLED IRON, OIL-FILLED MILD STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C
C CR CR CR
440CM 304HN 316
61 62 63 64 65 66 67 68 69 70
STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
440C 440C 17-4PH 304 316 347 17-4 PH 316 316 17-4 PH
71 72 73 74 75 76 77 78
STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR
410 15-5PH 410 21-55N 310 52100 52100 52100
HOT PRESSED K 162B
AG
2690 P-5AG S-95 T-0054 P-9 G-1 P-03 P-2W P-5 P-15
CU
AG
MGO Y2O3
OIL PM-103 H-46 K-714 NI-RESIST 1 NI-HARD 4 DURIRON NI-HARD HC250 MEEHANITE
CU CU
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TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING CONDITIONS
PROCESSING AND TREATMENT
SELF BOND
MOULDED
CO BONDED CARBPM GRAPHITE, HIGH TEMP. TREATED SILVER IMPREGNATED
MOULDED BAKED MOULDED BAKED BAKED BAKED, IMPREGNATED BABBITT IMPREGNATED
SILVER IMPREGNATED EXTRUDED CAST CAST SELF BOND HOT PRESS
SAE 863; ASTM B-439-70, GR4; MIL-B-5687C, 2B SAE 862; ASTM B-439-70, GR3; MIL-B-5687C, 2B SAE 850; ASTM B-439-70, GR1; MIL-B-5687C, 2A1
MOULDED COATING ON STEEL
MOLYBDENUM DISULFIDE, BONDED SINTERED
PLATE
SINTERED
CAST CAST CAST CAST CAST
ANNEALED
CAST POROUS, 8% ELECTROLYTIC POROUS, 20% POROUS, 20% POROUS, 20%
ANNEALED
COLD ROLLED
BAR BAR BAR BAR
ANNEALED HT WROUGHT, H900 ANNEALED ANNEALED HOT WORKED, ANNEALED HT ANNEALED ANNEALED HT
BAR BAR BAR
ANNEALED WROUGHT, H900 HT ANNEALED ANNEALED HT HT HT
600F TEMPER
925F:4h H-900 H-900 H-1100
1000 TEMPER
350F TEMPER 350F TEMPER 350F TEMPER
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TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
79 80
STEEL STEEL
METAL METAL
FERROUS FERROUS
FE FE
CR CR
52100 52100
81 82 83 84 85 86 87 88 89 90
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR C MN CR CR CR CR
52100 52100 52100 52100 1090 1020 52100 52100 52100 52100
91 92 93 94 95 96 97 98 99 100
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
101 102 103 104 105 106 107 108 109 110
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR C CR CR CR
52100 52100 52100 52100 52100 52100 1090 52100 52100 52100
111 112 113 114 115 116 117 118 119 120
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
121 122 123 124 125 126 127 128 129 130
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR C CR
52100 52100 52100 52100 52100 52100 52100 52100 1090 52100
131 132 133 134 135 136 137 138 139 140
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
141 142 143 144 145 146 147 148 149 150
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
151 152 153 154 155
STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE
CR CR CR CR CR
52100 52100 52100 52100 52100
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
BAR BAR
HT HT
350F TEMPER 350F TEMPER
BAR BAR BAR BAR SHEET SHEET BAR BAR BAR BAR
HT HT HT HT NORMALIZED ANNEALED HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 1610F:1h, FURNACE COOLED 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR SHEET BAR BAR BAR
HT HT HT HT HT HT NORMALIZED HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR SHEET BAR
HT HT HT HT HT HT HT HT NORMALIZED HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR
HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
8403/frame/ch15-Tbl 15.1(AB) Page 536 Friday, October 27, 2000 4:18 PM
536
TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
156 157 158 159 160
STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE
CR CR CR CR CR
52100 52100 52100 52100 52100
161 162 163 164 165 166 167 168 169 170
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 SS UNILOY 19-9DL 52100 52100 52100 52100 52100 52100 52100
171 172 173 174 175 176 177 178 179 180
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 SS A-286 52100 52100
181 182 183 184 185 186 187 188 189 190
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C C C C C C CR MN CR
81B45 9310 51100 50100 4820 C1080 9310 52100 C1080 FERRO TIC
191 192 193 194 195 196 197 198 199 200
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C C CR MN MN C C CR AL
8620 81B45 4820 52100 1118 1118 8620 4340 SS UHB AEB-L SUPER NITRALLOY
201 202 203 204 205 206 207 208 209 210
STEEL STEEL STEEL STEEL STEEL STEEL TOOL STEEL TOOL STEEL TOOL STEEL TOOL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
AL CR C C C CR W CR CR Cr
SUPER NITRALLOY 52100 4340 1040 1040 52100 MOD M2 D2 M50 M50
211 212 213 214 215 216 217 218 219 220
TOOL STEEL TOOL STEEL TOOL STEEL TOOL STEEL ALUMINUM ALUMINUM ALUMINUM ALUMINUM ALUMINUM ALLOY ALUMINUM BRONZE
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
FE FE FE FE AL AL AL AL AL CU
CR CR CR CR SI
H13 D2 D2 H11 380
SI FE CD AL
390 1100
221 222 223 224 225 226 227 228 229 230
ALUMINUM BRONZE ALUMINUM BRONZE ALUMINUM BRONZE ALUMINUM-BIMETAL ALUMINUM-LEAD ALUMINUM-SILICON ALUMINUM-TIN ALUMINUM, OIL-FILLED ANTIMONY BERYLLIUM COPPER
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU AL AL AL AL AL SB CU
AL AL AL SN PB SI SN CU
C61000
231 232
BERYLLIUM COPPER BRONZE
METAL METAL
NONFERROUS NONFERROUS
CU CU
BE SN
C61000
C60800
BE
C93200
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
BAR BAR BAR BAR BAR
HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR
HT HT HOT ROLLED HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER
HT HT HT HT HT HT HT QUENCHED, TEMPERED HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
CAST
BAR
HT CARBURIZED, HT ANNEALED ANNEALED ANNEALED ANNEALED ANNEALED ANNEALED HT
ANNEALED ANNEALED CARBURIZED, HT HT CARBURIZED, HT ANNEALED CARBURIZED, HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
350F TEMPER 900F TEMPER 400F TEMPER 300F, TEMPER
400F TEMPER
300F TEMPER 350F TEMPER 300F TEMPER 300F TEMPER 260C TEMPER
PH
BAR
BAR
BAR BAR
PH,NITRIDED HT ANNEALED HT ANNEALED ANNEALED HT HT HT ANNEALED HT HT HT HT
CAST ANNEALED CAST SAE 781 HARDENED CAST
ANNEALED
CAST
ANNEALED
CDA 954 SAE 780
SAE 783 POROUS, 19%
SAE 660
CAST
ANNEALED AGE HARDENED
CAST CAST
ANNEALED ANNEALED
350F TEMPER 300F TEMPER
300F TEMPER 1850F, TEMPER 400F, 1 h 600F TEMPER
25min.1875F, 2 TEMPER 1100F,2h 600F TEMPER 1850F, TEMPER 400F, 1 h 500F TEMPER
8403/frame/ch15-Tbl 15.1(AB) Page 538 Friday, October 27, 2000 4:18 PM
538
TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
233 234 235 236 237 238 239 240
BRONZE BRONZE BRONZE BRONZE, OIL-FILLED BRONZE, OIL-FILLED CADMIUM CADMIUM ALLOY CAST ALUMINUM ALLOY
METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU CU FE CD CD AL
241 242 243 244 245 246 247 248 249 250
COPPER COPPER-LEAD COPPER-LEAD ELECTROLESS NICKEL ELECTROLESS NICKEL GOLD GUN METAL HASTELLOY INCONEL INDIUM
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU NI NI AU CU NI NI IN
251 252 253 254 255 256 257 258 259 260
LEAD LEAD BABBITT LEAD BABBITT LEAD BABBITT LEAD BABBITT LEADED GUN METAL LEAD-TIN BRONZE LEAD-TIN BRONZE MANGANESE BRONZE MOLYBDENUM
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
PB PB PB PB PB CU CU CU CU MO
261 262 263 264 265 266 267 268 269 270
MONEL NAVY GUN METAL NICKEL-CHROMIUM ALLOY NICKEL-CHROMIUM ALLOY PHOSPHOR BRONZE PHOSPHOR BRONZE SEMIPLASTIC BRONZE SILICON BRONZE SILVER STELLITE
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
271 272 273 274 275 276 277 278 279 280
STELLITE STELLITE STELLITE STELLITE STELLITE STELLITE STOODY Ti-6Al-4V Ti-6Al-4V TIN
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
281 282 283 284 285 286 287 288 289 290
TIN BABBITT TIN BABBITT TIN BABBITT TIN BABBITT TRIBALOY TRIBALOY TRIBALOY TUNGSTEN VANASIL WASPALOY
291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310
SECOND COMPONENT PB PB SN SN CU
GRADE C98600 C94300 C93700
NI SN OFHC PB PB P P SN MO CR
C 718
SB SB SB SB SN SN SN ZN TI
15 13 7 8
NI CU FE FE CU CU CU CU AG CO
CU SN NI NI SN SN SN SI
K500
CR
S1016
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CO CO CO CO CO CO CO TI TI SN
CR CR CR CR CR CR CR AL AL
1 6 F STAR J S1016 S1016 6
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
SN SN SN SN CO CO NI W SI NI
SB SB SB SB MO MO MO NI NI CR
3 2 1
WASPALOY WAUKESHA ZINC ZINC-11 ALUMINUM ZINC-27 ALUMINUM ZIRCALLOY ACETAL ACRYLONITRILE-BUTADIENE-STYRENE (ABS) ARMALON DUROID
METAL METAL METAL METAL METAL METAL POLYMER POLYMER POLYMER POLYMER
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
NI NI ZN ZN ZN ZR
CR SN
23
AL AL SN
12 27 2
FEP IPC NYLON NYLON NYLON 6/6 PHENOLIC POLYCARBONATE POLYESTER POLYETHYLENE POLYIMIDE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
C86300 0.5 TI
16-25-6 16-25-6 C51100 C87200
T-800 T-400 T-700 77
5600
1832 6 TF
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
SAE 64 SAE 841; ASTM b-438-73, GR1 TYPE II; MIL-B-5678C, 1A ASTM B-612-70, GR3
CAST CAST CAST POROUS, 20% POROUS, 20%
SAE 770
CAST
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
ANNEALED ANNEALED ANNEALED
ANNEALED
ANNEALED SAE 480 PLATED PLATED
HEATED TO 400C AS DEPOSITED ANNEALED
CAST CAST
ANNEALED AGED ANNEALED
SAE 62, CDA 902
ANNEALED SAE 15 SAE 13 ASTM 7 ASTM B23/8 SAE 63, CDA 927 SAE 40, CDA 836 CDA943
CAST CAST CAST CAST
CAST ARC CAST
ANNEALED
CAST SAE 620, CDA 903 HOT ROLLED, HARDENED HOT ROLLED, ANNEALED SAE 64, SAE 792; SAE 797, CDA 937 COLD WORKED SAE 67, CDA 938 CAST BAR CAST CAST CAST CAST BAR BAR CAST CAST
ASTM B23/3 ASTM B23/2
ANNEALED ANNEALED WELD
OXY/ACETY
WELD WELDED
OXY/ACETY OXY/ACETY
ANNEALED BORONIZED, HT ANNEALED
CAST CAST CAST
SAE 11 CAST CAST CAST PM CAST CAST CAST CAST
SINTER, DRAWN AGE HARDENED ANNEALED HT, PH ANNEALED
ASTM B-669-82
CAST CAST CAST
MOULDED CAST CAST CAST LAMINATED
ANNEALED
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540
TABLE 15.1 NUMBER
Modern Tribology Handbook
Tribo-Materials Database (Part A) COMMON NAME
CLASS
SUBCLASS
311 312 313 314 315 316 317 318 319 320
POLYIMIDE (FILLED) POLYPHENYLENE OXIDE POLYPHENYLENE SULFIDE POLYPROPYLENE POLYSULFONE POLYURETHANE PTFE TORLON UHMWPE RUBBER
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
ELASTOMER
321 322 323 324 325 326 327 328 329 330
ACETAL-CARBON ACETAL-GLASS ACETAL-PTFE ACETAL-SILICONE ACRYLONITRILE-BUTADIENE-STYRENE (ABS) EPOXY-CELLULOSE NYLON 6/6-CARBON NYLON 6/6-GLASS NYLON 6/6-PTFE NYLON 6/6-SILICONE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
331 332 333 334 335 336 337 338 339 340
PEEK-GRAPHITE PHENOLIC-COTTON LAMINATE PHENOLIC-WOOD FLOUR POLYCARBONATE-CARBON POLYCARBONATE-GLASS POLYCARBONATE-PTFE POLYESTER-CARBON POLYESTER-GLASS POLYESTER-PTFE POLYESTER-SILICONE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
341 342 343 344 345 346 347 348 349 350
POLYETHYLENE-PTFE POLYIMIDE-GLASS POLYIMIDE-GRAPHITE POLYPHENYLENE OXIDE-GLASS POLYPHENYLENE OXIDE-PTFE POLYPHENYLENE SULFIDE-CARBON POLYPHENYLENE SULFIDE-GLASS POLYPHENYLENE SULFIDE-PTFE POLYPROPYLENE-PTFE POLYSULFONE-CARBON
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
351 352 353 354 355 356 357 358 359 360
POLYSULFONE-GLASS POLYSULFONE-PTFE POLYURETHANE-GLASS POLYURETHANE-PTFE PTFE-FABRIC PTFE-GLASS PTFE-GRAPHITE RULON RYTON VESPEL
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
361 362 363 364 365 366 367 368
VESPEL BUTYL NEOPRENE NITRILE SILICONE RUBBER URETHANE VITON FABROID
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED RUBBER RUBBER RUBBER RUBBER RUBBER RUBBER WOVEN
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE T-0454
PTFE
LD R4 SP1 SP21
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
MOULDED
MOULDED
MOULDED SINTERED
SINTERED MOULDED MOULDED MOULDED MOULDED MOULDED MOULDED WOVEN
PROCESSING CONDITIONS
8403/frame/ch15-Tbl 15.1(CD) Page 542 Friday, October 27, 2000 4:17 PM
542
Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Component Weight Percent
Component Names
Density (kg/m3) 4,429 2,510 6,643 3,045 4,429 5,536 6,089 3,045 1,938 2,353
C C, Ag
8,304 1,850 1,661 1,938 1,938 1,661 1,661 1,700 2,350 2,400
C C C C C C C, Babbitt C, copper
21 22 23 24 25 26 27 28 29 30
C, glass C, lithium fluoride C, resin C, silver C
31 32 33 34 35 36 37 38 39 40
Al2O3, TiO2
41 42 43 44 45 46 47 48 49 50
MoS2, Ta PTFE, Pb, bronze TiC,Cr,Mo,C,Fe
34.6,6.6,2,.8,56
C,Si,Ni,Cu,Cr,Fe C,Si,Mn,Ni,Cr,Fe C,Si,Mn,P,S,Fe C,Si,Ni,Cr,Fe C,Cr,Fe
3,1.5,15,6,2,71.5 3.5,1.5,0.5,6,8,80.5 .85,14.5,.5,.07,.08,84 3.5,.5,4,2,89.5 2.8,28,69.2
51 52 53 54 55 56 57 58 59 60
C,Mn,Si,Cu,Ni,Mo,Fe C, Fe C,Fe Cu, Fe Cu, Fe Fe
3,2,1.8,.5,2,.5,90.2 3, 97 .006,99.98 20, 80 10, 90
C,Mn,Si,Cr,Ni,Mo,Ti,Va,Fe C,Mn,P,S,Si,Cr,Ni,N,Fe C,Cr,Ni,Mo,Fe
.08,1,.6,15,26,1,2,.3,54 .08,2,.045,.03,1,18,8,.2,70.6 .1,18,14,3,65
7,197 6,700 7,861 6,000 6,100 6,000 7,800 7,473 8,027 8,027
61 62 63 64 65 66 67 68 69 70
C,Mn,Si,P,S,Cr,Mo,Fe C,Mn,Si,P,S,Cr,Mo,Fe C,Cr,Ni,Cu,Fe C,Cr,Ni,Fe C,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Fe C,Cr,Ni,Cu,Fe C,Cr,Ni,Mo,Fe C,Cr,Ni,Mo,Fe C,Cr,Ni,Cu,Fe
1,1.25,1,.04,.04,18,.75,78 1,1.25,1,.04,.04,18,.75,78 .05,16.5,4.0,4.0,75.5 .08,19,10,71 .1,18,14,3,65 .15,1.0,.5,12,86.5 .07,17,4,4,74 .08,18,14,3,64 .08,18,14,3,64 .07,17,4,4,74
71 72 73 74 75 76 77 78
C,Mn,Si,Cr,Fe C,Mn,P,S,Si,Cr,Ni,Cu,Cb,Fe C,Mn,P,S,Si,Cr,Ni,Cb&Ta C,Mn,Si,Cr,Ni,N,Fe C,Mn,Si,Cr,Ni,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
.15,1.0,.5,12,86.5 .07,1.0,.04,.03,1,14.5,4,3,.3,76 .08,2,.045,.03,1,18,11,.1 .52,9,.15,21,3.85,.45,65 .25,2,1.5,25,20,47 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
Y2O3,ZrO2
5.3,94
ZrO2, MgO Y2O3,Zr02
Melting Point (C)
2,400 1,890 2,699 3,140
2,800
3,652
2,000 1,900 1,900 2,400 1,570 2,491 2,491 3,045 5,536 3,875
1,538 1,122 1,899 2,950 1,849
4,152 2,214 6,089
1,750 2,570 2,700
5,536 3,97
5,813 3,045 4,152 1,200
2,593 1,710 1,838
5,900 7,750 14,200 14,200 7,197 7,473 7,197 7,473 7,473
1,269
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
8 5 10 4 8 9 10 6 1 5
26 19 19 147 26 17 19 2 36 26
1.0 2.0 1.0 1.0 1.0 1.0
4 5 4 8 8 10 9 5 5 5
138
5 9 5 5 2 57 10 2 8 7
78 17 9 14 170 2 1 15 66 35
8 36 10 20 10
25 2 3
10 16 9 5
3 164 5
9 19
43 42
6 6 10 10 12 9 9
87 87 40
12 2 69 17 9 9 13 14
0.0
1.0
1.0 1.0 1.0 1.0 0.0 1.0 2.0 1.0
2
1.0 1.0 2.0
1.0 17
8 16 12 12 13 10 23
29 28 50
1,427 1,427
17 11
16 16
0.0 0.0
7,473 7,473 7,750 8,030 8,027 7,889 7,750 8,027 8,027 7,750
1,538 1,538 1,400
29 29 18
1,427 1,427
11 11 11 17 11 19 11 11 11
0.0 0.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0 1.0
7,750 7,750 7,750 7,750 7,970 7,800 7,800 7,800
1,482
12 12 16 16 12 12 12
25 18 25
0.0
1,482
16 43 43 43
1.0 0.0 0.0 0.0
1,537
1,427 1,400
1,427 1,475 1,475 1,475
0.0 54
16 16 21 16 16
0.0
0.0
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
896 41 69
650 HV 650 HV 480 HV 170 HV 600 HV 320 HV 680 HV 85 SHORE 70 SHORE 95 SHORE
97 59 28 21 38 28 41 41 62 62
13,800 14,500 14,500 20,700 12,400 6,890 13,800 16,600 32,344 32,348
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Booser
90 SHORE 90 SHORE 90 SHORE 90 SHORE 3 HV
52 48 59 69 12 110
262
15,200 20,700 32,612 32,560 12,900 129,744 130,340 310,000 248,000 372,000
Booser Booser Booser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
545 103 1,172 276 689 172 1,020 103 52 8
358,000 379,000 200,000 200,000 200,000 172,000 205,000 379,000 234,000 12,400
675 HV
69
138,000
330 HV 85 HRA 90 HRA 150 HV 560 HV 530 HV 655 HV 530 HV
1,034 1,100 1,103 207 620 110 379 689
196 HV 30 HB 45 HV 83 HB 50 HB 150 HB
310 138 276 221 207 83 414
72 74
200 HV 200 HV
689 758
200,000 200,000 200,000 196,000
60 60 77
257 HV 650 HV 400 HV 160 HV 150 HV 150 HV 44 HRC 97 HRB 97 HRB 44 HRC
862 1,379 1,379 586 586 620 1,379 760 680 1,379
200,000 200,000 196,000 193,000 196,000 193,000 196,000 196,000 196,000 196,000
135 HV 420 HV 257 HV 264 HV 150 HV 62 HRC 62 HRC 62 HRC
517 1,379 758 862 654 1,640 1,640 1,640
196,000 196,000 196,000 193,000 200,000 199,000 199,000 199,000
2
4 3 2 5 4
820 HV
1.00E+12
60
0580 HV 1300 HV 2000 HV 1500 HV
1800 HV 1158 HV 1600 HV
1.46E+20 400 4.01E+13
71
10
74 72 77 74 74 77 57 77 57 78 20 20 20
286 HV 853 HV 900 HV
172 262 103 896 345
524
7 6
Data Source
345,000 441,000 372,000 379,000 483,000 414,000 407,000 552,000 6,890 32,344
100 100
3500 HV 3200 HV 2600 HV 2700 HV 3000 HV 3000 HV 1400 HV 1500 HV
Tensile Strength (MPa)
5
12
1 1 4 4 5 7 10 9 10 9 1 3
607,000 607,000 103,000 172,000 172,000 221,000
98
124,000 129,528 207,000
140
48
48
48
81 60
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
Wear Coefficient
3.0E-06
Glaeser Glaeser Glaeser Glaeser Glaeser Hughes/Rowe Hughes/Rowe Hughes/Rowe
9.5E-07 649 260
6.1E-05
371 650 288 204 538 288 316 316 190 260
2.4E-04
649 260 260 260 425 1,650 1,480 1,760
1,370 1,370 1,480 2,400 71 400 204 649 3.0E-05
4.5E-04 538 538 816 816 427
Glaeser Booser Glaeser Booser Booser Booser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser ASTM G2,RR3,5/18/76,3 labs,n=3 ASTM G2,RR2,12/9/75,5 labs,n=5 ASTM G2,RR1,5/23/75,2 labs,n=2 ASTM G2,RR9,6/10/82,8 labs,n=32
Wear Rate (mm3/m)
1,650
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser ASTM G2,RR2,12/9/75,5 labs,n=5 Booser Glaeser Glaeser Glaeser Glaeser Glaeser
Maximum Operating Temperature (C)
399 135 135 135 135 538
649
3.0E-05 7.6E-06
316 316 870 649 815
2.0E-03 9.0E-04 4.0E-04 3.0E-03
6.0E-05 1.7E-03
1.7E-02 1.9E-02 8.7E-03 8.5E-02 649
1.5E-05 3.7E-09 8.0E-09 3.0E-07
649 538 927 200 200 200
3.8E-03 3.0E-08 1.2E-07 2.4E-06
8403/frame/ch15-Tbl 15.1(CD) Page 544 Friday, October 27, 2000 4:17 PM
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
Density (kg/m3)
Melting Point (C)
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
79 80
C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800
1,475 1,475
12 12
43 43
0.0 0.0
81 82 83 84 85 86 87 88 89 90
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Mn,P,S,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 .2,.6,.04,.05,99 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,750 7,750 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,482 1,482 1,475 1,475 1,475 1,475
12 12 12 12 11 11 12 12 12 12
43 43 43 43 50 50 43 43 43 43
0.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0
91 92 93 94 95 96 97 98 99 100
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
101 102 103 104 105 106 107 108 109 110
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,750 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,482 1,475 1,475 1,475
12 12 12 12 12 12 11 12 12 12
43 43 43 43 43 43 50 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
111 112 113 114 115 116 117 118 119 120
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
121 122 123 124 125 126 127 128 129 130
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,750 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,482 1,475
12 12 12 12 12 12 12 12 11 12
43 43 43 43 43 43 43 43 50 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
131 132 133 134 135 136 137 138 139 140
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
141 142 143 144 145 146 147 148 149 150
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
151 152 153 154 155
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475
12 12 12 12 12
43 43 43 43 43
0.0 0.0 0.0 0.0 0.0
8403/frame/ch15-Tbl 15.1(CD) Page 545 Friday, October 27, 2000 4:17 PM
545
Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
20 20
62 HRC 62 HRC
1,640 1,640
199,000 199,000
Hughes/Rowe Hughes/Rowe
3.0E-08 2.0E-08
200 200
2.2E-06 2.4E-07
20 20 20 20 19 19 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 60 HRB 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR4,11/4/76,5 labs,n=5 ASTM G2,RR8,5/20/81,7 labs,n=28 Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.0E-08 1.2E-07 1.2E-07 2.4E-07 4.0E-04 7.0E-04 2.4E-07 2.4E-07 4.0E-09 2.0E-09
200 200 200 200
400 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 207,000 207,000 199,000 199,000 199,000 199,000
200 200 200 200
1.2E-07 1.1E-06 1.2E-06 1.8E-06 1.9E-02 8.4E-02 1.9E-06 3.8E-06 5.9E-08 1.4E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
9.5E-07 9.5E-07 4.0E-09 3.7E-09 5.0E-09 4.0E-08 8.0E-08 2.0E-08 7.4E-09 2.0E-08
200 200 200 200 200 200 200 200 200 200
6.7E-06 3.9E-06 5.9E-08 3.0E-08 3.8E-08 3.3E-07 6.6E-07 2.4E-07 6.0E-08 1.3E-07
20 20 20 20 20 20 19 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR5,3/7/78,6 labs,n=30 Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.2E-07 8.0E-09 4.0E-09 3.7E-09 3.0E-07 2.4E-07 4.0E-04 1.2E-07 4.0E-08 3.0E-08
200 200 200 200 200 200
1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 207,000 199,000 199,000 199,000
200 200 200
1.2E-07 1.2E-07 3.0E-08 2.8E-08 3.8E-06 1.5E-06 7.3E-03 9.3E-07 3.5E-07 2.3E-07
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.2E-07 1.0E-03 2.0E-10 2.4E-07 2.4E-07 1.0E-02 2.0E-08 4.0E-09 1.5E-05 1.2E-07
200 200 200 200 200 200 200 200 200 200
1.1E-05 8.5E-03 1.7E-09 1.9E-06 1.9E-06 8.5E-02 1.6E-07 5.9E-08 1.2E-04 9.4E-07
20 20 20 20 20 20 20 20 19 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR4,11/4/76,5 labs,n=5 Hughes/Rowe
1.2E-07 1.0E-08 3.7E-09 3.7E-09 5.9E-08 3.0E-07 2.0E-09 4.0E-09 5.0E-04 5.0E-09
200 200 200 200 200 200 200 200
1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 207,000 199,000
200
9.4E-07 1.2E-07 3.0E-08 3.0E-08 4.7E-07 2.4E-06 1.8E-08 5.9E-08 8.3E-03 3.8E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
3.0E-08 7.4E-09 5.9E-08 2.0E-09 3.0E-07 8.0E-08 4.7E-07 2.4E-07 4.0E-08 5.0E-09
200 200 200 200 200 200 200 200 200 200
2.3E-07 6.0E-08 4.7E-07 1.8E-08 2.9E-06 9.5E-07 3.8E-06 1.9E-06 3.5E-07 5.9E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
3.7E-09 1.2E-07 4.7E-07 1.0E-08 4.0E-09 1.2E-07 9.2E-10 6.0E-07 7.0E-07 5.9E-08
200 200 200 200 200 200 200 200 200 200
3.0E-08 9.4E-07 3.0E-06 1.2E-07 5.9E-08 9.5E-07 5.0E-09 5.3E-06 7.6E-06 4.7E-07
20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.0E-09 4.0E-09 5.9E-08 5.0E-09 4.0E-09
200 200 200 200 200
1.5E-08 3.6E-08 4.5E-07 5.9E-08 3.6E-08
8403/frame/ch15-Tbl 15.1(CD) Page 546 Friday, October 27, 2000 4:17 PM
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
Density (kg/m3)
Melting Point (C)
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
156 157 158 159 160
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475
12 12 12 12 12
43 43 43 43 43
0.0 0.0 0.0 0.0 0.0
161 162 163 164 165 166 167 168 169 170
C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,Si,Cr,Ni,Mo,W,Cb+Ta,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 .4,1,.5,19,9,1.5,1.5,.4,67 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,916 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475
12 12
43 43
0.0 0.0
1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12
43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0
171 172 173 174 175 176 177 178 179 180
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,Si,Cr,Mo,Va,Fe C,Cr,Mn,Si C,Mn,P,S,Si,Cr,Fe
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1,1,1,15,4,.15,87.25 1.0,1.5,.5,.3 1,.5,.025,.025,.3,1.5,96.5
7,800 7,800 7,800 7,800 7,800 7,800 7,800 8,248 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12
43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0
1,475 1,475
12 12
43 43
0.0 0.0
181 182 183 184 185 186 187 188 189 190
C,Mn,Si,Ni,Cr,Mo,B,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Fe C,Mn,Si,Cr,Fe C,Mn,P,S,Si,Ni,Mo,Fe C,Mn,Si,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,P,S,Si,Cr,Fe C,Mn,Si,Fe C,Mn,Si,Cr,Ni,Mo,V,Cb+Ta,Fe
.45,.8,.3,.3,.4,.1,.0005,98 .1,.5,.2,1.2,3.2,1,94.2 1,.3,.2,.5,98.1 1,.3,.2,1,97.5 .2,.6,.035,.04,.3,3.5,.25,95 .8,.7,.2,98 .1,.5,.2,1.2,3.2,1,94.2 1,.5,.025,.025,.3,1.5,96.5 1.0,12,.2,87 .15,.6,.4,12,.4,.6,.3,.3,85
7,750 7,750 7,800 7,800 7,861 7,750 7,750 7,800 7,750 6,366
13 15 12 12 16 15 15 12 15
47 43 43 45 47 47 43 47
1.0 0.0 0.0
191 192 193 194 195 196 197 198 199 200
C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Ni,Cr,Mo,B,Fe C,Mn,P,S,Si,Ni,Mo,Fe C,Cr,Mn,Si C,Mn,Fe C,Mn,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,P,S,Si,Ni,Cr,Mo,Fe C,Mn,Si,Cr,Fe C,Mn,Si,Ni,Cr,Mo,Al,Va,Fe
.2,.8,.2,.5,.6,.2,97.5 .45,.8,.3,.3,.4,.1,.0005,98 .2,.6,.035,.04,.3,3.5,.25,95 1.0,1.5,.5,.3 .16,1.4,98.44 .16,1.4,98.44 .2,.8,.2,.5,.6,.2,97.5 .4,.7,.025,.025,.3,1.7,.8,.25,96 .68,.6,.38,13.2,85.2 .2,.3,.2,5,.5,.2,2,.1,92
7,750 7,750 7,861 7,800 7,805 7,805 7,750 7,750 7,750 7,750
38
0.0
201 202 203 204 205 206 207 208 209 210
C,Mn,Si,Ni,Cr,Mo,Al,Va,Fe C,Cr,Mn,Si C,Mn,P,S,Si,Ni,Cr,Mo,Fe C,Mn,P,S,Si,Fe C,Mn,P,S,Si,Fe C,Mn,Si,Cr,Fe C,W,Mo,Cr,V,Fe C,Cr,V,Si,Mn,Fe C,Mn,Si,P,S,Cr,Ni,V,Mo,Fe C,Mn,Si,P,S,Cr,Ni,V,Mo,Fe
.2,.3,.2,5,.5,.2,2,.1,92 1.0,1.5,.5,.3 .4,.7,.025,.025,.3,1.7,.8,.25,96 .4,.7,.04,.05,.2,98.6 .4,.7,.04,.05,.2,98.6 1,1,.6,1,96.4 .8,6,5,4,2,82.2 1.6,13,1,.6,.6,83 .8,.25,.25,.015,.015,4,.1,1,4.5,89 .8,.25,.25,.015,.015,4,.1,1,4.5,89
7,750 7,800 7,750 7,750 7,750 7,800 8,027 7,750 7,890 7,890
211 212 213 214 215 216 217 218 219 220
C,Cr,Mo,V,Si,Fe C,Cr,Mo,V,Si,Mn,Fe C,Cr,V,Si,Mn,Fe C,Si,Mn,Cr,V,Mo,Fe Cu,Si,Fe,Mn,Mg,Zn,Ni,Al Al Cu,Si,Fe,Mn,Mg,Zn,Ti,Al Si + Fe, Cu, Mn, Zn, Al Al, Si, Cd Cu,Al
.35,5,1.5,1,1,91 .35,5,1.5,.4,.9,.3,91.6 1.6,13,1,.6,.6,83 1.5,.4,.3,12,.4,1,96.5 3.5,8,2,.5,.1,1,.5,84.5
7,750 7,750 7,750 7,750 2,768 2,685 2,491 2,713
221 222 223 224 225 226 227 228 229 230
Cu,Al Cu, Al, Fe Cu,Al Al, Sn, Cu, Ni, Si Al, Pb, Si, Sn, Cu Al, Si, Cu Al, Sn, Cu Al, Cu, Sn, Pb Sb Be,Co,Ni,Cu
92,8 85, 11, 4 95,5 90, 6.5, 1, 0.5, 1.5 85, 8.5, 4, 1.5, 0.5 88, 11, 1 79, 20, 1 87, 5, 4, 4
231 232
Be,Co,Ni,Cu Cu,Sn,Pb,Zn
1,475 1,475
1,475
1,507 1,510 1,475
1,482 649
1,475 1,482 1,482 1,482 1,475
15 13 16 12 12 12 15 15 12
45 43 52 52 38 38 28 52
12 12 15 11 11 12 10
52 43 38 50 51 43 38
0.0 1.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 1.0 0.0
11 11 16 10
29
650 649 510 649
16 40 24 11 22
29 97 221 134 221
1.0
7,760
1,041
18
69
0.0
7,760 7,500 8,304
1,041 1,045 1,054
18 16 18
69 59 80
0.0
1.8,,.2,99.5
2,300 6,643 8,304
631 982
23 9 17
137 18 121
1.8,,.2,99.5 83,7,7,3
8,304 8,857
982 1,038
17 10
121 58
4.5,17,1,.1,.5,.1,.2,77.5 1, .1, .05, .1, 99 95, 4, 1 92,8
1.0 1.0
0.0
0.0 0.0
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TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
2.4E-07 1.2E-07 5.9E-08 1.2E-07 7.4E-09
200 200 200 200 200
1.5E-06 9.8E-07 7.6E-06 6.1E-07 5.9E-08
20 20
62 HRC 62 HRC 217 HV 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 751 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000
Hughes/Rowe Hughes/Rowe Glaeser Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
5.0E-09 1.0E-09
200 200 760 200 200 200 200 200 200 200
4.0E-08 1.5E-08
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 330 HV 62 HRC 413 HV
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,000 1,640 1,379
199,000 199,000 199,000 199,000 199,000 199,000 199,000
9.0E-08 2.0E-09 4.0E-09 2.0E-08 2.0E-10 2.4E-07 5.0E-09
200 200 200 200 200 200 200 760 200 260
7.3E-07 1.4E-08 5.9E-08 1.6E-07 1.7E-09 1.5E-06 5.9E-08
199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Glaeser Hughes/Rowe Glaeser
617 HV 694 HV 200 HV 225 HV 230 HV 224 HV 200 HV 200 HV 404 HV 695 HV
2,041 1,241 689 689 758 820 689 689 1,303
207,000 207,000 207,000 207,000 207,000 207,000 207,000 199,000 207,000 290,000
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
180 HV 195 HV 424 HV 62 HRC 210 HV 140 HV 789 HV 350 HV 310 HV 435 HV
607 641 1,379 1,640 758 448 1,296 1,723 689 1,420
207,000 207,000 207,000 199,000 207,000 207,000 207,000 207,000 207,000 207,000
740 HV 62 HRC 260 HV 540 HV 150 HV 200 HV 765 HV 60 HRC 760 HV 160 HV
1,640 979 896 552 689 2,758 1,930 2,758 683
207,000 199,000 207,000 207,000 207,000 199,000 207,000 207,000 202,000 202,000
3
50 HRC 590 HV 60 HRC 598 HV 80 HB 15 HV 145 HV 30 HV
1,930 1,930 2,068 296 52 310 90
207,000 207,000 207,000 207,000 71,000 130,340 82,000 130,044
12
165 HV
448
79,300
12 23 10
100 HV 180 HB 70 HV 92 HRH
358 621 414 179
79,300 124,000 121,000 129,744
60 HB 35 HB 55 HRH 40 HV 393 HV
179 110 103 10 1,380 483 276
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
20 20 28 18 20 18
30 28 20 14 14 30 30 28 28 20 30 19 19
18
8 5
70 5
80 HV 80 HV
199,000 199,000 199,000 199,000 199,000 199,000 199,000
125
38
77 77
33
20 55
Glaeser Glaeser Glaeser Hughes/Rowe Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Hughes/Rowe Glaeser Glaeser Glaeser Glaeser Glaeser ASTM G2,RR6,6/6/78,,9 labs,n=40 Glaeser Glaeser
3.0E-07 5.0E-09 4.0E-09 2.0E-09 2.0E-09 1.2E-07 9.0E-08
1.2E-07
260
8.0E-08
4.0E-09
200 260
8.0E-03 3.1E-05 4.0E-04
9.5E-07
5.9E-08
2.0E-02 260 538
3.0E-05 8.0E-03
427 427
1.0E-04
78,332 131,000
Glaeser Booser Glaeser Booser Booser Booser Booser Booser Glaeser Glaeser
131,000 103,000
Glaeser Glaeser
64,800
200
260
2.0E-03 3.0E-05 4.0E-04 8.0E-04
275
9.5E-07
260 260
ASTM G2,RR11,7/13/83,10 labs,n=50 Glaeser ASTM G2,RR6,6/26/80,6 labs,n=6 Glaeser Glaeser Glaeser Glaeser Glaeser Booser Glaeser
60
2.4E-07 3.8E-08 5.9E-08 1.4E-08 1.5E-08 8.6E-08 9.4E-07
538
538
3.9E-02 4.4E-05 8.3E-03 5.0E-04
149 150 260 260 260 260 150 150 150 150 135
1.1E-03
6.1E-05
427
6.1E-05
2.0E-04
427 149
3.0E-03
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TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
233 234 235 236 237 238 239 240
Cu,Sn,Pb Cu,Pb,Sn Cu,Sn,Pb Cu, Sn, c Fe, Cu, Sn, C Cd Cd, Ni Al, Sn, Cu, Ni
65,.5,34.5 70,25,5 80,10,10 89, 10,1 59, 36, 4, 1
241 242 243 244 245 246 247 248 249 250
Cu Cu, Pb Cu, Pb P,Ni P,Ni Au Cu, Sn, Zn C,W,Fe,Cr,Mo,Va,Mn,Si,Ni C,Si,Mn,Cu,Ni,Cr,Co,Mo,Al,Ti,Fe In
99.94 70, 30 65, 35 1-12,88-99 1-12,88-99
251 252 253 254 255 256 257 258 259 260
Pb Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Cu, Sn, Pb Cu, Sn, Pb, Zn Cu, Sn, Pb Al,Cu,Fe,Mn,Zn C,Ti,Mo
261 262 263 264 265 266 267 268 269 270
Ni,Al,Fe,Mn,C,Si,Ti,Cu Cu, Sn, Zn C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Ni,Mo,Fe Cu, Sn, Pb Cu,Sn,P Cu, Sn, Pb Cu,Si,Sn,Zn,Fe,Al,Mn Ag
271 272 273 274 275 276 277 278 279 280
98.5, 1.5 91, 6.5, 1, 1
Density (kg/m3) 9,134 9,300 8,857 6,600 6,200 8,664 8,600 2,900
Melting Point (C)
925 1,038
321
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
20 19 19 17 13 31 31 24
294 63 47 29 31 92 92 206
17
393
12 12 14 20 13 13 25
294 4 4 294 74 135 14 69
9,134 9,000 9,000 8,027 8,027 32,692 8,700 8,860 8,027 7,197
1,083 985 955
11,350 10,200 10,800 9,688 10,520 8,800 8,700 9,000 7,833 10,240
327 281 240 240
29 25
975
18 18 19 22 15
65,3,2,1.5,.25,1.0,.5,27 88, 8, 4 .12,2,1,16,25,6,49.9 .12,2,1,16,25,6,49.9 80, 10, 10 95.6,4.2,.2 78, 6, 16 87,4,1,4,2,1,1
8,304 8,700 8,027 8,027 8,900 8,857 9,200 8,359 10,520
1,316 975
Cr,C,Si,Mo,Fe,Ni,W,Co C,Mn,Si,Fe,Ni,Cr,W,Co
30,2.5,1,1,3,3,12,47.5 1.4,1,1.5,3,3,31,5,54
C,Mn,SI,Fe,Ni,Cr,W,Co
2.5,1,1,3,2.5,32,17,41
9,134 8,304 9,000 8,857
C,Si,Fe,Ni,Cr,W,Co C,Al,V,Ti C,Al,V,Ti SN
1.2,1.2,1,1,30,5,60.5 .1,6,4,90 .1,6,4,90
281 282 283 284 285 286 287 288 289 290
Sn,Sb,Cu Sn,Sb,Cu Sn,Sb,Cu Sn, Sb, Cu Co,Mo,Cr,Si,C Co,Mo,Cr,Si,C Ni,Mo,Cr,Si,C Ni,Cu,W Si,Zn,Cu,Fe,Ti,Mn,Ni,Mg,Va C,Mn,Si,Cr,Ni,Mo,Co,Ti,Al,Zr
84,8,8 89,7.5,3.5 91,4.5,4.5 86, 7.5, 6.5 52,28,17,3,.08 62,28,8,2,.08 50,32,15,3,.08 7,3,90 22,.1,1.5,.75,.15,.1,2.2,1,.1 .1,.5,.75,20,57,4,13,3,1,.1
291 292 293 294 295 296 297 298 299 300
C,Mn,Si,Cr,Ni,Mo,Co,Ti,Al,Zr Ni,Pb,Sn,Zn,Mn Zn Zn,Al,Cu,Mg Zn,Al,Cu,Mg Sn,Fe,Cr,Ni,Zr
.1,.5,.75,20,57,4,13,3,1,.1 80,4,8,7,1
PTFE-40 % ceramic fibre filled
301 302 303 304 305 306 307 308 309 310
fluorinated ethylene propylene polyphenylene sulfide resin, fibrefilled polyamide polyamide polyamide
88, 10, 2 .15,4,6,16,17,.3,1,1,54.6 .1,.75,.5,.75,50,18,5,3,.8,1,20
82.5,15,1,1,.6 83,10,6,.25,.5 75,15,10,.5,.5 80,15,5,.5,.5 88, 10, 2 85, 5, 5, 5 70, 5, 25 5,63,3,3,25 .02,.5,99.4
88.2,11,.75,.02 70.8,27,2.2,.015 1.5,.1,.1,.05,98.4
8,304 4,429 4,429 7,307
1,064 975 1,304 1,370 179
923
750 1,060 971 961
14 18 16 16 19 18 19 17 19
1,275
0.0
0.0
0.0
0.0 0.0 0.0 0.0
35 24 24 24 24 69 71 62 35 128
0.0
14 74
0.0
47 84 52 28 415
0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0
176 14
1,600 231
7,470 7,473 7,473
420 241 273
8,664 9,134 8,857 17,000 2,768 8,138
1,288 1,288 1,243 3,410 538
8,138 8,857 7,141 6,089 4,982 6,700 1,410 1,050
12
Heat Capacity (kJ/kg C)
14 9 9 24
7 7 64
23
52
1.0 1.0 0.0
54.0 19 18 7 16 14
171 176 136 167 126 12
1.0
14 5 31 28 12 7 85 90
12 26 112 115 124 15 0.0
2.0
1,900
18
0.0
1.0
2,140 1,661 1,130 1,107 1,140 1,384 1,200 1,310 940 1,430
180 22 80
0.0
1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2.0
419 404 427
258 104
81 29 67 95 110 49
1.0 0.0
2.0 1.0
1.0 1.0
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TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness 28 HV 48 HV 60 HV 40 HB
7
2
90 90 2 140 13 9 24
7
50
4 9
2
91
171 171 12
6
21 HV 35 HB 45 HB 42 HV 28 HB 25 HB 1050 HV 500 HV 35 HV 75 HB 216 HV 410 HV 1 HV
Tensile Strength (MPa) 59 186 207 90 103 69 138 193 59 55
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
64,688 129,744 129,528 11,000
Data Source Glaeser Glaeser Glaeser Booser Booser Glaeser Booser Booser
65,440 65,440 129,044 103,000
Glaeser Booser Booser Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser
689 138 310 551 1,380 3
200,000 200,000 74,500 103,000 197,000 200,000 11,000
14 HV 20 HV 20 HV 22 HV 11 HV 77 HB 60 HB 48 HB 225 HV 264 HV
41 69 69 69 69 290 241 186 793 689
13,800 29,000 29,000 29,000 29,000 130,560 64,764 62,204 131,068 324,000
Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Booser Glaeser Glaeser
320 HV 70 HB 320 HV 202 HV 60 HB 145 HV 57 HB 85 HV 34 HV 52 HRC
689 310 1,103 827 241 552 214 310 207
179,000 96,500 197,000 197,000 64,744 110,000 129,744 103,000 71,000
Glaeser Booser Glaeser Glaeser Booser Glaeser Booser Glaeser Glaeser ASTM G2,RR2,12/9/75,5 labs,n=5
834
241,000 210,000
517
255,000
Glaeser Glaeser Glaeser Glaeser ASTM G2,RR5,3/7/78,8 labs,n=38 ASTM G2,RR1,5/23/75,3 labs,n=3 Glaeser Glaeser Glaeser Glaeser
562 HV 395 HV 383 HV 675 HV 52 HRC 52 HRC 526 HV 301 HV 1700 HV 8 HV 26 HV 24 HV 17 HV 26 HB 739 HV 655 HV 485 HV 257 HV 140 HV 157 HV
12
689 896 15 81 81 81 117
207,000 110,000 110,000 41,400 51,000 64,688 64,764
689 276 827
241,000 269,000 214,000 276,000 93,000 211,000
1,280 586 103 296 414 517 61 55
211,000 159,000 130,340 82,940 129,528 129,528 2,550 2,760
689
71
Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
5.48E+11
5 HV
18
13,800
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Glaeser Glaeser
4.01E+19
5 HV 15 HV 15 HV
5.02E+12 1.00E+11 2.80E+14 7.15E+16 1.00E+15 1.00E+13
121 HRR 115 HV 66 HRM 70 HRM 65 HRR 52 HRE
21 69 80 55 81 62 62 59 28 90
689 11,000 3,700 2,070 2,830 6,890 2,280 2,340 965 3,170
Glaeser Glaeser Glaeser Glaeser Booser Glaeser Booser Booser Booser Booser
6 28 30 74
373 HV 165 HV 47 HV 93 HV 107 HV 185 HV 80 HRM 103 HRR
96
21 21
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
176 1.0E-04
2.1E-03 121 135 135
3.0E-05
2.9E-03 260 150
1.0E-04
5.1E-03 177 177 320 320 260 649
204 232 232 232 260 232 204 538 538 260 649 649 232 232 4.0E-03 2.0E-04
204
6.1E-05 1.0E-03 1.5E-05
2.4E-01 4.4E-03 9.8E-04 1.1E-03 9.7E-04
649 2.0E-04 1.0E-04
3.8E-03 3.4E-03 400 400
1.0E-04 7.0E-05 7.0E-06
220 238 221 150 704 704 649
5.5E-03 1.4E-03 2.4E-04
260 871 871 649 5.0E-02
2.3E+00 121 149 400 93 82 260 204 204 85 60 88 121 116 149 82 316
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TABLE 15.1 Tribomaterials Database (Part C) Number
Component Weight Percent
Component Names
311 312 313 314 315 316 317 318 319 320
polyimide filled, self lubricating
graphite, PTFE, polyamide/imide ultra high molecular weight polyethylene
12, 3, 85
321 322 323 324 325 326 327 328 329 330
carbon fiber, acetal glass fiber, acetal PTFE, acetal silicone, acetal PTFE, ABS cellulose carbon fiber, nylon 6/6 glass fiber, nylon 6/6 PTFE, nylon 6/6 silicone, nylon 6/6
20, 80 30, 70 15, 85 2, 98 15, 85
331 332 333 334 335 336 337 338 339 340
polyetheretherketone cotton laminate wood flour carbon fiber, polycarbonate glass fiber, polycarbonate PTFE, polycarbonate carbon fiber, polyester glass fiber, polyester PTFE, polyester silicone, polyester
341 342 343 344 345 346 347 348 349 350
PTFE, polyethylene glass fiber, polyimide graphite, polyimide glass fiber, polyphenylene oxide PTFE, polyphenylene oxide carbon fiber, polyphenylene sulfide glass fiber, polyphenylene sulfide PTFE, polyphenylene sulfide PTFE, polypropylene carbon fiber, polysulfone
351 352 353 354 355 356 357 358 359 360
glass fiber, polysulfone PTFE, polysulfone glass fiber, polyurethane PTFE, polyurethane fabric, PTFE glass fiber, PTFE graphite, PTFE mineral filled PTFE polyphenylene sulfide resin graphite, polyimide
30, 70 15, 85 30, 70 15, 85
361 362 363 364 365 366 367 368
polyimide, graphite Isobutylene-isoprene chloroprene butadiene-acrylonitrile polysiloxane disocyanate polyester vinylidene fluoride-hexafluoropropylene PTFE - Glass woven fabric
40, 60
Density (kg/m3) 1,520 1,060 1,340 910 1,240 1,250 2,180 1,460 930 1,200
20, 80 30, 70 20, 80 2, 98
1,460 1,630 1,490 1,400 1,140 1,200 1,230 1,370 1,260 1,120
30, 70 30, 70 15, 85 30, 70 30, 70 20, 80 2, 98
1,430 1,330 1,400 1,330 1,430 1,280 1,410 1,520 1,440 1,290
20, 80
Melting Point (C)
160
Expansion Coefficient (µm/m) 8 59 54 72 56 72 55 25 200 77
334
20 22 40 16 23 70 9 22 99 95 128 14 49 25 63 11 27 59 76 11 25 59 45
15, 85 15, 85
1,450 1,320 1,460 1,330 2,500 2,190 2,080
121 126
15, 85
1,661 1,384
63
1,384 830 1,107 1,107 1,384 1,107 1,500
0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
Heat Capacity (kJ/kg C)
1.0 1.0 0.0 1.0 2.0 2.0
40 43 94 90 94 52 25 32 83 81
1,080 1,900 1,510 1,280 1,150 1,450 1,650 1,450 1,020 1,370
15, 85 30, 70 15, 85 30, 70 40, 60 20, 80 20, 80 30, 70
Thermal Conductivity (watt/m/C)
0.0 0.0
0.0
1.0
0.0
1.0
0.0
0.0 0.0 1.0 0.0 1.0
23 10 32 16 25 125
0.0 0.0 0.0 0.0 0.0
23
0.0
2.0
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TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
1.00E+17 5.00E+16 1.00E+12 1.00E+17 8.03E+13 5.01E+14 1.70E+16
Hardness
95 HRR
60 SHORE D 40 HV 50 HV 65 SHORE A
118 HRR
95 HRM
105 HRM 85 HRE 118 HRR
100 HRM
120 HRM 88 HRM
5.56E+14
123 HRR
1.40E+14
5068 HV
1.00E+12
35 HV 2 HV 2 HV 2 HV 3 HV 6 HV 3 HV
3.50E+10 1.40E+14 2.00E+11 2.00E+12
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
56 66 76 35 70 14 23 164 41 16
10,400 2,480 4,140 1,240 2,690 103 620 6,600 689 41
Glaeser Booser Booser Booser Booser Booser Booser Glaeser Glaeser Booser
288 116 188 77 171 110 260 260 77 66
81 135 48 55 45 90 193 179 62 75
9,310 8,960 2,070 2,410 2,550 2,410 16,600 8,960 2,550 2,760
Booser Booser Booser Booser Booser Booser Booser Booser Booser Booser
149 138 138 88 88
207 69 48 166 128 48 152 138 45 55
17,000
Glaeser Booser Booser Booser Booser Booser Booser Booser Booser Booser
220 138 138 116 116 116 204 204 149 149
26 186 66 128 55 186 159 59 28 159
896 3,790 7,930 2,280 32,260 12,400 3,790 1,170 14,100
Booser Booser Booser Booser Booser Booser Booser Booser Booser Booser
82 316 316 127 116 188 188 188 77 171
124 54 57 12
8,270 2,620 1,310 97
20
1,100 1,380
171 171 110 110 204 260 260
131 83
11,700 3,450
Booser Booser Booser Booser Booser Booser Booser Glaeser Glaeser Glaeser
62 21 21 21 7 34 14
4,140
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
371 149 116 149 316 116 232 204
827 13,100 8,270 2,070 15,900 8,270 1,720 2,280
93
260 371
Wear Rate (mm3/m)
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TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
2.0E-10
Contact Geometry
PIN-ON-RING
Load (N)
Temp. (C)
3.9
Velocity (m/s)
Distance (m)
Specimen Shape
1.8
1.0E+04
PIN
2.7
1.1E+07
RING PIN PIN PIN
0.25
83 207 0.35 0.7 0.7
6.0E-09 3.0E-09 2.0E-09 1.0E-09
0.15 2.5 0.16
0.7 0.53 0.7
6.0E-10 4.0E-09
0.16
2.5
RING-ON-RING PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER
37
PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER
PIN PIN PIN PIN
0.012
0.17
0.42
13.8
1.75
41
0.1 4.0E-09
BLOCK-ON-RING
1.75
14.5
2.3
1.23 1.05 1.05
27.6 51.7 20.7 1.38
1.1
124
24
2.4
4250
BLOCK
2 7.0E-06
4.0E-09
BLOCK-ON-RING
2.0E-09
BLOCK-ON-RING
657
9.8
3.0E-07 4.0E-07 2.0E-07 6.0E-07
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
45 45 45 130
5.0E-09 4.0E-13 1.0E-12 4.0E-11
BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL
657 60 60 60
1
3.6E+06
BLOCK
0.05
1.2
BLOCK
24 24 24 24
2.4 2.4 2.4 2.4
4310 4250 4280 1440
BLOCK BLOCK BLOCK BLOCK
50 50 50
0.05 0.58 0.58 0.58
1.2 2100 2100 2100
BLOCK BALL BALL BALL
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
AIR
AIR
TUNGSTEN CARBIDE
ADHESIVE
AIR AIR
CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE
AIR AIR AIR AIR
CAST IRON CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR
CARBON STEEL
ADHESIVE
AIR
CARBON STEEL
AIR
AIR
CARBON STEEL
AFS 50/70 sand; 471 g/min AIR
CHLOROBUTYL CARBON STEEL
Boundary lubricated, oil-filled material
CARBON STEEL
LUBRICATED
Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
LUBRICATED LUBRICATED LUBRICATED ADHESIVE
AIR
MILD STEEL
ADHESIVE
AIR
M2 TOOL STEEL
ADHESIVE
AFS 50/70 sand; 435 g/min AFS 50/70 sand; 471 g/min AFS 50/70 sand; 234 g/min AFS 50/70 sand; 329 g/min; 49% RH
AIR Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Cyclohexyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Benzyl NH2;4 mmol/100g Paraf.Oil;
[email protected]
ASTM G65-D ASTM G65-B
ADHESIVE A60 SHORE HARDNESS
ABRASIVE
CHLOROBUTYL CHLOROBUTYL CHLOROBUTYL CHLOROBUTYL
A57 SHORE HARDNESS A59 SHORE HARDNESS A62 SHORE HARDNESS A60 SHORE HARDNESS
ABRASIVE ABRASIVE ABRASIVE ABRASIVE
M2 TOOL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL
ADHESIVE LUBRICATED LUBRICATED LUBRICATED
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
60 60
50 50
0.58 0.58
2100 2100
BALL BALL
60 60 60 60 130 130 60 60 60 60
50 50 50 50 24 24 50 50 50 50
0.58 0.58 0.58 0.58 2.4 2.4 0.58 0.58 0.58 0.58
2100 2100 2100 2100 4310 1440 2100 2100 2100 2100
BALL BALL BALL BALL BLOCK BLOCK BALL BALL BALL BALL
79 80
4.0E-12 3.0E-12
FOUR BALL FOUR BALL
81 82 83 84 85 86 87 88 89 90
1.0E-12 2.0E-11 2.0E-11 3.0E-11 1.0E-07 6.0E-07 3.0E-11 3.0E-11 5.0E-13 2.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL FOUR BALL
91 92 93 94 95 96 97 98 99 100
1.0E-10 6.0E-11 5.0E-13 4.0E-13 6.0E-13 6.0E-12 1.0E-11 3.0E-12 9.0E-13 2.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58
2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
101 102 103 104 105 106 107 108 109 110
1.0E-11 1.0E-12 5.0E-13 5.0E-13 4.0E-11 3.0E-11 2.0E-07 2.0E-11 6.0E-12 4.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 45 60 60 60
50 50 50 50 50 50 24 50 50 50
0.58 0.58 0.58
2100 2100 2100
0.58 2.4 0.58 0.58 0.58
2100 4310 2100 2100 2100
BALL BALL BALL BALL BALL BALL BLOCK BALL BALL BALL
111 112 113 114 115 116 117 118 119 120
2.0E-11 1.0E-07 3.0E-14 3.0E-11 3.0E-11 1.0E-06 3.0E-12 5.0E-13 1.0E-09 1.0E-11
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58
2100
0.58 0.58
2100 2100
0.58 0.58
2100 2100
0.58
2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
121 122 123 124 125 126 127 128 129 130
1.0E-11 2.0E-12 4.0E-13 4.0E-13 7.0E-12 4.0E-11 3.0E-13 5.0E-13 2.0E-07 6.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING FOUR BALL
60 60 60 60 60 60 60 60 45 60
50 50 50 50 50 50 50 50 24 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 2.4 0.58
2100 2100 2100 2100 2100 2100 2100 2100 4310 2100
BALL BALL BALL BALL BALL BALL BALL BALL BLOCK BALL
131 132 133 134 135 136 137 138 139 140
4.0E-12 9.0E-13 8.0E-12 3.0E-13 5.0E-11 1.0E-11 5.0E-11 3.0E-11 6.0E-12 8.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58
2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
141 142 143 144 145 146 147 148 149 150
4.0E-13 1.0E-11 5.0E-11 1.0E-12 5.0E-13 1.0E-11 8.0E-14 9.0E-11 9.0E-11 7.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.47 0.47 0.58 0.58 0.47
2100 2100 2100 2100 2100 1680 1680 2100 2100 1680
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
151 152 153 154 155
2.0E-13 6.0E-13 7.0E-12 7.0E-13 6.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60
50 50 50 50 50
0.56 0.56 0.47 0.56 0.56
2010 2010 1680 2010 2010
BALL BALL BALL BALL BALL
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
Paraf.Oil;
[email protected];Addit:Phosphate ;Diethyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Di-n-butyl;4 mmol/100g
STEEL STEEL
52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphate ;Di-n-dodecyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Dodecyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,H;4 mmol/100g Mineral Oil;
[email protected] AFS 50/70 sand; 380 g/min AFS 50/70 sand; 323 g/min Paraf.Oil;
[email protected];Addit:Disulfide;Di-(para-t-nonylphenyl);18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Octyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Butyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;n-Octyl NH2;4 mmol/100g
STEEL STEEL STEEL STEEL CHLOROBUTYL CHLOROBUTYL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS A60 SHORE HARDNESS 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE ABRASIVE LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Disulfide;Diethyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Butyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Di-2-ethylhexyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;2-Ethylhexyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Benzyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Tributyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Hexadecyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Methyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Lauryl,H;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Ethyl,Ethyl;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-SCH2COOC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Phenyl,H;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;t-Butyl,H;4 mmol/100g paraffin oil;tricresyl phosphate paraffinic oil Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;n-Octyl NH2;4 mmol/100g AFS 50/70 sand; 239 g/min Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)2COOC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;n-Butyl NH2;4mmol/100g Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;n-PropylNH2;4mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL CHLOROBUTYL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Disulfide;Di-(para-t-butylphenyl);18 mmol/100g dry air Formulated Engine Oil Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,H;4 mmol/100g Paraf.Oil;
[email protected] dry argon Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Ethyl NH2;4 mmol/100g Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;CyclohexylNH2;4mmol/100g Cyclohexane Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Dodecyl NH2;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;2-EthylhexylNH2;4mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;2-Ethylhexyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Tricresyl;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Ethyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Octadecyl;18 mmol/100g Paraf.Oil;
[email protected] Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Dodecyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Dodecyl,H;4 mmol/100g AFS 50/70 sand; 380 g/min Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Allyl,H;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL CHLOROBUTYL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,Benzyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,o-Nitrophenyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Diphenyl;18 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Octadecyl,H;4 mmol/100g Par.Oil;
[email protected];Add:Disulfide;Di-2,4,4Trimethylpentyl;18mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Dibenzyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-t-Octyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Dicyclohexyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,Phenyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Cyclohexyl,H;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;
[email protected];Add:Dibuytlphoshoramidate;n-Octyl,n-Octyl;4mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,Hexyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-2-Ethylhexyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Dilauryl;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Dodecyl NH2;4 mmol/100g Min.Oil;Addit:1-Chloro Hexadecane;2.0 Wt% Min.Oil;Addit:Tricresyl Phosphate + Oleic Acid;1.5+1.5 Wt% Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-S(CH2)3OC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-S(CH2)2OC2H5]2;2.3mmol/100g Min.Oil;Addit:Antimony Diakyldithiocarbamate;2.0 Wt%
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:ZnDialkylphos'o-dithioate;Isopropyl/p-Octylphenyl;.056Wt%P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isobutyl/Pentyl;0.056 Wt% P Min.Oil;Addit:Lead Naphthenate;1.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;C6-C10;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;2-Ethylhexyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
ASTM G65-A ASTM G65-B
ASTM G65-D
ASTM G65-D
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
156 157 158 159 160
3.0E-11 2.0E-11 7.0E-12 1.0E-11 8.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60
50 50 50 50 50
0.58 0.58 0.58 0.58 0.56
2100 2100 2100 2100 2010
BALL BALL BALL BALL BALL
161 162 163 164 165 166 167 168 169 170
7.0E-13 2.0E-13
FOUR BALL FOUR BALL
60 60
50 50
0.56 0.56
2010 2010
BALL BALL
4.0E-12 6.0E-13 5.0E-13 2.0E-13 2.0E-13 1.0E-11 1.0E-11
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60
50 50 50 50 50 50 50
0.58 0.56 0.56 0.56 0.56 0.47 0.47
2100 2010 2010 2010 2010 1680 1680
BALL BALL BALL BALL BALL BALL BALL
171 172 173 174 175 176 177 178 179 180
1.0E-11 2.0E-13 5.0E-13 3.0E-12 3.0E-14 2.0E-11 7.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60
50 50 50 50 50 50 50
0.47 0.56 0.56 0.47 0.47 0.47 0.56
1680 2010 2010 1680 1680 1680 2010
BALL BALL BALL BALL BALL BALL BALL
1.0E-11
FOUR BALL
60
50
0.56
2010
BALL
1.0E-11
FOUR BALL
60
50
0.47
1680
BALL
5.0E-13
FOUR BALL
60
50
0.58
2100
BALL
5.0E-06
PIN-ON-RING
3.9
1.8
1.0E+04
PIN
3.0E-09 6.0E-08
BLOCK-ON-RING BLOCK-ON-RING
9.8 130
1 2.4
3.6E+06 4.3E+03
BLOCK BLOCK
3.0E-07 4.0E-09 6.0E-08 2.0E-07
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING PIN-ON-RING
130 9.8 130 3.9
2.4 1 2.4 1.8
1.4E+03 3.6E+06 4.3E+03 1.0E+04
BLOCK BLOCK BLOCK PIN
BLOCK-ON-RING
9.8
1
3.6E+06
BLOCK
181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232
24
24 24
34.5
206 41.4
1.75
1.0E-07 3.0E-07
34.5 34.5 34.5 34.5 13.8
0.46
6.1
344
1.0E-08
PIN-ON-RING
3.9
1.8
1.0E+04
PIN
17
3.0E-07
BLOCK-ON-RING
9.8
1
3.6E+06
BLOCK
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)10COOC2H5]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)2COOC10H21]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)3COOC2H5]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)5COOC2H5]2;2.3mmol/100g Min.Oil;Addit:ZnDialkylphosphoro-dithioate;1-Methylheptyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:ZnDialkylphosphoro-dithioate;n-Butyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isobutyl;0.056 Wt% P
STEEL STEEL
52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED
Paraffin Oil;
[email protected] Min.Oil;Addit:ZnDialkylphosphoro-dithioate;2,2-Dimenthylpnetyl;0.12Wt%P Min.Oil;Add:ZnDialkylphos'o-dithioate;2-Ethylhexyl/p-Octylphenyl;.056Wt%P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;p-Octylphenyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphos'o-dithioate;Isobutyl/p-Octylphenyl;.056Wt%P Mineral Oil Min.Oil;Addit:Hexachloro-1, 3-Butandiene;2.0 Wt%
STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:Oleic Acid;2.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isopropyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;n-Dodecyl;0.12 Wt% P Min.Oil;Addit:Tricresyl Phosphate;1.5 Wt% Min.Oil;Addit:Zinc 0, 0-Dialkylphosphorodithioate;2.0 Wt% Min.Oil;Addit:Bis-(B-Chloroethyl) vinylphosphonate;1.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Sec-Butyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Mineral Oil
STEEL
52100 STEEL
LUBRICATED
Min.Oil;Addit:Perfluoroctanoic Acid;0.05 Wt%
STEEL
52100 STEEL
LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphonate;Stearyl,H;4 mmol/100g
STEEL
52100 STEEL
LUBRICATED
AIR
MILD STEEL
AIR AFS 50/70 sand; 353 g/min
MILD STEEL CHLOROBUTYL
AIR
AFS 50/70 sand; 324 g/min; 51% RH AIR AFS 50/70 sand; 300 g/min AIR
ASTM G65-A
ASTM G65-B ASTM G65-A
CHLOROBUTYL MILD STEEL CHLOROBUTYL TOOL STEEL
ADHESIVE
A60 SHORE HARDNESS
A60 SHORE HARDNESS A60 SHORE HARDNESS
ADHESIVE ABRASIVE
ABRASIVE ADHESIVE ABRASIVE ADHESIVE
AIR
CARBON STEEL
AIR AIR
MILD STEEL CARBON STEEL
ADHESIVE ADHESIVE
AIR AIR AIR AIR Boundary lubricated, oil-filled material
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
LUBRICATED
AIR
HARD STEEL
ADHESIVE
AIR
440C STAINLESS STEEL
ADHESIVE
8403/frame/ch15-Tbl 15.1(EF) Page 558 Friday, October 27, 2000 4:17 PM
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part E) Number 233 234 235 236 237 238 239 240
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Maximum Velocity (m/s)
2.0E-07 1.75 1.23
Contact Geometry
BLOCK-ON-RING
10 13.8 17.2 13.8 34.5
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
9.8
1
3.6E+06
BLOCK
6.1 4.1 1.0E-07 2.0E-08
3.0E-07 13.8 13.8
PIN-ON-RING
19.6
1.9
6.7E+04
PIN
PIN-ON-RING
19.6
0.13
9.7E+03
PIN
1.9 2.4
6.7E+04 4.3E+03
PIN BLOCK
0.15 0.15 0.15
220 220 220
BLOCK BLOCK BLOCK
2.4 2.4
4310 4360
BLOCK BLOCK
0.15 0.15 0.15
220 220 220
BLOCK BLOCK BLOCK
1.9
6.7E+04
PIN
0.21 0.21 0.13 0.13
27.6
251 252 253 254 255 256 257 258 259 260
24 26 28 27 27.6 24.1 20.7
261 262 263 264 265 266 267 268 269 270
2.0E-07
0.18
20.7
2.0E-07
0.21
34.5
1.0E-05 4.0E-08
PIN-ON-RING BLOCK-ON-RING
19.6 124
7.0E-09 8.0E-09 2.0E-09
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
134 137 402
3.0E-08 3.0E-08
BLOCK-ON-RING BLOCK-ON-RING
130 124
1.0E-08 1.0E-08 2.0E-09
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
401 137 137
1.0E-04
PIN-ON-RING
27.6
27.6
271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290
301 302 303 304 305 306 307 308 309 310
Friction Coefficent
14
241 242 243 244 245 246 247 248 249 250
291 292 293 294 295 296 297 298 299 300
Wear Constant (mm3/mm*N)
10.3 33 26 10.3 248 124 124
24
24 24
19.6
1
0.12
6.89
1.0E-09 7.0E-08
0.21 0.35
2
BUSHING-SHAFT BUSHING-SHAFT
24 24
0.5 0.5
BUSHING BUSHING
3
BUSHING-SHAFT
24
0.5
BUSHING
5.1
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24
0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING
1.052 0.05
1.23 0.702 0.09 0.0175
827 41 21 6.89 34 6.89
4.0E-09 5.0E-08 4.0E-09 3.0E-10 2.0E-09
0.15 0.28 0.38 0.25 0.37
1.5 8.1
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
AIR
MILD STEEL
ADHESIVE
Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material AIR AIR AIR
CARBON STEEL CARBON STEEL MILD STEEL CARBON STEEL CARBON STEEL
LUBRICATED LUBRICATED ADHESIVE ADHESIVE
AIR AIR AIR
STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR
CARBON STEEL
AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE
AIR
CARBON STEEL CARBON STEEL
ADHESIVE
AIR
CARBON STEEL
AIR
CARBON STEEL
AIR AFS 50/70 sand; 471 g/min
SILVER CHLOROBUTYL
AIR AIR AIR
4620 CARBURIZED STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL
AFS 50/70 sand; 239 g/min AFS 50/70 sand; 197 g/min
ASTM G65-A
CHLOROBUTYL CHLOROBUTYL
ADHESIVE
A60 SHORE HARDNESS
ADHESIVE ABRASIVE ADHESIVE ADHESIVE ADHESIVE
A60 SHORE HARDNESS A62 SHORE HARDNESS
ABRASIVE ABRASIVE
AIR AIR AIR AIR
CARBON STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL
ADHESIVE ADHESIVE ADHESIVE
AIR
ZINC
ADHESIVE
AIR AIR
CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
AIR
CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
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TABLE 15.1 Tribomaterials Database (Part E) Number 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
0.017 0.11
6.0E-08 1.0E-08
0.07 0.39 0.24
0.18 0.053 0.049
3.0E-08 7.0E-09 4.0E-07
0.37 0.37 0.1 0.15
8.0E-10 5.0E-09 4.0E-10 5.0E-10 6.0E-09
0.14 0.34 0.16 0.12 0.16
8.0E-10 8.0E-10 2.0E-10 8.0E-10
0.2 0.31 0.18 0.09
3.45
Maximum Velocity (m/s)
0.25
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24
0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24
0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
7 0.3 0.7 0.44 0.32 0.14 0.88 0.35 0.61 0.21
0.53 1.58 0.3
13.8 13.8
50 41.4
0.7 0.77 0.54
0.7 0.56 0.18 0.3
1.23 0.53 0.56 0.351
4.1
0.2
2.0E-09 3.0E-09 2.0E-09 5.0E-10 2.0E-09 3.0E-10 1.0E-09
0.26 0.17 0.22 0.15 0.15 0.27 0.17 0.16
9.0E-10
0.13
6.0E-10 5.0E-09 2.0E-09 3.0E-09 5.0E-09 1.0E-09 7.0E-10 2.0E-09
0.27 0.16 0.2 0.29 0.1 0.11 0.14
3.0E-09 9.0E-10 3.0E-09 1.0E-09 4.0E-11 1.0E-10 6.0E-11
8.1
0.22 0.14 0.34 0.32
0.0105
138 17.2 17.2 7 41 55
0.0119
55
0.24
0.877
414
0.03
0.09 0.07
1 5.1 5.1
0.3
Notes: 1. This Table is a row/column array of size 368 rows by 43 columns. Each row is a database record (the results of one or more tests); each column is a database field (a significant test or material parameter). In printed form, it is necessary to subdivide the array to suit the printed page size. This was accomplished by division of the array into 6 parts (A, B, C,…F) each containing 6 or more columns, and further dividing each part into 5 pages, resulting in 30 pagesized sub-arrays. The first sub-array is set of columns and rows starting at the upper left corner of the array. The next sub-array fits below the first, etc. Each page contains appropriate headings and seventy to eighty records that are numbered in the left-most column so that they can be followed across the array. Every tenth record is followed by a solid line to facilitate reading. 2. The data records are sorted alphabetically by class, sub-class, and common name in that order. The common name field is shown first. 3. Each record contains material description data and many but not all records have tribological test data. 4. All records that contain tribological data result from sliding test conditions. All records refer to air environment testing unless special evironmental conditions were established at the tribological contact and are so stated. 5. The user is cautioned about use of any record where important test parameters are not given. This results from lack of reporting by the original source of data. The significance of an incomplete description of test conditions or material description, and any resulting effect on the reported data, must be judged by the individual user. Data Sources: Alloy Digest, (Alloy Digest, Inc, Orange, N.J.). Ashby, M. F. and Jones, D. R. H., Engineering Materials, Pergammon, Oxford, (1980). ASM, International, Metals Handbooks, 8th edition (ASM Intern., Metals Park, OH 44073). ASM, International, Aluminum-Properties, Physical Metallurgy, Phase Diagrams, Vol.1(1967).
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
AIR AIR AIR AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
AIR AIR AIR AIR AIR AIR AIR AIR AIR
AIR AIR AIR AIR AIR AIR
Counterface Description
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
Wear Type ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
ASME, Wear of Materials, Conference Proceedings, (ASME, NY, 1977-1987). ASTM, unpublished data in ASTM Research Report relative to Standard G-65, (ASTM, W. Conshohocken, PA) ASME, Metals Properties, ASME Handbook (1954). Battelle Tribology Laboratory, Columbus, Ohio., private communication of unpublished data. Booser, E. R., ed. Handbook of Lubrication, Vol. I (1983) and Vol. II (1984) (CRC Press, Boca Raton, FL 33431). CRC Publ. Co., Handbook of Chemistry and Physics, 69th Edition, (1988). Encyclopedia of Chemical Technology, 3rd Edition, Vols. 3,4,16,18,23. Glaeser, W., pp. 313-326, in Wear Control Handbook, Peterson, M. B. and Winer, W. O., eds., ASME, New York, NY, 1980. Hertzberg, R. W., Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., Wiley, NY, (1989). Lynch, C. T., Engineering Properties of Ceramics, AFML Report TR-66-52, WPAFB, (1966). Modern Plastics Encyclopedia-88 (McGraw Hill, NY, 1988). Morey, C. Properties of Glass, (1938). National Center of Tribology, Polymer Materials for Bearing Surfaces, (Risley, UK, 1983). NIST-Thermo-Physical Data Center, Thermophysical Properties of Matter; Data Series, Vols, 1,4 (1970). Rowe, C. N., pp. 143-160 in Wear Control Handbook, Peterson, M. B. and Winer, W. O., eds., ASME, New York, NY, 1980. Shah, Vishu, ed. Handbook of Plastics Testing Technology, (Wiley, 1984). Smithells Metal Reference Book, (Butterworths, London, 1955). Smithsonian Physical Tables, 9th Edition, (1964). Standards Handbook: Copper — Brass — Bronze, Alloy Data/7 and Alloy Data/2 (Copper Development Association Inc, 1985). Touloukin, Y. S. et al., Thermophysical Properties of Matter, (IFI Plenum, NY, 1972).
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II Micro/Nanotribology Bharat Bhushan The Ohio State University
Othmar Marti University of Ulm 16 Microtribology and Microrheology of Molecularly Thin Liquid Films Alan D. Berman and Jacob N. Israelachvili ......................................................................... 567 Introduction • Solvation and Structural Forces: Forces Due to Liquid and Surface Structure • Adhesion and Capillary Forces • Nonequilibrium Interactions: Adhesion Hysteresis • Rheology of Molecularly Thin Films: Nanorheology • Interfacial and Boundary Friction: Molecular Tribology • Theories of Interfacial Friction • Friction and Lubrication of Thin Liquid Films • Stick-Slip Friction
17 Measurement of Adhesion and Pull-Off Forces with the AFM Othmar Marti ......... 617 Introduction • Experimental Procedures to Measure Adhesion in AFM and Applications • Summary and Outlook
18 Atomic-Scale Friction Studies Using Scanning Force Microscopy Udo D. Schwarz and Hendrik Hölscher ............................................................................................ 641 Introduction • The Scanning Force Microscope as a Tool for Nanotribology • The Mechanics of a Nanometer-Sized Contact • Amontons’ Laws at the Nanometer Scale • The Influence of the Surface Structure on Friction • Atomic Mechanism of Friction • The Velocity Dependence of Friction • Summary
19 Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy Bharat Bhushan ................................................................................. 667 Introduction • Description of AFM/FFM and Various Measurement Techniques • Friction and Adhesion • Scratching, Wear, and Fabrication/Machining • Indentation • Boundary Lubrication • Closure
20 Computer Simulations of Friction, Lubrication, and Wear Mark O. Robbins and Martin H. Müser ........................................................................................................... 717 Introduction • Atomistic Computer Simulations • Wearless Friction in Low-Dimensional Systems • Dry Sliding of Crystalline Surfaces • Lubricated Surfaces • Stick-Slip Dynamics • Strongly Irreversible Tribological Processes
563
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564
M
Micro/Nanotribology
icro/nanotribology involve studies of friction and wear processes ranging from microscopic to atomic levels, whereas classical tribology and rheology deal with large sample volumes which can be viewed as a continuum. The experiments in the field of micro/nanotribology are conducted using either surface force apparatus or a variety of scanning probe microscopes (SPMs). Surface force apparatus is generally used to study rheology of molecular thick liquid films sandwiched between atomically smooth (many times, optically transparent) surfaces. At most solid–solid interfaces of technological relevance, contact occurs at numerous asperities. In a scanning probe microscope, a sharp tip sliding on a surface simulates just one such contact. Atomic force/friction force microscopes (AFM/FFM), a form of SPM, are used to study various tribological phenomena. AFM/FFM techniques are increasingly used for tribological studies of engineering surfaces at scales ranging from atomic and molecular to microscale; studies include surface roughness, adhesion, friction, scratching, wear, indentation, detection of material transfer and boundary lubrication. Molecular dynamic simulations are carried out to model interfacial processes on a nanoscale. The techniques dealt with in this section are on the borderline between the atomistic/molecular view and the classical one. The first chapter of this section deals with questions of dissipation in nanoscopic volumes using surface force apparatus. Micro- and nanorheology help us to understand how liquid or liquid-like films only a few molecules in thickness behave under shearing stress. It is found that the nature and shape of the molecules profoundly alter the shearing behavior of the systems. Specifically, the shear stiffness is a periodic function of the film thickness, with the diameter of the molecules determining the period. The findings, obtained with the surface force apparatus, give important design parameters for the lubrication of hard disks, for example. The possibility to measure the shear response at large shear rates with vanishingly small probe volumes may help in a first screening of new substances. The loading force of a contact is not only given by the external force, but also by the interfacial adhesion forces between the two bodies in contact. The next chapter outlines the measurement of adhesion and pull-off forces by the scanning probe microscope. It is shown that heterogeneous samples can be segmented into their components by the adhesion force. Again one of the important questions still open is that of the applicability of continuum mechanics models. Molecular interaction might have a non-negligible influence for small tips. Increasing the resolution of the instrument, the chapter on the atomic scale friction measurements explains the theory and experimental details of this technique. On an atomic level, one can have dissipative, but not plowing friction. Mapping of the samples enables the seasoned researcher to extract important information on the surface and its interaction potential with the tip. This means that the very nature of the surface determines friction coefficients. Since the wear part of the friction is mostly not present at atomic scales, the friction can be much lower than in the macroscopic case. Even though the AFM can be operated in the wearless regime it is also possible to operate the instrument at higher loads for friction studies as well as for scratch/wear and indentation studies. The nanoindentation and the nanoscratch operation allow us to probe the elastic/plastic response of nanometer films and of small amounts of material. The experiments are similar to the failure mechanism one would expect if a hard disk slider touched a surface or if a MEMS device were to undergo the first steps of a catastrophic failure. An overview of various tribological studies being conducted by scanning probe microscopy are given in the next chapter. Investigations of scratching, wear, and indentation on nanoscales using the AFM can provide insights into failure mechanisms of materials. Coefficients of friction, wear rates, and mechanical properties such as hardness have been found to be different on the nanoscale than on the macroscale; generally, coefficients of friction and wear rates on micro- and nanoscales are smaller, whereas hardness is greater. Therefore, micro/nanotribological studies may help define the regimes for ultra-low friction and near zero wear. The last chapter of this section gives an overview on the theoretical concepts behind simulations. Results derived from these simulations are compared to the theory. First a brief overview of common simulation methods concentrates on the relative strengths and weaknesses and the fields of application of these methods. The friction between two crystalline surfaces is calculated using simple spring models. Adsorbed layers are added to make the simulation more realistic. In a final step, friction between metals is considered. This part shows nicely where the difficulties lie when trying to bridge the gap between the
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565
world of atoms and single molecules and the macroscopic world. Then lubrication on an atomic scale is considered. This part of the chapter is a complement to the first chapter. This is also true for the wall induced structures, which were shown to be of utmost importance to understand the shear behavior in the first chapter. The flow boundary condition on the walls and the solidification of liquids in extremely constrained structures are additional features found both in the simulations and the experiment. Stickslip motion is finally explained using molecular models. This section gives an overview of the status of both the experimental and the theoretical work. It is clear that tremendous progress has been made, but there is a gap between the theoretical models and experimental data that needs to be bridged.
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16 Microtribology and Microrheology of Molecularly Thin Liquid Films 16.1 16.2
Introduction ..................................................................... 568 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure .......................................... 568 Effects of Surface Structure • Effect of Surface Curvature and Geometry
16.3
Adhesion and Capillary Forces ....................................... 572
16.4 16.5
Nonequilibrium Interactions: Adhesion Hysteresis....... 574 Rheology of Molecularly Thin Films: Nanorheology ................................................................... 576
Adhesion Mechanics
Different Modes of Friction: Limits of Continuum Models • Viscous Forces and Friction of Thick Films: Continuum Regime • Friction of Intermediate Thickness Films
16.6
Interfacial and Boundary Friction: Molecular Tribology........................................................................... 582 General Interfacial Friction • Boundary Friction of Surfactant Monolayer Coated Surfaces • Boundary Lubrication of Molecularly Thin Liquid Films • Transition from Interfacial to Normal Friction (with Wear)
16.7
Theories of Interfacial Friction....................................... 587 Theoretical Modeling of Interfacial Friction: Molecular Tribology • Adhesion Force Contribution to Interfacial Friction • Relation Between Boundary Friction and Adhesion Energy Hysteresis • External Load Contribution to Interfacial Friction • Simple Molecular Model of Energy Dissipation ε
16.8
Smooth and Stick-Slip Sliding • Role of Molecular Shape and Liquid Structure
Alan D. Berman Seagate Removable Storage Solutions
Jacob N. Israelachvili University of California
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
Friction and Lubrication of Thin Liquid Films............. 594
16.9
Stick-Slip Friction ............................................................ 600 Rough Surfaces Model • Distance-Dependent Model • Velocity-Dependent Friction Model • Phase Transitions Model • Critical Velocity for Stick-Slip • Dynamic Phase Diagram Representation of Tribological Parameters
567
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16.1 Introduction When a bow is gently pulled across a violin string to produce a rich C note, it sounds very elegant and simple. In analyzing the source of the sound — the sliding of a bow with resin over a tuned string — the physics seems simple. At first glance is would appear that the “lubricating” resin would be undergoing Couette flow between the bow and the string, but such dynamics would not produce the resonance in the string. Instead, it is the far more complex stick-slip type of frictional sliding between the moving parts that excites the resonance and creates the sound. Other similar examples such as door hinges or wheel bearings are ideally described by engineering hydrodynamics. However, when the door creaks or the wheel squeaks, there is a transition from a system described by bulk lubrication to a system controlled by microtribology (or what is now referred to as nanotribology). These latter two cases of lubrication failure result in the sliding surfaces interacting directly, or with a very thin lubricating film that behaves differently from the bulk lubricant in the “quiet” condition. This chapter seeks to explore the transition from bulk lubrication to microscale rheology and tribology, and how such systems are better described. As lubricating layers become thinner, their properties change not only quantitatively, but also qualitatively, as surface forces become dominant and liquid properties change under confinement. The effects of these on the tribology and rheology of thin films will be described.
16.2 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure When a liquid is confined within a restricted space, for example, a very thin film between two surfaces, it ceases to behave as a structureless continuum. Likewise, the forces between two surfaces close together in liquids can no longer be described by simple continuum theories. Thus, at small surface separations — below about 10 molecular diameters — the van der Waals force between two surfaces or even two solute molecules in a liquid (solvent) is no longer a smoothly varying attraction. Instead, there now arises an additional “solvation” force that generally oscillates with distance, varying between attraction and repulsion, with a periodicity equal to some mean dimension σ of the liquid molecules (Horn and Israelachvili, 1981). Figure 16.1 shows the force-law between two smooth mica surfaces across the hydrocarbon liquid tetradecane, whose inert chain-like molecules have a width of σ ≈ 0.4 nm. The short-range oscillatory force-law, varying between attraction and repulsion with a molecular-scale periodicity is related to the “density distribution function” and “potential of mean force” characteristic of intermolecular interactions in liquids. These forces arise from the confining effect that two surfaces have on the liquid molecules between them, forcing them to order into quasi-discrete layers which are energetically or entropically favored (and correspond to the free energy minima) while fractional layers are disfavored (energy maxima). The effect is quite general and arises with all simple liquids when they are confined between two smooth surfaces, both flat and curved. Oscillatory forces do not require that there be any attractive liquid–liquid or liquid–wall interaction. All one needs is two hard walls confining molecules whose shapes are not too irregular and which are free to exchange with molecules in the bulk liquid reservoir. In the absence of any attractive forces between the molecules, the bulk liquid density may be maintained by an external hydrostatic pressure. In real liquids, attractive van der Waals forces play the role of the external pressure, but the oscillatory forces are much the same. Oscillatory forces are now well understood theoretically, at least for simple liquids, and a number of theoretical studies and computer simulations of various confined liquids, including water, which interact via some form of the Lennard–Jones potentials have invariably led to an oscillatory solvation force at surface separations below a few molecular diameters (Snook and van Megan, 1979, 1980, 1981; van Megan and Snook, 1979, 1981; Kjellander and Marcelja, 1985a,b; Tarazona and Vicente, 1985; Henderson and Lozada-Cassou, 1986; Evans and Parry, 1990).
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FIGURE 16.1 Solid curve: Forces between two mica surfaces across saturated linear chain alkanes such as n-tetradecane (Christenson et al., 1987; Horn and Israelachvili, 1988; Israelachvili and Kott, 1988; Horn et al., 1989). The 0.4 nm periodicity of the oscillations indicates that the molecules align with their long axis preferentially parallel to the surfaces, as shown schematically in the upper insert. The theoretical continuum van der Waals force is shown by the dotted line. Dashed line: Smooth, nonoscillatory force-law exhibited by irregularly shaped alkanes, such as branched isoparaffins, that cannot order into well-defined layers (lower insert) (Christenson et al., 1987). Similar nonoscillatory forces are also observed between “rough” surfaces, even when these interact across a saturated linear chain liquid. This is because the irregularly-shaped surfaces (rather than the liquid) now prevent the liquid molecules from ordering in the gap. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
In a first approximation, the oscillatory force laws may be described by an exponentially decaying cosine function of the form
(
)
E ≈ Eo cos 2πD σ e − D σ
(16.1)
where both theory and experiments show that the oscillatory period and the characteristic decay length of the envelope are close to σ (Tarazona and Vicente, 1985). It is important to note that once the solvation zones of two surfaces overlap, the mean liquid density in the gap is no longer the same as that of the bulk liquid. And since the van der Waals interaction depends on the optical properties of the liquid, which in turn depend on the density, one can see why the van der Waals and oscillatory solvation forces are not strictly additive. Indeed, it is more correct to think of the solvation force as the van der Waals force at small separations, with the molecular properties and density variations of the medium taken into account. It is also important to appreciate that solvation forces do not arise simply because liquid molecules tend to structure into semi-ordered layers at surfaces. They arise because of the disruption or change of this ordering during the approach of a second surface. If there were no change, there would be no solvation force. The two effects are of course related: the greater the tendency toward structuring at an isolated surface, the greater the solvation force between two such surfaces, but there is a real distinction between the two phenomena that should always be borne in mind.
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Concerning the adhesion energy or force of two smooth surfaces in simple liquids, a glance at Figure 16.1 and Equation 16.1 shows that oscillatory forces lead to multivalued, or “quantized,” adhesion values, depending on which energy minimum two surfaces are being separated from. For an interaction energy that varies as described by Equation 16.1, the quantized adhesion energies will be Eo at D = 0 (primary minimum), Eo /e at D = σ (second minimum), Eo /e2 at D = 2σ, etc. Such multivalued adhesion forces have been observed in a number of systems, including the interactions of fibers. Most interesting, the depth of the potential energy well at contact (–Eo at D = 0) is generally deeper but of similar magnitude to the value expected from the continuum Lifshitz theory of van der Waals forces (at a cutoff separation of D0 ≈ 0.15 to 0.20 nm), even though the continuum theory fails to describe the shape of the force-law at intermediate separations. There is a rapidly growing literature on experimental measurements and other phenomena associated with short-range oscillatory solvation forces. The simplest systems so far investigated have involved measurements of these forces between molecularly smooth surfaces in organic liquids. Subsequent measurements of oscillatory forces between different surfaces across both aqueous and nonaqueous liquids have revealed their subtle nature and richness of properties (Christenson, 1985; Christenson and Horn, 1985; Israelachvili, 1987; Christenson, 1988a; Israelachvili and McGuiggan 1988), for example, their great sensitivity to the shape and rigidity of the solvent molecules, to the presence of other components, and to the structure of the confining surfaces. In particular, the oscillations can be smeared out if the molecules are irregularly shaped (e.g., branched) and therefore unable to pack into ordered layers, or when the interacting surfaces are rough or fluid-like (e.g., surfactant micelles or lipid bilayers in water) even at the Ångstrom level (Gee and Israelachvili, 1990).
16.2.1 Effects of Surface Structure It has recently been appreciated that the structure of the confining surfaces is just as important as the nature of the liquid for determining the solvation forces (Rhykerd et al., 1987; Schoen et al., 1987, 1989; Landman, et al., 1990; Thompson and Robbins, 1990; Han et al., 1993). Between two surfaces that are completely smooth or “unstructured,” the liquid molecules will be induced to order into layers, but there will be no lateral ordering within the layers. In other words, there will be positional ordering normal but not parallel to the surfaces. However, if the surfaces have a crystalline (periodic) lattice, this will induce ordering parallel to the surfaces as well, and the oscillatory force then also depends on the structure of the surface lattices. Further, if the two lattices have different dimensions (“mismatched” or “incommensurate” lattices), or if the lattices are similar but are not in register and are at some “twist angle” relative to each other, the oscillatory force-law is further modified. McGuiggan and Israelachvili (1990) measured the adhesion forces and interaction potentials between two mica surfaces as a function of the orientation (twist angle) of their surface lattices. The forces were measured in air, in water, and in an aqueous salt solution where oscillatory structural forces were present. In air, the adhesion was found to be relatively independent of the twist angle θ due to the adsorption of a 0.4-nm-thick amorphous layer of organics and water at the interface. The adhesion in water is shown in Figure 16.2. Apart from a relatively angle-independent “baseline” adhesion, sharp adhesion peaks (energy minima) occurred at θ = 0°, ±60°, ±120° and 180°, corresponding to the “coincidence” angles of the surface lattices. As little as ±1° away from these peaks, the energy decreases by 30 to 50%. In aqueous salt (KCl) solution, due to potassium ion adsorption, the water between the surfaces becomes ordered, resulting in an oscillatory force profile where the adhesive minima occur at discrete separations of about 0.25 nm, corresponding to integral numbers of water layers. The whole interaction potential was now found to depend on orientation of the surface lattices, and the effect extended at least four molecular layers. Although oscillatory forces are predicted from Monte Carlo and molecular dynamic simulations, no theory has yet taken into account the effect of surface structure, or atomic “corrugations,” on these forces, nor any lattice mismatching effects. As shown by the experiments, within the last one or two nanometers, these effects can alter the adhesive minima at a given separation by a factor of two. The force barriers,
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FIGURE 16.2 Adhesion energy for two mica surfaces in a primary minimum contact in water as a function of the mismatch angle θ about θ = 0° between the two contacting surface lattices (McGuiggan and Israelachvili, 1990). Similar peaks are obtained at the other “coincidence” angles: θ = ±60°, ±120°, and 180° (inset). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
or maxima, may also depend on orientation. This could be even more important than the effects on the minima. A high barrier could prevent two surfaces from coming closer together into a much deeper adhesive well. Thus, the maxima can effectively contribute to determining not only the final separation of two surfaces, but also their final adhesion. Such considerations should be particularly important for determining the thickness and strength of intergranular spaces in ceramics, the adhesion forces between colloidal particles in concentrated electrolyte solutions, and the forces between two surfaces in a crack containing capillary condensed water. The intervening medium profoundly influences how one surface interacts with the other. As experimental results show (McGuiggan and Israelachvili, 1990), when two surfaces are separated by as little as 0.4 nm of an amorphous material, such as adsorbed organics from air, then the surface granularity can be completely masked and there is no mismatch effect on the adhesion. However, with another medium, such as pure water which is presumably well ordered when confined between two mica lattices, the atomic granularity is apparent and alters the adhesion forces and whole interaction potential out to D > 1 nm. Thus, it is not only the surface structure but also the liquid structure, or that of the intervening film material, that together determine the short-range interaction and adhesion. On the other hand, for surfaces that are randomly rough, the oscillatory force becomes smoothed out and disappears altogether, to be replaced by a purely monotonic solvation force. This occurs even if the liquid molecules themselves are perfectly capable of ordering into layers. The situation of symmetric liquid molecules confined between rough surfaces is therefore not unlike that of asymmetric molecules between smooth surfaces (see Figure 16.1). To summarize some of the above points, for there to be an oscillatory solvation force, the liquid molecules must be able to be correlated over a reasonably long range. This requires that both the liquid molecules and the surfaces have a high degree of order or symmetry. If either is missing, so will be the oscillations. A roughness of only a few Ångstroms is often sufficient to eliminate any oscillatory component of a force law.
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16.2.2 Effect of Surface Curvature and Geometry It is easy to understand how oscillatory forces arise between two flat, plane parallel surfaces (Figure 16.2). Between two curved surfaces, e.g., two spheres, one might imagine the molecular ordering and oscillatory forces to be smeared out in the same way that they are smeared out between two randomly rough surfaces. However, this is not the case. Ordering can occur so long as the curvature or roughness is itself regular or uniform, i.e., not random. This interesting matter is due to the Derjaguin approximation (Derjaguin, 1934), which relates the force between two curved surfaces to the energy between two flat surfaces. If the latter is given by a decaying oscillatory function, as in Equation 16.1, then the energy between two curved surfaces will simply be the integral of that function, and since the integral of a cosine function is another cosine function, with some appropriate phase shift, we see why periodic oscillations will not be smeared out simply by changing the surface curvature. Likewise, two surfaces with regularly curved regions will also retain their oscillatory force profile, albeit modified, so long as the corrugations are truly regular, i.e., periodic. On the other hand, surface roughness, even on the nanometer scale, can smear out any oscillations if the roughness is random and the liquid molecules are smaller than the size of the surface asperities.
16.3 Adhesion and Capillary Forces When considering the adhesion of two solid surfaces or particles in air or in a liquid, it is easy to overlook or underestimate the important role of capillary forces, i.e., forces arising from the Laplace pressure of curved menisci which have formed as a consequence of the condensation of a liquid between and around two adhering surfaces (Figure 16.3). The adhesion force between a spherical particle of radius R and a flat surface in an inert atmosphere is
FS = 4 πRγ SV
(16.2)
but in an atmosphere containing a condensable vapor, the above becomes replaced by
(
FS = 4 πR γ LV cos θ + γ SL
)
(16.3)
where the first term is due to the Laplace pressure of the meniscus and the second is due to the direct adhesion of the two contacting solids within the liquid. Note that the above equation does not contain the radius of curvature, r, of the liquid meniscus (Figure 16.3). This is because for smaller r the Laplace pressure γ LV/r increases, but the area over which it acts decreases by the same amount, so the two effects cancel out. A natural question arises as to the smallest value of r for which Equation 16.3 will apply. Experiments with inert liquids, such as hydrocarbons, condensing between two mica surfaces indicate that Equation 16.3 is valid for values of r as small as 1 to 2 nm, corresponding to vapor pressures as low as 40% of saturation (Fisher and Israelachvili, 1981; Christenson, 1988b). With water condensing from vapor or from oil it appears that the bulk value of γ LV is also applicable for meniscus radii as small as 2 nm. The capillary condensation of liquids, especially water, from vapor can have additional effects on the whole physical state of the contact zone. For example, if the surfaces contain ions, these will diffuse and build up within the liquid bridge, thereby changing the chemical composition of the contact zone as well as influencing the adhesion. More dramatic effects can occur with amphiphilic surfaces, i.e., those containing surfactant or polymer molecules. In dry air, such surfaces are usually nonpolar — exposing hydrophobic groups such as hydrocarbon chains. On exposure to humid air, the molecules can overturn so that the surface nonpolar groups become replaced by polar groups, which renders the surfaces hydrophilic. When two such surfaces come into contact, water will condense around the contact zone and the adhesion force will also be affected — generally increasing well above the value expected for inert hydrophobic surfaces.
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FIGURE 16.3 Sphere on flat in an inert atmosphere (top) and in an atmosphere containing vapor that can “capillary condense” around the contact zone (bottom). At equilibrium the concave radius, r, of the liquid meniscus is given by the Kelvin equation. The radius r increases with the relative vapor pressure, but for condensation to occur, the contact angle θ must be less than 90° or else a concave meniscus cannot form. The presence of capillary condensed liquid changes the adhesion force, as given by Equations 16.2 and 16.3. Note that this change is independent of r so long as the surfaces are perfectly smooth. Experimentally, it is found that for simple inert liquids such as cyclohexane, these equations are valid at Kelvin radii as small as 1 nm — about the size of the molecules themselves. Capillary condensation also occurs in binary liquid systems, e.g., when small amounts of water dissolved in hydrocarbon liquids condense around two contacting hydrophilic surfaces, or when a vapor cavity forms in water around two hydrophobic surfaces. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
It is clear that the adhesion of two surfaces in vapor or a solvent can often be largely determined by capillary forces arising from the condensation of liquid that may be present only in very small quantities, e.g., 10 to 20% of saturation in the vapor, or 20 ppm in the solvent.
16.3.1 Adhesion Mechanics Modern theories of the adhesion mechanics of two contacting solid surfaces are based on the Johnson–Kendall–Roberts (JKR) theory (Johnson et al., 1971; Pollock et al., 1978; Barquins and Maugis, 1982). In the JKR theory two spheres of radii R1 and R2, bulk elastic moduli K, and surface energy γ per unit area, will flatten when in contact. The contact area will increase under an external load or force F, such that at mechanical equilibrium the contact radius r is given by
r3 =
R F + 6 πRγ + 12πRγF + 6 πRγ K
(
) 2
(16.4)
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where R = R1R2 /(R1+R2). Another important result of the JKR theory gives the adhesion force or “pull off ” force:
FS = −3πRγ S
(16.5)
where, by definition, the surface energy γS, is related to the reversible work of adhesion W, by W = 2γS. Note that according to the JKR theory a finite elastic modulus, K, while having an effect on the loadarea curve, has no effect on the adhesion force — an interesting and unexpected result that has nevertheless been verified experimentally (Johnson et al., 1971; Israelachvili, 1991). Equations 16.4 and 16.5 are the basic equations of the JKR theory and provide the framework for analyzing the results of adhesion measurements of contacting solids, known as “contact mechanics” (Pollock et al., 1978; Barquins and Maugis, 1982), and for studying the effects of surface conditions and time on adhesion energy hysteresis (see next section).
16.4 Nonequilibrium Interactions: Adhesion Hysteresis Under ideal conditions the adhesion energy is a well-defined thermodynamic quantity. It is normally denoted by E or W (the work of adhesion) or γ (the surface tension, where W = 2γ), and it gives the reversible work done on bringing two surfaces together or the work needed to separate two surfaces from contact. Under ideal, equilibrium conditions these two quantities are the same, but under most realistic conditions they are not: the work needed to separate two surfaces is always greater than that originally gained on bringing them together. An understanding of the molecular mechanisms underlying this phenomenon is essential for understanding many adhesion phenomena, energy dissipation during loading–unloading cycles, contact angle hysteresis, and the molecular mechanisms associated with many frictional processes. It is wrong to think that hysteresis arises because of some imperfection in the system, such as rough or chemically heterogeneous surfaces or because the supporting material is viscoelastic; adhesion hysteresis can arise even between perfectly smooth and chemically homogenous surfaces supported by perfectly elastic materials, and can be responsible for such phenomena as “rolling” friction and elastoplastic adhesive contacts (Bowden and Tabor, 1967; Greenwood and Johnson, 1981; Maugis, 1985; Michel and Shanahan, 1990) during loading–unloading and adhesion–decohesion cycles. Adhesion hysteresis may be thought of as being due to mechanical or chemical effects, as illustrated in Figure 16.4. In general, if the energy change, or work done, on separating two surfaces from adhesive contact is not fully recoverable on bringing the two surfaces back into contact again, the adhesion hysteresis may be expressed as
W
R Receding
> WA Advancing
or
(
)
∆W = WR − WA > 0
(16.6)
where WR and WA are the adhesion or surface energies for receding (separating) and advancing (approaching) two solid surfaces, respectively. Figure 16.5 shows the results of a typical experiment that measures the adhesion hysteresis between two surfaces (Chaudhury and Whitesides, 1991; Chen et al., 1991). In this case, two identical surfactant-coated mica surfaces were used in a Surface Forces Apparatus. By measuring the contact radius as a function of applied load both for increasing and decreasing loads, two different curves are obtained. These can be fitted to the JKR equation, Equation 16.4, to obtain the advancing (loading) and receding (unloading) surface energies.
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MECHANICAL ADHESION HYSTERESIS
A
S′
Approach (Advance)
S′
WA
S
Separation (Recede) Contact
Macroscopic jumps S′
Molecular jumps Out In
Popped bond
KS
B
WR
D
S S‘
Repulsion Distance, D
0
C
FORCE
Jump in
DR DA
o
pe
Sl
=
KS Attraction
Jump out D0
D CHEMICAL ADHESION HYSTERESIS FIGURE 16.4 Origin of adhesion hysteresis during the approach and separation of two solid surfaces. (A) In all realistic situations the force between two solid surfaces is never measured at the surfaces themselves, S, but at some other point, say S′, to which the force is elastically transmitted via the backing material supporting the surfaces. (B, left) “Magnet” analogy of how mechanical adhesion hysteresis arises for two approaching or separating surfaces, where the lower is fixed and where the other is supported at the end of a spring of stiffness KS. (B, right) On the molecular or atomic level, the separation of two surfaces is accompanied by the spontaneous breaking of bonds, which is analogous to the jump apart of two macroscopic surfaces or magnets. (C) Force–distance curve for two surfaces interacting via an attractive van der Waals-type force law, showing the path taken by the upper surface on approach and separation. On approach, an instability occurs at D = DA, where the surfaces spontaneously jump into “contact” at D ≈ Do. On separation, another instability occurs where the surfaces jump apart from ~Do to DR. (D) Chemical adhesion hysteresis produced by interdiffusion, interdigitation, molecular reorientations and exchange processes occurring at an interface after contact. This induces roughness and chemical heterogeneity even though initially (and after separation and reequilibration) both surfaces are perfectly smooth and chemically homogeneous. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Hysteresis effects are also commonly observed in wetting/dewetting phenomena (Miller and Neogi, 1985). For example, when a liquid spreads and then retracts from a surface, the advancing contact angle θA is generally larger than the receding angle θR. Since the contact angle, θ, is related to the liquid–vapor surface tension, γ, and the solid–liquid adhesion energy, W, by the Dupré equation:
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FIGURE 16.5 Measured advancing and receding radius vs. load curves for two surfactant-coated mica surfaces of initial, undeformed radii R ≈ 1 cm. Each surface had a monolayer of CTAB (cetyl-trimethyl-ammonium-bromide) on it of mean area 60 Å2 per molecule. The solid lines are based on fitting the advancing and receding branches to the JKR equation, Equation 16.4, from which the indicated values of γA and γR were determined, in units of mJ/m2 or erg/cm2. The advancing/receding rates were about 1 µm/sec. At the end of each unloading cycle the pull-off force, Fs, can be measured, from which another value for γR can be obtained using Equation 16.5. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
(1+ cosθ) γ
L
=W
(16.7)
we see that wetting hysteresis or contact angle hysteresis (θA > θR) actually implies adhesion hysteresis, WR > WA , as given by Equation 16.6. Energy dissipating processes such as adhesion and contact angle hysteresis arise because of practical constraints of the finite time of measurements and the finite elasticity of materials which prevent many loading–unloading or approach–separation cycles from being thermodynamically reversible, even though if these were carried out infinitely slowly they would be reversible. By thermodynamic irreversibility one simply means that one cannot go through the approach–separation cycle via a continuous series of equilibrium states because some of these are connected via spontaneous — and therefore thermodynamically irreversible — instabilities or transitions (Figure 16.4C) where energy is liberated and therefore “lost” via heat or phonon release (Israelachvili and Berman, 1995). This is an area of much current interest and activity, especially regarding the fundamental molecular origins of adhesion and friction, and the relationships between them.
16.5 Rheology of Molecularly Thin Films: Nanorheology 16.5.1 Different Modes of Friction: Limits of Continuum Models Most frictional processes occur with the sliding surfaces becoming damaged in one form or another (Bowden and Tabor, 1967). This may be referred to as “normal” friction. In the case of brittle materials, the damaged surfaces slide past each other while separated by relatively large, micron-sized wear particles. With more ductile surfaces, the damage remains localized to nanometer-sized, plastically deformed asperities. There are also situations where sliding can occur between two perfectly smooth, undamaged surfaces. This may be referred to as “interfacial” sliding or “boundary” friction, and is the focus of the following sections. The term “boundary lubrication” is more commonly used to denote the friction of surfaces that contain a thin protective lubricating layer, such as a surfactant monolayer, but here we shall use this term more broadly to include any molecularly thin solid, liquid, surfactant, or polymer film.
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TABLE 16.1 The Three Main Tribological Regimesa Characterizing the Changing Properties of Liquids Subjected to an Increasing Confinement Between Two Solid Surfacesb Regime
Conditions for Getting into This Regime
Static/Equilibrium Propertiesc
Bulk
• Thick films (>10σ, Rg), • Low or zero loads • High shear rates
Bulk, continuum properties: • Bulk liquid density • No long-range order
Mixed or Intermediate
• Intermediately thick films (4–10 molecular diameters, ~Rg for polymers) • Low loads
Boundary
• Molecularly thin films (<4 molecular diameters), • High loads • Low shear rates • Smooth surfaces or asperities
Modified fluid properties include: • Modified positional and orientational orderb • Medium to long-range molecular correlations • Highly entangled states Onset of non-fluidlike properties: • Liquid-like to solid-like phase transitions • Appearance of new liquidcrystalline states • Epitaxially induced long-range ordering
Dynamic Propertiesd Bulk, continuum properties: • Newtonian viscosity • Fast relaxation times • No glass temperature • No yield point • EHD lubrication Modified rheological properties include: • Non-Newtonian flow • Glassy states • Long relaxation times • Mixed lubrication Onset of tribological properties: • No flow until yield point or critical shear stress reached • Solid-like film behavior characterized by defect diffusion, dislocation motion, shear melting • Boundary lubrication
a Based on work by Granick (1991), Hu and Granick (1992), and others (Gee et al., 1990; Hirz et al., 1992; Yoshizawa et al., 1993) on the dynamic properties of short-chain molecules such as alkanes and polymer melts confined between surfaces. b Confinement can lead to an increased or decreased order in a film, depending both on the surface lattice structure and the geometry of the confining cavity. c In each regime both the static and dynamic properties change. The static properties include the film density, the density distribution function, the potential of mean force, and various positional and orientational order parameters. d By dynamic properties are included viscosity, viscoelastic constants, and tribological yield points such as the friction coefficient and critical shear stress.
Experiments have shown that as a liquid film becomes progressively thinner, its physical properties change, at first quantitatively then qualitatively (Van Alsten and Granick, 1990a,b; Peachey et al., 1991; Granick, 1991; Hu et al., 1991; Hu and Granick, 1992; Luengo et al., 1997a). The quantitative changes are manifested by an increased viscosity, non-Newtonian flow behavior, and the replacement of normal melting by a glass transition, but the film remains recognizable as a liquid. In tribology, this regime is commonly known as the “mixed lubrication” regime, where the rheological properties of a film are intermediate between the bulk and boundary properties. One may also refer to it as the “intermediate” regime (Table 16.1). For even thinner films, the changes in behavior are more dramatic, resulting in a qualitative change in properties. Thus, first-order phase transitions can now occur to solid or liquid-crystalline phases (Gee et al., 1990; Israelachvili et al., 1990a,b; Thompson and Robbins, 1990; Yoshizawa et al., 1993; Klein and Kumacheva, 1995), whose properties can no longer be characterized — even qualitatively — in terms of bulk or continuum liquid properties such as viscosity. These films now exhibit yield points (characteristic of fracture in solids) and their molecular diffusion and relaxation times can be 10 orders of magnitude longer than in the bulk liquid or even in films that are just slightly thicker. The three friction regimes are summarized in Table 16.1.
16.5.2 Viscous Forces and Friction of Thick Films: Continuum Regime Experimentally, it is usually difficult to unambiguously establish which type of sliding mode is occurring, but an empirical criterion, based on the Stribeck Curve (Figure 16.6A) is often used as an indicator. This curve shows how the friction force or the coefficient of friction is expected to vary with sliding speed depending on which type of friction regime is operating. For thick liquid lubricant films whose behavior
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FIGURE 16.6 (A) Stribeck Curve: empirical curve giving the trend generally observed in the friction forces or friction coefficients as a function of sliding velocity, the bulk viscosity of the lubricating fluid, and the applied load. The three friction/lubrication regimes are known as the thick film or EHD lubrication regime (see B below), the intermediate or mixed lubrication regime (see Figure 16.7), and the boundary lubrication regime (see Figure 16.17). The film thicknesses, believed to correspond to each of these regimes, are also shown. For thick films the “friction” force is purely viscous, e.g., Couette flow at low shear rates, but may become complicated at higher shear rates where elastohydrodynamic (EHD) deformations of surfaces can occur during sliding, as shown in (B). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
can be described by bulk, continuum properties, the friction forces are essentially the hydrodynamic or viscous drag forces. For example, for two plane parallel surfaces of area A separated by a distance D and moving laterally relative to each other with velocity v, if the intervening liquid is Newtonian, i.e., if its viscosity η is independent of the shear rate, the frictional force experienced by the surfaces is given by
F=
ηAv D
(16.8)
where the shear rate γ· is defined by
v γ˙ = D
(16.9)
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At higher shear rates, two additional effects often come into play. First, certain properties of liquids may change at high γ· values. In particular, the “effective” viscosity may become non-Newtonian, one form given by
ηeff ∝ γ˙ n
(16.10)
where n = 0 (i.e., ηeff = constant) for Newtonian fluids, n > 0 for shear thickening (dilatent) fluids, and n < 0 for shear thinning (pseudoplastic) fluids (the latter become less viscous, i.e., flow more easily, with increasing shear rate, e.g., Figure 16.7B). An additional effect on η can arise from the higher local stresses
FIGURE 16.7 Typical rheological behavior of liquid film in the mixed lubrication regime. (A) Increase in effective viscosity of dodecane film between two mica surfaces with decreasing film thickness (Granick, 1991). Beyond 40 to 50 Å, the effective viscosity ηeff approaches the bulk value ηbulk. (B) Non-Newtonian variation of ηeff with shear rate of a 27 Å thick dodecane film (data from Luengo et al., 1996). The effective viscosity decays as a power law, as in Equation 16.10. In this example, n = 0 at the lowest γ,· then transitions to n = –1 at higher γ.· For bulk thick films, dodecane is a low-viscosity Newtonian fluid (n = 0). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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(pressures) experienced by the liquid film as γ· increases. Since the viscosity is generally also sensitive to the pressure (usually increasing with P), this effect also acts to increase ηeff and thus the friction force. A second effect that occurs at high shear rates is surface deformation, arising from the large hydrodynamic forces acting on the sliding surfaces. For example, Figure 16.6B shows how two surfaces elastically deform when the sliding speed increases to a high value. These deformations alter the hydrodynamic friction forces, and this type of friction is often referred to as elastohydrodynamic lubrication (EHD or EHL) as mentioned in Table 16.1. One natural question is: How thin can a liquid film be before its dynamic, e.g., viscous flow, behavior ceases to be described by bulk properties and continuum models? Concerning the static properties, we have already seen that films composed of simple liquids display continuum behavior down to thicknesses of 5 to 10 molecular diameters. Similar effects have been found to apply to the dynamic properties, such as the viscosity, of simple liquids in thin films. Concerning viscosity measurements, a number of dynamic techniques have been developed (Chan and Horn, 1985; Israelachvili, 1986a; Van Alsten and Granick, 1988; Israelachvili and Kott, 1989) for directly measuring the viscosity as a function of film thickness and shear rate across very thin liquid films between two surfaces. By comparing the results with theoretical predictions of fluid flow in thin films, one can determine the effective positions of the shear planes and the onset of non-Newtonian behavior in very thin films. The results show that for simple liquids, including linear chain molecules such as alkanes, their viscosity in thin films is the same, within 10%, as the bulk even for films as thin as 10 molecular diameters (or segment widths) (Chan and Horn, 1985; Israelachvili, 1986a; Israelachvili and Kott, 1989). This implies that the shear plane is effectively located within one molecular diameter of the solid–liquid interface, and these conclusions were found to remain valid even at the highest shear rates studied (~2 × 105 s–1). With water between two mica or silica surfaces (Chan and Horn, 1985; Israelachvili, 1986a; Horn et al., 1989; Israelachvili and Kott, 1989), this has been found to be the case (to within ±10%) down to surface separations as small as 2 nm, implying that the shear planes must also be within a few Ångstrom of the solid–liquid interfaces. These results appear to be independent of the existence of electrostatic “double layer” or “hydration” forces. For the case of the simple liquid toluene confined between surfaces with adsorbed layers of C60 molecules, this type of viscosity measurement has shown that the traditional noslip assumption for flow at a solid interface does not always hold (Campbell, et al., 1996). For this system, the C60 layer at the mica–toluene interface results in a “full slip” boundary, which dramatically lowers the viscous drag or “effective” viscosity for regular Couette or Poiseuille flow. With polymeric liquids (polymer melts) such as polydimethylsiloxanes (PDMS) and polybutadienes (PBD), or polystyrene (PS) adsorbed onto surfaces from solution, the far-field viscosity is again equal to the bulk value, but with the non-slip plane (hydrodynamic layer thickness) being located at D = 1 to 2 Rg away from each surface (Israelachvili, 1986b; Luengo et al., 1997a), or at D = L for polymer brush layers of thickness L per surface (Klein et al., 1993). In contrast, the same technique was used to show that for nonadsorbing polymers in solution, there is actually a depletion layer of nearly pure solvent that exists at the surfaces that affects the confined solution flow properties (Kuhl et al., 1997). These effects are observed from near contact to surface separations in excess of 200 nm. Further experiments with surfaces closer than a few molecular diameters (D < 20 to 40 Å for simple liquids, or D < 2 to 4 Rg for polymer fluids) indicate that large deviations occur for thinner films, described below. One important conclusion from these studies is that the dynamic properties of simple liquids, including water, near an isolated surface are similar to those of the bulk liquid already within the first layer of molecules adjacent to the surface, only changing when another surface approaches the first. In other words, the viscosity and position of the shear plane near a surface are not simply a property of that surface, but of how far that surface is from another surface. The reason for this is that when two surfaces are close together, the constraining effects on the liquid molecules between them are much more severe than when there is only one surface. Another obvious consequence of the above is that one should not make measurements on a single, isolated solid–liquid interface and then draw conclusions about the state of the liquid or its interactions in a thin film between two surfaces.
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16.5.3 Friction of Intermediate Thickness Films The properties of liquid films between 6 and 10 molecular diameters thick can be significantly different from those of bulk films. But the fluids remain recognizable as fluids; in other words, they do not undergo a phase transition into a solid or liquid-crystalline phase. This regime has been studied by Granick and co-workers (Van Alsten and Granick, 1990a,b, 1991; Granick, 1991; Hu et al., 1991; Hu and Granick, 1992; Klein and Kumacheva, 1995), who used a different type of friction attachment (Van Alsten and Granick, 1988, 1990b) to the SFA where the two surfaces are made to vibrate laterally past each other at small amplitudes. This method provides information on the real and imaginary parts (elastic and dissipative components, respectively) of the shear modulus of thin films at different shear rates and film thickness. Granick (1991) and Hu et al. (1991) found that films of simple liquids become non-Newtonian in the 25 to 50 Å regime (about 10 molecular diameters; see Figure 16.7), whereas polymer melts become non-Newtonian at much thicker films, depending on their molecular weight (Luengo et al., 1997a). Klein and Kumacheva (1998; Kumacheva and Klein, 1998) studied the interaction forces and friction of small quasispherical liquid molecules such as cyclohexane between molecularly smooth mica surfaces. They concluded that surface epitaxial effects can cause the liquid film to solidify at 6 molecular diameters, resulting in a sudden (discontinuous) jump to high friction at low shear rates. Such “dynamic” firstorder transitions, however, may depend on the shear rate. A generalized friction map (Figure 16.8) has been proposed by Luengo et al. (1996) that illustrates the changes in ηeff from bulk Newtonian behavior (n = 0, ηeff = ηbulk) through the transition regime where n reaches a minimum of -1 with decreasing shear rate, to the solid-like creep regime at very low γ· where n returns to 0. The data in Figure 16.9 show the transition for thicker polymer films from bulk behavior to the tribological regime where n reaches –1 (Luengo et al., 1997a). With further decreasing shear rates the exponent n increases from –1 to 0, as illustrated in Figure 16.7B for a dodecane system. A number
FIGURE 16.8 Proposed generalized friction map of effective viscosity plotted against effective shear rate on a loglog scale (data from Luengo et al., 1996). Three main classes of behavior emerge: (1) Thick films; elastohydrodynamic sliding. At zero load (L = 0), approximating bulk conditions, ηeff is independent of shear rate except when shearthinning may occur at sufficiently large γ.· (2) Boundary layer films, intermediate regime. A Newtonian regime is again observed (ηeff = constant, n = 0 in Equation 16.10) at low loads and low shear rates, but ηeff is much higher than the bulk value. As the shear rate γ· increases beyond γ·min, the effective viscosity starts to drop with a power-law dependence on the shear rate (see Figure 16.7B), with n in the range of –1/2 to –1 most commonly observed. As the shear rate γ· increases still more, beyond γ·max, a second Newtonian plateau is again encountered. (3) Boundary layer films, high load. The ηeff continues to grow with load and to be Newtonian provided that the shear rate is sufficiently low. Transition to sliding at high velocity is discontinuous (n < –1) and usually of the stick-slip variety. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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FIGURE 16.9 Effective viscosity plotted against effective shear rate on log-log scales for polybutadiene (MW = 7000) at four different separations, D (adapted from Luengo et al., 1997a). Open data points were obtained from sinusoidally applied shear at zero load (L = 0) at the indicated separations. Solid points were obtained from friction experiments at constant sliding velocities. These tribological results extrapolate, at high shear rate, to the bulk viscosity. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
of results from experimental, theoretical, and computer simulation work have shown values of n from –1/2 to –1 for this transition regime for a variety of systems and assumptions (Hu and Granick, 1991; Granick, 1991; Thompson et al., 1992; Thompson et al., 1995; Urbakh et al., 1995; Rabin and Hersht, 1993). The intermediate regime appears to extend over a narrow range of film thickness, from about 4 to 10 molecular diameters or polymer radii of gyration. Thinner films begin to adopt “boundary” or “interfacial” friction properties (described below; see also Table 16.1). Note that the intermediate regime is actually a very narrow one when defined in terms of film thickness, for example, varying from about D = 20 to 40 Å for hexadecane films (Granick, 1991). A fluid’s effective viscosity ηeff in the intermediate regime is usually higher than in the bulk, but ηeff usually decreases with increasing sliding velocity, v (known as shear thinning). When two surfaces slide in the intermediate regime, the motion tends to thicken the film (dilatency). This sends the system into the bulk EHL regime where, as indicated by Equation 16.8, the friction force now increases with velocity. This initial decrease, followed by an increase, in the frictional forces of many lubricant systems is the basis for the empirical Stribeck Curve of Figure 16.6A. In the transition from bulk to boundary behavior there is first a quantitative change in the material properties (viscosity and elasticity) which can be continuous, then discontinuous qualitative changes which result in yield stresses and non-liquid-like behavior. The rest of this chapter is devoted to friction in the interfacial and boundary regimes. The former (interfacial friction) may be thought of as applying to the sliding of two dry, unlubricated surfaces in true molecular contact. The latter (boundary friction) may be thought of as applying to the case where a lubricant film is present, but where this film is of molecular dimensions — a few molecular layers or less.
16.6 Interfacial and Boundary Friction: Molecular Tribology 16.6.1 General Interfacial Friction When a lateral force, or shear stress, is applied to two surfaces in adhesive contact, the surfaces initially remain “pinned” to each other until some critical shear force is reached. At this point, the surfaces begin
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to slide past each other either smoothly or in jerks. The frictional force needed to initiate sliding from rest is known as the static friction force, denoted by Fs , while the force needed to maintain smooth sliding is referred to as the kinetic or dynamic friction force, denoted by Fk . In general, Fs > Fk . Two sliding surfaces may also move in regular jerks, known as “stick-slip” sliding, which is discussed in more detail in Section 16.9. Note that such friction forces cannot be described by equations, such as Equation 16.10, used for thick films that are viscous and therefore shear as soon as the smallest shear force is applied. Experimentally, it has been found that during both smooth and stick-slip sliding the local geometry of the contact zone remains largely unchanged from the static geometry, and that the contact area vs. load is still well described by the JKR equation, Equation 16.4. The friction force of two molecularly smooth surfaces sliding while in adhesive contact with each other is not simply proportional to the applied load, L, as might be expected from Amontons’ Law. There is an additional adhesion contribution that is proportional to the area of contact, A, which is described later. Thus, in general, the interfacial friction force of dry, unlubricated surfaces sliding smoothly past each other is given by
F = Fk = Sc A + µL
(16.11)
where Sc is the “critical shear stress” (assumed to be constant), A = πr2 is the contact area of radius r given by Equation 16.4, and µ is the coefficient of friction. For low loads we have:
R 2 F = Sc A = Sc πr = Sc π L + 6 πRγ + 12πRγL + 6 πRγ K
(
2
)
2 3
(16.12)
while for high loads, Equation 16.11 reduces to Amontons’ law:
F = µL
(16.13)
Depending on whether the friction force, F, in Equation 16.11 is dominated by the first or second terms, one may refer to the friction as “adhesion-controlled” or “load-controlled,” respectively. Figure 16.10 shows a plot of contact area, A, and friction force, F, both plotted against the applied load, L, in an experiment where two molecularly smooth surfaces of mica in adhesive contact were slid past each other in an atmosphere of dry nitrogen gas. This is an example of the low load, adhesioncontrolled limit, which is excellently described by Equation 16.12. In a number of different experiments, Sc was measured to be 2.5 × 107 N/m2, and to be independent of the sliding velocity. Note that there is a friction force even at negative loads, where the surfaces are still sliding in adhesive contact.
16.6.2 Boundary Friction of Surfactant Monolayer Coated Surfaces The high friction force of unlubricated sliding can often be reduced by treating the solid surface with a “boundary layer” of some other solid material that exhibits lower friction, such as a surfactant monolayer, or by ensuring that during sliding, a thin liquid film remains between the surfaces. The effectiveness of a solid boundary lubricant layer on reducing the forces of friction is illustrated in Figure 16.11. Comparing this with the friction of the unlubricated/untreated surfaces (Figure 16.10) shows that the critical shear stress has been reduced by a factor of about 10: from 2.5 × 107 to 3.5 × 106 N/m2. At much higher applied loads or pressures, the friction force is proportional to the load rather than the area of contact (Briscoe et al., 1977), as expected from Equation 16.11. Yamada and Israelachvili (1998) studied the adhesion and friction of fluorocarbon surfaces (surfactantcoated boundary lubricant layers), which were compared to those of hydrocarbon surfaces. They concluded that well-ordered fluorocarbon surfaces have a high friction, in spite of their lower adhesion energy (in agreement with previous findings). The low friction coefficient of PTFE (Teflon®) must
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FIGURE 16.10 Friction force F and contact area A vs. load L for two mica surfaces sliding in adhesive contact in dry air. The contact area is well described by the JKR theory, Equation 16.4, even during sliding, and the frictional force is found to be directly proportional this area, Equation 16.12. The vertical dashed line and arrow show the transition from “interfacial” to “normal” friction with the onset of wear (lower curve). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 16.11 Sliding of mica surfaces each coated with a 25 Å thick monolayer of calcium stearate surfactant in the absence of damage (obeying JKR type boundary friction) and in the presence of damage (obeying Amontons’ type “normal” friction) (data from Homola et al., 1989, 1990). At much higher applied loads the undamaged surfaces also follow Amontons’ type sliding, but for different reasons. Lower line: interfacial sliding with a monolayer of water between the mica surfaces, shown for comparison. Note that in both cases, after damage occurs, the friction force obeys Amontons’ law with the same coefficient of friction of µ ≈ 0.3. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
therefore be due to some effect other than a low adhesion, for example, the softness of PTFE which allows material to flow at the interface, behaving like a fluid lubricant. On a related issue, Luengo et al. (1997b) found that C60 surfaces also exhibited low adhesion but high friction. In both cases the high friction appears to arise from the bulky surface groups — fluorocarbon compared to hydrocarbon groups in the former, large fullerene spheres in the latter. Apparently, the fact that C60 molecules rotate in their lattice does not make them a good lubricant: the molecules of the opposing surface must still climb over them in order to move, and this requires energy which is independent of whether the surface molecules are fixed or freely rotating. Larger particles, such as ~25 nm sized nanoparticles (also known as “inorganic
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FIGURE 16.12 Two mica surfaces sliding past each other while immersed in a 0.01 M KCl salt solution. In both cases the water film is molecularly thin: 2.5 to 5.0 Å thick, and the interfacial friction force is very low: Sc ≈ 5 × 105 N/m2, µ ≈ 0.015 (before damage occurs). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
fullerenes”) do appear to produce low friction by behaving like molecular ball bearings, but the potential of this promising new class of solid lubricant has still to be explored (Rapoport et al., 1997).
16.6.3 Boundary Lubrication of Molecularly Thin Liquid Films A liquid lubricant film is usually much more effective at lowering the friction of two surfaces than a solid boundary lubricant layer. However, to successfully use a liquid lubricant, it must “wet” the surfaces; that is, it should have a high affinity for the surfaces so that the liquid molecules do not become squeezed out when the surfaces come close together, even under a large compressive load. Another important requirement is that the liquid film remains a liquid under tribological conditions, i.e., that it does not epitaxially solidify between the surfaces. Effective lubrication usually requires that the lubricant be injected between the surfaces, but in some cases the liquid can be made to condense from the vapor. Both of these effects are illustrated in Figure 16.12 for two untreated mica surfaces sliding with a thin layer of water between them. We may note that a monomolecular film of water (of thickness 2.5 Å per surface) has reduced Sc by a factor of more than 30, which may be compared with the factor of 10 attained with the boundary lubricant layer (of thickness 25 Å per surface). The effectiveness of a water film only 2.5 Å thick to lower the friction force by more than an order of magnitude is attributed to the “hydrophilicity” of the mica surface (mica is “wetted” by water) and to the existence of a strongly repulsive short-range hydration force between such surfaces in aqueous solutions which effectively removes the adhesion-controlled contribution to the friction force (Berman et al., 1998a). It is also interesting that a 2.5 Å thick water film between two mica surfaces is sufficient to bring the coefficient of friction down to between 0.01 and 0.02, a value that corresponds to the unusually low friction of ice. Clearly, a single monolayer of water can be a very good lubricant — much better than most other monomolecular liquid films, for reasons that will be discussed below.
16.6.4 Transition from Interfacial to Normal Friction (with Wear) Frictional damage can have many causes such as adhesive tearing at high loads or overheating at high sliding speeds. Once damage occurs, there is a transition from “interfacial” to “normal” or load-controlled friction as the surfaces become forced apart by the torn-out asperities (wear particles). For low loads, the friction changes from obeying F = ScA to obeying Amontons’ law: F = µL, as shown in Figures 16.10 to
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FIGURE 16.13 Friction forces as a function of load for smooth (undamaged) and rough (damaged) surfaces (data from Berman et al., 1998b). Untreated alumina surfaces (curve a) exhibit the lowest friction due to a thin physisorbed layer of lubricating contaminants, but these are easily damaged upon sliding, resulting in rough surface (curve b) with a higher friction. Monolayer coated surfaces (curve c) slide with higher friction at lower loads than untreated alumina, but remain undamaged even after prolonged sliding, keeping the friction and wear substantially lower than rough surfaces at high loads. Smooth sliding was “adhesion controlled,” i.e., the contact area A is well described by the JKR equation (Equation 16.4), and F/A = constant (Equation 16.12). In addition, F is finite at L = 0. Rough, damaged sliding was “load controlled,” i.e., the “real” contact area is undefined, and F ∝ L (Equation 16.13) with F ≈ 0 at L = 0. Experimental conditions: sliding velocity V = 0.05 to 0.5 µm/s; undeformed radius of curved surfaces, R ≈ 1 cm; temperature T = 25°C; contact pressure range, P = 0 to 10 MPa; relative humidity, RH = 0% (curves a and c), RH = 0% and 100% (curve b). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.13, and sliding now proceeds smoothly with the surfaces separated by a 100 to 1000 Å forest of wear debris (mica or alumina flakes in this case). The wear particles keep the surfaces apart over an area that is much greater than their size, so that even one submicroscopic particle or asperity can cause a significant reduction in the area of contact and therefore in the friction (Homola et al., 1990). For this type of frictional sliding, one can no longer talk of the molecular contact area of the two surfaces, although the macroscopic or “apparent” area is still a useful parameter. A further discussion on the impact of normal load and contact area is found in Section 16.7.4. One remarkable feature of the transition from interfacial to normal friction of brittle surfaces is that while the strength of interfacial friction, as reflected in the values of Sc, is very dependent on the type of surface and on the liquid film between the surfaces, this is not the case once the transition to normal friction has occurred. At the onset of damage, it is the material properties of the underlying substrates that control the friction. In Figures 16.10 to 16.12 the friction for the damaged surfaces is that of any damaged mica–mica system, while in Figure 16.13 the damaged surfaces friction is that of general alumina–alumina sliding (with a friction coefficient that agrees with literature values for the bulk materials), independent of the initial surface coatings or liquid films between the surfaces. In order to practically modify the frictional behavior of such brittle materials, it is important to use coatings that will both alter the interfacial tribological character and remain intact and protect the surfaces from damage during sliding (Berman et al., 1998b). An example of the friction behavior of a strongly bound octadecyl phosphonic acid monolayer on alumina surfaces is shown in Figure 16.13. In this case, the friction is higher than untreated, undamaged α-alumina surfaces, but the bare surfaces easily damage upon sliding, resulting in an ultimately higher friction system with greater wear rates than the more robust monolayer-coated surfaces.
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Clearly, the mechanism and factors that determine normal friction are quite different from those that govern interfacial friction. These mechanisms are described in the theoretical section below, but one should point out that this effect is not general and may only apply to brittle materials. For example, the friction of ductile surfaces is totally different and involves the continuous plastic deformation of contacting surface asperities during sliding rather than the rolling of two surfaces on hard wear particles (Bowden and Tabor, 1967). Furthermore, in the case of ductile surfaces, water and other surface-active components do have an effect on the friction coefficients under “normal” sliding conditions.
16.7 Theories of Interfacial Friction 16.7.1 Theoretical Modeling of Interfacial Friction: Molecular Tribology The following friction model, first proposed by Tabor (1982) and developed further by Sutcliffe et al. (1978), McClelland (1989), and Homola et al. (1989), has been quite successful at explaining the interfacial and boundary friction of two solid crystalline surfaces sliding past each other in the absence of wear. The surfaces may be unlubricated, or they may be separated by a monolayer or more of some boundary lubricant or liquid molecules. In this model, the values of the critical shear stress Sc , and coefficient of friction µ, of Equation 16.11 are calculated in terms of the energy needed to overcome the attractive intermolecular forces and compressive externally applied load as one surface is raised and then slid across the molecular-sized asperities of the other. This model (variously referred to as the interlocking asperity model, Coulomb friction, or the cobblestone model) is akin to pushing a cart over a road of cobblestones where the cart wheels (which represent the molecules of the upper surface or film) must be made to roll over the cobblestones (representing the molecules of the lower surface) before the cart can move. In the case of the cart, the downward force of gravity replaces the attractive intermolecular forces between two material surfaces. When at rest the cartwheels find grooves between the cobblestones where they sit in potential energy minima and so the cart is at some stable mechanical equilibrium. A certain lateral force (the “push”) is required to raise the cart wheels against the force of gravity in order to initiate motion. Motion will continue as long as the cart is pushed, and rapidly stops once it is no longer pushed. Energy is dissipated by the liberation of heat (phonons, acoustic waves, etc.) every time a wheel hits the next cobblestone. The cobblestone model is not unlike the old Coulomb and interlocking asperity models of friction (Dowson, 1979) except that it is being applied at the molecular level and the external load is augmented by attractive intermolecular forces. There are thus two contributions to the force pulling two surfaces together: the externally applied load or pressure, and the (internal) attractive intermolecular forces which determine the adhesion between the two surfaces. Each of these contributions affects the friction force in a different way, and we start by considering the role of the internal adhesion forces.
16.7.2 Adhesion Force Contribution to Interfacial Friction Consider the case of two surfaces sliding past each other as shown in Figure 16.14. When the two surfaces are initially in adhesive contact the surface molecules will adjust themselves to fit snugly together, in a manner analogous to the self-positioning of the cart wheels on the cobblestone road. A small tangential force applied to one surface will therefore not result in the sliding of that surface relative to the other. The attractive van der Waals forces between the surfaces must first be overcome by having the surfaces separate by a small amount. To initiate motion, let the separation between the two surfaces increase by a small amount ∆D, while the lateral distance moved is ∆d. These two values will be related via the geometry of the two surface lattices. The energy put into the system by the force F acting over a lateral distance ∆d is
Input energy: F × ∆d
(16.14)
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L ∆d
F
∆D
Impact
D0
FIGURE 16.14 Schematic illustration of how one molecularly smooth surface moves over another when a lateral force F is applied. As the upper surface moves laterally by some fraction of the lattice dimension ∆d, it must also move up by some fraction of an atomic or molecular dimension ∆D, before it can slide across the lower surface. On impact, some fraction ε of the kinetic energy is “transmitted” to the lower surface, the rest being “reflected” back to the colliding molecule (upper surface). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
This energy may be equated with the change in interfacial or surface energy associated with separating the surfaces by ∆D, i.e., from the equilibrium separation D = D0 to D = (D0 + ∆D). Since γ ∝ D–2, the surface energy cost may be approximated by
Surface energy change: 2γA 1 − D20
(D
0
)
(
2 + ∆D ≈ 4 γA ∆D D0
)
(16.15)
where γ is the surface energy, A the contact area, and where D0 is the surface separation at equilibrium. During steady-state sliding (kinetic friction), not all of this energy will be “lost” or absorbed by the lattice every time the surface molecules move by one lattice spacing: some fraction will be reflected during each impact of the “cart wheel” molecules (McClelland, 1989). Assuming that a fraction ε of the above surface energy is lost every time the surfaces move across the characteristic length ∆d (Figure 16.14), we obtain, after equating the above two equations,
Sc =
F 4 γε ⋅ ∆D = A D0 ⋅ ∆d
(16.16)
For a typical hydrocarbon or a van der Waals surface, γ ≈ 25 × 10–3 J/m2. Other typical values would be: ∆D ≈ 0.5 Å, D0 ≈ 2 Å, ∆d ≈ 1 Å, and ε ≈ 0.1 to 0.5. Using the above parameters, Equation 16.16 predicts
(
)
Sc ≈ 2.5 − 12.5 × 107 N m2
for van der Waals surfaces
This range of values compares very well with typical experimental values of 2 × 107 N/m2 for hydrocarbon or mica surfaces sliding in air or separated by one molecular layer of cyclohexane (Homola et al., 1989). The above model suggests that all interfaces, whether dry or lubricated, dilate just before they shear or slip. This is a small but important effect: the dilation provides the crucial extra space needed for the molecules to slide across each other or flow. This dilation has been measured by Granick et al. (1999) and computed by Robbins and Thompson (1991). This model may be extended, at least semiquantitatively, to lubricated sliding, where a thin liquid film is present between the surfaces. With an increase in the number of liquid layers between the surfaces, D0
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increases while ∆D decreases, hence a lower friction force. This is precisely what is observed. But with more than one liquid layer between two surfaces the situation becomes too complex to analyze analytically. (Actually, even with one or no interfacial layers, the calculation of the fraction of energy dissipated per molecular collision ε is not a simple matter.) Sophisticated modeling based on computer simulations is now required, as described in the following section.
16.7.3 Relation Between Boundary Friction and Adhesion Energy Hysteresis While the above equations suggest that there is a direct correlation between friction and adhesion, this is not the case. The correlation is really between friction and adhesion hysteresis, described in Section 16.4. In the case of friction, this subtle point is hidden in the factor ε, which is a measure of the amount of energy absorbed (dissipated, transferred, or “lost”) by the lower surfaces when it is impacted by a molecule from the upper surface. If ε = 0, all the energy is reflected and there will be no kinetic friction force, nor any adhesion hysteresis, but the absolute magnitude of the adhesion force or energy would remain finite and unchanged. This is illustrated in Figure 16.15. The following simple model shows how adhesion hysteresis and friction may be quantitatively related. Let ∆γ = (γR – γA) be the adhesion energy hysteresis per unit area, as measured during a typical loading–unloading cycle (see Figure 16.15C, D). Now consider the same two surfaces sliding past each other
FIGURE 16.15 Top: Friction traces (data from Chen et al., 1991) for two fluid-like monolayer-coated surfaces at 25°C showing that the friction force is much higher between dry monolayers (A) than between monolayers whose fluidity has been enhanced by hydrocarbon penetration from vapor (B). Bottom: Contact radius vs. load (r 3 – L) curves measured for the same two surfaces as above and fitted to the JKR Equation 16.4 — shown by the solid lines. For dry monolayers (C) the adhesion energy on unloading (γR = 40 mJ/m2) is greater than that on loading (γA = 28 mJ/m2), indicative of an adhesion energy hysteresis of ∆γ = γR – γA = 12 mJ/m2. For monolayers exposed to saturated decane vapor (D) their adhesion hysteresis is zero (γA = γR), and both the loading and unloading curves are wellfitted by the thermodynamic value of the surface energy of fluid hydrocarbon chains, γ ≈ 24 mJ/m2. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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and assume that frictional energy dissipation occurs through the same mechanism as adhesion energy dissipation, and that both occur over the same characteristic molecular length scale σ. Thus, when the two surfaces (of contact area A = πr2) move a distance σ, equating the frictional energy (F × σ) to the dissipated adhesion energy (A × ∆γ), we obtain
Friction force: F =
A ∆γ πr 2 γ −γA = σ σ R
(
)
(16.17)
or
Friction stress: Sc = F A = ∆γ σ
(16.18)
which is the desired expression and which has been found to give order of magnitude agreement between measured friction forces and adhesion energy hysteresis (Chen et al., 1989). If we equate Equation 16.18 with Equation 16.16, since 4∆D/D0∆d ≈ σ, we obtain the intuitive relation
ε≈
∆γ γ
(16.19)
Figure 16.15 illustrates the relationship between adhesion hysteresis and friction for surfactant-coated surfaces under different conditions. This effect, however, is much more general, and has been shown to hold for other surfaces as well (Vigil et al., 1994; Israelachvili et al., 1994, 1995). Direct comparisons between absolute adhesion energies and friction forces show little correlation. In some cases higher adhesion energies for the same system under different conditions correspond with lower friction forces. For example, for hydrophilic silica surfaces it was found that with increasing relative humidity the adhesion energy increases, but the adhesion energy hysteresis measured in a loading–unloading cycle decreases, as does the friction force (Vigil et al., 1994). For hydrophobic silica surfaces under dry conditions, the friction at load L = 5.5 mN was F = 75 mN. For the same sample, the adhesion energy hysteresis was ∆γ = 10 mJ/m2, with a contact area of A ≈ 10–8 m2 at the same load. Assuming a value for the characteristic distance σ on the order of one lattice spacing, σ ≈ 1 nm. Inserting these values into Equation 16.17, the friction force is predicted to be F ≈ 100 mN for the kinetic friction force, which is close to the measured value of 75 mN. Alternatively, we may conclude that the dissipation factor is ε = 0.75, i.e., that almost all the energy is dissipated as heat at each molecular collision.
16.7.4 External Load Contribution to Interfacial Friction When there is no interfacial adhesion Sc is zero. Thus, in the absence of any adhesive forces between two surfaces, the only “attractive” force that needs to be overcome for sliding to occur is the externally applied load or pressure. For a preliminary discussion of this question, it is instructive to compare the magnitudes of the externally applied pressure to the internal van der Waals pressure between two smooth surfaces. The internal van der Waals pressure is given by P = A/6πD03 ≈ 104 atm (using a typical Hamaker constant of A = 10–12 erg, and assuming D0 ≈ 2 Å for the equilibrium interatomic spacing). This implies that we should not expect the externally applied load to affect the interfacial friction force F, as defined by Equation 16.11, until the externally applied pressure L/A begins to exceed ~1000 atm. This is in agreement with experimental data (Briscoe et al., 1977) where the effect of load became dominant at pressures in excess of 1000 atm. For a more general semiquantitative analysis, again consider the cobblestone model as used to derive Equation 16.16, but now include an additional contribution to the surface energy change of Equation 16.15 due to the work done against the external load or pressure, L∆D = PextA·∆D. (This is equivalent to the work done against gravity in the case of a cart being pushed over cobblestones.)
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Thus:
Sc =
F 4 γε ⋅ ∆D Pext ε ⋅ ∆D = + ∆d A D0 ⋅ ∆d
(16.20)
which gives the more general relation
Sc = F A = C1 + C 2Pext
(16.21)
where Pext = L/A, and where C1 and C2 are constants characteristic of the surfaces and sliding conditions. The constant C1 = (4γε·∆D/D0 ·∆d) depends on the mutual adhesion of the two surfaces, while both C1 and C2 = ε·∆D/∆d depend on the topography or atomic bumpiness of the surface groups (Figure 16.14) — the smoother the surface groups, the smaller the ratio ∆D/∆d and hence the lower the value of C2. In addition, both C1 and C2 depend on ε — the fraction of energy dissipated per collision which depends on the relative masses of the shearing molecules, the sliding velocity, the temperature, and the characteristic molecular relaxation processes of the surfaces. This is by far the most difficult parameter to compute, and yet it is the most important since it represents the energy transfer mechanism in any friction process, and since ε can vary between 0 and 1, it determines whether a particular friction force will be large or close to zero. Molecular simulations offer the best way to understand and predict the magnitude of ε, but the complex multibody nature of the problem makes simple conclusions difficult to draw. Some of the basic physics of the energy transfer and dissipation of the molecular collisions can be drawn from simplified models (Urbakh et al., 1995; Rozman et al., 1996, 1997) such as a one-dimensional three-body system (Israelachvili and Berman, 1995). This system, described in more detail in Section 16.7.5, offers insight into the mechanisms of energy transfer and relates them back to the familiar parameter De, the Deborah number. Finally, the above equation may also be expressed in terms of the friction force F:
F = Sc A = C1A + C 2L
(16.22)
Equations similar to Equations 16.21 and 16.22 were previously derived by Derjaguin (1988, 1934) and by Briscoe and Evans (1982), where the constants C1 and C2 were interpreted somewhat differently than in this model. In the absence of any attractive interfacial force, we have C1 ≈ 0, and the second term in Equations 16.21 and 16.22 should dominate. Such situations typically arise when surfaces repel each other across the lubricating liquid film, for example, when two mica surfaces slide across a thin film of water (Figure 16.11). In such cases the total frictional force should be low, and it should increase linearly with the external load according to
F = C 2L
(16.23)
An example of such lubricated sliding occurs when two mica surfaces slide in water or in salt solution, where the short-range “hydration” forces between the surfaces are repulsive. Thus, for sliding in 0.5 M KCl it was found that C2 = 0.015 (Berman et al., 1998a). Another case where repulsive surfaces eliminate the adhesive contribution to friction is for tethered polymer chains attached to surfaces at one end and swollen by a good solvent (Klein et al., 1994). For this class of systems C2 < 0.001 for a finite range of polymer layer compressions (normal loads, L). The low friction between the surfaces in this regime is attributed to the entropic repulsion between the opposing brush layers with a minimum of entanglement between the two layers. However, with higher normal loads, the brush layers become compressed and begin to entangle, resulting in higher friction.
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It is important to note that Equation 16.23 has exactly the same form as Amontons’ law
F = µL
(16.24)
where µ is the coefficient of friction. When damage occurs, there is a rapid transition to “normal” sliding in the presence of wear debris. As previously described, the mechanisms of interfacial friction and normal friction are vastly different on the submicroscopic and molecular levels. However, under certain circumstances both may appear to follow a similar equation (see Equations 16.23 and 16.24) even though the friction coefficients C2 and µ are determined by quite different material properties in each case. At the molecular level, a thermodynamic analog of the Coulomb or cobblestone models (see Section 16.7.1) based on the contact value theorem (Berman et al., 1998a; Berman and Israelachvili, 1997; Israelachvili, 1991) can explain why F ∝ L also holds at the microscopic or molecular level. In this analysis we consider the surface molecular groups as being momentarily compressed and decompressed as the surfaces move along. Under irreversible conditions, which always occur when a cycle is completed in a finite amount of time, the energy lost in the compression/decompression cycle is dissipated as heat. For two nonadhering surfaces, the stabilizing pressure Pi acting locally between any two elemental contact points i of the surfaces may be expressed by the contact value theorem (Israelachvili, 1991):
Pi = ρi k B T = k B T Vi
(16.25)
where ρi = 1/Vi is the local number density (per unit volume) or activity of the interacting entities, be they molecules, atoms, ions, or the electron clouds of atoms. This equation is essentially the osmotic or entropic pressure of a gas of confined molecules. As one surface moves across the other, as local regions become compressed and decompressed by a volume ∆Vi, the work done per cycle can be written as ε Pi ∆Vi where ε (ε ≤ 1) is the fraction of energy per cycle lost as heat, as defined earlier. The energy balance shows that for each compression/decompression cycle, the dissipated energy is related to the friction force by
Fi x i = ε Pi ∆Vi
(16.26)
where xi is the lateral distance moved per cycle, which can be the distance between asperities or the distance between surface lattice sites. The pressure at each contact junction can be expressed in terms of the local normal load Li and local area of contact Ai as Pi = Li /Ai . The volume change over a cycle can thus be expressed as ∆Vi = Aizi, where zi is the vertical distance of confinement. Plugging these back into Equation 16.26, we get
(
Fi = ε Li z i x i
)
(16.27)
which is independent of the local contact area Ai . The total friction force is thus
(
) (
)
F = Σ Fi = Σ ε Li z i x i = ε z i x i Σ Li = µ L
(16.28)
where it is assumed that on average, the local values of Li and Pi are independent of the local “slope” zi /xi . Therefore, the friction coefficient µ is a function only of the average surface topography and the sliding velocity, but is independent of the local (real) or macroscopic (apparent) contact areas. While this analysis explains nonadhering surfaces, there is still an additional explicit contact area contribution for the case of adhering surfaces, as in Equation 16.22. The distinction between the two cases arises because the initial assumption of the contact value theorem, Equation 16.25, is incomplete
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A
m1
k1
m2
k2
593
m3
v0 Interaction Energy
Energy transferred from mass 1
B
1
C
0.8 0.6 0.4 0.2 0 0.01
0.1
1
10
100
Deborah Number, De (System relaxation time/ Collision time)
FIGURE 16.16 (a) Schematic diagram of a basic three-body collision. Mass 1 approaches the other masses with an initial velocity, v0. The kinetic energy of mass 1 after the collision is compared to its initial kinetic energy. The characteristic times of the m1–m2 and m2–m3 interactions are functions of the respective masses and the strengths of the connecting springs k1 and k2 (b). The Deborah number for this system is the ratio of the collision time between masses 1 and 2 to the harmonic oscillating frequency of masses 2 and 3. (c) The energy transferred from mass 1 to the rest of the system (masses 2 and 3) is plotted as a function of the Deborah number. In this calculation k1 = 1, k2 = 10, m1 = 1, and masses m2 = m3 were varied. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
for adhering systems. A more appropriate starting equation would reflect the full intermolecular interaction potential, including the attractive interactions in addition to the purely repulsive contributions of Equation 16.25, much as the van der Waals equation of state modifies the ideal gas law.
16.7.5 Simple Molecular Model of Energy Dissipation ε The simple three-body system of balls and springs illustrated in Figure 16.16a provides molecular insight into dissipative processes such as sliding friction and adhesion hysteresis. Mass m1 may be considered to constitute one body or surface that approaches another at velocity v0 . Masses m2 and m3 represent the other surface. As shown in Figure 16.16b, the masses of the second surface are bound together via a parabolic (Hookian spring) potential, while masses m1 and m2 interact via a nonadhesive repulsion modeled as a half-parabola. Although this system is simple in appearance, it is rich in physics. Different relative values of the masses and spring constants lead to very different collision outcomes where the initial translational or kinetic energy of m1 is distributed among the final kinetic, translational, and vibrational energies of m1 and the m2–m3 couple. The collision is a molecular analogy, and perhaps a good microscopic representation of an adhesive loading–unloading cycle (see Figure 16.4) or a frictional sliding process. The finer molecular model of Figure 16.16a allows us to determine exactly how the energy is being dissipated in these cycles. In a
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loading–unloading process, m1 represents the surface molecules of one body approaching the surface molecules of a second body (m2 and m3). Solutions to the equations of motion show that in the collision the first mass can be reflected, stopped, or even continue forward at a different velocity. In the case of lateral sliding, the molecules of the two surfaces can still be considered to interact in this way; the surface groups from the slider continually collide with those of the opposing surface, with the amount of the energy transferred during the collisions defining the friction. Analysis of this problem shows that the essential determinant of the amount of energy transferred from m1 is based on the ratio of the collision time to the characteristic relaxation time of the system, in other words, to the Deborah number
De = Relaxation time Measuring time
(16.29)
Thus, it is found that m1 loses most of its energy to the m2–m3 couple when the collision time is close to the characteristic vibration time of the m2–m3 harmonic system, which corresponds to De = 1. When the collision time is much larger or smaller than the system characteristic time, mass m1 is found to retain most of its original kinetic energy (Figure 16.16c). In this simple example the interaction times are functions only of the three masses, the intermolecular potential between m1 and m2, and the potential or spring constant of the m2–m3 couple. In more complex systems with more realistic interaction potentials (i.e., attractive interactions between m1 and m2), the velocity v0 becomes an important factor as well, and also affects the Deborah number. It is important to note that in this simple one-dimensional analysis, additional energy modes and degrees of freedom of the molecules have not been considered. These modes, when present, will also be involved in the interaction, affecting the energy transferred from m1 and sharing in the final distribution of the energy transferred. In addition, different types of energy modes (e.g., rotational modes) will generally have different relaxation times, so that their energy peaks will occur at different measuring times. Such real systems may be considered to have more than one Deborah number. The three-body system sheds some light on the molecular mechanisms of energy dissipation and the impact of the Deborah number on the dissipation parameter ε, but because of its simplicity, does not offer predictive capabilities for real systems. More sophisticated models have been presented by Urbakh et al. (1995) and Rozman et al. (1996, 1997).
16.8 Friction and Lubrication of Thin Liquid Films When a liquid is confined between two surfaces or within any narrow space whose dimensions are less than 5 to 10 molecular diameters, both the static (equilibrium) and dynamic properties of the liquid, such as its compressibility and viscosity, can no longer be described even qualitatively in terms of the bulk properties. The molecules confined within such molecularly thin films become ordered into layers (“out-of-plane” ordering), and within each layer they can also have lateral order (“in-plane” ordering). Such films may be thought of as behaving more like a liquid crystal or a solid than a liquid. As described in Section 16.2, the measured normal forces between two solid surfaces across molecularly thin films exhibit exponentially decaying oscillations, varying between attraction and repulsion with a periodicity equal to some molecular dimension of the solvent molecules. Thus, most liquid films can sustain a finite normal stress, and the adhesion force between two surfaces across such films is “quantized,” depending on the thickness (or number of liquid layers) between the surfaces. The structuring of molecules in thin films and the oscillatory forces it gives rise to are now reasonably well understood, both experimentally and theoretically, at least for simple liquids. Work has also recently been done on the dynamic, e.g., viscous or shear, forces associated with molecularly thin films. Experiments (Israelachvili et al., 1988; Gee et al., 1990; Hirz et al., 1992; Homola et al., 1991) and theory (Schoen et al., 1989; Thompson and Robbins, 1990; Thompson et al., 1992) indicate that even when two surfaces are in steady-state sliding they still prefer to remain in one of their stable potential energy minima, i.e., a sheared film of liquid can retain its basic layered structure. Thus,
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even during motion the film does not become totally liquid-like. Indeed, if there is some “in-plane” ordering within a film, it will exhibit a yield-point before it begins to flow. Such films can therefore sustain a finite shear stress, in addition to a finite normal stress. The value of the yield stress depends on the number of layers comprising the film and represents another “quantized” property of molecularly thin films. The dynamic properties of a liquid film undergoing shear are very complex. Depending on whether the film is more liquid-like or solid-like, the motion will be smooth or of the stick-slip type. During sliding, transitions can occur between n layers and (n – 1) or (n + 1) layers, and the details of the motion depend critically on the externally applied load, the temperature, the sliding velocity, the twist angle between the two surface lattices and the sliding direction relative to the lattices.
16.8.1 Smooth and Stick-Slip Sliding Recent advances in friction-measuring techniques have enabled the interfacial friction of molecularly thin films to be measured with great accuracy. Some of these advances have involved the surface forces apparatus technique (Israelachvili et al., 1988; Gee et al., 1990; Hirz et al., 1992; Homola et al., 1989, 1990, 1991), while others have involved the atomic force microscope (McClelland, 1989; McClelland and Cohen, 1990). In addition, molecular dynamics computer simulations (Schoen et al., 1989; Landman et al., 1990; Thompson and Robbins, 1990; Robbins and Thompson, 1991) have become sufficiently sophisticated to enable fairly complex tribological systems to be studied for the first time. All these advances are necessary if one is to probe such subtle effects as smooth or stick-slip friction, transient and memory effects, and ultra-low friction mechanisms at the molecular level. Figure 16.17 shows typical results for the friction traces measured as a function of time (after commencement of sliding) between two molecularly smooth mica surfaces separated by three molecular layers of the liquid OMCTS, and how the friction increases to higher values in a quantized way when the number of layers falls from n = 3 to n = 2 and then to n = 1. With the much added insights provided by recent computer simulations of such systems, a number of distinct molecular process have been identified during smooth and stick-slip sliding. These are shown
FIGURE 16.17 Measured change in friction during interlayer transitions of the silicone liquid octamethylcyclotetrasiloxane (OMCTS, an inert liquid whose quasispherical molecules have a diameter of 8 Å) (Gee et al., 1990). In this system, the shear stress Sc = F/A, was found to be constant so long as the number of layers n remained constant. Qualitatively similar results have been obtained with other quasispherical molecules such as cyclohexane (Israelachvili et al., 1988). The shear stresses are only weakly dependent on the sliding velocity v. However, for sliding velocities above some critical value vc, the stick-slip disappears and sliding proceeds smoothly in the purely kinetic value. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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stress
Applied stress
(a) AT REST stress
(b) STICKING
(c) SLIPPING (whole film melts)
stress Slip planes
(c') SLIPPING (one layer melts)
(c") SLIPPING (interlayer slip)
(d) REFREEZING
FIGURE 16.18 Idealized schematic illustration of molecular rearrangements occurring in a molecularly thin film of spherical or simple chain molecules between two solid surfaces during shear. Note that, depending on the system, a number of different molecular configurations within the film are possible during slipping and sliding, shown here as stages (c) total disorder as whole film melts, (c′) partial disorder, and (c″) order persists even during sliding with slip occurring at a single slip-plane either within the film or at the walls. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
schematically in Figure 16.18 for the case of spherical liquid molecules between two solid crystalline surfaces. The following regimes may be identified: Surfaces at rest — Figure 16.18a: Even with no externally applied load, solvent–surface epitaxial interactions can induce the liquid molecules in the film to solidify. Thus at rest the surfaces are stuck to each other through the film. Sticking regime (frozen, solid-like film) — Figure 16.18b: A progressively increasing lateral shear stress is applied. The film, being solid, responds elastically with a small lateral displacement and a small increase or “dilatency” in film thickness (less than a lattice spacing or molecular dimension, σ). In this regime the film retains its frozen, solid–like state — all the strains are elastic and reversible, and the surfaces remain effectively stuck to each other. However, slow creep may occur over long time periods. Slipping and sliding regimes (molten, liquid-like film) — Figure 16.18c, c′, c″: When the applied shear stress or force has reached a certain critical value Fs, the static friction force, the film suddenly melts (known as “shear melting”) or rearranges to allow for wall-slip or film-slip to occur, at which point the two surfaces begin to slip rapidly past each other. If the applied stress is kept at a high value, the upper surface will continue to slide indefinitely. Refreezing regime (resolidification of film) — Figure 16.18d: In many practical cases, the rapid slip of the upper surface relieves some of the applied force, which eventually falls below another critical value Fk, the kinetic friction force, at which point the film resolidifies and the whole stick-slip cycle is repeated. On the other hand, if the slip rate is smaller than the rate at which the external stress is applied, the surfaces will continue to slide smoothly in the kinetic state and there will be no more stick-slip. The critical velocity at which stick-slip disappears is discussed in more detail in Section 16.9.
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Experiments with linear chain (alkane) molecules show that the film thickness remains quantized during sliding, so that the structure of such films is probably more like that of a nematic liquid crystal where the liquid molecules have become shear aligned in some direction enabling shear motion to occur while retaining some order within the film. Computer simulations for simple spherical molecules (Thompson and Robbins, 1990) further indicate that during the slip, the film thickness is roughly 15% higher than at rest (i.e., the film density falls), and that the order parameter within the film drops from 0.85 to about 0.25. Both of these are consistent with a disorganized liquid–like state for the whole film during the slip, as illustrated schematically in Figure 16.18c. At this stage, we can only speculate on other possible configurations of molecules in the slipping and sliding regimes. This probably depends on the shapes of the molecules (e.g., whether spherical or linear or branched), on the atomic structure of the surfaces, on the sliding velocity, etc. Figure 16.18c, c′, and c″ show three possible sliding modes wherein the shearing film either totally melts, or where the molecules retain their layered structure and where slip occurs between two or more layers. Other sliding modes, for example, involving the movement of dislocations or disclinations are also possible, and it is unlikely that one single mechanism applies in all cases.
16.8.2 Role of Molecular Shape and Liquid Structure The above scenario is already quite complicated, and yet this is the situation for the simplest type of experimental system. The factors that appear to determine the critical velocity vc (Section 16.9.5) depend on the type of liquid between the surfaces (as well as on the surface lattice structure). Small spherical molecules such as cyclohexane and OMCTS have been found to have very high vc, which indicates that these molecules can rearrange relatively quickly in thin films. Chain molecules, and especially branched chain molecules, have been found to have much lower vc, which is to be expected, and such liquids tend to slide smoothly rather than in a stick-slip fashion (see Table 16.2). With highly asymmetric molecules, such as multiply branched isoparaffins and polymer melts, no regular spikes or stick-slip behavior occurs at any speed since these molecules can never order themselves sufficiently to “solidify.” Examples of such liquids are perfluoropolyethers and polydimethylsiloxanes (PDMS) (Figure 16.19). Recent computer simulations (Gao, et al., 1997a,b; He et al., 1999) of the structure, interaction forces, and tribological behavior of chain molecules between two shearing surfaces indicate that both linear and singly or doubly branched chain molecules order between two flat surfaces by aligning into discrete layers parallel to the surfaces. However, in the case of the weakly branched molecules the expected oscillatory forces do not materialize because of a complex cancellation of entropic and enthalpic contributions to the interaction free energy which results in a monotonically smooth interaction, exhibiting a weak energy
TABLE 16.2
Effect of Molecular Shape and Short-Range Forces on Tribological Propertiesa
Liquid (dry)
Short-Range Force
Type of Friction
Friction Coefficient
Bulk Liquid Viscosity (cP)
Quantized stick-slip Quantized stick-slip Stick-slip ↔ smooth Stick-slip ↔ smooth Smooth Smooth
1 1.5 1.0 0.3 0.4 0.03
0.6 0.5 2.3 5.5 50 800
Organic Cyclohexane Octane Tetradecane Octadecane (branched) PDMSb (M = 3700, melt) PBDb (M = 3500, branched)
Oscillatory Oscillatory Oscil ↔ smooth Oscil ↔ smooth Oscil ↔ smooth Smooth
Water Water (KCl solution) a b
Smooth
Smooth
0.01–0.03
For molecularly thin liquid films between two shearing mica surfaces at 20°C. PDMS: polydimethylsiloxane, PBD: polybutadiene, OMCTS: octamethylcyclotetrasiloxane.
1.0
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Stiction spike
Fs
Friction force
Fk
Stop sliding
Start sliding Time FIGURE 16.19 Stiction is the high starting frictional force Fs experienced by two moving surfaces which causes them to jerk forward rather than accelerate smoothly from rest. It is a major cause of surface damage and wear. The figure shows a typical “stiction spike” or “starting spike,” followed by smooth sliding in the kinetic state. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
minimum rather than the oscillatory force profile that is characteristic of linear molecules. During sliding, however, these molecules can be induced to align further, which can result in a transition from smooth to stick-slip sliding. Table 16.2 shows the trends observed with some organic and polymeric liquids between smooth mica surfaces. Also listed are the bulk viscosities of the liquids. From the data of Table 16.2 it appears that there is a direct correlation between the shapes of molecules and their coefficient of friction or effectiveness as lubricants (at least at low shear rates). Small spherical or chain molecules have high friction with stick-slip because they can pack into ordered solid–like layers. In contrast, longer chained and irregularly shaped molecules remain in an entangled, disordered, fluid-like state even in very thin films, and these give low friction and smoother sliding. It is probably for this reason that irregularly shaped branched chain molecules are usually better lubricants. It is interesting to note that the friction coefficient generally decreases as the bulk viscosity of the liquids increases. This unexpected trend occurs because the factors that are conducive to low friction are generally conducive to high viscosity. Thus, molecules with side groups such as branched alkanes and polymer melts usually have higher bulk viscosities than their linear homologues for obvious reasons. However, in thin films the linear molecules have higher shear stresses because of their ability to become ordered. The only exception to the above correlations is water, which has been found to exhibit both low viscosity and low friction (see Figure 16.12). In addition, the presence of water can drastically lower the friction and eliminate the stick-slip of hydrocarbon liquids when the sliding surfaces are hydrophilic. If an “effective” viscosity ηeff were to be calculated for the liquids in Table 16.2, the values would be many orders of magnitude higher than those of the bulk liquids. This can be demonstrated by the following simple calculation based on the usual equation for Couette flow (see Equation 16.8):
ηeff = Fk D Av
(16.30)
where Fk is the kinetic friction force, D is the film thickness, A the contact area, and v the sliding velocity. Using typical values for experiments with hexadecane (Yoshizawa and Israelachvili, 1993): Fk = 5 mN, D = 1 nm, A = 3 × 10–9 m2 and v = 1 µm/sec, yields ηeff ≈ 2000 N m–2 s, or 20,000 Poise, which is ~106 times higher than the bulk viscosity ηbulk of the liquid. It is instructive to consider that this very high effective viscosity nevertheless still produces a low friction force or friction coefficient µ of about 0.25. It is interesting to speculate that if a 1 nm film were to exhibit bulk viscous behavior, the friction coefficient under the same sliding conditions would be as low as 0.000001. While such a low value has never been
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FIGURE 16.20 Schematic view of interfacial film composed of spherical molecules under a compressive pressure between two solid crystalline surfaces. If the two surface lattices are free to move in the XYZ directions so as to attain the lowest energy state, they could equilibrate at values of X, Y, and Z, which induce the trapped molecules to become “epitaxially” ordered into a solid-like film. (B) Similar view of trapped molecules between two solid surfaces that are not free to adjust their positions, for example, as occurs in capillary pores or in brittle cracks. (C) Similar to (A) but with chain molecules replacing the spherical molecules in the gap. These may not be able to order as easily as do spherical molecules even if X, Y, and Z can adjust, resulting in a situation that is more akin to (B). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
reported for any tribological system, one may consider it as a theoretical lower limit that could, conceivably, be attained under certain experimental conditions. Various studies (Van Alsten and Granick, 1990a,b, 1991; Granick, 1991; Hu and Granick, 1992) have shown that confinement and load generally increase the effective viscosity and/or relaxation times of molecules, suggestive of an increased glassiness or solid-like behavior. This is in marked contrast to studies of liquids in small confining capillaries, where the opposite effects have been observed (Warnock et al., 1986; Awschalom and Warnock, 1987). The reason for this is probably that the two modes of confinement are different. In the former case (confinement of molecules between two structured solid surfaces), there is generally little opposition to any lateral or vertical displacement of the two surface lattices relative to each other. This means that the two lattices can shift in the x-y-z space (Figure 16.20A) to accommodate the trapped molecules in the most crystallographically commensurate or “epitaxial” way, which would favor an ordered, solid-like state. In contrast, the walls of capillaries are rigid and cannot easily move or adjust to accommodate the confined molecules (Figure 16.20B), which will therefore be forced into a more disordered, liquid-like state (unless the capillary wall geometry and lattice is exactly commensurate with the liquid molecules, as occurs in certain zeolites). Experiments have demonstrated the effects of surface lattice mismatch on the friction between surfaces (Hirano et al., 1991; Berman, 1996). Similar to the effects of lattice mismatch on adhesion (Figure 16.2, Section 16.2.1), the static friction of a confined liquid film is maximum when the lattices of the confining surfaces are aligned. For OMCTS confined between mica surfaces (Berman, 1996) the static friction was found to vary by more than a factor of 4 (Figure 16.21), while for bare mica surfaces the variation was by a factor of 3.5 (Hirano et al., 1991). In contrast to the sharp variations in adhesion energy over small twist angles, the variations in friction as a function of twist angle were much more broad — both in magnitude and angular spread. Similar variations in friction as a function of twist or misfit angles have also been observed in computer simulations (Gyalog and Thomas, 1997).
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FIGURE 16.21 Static friction of a 2-nm-thick OMCTS film as a function of the lattice twist angle between the two confining crystalline mica surfaces. The variation in friction is comparable to variations in an unlubricated mica–mica system (Hirano et al., 1991). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Robbins and co-workers (He et al., 1999) computed the friction forces of two clean crystalline surfaces as a function of the angle between their surface lattices. They found that for all nonzero angles (finite “twist” angles) the friction forces fell to zero due to incommensurability effects. They further found that submonolayer amounts of organic or other impurities trapped between two incommensurate surfaces can generate a finite friction force, and they therefore concluded that any finite friction force measured between incommensurate surfaces is probably due to such “third-body” effects. With rough surfaces, i.e., those that have random protrusions rather than being periodically structured, we expect a smearing out of the correlated intermolecular interactions that are involved in film freezing and melting (and in phase transitions in general). This should effectively eliminate the highly regular stick-slip and may also affect the location of the slipping planes. The stick-slip friction of “real” surfaces, which are generally rough, may therefore be quite different from those of perfectly smooth surfaces composed of the same material (see next section). We should note, however, that even between rough surfaces, most of the contacts occur between the tips of microscopic asperities, which may be smooth over their microscopic contact area.
16.9 Stick-Slip Friction An understanding of stick-slip is of great practical importance in tribology (Rabinowicz, 1965) since these spikes are the major cause of damage and wear of moving parts. But stick-slip motion is a much more common phenomenon and is also the cause of sound generation (the sound of a violin string, a squeaking door, or the chatter of machinery), sensory perception (taste texture and feel), earthquakes, granular flow, nonuniform fluid flow such as the “spurting” flow of polymeric liquids, etc. In the previous section the stick-slip motion arising from freezing–melting transitions in thin interfacial films was described, but there are other mechanisms that can give rise to stick-slip friction, which will now be considered. However, before proceeding with this, it is important to clarify exactly what one is measuring during a friction experiment. Figure 16.22 shows the basic mechanical coupling and equivalent mechanical circuit characteristic of most tribological systems and experiments. The distinction between F and F0 is important because in almost all practical cases, the applied, measured, or detected force, F, is not the same as the “real” or “intrinsic” friction force, F0, generated at the surfaces. F and F0 are coupled in a way that depends on
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A. Typical system geometry Friction force F measured here
Sliding velocity V Mechanical coupling K
Friction force F 0 generated here
B. Equivalent mechanical circuit load L
X=Vt
F Spring stiffness K
F0
Drive
Stage (M) V0=X0 Surfaces
Contact area A Surface energy ϒ Film thickness D Film viscosity η
FIGURE 16.22 (A) Schematic geometry of two shearing surfaces illustrating how the friction force, F0, which is generated at the surfaces, is generally measured as F at some other place. The mechanical coupling between the two may be described in terms of a simple elastic stiffness or compliance, K, or in terms of more complex nonelastic coefficients, depending on the system. Here, the mechanical coupling is simply via the backing material supporting one of the surfaces. (B) Equivalent mechanical circuit for the above set-up applicable to most tribological systems. Note that F0 is the force generated at the surfaces, but that the measured or detected force is F = (X – Xo)K. The differences between the forces, the velocities, and the displacements at the surfaces and at the Drive (or detector) are illustrated graphically in Figures 16.24 through 16.27. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
the mechanical construction of the system, for example, the axle of a car wheel which connects it to the engine. In Figure 16.22A, this coupling is shown to act via the material supporting the upper surface, which can be modeled (Figure 16.22B) as an elastic spring of stiffness K and mass M. This is the simplest type of mechanical coupling and is also the same as in SFA- and AFM-type experiments, illustrated in Figure 16.23. More complicated real systems can be reduced to a system of springs and dashpots, as described by Luengo et al. (1997a). We now consider four different models of stick-slip friction. These are illustrated in Figures 16.24 to 16.27, where the mechanical couplings are assumed to be of the simple elastic spring type as shown in Figures 16.22 and 16.23. The first two mechanisms (Figures 16.24 and 16.26) may be considered as the “traditional” or “classical” mechanisms or models (Rabinowicz, 1965); the third (Figure 16.27) is essentially the same as the freezing–melting phase-transition model described in Section 16.8.
16.9.1 Rough Surfaces Model Rapid slips can occur whenever an asperity on one surface goes over the top of an asperity on the other surface. As shown in Figure 16.24, the extent of the “slip” will depend on asperity heights and slopes, on the speed of sliding, and on the elastic compliance of the surfaces and the moving stage. We may note that, as in all cases of stick-slip motion, the driving velocity (V) may be constant, but the resulting motion at the surfaces (V0) will display large slips as shown in the inset. This type of stick-slip has been described by Rabinowicz (1965). It will not be of much concern here since it is essentially a noise-type fluctuation, resulting from surface imperfections rather than from the intrinsic interaction between two surfaces. Actually, at the atomic level, the regular atomic-scale corrugations of surfaces can lead to periodic stickslip motion of the type shown here. This is what is sometimes measured by AFM tips (McClelland, 1989; McClelland and Cohen, 1990).
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FIGURE 16.23 (A) Schematic geometry of two contacting asperities separated by a thin liquid film. This is also the geometry adopted in most pin-on-disc, SFA and AFM experiments. In the SFA experiments described here, typical experimental values were: undeformed radius of surfaces, R ≈ 1 cm; radius of contact area, r = 10 to 40 µm; film thickness, D ≈ 10 Å; externally applied load, L = –10 to +100 mN; measured friction forces, F = 0.001 to 100 mN; contact pressures, p = 0 to 0.5 GPa; sliding or driving velocity, V = 0.001 to 100 µm/s; surface or interfacial energy, γ = 0 to 30 mJ/m2 (erg/cm2); effective elastic constant of supporting material, K = 108 N/m; elastic constant of frictionmeasuring spring, K = 500 N/m; temperature, T = 15 to 40°C. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 16.24 Figures 16.24 through 16.27 show three different models of friction and the stick-slip friction force vs. time traces they give rise to. Figure 16.24 shows Rabinowicz’ model (Rabinowicz, 1965) for rough surfaces which produces irregular stick-slip (inset) when the elastic stiffness of the system (reflected by the slopes of the SLIP lines) is not too high. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.2 Distance-Dependent Model Another theory of stick-slip, observed in solid-on-solid sliding, is one that involves a characteristic distance (but also a characteristic time, τs, this being the characteristic time required for two asperities to increase their adhesion strength after coming into contact). Originally proposed by Rabinowicz (1965, 1958), this model suggests that two rough macroscopic surfaces adhere through their microscopic asperities of characteristic length Dc. During shearing, each surface must first creep a distance Dc — the size of the contacting junctions — after which the surfaces continue to slide, but with a lower (kinetic) friction force that the original (static) value. The reason for the decrease in the friction force is that even though, on average, new asperity junctions should form as rapidly as the old ones break, the time-dependent adhesion and friction of the new ones will be lower than the old ones. This is illustrated in Figure 16.25.
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Dry
603
Lubricated
t=0 Contact
t=τs Creep Dc
FIGURE 16.25 Distance-dependent friction model (also known as the creep model) in which a characteristic distance Dc has to be moved to break adhesive junctions. The model also has a characteristic, τs, this being the time needed for the adhesion and friction forces per junction to equilibrate after each contact is made. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
The friction force therefore remains high during the creep stage of the slip, but once the surfaces have moved the characteristic distance Dc, the friction rapidly drops to the kinetic value. Any system where the kinetic friction is less than the static force (or one that has a negative slope over some part of its F0–V0 curve) will exhibit regular stick-slip sliding motion for certain values of K, m, and driving velocity, V. This type of friction has been observed in a variety of dry (unlubricated) systems such as paper-onpaper (Baumberger et al., 1994; Heslot et al., 1994) and steel-on-steel (Rabinowicz, 1958; Sampson et al., 1943; Heymann et al., 1954). This model is also used extensively in geologic systems to analyze rock-onrock sliding (Dieterich, 1978, 1979). While originally described for adhering macroscopic asperity junctions, the distance-dependent model may also apply to molecularly smooth surfaces. For example, for polymer lubricant films, the characteristic length Dc would now be the chain–chain entanglement length, which could be much larger in a confined geometry than in the bulk.
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FIGURE 16.26 The lower part of the figure shows the Stage or surface displacement X0, surface velocity V0 (= dX0/dt · or X0), and measured friction force F, as functions of time t for surfaces whose intrinsic friction force is F0. In general, F0 is a function of X0, V0, and t. Three specific examples are shown here corresponding to F0 either increasing monotonically (Case a), remaining constant (Case b), or decreasing monotonically (Case c) with V0. The latter case corresponds to a film that exhibits “shear thinning.” Only when F0(V0) has a negative slope is the resulting motion of the stick-slip type, characterized by very different motions and friction forces being detected at the surfaces (the Stage) and the detector (the Drive). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.3 Velocity-Dependent Friction Model This is the most studied mechanism of stick-slip and, until recently was considered to be the only cause of intrinsic stick-slip. If a friction force decreases with increasing sliding velocity, as occurs with boundary films exhibiting shear-thinning, the force (Fs) needed to initiate motion will be higher than the force (Fk) needed to maintain motion. Such a situation is depicted in Figure 16.26 (Case c) where a decreasing intrinsic friction force F0 with sliding velocity V0 results in the sliding surface or stage moving in a periodic fashion where, during each cycle, rapid acceleration is followed by rapid deceleration (see curves for X0 and V0 in Figure 16.26). So long as the drive continues to move at a fixed velocity V, the surfaces will continue to move in a periodic fashion punctuated by abrupt stops and starts whose frequency and amplitude depend not only on the function F0(V0) but also on the stiffness K and mass M of the moving stage, and on the starting conditions at t = 0. More precisely, referring to Figures 16.22 and 16.26, the motion of the sliding surface or stage can be determined by solving the following differential equation:
(
)
(
)
˙˙ = F − F = F − X − X K MX 0 0 0 0
(16.31)
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SLIP
STICK
STICK
Liquidlike state
Solidlike State
605
Solidlike state
Increasing velocity
V>Vc
V
Stick Slip
Fk
F
FS Fk
Velocity
Time
FIGURE 16.27 ”Phase transition” model of stick-slip, for example, where a thin liquid film alternately freezes and melts as it shears, shown here for 22 spherical molecules confined between two solid crystalline surfaces. This model differs from that of Figure 16.26 in that the intrinsic friction force F0 is here assumed to change abruptly (at the transitions) rather than smoothly or continuously. The resulting stick-slip is also different; for example, the peaks are sharper and the stick-slip disappears above some critical velocity, Vc. Note that while the slip displacement is here shown to be only two lattice spacings, in most practical situations it is much larger. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
or
(
)
˙˙ + X − X K − F = 0 MX 0 0 0
(16.32)
where F0 = F0(X0, V0, t) is the intrinsic or “real” friction force at the shearing surfaces which is generally · a function of X0, V0 = X0 and t, F is the force on the spring (the externally applied or measured force), and Fs = (F0 – F) is the force on the stage. To fully solve Equation 16.31, one must also know the initial (starting) conditions at t = 0, and the driving or steady-state conditions at finite t. For example, in the present experiments, the driving condition is
X =0
for t < 0,
X = Vt for t > 0, where V = constant
(16.33)
In other systems, the appropriate driving condition may be F = constant. Various forms for F0 = F0(X0,V0,t) have been proposed, mainly phenomenological, to explain various kinds of stick-slip phenomena. These models generally assume a particular functional form for the friction as a function of velocity only, F0 = F0(V0), and they may also contain a number of mechanically coupled elements comprising the stage (Tomlinson, 1929; Carlson and Langer, 1989). One version is a two-state model characterized by two friction forces, Fs and Fk, which is a simplified version of the phase transitions model (next section). More complicated versions can have a rich F–v spectrum, as proposed by Persson (1994). Unless the experimental data are very detailed and extensive, these models cannot generally distinguish between different types of mechanisms. Neither do they address the basic question of the origin of the friction force, since this is assumed to begin with.
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Experimental data have been used to calculate the friction force as a function of velocity within an individual stick-slip cycle (Nasuno et al., 1997). For a macroscopic granular material confined between solid surfaces, the data show a velocity-weakening friction force during the first half of the slip. However, the data also show a hysteresis loop in the friction–velocity plot, with a different behavior in the deceleration half of the slip phase. Similar results were observed for a 1 to 2 nm liquid lubricant film between mica surfaces (Berman, Carlson, and Ducker, unpublished results). These results indicate that a purely velocity-dependent friction law is insufficient to describe such systems, and an additional element such as the state of the confined material must be considered (next section).
16.9.4 Phase Transitions Model Recent molecular dynamics computer simulations have found that thin interfacial films undergo firstorder phase transitions between solid-like and liquid-like states during sliding (Thompson and Robbins, 1990; Robbins and Thompson, 1991) and have suggested this is responsible for the observed stick-slip behavior of simple isotropic liquids between two solid crystalline surfaces. With this interpretation, stickslip is seen to arise because of the abrupt change in the flow properties of a film at a transition (Israelachvili et al., 1990; Thompson et al., 1992) rather than the gradual or continuous change as occurs in the previous example. Such simulations have accounted for many of the observed properties of shearing liquids in ultrathin films between molecularly smooth surfaces, and have so far offered the most likely explanation for experimental data on stick-slip friction, such as shown in Figure 16.28. A novel interpretation of the well-known phenomenon of decreasing coefficient of friction with increasing sliding velocity has been proposed by Thompson and Robbins (1990) based on their computer simulation. This postulates that it is not the friction that changes with sliding speed v, but rather the time various parts of the system spend in the sticking and sliding modes. In other words, at any instant during sliding, the friction at any local region is always Fs or Fk, corresponding to the “static” or “kinetic” values. The measured frictional force, however, is the sum of all these discrete values averaged over the whole contact area. Since as v increases each local region spends more time in the sliding regime (Fk) and less in the sticking regime (Fs), the overall friction coefficient falls. One may note that this interpretation reverses the traditional way that stick-slip has been explained, for rather than invoking a decreasing friction with velocity to explain stick-slip, it is now the more fundamental stick-slip phenomenon that is producing the apparent decrease in the friction force with increasing sliding velocity. This approach has been studied analytically by Carlson and Batista (1996), with a comprehensive rate-and-state dependent friction force law. This model includes an analytic description of the freezing–melting transitions of a film, resulting in a friction force that is a function of sliding velocity in a natural way. This model predicts a full range of stick-slip behavior observed experimentally. An example of the rate- and state-dependent model is observed when shearing thin films of OMCTS between mica surfaces (Berman et al., 1996a,b). In this case the static friction between the surfaces is dependent on the time that the surfaces are at rest with respect to each other, while the intrinsic kinetic friction Fk0 is relatively constant over the range of velocities (Figure 16.29). At slow driving velocities, the system responds with stick-slip sliding, with the surfaces reaching maximum static friction before each slip event, and the amplitude of the stick-slip, Fs – Fk, is relatively constant. As the driving velocity increases, the static friction decreases as the time at relative rest becomes shorter with respect to the characteristic time of the lubricant film. As the static friction decreases with increasing drive velocity, it eventually equals the intrinsic kinetic friction Fk0, which defines the critical velocity Vc, above which the surfaces slide smoothly, without the jerky stick-slip motion. The above classifications of stick-slip are not exclusive, and molecular mechanisms of real systems may exhibit aspects of different models simultaneously. They do, however, provide a convenient classification of existing models and indicate which experimental parameters should be varied to test the different models.
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FIGURE 16.28 Exact reproductions of chart-recorded traces of friction forces at increasing sliding velocities V (in µm/s) plotted as a function of time for a hydrocarbon liquid (A) and a boundary monolayer (B). In general, with increasing sliding speed, the stick-slip spikes increase in frequency and decrease in magnitude. As the critical sliding velocity Vc is approached the spikes become erratic, eventually disappearing altogether at V = Vc. At higher sliding velocities the sliding continues smoothly in the kinetic state. Such friction traces are fairly typical for simple liquid lubricants and dry boundary lubricant systems, and may be referred to as the “conventional” type of static–kinetic friction. (A) Liquid hexadecane (C16H34) film between two untreated mica surfaces. Experimental conditions (see Figure 16.23): contact area, πr2 = 4 × 10–9 m2; load, L≈1 gm; film thickness, D = 0.4 to 0.8 nm; V = 0.08 to 0.4 µm/sec; Vc ≈ 0.3 µm/sec; atmosphere: dry N2 gas; T = 18°C. (B) Close-packed surfactant monolayers on mica (dry boundary lubrication) showing behavior qualitatively similar to that obtained above with a liquid hexadecane film. In this case, Vc ≈ 0.1 µm/sec. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.5 Critical Velocity for Stick-Slip For any given set of conditions, stick-slip disappears above some critical sliding velocity Vc, above which the motion continues smoothly in the liquid-like or kinetic state. The critical velocity is found to be well described by two simple equations. Both are based on the phase transition model, and both include some parameter associated with the inertia of the measuring instrument. The first equation is based on both experiments and simple theoretical modeling (Yoshizawa and Israelachvili, 1993):
Vc ≈
(F − F ) S
k
5Kτo
(16.34)
where το is the characteristic nucleation time or freezing time of the film. For example, inserting the following typically measured values for a ~10 Å thick hexadecane film between mica: (Fs – Fk) ≈ 5 mN, spring constant K ≈ 500 N/m, and nucleation time (Yoshizawa and Israelachvili, 1993) τo ≈ 5 sec, we obtain Vc ≈ 0.4 µm/s, which is close to typically measured values (Figure 16.28). The second equation is based on computer simulations (Robbins and Thompson, 1991):
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FIGURE 16.29 Measured friction Fs and Fk for increasing drive velocity V with OMCTS confined between two mica surfaces. Fs (solid circles) decreases with increasing velocity because at higher drive speeds the sticking time is shorter, resulting in less complete freezing of the lubricant layer. The observed Fk (open circles) increases as Fs decreases, resulting in a nearly constant intrinsic friction force Fk (triangles) ≈ (Fs + Fk)/2 for these underdamped conditions. The critical velocity is reached when Fs decreases to the intrinsic friction Fk. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Vc ≈ 0.1
∆F ⋅ σ M
(16.35)
where σ is a molecular dimension and M is the mass of the stage. Again, inserting typical experimental values into this equation, viz., M ≈ 20 gm, σ ≈ 0.5 nm, and (Fs – Fk) ≈ 5 mN as before, we obtain Vc ≈ 0.3 µm/s, which is also close to measured values. Stick-slip also disappears above some critical temperature Tc, which is not the same as the melting temperature of the bulk fluid. Certain correlations have been found between Vc and Tc , and between various other tribological parameters, that appear to be consistent with the principle of “time-temperature superposition,” similar to that occurring in viscoelastic polymer fluids (Ferry, 1980). We end by considering these correlations.
16.9.6 Dynamic Phase Diagram Representation of Tribological Parameters Both friction and adhesion hysteresis vary nonlinearly with temperature, often peaking at some particular temperature, T0. The temperature-dependence of these forces can therefore be represented on a “dynamic” phase diagram such as that shown in Figure 16.30. Experiments have shown that T0, and the whole bellshaped curve, are shifted along the temperature-axis (as well as in the vertical direction) in a systematic way when the load, sliding velocity, etc., are varied. These shifts also appear to be highly correlated with one another; for example, an increase in temperature produces effects that are similar to decreasing the sliding speed or load. Such effects are also commonly observed in other energy-dissipating phenomena such as polymer viscoelasticity (Ferry, 1980), and it is likely that a similar physical mechanism is at the heart all of such phenomena. A possible molecular process underlying the energy dissipation of chain molecules during
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FIGURE 16.30 Schematic “friction phase diagram” representing the trends observed in the boundary friction of a variety of different surfactant monolayers (Yoshizawa et al., 1993). The characteristic bell-shaped curve also correlates with the monolayers’ adhesion energy hysteresis. The arrows indicate the direction in which the whole curve is dragged when the load, velocity, etc., is increased. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
A
Solidlike
B
Amorphous
C
Liquidlike
FIGURE 16.31 Different dynamic phase states of boundary monolayers during adhesive contact and/or frictional sliding. Low adhesion hysteresis and friction is exhibited by solid-like and liquid-like layers (A and C). High adhesion hysteresis and friction is exhibited by amorphous layers (B). Increasing the temperature generally shifts a system from the left to the right. Changing the load, sliding velocity, and other experimental conditions can also change the “dynamic phase state” of surface layers, as shown in Figure 16.30. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
boundary layer sliding is illustrated in Figure 16.31, which shows the three main “dynamic” phase states of boundary monolayers. In contrast to the characteristic relaxation time associated with fluid lubricants, for unlubricated (dry, solid, rough) surfaces it has been established that there is a characteristic “memory distance” which must be exceeded before that system loses all memory of its initial state (original surface topography). The underlying mechanism for a characteristic distance was first used to successfully explain rock mechanics and earthquake faults (Ruina, 1983) and, more recently, the tribological behavior of unlubricated surfaces of ceramics, paper, and elastomeric polymers (Berthoud et al., 1999; Baumberger et al., 1999). Recent experiments (Israelachvili et al., 1999) suggest that fluid lubricants composed of complex branched-chain or polymer molecules may also have “characteristic distances” (in addition to characteristic relaxation times) associated with their tribological behavior — the “characteristic distance” being total sliding distance that must be exceeded before the system reaches its steady-state tribological conditions.
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Acknowledgment This work was supported by ONR grant N00014-931D269.
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17 Measurement of Adhesion and Pull-Off Forces with the AFM 17.1
Introduction ..................................................................... 617 Importance of Adhesion Measurements • Review of Adhesion Properties
17.2
Tip Properties • Surface Topography • Force–Distance Curves • Influence of Pull-Off Force on Tapping Mode • Pulsed-Force Mode
Othmar Marti University of Ulm
Experimental Procedures to Measure Adhesion in AFM and Applications..................................................... 624
17.3
Summary and Outlook.................................................... 633
17.1 Introduction The key to the successful operation of an AFM (Binnig et al., 1986) in the materials sensitive regime (Burnham and Colton, 1989; Miyamoto et al., 1990; Mizes et al., 1991) is the measurement of the interaction forces between the tip and the sample surface. The tip would ideally consist of only one atom, which is brought in the vicinity of the sample surface. A crude estimation shows that the interaction forces between the AFM tip and the sample surface should be smaller than about 10–7 N for bulk materials and preferably well below 10–9N for organic macromolecules. On the other hand, there are indications that the measured values, especially of the pull-off force, are considerably off from the theoretically expected values. The reasons are manifold: the shape and size of the tip is not well known (Godowski et al., 1995; Lekka et al., 1997; Ramirez-Aguilar and Rowlen, 1998). The composition of the surfaces of the tip and the sample might differ strongly from their bulk values. Another possibility is that the continuum mechanical models (Johnson, 1992; 1996; Johnson et al., 1971; Maugis, 2001) usually employed to analyze the data might fail. Pull-off force measurements (Creuzet et al., 1992; Mizes et al., 1991; Weisenhorn et al., 1992), often called adhesion measurements, have been carried out for some years. The number of published papers shows that the method has become more and more popular. The theories of contact mechanics that are used in these investigations date back to the time when the only available test bodies were macroscopic. The remarkable precision with which these theories work in the sub-mm regime was first questioned by Stalder and Dürig (Dürig and Stalder, 1997; Stalder and Dürig, 1996). This chapter will discuss the measurement of adhesion with the AFM and the data interpretation with respect to macroscopic theories. The discussion of limiting cases will pinpoint possible limitations.
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FIGURE 17.1 Contact angle measurement. Surface energies are often measured by the contact angle method. A drop of liquid is placed on the sample. The surface energies of the liquid vs. the gas, of sample surface vs. the gas, and of the sample surface vs. the liquid have to balance tangentially, resulting in the equation given above.
17.1.1 Importance of Adhesion Measurements The tip in an AFM is in contact, in intermittent contact, or close to the sample surface. The interaction of the tip and the sample therefore depends on the surface properties of both bodies. The physics of the interaction therefore dominates the imaging process in an AFM. Moreover it strongly affects the measurement of other quantities, such as the tapping phase (Sarid et al., 1998). The adhesion properties of sample surfaces are important in many applications. Adhesive tapes, for instance, require a high adhesive force almost independent of the opposite material (Jiaa et al., 1994; Koinkar and Bhushan, 1996a). Magnetic tapes and computer hard disks, on the other hand, work best if the adhesion with the read and write heads is minimal. Micromechanical devices (MEMS) require a careful control of adhesion (Bhushan, 1996). Bearings should have low adhesion, parts where two materials are joined should have a higher adhesion. As these examples have shown, if it is necessary to control adhesion properties, it is also necessary to measure adhesion which is often correlated with surface energies. Figure 17.1 shows the classical way to measure adhesive properties. A drop of a liquid with a known surface energy is put on the sample. As Figure 17.1 shows, there has to be a balance of forces parallel to the sample surface. This results in the drop having a contact angle Θ with the sample. The equilibrium is reached when
γ S = γ SL + γ L cosΘ
(17.1)
Here the subscript S denotes surface energy of the sample with respect to the ambient medium, SL denotes the surface energy of the sample and the liquid, and L the surface energy of the liquid with respect to the ambient. This measurement method works reliably, but it is almost impossible to characterize areas with micrometer diameters. Therefore it is necessary to use a microscopic tool such as the AFM for these measurements.
17.1.2 Review of Adhesion Properties Adhesion is one of the main forces holding bodies of different materials together. As outlined above, adhesion is measured using test bodies. This chapter summarizes the literature (Dürig and Stalder, 1997; Johnson, 1992, 1996, 1997; Maugis, 2001), as it applies to AFM. The most common test body is the sphere. Figure 17.2 shows a sketch of such an interaction. The spherical body (radius R) is in contact with the sample with a circular region with radius Rc . A force F is applied to the body. A positive force means that the body is pressed against the surface. A negative force means that the adhesion keeps the contact, although the force is trying to separate sample and test body. The indentation of the spherical test body into the sample is called δ. 17.1.2.1 Hertz The laws of indentation and adhesion are highly nonlinear. Hertz was the first to formulate the laws of interaction of a spherical test body with a planar surface (Hertz, 1881). Figure 17.2 shows the definitions
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FIGURE 17.2 Definition of the quantities for the indentation of a spherical test body. The sphere has the radius R. The radius of the contact area is RC . The indentation depth is δ.
for the equations. Hertz formulated his theory of indentation without any adhesive or other long-range forces. The contact radius Rc is then
Rc3 = DRF
(17.2)
2 1 − ν2 3 E
(17.3)
D=
where F is the applied force, R the radius of the spherical test body, E the Young’s modulus, and ν the Poisson number. Figure 17.3 shows the function. The indentation depth δ is then given by
δ3 =
D2 F 2 R
(17.4)
2.00
Yield line
1.80 1.60
JKR 1.40
Rc/R0
1.20
DMT
1.00 0.80
Hertz
0.60 0.40 0.20 0.00 -1.50
-1.00
-0.50
0.00
0.50
1.00
f/f0
FIGURE 17.3 Curves from different contact mechanics theories. The thin line shows the Hertz theory; the fat solid line, the main branch of the JKR theory; the faint fat line is the second branch of the JKR theory; the long-dashed line is the DMT theory; and the dotted line is the yield stress line. The values were calculated for polypropylene, as shown in Table 17.1.
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Equation 17.4 shows that there is a nonlinear law connecting the indentation depth and the applied force. Also the indentation depth is inversely proportional to the tip radius. The force, although depending in a nonlinear fashion on the indentation, is a single-valued function. Therefore any interaction will be well behaved with no hysteresis. The contact stiffness kc is then given by 1
F FR 3 R 3 kc = = 2 = c δ D D
(17.5)
This equation is the basis for the conversion of the indentation δ and the applied force F to the contact radius Rc . 17.1.2.2 DMT The Derjaguin Muller–Toporov–Theory (Derjaguin et al., 1975) is closely related to the Hertz theory. In addition to the Hertz theory, DMT takes into account adhesion inside the junction. This leads to the equation
Rc3 FDR 2π%γR2D
(17.6)
The indentation depth is then given by the same Equation 17.4 as for the Hertz case. Figure 17.3 shows this curve. The force as a function of the contact radius is given by
Rc3 − 2π∆γ R DR
F=
(17.7)
17.1.2.3 JKR One of the most popular models for contact mechanics which includes adhesion effects is the model by Johnson, Kendall, and Roberts (Johnson et al., 1971). The adhesion is included by defining the pull-off force F0
F0
3 πR%γ 2
(17.8)
where ∆γ is the surface energy difference between the spherical test body and the sample surface. The minimum contact area is
R0 = DRF0
(17.9)
The applied force F and the contact radius Rc are connected by the following equation
F Rc3 = DR F + 2F0 1 ± 1 + F0
(17.10)
Figure 17.3 shows this function. The branch with the + sign is the stable one, whereas the other can not be probed by a force controlled setup. The equation can be solved for F. One then obtains 2
R3 c F = − F0 − F0 DR
(17.11)
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17.1.2.4 Maugis The theory of Maugis (2001) gives a smooth interpolation between the two extreme cases shown above: the DMT theory and the JKR theory. Generally, the real sample behaves in the intermediate range of the two theories. Chapter 4 gives a detailed account of this theory. 17.1.2.5 Effect of Tensile Stress Adhesion measurement in AFM is closely related to the measurement of pull-off forces. The interactions of the tip with the sample as well as the deformation of the sample before the separation influence the measurement. The speed of separation does influence materials made of long molecules. Therefore we limit our discussion to the case of tensile stress on the sample, the situation just before the breaking of the adhesive junction with the tip. Compressive stress and the dwell time in the indentation regime affect the contact area. This section is intended to raise the reader’s awareness of the fact that the deformation of the sample may not be neglected. When the spherical test body is pulling on the sample, the tensile stress might exceed the yield stress of the junction (Dürig and Stalder, 1997). The tensile yield stress H relates to the force Fyield with the following equation
Fyield = − σ π Rc2
(17.12)
where Rc is the radius of the contact area, which is assumed to be circular. The JKR or the DMT theory relates Rc to the applied force. Assuming that the starting force is set at a constant value such as is the case in the pulsed force mode (Krotil et al., 1999; Rosa-Zeiser et al., 1997) the starting contact area is kept constant. Since the two force laws (Equations 17.12 and 17.11 or 17.6) have a different dependence on the contact radius, only the law which has the lower contact radius Rc will prevail. Hence there will be a crossover force Fmax which is given by
( )
Fmax = Fyield = F Rc
(17.13)
This equation always has a solution for the DMT theory. By equating Equations 17.13 and 17.7 one obtains an implicit equation for the maximum force:
[
F 3 = −π 3 σ 3 D 2 FR + 2π∆γ R2
]
2
(17.14)
The crossing of the two curves is given by the solution of the above equation. This value in the same time is the maximum negative force sustainable by the junction. For the JKR theory we can do a similar calculation. The point where the two curves cross is given by 2
3 F Fmax = − σπ Rc2 = − σπ D R Fmax + 2F0 1 ± 1 + max F0 2 3
2 3
(17.15)
This is an implicit equation for the force F. Due to its nonlinear behavior it must be solved numerically. Large tensile yield stresses mean that the curve Equation 17.12 crosses curve Equation 17.10 on the negative branch. This is the situation where the finite tensile yield stress of the junction is not relevant. However, if the curve Equation 17.12 crosses curve Equation 17.10 exactly at F0 we have the limiting case. In that case the equation can be solved. 2
2
2
− F0 = −π D 3 R 3 σF03
(17.16)
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Modern Tribology Handbook
Critical Radius for Different Materials
Quantity
Symbol
PP
HDPE
LDPE
PVC
PS
PMMA
Nylon 6
V2A Steel
Young’s modulus Poisson ratio Yield stress Ratio JKR Ratio DMT Max force before yield Critical radius (20)
E ν σ αJKR αDMT Fmax Rcrit
1.4 GPa 0.43 32 MPa 35% 16% 1.5 nN 31 µm
1 GPa 0.47 30 MPa 36% 19% 2.3 nN 21 µm
0.2 GPa 0.49 8 MPa 28% 13% 1 nN 46 µm
2.6 GPa 0.42 48 MPa 35% 16% 1.5 nN 31 µm
3.4 GPa 0.38
3.2 GPa 0.40
1.9 GPa 0.44 50 MPa 42% 22% 3.1 nN 15 µm
195Gpa 0.28
Break stress Ratio JKR Ratio DMT Max force before break Critical radius (20)
B αJKR αDMT Fmax Rcrit,B
33 MPa 34% 16% 1.7 nN 28 µm
30 MPa 36% 19% 2.3 nN 21 µm
10 MPa 37% 20% 2 nN 24 µm
50 MPa 33% 15% 1.7 nN 27 µm
50 MPa 28% 13% 1.1 nN 43 µm
65 MPa 39% 18% 2.6 nN 18 µm
75 MPa 57% 29% 10 nN 4.5 µm
700MPa 28% 13% 1.1 nN 45 µm
The critical radius is calculated both for the yield and the break stress. The ratio values were calculated with R = 100 nm and ∆γ = 1 N/m. They give the pull-off force as a percentage of the pull-off force one would measure if DMT or JKR were applicable references: polymers: van Kevele, 1976; steel: Vogel, 1995.
From this equation one can calculate the maximum sustainable force for a tip with the radius R
Fmax = π 3 σ 3 D 2 R2
(17.17)
Likewise one can calculate for a given force the critical tensile yield stress H.
σ crit =
3 ∆γ 1 3 F0 1 3 πR∆γ = 3 2 2 2 = 3 22 2 2 2 π D R π D R π D R
(17.18)
For H > Hcrit the contact mechanics shows full JKR behavior. However, for softer materials this is no longer true. One can also solve Equation 17.18 for the radius Rcrit of the spherical test body.
Rcrit =
F0 = 3 2 3 π D σ
3 2
π Rcrit ∆γ
π 3 D2 σ 3
(17.19)
Solving Equation 17.19 for the critical tip radius Rcrit , one obtains
Rcrit =
3∆γ 2π D 2 σ 3 2
(17.20)
For a tip radius R < Rcrit , the junction becomes unstable before the JKR limit is reached. Hence for certain materials there will always be a deviation from JKR behavior. Table 17.1 shows results for selected materials, mainly from the polymers group. The critical tip radius Rcrit gives the radius of curvature which must be exceeded to observe the JKR behavior to the end. Table 17.1 clearly demonstrates that the pull-off force is a distinct function of the tensile yield stress σ. The measured pull-off forces are as small as 10% of what one would have detected without the yield barrier. The “max force before break” or the “max force before yield” values show that the JKR theory is applicable without any corrections, provided the pull-off force is below the value shown. The simple JKR theory Equation 17.8 gives for the surface energy
∆γ = −
2 Fmax 3π R
(17.21)
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FIGURE 17.4 Correction factors to compensate for the effect of the finite yield stress of materials. Shown is a calculation for a tip radius of 100 nm and the sample material polypropylene (see Table 17.1) The squares show the result for the DMT theory; the diamonds represent the JKR theory.
The DMT theory Equation 17.7, on the other hand, predicts
∆γ = −
1 Fmax 2π R
(17.22)
If one includes the effects of the finite tensile yield stress σ, one must use Equation 17.15. Whereas it is not possible to find a simple solution for the pull-off force Fmax , one can easily solve Equation 17.15 for F0 and hence for ∆γ
2 Fmax ∆γ = D − 3π πσ
−3
2
3 2 F 1 − max −F πσ DR max
2
(17.23)
Likewise one can also solve for the DMT value of the surface energy using Equation 17.14 3 1 Fmax 1 Fmax 2 ∆γ = − + 2 − 2π R R D πσ
(17.24)
Hence, even though the tensile yield stress reduces the pull-off forces in an AFM experiment, there is an analytical way to correct for these problems. Curves calculated with Equations 17.23 and 17.24 are shown in Figure 17.4. The surface energy for samples obeying the DMT laws is always below the correct value and has to be corrected. The measurement of the surface energy for a JKR-type sample is correct when
2 ∆γ < π2 σ 3 D 2 R 3
(17.25)
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is measured. Equivalently, one might state that the surface energy is correct according to JKR if
Fmax < π 3 σ 3D 2 R2
(17.26)
You find a calculation of this force in Table 17.1. What does it mean if the contact mechanics equations say that tensile stress will be the failure mechanism of the tip–sample junction? • When the pull-off force is larger than predicted by the yield stress argument, one can conclude that continuums theories such as JKR, DMT, or Hertz do not adequately describe the physics of the separation. It was shown by several authors (Cross et al., 1998; Landman et al., 1992; Rubio et al., 1996; Stalder and Dürig, 1996b) both theoretically and experimentally that the tensile stress on the junction shortly before the separation from the tip can exceed the limits set by continuums mechanical theories. Hence a comparison of the actual data with the Dürig (Dürig and Stalder, 1997) theory discussed above gives a criterion for the applicability of standard theories. • In an intermediate regime of AFM tip radii of 50 nm, it is often the case that the yield stress is reached before the crazing mechanism usually responsible for the detachment of the tip and the sample sets in. As a consequence, one expects (and also finds in certain cases) that the tips are contaminated by the sample.
17.2 Experimental Procedures to Measure Adhesion in AFM and Applications The forces of an AFM tip in contact with the sample should in principle be given by the contact mechanics. The tip of the AFM, however, is usually small. Hence the ideas outlined above show that one needs to know the shape and the surface properties of the tip. The ideas above were deduced assuming a flat surface. Real sample topographies are usually rough. Hence one has to calculate the effect of steps on the pull-off force image. This is done using a simple theory based on continuum mechanics. Finally, we discuss force–distance curves, the influence of pull-off force on the tapping mode, and pulsed force mode techniques for AFM. The measurement in the AFM are further complicated by the compliance of the cantilever necessary to measure forces.
17.2.1 Tip Properties Cantilevers are made from a wide range of materials (Akamine et al., 1990; Grütter et al., 1990; Marti, 1998; Pitsch et al., 1989; Wolter et al., 1991). Most cantilevers are made of Si and of Si3N4 . The realizable thickness depends on the fabrication process and the material properties. Grown materials such as Si3N4 can be made thinner than those fabricated out of the bulk. Cantilevers come basically in two flavors. Straight dashboard-like types are preferentially used for lateral force measurements and noncontact modes. Their properties are rather easy to calculate. Triangular shaped cantilevers are easier to align, but harder to handle numerically. They are usually made of silicon nitride. Their response to lateral forces is more complicated. Whereas triangular cantilevers must be calculated using finite element methods, one can get a good estimate of the normal force compliance of the straight ones using analytical methods. Using the equation for straight cantilevers
kN =
F Eb h = z 4 l
3
(17.27)
2 and observing that the length of the two joined cantilever beams in a triangular cantilever are leff = l2 + 2 (w/2) , where w is the width of the base of the cantilever, one gets for the compliance
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Ebh 3 2 w 2 kN = l + 2 4
3
625
2
(17.28)
The radius of curvature of silicon nitride cantilevers is limited to about 30 to 50 nm, because of the manufacturing process. The imperfections of the etch pits and the filled in silicon nitride limit the sharpness. Silicon nitride tips can be sharpened during the production by thermal oxidation (Akamine and Quate, 1992). Instead of directly depositing silicon nitride on the wafers with the pyramidal etch pits, an oxide layer is deposited first. Then the silicon nitride is added. When the oxide is removed with buffered oxide etch, a sharpening effect is observed. Details of the process are described by the inventors (Akamine and Quate, 1992). A second method is to grow in an electron microscope a so-called “supertip” on top of the silicon nitride. It is well known that in scanning electron microscopes with a base pressure of more than 10-10 mbar, hydrocarbon residues are present. These residues are cracked at the surface of the sample by the electron beam, leaving carbon in a presumed amorphous state on the surface. It is known that prolonged imaging in such an instrument degrades the surface. If the electron beam is not scanned, but stays at the same place, one can build up tips with a diameter comparable to the electron beam diameter and with a height determined by the dwell time. These tips are extremely sharp and can reach radii of curvature of a few nanometers. Therefore, they allow imaging with a very high resolution. In addition they enable the microscope to image the bottoms of small crevasses and ditches on samples. Unprocessed silicon nitride tips are not able to do this, since their sides enclose an angle of 90°, due to the crystal structure of the silicon. Alternatives to silicon nitride cantilevers are those made of silicon. The basic manufacturing idea is the same as for silicon nitride. Masks determine the shape of the cantilevers. Processes from the microelectronics fabrication are used. Since the thickness of the cantilevers is determined by etching and not by growth, wafers have to be more precise than for the manufacturing of the silicon nitride cantilevers. The manufacturing process of silicon cantilevers guarantees that the tip asperity has a well defined radius of curvature of 2 to 5 nm. Since the thickness of the silicon cantilever is determined by etching, it cannot be made as thin as the silicon nitride cantilever. The lower limit is typically 1 µm. Therefore the stiffness of silicon cantilevers is higher, ranging from 1 to 100 N/m. Since the material is a single crystal, unlike the silicon nitride, it has a very high quality of resonance. Values exceeding 100,000 have been observed in vacuum. Therefore silicon cantilevers are often used for noncontact or tapping mode experiments. The cantilevers have two drawbacks when working in contact mode. First, they have a very high affinity to organic materials. They often destroy such samples. Second, their index of refraction matches that of water rather closely. Silicon cantilevers have a very poor reflectivity in aqueous environments. Occasionally cantilevers are made with tungsten wire (Marti et al., 1987) or thin metal foils, with tips of diamond (Marti et al., 1988) or other materials glued to them. The radius of curvature of a tip is not well defined. As outlined above and in the literature, the tip shape and the tip radius of curvature are often the results of uncontrollable processes. The initial variation of the tip radius is further increased by wear during use. Therefore the tip radius is one of the least known parameters in an AFM experiment. In many experiments one does not pay attention to the tip shape or radius. To obtain quantitative results it is imperative to inspect the tip before and after the AFM experiment. The size and shape of the tip influence the measured adhesion values (Bhushan and Sundararajan, 1998). Silicon nitride cantilevers were used to probe the adhesion forces vs. a silicon (100) sample. It was found that tip sizes in the order of 1 to 10 µm affect the adhesive forces. At high humidity, capillary forces increase the adhesion considerably. The main properties of an AFM tip are its surface energy and its radius. The surfaces of most cantilevers are made of silicon or silicon nitride. Since cantilevers are usually stored in air, their surfaces are often covered by a thin oxide layer. The surface energy of silicon ranges between 1 and 1.4 N/m (Burdorf, 1999). That of silicon oxide might be as high as 3.5 N/m. Silicon nitride, on the other hand, has a surface energy of 0.7 N/m.
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→
FIGURE 17.5 Geometry of the model calculation. The distance r between a point in the tip and a point in the → → sample is a combination of the distance z between the tip and the sample and the positions of the point in the tip rt → and of the point in the sample rS.
17.2.2 Surface Topography It was mentioned above that the models usually used to describe adhesion do not include effects of the topography (Bhushan, 1999; Koinkar et al., 1996). Therefore a model investigation was done at the University of Ulm. A model based on continuum mechanics and taking into account only interactions due to the shape of the tip and surface topography was established (Stifter et al., 1998). Interactions between the atoms of the tip and the sample were summed up (Figure 17.5). In the model, atoms are represented by a spherically symmetric potential that cannot account for chemical bonding. The interaction is composed of the attractive van der Waals force and the repulsive Pauli force. Both are combined in the Lennard–Jones potential
Vatom
r r r r r r = Vattr r + Vrep r = ε 0 − 2 0 r r
()
()
()
12
6
(17.29)
or
r a b Vatom r = − 6 + 12 r r
()
(17.30)
Here r0 is the position of the potential minimum and ε the depth of the potential minimum. The two potential parameters a and b are defined by
a = 2εr06 and b = εr012 →
(17.31) →
The vector r consists of a contribution of the tip–sample distance z and the local positions of the tip → → and sample, rs and rt , respectively. Equation 17.30 is used for the Lennard–Jones potentials because the two parts of the potential — attractive and repulsive — can be treated separately. Integrating the Lennard–Jones potential over the volume of the tip and the volume of the sample gives the interaction potential between the tip and sample. The integration is performed in two steps, first on the tip and then on the sample, to simplify changes in the surface shape. To simulate an SFM operating in the constant force mode, the force acting in the direction perpendicular to the sample surface is calculated. The
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FIGURE 17.6 Principle of the measurement of force–distance curves. Far away from the sample surface the cantilever spring is not deflected from the zero position (right side of the image). When the tip approaches the sample, an instability for soft cantilevers occurs. The tip snaps to the sample (“snap on peak”). The cantilever is deflected toward the sample (middle of the image), indicating a tensile stress at the tip–sample junction. Finally, at close approach the tip penetrates slightly into the sample. The cantilever spring is deflected away from the sample. When retracting the cantilever from the sample, the tip–sample junction breaks at a value larger than the snap-on peak. This force we call the pull-off force.
coordinate in this direction is the z axis. The x and y axes are in the plane of the sample surface. Figure 17.5 shows the coordinate system used for these calculations. The derivative of the potential with respect to z gives the force between the tip and the sample. For a (x, y) position on the sample, the z-feedback of the SFM determines the value the tip has to be moved to realize the preset force. The calculation works in the same way. For a given (x, y) position and a fixed force value Ffix , the surface distance ztopo was calculated. The pull-off force in the experiment is the maximal negative force appearing as the tip is removed from the surface. This corresponds to the minimum of the force Fmax curve vs. z (see Figure 17.6). A commonly used model for the tip is a sphere with radius R. The sample is represented as a plane. This model was solved in the literature (Stifter et al., 1998). Then the model can be expanded to include the effects of a surface step. The step represents a sharp topographical change. Only forces along a line perpendicular to the step have to be calculated. To get the force for the step, it was necessary to make two volume integrations. To simplify the calculation, the attractive and the repulsive parts of the Lennard–Jones potential (Equation 17.30) are treated separately. The first integration — over the volume of the tip — can be done analytically. The result of the integration is the potential between an atom in the surface and a sphere with radius R. The second integration is split into two parts: the infinite plane is handled analytically, and the terrace (a semiinfinite slab) is treated numerically. The step changes the interaction of the sample with the tip. Because of the curvature, the tip can approach closer to the surface. Its interaction changes. Figure 17.7 shows the influence of the material on the appearance of a step. The figure, calculated with the model outlined above, using a tip radius of 10 nm and a step height of 1 nm, nicely demonstrates that, within this theoretical framework which treats surfaces as infinitely stiff, the surface potential, given by parameters A and B, determines the adhesion. For a materials pairing with equal adhesive properties, a characteristic rim of higher adhesion appears. This feature is also present when the terrace has a higher adhesion. The conclusion from Figure 17.7 is that adhesion forces or pull-off forces are only meaningful at the flat parts of the sample. Figure 17.8 is a measurement by AFM of the adhesion across a step. The measurement confirms the theoretical model.
17.2.3 Force–Distance Curves The easiest way to measure pull-off force properties of a sample surface is to perform force–distance curves. Force–distance curves are obtained by slowly (1 nm/s to 1 µm/s) lowering the tip onto the sample.
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FIGURE 17.7 Adhesion at a step as a function of the material composition. The top part of the image shows the topography. The bottom part depicts the calculated adhesion trace across the step. A Lennard–Jones-type model was used. The three curves are calculated for the binding energy ε and binding distance R0 indicated in the figure. The tighter the tip is bound to the sample, the larger are the artifacts at the steps. The parameters for the sample away from the step correspond to Curve 2.
FIGURE 17.8 Pull-off force of a graphite step. The image size is 210 × 300 nm. The data were measured in a 1 mM solution of NaClO4. The simulations were calculated with a tip radius of 100 nm and a step size of 1.55 nm (multi step). Details of the calculation can be found in Stifter et al. (1998).
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FIGURE 17.9 Correction of the influence of the cantilever compliance. The cantilever compliance is the reason for the double minimum potential landscape when the tip interacts with the sample. On a stiff surface, the change of force when the cantilever base approaches the sample is given by the cantilever compliance. This compliance must be subtracted from the measured force–distance curves. On the adhesive part, the cantilever compliance creates a multivalued force curve, giving rise to adhesive hysteresis. The corrected curve has been calculated from the uncorrected curve. Both have the same underlying potential.
Figure 17.6 shows the principle of such an experiment. Far away from the sample, no force will act on the cantilever. When coming close to the sample, the nonlinear interaction of the tip with the sample will result in an, at least, double well potential. This potential has two stable positions. Which one will be realized depends on the history. At the point where the tip snaps to the surface, it jumps from one minimum to the second one. Upon further approaching the tip, the sample becomes indented. The slope of the force distance curve is now mainly given by the compliance kt of the cantilever. Assume that the sample has a compliance ks and the tip kt
1 1 1 = + keff ks kt
(17.32)
Hence the effective compliance of a soft cantilever and a stiff sample is almost entirely given by the soft cantilever. The effect of the cantilever can be compensated for. If one knows the sensitivity of the detection system (which deflection is necessary to measure a certain force), one can correct the slopes by subtracting the deflection of the cantilever from the position one imposed on the cantilever from the outside (Figure 17.9).
z true = z measured −
F k
(17.33)
The true z-position ztrue is calculated from the measured one zmeasured with Equation 17.33. The force F is determined by the AFM calibration, the compliance of the cantilever k has to be determined independently, or, as a first guess, to be taken from the manufacturer’s data sheets. The corrected curve should then be the real force interaction. As an example, Figure 17.10 shows a measured and corrected force–distance curve on a polystyrene sample. The cantilever compliance and response have been measured with a silicon sample. The values
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FIGURE 17.10 Measured force–distance curve. Shown on the horizontal axis is the distance to the sample surface. Zero is just before the position where the approach curve has its snap-on peak. The vertical axis depicts the force. There is a considerable hysteresis in the retract (unloading) curve. The molecules in the polystyrene samples seem to adhere to the tip; the tensile forces can considerably stretch the molecules before their adhesion bonds to the tip fail.
obtained in this way were used for the correction. The data clearly show that the simple model outlined here is not sufficient. First, the piezo actuators in the AFMs are hampered by hysteretic behavior. This behavior is not easily cast into equations. Therefore a good nano-indentation experiment would need a position control for z. Second, if plastic deformations occur in the sample (which, according to the reasoning above are almost inevitable), dissipation will separate the approach and the retract curves. The pull-off force in Figure 17.10 is about 30% of what the JKR theory predicts. This is why the pull off force has about the same magnitude as the snap-in force. The latter should not depend on the yield stress of the sample, since there is no contact before the sudden change in force.
17.2.4 Influence of Pull-Off Force on Tapping Mode A popular imaging mode in scanning force microscopy is the tapping mode (Anczykowski et al., 1996a,b, 1998; Sarid et al., 1996; Spatz et al., 1995, 1997; Winkler et al., 1996; Zhong et al., 1993). It was realized that adhesion can play an important role in the imaging properties (Evans and Ritchie, 1997; Izrailev et al., 1997; Sarid et al., 1998; Schmitz et al., 1997). In the tapping mode operation (also called dynamic mode operation) the cantilever of the AFM is operated at or near its resonance. The amplitude and phase of the oscillation are complex functions of the drive amplitude, frequency, and of the interaction potential between the tip and the sample. Experience showed that the phase was very sensitive to changes in the materials properties. The equation of motion for the cantilever can be formulated as follows:
∂2 mz˙˙ + 2δz˙ + 2 U z − d − z 0 cos ω 0t z − z 0 cos ω 0t = 0 ∂z
(
)(
)
(17.34)
where z is the position of the end of the cantilever, z0 the drive amplitude, d the separation of the cantilever reference point and the sample. δ is the damping of the cantilever, m its reduced mass, and U(z) the interaction potential. ω0 is the drive frequency. The instantaneous resonance frequency now changes along the trajectory of the tip. The resulting amplitude and phase will be an averaged function of the second derivative of the potential energy of the tip over a full period.
∂2 z˜ t = z ω 0 , f zU z 2 ∂z
()
() ()
(17.35)
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FIGURE 17.11 Phase change as a function of the adhesion properties for a polymer with E = 100 GPa. The solid and dashed lines show the theoretical calculation for the tapping-mode phase with and without taking adhesion into account. (From Sarid, D., Hunt, J.P., Workman, R.K., Yao, X., and Peterson, C.A. (1998), The role of adhesion in tapping-mode atomic force microscopy, Applied Physics A Materials Science & Processing, 66, S283-S286. With permission.)
The potential U(z) is weighted by some function f(z), which has a complicated dependence on the interaction details. From Equations 17.34 and 17.35, it is clear that the compliance of the sample will affect the resonance frequency. Since the tapping mode is usually performed with a constant resonance frequency, this means that the mechanical properties of the sample will show up in the amplitude, and also more prominently in the phase. Hard samples will increase the potential on the average, hence increasing the resonance frequency of the tip–sample system. Samples which exert a nonvanishing adhesive force on the tip lower the average potential for the tip–sample system. In a mean-field reasoning, the resonance frequency has to go down. The stronger the adhesion, the larger the phase shift of the system. Figure 17.11 shows data from Sarid et al. (1998). The phase change for a given set point as a function of the adhesion is clearly visible. A strong adhesive force can create multiwell potential landscapes. The oscillation of the cantilever can then be confined to one or the other well. Jumps between the wells can occur. This behavior has been observed, for instance by Anczykowski et al. (1998) (Figure 17.12). The jumps from one potential well to the other occur when the original well becomes unstable, i.e., loses its confinement. The result is a hysteresis when the set-point of the microscope is brought closer to the sample surface and then back again. It is not trivial to extract meaningful quantitative adhesion data from tapping-mode phase measurements. The effects of the finite yield stress of the material certainly have an influence on the depth of the potential wells. They will reduce the effects of adhesion. On the other hand, adhesion for macromolecules is always connected with a rearrangement of molecules. This rearrangement has its own time constants. In principle it should be calculated with molecular dynamics methods. Unfortunately these methods are not yet able to calculate the dynamics on the time scale relevant for a tapping-mode experiment.
17.2.5 Pulsed-Force Mode A third method to measure pull-off force properties (or better, pull-off forces) is the pulsed-force mode (PFM). A sinusoidal z-modulation is used to continuously acquire force vs. distance curves. The PFM is one of the so-called intermittent contact modes in AFM. The key to the operation of the PFM (and the tapping mode) is the frequency dependence of the elastic moduli of samples. The apparent shear modulus increases when the frequency of the acquisition of force-distance curves is increased. The time the tip is in contact with the surface can be directly estimated by the modulation frequency. Typically the AFM
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FIGURE 17.12 Influence of multiple potential wells on the tapping mode amplitude and phase behavior, experimental data. The cantilever was driven at the harmonic resonance frequency. A bias voltage was applied for the measurement at the right side to increase the attractive part of the potential. When combining the harmonic potential related to a Hookian spring with the interaction potential for two bodies, e.g., the Lennard–Jones potential or similar potentials, a double-well potential landscape is formed. Shown are the amplitude of the tapping-mode oscillation on the top and the phase on the bottom. In every part the sample surface is at zero z-position. (From Anczykowski, B., Cleveland, J.P., Kruger, D., Elings, V., and Fuchs, H. (1998), Analysis of the interaction mechanisms in dynamic mode SFM by means of experimental data and computer simulation, Appl. Phys. A Materials Science & Processing, 66, S885-S889. With permission.)
cantilever in the PFM is brought into contact at a rate of 1 to 10 kHz. Thus, the PFM has a contact time of about 10 µs (as measured from oscilloscope traces), compared to > 10 ms when measuring force–distance curves and ≈1 µs in tapping mode. Delicate samples can be measured this way, with a resolution and gentleness comparable to that of the tapping mode. Electronic circuitry (Krotil et al., 1999; Miyatani et al., 1998; Rosa-Zeiser et al., 1997) creates the sinusoidal modulation frequency, which is applied either to the z-electrode of the scan piezo or to a special modulation piezo. The sinusoidal shape is necessary to avoid the excitation of resonances in the microscope. The cantilever-base moves up and down, as depicted in Figures 17.13 and 17.14. The resulting force signal, as detected by the AFM head, is a repetitive measurement of force–distance curves. The peak positive force (1 in Figure 17.14) is detected by a “sample and hold” circuit. It serves as the input of the control loop and is fed into the AFM control electronics, faking a constant force measurement. The feedback loop now maintains a constant peak positive force. The PFM allows an exact determination of the peak interaction force independent of the operating environment.
FIGURE 17.13 Movement of the tip in the pulsed-Force mode measurement. In a typical setup the cantilever is mounted on a piezo. This piezo moves the cantilever base up and down with a predefined curve form. Most often a sinusoidal movement is used. As long as the cantilever is free, it is not bent, indicating that no interaction force is present. Indentation causes the cantilever to bend upwards, tensile forces before pull-off deflect the cantilever beam downwards.
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FIGURE 17.14 Operation of the pulsed force mode measurement (Krotil et al., 1999; Rosa-Zeiser et al., 1997). At point 1 a sample and hold circuit measures the peak indentation force. This force is kept constant by the feedback control circuits of the microscope. The peak force (Fmax) minus the force measured at 3 (Fis) is a function of the local sample stiffness and the cantilever stiffness kc. The force at 2 is the zero point value. It is constant if there are no long-range forces. It varies if magnetic, electrostatic, or other forces are present. Finally, the force at 4 measured by a peak picker circuit is the pull-off force.
The PFM automates the measurement of surface properties at every point on the sample by additionally sampling a few characteristic values of the force–distance curves using additional “sample and hold” circuits. It has a minimal impact on the data acquisition rate. Data taken from the curve are the local stiffness, the local pull-off force (adhesion), and local charges (Figure 17.14). The pull-off force output is the difference between the output of a peak-detector for negative forces and a sample and hold measuring the zero base line. These quantities are complementary to what one would get from tapping mode, where the phase signal is related to the energy dissipation and, sometimes, to the adhesion on the sample surface. As pointed out above, the measured pull-off forces have to be corrected for the finite yield stress of the samples. If this is done, then reliable values for the surface energies can be extracted. Figure 17.15 shows the effect of a changing Young’s modulus of the sample surface. The force curve on the hard material is shorter; the pull-off force is less. This is the behavior one would expect from the JKR theory. As an example, we show a measurement of spherulites in polypropylene (Hild et al., 1998; Marti et al., 1999). The images in Figure 17.16 were acquired in the PFM with a frequency of 1.6 kHz. The left side shows the topography; the right side, the pull-off force. The amorphous parts in the topography images appear to be lower than the crystalline areas. This can be explained by differences in local stiffness. For a given force, the tip indentation in the softer material is larger than in the harder one. Because of the different indentation at a given applied force, harder parts of a surface appear to be higher. In the pulloff force image, the amorphous parts between the crystalline lamellae exert a high force on the tip (dark color). The data on the right side of Figure 17.16 have not been corrected for the yield stress phenomenon.
17.3 Summary and Outlook The measurement of pull-off forces with the AFM is widespread nowadays. The interaction of the AFM tips and the sample surfaces yields valuable information on the surface energies of the samples. However, in day-to-day work, one is using methods like tapping mode, force–distance curves, and pulsed-force-mode
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FIGURE 17.15 Signals in the pulsed-force mode measurement. The top trace shows the movement of the piezo, which is the same as that of the mounting point of the cantilever spring. The bottom trace shows a typical force vs. time curve. The left side simulates the behavior on a stiff surface; the right side shows a typical trace obtained on a compliant, nonviscous surface. The measurement system determines the peak force Fmax and a second force value at a fixed time offset, Fis. The difference between these two forces depends on the stiffness of the sample.
FIGURE 17.16 Spherulite of polypropylene. The left image shows the topography; the right image, the pull-off force measurement. The scan size of both images is 1200 × 1200 nm. The height range in the left image is 35 nm (white corresponds to high lying areas; black to low lying areas). The pull-off force values range from –40 to –90 nN (white corresponds to low pull-off forces).
to get a quick overview of the sample. Usually one is interested in finding differences in the morphology of the samples. The quantitative nature of the pull-off force measurement is usually not necessary. However, experiments trying to correlate pull-off force measurements with theories sometimes fail. Usually one is able to range samples correctly with different methods. For polymer samples, often the absolute surface energies calculated from reasonable assumptions of the tip shape do not agree with measurements by contact angles. The idea of Stalder and Dürig (Dürig and Stalder, 1997) that the yield stress is an important quantity for the determination of surface energies has not been fully exploited yet. From the considerations in this chapter it is clear that probably no AFM, independent of the operating mode, works in the “adhesion” dominated regime. It rather operates in the yield stress or break stress dominated regime. The theoretical considerations show that the shape of the force–distance curve, if the movement of the z-piezo were linear, and the pull-off force together are sufficient to extract both the surface energy and the yield (break) stress from the data.
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If the shape of force–distance curves is not known, then one can use the macroscopic yield stress to infer the surface energy. One wonders why the tips of an AFM do not show substantial contamination with the sample material, since the failure of an AFM–sample junction seems to be located entirely within the sample. In the case of polymers, the situation is not as simple as one might guess. The macromolecules have typical gyration radii of up to 30 nm. Hence a junction might consist of only a few molecules. The yield-stress limit is an indication of the point up to which continuum mechanics apply. For smaller tips, one will have to take into account the discrete nature of the interaction. When one has to measure adhesion forces, or more specifically pull-off forces, one has to select the methods according to the priorities of the experiment. If a fast overview on the variations of surface properties and on the spatial distribution of them is desired, tapping-mode phase imaging is the method of choice. However, its physics is not easily handled. Extensive calculations and, probably, modeling of the sample–tip system are required to get quantitative data. The force–distance curves, on the other hand, allow a rather precise measurement of the pull-off forces, at the expense of speed. Imaging is almost impossible. Force–distance curves give the shape of the interaction, making it comparatively easy to calculate quantitative data. The pulsed-force mode is a compromise between the previous two measurement modes. It only acquires some selected values of the force–distance curve. This is done efficiently and poses no obstacle to imaging in reasonable time. Data from force–distance curves and from the pulsed-force mode can be corrected for the yield-stress effect. There is still considerable research necessary to sort out all the effects besides the adhesion forces in pull-off force measurements. Nevertheless, meaningful measurements can be done, provided the experiment is carefully planned. Therefore the AFM has a good chance to become a versatile mechanical testing device for ultra-small amounts of materials.
Acknowledgments The overview presented here is based on the contributions of many persons. I would like to thank Thomas Stifter, Hans-Ulrich Krotil, Sabine Hild, and Charly Imhof for the measurements. I had long discussions with Martin Pietralla, Sabine Hild, Thomas Stifter, Gerd-Ingo Asbach, and Bharat Bhushan on this subject. Gerhard Volswinkler built the electronics. This work was funded in part by the Deutsche Forschungsgemeinschaft (SFB 239), the Land Baden-Württemberg, and by Witec GmbH Ulm.
References Akamine, S., Barrett, R.C., and Quate, C.F. (1990), Improved atomic force microscope images using microcantilevers with sharp tips, Appl. Phys. Lett., 57, 316. Akamine, S. and Quate, C.F. (1992), Low temperature thermal oxidation sharpening of microcast tips, J. Vac. Sci. Technol., B10 (6), 2307-2311. Anczykowski, B., Cleveland, J.P., Kruger, D., Elings, V., and Fuchs, H. (1998), Analysis of the interaction mechanisms in dynamic mode SFM by means of experimental data and computer simulation, Appl. Phys. A Materials Science & Processing, 66, S885-S889. Anczykowski, B., Kruger, D., Babcock, K.L., and Fuchs, H. (1996), Basic properties of dynamic force spectroscopy with the scanning force microscope in experiment and simulation, Ultramicroscopy, 66 (3-4), 251-259. Anczykowski, B., Kruger, D., and Fuchs, H. (1996), Cantilever dynamics in quasinoncontact force microscopy: spectroscopic aspects, Phys. Rev. B Condensed Matter, 53 (23), 15485-15488. Bhushan, B. (1996), Nanotribology and nanomechanics of MEMS devices, in Proceedings of the 9th Annual Workshop on Micro-Electro-Mechanical Systems, IEEE, New York, 91. Bhushan, B. (1999), Principles and Applications of Tribology, John Wiley & Sons, New York. Bhushan, B. and Sundararajan, S. (1998), Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy, Acta Metallurgica, 46 (11), 3793-3804. Binnig, G., Quate, C.F., and Gerber, C. (1986), Atomic force microscope, Phys. Rev. Lett. 56 (9), 930-933.
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Burdorf, K. (1999), Silicon-direct-bonding: packaging technology on wafer level, Institute for Microsensors, -actuators and -systems (IMSAS), University of Bremen, http://www.imsas.unibremen.de/service/sdb.html. Burnham, N.A. and Colton, R.J. (1989), Measuring the nanomechanical properties and surface forces of materials using an atomic force microscope, J. Vac. Sci. Technol. A (Vacuum, Surfaces, and Films), 7 (4), 2906-13. Creuzet, F., Ryschenkow, G., and Arribart, H. (1992), A new tool for adhesion science: the atomic force microscope, J. Adhes., 40 (1), 15-25. Cross, G., Schirmeisen, A., Stalder, A., Grütter, P., Tschudy, M., and Dürig, U. (1998), Adhesion interaction between atomically defined tip and sample, Phys. Rev. Lett., 80 (21), 4685-4688. Derjaguin, B.V., Muller, V.M., and Toporov, Y.P. (1975), Effect of contact deformations on the adhesion of particles, J. Colloid Interface Sci., 53, 314-320. Dürig, U. and Stalder, A. (1997), Adhesion on the nanometer scale, in Micro/Nanotribology and Its Applications, Bhushan, B. (Ed.), Kluwer, Dordrecht, Vol. E330, 61. Evans, E. and Ritchie, K. (1997), Dynamic strength of molecular adhesion bonds, Biophys. J., 72 (4), 1541-1555. Godowski, P.J., Maurice, V., and Marcus, P. (1995), Analytical problems in atomic force microscopy: distortion of surface structures during imaging, Chem. Anal., 40, 231-242. Grütter, P., Rugar, D., Mamin, H.J., Castillo, G., Lambert, S.E., Lin, C.-J., Valletta, R.M., Wolter, O., Bayer, T., and Greschner, J. (1990), Batch fabricated sensors for magnetic force microscopy, Appl. Phys. Lett., 57, 1820. Hertz, H. (1881), Über die Berührung fester elastischer Körper, J. Reine Angew. Math., 92, 156-171. Hild, S., Rosa, A., and Marti, O. (1998), Deformation induced changes in surface properties of polymers investigated by scanning force microscopy, in Scanning Probe Microscopy of Polymers, Ratner, B.D. and Tsukruk, V.V. (Eds.), Oxford University Press, Vol. 694, 110. Izrailev, S., Stepaniants, S., Balsera, M., Oono, Y., and Schulten, K. (1997), Molecular dynamics study of unbinding of the avidin–biotin complex, Biophys. J., 72 (4), 1568-1581. Jiaa, C.L., Nguyen, P., Teng, E., and Eltoukhy, A. (1994), The role of surface properties in the mechanical performance of thin film rigid disks, Thin Solid Films, 248 (1), 41-6. Johnson, K.L. (1992), Introduction to contact mechanics: a summary of the principal formulae, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, Vol. 220, 589. Johnson, K.L. (1996), A continuum mechanics model of adhesion and friction in a single asperity contact, in Micro/Nanotribology and its Applications, Bhushan, B. (Ed.), Kluwer Academic Publishers, Dordrecht. Johnson, K.L. (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface, Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences, 453 (1956), 163-179. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London, Ser. A, 324, 301-313. Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79 (10), 8071-5. Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force friction force microscopy, J. Vac. Sci. Technol. A Vacuum Surfaces and Films, 14 (4), 2378-2391. Krotil, H.-U., Stifter, T., Waschipky, H., Weishaupt, K., Hild, S., and Marti, O. (1999), Pulsed force mode: a new method for the investigation of surface properties, Surface and Interface Analysis, 27, 336-340. Landman, U., Luedtke, W.D., and Ringer, E.M. (1992), Atomistic mechanisms of adhesive contact formation and interfacial processes, Wear, 153 (1), 3-30.
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Lekka, M., Laidler, P., Gil, D., Cleff, B., and Stachura, Z. (1997), Elastic surface properties studied using scanning force microscopy, Electron Technology, 30 (2), 173-6. Marti, O. (1998), AFM instrumentation and tips, in Handbook of Micro/Nanotribology, Bhushan, B. (Ed.), CRC Press, Boca Raton, 81. Marti, O., Drake, B., and Hansma, P.K. (1987), Atomic force microscopy of liquid-covered surfaces: atomic resolution images, Appl. Phys. Lett., 51 (7), 484-486. Marti, O., Ribi, H.O., Drake, B., Albrecht, T.R., Quate, C.F., and Hansma, P.K. (1988), Atomic force microscopy of an organic monolayer, Science, 239, 50-52. Marti, O., Waschipky, H., Quintus, M., and Hild, S. (1999), Scanning probe microscopy of heterogeneous polymers, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 154 (1-2), 65-73. Maugis, D. (2001), Adhesion of solids: mechanical aspects, in Modern Tribology Handbook, Bhushan, B. (Ed.), CRC Press, Boca Raton. Miyamoto, T., Kaneko, R., and Ando, Y. (1990), Interaction force between thin film disk media and elastic solids investigated by atomic force microscope, J. Tribol., 112 (3), 567-72. Miyatani, T., Okamoto, S., Rosa, A., Marti, O., and Fujihira, M. (1998), Surface charge mapping of solid surfaces in water by pulsed-force-mode atomic force microscopy, Appl. Phys. A Materials Science & Processing, 66, S349-S352. Mizes, H.A., Loh, K.-G., Miller, R.J.D., Ahuja, S.K., and Grabowski, E.F. (1991b), Submicron probe of polymer adhesion with atomic force microscopy: dependence on topography and material inhomogeneities, Appl. Phys. Lett., 59, 2901-2903. Pitsch, M., Metz, O., Kohler, H.-H., Heckmann, K., and Strnad, J. (1989), Atomic resolution with a new atomic force tip, Thin Solid Films, 175, 81. Ramirez-Aguilar, K.A. and Rowlen, K.L. (1998), Tip characterization from AFM images of nanometric spherical particles, Langmuir, 14 (9), 2562-2566. Rosa-Zeiser, A., Weilandt, E., Hild, S., and Marti, O. (1997), The simultaneous measurement of viscoelastic, electrostatic and adhesive properties by SFM: pulsed force mode operation, Measurement Science and Technology, 8, 1333-1338. Rubio, G., Agraït, N., and Vieira, S. (1996), Atomic-sized metallic contacts: mechanical properties and electronic transport, Phys. Rev. Lett., 76 (13), 2302-2305. Sarid, D., Hunt, J.P., Workman, R.K., Yao, X., and Peterson, C.A. (1998), The role of adhesion in tappingmode atomic force microscopy, Applied Physics A Materials Science & Processing, 66, S283-S286. Sarid, D., Ruskell, T.G., Workman, R.K., and Chen, D. (1996), Driven nonlinear atomic force microscopy cantilevers: from noncontact to tapping modes of operation, J. Vac. Sci. Technol. B, 14 (2), 864-867. Schmitz, I., Schreiner, M., Friedbacher, G., and Grasserbauer, M. (1997), Phase imaging as an extension to tapping mode AFM for the identification of material properties on humidity-sensitive surfaces, Appl. Surf. Sci., 115 (2), 190-198. Spatz, J.P., Sheiko, S., Möller, M., Winkler, R.G., and Marti, O. (1995), Forces affecting a substrate in tapping mode, Nanotechnology, 6, 40-44. Spatz, J.P., Sheiko, S., Möller, M., Winkler, R.G., Reineker, P., and Marti, O. (1997), Tapping scanning force microscopy in air — theory and experiment, Langmuir, 13, 4699-4703. Stalder, A. and Dürig, U. (1996a), Study of plastic flow in ultrasmall Au contacts, J. Vac. Sci. Technol. B, 14 (2), 1259-1263. Stalder, A. and Dürig, U. (1996b), Study of yielding mechanics in nanometer-sized Au contacts, Appl. Phys. Lett., 68 (5), 637-639. Stifter, T., Weilandt, E., Marti, O., and Hild, S. (1998), Influence of the topography on adhesion measured by SFM, Appl. Phys. A Materials Science & Processing, 66, S597-S605. van Kevele, D.W. (1976), Properties of Polymers, Elsevier, Amsterdam, 303. Vogel, H. (1995), Gerthsen: Physik, 18 ed. Springer, Heidelberg.
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Weisenhorn, A.L., Maivald, P., Butt, H.-J., and Hansma, P.K. (1992), Measuring adhesion, attraction, and repulsion between surfaces in liquids with an atomic-force microscope, Physical Review B, 45 (19), 11226-11232. Winkler, R.G., Spatz, J.P., Sheiko, S., Moller, M., Reineker, P., and Marti, O. (1996), Imaging material properties by resonant tapping-force microscopy: A model investigation, Phys. Rev. B Condensed Matter, 54 (12), 8908-8912. Wolter, O., Bayer, T., and Gerschner, J. (1991), Micromachined silicon sensors for scanning force microscopy, J. Vac. Sci. Technol., B9, 1353. Zhong, Q., Inniss, D., Kjoller, K., and Elings, V.B. (1993), Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy, Surf. Sci., 290 (1-2), L688-92.
Symbols Symbol
Unit
Meaning
z~ a b b D
m Nm7 m Nm13 m -----N
Compliance factor
E
N ------2 m
Modulus of elasticity, Young’s modulus
F F(z) F0 Fmax Fyield h Hcrit
N — N N N m
Force applied to spherical test body Weight function for averaging the potential Pull-off force (JKR) Maximum force in the junction before yielding Yield force Thickness of cantilever
N ------2 m
Critical yield stress
k
N ---m
Cantilever compliance
kc
N ---m
Contact stiffness
keff
N ---m
Effective compliance of the junction
kN
N ---m
Compliance of the cantilever for normal forces
kS
N ---m
Sample compliance
kT
N ---m
Tip compliance
l m R r0 R0 Rc Rcrit U(z) Vatom
m kg m m m m m Nm Nm
Length of cantilever Effective mass of cantilever Radius of the spherical test body Distance of potential minimum in the Lennard–Jones potential Minimum contact radius Contact radius Critical radius of spherical test body for yield failure Interaction potential between tip and sample Potential of a single atom
Averaged movement of tip Coefficient of attractive part of the Lennard–Jones potential Width of cantilever Coefficient of repulsive part of the Lennard–Jones potential
2
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Vattr Vrep w z zmeasured ztrue ∆γ
Nm Nm m M M M
Attractive component of the potential of a single atom Repulsive component of the potential of a single atom Base width of a triangular cantilever Coordinate perpendicular to sample or cantilever Measured displacement of the cantilever end-point True displacement of the cantilever end-point
N ---m
Difference in the contact potential
Θ δ ε γL
rad m Nm
Contact angle Indentation depth Magnitude of the potential in the Lennard–Jones potential
N ---m
Contact potential of the test liquid vs. air
N ---m
Contact potential of the sample vs. air
—
Poisson number
N ------2 m
Yield stress
N ------2 m
Critical yield stress for a given tip radius
1 --s
Angular frequency of excitation
γS ν σ
σcrit ω0
639
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18 Atomic-Scale Friction Studies Using Scanning Force Microscopy 18.1 18.2 18.3 18.4 18.5
Frictional Contrast Caused by Local Changes in the Chemical Composition • Friction of Surfaces Possessing Identical Chemical Composition • Direction Dependence of Sliding Friction
Udo D. Schwarz University of Hamburg
Hendrik Hölscher University of Hamburg
Introduction ..................................................................... 641 The Scanning Force Microscope as a Tool for Nanotribology .................................................................. 642 The Mechanics of a Nanometer-Sized Contact ............. 644 Amontons’ Laws at the Nanometer Scale....................... 646 The Influence of the Surface Structure on Friction ...... 648
18.6 18.7 18.8
Atomic Mechanism of Friction....................................... 652 The Velocity Dependence of Friction............................. 658 Summary .......................................................................... 660
18.1 Introduction Although frictional forces are familiar to everyone from daily life experiences, little progress has been made in finding an exact physical description of friction since the following phenomenological friction laws were established by Amontons (1699) and Coulomb (1783): 1. Friction is proportional to the load (i.e., to the applied normal force). 2. Friction is independent of the (apparent) contact area. 3. Sliding friction is independent of the sliding velocity. These laws hold surprisingly well in the case of dry friction or Coulomb friction, if there is no lubrication between the two interacting bodies. Nevertheless, they could not be derived from first principles up to now. Moreover, the understanding of the fundamental mechanisms of friction on the atomic scale is poor since most macroscopic and microscopic frictional effects are normally dominated by the influence of wear, plastic deformation, lubrication, surface roughness, and surface asperities. Macroscopic friction experiments (see Figure 18.1a), especially if performed under ambient conditions are therefore difficult to analyze in terms of a universal theory. Moreover, the complexity of the phenomena prevented the observation of pure wearless friction for many years, thus disabling all attempts to understand the origins of friction on the molecular and atomic scale. In the last decades, however, the field of nanotribology was established by introducing new experimental tools which opened the nanometer and the atomic scale to tribologists. One of the basic ideas of
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FIGURE 18.1 (a) The well-known experimental setup to confirm the frictional laws (1) and (2) of dry friction on the macroscopic scale. (b) The apparent contact area observed on the macroscopic scale consists of many individual small asperities. A nanometer-sized single asperity contact (“point contact”) can be realized in a scanning force microscope.
nanotribology is that for a better understanding of friction in macroscopic systems, the frictional behavior of a single asperity contact should be investigated first. Macroscopic friction could then possibly be explained with the help of statistics, i.e., by adding the interactions of a large number of individual contacts, which together form the macroscopic roughness of the interface between the two bodies which are in relative motion (see Figure 18.1b for illustration). The first big step toward such experiments at the atomic level was taken when the surface force apparatus was equipped with special stages enabling the measurement of lateral forces between two molecularly smooth surfaces sliding against each other (Israelachvili and Tabor, 1973; Briscoe and Evans, 1982). The biggest step concerning the reduction of the asperity size was accomplished with the development of the friction force microscope (FFM) (Mate et al., 1987). The FFM is derived from the scanning force microscope (SFM) (Binnig et al., 1986) and enables the local measurement of lateral forces by moving a sharp tip, representing (approximately) a point contact, over a sample surface. In this chapter, we intend to describe how the FFM can contribute to the understanding of the origin and nature of the fundamental laws of friction by the investigation of atomic-scale frictional effects. As shown in the following sections, friction at the nanometer scale manifests itself in a significantly different manner than the Coulomb friction at the macroscopic scale. The friction laws (1) and (2) are found to be not valid for point contact friction, since the frictional forces on the nanometer scale are proportional to the actual area of contact, which is generally not proportional to the load (Section 18.4). On the other hand, friction law (3) could be confirmed for moderate sliding velocities also on this scale (Section 18.7). The analysis of the frictional behavior of such approximate point contacts in terms of a simple mechanical model exhibits a two-dimensional nature of friction on the atomic scale, which is determined by a “stickslip” type movement of the foremost tip atoms (Section 18.6). Molecular-scale effects involving wear or lubrication, however, will be discussed in the next chapter.
18.2 The Scanning Force Microscope as a Tool for Nanotribology The principle of scanning force microscopy is rather simple and resembles that of a record player. A force microscope (Figure 18.2) detects forces acting between a sample surface and a sharp tip which is mounted on a soft leaf spring (the cantilever). A feedback system which controls the vertical z-position of the tip on the sample surface keeps the deflection of the cantilever (and thus the force between tip and sample) constant. Moving the tip relative to the sample in the x–y-plane of the surface by means of piezoelectric drives, the actual z-position of the tip is recorded as a function of the lateral x–y-position with (ideally)
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laser
photo diode
A C
B
z x y
D cantilever tip sample Fx
Fz
x-, y-, z-scanner
Fy
a)
b)
FIGURE 18.2 (a) Principle of the scanning force microscope. Bending and torsion of the cantilever are measured simultaneously by measuring the lateral and vertical deflection of a laser beam while the sample is scanned in the x–y-plane. The laser beam deflection is determined using a four-quadrant photo diode: (A+B)–(C+D) is a measure for the bending and (A+C)–(B+D) a measure for the torsion of the cantilever, if A, B, C, and D are proportional to the intensity of the incident light of the corresponding quadrant. (b) The torsion of the cantilever (middle) is solely due to lateral forces acting in the x-direction, whereas both forces acting normal to the surface (Fz) as well as acting in plane in the y-direction (Fy) cause a bending of the cantilever (bottom).
sub-Ångström precision. The obtained three-dimensional data represent a map of equal forces; the necessary conversion of the cantilever deflection into the normal force is basically performed by applying Hook’s law. The data can be analyzed and visualized through computer processing. A more detailed description of the method and the generally used instrumentation is given, e.g., by Meyer and Heinzelmann (1992), Wiesendanger (1994), Bhushan and Ruan (1994), or Schwarz (1997). The experimental setup for the deflection detection measurement, which is most frequently used in SFM studies on friction, is the beam deflection scheme sketched in figure 18.2a (Marti et al., 1990; Meyer and Amer, 1990). With this detection scheme, not only the deflection, but also the torsion of the cantilever can be measured (see the caption of Figure 18.2a for further details). Force microscopes, which can record bending and torsion of the cantilever simultaneously, are often referred to as friction force microscopes (FFMs) or lateral force microscopes (LFMs). What are the specific advantages of friction force microscopy in comparison with other methods? As we have seen in the introduction, macroscopic friction experiments are often difficult to analyze due to the complexity of the experimental system. For the unambiguous analysis of physical phenomena, the experiments performed to clarify their nature are preferably arranged as simply as possible. Friction force microscopy is an especially suitable tool for nanotribological investigations because it meets this requirement quite well: 1. Measurements within the purely elastic regime prevent plastic deformation or wear of tip or sample. Consequently, all experiments presented in this chapter were performed at loading forces which were sufficiently low such that no effects due to plastic deformation could be observed. 2. The contact area of the sliding tip with the sample surface is very small (typically some nm2), thus enabling the localized detection of frictional forces. 3. The apparent and the actual contact area are identical. Therefore, problems occurring from surface roughness and surface asperities can be neglected if the experiments are performed on atomically smooth surfaces. 4. If measured under controlled conditions (e.g., in ultra-high vacuum or in an argon atmosphere), an influence of adsorbates on the measured friction can be reduced or completely avoided.
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FIGURE 18.3 (a) Macroscopic tip–sample contact; Fl denotes the externally applied loading force. The contact area-load dependence is difficult to describe due to the irregular shape of both tip and sample surface. (b) Geometry of a Hertzian contact (see text). R = radius of the tip apex; a = radius of the contact area.
Finally, two more points should be noted: (1) During scanning, the torsion of the cantilever is exclusively induced by lateral forces acting in the x-direction (Fx), whereas for corrugated samples, the bending of the cantilever is mainly caused by forces acting perpendicular to the sample surface in the z-direction (Fz). Nevertheless, a bending of the cantilever induced by lateral forces acting in the y-direction (Fy) cannot be excluded (see Figure 18.2b, bottom). For atomically flat surfaces, Fujisawa et al. (1993a,b; 1995) pointed out that the variation of Fz is so small that the measured signal of an SFM equipped with the beam deflection method is mostly determined by lateral forces. Therefore, on the atomic scale, the lateral forces both in scan direction and perpendicular to the scan direction are measured. (2) The correct calibration of the bending and the torsion of the cantilever in terms of lateral forces is much more difficult than the conversion of the cantilever deflection into the normal force, which can simply be performed by applying Hook’s law. Many parameters such as the cantilever dimensions, the elastic moduli of the cantilever material, the tip length, the position on the cantilever backside where the laser beam is reflected and the sensitivity of the four-quadrant photo diode have to be known. Different procedures for the quantitative analysis of lateral force microscopy experiments are described, e.g., by Marti et al. (1993), Bhushan and Ruan (1994), Lüthi et al. (1995), Putman et al. (1995), Ogletree et al. (1996), and Schwarz et al. (1996a).
18.3 The Mechanics of a Nanometer-Sized Contact Since it is the attempt of nanotribology to reconstruct the macroscopic frictional behavior from the frictional properties of an individual nanometer-sized contact, it is clear that a knowledge of the mechanics of such small single asperity contacts is essential. For example, the exact contact area of tip and sample as a function of the applied loading force has to be known in order to compare the data obtained by scanning force microscopy with theoretical models, as we will see in Section 18.4. Scanning force microscopy, however, does not allow an independent measurement of the contact area. In order to circumvent this restriction, it is a common approach in SFM to use tips with a geometrically well-defined apex and to calculate the effective contact area (and other important parameters such as deformation or stiffness of the contacts) on the basis of continuum elasticity theory. A detailed description of contact mechanics is given by Johnson (1994). Here, we will restrict ourselves to the mathematically simplest and most frequently used case of a spherical tip which is in contact with a flat surface (the so-called Hertzian contact, Figure 18.3), in spite of the fact that there also exist extensions to other geometries (see, e.g., Carpick et al., 1996). Without adhesion, the contact area of such a Hertzian contact can be determined using the Hertzian theory (Hertz, 1881), which was already developed in 1881. It predicts a contact area-load dependence of the following form:
RF A = π l K
2 3
(18.1)
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Here, R is the radius of the tip, Fl the loading force, and
4 1 − ν12 1 − ν22 K= + E2 3 E1
−1
(18.2)
the “effective elastic modulus” (with E1,2 and ν1,2 as Young’s moduli and Poisson’s ratios of sphere and flat, respectively). Other useful quantities are, e.g., the contact radius a of the interface region
a3 =
RFl K
(18.3)
the vertical displacement δ of the two bodies in contact
δ=
a 2 Fl = R Ka
(18.4)
and the pressure or stress distribution p(r) within the contact region 2
r r 3Fl 3Ka pr = 1− = 1− 2 2πR a a 2πa
()
2
(18.5)
Since the early 1970s, however, theories have been developed which include attractive forces (Johnson et al., 1971; Derjaguin et al., 1975; Muller et al., 1983; Maugis, 1987; Fogden and White, 1990; Maugis, 1992; Maugis and Gauthier-Manuel, 1994). The general mathematical formulation of the contact areaload dependence of a Hertzian contact including adhesion cannot be solved analytically (Fogden and White, 1990; Maugis, 1992). Nevertheless, depending on how the attractive forces act, approximations can be derived. In order to decide which of the above-mentioned approximations applies under which conditions, Tabor (1977) introduced the nondimensional parameter Φ
9Rγ 2 Φ= 2 3 4K z0
13
(18.6)
(γ: surface energy of sphere and flat [for equal surfaces] and z0: equilibrium distance in contact), which represents basically a measure for the magnitude of the elastic deformation outside the effective contact area compared with the range of the surface forces. When Φ is large (Φ > 5 [Johnson, 1997]), the Johnson–Kendall–Roberts (JKR) theory (Johnson et al., 1971) applies, which has been confirmed in many experiments (see, e.g., Israelachvili et al. [1980] and Homola et al. [1990]). If Φ < 0.1, however, contacts should be appropriately described by the analysis of Derjaguin, Muller, and Toporov (DMT) (Derjaguin et al., 1975; Muller et al., 1983). Nevertheless, since the small value of Φ indicates that there is only negligible elastic deformation outside the effective contact area, the influence of attractive forces can in further simplification be considered by introducing an effective normal force Fn = F1 + F0, where F0 is the sum of all acting attractive forces. Replacing F1 with Fn in Equation 18.1 leads to
(
)
R Fl + F0 A = π K
2 3
RF = π n K
2 3
(18.7)
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FIGURE 18.4 Three examples of tip specially prepared in a transition electron microscope with spherical tip apexes of (a) 21 ± 5 nm, (b) 35 ± 5 nm, and (c) 112 ± 5 nm radius.
This model will be referred to as the Hertz-plus-offset model in the following to distinguish between the original and more precise DMT formalism and the present further simplification. Detailed mathematical derivations of Equation 18.7 for the case of capillary forces were published by Fogden and White (1990) and Maugis and Gauthier-Manuel (1994). By introducing typical values for contacts as they occur in SFMs into Equation 18.6 (R = 30 nm, γ = 25 mJ/m2 [typical for van der Waals surfaces], K = 50 GPa, and z0 = 3 Å), we find a value for Φ of ≈ 0.09. Therefore, Equation 18.7 should represent the correct contact area-load dependence for typical contacts found in SFMs. A more detailed discussion of the contact mechanics of a nanometer-sized Hertzian contact is given by Schwarz et al. (1996a, 1997a). However, Equation 18.7 only applies for tips with exactly spherical apex. Using SFM tips as supplied by the manufacturer, such a shape is only accidentally realized, and thus all kinds of power laws A ∝ Fn with n ranging from n ≈ 0.4 to n ≈ 1.2 have been found (Schwarz et al., 1997a). Consequently, tips of exactly defined spherical tip apex and a tip radius which is known with nanometer accuracy are mandatory for quantitatively reproducible friction force measurements. Mainly two different methods to prepare such well-defined tips have been introduced in the past. The first method is to heat a very sharp tip in high vacuum (Binh and Uzan, 1987; Binh and Garcia, 1992). Surface diffusion will then induce migration of atoms from regions of higher curvature to regions of lower curvature. Another method was realized by covering doped single-crystalline silicon tips (apex radii 5 to 15 nm without coating) with a layer of amorphous carbon in a transmission electron microscope (Schwarz et al., 1997b). Molecules from the residual gas are ionized in the electron beam and accelerated to the tip end. There, the molecules spread out evenly due to their charge, forming a well-defined spherical tip end. With this method, tips with radii from 7 nm up to 112 nm could be successfully produced. Three examples of tips prepared using the second method described above are shown in Figure 18.4.
18.4 Amontons’ Laws at the Nanometer Scale Amontons’ macroscopic friction laws (1) and (2) can be condensed in the well-known equation
Ff = µFn
(18.8)
where Ff denotes the observed friction force. µ represents a value which is constant for a given material combination in a wide range of applied normal forces Fn and which is usually referred to as the friction coefficient. Nevertheless, for the description of the frictional behavior of materials at the nanometer scale, it is practical to introduce the mean friction per unit area (the so-called shear stress S)
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FIGURE 18.5 The frictional force Ff as a function of the normal force Fn, measured on amorphous carbon with geometrically well-defined spherical tips in argon atmosphere (Schwarz et al., 1997a). The data presented in (a) were obtained using a tip with a radius of R = 17 ± 5 nm; the data in (b) using a tip with R = 58 ± 10 nm. Both curves are in excellent agreement with fits according to Equation 18.10 (solid lines); the dashed lines illustrate the deviation from the linear macroscopic model (Equation 18.8). The offsets of the solid lines from the zero point of the normal force are caused by the experimental uncertainty in the determination of the zero point by means of force-vs.-distance curves.
S = Ff A
(18.9)
Combining Equations 18.7 and 18.9, we find
R Ff = πS K
2 3
Fn2 3 = µ˜ R2 3 Fn2 3
(18.10)
with µ˜ = πS/K 2/3. There have already been many reports in the literature when the frictional force has been measured as a function of the normal force using an FFM (Mate et al., 1987; Mate, 1993; Hu et al., 1995; Bhushan and Kulkarni, 1995; Carpick et al., 1996; Meyer et al., 1996; Lantz et al., 1997; Schwarz et al., 1997a; Enachescu et al., 1998). In most of these reports, the frictional force showed a strongly nonlinear dependence on the normal force. Figure 18.5 features results published by Schwarz et al. (1997a), which were acquired in argon atmosphere on amorphous carbon with tips showing exactly spherical tip apexes (tip radii of 17 ± 5 nm [a] and 58 ± 10 nm [b], respectively). The fits according to Equation 18.10 show excellent agreement between the experimental results and theory. The dashed lines illustrate the deviation of the present friction law from the macroscopic linear law Equation 18.8. It is interesting to note that not only can the relationship Ff ∝ F n2/3 be confirmed, but also the Ff ∝ 2/3 R -dependence. Comparing Figure 18.5a with 18.5b, much higher friction is observed in (b); the frictional force at Fn = 10 nN, for example, is about three times larger (≈15 nN) than the frictional force of only 5.5 nN observed in (a). However, the calculated numerical value of µ˜ = 0.17 ± 0.07 GPa1/3 for the second measurement is in good agreement with the value of µ˜ = 0.17 ± 0.09 GPa1/3 obtained in the first measurement. Summarizing the main results obtained from the different research groups on a large variety of materials, it was found that the friction as a function of the normal load showed good agreement of experimental data and theoretical fits using Equation 18.9 combined with contact mechanical models appropriate for the specific tip-sample contact, if S is set constant. This finding leads to the following remarkable consequences:
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• The observed frictional force Ff is in opposition to law (2) proportional to the crack area A (see Equation 18.9). In the special case of a Hertzian contact, this leads to a Ff(Fn)-dependence of Ff ~ F 2/3 n . • The shear stress S depends only on the materials used and on environmental conditions such as temperature and humidity, but not on the mean contact pressure p = Fn/A.* • The independence of the shear stress S from the mean contact pressure p = Fn/A is in flagrant contradiction to Amontons’ law (1). • The continuum elasticity theory also applies at the nanometer scale. Since the continuum elasticity theory also applies at the nanometer scale, Equation 18.7 can be used to calculate the actual contact area of an SFM tip and the sample surface. Typical normal forces Fn occurring in an SFM during measurement are between 1 nN and 100 nN. This results in contact areas of a few nm2, with the effect that only some tens or some hundreds of atoms are in direct contact. The deformations of tip and sample are then fully elastical, i.e., fully reversible. Therefore, with an SFM, it is indeed possible to study wearless friction of a quasipoint contact. Another outcome from the above considerations is the finding that it is obviously useless to determine “friction coefficients” µ (see Equation 18.8) from point contact measurements, since these values will heavily depend on the specific geometry of the tip–sample contact. For a classification of the microscopic frictional properties of materials, Schwarz et al. (1997a) have therefore proposed the factor µ˜ = πS/K2/3 (see Equation 18.10), which combines the frictional and elastic properties of tip and sample and which can be regarded as an effective friction coefficient for point contact-like single-asperity friction in the case of a nanometer-sized Hertzian contact. The definition of such a coefficient is advantageous for two main reasons: (1) If materials with identical intrinsic frictional properties (i.e., the materials show the same friction per unit area) but different Young moduli are examined in measurements performed with identical tips and normal forces, higher friction will be found on the softer material due to the larger ˜ however, will always show the same friction during an contact area. Materials which have the same µ, experiment. (2) If the same sample is investigated with tips featuring different apex radii, lower friction will be found in the experiment carried out with the sharper tip. Nevertheless, consideration of the ˜ as we have seen in Figure 18.5. geometry by the calculation of µ˜ will lead to identical values of µ, How can the above results now be correlated with the macroscopic laws of friction? As we have seen in the introduction, it is the general attempt of nanotribology to conclude from the frictional properties of an individual nanocontact to the behavior of macroscopic bodies by the statistical adding of the interactions of a large number of individual contacts with represent the macroscopical roughness of the contact interface. This means for the given situation that the contradiction between Amontons’ laws (1) and (2) and their corresponding counterparts on the nanometer scale could be entirely eliminated if the effective contact area of such a macroscopic contact increased proportionally to the externally applied loading force. Then, the observed frictional force would also increase linearly with the load, according to the nanoscopic friction law found above. Such a linear Ff(Aeff )-dependence for macroscopically flat, but microscopically rough surfaces has indeed been demonstrated by Greenwood (1967, 1992). Interestingly, the apparent contact area of the two bodies does not matter in this case.
18.5 The Influence of the Surface Structure on Friction In the preceding sections, we dealt with the mechanical and tribological properties of nanometer-sized contacts. Questions concerning the fundamental mechanisms of friction at the atomic scale, however, *The same result has been found by Carpick et al. (1997) and Enachescu et al. (1998) with different approaches, which both circumvent the assumption of a specific contact mechanical model. Additionally, experiments performed with the surface force apparatus and consequently much larger contact areas A also show the same behavior (Israelachvili and Tabor, 1973; Homola et al., 1990).
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FIGURE 18.6 (a) Topography and (b) lateral force map of an AgBr thin film deposited on NaCl(001) at room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas with about ten times higher friction than the corresponding friction observed on the NaCl surface. (From Meyer, E., Lüthi, R., Howald, L., and Güntherodt, H.-J., 1995. Friction force microscopy, in Forces in Scanning Probe Methods, Güntherodt, H.-J., Anselmetti, D., and E. Meyer (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 285. With permission.)
are still unanswered. Since we focus in this chapter on the analysis of wearless friction on atomically flat surfaces without defects, it is reasonable to expect that the origin for the different friction observed on the different materials can be found in the local arrangement of the atoms at the tip–sample contact area. If this expectation holds, it should be possible to distinguish areas of different chemical composition by lateral force microscopy. This ability is sometimes called “chemical imaging”; examples for such investigations will be discussed in Section 18.5.1. Another interesting consequence of the above expectation is that the friction should depend on the direction with which the tip profiles the sample surface. This frictional anisotropy is especially easy to verify experimentally if a material exhibiting an asymmetric surface potential is used as a sample, as presented in Section 18.5.3. Finally, we will see in Section 18.5.2 that even small conformational (i.e., purely geometrical) changes within a surface unit cell give rise to different friction in lateral force maps.
18.5.1 Frictional Contrast Caused by Local Changes in the Chemical Composition The ability of the FFM to provide a contrast between surfaces of different chemical composition is not only important for tribologists, but also of considerable general interest for users from the whole field of scanning force microscopy, where contrast mechanisms are needed which provide information in addition to the pure topography. Since the lateral forces acting on the FFM tip are not independent of the topography,* atomically or molecularly flat terraces give the most unambiguous results. Consequently, chemical contrast has first been demonstrated for Langmuir–Blodgett films, which can easily be prepared and investigated under atmospheric conditions and exhibit large, molecularly flat surfaces. See, for example, Overney et al. (1992), or Meyer et al. (1992). However, in this chapter we will restrict the discussion to the atomic-scale frictional effects at crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure 18.6a), which has the same crystalline structure as NaCl. In the corresponding FFM investigations (Figure 18.6b), they found a strong frictional contrast between the AgBr islands and the NaCl substrate due to the different chemical composition of the two materials. *Scanning “up hill” causes more torsion of the cantilever than scanning “down hill”; see, for example, Grafström et al. (1993), Fujisawa et al. (1993b), Ruan and Bhushan (1994a), or Aimé et al. (1995).
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According to the same principle, basically all areas of different chemical composition can be distinguished in force microscopical investigations. Fompeyrine et al. (1998), for example, could differentiate areas terminated by SrO from areas terminated by TiO2 on an SrTiO3 single crystal. This ability of the SFM is sometimes called “chemical imaging.” It should be noted, however, that chemical imaging does not mean chemical identification. The reason for this has been discussed in Section 18.4. If the contact mechanics of the tip–sample contact is not exactly known, the results obtained are difficult to interpret without additional information. In order to circumvent this restriction at least partially, chemically modified tips have been used to sensitize the tip to certain functional groups which have been patterned on suitable sample surfaces. See, for example, Frisbie et al. (1994) or Sasaki et al. (1998). A theoretical study on the bases of “chemical force microscopy” on organic monolayers has been published recently by Fujihira and Ohzono (1999).
18.5.2 Friction of Surfaces Possessing Identical Chemical Composition After what has been discussed above, it seems promising to analyze the influence of differences in the structure of surfaces possessing identical chemical composition on the friction observed by a point probe. Probably the first observation on this issue was published by Ruan and Bhushan (1994b). They observed graphite(0001) areas with unusually high friction, which could be identified as areas exhibiting graphite planes of different orientations (other than [0001]) as well as amorphous carbon. Comparative quantitative studies for different carbon compounds have been performed by Mate (1993) and Schwarz et al. (1997a) on diamond, graphite, C60 thin films, and amorphous carbon. High frictional forces have been found especially on the C60 thin films, whereas friction nearly vanishes on graphite. These examples demonstrate that even on materials that consist of the same chemical species, large variations in the observed friction might occur. As a consequence, it follows that it is not the specific atomic species which form a crystal, but factors such as the crystalline structure, the charge distribution, and/or the binding conditions that might decide the frictional properties of a material. The “chemical differentiation” postulated in Section 18.5.1 is therefore based more on structural and electronical differences between the materials than on the fact that they represent chemically different species. This issue will be further illustrated with the example of the ferroelectric material guanidinium aluminum sulfate hexahydrate (GASH) in the following. Since the Curie point of GASH is above its decomposition temperature, the crystals always show the ferroelectric phase. The surfaces of positively and negatively charged domains not only have the same chemical composition, the surface atoms are also bound in the exact same manner on both domains. The difference is that the surface undergoes a conformational (i.e., geometrical) change of the surface structure if the polarity of a certain surface area is flipped. Certain aluminum ions which are octahedrally coordinated by water molecules stick on the positive domain more out from the surface (by 0.5 Å) than they do no the negative domain, resulting in a different surface corrugation. Bluhm et al. (1998) showed in a combination of voltage-dependent friction force microscopy experiments and electrostatic force microscopy experiments that the domain contrast observed in FFM images is not caused by the electrostatic interaction between a charged tip and the electric field of the sample, but is explained by the geometrical differences exhibited by the surfaces of domains with opposite polarity (Figure 18.7). This example elegantly demonstrates that even small changes in the arrangement of the atoms located at the sample surface influence the friction occurring during the sliding of nanocontacts.
18.5.3 Direction Dependence of Sliding Friction In the above sections, we have seen that friction is very sensitive to the structure of the surface. In everyday life, it is often observed that friction depends on the sliding direction. This phenomenon can be observed rubbing by one’s hand over certain pieces of cloth. Another example is that of a saw; there, how much
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FIGURE 18.7 (a) Topographical image of GASH(0001) (image size: 30 µm × 30 µm). The surface is featureless and without any steps. (b) Friction force map of the same surface spot as in (a) (slight zoom-out; image size: 40 µm × 40 µm). A well-expressed contrast is visible. (c) Image acquired with electrostatic force microscopy at the same surface area as in (a), showing the structure and absolute sign of the ferroelectric domains. By comparison of (b) and (c), it can be concluded that the contrast in the friction image represents the domain structure of GASH.
FIGURE 18.8 Principle of FFM contrast formation. (a) On materials that have no directional dependence of friction (i.e., the friction coefficient µ is the same in the forward and backward scan directions), the contrast between surface areas exhibiting different µ is reversed when scanning forward compared to scanning backward since the FFM signal is a measure for the torsion of the cantilever. At the surface steps, peaks occur in the FFM signal due to some torque of the tip. (b) FFM tip probing the frictional force of a surface with asymmetric surface potential, illustrated by a sawtooth-like structure. The surface structure on the lower terrace is rotated by 180° along the surface normal compared to the structure on the upper terrace. The friction coefficient of one single terrace is, e.g., µ→ in the forward scan direction, whereas it changes to µ← for the backward scan direction due to effects as described in the text; i.e., the friction coefficient is direction-dependent. The contrast recorded in the FFM signal is the same for both directions. The direction dependence, however, has no influence on the torque of the FFM tip at the surface steps.
one has to pull or push depends on the direction. It is now instructive to investigate how this mechanism also applies on the atomic scale. The basic idea of this issue is illustrated in Figure 18.8 by contrasting the behavior of a tip moving (a) in a symmetric and (b) in an asymmetric surface potential. The asymmetric surface potential is represented by a sawtooth-like structure. Intuitively, one might assume that a sharp tip which profiles such an asymmetric potential would experience a larger lateral force at the steep sides of the sawtooth than
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FIGURE 18.9 Perspective view of the (010) surface of a negative domain exhibiting a surface step of half of the unit cell height.
on the less inclined sides.* Therefore, lower friction is expected for the upper terrace in comparison with the lower terrace for the “forward” scan direction. Additionally, the frictional contrast between the upper and the lower terrace should vanish if the tip is moved along the grooves of the sawtooth, i.e., perpendicular to the sketched figure. For the first time, effects due to the atomic-scale asymmetry of a surface potential were reported by Overney et al. (1994) for a lipid bilayer on oxidized Si(100). A similar domain contrast was also found by Gourdon et al. (1997) and Liley et al. (1998) with a thiolipid monolayer on mica. As a possible explanation, the observed contrast was considered to be caused by different molecular tilts within the individual domains. On crystalline surfaces, however, such effects can be studied in a more controlled manner. Here, we will use the ferroelectric material triglycine sulfate (TGS) as an example; similar results have recently been published by Shindo et al. (1999) for alkaline earth sulfate crystals. Figure 18.9 displays a perspective view on two neighboring terraces separated by a b/2 step within a negative domain. The glycine molecules form a sawtooth-like pattern perpendicular to the c-axis. The most remarkable feature of the surface structure in this context is that the arrangement of the molecules on the upper terrace is rotated by 180° compared to the structure on the lower terrace. This sawtoothlike surface structure is very similar to the case considered above, and an asymmetry in friction is therefore expected. Measurements by Bluhm et al. (1995) fully confirm the expected behavior. Figure 18.10 shows the relative frictional contrast between neighbored terraces (i.e., the difference of the friction on the upper and on the lower terrace) in arbitrary units as a function of the sample rotation angle; 0° is orthogonal to the a-axis. Due to a 105° angle between the a and the c-axis of the TGS crystal, the sample orientation is for 165° and 345° parallel to the grooves of the sawtooth structure. For these angles, the frictional contrast vanishes as predicted. A detailed discussion of the frictional anisotropy on TGS(010), including a simple theoretical model, can be found by Schwarz et al. (1996b).
18.6 Atomic Mechanism of Friction Although the experiments described above were performed with sliding distances in the micrometer range, it is clear that the origins for the studied effects can only be found on the atomic scale. In Section 18.2, we have seen that it is possible to measure frictional forces with a scanning force microscope down to the atomic scale. The analysis of such measurements gives interesting insight into the basic mechanism of friction. *Such a correlation between surface slope and lateral force can indeed not only be observed on the macroscopic scale, but has also been demonstrated at length scales of some 10 or 100 nanometers (Fujisawa et al., 1993b; Grafström et al., 1993; Bhushan et al., 1994; Ruan and Bhushan, 1994a), making our assumption even more substantial.
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FIGURE 18.10 Relative frictional contrast for neighbored terraces on the negative domain of TGS(010) as a function of the sample rotation angle.
FIGURE 18.11 (a) A simple model for a tip sliding on an atomically flat surface based on the Tomlinson model. A point-like tip is coupled elastically to the body M by a spring with spring constant cx in the x-direction; xt represents its position within an external potential V(xt) with periodicity a. If xt = xM, the spring is in its equilibrium position. For sliding, the body M is moved with the velocity νM in the x-direction. (b) A schematic view of the tip movement in a sinusoidal interaction potential. If condition (18.13) holds, the tip shows the typical stick-slip-type movement, i.e., it jumps from one potential minimum to another. (c) If the tip moves with stick-slips over the sample surface, the lateral force Fx manifests as a sawtooth-like function.
Many issues observed on the atomic scale can be illustrated by using a simple but instructive mechanical model based on the so-called Tomlinson (Tomlinson, 1929) or independent oscillator (IO) model (Prandtl, 1928; McClelland, 1989; Helman et al., 1994). A schematic view of this simple spring model is shown in Figure 18.11. A point-like tip is coupled elastically to the main body M with a spring possessing a spring constant cx in the x-direction, and it interacts with the sample surface via a periodic potential Vint(xt), where xt represents the actual position of the tip. During sliding, the body M is moved with the sliding velocity νM in the x-direction. All energy dissipation — independent of the actual dissipation channel . (phonons or electronic excitations) — is considered by a simple velocity-dependent damping term (–γx x t). Within this model, the point-like tip represents the average of the real tip–sample contact or single asperity contact, where up to hundreds of atoms might be involved (see Section 18.4). In principle, the real tip–sample contact could also be treated as a system consisting of many individual atomically sharp tips interacting through springs, leading to more complex models of friction. However, we will restrict ourselves to the simple model introduced above, which has proven to describe successfully the tip motion for many materials (Table 18.1). The resulting equation of motion for the tip in the interaction potential is given by
(
)
m x x˙˙t = c x x M − x t −
( ) − γ x˙
∂ Vint x t ∂x t
x t
(18.11)
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TABLE 18.1 Some Examples of Materials where the Tomlinson or Independent Oscillator Model Has Been Successfully Applied to Simulate Experimental Data Sample
Reference
Graphite(0001)
KBr(001) MoS2(001) β-MoTe2(001) NaF(001) Organic Monolayers
Sasaki et al., Phys. Rev. B, 54, 2138 (1996) Toussaint et al., Surf. Interface Anal., 25, 620 (1997) Hölscher et al., Phys. Rev. B, 57, 2477 (1998) Lüthi et al., J. Vac. Sci. Technol. B, 14, 1280 (1996) Hölscher et al., Surf. Sci., 375, 395 (1997) Hölscher et al., Phys. Rev. B, 59, 1661 (1999) Hölscher et al., Europhys. Lett., 39, 19 (1996) Ohzono et al., Jpn. J. Appl. Phys., 37, 6535 (1999)
where mx is the effective mass of the system, xM = νMt the equilibrium position of the spring, and γx the damping constant. The solution of this differential equation is the path of the tip xt(t). The lateral force Fx to move the tip in the x-direction can be calculated from Fx = cx(xM – xt), whereas the friction force Ff is defined as the averaged lateral force (Fx). If the sliding velocities are very low, analytical solutions of Equation 18.11 can be derived. In this case, the tip will always be in its stable equilibrium position, and Equation 18.11 can be solved for x¨ t = 0 and . xt = 0:
(
)
c x xM − xt =
( )
∂ Vint x t
(18.12)
∂x t
From this equation, a path xt(xM) can be determined.* For a stiff spring, there is only one solution for all xM, resulting in a continuous tip movement and vanishing friction, since the averaged lateral force (Fx) is zero (Figure 18.12). However, the tip movement changes dramatically if the condition
∂2 Vint cx < − 2 ∂x t min
(18.13)
is fulfilled. Now the tip moves discontinuously in a stick-slip-type motion over the sample surface and jumps from one potential minimum to another. This specific movement of the tip results in a sawtoothlike function for the lateral force Fx (see Figures 18.11c and 18.12). Since the averaged lateral force (Fx) is nonzero in this case, the friction force Ff is necessary to move the body M in the x-direction. To simulate experimental data obtained with a scanning force microscope, it is important to remember that an SFM can measure the lateral forces along and perpendicular to the scan direction (Section 18.2). Therefore, it is necessary to extend the one-dimensional model introduced above to two dimensions in a manner that considers explicitly the tip movement perpendicular to the scan direction (Gyalog et al., 1995). In the further analysis, we will show that this two-dimensional movement of the tip is significant and thus has a considerable effect on SFM images. The extension of the model to two dimensions leads to the following coupled second-order differential equation
(
)
m x x˙˙t = c x νMt − x t −
(
∂ Vint x t , y t ∂x t
) − γ x˙
x t
(18.14)
*An alternative way to determine the path of the tip is to calculate the minimum of its energy (McClelland, 1989).
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FIGURE 18.12 The tip movement in the Tomlinson model, illustrated with the example of the simple sinusoidal potential displayed in (a). If the tip moves in such a potential, its path can be determined from the solution of Equation 18.12. The graphical solution of this equation is shown in (b) for two different cases. For a stiff spring, ∂V x δx t
sin t there is only one point of intersection between cx(xM – xt) (dotted lines in [b]) and --------------(solid line). Consequently,
the obtained path xt(xM) and the lateral force Fx — displayed by dotted lines in (c) and (d) — are continuous, with the effect that the lateral force averages to zero and no friction occurs. If condition (18.13) holds, however, there is more than one point of intersection for certain support positions xM (dashed lines in [b]). This leads to instabilities, which manifest as “jumps” of the tip, as shown in (c) and (d). The occurrence of more than one intersection in (b) means that more than one value xt is possible for the same support position xM (dashed line in [c]). Thus, xt jumps for increasing xM instantaneously from one stable value to the next (solid line with arrows), leading to a discontinuous lateral force which looks like a sawtooth (solid line with arrows in [d]). The averaged lateral force Ff is now nonzero.
(
)
m y y˙˙t = c y y M − y t −
(
∂ Vint x t , y t ∂y t
)−γ
y˙
(18.14)
y t
which describes the movement of the tip in the tip–sample potential of an idealized SFM (Hölscher et al., 1997). The simulation of experimental data is performed by moving the support M with constant velocity νM in the “forward” direction (i.e., from left to right) as well as the “backward” direction (i.e., from right to left) continuously along a certain line in the x-direction while yM is held constant. Calculating the position of the tip (xt, yt) from Equation 18.14, the lateral forces Fx = cx(xM – xt) and Fy = cy(yM – yt) can be determined as a function of the support position (xM, yM). Then, after increasing yM, a new scan line is computed parallel to the previous line. The application of the model to a realistic sample system (and thus the movement of a sharp singleasperity tip in general) is illustrated in the following with the example of the MoS2(001) surface, where the simulated results are compared with experimental data of Fujisawa et al. (1994, 1995). For the calculations, it is necessary to choose a suitable tip–sample interaction potential Vint(xt, yt), which has to be used to solve Equation 18.14. The exact tip–sample interaction potential is difficult to determine, since the precise structure of the tip is usually unknown. However, it can be shown that all basic features of SFM measurements are reproduced by the simulation as long as Vint reflects the translational symmetry
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FIGURE 18.13 A schematic view of the MoS2 surface structure. The spheres represent the positions of the sulfate surface atoms. The dashed line marks the position yM = 0 used in Figure 18.15.
of the sample surface. A comparison with the surface structure of the MoS2(001) sample surface displayed in Figure 18.13 shows that this requirement is met by
2π 2π VMoS2 x t , y t = V0 cos x t cos y t ax ay
(
)
(18.15)
where ax = 3.16 Å and ay = 5.48 Å; the actual value of V0 depends on the loading force. With this potential, numerical solutions of Equation 18.14 were computed. The resulting images and line plots presented here were obtained with the following set of parameters: V0 = 1 eV, cx = cy = 10 N/m, mx = my = 10–8 kg, νM = 400 Å/s, γx = γy = 10–3 Ns/m ~ 2 c x ⁄ m x (critical damping is assumed). These parameters have typical magnitude, but qualitatively similar results are obtained with other choices. Figure 18.14 shows a comparison of lateral force images calculated using the two-dimensional IOmodel with experimental data acquired in the [100]- and [120]-directions. The good agreement demonstrates that the presented method has the capability to simulate experimental lateral force maps. Moreover, it suggests that the model is able to describe the basic mechanism of atomic-scale friction, although it is based on comparably simple assumptions. A better insight into the scan process allows Figure 18.15a, where both lateral forces Fx and Fy are plotted as a function of the support position xM for the [100]-direction and scan positions yM = 0.0, 0.2, 1.0, 1.3, 1.4, 1.7, 2.5, and 2.7 Å (from left to right) according to the definition of yM given in Figure 18.13. The lateral force in scan direction Fx(xM) exhibits a sawtooth-like shape, whereas the force perpendicular to the scan direction, Fy(xM), looks like a step function. All features of the calculated forces are in good agreement with experimental data, which is shown for comparison in Figure 18.15b. The origin of this behavior is analyzed in Figure 18.16. Figure 18.16a shows the paths of the tip in the potential of VMoS2(xt , yt) for different values of yM. For yM = 0 Å, no movement of the tip perpendicular to the scan direction can be observed, as expected from Figure 18.15. However, with increasing yM-values, the path of the tip becomes zigzag. A smaller area of the potential is shown in Figure 18.16b, where the path of the tip for yM = 1.4 Å and 0.7 Å is plotted “time-resolved” by points of equal time distance with ∆t = 62.5 µs. It can be seen that the tip only moves slowly as long as it is in the areas which are framed by white lines. These areas are obtained by calculating the surface areas where the tip has a stable position for very slow scan velocities (νM → 0) (Gyalog et al., 1995). If the tip leaves these “areas of stability,” it becomes unstable and jumps into the next “area of stability.” This explains the stick-slip-type behavior of the lateral force Fx as well as the “step-function”-like shape of the force Fy .
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FIGURE 18.14 A comparison between the simulated (top) and measured (bottom) lateral force images for the scan directions indicated in Figure 18.13. The movement of the support was in positive x-direction (“forward”); the scan size was 25 Å × 25 Å. (Data from Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a two-dimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857.)
a) Fx [nN]
4
-4
Fy [nN]
2
0
o
xM [A]
25
LFM (fx)
o
b)
o 1.1x10-10 N (1.5A) 4.8x10-7N (8.8A )
-2
AFM (fY ) o
25 A
FIGURE 18.15 A comparison between the calculated (a) and measured (b) lateral forces Fx and Fy for a scan in the [100]-direction and different support positions yM as defined in Figure 18.13. (Data from Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a two-dimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857.)
One consequence of this behavior is that the maximum of Fx might appear at different positions than the maximum values of Fy (see Hölscher et al., 1998), as it was first observed experimentally by Ruan and Bhushan (1994a). Another consequence is that a large part of the surface is skipped by the tip and, therefore, no information about these skipped surface areas can be extracted from the acquired images. This latter behavior has been experimentally verified for mica by Kawakatsu and Saito (1996); a visualization of this issue based on the MoS2 data presented in Figures 18.14 and 18.15 is shown in Figure 18.16c. Here, the “position probability density” of the tip during the scan is plotted, i.e., only the parts of the surface that show a high density of black points have contact with the tip for a significant time; the white areas are skipped by the tip.
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FIGURE 18.16 (a) The interaction potential V(xt, yt) (image size: 25 Å × 25 Å) and the calculated paths of the tip (xt(t), yt(t)) in this potential for the support positions yM = 0.0, 0.2, 0.7, 1.0, and 1.4 Å (from top to bottom; for the definition of yM see Figure 18.13). If yM ≠ 0, the tip performs a zigzag movement. (b) A detail of (a) (image size: 10 Å × 10 Å). The contours of the “areas of stability” (see text) are marked by white lines. In order to show that the tip stays in these areas most of time, the path of the tip is drawn for yM = 1.4 Å (top) and 0.7 Å (bottom) by points separated by equal time intervals ∆t = 62.5 µs. (c) Visualization of the tip position during the scanning of the sample. All calculated paths (54 lines per period) are plotted as in (b). Consequently, the density of points can be interpreted as the “position probability density” of the tip on the surface during the scan. The “areas of stability” are framed by black lines. Only parts of the stable areas — the dark areas — are in contact with the tip for a significant time.
At the end of this section, the question arises of how far the situation described above corresponds with the tribological behavior of a nanocontact which is not connected to a cantilever. By the comparison of experiment and simulation, however, it can be demonstrated that elastic deformations between the atoms at or close to the tip–sample contact area are responsible for the stick-slip movement of the tip; astonishingly the cantilever has only a minor influence. Additionally, in molecular dynamics simulations, atomic stick-slips as found in the above analysis are found to take place as a direct consequence of the interplay between the surface forces and interatomic interactions within tip and sample (Landman et al., 1989; Harrison et al., 1992, 1993a; Schimizu et al., 1998). Even the zigzagging of the tip atoms in the interaction potential of the surface has been reproduced (Harrison et al., 1993a,b; Shluger et al., 1999). Thus, it can be concluded that the scanning force microscope indeed measures the “real” frictional behavior of a nanocontact.
18.7 The Velocity Dependence of Friction So far, we have discussed different phenomenological aspects as well as theoretical concepts of friction on the nanometer scale, but we still have to find an explanation for Coulomb’s law (3) on the independence of sliding friction from the sliding velocity νM. As already mentioned in the introduction, this law has also been confirmed on the nanometer scale within a wide velocity range for crystalline surfaces (Hu et al., 1995; Bouhacina et al., 1997; Zwörner et al., 1998).* Figure 18.17 shows two examples of experimental data sets for amorphous carbon and diamond. It is found that the friction force Ft is nearly constant for the velocities that can be reached with an SFM. To get a basic idea of the mechanism which causes the velocity independence of the frictional forces, we again apply the simple mechanical model introduced in Section 18.6. For this purpose, we are interested in the solutions of Equation 18.11 for moderate scan velocities. The qualitative behavior within the one-dimensional case is shown for a sinusoidal potential Vint(xt) = V0sin(2πxt). All data presented here are obtained with the parameters V0 = 1.0 eV, a = 3 Å, cx = 10 N/m (condition [13] holds for these *There is, however, experimental evidence that friction has a logarithmic or even more complicated dependence on the sliding velocity for noncrystalline overlayers (e.g., polymeric, self-assembled, or Langmuir–Blodgett-type layers), probably due to a certain viscosity of the layers due to a liquid-like structure (Liu et al., 1994; Koinkar and Bhushan, 1996; Bouhacina et al., 1997). Additionally, it should be mentioned that there have been reports where even on crystalline surfaces, a slight logarithmic dependence of the friction on the sliding velocity was observed by SFM (Liu et al., 1994; Koinkar and Bhushan, 1996).
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FIGURE 18.17 The friction forces Ff as a function of the sliding velocity νM measured with a silicon tip on (a) amorphous carbon, and (b) diamond. Ff is independent of the sliding velocity in good approximation.
parameters, i.e., stick-slips will occur), mx = 10–10 kg (with this effective mass, the system [tip and sample in contact] has a typical resonance frequency of 1/(2π) c x ⁄ m x ≈ 50 kHz, which is typical for SFM experiments), and γx = 2 c x ⁄ m x (critical damping). With this set of parameters, we calculate the numerical solutions of Equation 18.11 and determine the lateral forces Fx as well as the frictional force Ff for different sliding velocities (νM = 10 nm/s … 100 µm/s). In Figure 18.18, the calculated lateral force Fx is displayed for different sliding velocities νM. It is obvious that the obtained results change only little within the wide range of sliding velocities νM = 10 nm/s … 10 µm/s. Only for high sliding velocities, where the solution of Equation 18.11 is dominated by the velocity-dependent damping term (see Fx for 100 µm/s in Figure 18.18), the lateral force increases significantly. Consequently, since the friction force is the average of the lateral force, Ff is approximately independent of the sliding velocity in a wide range. What is now the reason for the relative independence of the lateral forces on the sliding velocities at moderate values of νM? This issue is illustrated in Figure 18.11b. We have seen above that the tip usually moves in a stick-slip-type motion over the sample surface. With this type of motion, the tip stays in the minima of the interaction potential most of the time where it slides very slowly or “sticks.” Therefore, almost no energy is dissipated in this “stick”-state, since we assumed that the damping is proportional to the sliding velocity. In the “slip”-state, however, the tip “jumps” from one to another minimum. During this jump, the tip reaches very high peak velocities and dissipates significant amounts of energy due to the velocity-dependent damping mechanism. It is now important to note that the maximum velocity reached during the slip depends for low values of νM in first approximation only on the spring constant cx, the height and the shape of the potential, the chosen damping constant, and the effective mass of the system, but not on the sliding velocity νM. As a consequence, the total amount of energy dissipated during sliding does not change significantly as long as νM is much smaller than the slip velocity of the tip. From Figure 18.18, we obtain a slip velocity of about 60 µm/s for sliding speeds up to 10 µm/s.* For larger sliding velocities, the mechanism of energy dissipation through the “stick-slip” effects breaks down, as can be seen for νM = 100 µm/s. However, despite its success, the model introduced above is still unsatisfactory from an atomistic view, since it is fully phenomenological in the way that it does not give any insight into the dissipation mechanism involved. It is clear that the energy dissipation process will be much more complicated in a real physical system than that considered here; more complete theories can be found in, for example, Sokoloff (1990, 1993) or Colchero et al. (1996). *The numerical value of the slip velocity obtained within this simple mechanical model is determined by the onedimensional interaction potential and the chosen numerical values of the parameters, which partially might vary in a very large range without changing the obtained results qualitatively. Consequently, the slip velocity of 60 µm/s is not a prediction for an experimental measurement and could actually be much higher without contradiction of the general mechanism discussed here.
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FIGURE 18.18
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The lateral force Fx and the tip velocity νt for different sliding velocities νM = 10 nm/s … 100 µm/s.
18.8 Summary In this chapter, we have reviewed some of our present understanding of atomic-scale friction gained from scanning force microscopy experiments. Our analysis, however, has always been restricted to fundamental aspects of wearless Coulomb friction (i.e., dry friction); effects due to boundary lubrication and wetting of surfaces were not considered. It has been shown that the main advantage of the SFM in this context is its ability to enable detailed studies of the friction of “point contacts” (which have been found to exhibit, in reality, contact areas of some nm2, depending on the applied load, the elastic properties of tip and sample, and the tip radius) with high spatial resolution as a function of the contact geometry, the applied load, the effective contact area, the sliding velocity, and the surface structure of the profiled sample. Remarkably, it has been found that some phenomena manifest similarly on the nanometer scale compared to their macroscopic behavior, whereas others show a very different behavior. Most strikingly, friction on the nanometer scale is proportional to the effective contact area, contrary to the macroscopic case. Consequently, the concept of the “friction coefficient,” which is independent of the actual contact geometry, fails on this scale. In the corresponding experiments, contact pressures of up to 1 GPa are easily reached. Such pressures are already above the yield stress of many materials and therefore seem very high at first sight, but might match the “realistic” pressures of individual nanocontacts within a macroscopical contact far better than lower contact pressures. However, despite these high
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pressures and the small dimensions of the individual contact with only some tens or some hundreds of atoms in intimate contact, contact mechanics, which has been derived from continuum elasticity theory, has proved to be still valid. Another interesting point is that the shear stress is independent of the mean contact pressure — at least in the case of nanometer-sized Hertzian or approximately Hertzian contacts. Again, very high shear stresses of up to 1 GPa are found, orders of magnitude more than typically obtained from other friction experiments. These high values can possibly be accounted for as representing approximately the theoretical shear stress of the contact, which is about 1/30 of the shear modulus of the contact (Cottrell, 1953) and therefore has about the correct order of magnitude. Much more difficult to answer is the question of which factors determine whether a given contact shows high or low friction. In many experiments, it has been demonstrated that friction is very sensitive to even small changes in the surface structure and might additionally show a strong dependence on the sliding direction relative to the crystal lattice. This feature has been used frequently to distinguish between chemically different areas of samples or to obtain a contrast between individual domains that differ due to structural effects, but has not yet resulted in significant progress in our understanding of why certain surfaces have higher friction than others. Nevertheless, studying such issues, the atomic-scale movement of the individual atoms which are in intimate contact has been clarified to a certain degree. By comparison with theoretical models, it can be shown that the tip atoms move in a “stick-slip”-type motion over the sample surface, “jumping” from one minima of the tip–sample interaction potential to the next. Since they try to avoid passing over the position of a sample atom which represents a maximum of the interaction potential, their paths often resemble a zigzag curve. Due to this specific behavior, it follows that the “atomically resolved” images of contact force microscopy represent solely the periodicity of the potential minima of the interaction potential, which does not generally match the atomic structure of a sample for nontrivial unit cells. Another intention of this chapter was to bridge the gap between the macroscopic and the microscopic/nanoscopic scale. As we have seen in the introduction, it is one of the basic aims of nanotribology to explain the macroscopic frictional behavior of materials and contacts with fundamental processes occurring on the atomic scale. And it seems indeed possible to derive Amontons’ and Coulomb’s laws of friction from nanoscopic effects. Greenwood (1967, 1992) showed that the effective contact area between macroscopically flat bodies, which nevertheless exhibit a statistical microscopical roughness, increases linearly with the load, which eliminates any contradiction between the corresponding macroscopic and the nanoscopic friction laws. Moreover, the relative independence of friction on the sliding velocity on both the macroscopic and the nanoscopic scale might be explained with the stick-slip-type motion of the atoms in the tip–sample interaction potential. As long as the relative velocity of the two bodies is much lower than the intrinsic “slip velocity” of the atoms, the dissipated energy will be independent of variations in the sliding velocity. To conclude, nanotribology is a young field which has developed rapidly during the last one or two decades. Considerable progress has been made during this time in our understanding of fundamental frictional processes on the nanometer scale, as we hope to have demonstrated above, and first attempts to connect the atomic-scale effects with macroscopic phenomena seem to be successful. However, in spite of this progress, there are still many more open than answered questions. For example, it is still impossible with our present knowledge to predict the frictional properties of a specific contact from first principles. Nevertheless, the optimization of the frictional properties of surfaces for a given purpose will be increasingly important in the future for the further miniaturization of motors and other moving parts in, for example, hard discs or micro electromechanical systems. A further unsolved question is how energy is dissipated during wearless friction. It seems that the excitation of phonons represents the main channel for energy dissipation, even though electronic processes might be equally important in the case of conducting materials. Thus, the exact control of the dissipation channels might be a prerequisite for the tailoring of surfaces with given frictional properties — and simultaneously offers plenty of room for original and innovative nanotribological research.
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References Aimé, J.P., Elkaakour, Z., Gauthier, S., Michel, D., Bouhacina, T., and Curély, J. (1995), Role of the force of friction on curved surfaces in scanning force microscopy, Surf. Sci., 329, 149-156. Bhushan, B., Koinkar, V.N., and Ruan, J. (1994), Microtribology of magnetic media, Proc. Inst. Mech. Part J: J. Eng. Tribol., 208, 17-29. Bhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction force microscopy: Part I — General principles and new measurement techniques, ASME J. Tribol., 116, 378-388. Bhushan, B. and Kulkarni, A.V. (1995), Effect of normal load on microscale friction measurements, Thin Solid Films, 278, 49-56. Binh, V.T. and Garcia, N. (1992), On the electron and metallic ion emission from nanotips fabricated by field-surface-melting technique: experiments on W and Au tips, Ultramicroscopy, 42-44, 80-90. Binh, V.T. and Uzan, R. (1987), Tip-shape evolution: capillary induced matter transport by surface diffusion, Surf. Sci., 179, 540-560. Binnig, G., Quate, C.F., and Gerber, Ch. (1986), Atomic force microscope, Phys. Rev. Lett., 56, 930-933. Bluhm, H., Schwarz, U.D., Meyer, K.-P., and Wiesendanger, R. (1995), Anisotropy of sliding friction on the triglycine sulfate (010) surface, Appl. Phys. A, 61, 525-533. Bluhm, H., Schwarz, U.D., and Wiesendanger, R. (1998), Origin of the ferroelectric domain contrast observed in lateral force microscopy, Phys. Rev. B, 57, 161-169. Bouhacina, T., Aimé, J.P., Gauthier, S., Michel, D., and Heroguez, V. (1997), Tribological behavior of a polymer grafted on silanized silica probed with a nanotip, Phys. Rev. B, 56, 7694-7703. Briscoe, B.J. and Evans, D.C.B. (1982), The shear properties of Langmuir–Blodgett layers, Proc. R. Soc. Lond. A, 380, 389-407. Carpick, R.W., Agrait, N., Ogletree, D.F., and Salmeron, M. (1996), Measurement of the interfacial shear (friction) with an ultrahigh vacuum atomic force microscope, J. Vac. Sci. Technol. B, 14, 1289-1295. Carpick, R.W., Ogletree, D.F., and Salmeron, M. (1997), Lateral stiffness: a new nanomechanical measurement for the determination of shear strengths with friction force microscopy, Appl. Phys. Lett., 70, 1548-1550. Colchero, J., Baró, A.M., and Marti, O. (1996), Energy dissipation in scanning force microscopy — friction on an atomic scale, Tribol. Lett., 2, 327-343. Cottrell, A.H. (1953), Dislocations and Plastic Flow in Crystals, Oxford University Press, Oxford, U.K. Derjaguin, B.V., Muller, V.M., and Toporov, Y.P. (1975), Effect of contact deformations on the adhesion of particles, J. Colloid Interface Sci., 53, 314-326. Enachescu, M., van den Oetelaar, R.J.A., Carpick, R.W., Ogletree, D.F., Flipse, C.F.J., and Salmeron, M. (1998), Atomic force microscopy study of an ideally hard contact: the diamond(111)/tungsten carbide interface, Phys. Rev. Lett., 81, 1877-1880. Fogden, A. and White, L.R. (1990), Contact elasticity in the presence of capillary condensation, J. Colloid Interface Sci., 138, 414-430. Fompeyrine, J., Berger, R., Lang, H.-P., Perret, J., Mächler, E., Gerber, Ch., and Locquet, J.-P. (1998), Local determination of the stacking sequence of layered materials, Appl. Phys. Lett., 72, 1697-1699. Frisbie, C.D., Rozsnyai, L.F., Noy, A., Wrighton, M.S., and Lieber, C.M. (1994), Functional group imaging by chemical force microscopy, Science, 265, 2071-2074. Fujihara, M. and Ohzono, T. (1999), Basis of chemical force microscopy by friction: energetics and dynamics of wearless friction between organic monolayers in terms of chemical and physical properties of molecules, Jpn. J. Appl. Phys., 38, 3918-3931. Fujisawa, S., Sugawara, Y., Ito, S., Mishima, S., Okada, T., and Morita, S. (1993a), The two-dimensional stick-slip phenomenon with atomic resolution, Nanotechnology, 4, 138-142. Fujisawa, S., Sugawara, Y., and Morita, S. (1993b), Origins of the forces measured by atomic force/lateral force microscope, Microbeam Analysis, 2, 311-316. Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1994), Fluctuation in the two-dimensional stick-slip phenomenon observed with two-dimensional frictional microscope, Jpn. J. Appl. Phys., 33, 3752-3755.
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Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a twodimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857. Gourdon, D., Burnham, N.A., Kulik, A., Dupas, E., Oulevey, F., Gremaud, G., Stamou, D., Liley, M., Dienes, Z., Vogel, H., and Duschl, C. (1997), The dependence of friction anisotropies on the molecular organisation of LB films as observed by AFM, Tribol. Lett., 3, 317-324. Grafström, S., Neitzert, M., Hagen, T., Ackermann, J., Neumann, R., Probst, O., and Wörtge, M. (1993), The role of topography and friction for the image contrast in lateral force microscopy, Nanotechnology, 4, 143-151. Greenwood, J.A. (January 1967), The area of contact between rough surfaces and flats, J. Lub. Technol., 81-91. Greenwood, J.A. (1992), Contact of rough surfaces, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I. L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 37. Gyalog, T., Bammerlin, M., Lüthi, R., Meyer, E., and Thomas, H. (1995), Mechanism of atomic friction, Europhys. Lett., 31, 269-274. Harrison, J.A., Colton, R.J., White, C.T., and Brenner, D.W. (1993a), Effect of atomic-scale surface roughness on friction: a molecular dynamics study of diamond surfaces, Wear, 168, 127-133. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1993b), Effects of chemically-bound, flexible hydrocarbon species on the frictional properties of diamond surfaces, J. Chem. Phys., 97, 6573-6576. Helman, J.S., Baltensberger, W., and Holyt, J.A. (1994), Simple model for dry friction, Phys. Rev. B, 49, 3831-3838. Hertz, H. (1881), Über die Berührung fester elastischer Körper, J. Reine Angew. Math., 92, 156-171. Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1997), Modelling of the scan process in lateral force microscopy, Surf. Sci., 375, 395-402. Hölscher, H., Schwarz, U.D., Zwörner, O., and Wiesendanger, R. (1998), Consequences of the stick-slip movement for the scanning force microscopy imaging of graphite, Phys. Rev. B, 57, 2477-2481. Homola, A.M., Israelachvili, J.N., McGuiggan, P.M., and Gee, M.L. (1990), Fundamental experimental studies in tribology: the transition from “interfacial” friction of undamaged molecularly smooth surfaces to “normal” friction with wear, Wear, 136, 65-83. Hu, J., Xiao, X.-D., Ogletree, D.F., and Salmeron, M. (1995), Atomic scale friction and wear of mica, Surf. Sci., 327, 358-370. Israelachvili, J.N. and Tabor, D. (1973), The shear properties of molecular films, Wear, 24, 386-390. Israelachvili, J.N., Perez, E., and Tandon, R.K. (1980), On the adhesion force between deformable surfaces, J. Colloid Interface Sci., 78, 260-261. Johnson, K.L. (1994), Contact Mechanics, Cambridge University Press, Cambridge, U.K. Johnson, K.L. (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface, Proc. R. Soc. Lond. A, 453, 163-179. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London A, 324, 301-313. Kawakatsu, H. and Saito, T. (1996), Scanning force microscopy with two optical levels for detection of deformations of the cantilever, J. Vac. Sci. Technol. B, 14, 872-876. Koinkar, V.N. and Bhushan, B. (1996), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391. Landman, U., Luedtke, W.D., and Nitzan, A. (1989), Dynamics of tip–substrate interactions in atomic force microscopy, Surf. Sci., 210, L177-L184. Lantz, M.A., O’Shea, S.J., Welland, M.E., and Johnson, K.L. (1997), Atomic-force-microscope study of contact area and friction on NbSe2, Phys. Rev. B, 55, 10776-10785. Liley, M., Gourdon, D., Stamou, D., Meseth, U., Fischer, T.M., Lautz, C., Stahlberg, H., Vogel, H., Burnham, N.A., and Duschl, C. (1998), Friction anisotropy and asymmetry of a compliant monolayer induced by a small molecular tilt, Science, 280, 273-275. Liu, Y., Wu, T., and Evans, D.F. (1994), Lateral force microscopy study on the shear properties of selfassembled monolayers of dialkylammonium surfactant on mica, Langmuir, 10, 2241-2245.
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Lüthi, R., Meyer, E. Haefke, H., Howald, L., Gutmannsbauer, W., Guggisberg, M., Bammerlin, M., and Güntherodt, H.-J. (1995), Nanotribology: an UHV–SFM study on thin films of C60 and AgBr, Surf. Sci., 338, 247-260. Marti, O., Colchero, J., and Mlynek, J. (1990), Combined scanning force and friction microscopy of mica, Nanotechnology, 1, 141-144. Marti, O., Colchero, J., and Mlynek, J. (1993), Friction and forces on the atomic scale, in Nanosources and Manipulation of Atoms Under High Fields and Temperatures: Applications, Binh V.T. et al. (Eds.) Kluwer Academic Publishers, Dordrecht, The Netherlands, 253. Mate, C.M., McClelland, G.M., Erlandsson, R., and Chiang, S. (1987), Atomic-scale friction of a tungsten tip on a graphite surface, Phys. Rev. Lett., 59, 1942-1945. Mate, C.M. (1993), Nanotribiology studies of carbon surfaces by force microscopy, Wear, 168, 17-20. Maugis, D. (1987), Adherence of elastomers: fracture mechanics aspects, J. Adhesion Sci. Technol., 1, 105-134. Maugis, D. (1992), Adhesion of spheres: the JKR–DMT transition using a Dugdale model, J. Colloid Interface Sci., 73, 294-269. Maugis, D. and Gauthier-Manuel, B. (1994), JKR–DMT transition in the presence of a liquid meniscus, J. Adhesion Sci. Technol., 8, 1311-1322. McClelland, G.M. (1989), Friction at weakly interacting interfaces, in Adhesion and Friction, Grunze, M. and Kreuzer, H.J. (Eds.), Springer Series in Surface Science, Vol. 17, Springer Verlag, Heidelberg, 1. Meyer, E., Overney, R., Brodbeck, D., Howald, L., Lüthi, R., Frommer, J., and Güntherodt, H.-J. (1992), Friction and wear of Langmuir–Blodgett films observed by friction force microscopy, Phys. Rev. Lett., 69, 1777-1780. Meyer, E. and Heinzelmann, H. (1992), Scanning force microscopy, in Scanning Tunneling Microscopy II, Wiesendanger, R. and Güntherodt, H.-J. (Eds.), Springer Series in Surface Science, Vol. 28, Springer-Verlag, Heidelberg, 99. Meyer, E., Lüthi, R., Howald, L., Bammerlin, M., Guggisberg, M., and Güntherodt, H.-J. (1996), Sitespecific friction force microscopy, J. Vac. Sci. Technol. B, 14, 1285-1288. Meyer, G. and Amer, N.M. (1990), Simultaneous measurement of lateral and normal forces with opticalbeam-deflection atomic force microscope, Appl. Phys. Lett., 57, 2089-2091. Muller, V.M., Yuschenko, V.S., and Derjaguin, B.V. (1983), General theoretical consideration of the influence of surface forces on contact deformations and the reciprocal adhesion of elastic spherical particles, J. Colloid Interface Sci., 92, 92-101. Ogletree, D.F, Carpick, R.W., and Salmeron, M. (1996), Calibration of frictional forces in atomic force microscopy, Rev. Sci. Instrum., 67, 3298-3306. Overney, R.M., Meyer, E., Frommer, J., Brodbeck, D., Lüthi, R., Howald, L. Güntherodt, H.-J., Fujihira, M., Takano, H., and Gotoh, Y. (1992), Friction measurements on phase-separated thin films with a modified atomic force microscopy, Nature, 359, 133-135. Overney, R.M., Takano, H., Fujihira, M., Paulus, W., and Ringsdorf, H. (1994), Anisotropy in friction and molecular stick-slip motion, Phys. Rev. Lett, 72, 3546-3549. Prandtl, L. (1928), Ein Gedankenmodell zur kinetischen Energie der festen Körper, Z. Angew. Math. Mech., 8, 85-106. Putman, C., Igarashi, M., and Kaneko, R. (1995), Quantitative determination of friction coefficients by friction force microscopy, Jpn. J. Appl. Phys., 34, L264-L267. Ruan, J. and Bhushan, B. (1994a), Atomic-scale and microscale friction studies of graphite and diamond using friction force microscopy, J. Appl. Phys., 76, 5022-5035. Ruan, J. and Bhushan, B. (1994b), Frictional behavior of highly oriented pyrolytic graphite, J. Appl. Phys., 76, 8117-8120. Sasaki, K., Koike, Y., Azehara, H., Hokari, H., and Fujihara, M., (1998), Lateral force microscope and phase imaging of patterned thiol self-assembling monolayer using chemically modified tips, Appl. Phys. A, 66, S1275-S1277. Schluger, A.L., Livshits, A.I., Foster, A.S., and Catlow, C.R.A. (1999), Models of image contrast in scanning force microscopy on insulators, J. Phys: Condens, Matter, 11, R295-R322.
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Schwarz, U.D. (1997), Scanning force microscopy, in Handbook of Microscopy II, Amelinckx, S., Van Dyck, D., Van Landuyt, J.F., and Van Tendeloo, G., (Eds.), VCH Verlagsgesellschaft, Weinheim, Germany, 827. Schwarz, U.D., Köster, P., and Wiesendanger, R. (1996a), Quantitative analysis of lateral force microscopy experiments, Rev. Sci. Instrum., 67, 2560-2567. Schwarz, U.D., Bluhm, H., Hölscher, H., Allers, W., and Wiesendanger, R. (1996b), Friction in the lowload regime: studies on the pressure and direction dependence of frictional forces by means of friction force microscopy, in Physics of Sliding Friction, Persson, B.N.J. and Tosatti, E. (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 369. Schwarz, U.D., Zwörner, O., Köster, P., and Wiesendanger, R. (1997a), Quantitative analysis of the frictional properties of solid materials at low loads. I. Carbon compounds, Phys. Rev. B, 56, 6987-6996. Schwarz, U.D., Zwörner, O., Köster, P., and Wiesendanger, R. (1997b), Preparation of probe tips with well-defined spherical apexes for quantitative scanning force spectroscopy, J. Vac. Sci. Technol. B, 15, 1527-1530. Shimizu, J., Eda, H., Yoritsune, M., and Ohmura, E. (1998), Molecular dynamics simulation of friction on the atomic scale, Nanotechnology, 9, 118-123. Shindo, H., Shitagami, T., and Kondo, S.-I. (1999), Evidence of the contribution of molecular orientations on the surface force friction of alkaline earth sulfate crystals, Phys. Chem. Chem. Phys., 1, 1597-1600. Sokoloff, J.B. (1990), Theory of energy dissipation in sliding crystal surfaces, Phys. Rev. B, 42, 760-765. Sokoloff, J.B. (1993), Fundamental mechanisms for energy dissipation at small solid sliding surfaces, Wear, 167, 59-68. Tabor, D. (1977), Surface forces and surface interactions, J. Colloid Interface Sci., 58, 2-13. Tomlinson, G.A. (1929), A molecular theory of friction, Philos. Mag. S., 7, 7, 905-939. Wiesendanger, R. (1994), Scanning Probe Microscopy and Spectroscopy: Methods and Applications, Cambridge University Press, Cambridge, U.K. Zwörner, O., Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1998), The velocity dependence of frictional forces in point-contact friction, Appl. Phys. A, 66, S263-S267.
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19 Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy 19.1 19.2
Introduction ..................................................................... 667 Description of AFM/FFM and Various Measurement Techniques ........................................................................ 669 Surface Roughness and Friction Force Measurements • Adhesion Measurements • Scratching, Wear, and Fabrication/Machining • Surface Potential Measurements • Nanoindentation Measurements • Boundary Lubrication Measurements
19.3
Friction and Adhesion ..................................................... 678 Atomic-Scale Friction • Microscale Friction • Comparison of Microscale and Macroscale Friction Data • Effect of Tip Radii and Humidity on Adhesion and Friction
19.4
Scratching, Wear, and Fabrication/Machining............... 694 Nanoscale Wear • Microscale Scratching • Microscale Wear • Nanofabrication/Nanomachining
19.5
Indentation ....................................................................... 703
19.6 19.7
Boundary Lubrication ..................................................... 708 Closure .............................................................................. 712
Picoindentation • Nanoscale Indentation
Bharat Bhushan The Ohio State University
19.1 Introduction The atomistic mechanisms and dynamics of the interactions of two materials during relative motion need to be understood in order to develop a fundamental understanding of adhesion, friction, wear, indentation, and lubrication processes. At most solid–solid interfaces of technological relevance, contact occurs at many asperities. Consequently, the importance of investigating single asperity contacts in studies of the fundamental micromechanical and tribological properties of surfaces and interfaces has long been recognized. The recent emergence and proliferation of proximal probes, in particular scanning probe microscopies (the scanning tunneling microscope and the atomic force microscope) and the surface force apparatus, and of computational techniques for simulating tip–surface interactions and interfacial properties, has allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifying and manipulating nanoscale structures. These advances have led to the appearance of the new field of micro/nanotribology, which pertains to experimental and theoretical investigations of interfacial processes on scales ranging from the atomic- and molecular- to the microscale, occurring during adhesion, friction, scratching, wear, nanoindentation, and thin-film lubrication at
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TABLE 19.1 Comparison of Typical Operating Parameters in SFA, STM, and AFM/FFM Used for Micro/Nanotribological Studies Operating Parameter
SFA
Radius of mating surface/tip Radius of contact area Normal load Sliding velocity
~10 mm 10–40 µm 10–100 mN 0.001–100 µm/s
Sample limitations
Typically atomically smooth, optically transparent mica; opaque ceramic, smooth surfaces can also be used
STM*
AFM/FFM
5–100 nm N/A N/A 0.02–2 µm/s (scan size ~1 nm × 1 nm to 125 µm x 125 µm; scan rate <1–122 Hz) Electrically conducting samples
5–100 nm 0.05–0.5 nm <0.1 nN–500 nN 0.02–2 µm/s (scan size ~1 nm × 1 nm to 125 µm × 125 µm; scan rate <1–122 Hz) None
* Can only be used for atomic-scale imaging
sliding surfaces (Singer and Pollock, 1992; Persson and Tosatti, 1996; Bhushan, 1995, 1997, 1998a,b, 1999a,b,c; Bhushan et al., 1995a; Guntherodt et al., 1995). The micro/nanotribological studies are needed to develop fundamental understanding of interfacial phenomena on a small scale and to study interfacial phenomena in micro- and nanostructures used in magnetic storage systems, microelectromechanical systems (MEMS), and other applications (Bhushan, 1996, 1997, 1998a). Friction and wear of lightly loaded micro/nanocomponents are highly dependent on surface interactions (few atomic layers). These structures are generally lubricated with molecularly thin films. Micro/nanotribological studies are also valuable in a fundamental understanding of interfacial phenomena in macrostructures to provide a bridge between science and engineering. The surface force apparatus (SFA), the scanning tunneling microscope (STM), and atomic force and friction force microscopes (AFM and FFM) are widely used in micro/nanotribological studies. Typical operating parameters are compared in Table 19.1. The SFA was developed in 1968 and is commonly employed to study both static and dynamic properties of molecularly thin films sandwiched between two molecularly smooth surfaces. The STM, developed in 1981, allows imaging of electrically conducting surfaces with atomic resolution, and has been used for imaging clean surfaces as well as lubricant molecules. The introduction of the atomic force microscope in 1985 provided a method for measuring ultra-small forces between a probe tip and an engineering (electrically conducting or insulating) surface, and has been used for topographical measurements of surfaces on the nanoscale, as well as for adhesion and electrostatic force measurements. Subsequent modifications of the AFM led to the development of the friction force microscope (FFM), designed for atomic-scale and microscale studies of friction. This instrument measures forces transverse to the surface. The AFM is also being used for investigations of scratching, wear, indentation, detection of transfer of material, boundary lubrication, and fabrication and machining. Meanwhile, significant progress in understanding the fundamental nature of bonding and interactions in materials, combined with advances in computer-based modeling and simulation methods, has allowed theoretical studies of complex interfacial phenomena with high resolution in space and time. Such simulations provide insights into atomic-scale energetics, structure, dynamics, thermodynamics, transport, and rheological aspects of tribological processes. The nature of interactions between two surfaces brought close together, and those between two surfaces in contact as they are separated, have been studied experimentally with the surface force apparatus. This has led to a basic understanding of the normal forces between surfaces and the way in which these are modified by the presence of a thin liquid or polymer film. The frictional properties of such systems have been studied by moving the surfaces laterally, and such experiments have provided insights into the molecular-scale operation of lubricants such as thin liquid or polymer films. Complementary to these studies are those in which the AFM or FFM is used to provide a model asperity in contact with a solid or lubricated surface. These experiments have demonstrated that the relationship between friction and
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surface roughness is not always simple or obvious. AFM studies have also revealed much about the nanoscale nature of intimate contact during wear and indentation. In this chapter, we present a review of significant aspects of micro/nanotribological studies conducted using AFM/FFM.
19.2 Description of AFM/FFM and Various Measurement Techniques An atomic force microscope (AFM), developed by Gerd Binnig and his colleagues in 1985, is capable of investigating surfaces of scientific and engineering interest on an atomic scale (Binnig et al., 1986, 1987). The AFM relies on a scanning technique to produce very high-resolution, three-dimensional images of sample surfaces. AFM measures ultrasmall forces (less than 1 nN) present between the AFM tip surface mounted on a flexible cantilever beam and a sample surface. These small forces are measured by measuring the motion of a very flexible cantilever beam having an ultrasmall mass, by a variety of measurement techniques including optical deflection, optical interference, capacitance, and tunneling current. The deflection can be measured to within 0.02 nm, so for a typical cantilever force constant of 10 N/m, a force as low as 0.2 nN can be detected. In the operation of high-resolution AFM, the sample is generally scanned rather than the tip because any cantilever movement would add vibrations. AFMs are now available for measurement of large samples, where the tip is scanned and the sample is stationary. To obtain atomic resolution with AFM, the spring constant of the cantilever should be weaker than the equivalent spring between atoms. A cantilever beam with a spring constant of about 1 N/m or lower is desirable. Tips have to be as sharp as possible. Tips with a radius ranging from 10 to 100 nm are commonly available. Subsequent modifications to AFM led to the development of the friction force microscope (FFM) or the lateral force microscope (LFM), designed for atomic-scale and microscale studies of friction (Mate et al., 1987; Bhushan and Ruan, 1994; Ruan and Bhushan, 1994a,b,c; Bhushan et al., 1994; Bhushan et al., 1995a; Scherer et al., 1999) and lubrication (Bhushan et al., 1995b; Koinkar and Bhushan, 1996a,b). This instrument measures lateral or friction forces (in the plane of sample surface and in the direction of sliding). By using a standard or a sharp diamond tip mounted on a stiff cantilever beam, AFM is also used in investigations of scratching and wear (Bhushan et al., 1994; Bhushan and Koinkar, 1994a; Koinkar and Bhushan, 1997a; Bhushan, 1999c; Sundararajan and Bhushan, 2000a), indentation (Bhushan et al., 1994; Bhushan and Koinkar, 1994a; Bhushan et al., 1996; Bhushan 1999c), and fabrication/machining (Bhushan et al., 1994). Surface roughness, including atomic-scale imaging, is routinely measured using the AFM (Figure 19.1). Adhesion, friction, wear, and boundary lubrication at the interface between two solids with and without liquid films have been studied using AFM and FFM. Nanomechanical properties are also measured using an AFM.
19.2.1 Surface Roughness and Friction Force Measurements Simultaneous measurements of surface roughness and friction force can be made with commercial AFM/FFM. These instruments are available for measurements of small and large samples. In a small sample AFM shown in Figure 19.1a, the sample is mounted on a PZT tube scanner, which consists of separate electrodes to scan precisely the sample in the x-y plane in a raster pattern and to move the sample in the vertical (z) direction. A sharp tip at the end of a flexible cantilever is brought in contact with the sample. Normal and frictional forces being applied at the tip–sample interface are measured using a laser beam deflection technique. A laser beam from a diode laser is directed by a prism onto the back of a cantilever near its free end, tilted downward at about 10 degrees with respect to the horizontal plane. The reflected beam from the vertex of the cantilever is directed through a mirror onto a quad photodetector (split photodetector with four quadrants). The differential signal from the top and bottom photodiodes provides the AFM signal which is a sensitive measure of the cantilever vertical deflection.
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(a) Mirrored prism Diode laser & lens
AFM signal (A+B)-(C+D)
Mirror
FFM signal (A+C)-(B+D) Split-diode photodetector
Cantilever & substrate
Sample z x
y
xyz PZT tube scanner
(b)
Feedback
Laser
Computer
Ph de oto tec to r
Substrate holder Cantilever piezo
Cantilever substrate
Sample X-Y-Z- Piezo X-Y Control Z Control
FIGURE 19.1 Schematics (a) of a commercial small sample atomic force microscope/friction force microscope (AFM/FFM), (b) of tapping mode used for surface topography measurements, and (c) of a large sample AFM/FFM.
Topographic features of the sample cause the tip to deflect in the vertical direction as the sample is scanned under the tip. This tip deflection will change the direction of the reflected laser beam, changing the intensity difference between the top and bottom sets of photodetectors (AFM signal). In the AFM operating mode called the height mode, for topographic imaging or for any other operation in which the applied normal force is to be kept constant, a feedback circuit is used to modulate the voltage applied to the PZT scanner to adjust the height of the PZT, so that the cantilever vertical deflection (given by the intensity difference between the top and bottom detector) will remain constant during scanning. The PZT height variation is thus a direct measure of the surface roughness of the sample.
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(c)
Split-diode photodetector
Laser diode, collimator & lens
Adjustable mirror Laser path Fixed mirror
Lens Mirror Lens y x
Camera objective lens
z
Sample
xyz PZT tube scanner
Cantilever holder Motorized Stage X Y
FIGURE 19.1 (continued)
Many multimode AFMs can be used for topography measurements in the so-called tapping mode, also referred to as dynamic force microscopy. In the tapping mode, during scanning over the surface, the cantilever is vibrated by a piezo mounted above it, and the oscillating tip slightly taps the surface at the resonant frequency of the cantilever (70 to 400 Hz) with a 20- to 100-nm oscillating amplitude introduced in the vertical direction with a feedback loop keeping the average normal force constant (Figure 19.1b). The oscillating amplitude is kept large enough so that the tip does not get stuck to the sample because of adhesive attractions. The tapping mode is used in topography measurements to minimize effects of friction and other lateral forces and to measure topography of soft surfaces. For measurement of friction force being applied at the tip surface during sliding, left-hand and righthand sets of quadrants of the photodetector are used. In the so-called friction mode, the sample is scanned back and forth in a direction orthogonal to the long axis of the cantilever beam. A friction force between the sample and the tip will produce a twisting of the cantilever. As a result, the laser beam will be reflected out of the plane defined by the incident beam and the beam reflected vertically from an untwisted cantilever. This produces an intensity difference of the laser beam received in the left-hand and righthand sets of quadrants of the photodetector. The intensity difference between the two sets of detectors (FFM signal) is directly related to the degree of twisting and hence to the magnitude of the friction force. One problem associated with this method is that any misalignment between the laser beam and the photodetector axis would introduce error in the measurement. However, by following the procedures developed by Ruan and Bhushan (1994a), in which the average FFM signal for the sample scanned in two opposite directions is subtracted from the friction profiles of each of the two scans, the misalignment effect is eliminated. This method provides three-dimensional maps of friction force. By following the friction force calibration procedures developed by Ruan and Bhushan (1994a), voltages corresponding to friction forces can be converted to force units. Coefficient of friction is obtained from the slope of
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friction force data measured as a function of normal loads typically ranging from 10 to 150 nN. This approach eliminates any contributions due to the adhesive forces. For calculation of coefficient of friction based on a single point measurement, friction force should be divided by the sum of applied normal load and intrinsic adhesive force. Furthermore, it should be pointed out that for a single asperity contact, the coefficient of friction is not independent of load (see discussion later). In a large-sample AFM, both force sensors using the optical deflection method and scanning unit are mounted on the microscope head (Figure 19.1c). Lateral resolution of this design is somewhat poorer than the design in Figure 19.1a in which the sample is scanned instead of the cantilever beam. The advantage of the large-sample AFM is that large samples can be measured readily. Topographic measurements in the contact mode are typically made using a sharp, microfabricated square pyramidal Si3N4 tip on a cantilever beam (Figure 19.2a) with normal stiffness of about 0.5 N/m at a normal load of about 10 nN, and friction measurements are carried out in the load range of 10 to 150 nN. Topography measurements in the tapping mode utilize a stiff cantilever with high resonant frequency; typically a square-pyramidal etched single-crystal silicon tip, with a tip radius ranging from 10 to 50 nm, mounted on a stiff rectangular silicon cantilever beam with a normal stiffness of about 50 N/m, is used. To study the effect of radius of a single asperity (tip) on adhesion and friction, microspheres of silica with radii ranging from about 4 to 15 µm are attached with epoxy at the ends of tips of Si3N4 cantilever beams. Optical micrographs of two of the microspheres mounted at the ends of triangular cantilever beams are shown in Figure 19.2b. The tip is scanned in such a way that its trajectory on the sample forms a triangular pattern (Figure 19.3). Scanning speeds in the fast and slow scan directions depend on the scan area and scan
2µm
Square pyramidal Si3N4 tip
10µm
(a)
Three sided pyramidal (natural) diamond tip
FIGURE 19.2 (a) SEM micrographs of a PECVD Si3N4 cantilever beam with tip and a stainless steel cantilever beam with diamond tip, and (b) optical micrographs of commercial Si3N4 tip and two modified tips showing SiO2 spheres mounted over the sharp tip, at the end of the triangular Si3N4 cantilever beams (radii of the tips are given in the figure).
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Si3N4 - 0.05 µm
SiO2 - 3.8 µm
SiO2 - 14.5 µm
(b)
25 µm
FIGURE 19.2 (continued)
frequency. Scan sizes ranging from less than 1 nm × 1 nm to 125 µm × 125 µm and scan rates from less than 0.5 to 122 Hz can typically be used. Higher scan rates are used for smaller scan lengths. For example, scan rates in the fast and slow scan directions for an area of 10 µm × 10 µm scanned at 0.5 Hz are 10 µm/s and 20 nm/s, respectively.
19.2.2 Adhesion Measurements Adhesive force measurements are performed in the so-called force calibration mode. In this mode, force distance curves are obtained (Figure 19.4). The horizontal axis gives the distance the piezo (and hence
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FIGURE 19.3 Schematic of triangular pattern trajectory of the tip as the sample (or the tip) is scanned in two dimensions. During scanning, data are recorded only during scans along the solid scan lines.
FIGURE 19.4 Typical force–distance curve for a contact between Si3N4 tip and single-crystal silicon surface in measurements made in the ambient environment. Contact between the tip and silicon occurs at point B; tip breaks free of adhesive forces at point C as the sample moves away from the tip.
the sample) travels, and the vertical axis gives the tip deflection. As the piezo extends, it approaches the tip, which is at this point in free air and hence shows no deflection. This is indicated by the flat portion of the curve. As the tip approaches the sample within a few nanometers (point A), an attractive force exists between the atoms of the tip surface and the atoms of the sample surface. The tip is pulled toward the sample, and contact occurs at point B on the graph. From this point on, the tip is in contact with the surface, and as the piezo extends further, the tip is further deflected. This is represented by the sloped portion of the curve. As the piezo retracts, the tip goes beyond the zero deflection (flat) line, because of attractive forces (van der Waals forces and long-range meniscus forces), into the adhesive regime. At point C in the graph, the tip snaps free of the adhesive forces and is again in free air. The horizontal distance between points B and C along the retrace line gives the distance moved by the tip in the adhesive regime. This distance multiplied by the stiffness of the cantilever gives the adhesive force. Incidentally, the horizontal shift between the loading and unloading curves results from the hysteresis in the PZT tube.
19.2.3 Scratching, Wear, and Fabrication/Machining For microscale scratching, microscale wear, nanofabrication/nanomachining, and nanoindentation hardness measurements, an extremely hard tip is required. A three-sided pyramidal single-crystal natural diamond tip with an apex angle of 80° and a radius of about 100 nm mounted on a stainless steel cantilever beam with normal stiffness of about 25 N/m is used at relatively higher loads (1 µN to 150 µN) (Figure 19.2a). For scratching and wear studies, the sample is generally scanned in a direction orthogonal
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to the long axis of the cantilever beam (typically at a rate of 0.5 Hz) so that friction can be measured during scratching and wear. The tip is mounted on the beam such that one of its edges is orthogonal to the long axis of the beam; therefore, wear during scanning along the beam axis is higher (about 2× to 3×) than that during scanning orthogonal to the beam axis. For wear studies, typically an area of 2 µm × 2 µm is scanned at various normal loads (ranging from 1 to 100 µN) for a selected number of cycles. Scratching can also be performed at ramped loads, and the coefficient of friction can be measured during scratching (Sundararajan and Bhushan, 2000a). A linear increase in the normal load approximated by a large number of normal load increments of small magnitude is applied using a software interface (lithography module in Nanoscope III) that allows the user to generate controlled movement of the tip with respect to the sample. The friction signal is tapped out of the AFM and is recorded on a computer. For most experiments, a scratch length of 25 µm and a velocity of 0.5 µm/s are used, and the number of loading steps is usually taken to be 50. Nanofabrication/nanomachining is conducted by scratching the sample surface with a diamond tip at specified locations and scratching angles. The normal load used for scratching (writing) is on the order of 1 to 100 µN with a writing speed on the order of 0.1 to 200 µm/s (Bhushan, 1995, 1998b, 1999a,b; Bhushan et al., 1994, 1995a).
19.2.4 Surface Potential Measurements To detect wear precursors and to study the early stages of localized wear, the multimode AFM can be used to measure the potential difference between the tip and the sample by applying a DC bias potential and an oscillating (AC) potential to a conducting tip over a grounded substrate in a Kelvin probe microscopy or so-called nano-Kelvin probe technique (DeVecchio and Bhushan, 1998; Bhushan and Goldade, 2000a,b). Mapping of the surface potential is made in the so-called lift mode (Figure 19.5). These measurements are made simultaneously with the topography scan in the tapping mode, using an electrically conducting (nickel-coated single-crystal silicon) tip. After each line of the topography scan is completed, the feedback loop controlling the vertical piezo is turned off, and the tip is lifted from the surface and traced over the same topography at a constant distance of 100 nm. During the lift mode, a DC bias potential and an oscillating potential (3 to 7 Volts) is applied to the tip. The frequency of oscillation is chosen to be equal to the resonant frequency of the cantilever (~80 kHz). When a DC bias potential equal to the negative value of surface potential of the sample (on the order of ±2 Volts) is applied to the tip, it does not vibrate. During scanning, a difference between the DC bias potential applied to the tip and the potential of the surface will create DC electric fields that interact with the oscillating charges (as a result of the AC potential), causing the cantilever to oscillate at its resonant frequency, as in the tapping mode. However, a feedback loop is used to adjust the DC bias on the tip to exactly nullify the electric field, and thus the vibrations of the cantilever. The required bias voltage follows the localized potential of the surface. The surface potential was obtained by reversing the sign of the bias potential provided by the electronics (Bhushan and Goldade, 2000a,b). Surface and subsurface changes of structure and/or chemistry can cause changes in the measured potential of a surface. Thus, mapping of the surface potential after sliding can be used for detecting wear precursors and studying the early stages of localized wear.
19.2.5 Nanoindentation Measurements For nanoindentation hardness measurements, the scan size is set to zero and then a normal load is applied to make the indents using the diamond tip. During this procedure, the tip is continuously pressed against the sample surface for about 2 seconds at various indentation loads. The sample surface is scanned before and after the scratching, wear, or indentation to obtain the initial and the final surface topography, at a low normal load of about 0.3 µN using the same diamond tip. An area larger than the indentation region is scanned to observe the indentation marks. Nanohardness is calculated by dividing the indentation load by the projected residual area of the indents.
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Feedback
Laser
Computer
Ph de oto tec to r
Substrate holder
Sum
Cantilever piezo
Sample
X-Y-Z Piezo X-Y-Z Control
FIGURE 19.5 Schematic of lift mode used to make surface potential measurement. The topography is collected in tapping mode in the primary scan. The cantilever piezo is deactivated. Using topography information of the primary scan, the cantilever is scanned across the surface at a constant height above the sample. An oscillating voltage at the resonant frequency is applied to the tip, and a feedback loop adjusts the DC bias of tip to maintain the cantilever amplitude at zero. The output of the feedback loop is recorded by the computer and becomes the surface potential map. (From Bhushan, B. (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. With permission.)
Direct imaging of the indent allows one to quantify the piling up of ductile material around the indenter. However, it becomes difficult to identify the boundary of the indentation mark with great accuracy. This makes the direct measurement of contact area somewhat inaccurate. A technique with the dual capability of depth-sensing and in situ imaging, which is most appropriate in nanomechanical property studies, is used for accurate measurement of hardness with shallow depths (Bhushan, 1999a; Bhushan et al., 1996). This indentation system is used to make load-displacement measurement and subsequently carry out in situ imaging of the indent, if required. The indentation system consists of a three-plate transducer with electrostatic actuation hardware used for direct application of normal load and a capacitive sensor used for measurement of vertical displacement. The AFM head is replaced with this transducer assembly while the specimen is mounted on the PZT scanner, which remains stationary during indentation experiments. Indent area and, consequently, hardness value can be obtained from the load-displacement data. The Young’s modulus of elasticity is obtained from the slope of the unloading curve. Indentation experiments provide a single-point measurement of the Young’s modulus of elasticity calculated from the slope of the indentation curve during unloading. Localized surface elasticity maps can be obtained using a force modulation technique (Maivald et al., 1991; DeVecchio and Bhushan, 1997; Scherer et al., 1997). An oscillating tip is scanned over the sample surface in contact under steady and oscillating load. The oscillations are applied to the cantilever substrate with a bimorph (Figure 19.6a). For measurements, an etched silicon tip is first brought in contact with a sample under a static load of
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FIGURE 19.6 Schematics (a) of the bimorph assembly, and (b) of the motion of the cantilever and tip as a result of the oscillations of the bimorph for an infinitely stiff sample, an infinitely compliant sample, and an intermediate sample. The thin line represents the cantilever at the top cycle, and the thick line corresponds to the bottom of the cycle. The dashed line represents the position of the tip if the sample were not present or were infinitely compliant. dc, ds, and db are the oscillating (ac) deflection amplitude of the cantilever, penetration depth and oscillating (ac) amplitude of the bimorph, respectively. (From DeVecchio, D. and Bhushan, B. (1997), Localized surface elasticity measurements using an atomic force microscope, Rev. Sci. Instrum., 68, 4498-4505. With permission.)
50 to 300 nN. In addition to the static load applied by the sample piezo, a small oscillating (modulating) load is applied by a bimorph, generally at a frequency (about 8 kHz) far below that of the natural resonance of the cantilever (70 to 400 kHz). When the tip is brought in contact with the sample, the surface resists the oscillations of the tip, and the cantilever deflects. Under the same applied load, a stiff area on the sample would deform less than a soft one; i.e., stiffer surfaces cause greater deflection amplitudes of the cantilever (Figure 19.6b). The variations in the deflection amplitudes provide a measure of the relative stiffness of the surface. Contact analyses can be used to obtain a quantitative measure of localized elasticity of soft surfaces (DeVecchio and Bhushan, 1997). The elasticity data are collected simultaneously with the surface height data using a so-called negative lift mode technique. In this mode each scan line of each topography image (obtained in tapping mode) is replaced with the tapping action disabled and with the tip lowered into steady contact with the surface.
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19.2.6 Boundary Lubrication Measurements For nanoscale boundary lubrication studies, the samples are typically scanned using a Si3N4 tip over an area of 1 µm × 1 µm at a normal load of about 300 nN, in a direction orthogonal to the long axis of the cantilever beam. The samples are generally scanned with a scan rate of 1 Hz and a scanning speed of 2 µm/s. Coefficient of friction is monitored during scanning for a desired number of cycles. After a scanning test, a larger area of 2 µm × 2 µm is scanned at a normal load of 40 nN to observe any wear scar.
19.3 Friction and Adhesion 19.3.1 Atomic-Scale Friction To study friction mechanisms on an atomic scale, a well-characterized freshly cleaved surface of highly oriented pyrolytic graphite (HOPG) has been studied by Mate et al. (1984) and Ruan and Bhushan (1994b). The atomic-scale friction force of HOPG exhibited the same periodicity as that of the corresponding topography (Figure 19.7a), but the peaks in friction and those in topography were displaced relative to each other (Figure 19.7b). A Fourier expansion of the interatomic potential was used to calculate the conservative interatomic forces between atoms of the FFM tip and those of the graphite surface. Maxima in the interatomic forces in the normal and lateral directions do not occur at the same location, which explains the observed shift between the peaks in the lateral force and those in the corresponding topography. Furthermore, the observed local variations in friction force were explained by variation in the intrinsic lateral force between the sample and the FFM tip (Ruan and Bhushan, 1994b). These variations may not necessarily occur as a result of an atomic-scale stick-slip process (Mate et al., 1984), but can be due to variation in the intrinsic lateral force between the sample and the FFM tip.
19.3.2 Microscale Friction Local variations in the microscale friction of cleaved graphite are observed. These arise from structural changes that occur during the cleaving process (Ruan and Bhushan, 1994c). The cleaved HOPG surface is largely atomically smooth but exhibits line-shaped regions in which the coefficient of friction is more than an order of magnitude larger (Figure 19.8). Transmission electron microscopy indicates that the line-shaped regions consist of graphite planes of different orientation, as well as of amorphous carbon. Differences in friction have also been observed for multiphase ceramic materials (Koinkar and Bhushan, 1996c). Figure 19.9 shows the surface roughness and friction force maps of Al2O3–TiC (70 to 30 wt%). TiC grains have a Knoop hardness of about 2800 kg/mm2; therefore, they do not polish as much and result in a slightly higher elevation (about 2 to 3 nm higher than that of Al2O3 grains). TiC grains exhibit higher friction force than Al2O3 grains. The coefficients of friction of TiC and Al2O3 grains are 0.034 and 0.026, respectively, and the coefficient of friction of Al2O3–TiC composite is 0.03. Local variation in friction force also arises from the scratches present on the Al2O3–TiC surface. Meyer et al. (1992) also used FFM to measure structural variations of organic mono- and multilayer films. All of these measurements suggest that the FFM can be used for structural mapping of the surfaces. FFM measurements can be used to map chemical variations, as indicated by the use of the FFM with a modified probe tip to map the spatial arrangement of chemical functional groups in mixed organic monolayer films (Frisbie et al., 1994). Here, sample regions that had stronger interactions with the functionalized probe tip exhibited larger friction. Local variations in the microscale friction of nominally rough, homogeneous surfaces can be significant, and are seen to depend on the local surface slope rather than the surface height distribution (Figure 19.10). This dependence was first reported by Bhushan and Ruan (1994) and Bhushan et al. (1994) and later discussed in more detail by Koinkar and Bhushan (1997b) and Sundararajan and Bhushan (2000b). In order to show elegantly any correlation between local values of friction and surface roughness, surface roughness and friction force maps of a gold-coated ruling with somewhat rectangular
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1.00
0.2 nm
0.75
0.1 nm
0.50
1.00
0.75
0.0 nm 0.50
0.25
0
0.25
0.50
0.75
0.2 V
0.1 V
0.0 V
0.25
0 1.00 nm
0
Topography
0.25
0.50
0.75
0 1.00 nm
Friction (a)
FIGURE 19.7 (a) Gray-scale plots of surface topography and friction force maps of a 1 nm × 1 nm area of freshly cleaved HOPG, showing the atomic-scale variation of topography and friction, and (b) schematic of superimposed topography and friction maps from (a); the symbols correspond to maxima. Note the spatial shift between the two plots. (From Ruan, J. and Bhushan, B. (1994b), Atomic-scale and microscale friction of graphite and diamond using friction force microscopy, J. Appl. Phys., 76, 5022-5035. With permission.)
grids and a silicon grid with square pits were obtained (Figure 19.11) (Sundararajan and Bhushan (2000b). Figures 19.10 and 19.11 show the surface roughness map, the slopes of the roughness map taken along the sliding direction (surface slope map) and the friction force map for various samples. There is a strong correlation between the surface slopes and friction forces. For example, in Figure 19.11, friction force is high locally at the edge of the grids and pits with a positive slope, and is low at the edges with a negative slope. We now examine the mechanism of microscale friction, which may explain the resemblance between the slope of surface roughness maps and the corresponding friction force maps (Ruan and Bhushan, 1994b,c; Bhushan and Ruan, 1994; Bhushan et al., 1994; Bhushan, 1999a,b; Sundararajan and Bhushan, 2000b). There are three dominant mechanisms of friction; adhesive, adhesive and roughness (ratchet), and plowing. As a first order, we may assume these to be additive. The adhesive mechanism alone cannot
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FIGURE 19.8 (a) Surface roughness and (b) friction force maps at a normal load of 42 nN of freshly cleaved HOPG surface against a Si3N4 FFM tip. Friction in the line-shaped region is over an order of magnitude larger than in the smooth areas. (From Ruan, J. and Bhushan, B. (1994b), Atomic-scale and microscale friction of graphite and diamond using friction force microscopy, J. Appl. Phys., 76, 5022-5035. With permission.)
explain the local variation in friction. Let us consider the ratchet mechanism (Makinson, 1948). We consider a small tip sliding over an asperity making an angle θ with the horizontal plane (Figure 19.12). The normal force W (normal to the general surface) applied by the tip to the sample surface is constant. The friction force F on the sample would be a constant µoW for a smooth surface if the friction mechanism does not change. For a rough surface shown in Figure 19.12, if the adhesive mechanism does not change during sliding, the local value of coefficient of friction would remain constant,
µ0 = S N
(19.1)
where S is the local friction force and N is the local normal force. However, the friction and normal forces are measured with respect to global horizontal and normal axes, respectively. The measured local coefficient of friction µ1 in the ascending part is
(
µ1 = F W = µ 0 + tan θ
) (1 − µ
0
)
tan θ ~ µ 0 + tan θ, for small µ 0 tan θ
(19.2)
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Surface Height 5.00
20.0 nm
10.0 nm
0.0 nm
2.50
0
0 5.00 µm
2.50
Friction Force 5.00
50 nN
25 nN
0 nN
2.50
0
0 5.00 µm
2.50
FIGURE 19.9 Gray-scale surface roughness (σ = 0.80 nm) and friction force maps (mean = 7.0 nN, σ = 0.90 nN) for Al2O3-TiC (70 to 30 wt%) at a normal load of 138 nN. (From Koinkar, V.N. and Bhushan, B. (1996c), Microtribological studies of Al2O3-TiC, polycrystalline and single-crystal Mn–Zn ferrite and SiC head slider materials, Wear, 202, 110-122. With permission.)
indicating that in the ascending part of the asperity one may simply add the friction force and the asperity slope to one another. Similarly, on the right-hand side (descending part) of the asperity,
(
µ 2 = µ 0 − tan θ
) (1 + µ
0
)
tan θ ~ µ 0 − tan θ, for small µ 0 tan θ
(19.3)
For a symmetrical asperity, the average coefficient of friction experienced by the FFM tip traveling across the whole asperity is
(
)
µ ave = µ1 + µ 2 2
(
= µ 0 1 + tan2 θ
)(
)
(
)
1 − µ 20 tan2 θ ~ µ 0 1 + tan2 θ , for small µ 0 tan θ
(19.4)
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FIGURE 19.10 Surface roughness map (σ = 4.4 nm), surface slope map taken in the sample sliding direction (the horizontal axis; mean = 0.023, σ = 0.197), and friction force map (mean = 6.2 nN, σ = 2.1 nN) for a lubricated thinfilm magnetic rigid disk for a normal load of 160 nN. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994), Microtribology of magnetic media, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, 17-29. With permission.)
Next we consider, the plowing component of friction with the tip sliding in either direction, which is
µ p ~ tanθ
(19.5)
Because in the FFM measurements we notice little damage to the sample surface, the contribution by plowing is expected to be small, and the ratchet mechanism is believed to be the dominant mechanism for the local variations in the friction force map. With the tip sliding over the leading (ascending) edge of an asperity, the surface slope is positive; it is negative during sliding over the trailing (descending) edge of an asperity. Thus, measured friction is high at the leading edge of asperities and low at the trailing
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FIGURE 19.11 Surface roughness map, surface slope map taken in the sample sliding direction (the horizontal axis), and friction force map for (a) a gold-coated ruling (with somewhat rectangular grids with a pitch of 1 µm and a ruling step height of about 70 nm) at a normal load of 25 nN, and (b) a silicon grid (with 5 µm square pits of depth 180 nm and a pitch of 10 µm). (From Sundararajan, S. and Bhushan, B. (2000b), Topography-induced contributions to friction forces measured using an atomic force/friction force microscope, J. Appl. Phys., 88, in press. With permission.)
edge. In addition to the slope effect, the collision of tip when encountering an asperity with a positive slope produces additional torsion of the cantilever beam leading to higher measured friction force. When encountering an asperity with the same negative slope, however, there is no collision effect and hence no effect on torsion. This effect also contributes to the difference in friction forces when the tip scans up and down on the same topography feature. The ratchet mechanism and the collision effects thus semiquantitatively explain the correlation between the slopes of the roughness maps and friction maps observed in Figures 19.10 and 19.11. We note that in the ratchet mechanism, the FFM tip is assumed to be small compared to the size of asperities. This is valid since the typical radius of curvature of the tips
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10.0
(b)
5.0
Surface height (mm)
0
0 10.0
5.0
250
0
Surface slope
-250 2
0
Friction force (V)
-2 0.35 High friction
0 Low friction
-0.35 0
10
Scan distance (µm) FIGURE 19.11 (continued)
is about 10 to 50 nm. The radii of curvature of the asperities of the samples measured here (the asperities that produce most of the friction variation) are found to be typically about 100 to 200 nm, which is larger than that of the FFM tip (Bhushan and Blackman, 1991). It is important to note that the measured local values of friction and normal forces are measured with respect to global (and not local) horizontal and vertical axes, which are believed to be relevant in applications. Next, we study the directionality effect on friction. During friction measurements, the friction force data from both the forward (trace) and backward (retrace) scans are useful in understanding the origins of the observed friction forces. Magnitudes of material-induced effects are independent of the scan direction, whereas topography-induced effects are different between forward and backward scanning directions. Since the sign of the friction force changes as the scanning direction is reversed (because of the reversal of torque applied to the end of the tip), addition of the friction force data of the forward and backward scan eliminates the material-induced effects while topography-induced effects remain. Subtraction of the data between forward and backward scans does not eliminate either effects (Figure 19.13) (Sundararajan and Bhushan, 2000b). Due to the reversal of the sign of the retrace (R) friction force with respect to the trace (T) data; the friction force variations due to topography are in the same direction (peaks in trace correspond to peaks
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FIGURE 19.12 Schematic illustration showing the effect of an asperity (making an angle θ with the horizontal plane) on the surface in contact with the tip on local friction in the presence of adhesive friction mechanism. W and F are the normal and friction forces, respectively, and S and N are the force components along and perpendicular to the local surface of the sample at the contact point, respectively.
in retrace). However, the magnitudes of the peaks in trace and retrace at a given location are different. An increase in the friction force experienced by the tip when scanning up a sharp change in topography is more than the decrease in the friction force experienced when scanning down the same topography change, partly because of collision effects discussed earlier. Asperities on engineering surfaces are asymmetrical, which also affects the magnitude of friction force in the two directions. Asymmetry in tip shape may also have an effect on the directionality effect of friction. We notice from Figure 19.15 that since magnitude of surface slopes is virtually identical, the tip shape asymmetry should not have much effect. Because of the differences in the magnitude of friction forces in the two directions, subtracting the two friction data yields a residual peak (Figure 19.14). From Figure 19.14a, we note that this effect occurs at all locations of significant topography changes. In order to facilitate comparison of the directionality effect on friction, it is important to take into account the sign change of the surface slope and friction force in the trace and retrace directions. Figure 19.15 shows topography, slope, and friction force data for the gold ruler and silicon grid in the trace and retrace directions. The correlation between surface slope and friction forces is clear. The third column in the figures shows retrace slope and friction data with an inverted sign (-retrace). Now we can compare trace data with -retrace data. It is clear the friction experienced by the tip is dependent upon the scanning direction because of surface topography. In addition to the effect of topographical changes discussed earlier, during surface finishing processes, material can be transferred preferentially onto one side of the asperities, which also causes asymmetry and direction dependence. Reduction in local variations and in directionality of friction properties requires careful optimization of surface roughness distributions and of surface finishing processes. The directionality as a result of the surface asperities effect will also be manifested in macroscopic friction data; that is, the coefficient of friction may be different in one sliding direction than in the other direction. Asymmetrical asperities accentuate this effect. The frictional directionality can also exist in materials with particles having a preferred orientation. The directionality effect in friction on a macroscale is observed in some magnetic tapes. In a macroscale test, a 12.7-mm-wide polymeric magnetic tape was wrapped over an aluminum drum and slid in a reciprocating motion with a normal load of 0.5 N and a sliding speed of about 60 mm/s (Bhushan, 1997). The coefficient of friction as a function of sliding distance in either direction is shown in Figure 19.16. We note that the coefficient of friction on a macroscale for this tape is different in different directions. Directionality in friction is sometimes observed on the macroscale; on the microscale this is the norm (Bhushan 1996, 1999a). On the macroscale, the effect of surface asperities normally is averaged over a large number of contacting asperities.
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FIGURE 19.13 Schematic of friction forces expected when a tip traverses a sample that is composed of different materials and sharp changes in topography. A schematic of surface slope is also shown.
AFM/FFM experiments are generally conducted at relative velocities as high as a few tens of µm/s. To simulate applications, it is of interest to conduct friction experiments at higher velocities. High velocities can be achieved by mounting either the sample or the cantilever beam on a shear wave transducer (ultrasonic transducer) to produce surface oscillations at MHz frequencies (Scherer et al., 1998, 1999). Velocities on the order of a few mm/s can thus be achieved. The effect of in-plane and out-of-plane sample vibration amplitude on the coefficient of friction is shown in Figure 19.17. Vibration of a sample at ultrasonic frequencies (>20 kHz) can substantially reduce the coefficient of friction, known as ultrasonic lubrication or sonolubrication. When the surface is vibrated in-plane, classical hydrodynamic lubrication develops hydrodynamic pressure, which supports the tip and reduces friction. When the
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50
(a)
0 nm
Surface height -50 0.35
0V
Friction force (T) -0.35 0.35
0V
Friction force (R) -0.35 0.35
0V
Friction force (T-R) 0
1.50 µm
-0.35 0
0.75
1.50
Scan distance (µm)
FIGURE 19.14 (a) Gray-scale images and two-dimensional profiles of surface height and friction forces across a single ruling of the gold-coated ruling, and (b) two-dimensional profiles of surface height and friction forces across a silicon grid pit. Friction force data in trace and retrace directions, and substrated force data are presented.
surface is vibrated out-of-plane, a lift-off caused by the squeeze-film lubrication (a form of hydrodynamic lubrication) reduces friction.
19.3.3 Comparison of Microscale and Macroscale Friction Data Table 19.2 shows the coefficient of friction measured for single-crystal silicon surfaces on micro- and macroscales. To study the effect of sample material, data for virgin and ion-implanted silicon are presented. The values on the microscale are much lower than those on the macroscale. There can be the following four and possibly more differences in the operating conditions responsible for these differences. First, the contact stresses at AFM conditions generally do not exceed the sample hardness, which minimizes plastic deformation. Second, when measured for the small contact areas and very low loads used in microscale studies, indentation hardness and modulus of elasticity are higher than at the macroscale, as will be discussed later (Bhushan et al., 1995a, 1996). Lack of plastic deformation and improved mechanical properties reduce the degree of wear and friction. Next, the small apparent areas of contact reduce the number of particles trapped at the interface, and thus minimize the plowing contribution to the friction force (Bhushan et al., 1995a). As a fourth and final difference, we will note in the next section that coefficient of friction increases with an increase in the AFM tip radius. AFM data presented so far
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FIGURE 19.14 (continued)
were taken with a sharp tip, whereas asperities coming in contact in macroscale tests, range from nanoasperities to much larger asperities, which may be responsible for larger values of friction force on the macroscale. To demonstrate the load dependence on the coefficient of friction, stiff cantilevers were used to conduct friction experiments at high loads (Figure 19.18) (Bhushan and Kulkarni, 1996). At higher loads (with contact stresses exceeding the hardness of the softer material), as anticipated, the coefficient of friction for microscale measurements increases toward values comparable with those obtained from macroscale measurements, and surface damage also increases. Thus Amontons’ law of friction, which states that the coefficient of friction is independent of apparent contact area and normal load, does not hold for microscale measurements. These findings suggest that microcomponents sliding under lightly loaded conditions should experience ultra low friction and near-zero wear (Bhushan et al., 1995a).
19.3.4 Effect of Tip Radii and Humidity on Adhesion and Friction The tip radius and relative humidity affect adhesion and friction for dry and lubricated surfaces (Bhushan and Sundararajan, 1998; Bhushan and Dandavate, 2000). Figure 19.18 shows the variation of single point adhesive force measurements as a function of tip radius on a Si(100) sample for a given humidity for several humidities. The adhesive force data are also plotted as a function of relative humidity for a given tip radius for several tip radii. The general trend at humidities up to the ambient is that a 50-nm-radius
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FIGURE 19.15 (a) Gray-scale images of surface heights, surface slopes, and friction forces for scans across a goldcoated ruling, and (b) two-dimensional profiles of surface heights, surface slopes, and friction forces for scans across the silicon grid pit. (From Sundararajan, S. and Bhushan, B. (2000b), Topography-induced contributions to friction forces measured using an atomic force/friction force microscope, J. Appl. Phys., 88, in press. With permission.)
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FIGURE 19.16 Coefficient of macroscale friction as a function of drum passes for a polymeric magnetic tape sliding over an aluminum drum in a reciprocating mode in both directions. Normal load = 0.5 N over 12.7-mm-wide tape, sliding speed = 60 mm/s. (From Bhushan, B. (1995), Micro/Nanotribology and its applications to magnetic storage devices and MEMS, Tribol. Int., 28, 85-95. With permission.)
FIGURE 19.17 Reduction of coefficient of friction, measured at a normal load of 100 nN and average tip separation as a function of surface amplitude on a single-crystal silicon subjected to (a) in-plane and (b) out-of-plane vibrations at about 1 MHz against a silicon nitride tip. (From Scherer, V., Arnold W., and Bhushan, B. (1998), Active friction control using ultrasonic vibration, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic Pub., Dordrecht, Netherlands, 463. With permission.) TABLE 19.2 Surface Roughness (Standard Deviation of Surface Heights or σ) and Coefficients of Friction on Micro- and Macroscales of Single-Crystal Silicon Samples in Air Material Si (111) C+-implanted Si (111)
σ (nm)
Coefficient of Microscale Friction vs. Si3N4 tipa
Coefficient of Macroscale Friction vs. Alumina Ballb
0.11 0.33
0.03 0.02
0.18 0.18
a Tip radius of about 50 nm in the load range of 10–150 nN (2.5–6.1 GPa), a scanning speed of 5 µm/s and scan area of 1 µm × 1 µm. b Ball radius of 3 mm at a normal load of 0.1 N (0.3 GPa) and average sliding speed of 0.8 mm/s.
Si3N4 tip exhibits a slightly lower adhesive force as compared to the other microtips of larger radii; in the latter case, values are similar. Thus for the microtips there is no appreciable variation in adhesive force with tip radius at a given humidity up to the ambient. The adhesive force increases as relative humidity increases for all tips. The trend in adhesive forces as a function of tip radii and relative humidity can be explained by the presence of meniscus forces, which arise from capillary condensation of water vapor from the environment forming meniscus bridges. If enough liquid is present to form a meniscus
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FIGURE 19.18 (a) Coefficient of friction as a function of normal load and (b) corresponding wear depth as a function of normal load for silicon, SiO2 coating, and natural diamond. Inflections in the curves for silicon and SiO2 correspond to the contact stresses equal to the hardnesses of these materials. (From Bhushan, B. and Kulkarni, A.V. (1996), Effect of normal load on microscale friction measurements, Thin Solid Films, 278, 49-56; 293, 333. With permission.)
bridge, the meniscus force should increase with an increase in tip radius (proportional to tip radius for a spherical tip) and should be independent of the relative humidity or water film thickness. In addition, an increase in tip radius in a dry environment results in increased contact area, leading to higher values of van der Waals forces. However, if nanoasperities on the tip and the sample are considered, then the number of contacting and near-contacting asperities forming meniscus bridges increases with an increase of humidity, leading to an increase in meniscus forces. This explains the trends observed in Figure 19.19. From the data, the tip radius has little effect on the adhesive forces at low humidities but increases with tip radius at high humidity. Adhesive force also increases with an increase in humidity for all tips. This observation suggests that thickness of the liquid film at low humidities is insufficient to form continuous meniscus bridges to affect adhesive forces in the case of all tips. Figure 19.19 also shows the variation in coefficient of friction as a function of tip radius at a given humidity, and as a function of relative humidity for a given tip radius for Si(100). It can be seen that for 0% RH, the coefficient of friction is about the same for the tip radii except for the largest tip, which shows a higher value. At all other humidities, the trend consistently shows that the coefficient of friction
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FIGURE 19.19 Adhesive force and coefficient of friction as a function of tip radius at several humidities and as a function of relative humidity at several tip radii on Si(100). (From Bhushan, B. and Sundararajan, S. (1998), Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy, Acta Mater., 46, 3793-3804. With permission.)
increases with tip radius. An increase in friction with tip radius at low to moderate humidities arises from increased contact area (higher van der Waals forces) and higher values of shear forces required for larger contact area. At high humidities, similar to adhesive force data, an increase with tip radius occurs because of both contact area and meniscus effects. Although AFM/FFM measurements are able to measure the combined effect of the contribution of van der Waals and meniscus forces to friction force or adhesive force, it is difficult to measure their individual contributions separately. It can be seen that for all tips, the coefficient of friction increases with humidity to about ambient, beyond which it starts to decrease. The initial increase in the coefficient of friction with humidity arises from the fact that the thickness of the water film increases with an increase in the humidity, which results in a larger number of nanoasperities forming meniscus bridges and leads to higher friction (larger shear force). The same trend is expected with the microtips beyond 65% RH. This is attributed to the fact that at higher humidities, the adsorbed water film on the surface acts as a lubricant between the two surfaces. Thus the interface is changed at higher humidities, resulting in lower shear strength and hence lower friction force and coefficient of friction. 19.3.4.1 Adhesion and Friction Expressions for a Single Asperity Contact We now obtain the expressions for the adhesive force and coefficient of friction for a single asperity contact with a meniscus formed at the interface. For a spherical asperity of radius R in contact with a flat and smooth surface with the composite modulus of elasticity E* and with a concave meniscus, the attractive meniscus force (adhesive force) Wad is given as,
(
Wad = 2πRγ 1 cos θ1 + cos θ2
)
(19.6)
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For an elastic contact, the friction force is given as,
(
)
3 W + Wad R Fe = πτ 4E *
2 3
(19.7)
where γl is the surface tension of the liquid in air, θ1 and θ2 are the contact angles between the liquid and the two surfaces, W is the external load, and τ is the average shear strength of the contacts (surface energy effects are not considered here). Note that adhesive force increases linearly with an increase in the tip radius, and the friction force increases with an increase in tip radius as R2/3 and with normal load as (W + Wad)2/3. The experimental data in support of W2/3 dependence on the friction force can be found in various references (see e. g., Schwarz et al., 1997). The coefficient of friction µe is obtained from Equation 19.7 as
µe =
(
3R Fe = πτ W + Wad 4E *
2 3
)
1
(W + W )
13
(19.8)
ad
In the plastic contact regime (Bhushan, 1999d), the coefficient of friction µp is obtained as
µp =
(
Fp W + Wad
)
τ HS
=
(19.9)
where Hs is the hardness of the softer material. Note that in the plastic contact regime, the coefficient of friction is independent of external load, adhesive contributions, and surface geometry. For comparisons, for multiple asperity contacts in the elastic contact regime the total adhesive force Wad is the summation of adhesive forces at n individual contacts, n
Wad =
∑ (W ) i =1
ad i
(19.10)
and
µe ≈
(
3.2τ
E * σp R p
)
12
where σp and Rp are the standard deviation of summit heights and average summit radius, respectively. Note that the coefficient of friction is independent of external and adhesive forces and depends only on the surface roughness. In the plastic contact regime, the expression for µp in Equation 19.9 does not change. The source of the adhesive force, in a wet contact in the AFM experiments being performed in an ambient environment, includes mainly attractive meniscus forces due to capillary condensation of water vapor from the environment. The meniscus force for a single contact increases with an increase in tip radius. A sharp AFM tip in contact with a smooth surface at low loads (on the order of a few nN) for most materials can be simulated as a single asperity contact. At higher loads, for rough surfaces and for soft surfaces, multiple contacts will occur. Furthermore, at low loads (nN range) for most materials, the local deformation will be primarily elastic. Assuming that shear strength of contacts does not change, the adhesive force for smooth and hard surfaces at low normal load (on the order of a few nN) (for a
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single asperity contact in the elastic contact regime) will increase with an increase in tip radius, and the coefficient of friction will decrease with an increase in total normal load as (W + Wad)–1/3 and will increase with an increase of tip radius as R2/3. In this case, Amontons’ law of friction, which states that coefficient of friction is independent of normal load and is independent of apparent area of contact, does not hold. For a single asperity plastic contact and multiple asperity plastic contacts, neither the normal load or tip radius come into play in calculation of coefficient of friction. In the case of multiple asperity contacts, the number of contacts increases with an increase of normal load; therefore adhesive force increases with an increase in load. In the data presented earlier in this section, the effect of tip radius and humidity on the adhesive forces and coefficient of friction is investigated for experiments with a Si(100) surface at loads in the range of 10 to 100 nN. The multiple asperity elastic-contact regime is relevant for this study. An increase in humidity generally results in an increase in the number of meniscus bridges, which would increase the adhesive force. As was suggested earlier, that increase in humidity also may decrease the shear strength of contacts. A combination of an increase in adhesive force and a decrease in shear strength will affect the coefficient of friction. An increase in tip radius will increase the meniscus force (adhesive force). A substantial increase in the tip radius may also increase interatomic forces. These effects influence the coefficient of friction with an increase in the tip radius.
19.4 Scratching, Wear, and Fabrication/Machining 19.4.1 Nanoscale Wear Bhushan and Ruan (1994) conducted nanoscale wear tests on polymeric magnetic tapes using conventional silicon nitride tips at two different loads of 10 and 100 nN (Figure 19.20). For a low normal load of 10 nN, measurements were made twice. There was no discernible difference between consecutive measurements for this load. However, as the load was increased from 10 nN to 100 nN, topographical changes were observed during subsequent scanning at a normal load of 10 nN; material was pushed in the sliding direction of the AFM tip relative to the sample. The material movement is believed to occur as a result of plastic deformation of the tape surface. Thus, deformation and movement of the soft materials on a nanoscale can be observed.
19.4.2 Microscale Scratching The AFM can be used to investigate how surface materials can be moved or removed on micro- to nanoscales, for example, in scratching and wear (Bhushan, 1999a) (where these things are undesirable), and nanofabrication/nanomachining (where they are desirable). Figure 19.21a shows microscratches made on Si(111) at various loads and scanning velocity of 2 µm/s after 10 cycles (Bhushan et al., 1994). As expected, the scratch depth increases linearly with load. Such microscratching measurements can be used to study failure mechanisms on the microscale and to evaluate the mechanical integrity (scratch resistance) of ultra-thin films at low loads. To study the effect of scanning velocity, unidirectional scratches, 5 µm in length, were generated at scanning velocities ranging from 1 to 100 µm/s at various normal loads ranging from 40 to 140 µN. There is no effect of scanning velocity obtained at a given normal load. For representative scratch profiles at 80 µN, see Figure 19.21b. This may be because of a small effect of frictional heating with the change in scanning velocity used here. Furthermore, for a small change in interface temperature, there is a large underlying volume to dissipate the heat generated during scratching (Bhushan and Sundararajan, 1998). Scratching can be performed at random loads to determine the scratch resistance of materials and coatings. The coefficient of friction is measured during scratching and the load at which the coefficient of friction increases rapidly is known as the “critical load,” which is a measure of scratch resistance. In addition, the post-scratch imaging can be performed in situ with the AFM in tapping mode to study failure mechanisms. Figure 19.22 shows data from a scratch test on Si(100) with a scratch length of 25 µm
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FIGURE 19.20 Surface roughness maps of a polymeric magnetic tape at the applied normal load of (a) 10 nN and (b) 100 nN. Location of the change in surface topography as a result of nanowear is indicated by arrows. (From Bhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction force microscopy: part II — application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)
and a scratching velocity of 0.5 µm/s. At the beginning of the scratch, the coefficient of friction is 0.04, which is a typical value for silicon. At about 35 µN (indicated by the arrow in the figure), there is a sharp increase in the coefficient of friction, which is the critical load. Beyond the critical load, the coefficient of friction continues to increase steadily. In the post-scratch image, we note that at the critical load, a clear groove starts to form. This implies that Si(100) was damaged by plowing at the critical load, associated with the plastic flow of the material. At and after the critical load, small and uniform debris is observed, and the amount of debris increases with increasing normal load. Sundararajan and Bhushan (2000a) have also used this technique to measure scratch resistance of diamond-like carbon coatings ranging in thickness from 3.5 to 20 nm.
19.4.3 Microscale Wear By scanning the sample in two dimensions with the AFM, wear scars are generated on the surface. Figure 19.23 shows the effect of normal load on the wear depth. We note that wear rate is very small below 20 µN of normal load (Koinkar and Bhushan, 1997c; Zhao and Bhushan, 1998). A normal load of 20 µN corresponds to contact stresses comparable to the hardness of the silicon. Primarily, elastic deformation at loads below 20 µN is responsible for low wear (Bhushan and Kulkarni, 1996). A typical wear mark, of the size 2 µm × 2 µm, generated at a normal load of 40 µN for one scan cycle and imaged using AFM with scan size of 4 µm × 4 µm at 300 nN load, is shown in Figure 19.24a (Koinkar and Bhushan, 1997c). The inverted map of wear marks shown in Figure 19.24b indicates the uniform material removal at the bottom of the wear mark. An AFM image of the wear mark shows small debris
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FIGURE 19.21 Surface plots of (a) Si(111) scratched for ten cycles at various loads and a scanning velocity of 2 µm/s. Note that x and y axes are in µm and z axis is in nm, and (b) Si(100) scratched in one unidirectional scan cycle at a normal force of 80 µN and different scanning velocities.
at the edges, swiped during AFM scanning. Thus the debris is loose (not sticky) and can be removed during the AFM scanning. Next we examine the mechanism of material removal on a microscale in AFM wear experiments (Koinkar and Bhushan, 1997c; Bhushan and Sundararajan, 1998; Zhao and Bhushan, 1998). Figure 19.25 shows a secondary electron image of the wear mark and associated wear particles. The specimen used for the scanning electron microscope (SEM) was not scanned with the AFM after initial wear, in order to retain wear debris in the wear region. Wear debris is clearly observed. In the SEM micrographs, the wear debris appears to be agglomerated because of high surface energy of the fine particles. Particles appear to be a mixture of rounded and so-called cutting type (feather-like or ribbon-like). Zhao and Bhushan (1998) reported an increase in the number and size of cutting-type particles with the normal load. The presence of cutting-type particles indicates that the material is removed primarily by plastic deformation. To better understand the material removal mechanisms, transmission electron microscopy (TEM) has been used. The TEM micrograph of the worn region and associated TEM diffraction pattern are shown in Figures 19.26a and b. The bend contours are observed to pass through the wear mark in the micrograph. The bend contours around and inside the wear mark are indicative of a strain field, which in the absence of applied stresses, can be interpreted as plastic deformation and/or residual stresses. Often, localized plastic deformation during loading would lead to residual stresses during unloading; therefore, bend contours reflect a mix of elastic and plastic strains. The wear debris is observed outside the wear mark. The enlarged view of the wear debris in Figure 19.24c shows that much of the debris is ribbon-like,
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FIGURE 19.22 (a) Applied normal load and friction signal measured during the microscratch experiment on Si(100) as a function of scratch distance, (b) friction data plotted in the form of coefficient of friction as a function of normal load, and (c) AFM surface height image of scratch obtained in tapping mode. (From Sundararajan, S. and Bhushan, B. (2000a), Development of a continuous microscratch technique in an atomic force microscope and its application to study scratch resistance of ultra-thin hard amorphous carbon coatings, J. Mater. Res., in press. With permission.)
FIGURE 19.23 Wear depth as a function of normal load for Si(100) after one cycle. (From Zhao, X. and Bhushan, B. (1998), Material removal mechanism of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78. With permission.)
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FIGURE 19.24 (a) Typical gray-scale, and (b) inverted AFM images of wear mark created using a diamond tip at a normal load of 40 µN and one scan cycle on Si(100) surface.
Tip sliding direction 40 µN
1 µm FIGURE 19.25 Secondary electron image of wear mark and debris for Si(100) produced at a normal load of 40 µN and one scan cycle.
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40 µNOutside wear mark
Tip sliding direction
40 µN
a
1 µm
40 mNWear debris
c
200 nm
b 40 µN Wear debris
d
FIGURE 19.26 Bright-field TEM micrographs (left) and diffraction patterns (right) of wear mark (a, b) and wear debris (c, d) in Si(100) produced at a normal load of 40 µN and one scan cycle. Bend contours around and inside wear mark are observed.
indicating that material is removed by a cutting process via plastic deformation, which is consistent with the SEM observations. The diffraction pattern from inside the wear mark is similar to that of virgin silicon, showing no evidence of any phase transformation (amorphization) during wear. A selected area diffraction pattern of the wear debris shows some diffuse rings, which indicates the existence of amorphous material in the wear debris, confirmed as silicon oxide products by chemical analysis. It is known that plastic deformation occurs by generation and propagation of dislocations. No dislocation activity or cracking was observed at 40 µN. However, dislocation arrays could be observed at 80 µN. Figure 19.27 shows the TEM micrographs of the worn region at 80 µN; for better observation of the worn surface, wear debris was moved out of the wear mark by using AFM with a large area scan at 300 nN after the wear test. The existence of dislocation arrays confirms that material removal occurs by plastic deformation. It is concluded that the material on microscale at high loads is removed by plastic deformation with a small contribution from elastic fracture (Zhao and Bhushan, 1998). To understand wear mechanisms, evolution of wear can be studied using AFM. Figure 19.28 shows evolution of wear marks of a DLC-coated disk sample. The data illustrate how the microwear profile for a load of 20 µN develops as a function of the number of scanning cycles (Bhushan et al., 1994). Wear is not uniform, but is initiated at the nanoscratches. Surface defects (with high surface energy) present at nanoscratches act as initiation sites for wear. Coating deposition also may not be uniform on and near nanoscratches, which may lead to coating delamination. Thus, scratch-free surfaces will be relatively resistant to wear. Wear precursors (precursors to measurable wear) can be studied by making surface potential measurements (DeVecchio and Bhushan, 1998; Bhushan and Goldade, 2000a,b). The contact potential difference
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80 µN
1 µm
Tip sliding direction
a 80 µN
b
200 nm
FIGURE 19.27 (a) Bright-field and (b) weak-beam TEM micrographs of wear mark in Si(100) produced at a normal load of 80 µN and one scan cycle showing bend contours and dislocations. (From Zhao, X. and Bhushan, B. (1998), Material removal mechanism of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78. With permission.)
or simply surface potential between two surfaces depends on a variety of parameters such as electronic work function, adsorption, and oxide layers. The surface potential map of an interface gives a measure of changes in the work function which is sensitive to both the physical and chemical conditions of the surfaces, including structural and chemical changes. Before material is actually removed in a wear process, the surface experiences stresses that result in surface and subsurface changes of structure and/or chemistry. These can cause changes in the measured potential of a surface. An AFM tip allows mapping of surface potential with nanoscale resolution. Surface height and change in surface potential maps of a polished single-crystal aluminum(100) sample, abraded using a diamond tip at two loads of approximately 1 µN and 9 µN, are shown in Figure 19.29a. [Note that the sign of the change in surface potential is reversed here from that in DeVecchio and Bhushan (1998)]. It is evident that both abraded regions show a large potential contrast (~0.17 Volts), with respect to the nonabraded area. The black region in the lower righthand part of the topography scan shows a step that was created during the polishing phase. There is no potential contrast between the high region and the low region of the sample, indicating that the technique is independent of surface height. Figure 19.29b shows a closeup scan of the upper (low load) wear region in Figure 19.29a. Notice that while there is no detectable change in the surface topography, there is nonetheless a large change in the potential of the surface in the worn region. Indeed the wear mark of Figure 19.29b might not be visible at all were it not for the noted absence of wear debris generated nearby and then swept off during the low load scan. Thus, even in the case of zero wear (no measurable deformation of the surface using AFM), there can be a significant change in the surface potential inside
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FIGURE 19.28 Surface plots of diamond-like carbon-coated thin-film disk showing the worn region; the normal load and number of test cycles are indicated. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994), Microtribology of magnetic media, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, 17-29. With permission.)
the wear mark, which is useful for study of wear precursors. It is believed that the removal of a thin contaminant layer, including the natural oxide layer, gives rise to the initial change in surface potential. The structural changes, which precede generation of wear debris and/or measurable wear scars, occur
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Surface Potential
Surface Height
10 µm
10 µm 0
100 nm
(a)
0
Surface Potential
Surface Height
5 µm
5 µm 0
200 mV
25 nm
(b)
0
150 mV
FIGURE 19.29 (a) Surface height and change in surface potential maps of wear regions generated at 1 µN (top) and 9 µN (bottom) on a single-crystal aluminum sample showing bright contrast in the surface potential map on the worn regions. (b) Closeup of upper (low load) wear region. (From DeVecchio, D. and Bhushan, B. (1998), Use of a nanoscale Kelvin probe for detecting wear precursors, Rev. Sci. Instrum., 69, 3618-3624. With permission.)
under ultra-low loads in the top few nanometers of the sample, and are primarily responsible for the subsequent changes in surface potential.
19.4.4 Nanofabrication/Nanomachining An AFM can be used for nanofabrication/nanomachining by extending the microscale scratching operation (Bhushan, 1995, 1998b, 1999a; Bhushan et al., 1994, 1995a). Figure 19.30 shows two examples of nanofabrication. The patterns were created on a single-crystal silicon(100) wafer by scratching the sample surface with a diamond tip at specified locations and scratching angles. Each line is scribed manually at a normal load of 15 µN and a writing speed of 0.5 µm/s. The separation between lines is about 50 nm, and the variation in line width is due to the tip asymmetry. Nanofabrication parameters such as normal load, scanning speed, and tip geometry can be controlled precisely to control depth and length of the devices. Nanofabrication using mechanical scratching has several advantages over other techniques. Better control over the applied normal load, scan size, and scanning speed can be used for nanofabrication of devices. Using the technique, nanofabrication can be performed on any engineering surface. Use of chemical etching or reactions is not required, and this dry nanofabrication process can be used where use of chemicals and electric field is prohibited. One disadvantage of this technique is the formation of
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Si(100) 10.0nm
(a) 1.50
5.0nm
1.00 0.0nm
0.50
1.50
1.00
0.50
0
0 µm
W = 15 µn v = 0.5 µ
1.00
10.00nm
0.75
5.0nm
(b)
0.0nm 0.50
0.25
0
0.25
0.50
0.75
0 1.00
FIGURE 19.30 (a) Trim and (b) spiral patterns generated by scratching a Si(100) surface using a diamond tip at a normal load of 15 µN and writing speed of 0.5 µm/s.
debris during scratching. At light loads, debris formation is not a problem compared to high-load scratching. However, debris can be removed easily out of the scan area at light loads during scanning.
19.5 Indentation Mechanical properties, such as hardness and Young’s modulus of elasticity can be determined on the micro- to picoscales using the AFM (Bhushan and Ruan, 1994; Bhushan et al., 1994; Bhushan and Koinkar, 1994a,b) and a depth-sensing indentation system used in conjunction with an AFM (Bhushan et al., 1996; Kulkarni and Bhushan, 1996a,b, 1997).
19.5.1 Picoindentation Indentability on the scale of subnanometers of soft samples can be studied in the force calibration mode (Figure 19.4) by monitoring the slope of cantilever deflection as a function of sample traveling distance after the tip is engaged and the sample is pushed against the tip. For a rigid sample, cantilever deflection equals the sample traveling distance, but the former quantity is smaller if the tip indents the sample. In an example for a polymeric magnetic tape shown in Figure 19.31, the line in the left portion of the figure is curved with a slope of less than 1 shortly after the sample touches the tip, which suggests that the tip
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FIGURE 19.31 Tip deflection (normal load) as a function of the Z (separation distance) curve for a polymeric magnetic tape. (From Bhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction force microscopy: part II — application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)
has indented the sample (Bhushan and Ruan, 1994). Later, the slope is equal to 1, suggesting that the tip no longer indents the sample. This observation indicates that the tape surface is soft locally (polymer rich) but hard (as a result of magnetic particles) underneath. Since the curves in extending and retracting modes are identical, the indentation is elastic up to a maximum load of about 22 nN used in the measurements. Detection of transfer of material on a nanoscale is possible with the AFM. Indentation of C60-rich fullerene films with an AFM tip has been shown (Ruan and Bhushan, 1993) to result in the transfer of fullerene molecules to the AFM tip, as indicated by discontinuities in the cantilever deflection as a function of sample traveling distance in subsequent indentation studies.
19.5.2 Nanoscale Indentation The indentation hardness of surface films with an indentation depth of as small as about 1 nm can be measured using AFM (Bhushan and Koinkar, 1994b; Bhushan et al., 1996). Figure 19.32 shows the grayscale plots of indentation marks made on Si(111) at normal loads of 60, 65, 70, and 100 µN. Triangular indents can be clearly observed with very shallow depths. At a normal load of 60 µN, indents are observed and the depth of penetration is about 1 nm. As the normal load is increased, the indents become clearer and indentation depth increases. For the case of hardness measurements at shallow depths on the same order as variations in surface roughness, it is desirable to subtract the original (unindented) map from the indent map for accurate measurement of the indentation size and depth (Bhushan et al., 1994). To make accurate measurements of hardness at shallow depths, a depth-sensing indentation system is used. Figure 19.33 shows the load-displacement curves at different peak loads for Si(100). Load-displacement data at residual depths as low as about 1 nm can be obtained. Loading/unloading curves are not smooth but exhibit sharp discontinuities, particularly at high loads. Any discontinuities in the loading part of the curve probably results from slip of the tip. The sharp discontinuities in the unloading part of the curves are believed to be due to formation of lateral cracks that form at the base of the median crack, which results in the surface of the specimen being thrust upward. The indentation hardness of surface films with an indentation depth of as small as about 1 nm has been measured for Si(100) (Bhushan et al., 1996; Kulkarni and Bhushan, 1996a,b, 1997). The hardness of silicon on a nanoscale is found to be higher than on a microscale (Figure 19.34). This decrease in hardness with an increase in indentation depth can be rationalized on the basis that as the volume of deformed material increases, there is a higher probability of encountering material defects. Thus mechanical properties show size effect. Bhushan and Koinkar (1994a) have used AFM measurements to show that ion implantation of silicon surfaces increases their hardness and thus their wear resistance. Formation of surface alloy films with improved mechanical properties by ion implantation is of growing technological importance as a means of improving the mechanical properties of materials. Hardness of 20-nm-thick diamond-like carbon films have been measured by Kulkarni and Bhushan (1997).
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20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250 0 250
60 µN, 1.0 nm
0 500 nm 20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250 0 250
65 µN, 2.5 nm, 16.6 GPa
0 500 nm 20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250 0 250
70 µN, 3.0 nm, 15.8 GPa
0 500 nm 20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250 0 250
100 µN, 7.0 nm, 11.7 GPa
0 500 nm
FIGURE 19.32 Gray-scale plots of indentation marks on the Si(111) sample at various indentation loads. Loads, indentation depths, and hardness values are listed in the figure. (From Bhushan, B. and Koinkar V.N. (1994b), Nanoindentation hardness measurements using atomic force microscopy, Appl. Phys. Lett., 64, 1653-1655. With permission.)
The creep and strain-rate effects (viscoelastic effects) of ceramics can be studied using a depth-sensing indentation system. Bhushan et al. (1996) and Kulkarni et al. (1996a,b, 1997) have reported that ceramics exhibit significant plasticity and creep on a nanoscale. Figure 19.35a shows the load-displacement curves
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FIGURE 19.33 Load-displacement curves at various peak loads for Si(100). (From Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system in atomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)
FIGURE 19.34 Indentation hardness as a function of residual indentation depth for Si(100). (From Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system in atomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)
for single-crystal silicon at various peak loads held at 180 s. To demonstrate the creep effects, the loaddisplacement curves for a 500 µN peak load held at 0 and 30 s are also shown as an inset. Note that significant creep occurs at room temperature. Nanoindenter experiments conducted by Li et al. (1991) exhibited significant creep only at high temperatures (greater than or equal to 0.25 times the melting point of silicon). The mechanism of dislocation glide plasticity is believed to dominate the indentation creep process on the macroscale. To study strain-rate sensitivity of silicon, data at two different (constant) rates of loading are presented in Figure 19.35b. Note that a change in the loading rate by a factor of about five results in a significant change in the load-displacement data. The viscoelastic effects observed here for silicon at ambient temperature could arise from the size effects mentioned earlier. Most likely, creep
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FIGURE 19.35 (a) Creep behavior and (b) strain-rate sensitivity of Si(100). (From Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system in atomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)
and strain-rate experiments are being conducted on the hydrated films present on the silicon surface in ambient environment, and these films are expected to be viscoelastic. The Young’s modulus of elasticity is calculated from the slope of the indentation curve during unloading. However, these measurements provide a single-point measurement. By using the force modulation
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Elasticity
Surface Height
0
100
0.0 nm
200
300
300
200
200
100
100
0 300 nm
25.0 nm
0
100
Compliant
200
0 300 nm
Stiff
FIGURE 19.36 Surface height and elasticity maps on a polymeric magnetic tape (σ = 6.72 nm and P-V = 31.7 nm; σ and P-V refer to standard deviation of surface heights and peak-to-valley distance, respectively). The gray-scale on the elasticity map is arbitrary. (From DeVecchio, D. and Bhushan, B. (1997), Localized surface elasticity measurements using an atomic force microscope, Rev. Sci. Instrum., 68, 4498-4505. With permission.)
technique, it is possible to get localized elasticity maps of soft and compliant materials with penetration depths of less than 100 nm. This technique has been used successfully for polymeric magnetic tapes, which consist of magnetic and nonmagnetic ceramic particles in a polymeric matrix. Elasticity maps of a tape can be used to identify relative distribution of hard magnetic and nonmagnetic ceramic particles on the tape surface, which has an effect on friction and stiction at the head-tape interface (Bhushan, 1996). Figure 19.36 shows surface height and elasticity maps on a polymeric magnetic tape. The elasticity image reveals sharp variations in surface elasticity due to the composite nature of the film. As can be clearly seen, regions of high elasticity do not always correspond to high or low topography. Based on a Hertzian elastic-contact analysis, the static indentation depth of these samples during the force modulation scan is estimated to be about 1 nm. We conclude that the contrast seen is influenced most strongly by material properties in the top few nanometers, independent of the composite structure beneath the surface layer.
19.6 Boundary Lubrication The classical approach to lubrication uses freely supported multimolecular layers of liquid lubricants (Bowden and Tabor, 1950; Bhushan, 1996, 1999d). The liquid lubricants are sometimes chemically bonded to improve their wear resistance (Bhushan, 1996, 1999d). To study depletion of boundary layers, the microscale friction measurements are made as a function of number of cycles. For an example of experiments with virgin Si(100) surfaces and silicon surfaces lubricated with Z-15 and Z-Dol a PFPE lubricants, see Figure 19.37 (Koinkar and Bhushan, 1996a,b). Z-Dol is PFPE lubricant with hydroxyl end groups. Its film was thermally bonded at 150°C for 30 min (BUW-bonded, unwashed) and, in some cases the unbonded fraction was washed off with a solvent to provide a chemically bonded layer of the lubricant (BW) film. In Figure 19.37a, the unlubricated silicon sample shows a slight increase in friction force followed by a drop to a lower steady-state value after 20 cycles. Depletion of native oxide and possible roughening of the silicon sample are believed to be responsible for the decrease in friction force after
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FIGURE 19.37 Friction force as a function of number of cycles using Si3N4 tip at a normal load of 300 nN for (a) unlubricated Si(100), Z-15 and bonded washed (BW) Z-Dol, and (b) bonded Z-Dol before washing (BUW) and after washing (BW) with different film thicknesses. (From Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. With permission.)
20 cycles. The initial friction force for the Z-15 lubricated sample is lower than that of unlubricated silicon and increases gradually to a friction force value comparable to that of the silicon after 20 cycles. This suggests the depletion of the Z-15 lubricant in the wear track. In the case of the Z-Dol coated silicon sample, the friction force starts out very low and remains low during the 100 cycles test. This suggests that Z-Dol does not become displaced/depleted as readily as Z-15. The nanowear results for BW and BUW/Z-Dol samples with different film thicknesses are shown in Figure 19.37b. The BW with thickness of 2.3 nm exhibits an initial decrease in the friction force in the first few cycles and then remains steady for more than 100 cycles. The decrease in friction force possibly arises from the alignment of any free liquid lubricant present over the bonded lubricant layer. BUW with a thickness of 4.0 nm exhibits behavior similar to BW (2.3 nm). Lubricated BW and BUW samples with thinner films exhibit a higher value of coefficient of friction. Among the BW and BUW samples, BUW samples show the lower friction because of an extra unbonded fraction of the lubricant. The effect of the operating environment on coefficient of friction of unlubricated and lubricated samples is shown in Figure 19.38. Silicon(100) samples were lubricated with 2.9-nm-thick Z-15 and 2.3-nm-thick Z-Dol bonded and washed (BW) lubricants. The coefficient of friction in a dry environment
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FIGURE 19.38 Coefficient of friction for unlubricated and lubricated Si(100) samples in ambient (~50% RH), dry nitrogen (~5% RH), and dry air (~5 RH). (From Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391. With permission.)
FIGURE 19.39 Coefficient of friction as a function of scanning velocity for unlubricated and lubricated Si(100) samples in ambient (~50% RH), dry nitrogen (~5% RH), and dry air (~5% RH). (From Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391. With permission.)
is lower than that in a high humidity environment. We believe that in the humid environment, the condensed water from the humid environment competes with the liquid film present on the sample surface, and interaction of the liquid film (water for the unlubricated sample and polymer lubricant for the lubricated sample) with the substrate is weakened and a boundary layer of the liquid forms puddles. This dewetting results in poorer lubrication performance and high friction. Since Z-Dol is a bonded lubricant with superior frictional properties, the dewetting effect in a humid environment for Z-Dol is more pronounced than for Z-15. The effect of scanning speed on the coefficient of friction of unlubricated and lubricated samples is shown in Figure 19.39. The coefficient of friction for an unlubricated silicon sample and a lubricated sample with Z-15 decreases with an increase in scanning velocity in the ambient environment. These
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FIGURE 19.40 Surface plots showing the worn region after one scan cycle for self-assembled monolayers of methylterminated, octadecyldimethylchlorosilane (C18), and zinc arachidate (ZnA). Normal loads and wear depths are indicated. Note that wear of ZnA occurs at only 200 nN as compared to 40 µN for C18 film.
samples are insensitive to scanning velocity in dry environments. Samples lubricated with Z-Dol do not show any effect of scanning velocity on the friction. Alignment of liquid molecules (shear thinning) is believed to be responsible for the drop in friction with an increase in scanning velocity for samples with mobile films and exposed to ambient environment. For lubrication of microdevices, a more effective approach involves the deposition of organized, dense molecular layers of long-chain molecules on the surface contact. Such monolayers and thin films are commonly produced by Langmuir–Blodgett (L–B) deposition and by chemical grafting of molecules into self-assembled monolayers (SAMs). Based on the measurements, SAMs of octodecyl (C18) compounds based on methyl-terminated octadecyldimethylchlorosilane on an oxidized silicon exhibited lower coefficient of friction (0.018) and greater durability than LB films of zinc arachidate adsorbed on a gold surface coated with octadecylthiol (ODT; coefficient of friction of 0.03; Figure 19.40) (Bhushan et al., 1995b). LB films are bonded to the substrate by weak van der Waals attraction, whereas SAMs are chemically bound via covalent bonds. Because of the choice of chain length and terminal linking group that SAMs offer, they hold great promise for boundary lubrication of microdevices. Liquid film thickness measurement of thin lubricant films (on the order of 10 nm or thicker) with nanometer lateral resolution can be made with the AFM (Bhushan and Blackman, 1991; Bhushan, 1999a). The lubricant thickness is obtained by measuring the force on the tip as it approaches, contacts, and pushes through the liquid film and ultimately contacts the substrate. The distance between the sharp snap-in (owing to the formation of a liquid meniscus between the film and the tip) at the liquid surface and the hard repulsion at the substrate surface is a measure of the liquid film thickness. Lubricant film thickness mapping of ultra-thin films (on the order of a couple of 2 nm) can be obtained using friction force microscopy (Koinkar and Bhushan, 1996a) and adhesive force mapping (Bhushan and Dandavate, 2000). Figure 19.41 shows gray-scale plots of the surface topography and friction force obtained simultaneously for unbonded Demnum-type PFPE lubricant film on silicon. The friction force plot shows well-distinguished low and high friction regions roughly corresponding to high and low regions in surface topography (thick and thin lubricant regions). A uniformly lubricated sample does not show such a variation in the friction. Friction force imaging can thus be used to measure the lubricant uniformity on the sample surface, which cannot be identified by surface topography alone. Figure 19.42 shows the gray-scale plots of the adhesive force distribution for silicon samples coated uniformly and nonuniformly with Z-DOL-type PFPE lubricant. It can be clearly seen that there exists a region which has an adhesive force distinctly different from the other region for the nonuniformly coated sample. This implies that the liquid film thickness is nonuniform, giving rise to a difference in the meniscus forces.
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Surface Topography 0
1.3
Friction Force
2.5 nm 0
0
2.50
4.0
8.0 nN
5.00
5.00
2.50
2.50
0 5.00 0 µm
2.50
0 5.00 µm
FIGURE 19.41 Gray-scale plots of the surface topography and friction force obtained simultaneously for unbonded perfluoropolyether lubricant film on silicon. (From Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. With permission.)
19.7 Closure At most solid–solid interfaces of technological relevance, contact occurs at many asperities. A sharp AFM/FFM tip sliding on a surface simulates just one such contact. However, asperities come in all shapes and sizes. The effect of the radius of a single asperity (tip) on the friction/adhesion performance can be studied using tips of different radii. AFM/FFM are used to study various tribological phenomena, which include surface roughness, adhesion, friction, scratching, wear, indentation, detection of material transfer, and boundary lubrication. Measurement of atomic-scale friction of a freshly cleaved, highly oriented pyrolytic graphite exhibits the same periodicity as that of the corresponding topography. However, the peaks in friction and those in the corresponding topography are displaced relative to each other. Variations in atomic-scale friction and the observed displacement can be explained by the variation in interatomic forces in the normal and lateral directions. Local variations in microscale friction occur and are found to correspond to the local slopes, suggesting that a ratchet mechanism and collision effects are responsible for this variation. Directionality in the friction is observed on both micro- and macroscales, which results from the surface roughness and surface preparation. Anisotropy in surface roughness accentuates this effect. Microscale friction is generally found to be smaller than the macrofriction because there is less plowing contribution in microscale measurements. Microscale friction is load dependent and friction values increase with an increase in the normal load, approaching the macrofriction at contact stresses higher than the hardness of the softer material. The tip radius also has an effect on the adhesion and friction. Mechanism of material removal on the microscale is studied. Wear precursors can be detected at early stages of wear using a surface potential measurement. Wear rate for single-crystal silicon is negligible below 20 µN and is much higher and remains approximately constant at higher loads. Elastic deformation at low loads is responsible for negligible wear. Most of the wear debris is loose. SEM and TEM studies of the wear region suggest that the material on the microscale is removed by plastic deformation with a small contribution from elastic fracture; this observation is corroborated with the scratch data. Evolution of wear has also been studied using AFM. Wear is found to be initiated at nanoscratches. For a sliding interface requiring near-zero friction and wear, contact stresses should be below the hardness of the softer material to minimize plastic deformation, and surfaces should be free of nanoscratches. Further, wear precursors can be studied by making surface potential measurements. It is found that even in the case
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FIGURE 19.42 Gray-scale plots of the adhesive force distribution of a uniformly-coated, 3.5-nm-thick unbonded perfluoropolyether lubricant film on silicon and 3- to 10-nm-thick unbonded perfluoropolyether lubricant film on silicon that was deliberately coated nonuniformly by vibrating the sample during the coating process. (From Bhushan, B. and Dandavate, C. (2000), Thin-film friction and adhesion studies using atomic force microscopy J. Appl. Phys., 87, 1201-1210. With permission.)
of zero wear (no measurable deformation of the surface using AFM), there can be a significant change in the surface potential inside the wear mark, which is useful for studying wear precursors. By using the force modulation technique, localized surface elasticity maps of composite materials with penetrating depths of less than 100 nm, can be obtained. Modified AFM can be used to obtain loaddisplacement curves and for measurement of nanoindentation hardness and Young’s modulus of elasticity,
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with depth of indentation as low as 1 nm. Hardness of ceramics on nanoscales is found to be higher than that on the microscale. Ceramics exhibit significant plasticity and creep on a nanoscale. Scratching and indentation on nanoscales are powerful ways to screen for adhesion and resistance to deformation of ultrathin films. Detection of material transfer on a nanoscale is possible with AFM. Boundary lubrication studies and measurement of lubricant film thickness with a lateral resolution on a nanoscale can be conducted using AFM. Self-assembled monolayers and chemically bonded lubricant films with a mobile fraction are superior in wear resistance. Investigations of wear, scratching, and indentation on nanoscales using the AFM can provide insights into failure mechanisms of materials. Coefficients of friction, wear rates, and mechanical properties such as hardness have been found to be different on the nanoscale than on the macroscale; generally, coefficients of friction and wear rates on micro- and nanoscales are smaller, whereas hardness is greater. Therefore, micro/nanotribological studies may help define the regimes for ultra-low friction and nearzero wear.
References Bhushan, B. (1995), Micro/Nanotribology and its applications to magnetic storage devices and MEMS, Tribol. Int., 28, 85-95. Bhushan, B. (1996), Tribology and Mechanics of Magnetic Storage Devices, 2nd ed., Springer-Verlag, New York. Bhushan, B. (1997), Micro/Nanotribology and Its Applications, Vol. E330, Kluwer Academic Pub., Dordrecht, Netherlands. Bhushan, B. (1998a), Tribology Issues and Opportunities in MEMS, Kluwer Academic Pub., Dordrecht, Netherlands. Bhushan, B. (1998b), Micro/nanotribology using atomic force/friction force microscopy: state of the art, Proc. Inst. Mech. Engrs. Part J: J. Eng. Tribol., 212, 1-18. Bhushan, B. (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. Bhushan, B. (1999b), Nanoscale tribophysics and tribomechanics, Wear, 225-229, 465-492. Bhushan, B. (1999c), Wear and mechanical characterisation on micro- to picoscales using AFM, Int. Mat. Rev., 44, 105-117. Bhushan, B. (1999d), Principles and Applications of Tribology, John Wiley & Sons, New York. Bhushan, B. and Blackman, G.S. (1991), Atomic force microscopy of magnetic rigid disks and sliders and its applications to tribology, ASME J. Tribol., 113, 452-458. Bhushan, B. and Dandavate, C. (2000), Thin-film friction and adhesion studies using atomic force microscopy J. Appl. Phys., 87, 1201-1210. Bhushan, B. and Goldade, A.V. (2000a), Measurements and analysis of surface potential change during wear of single crystal silicon (100) at ultralow loads using Kelvin probe microscopy, Appl. Surf. Sci., 157, 373-381. Bhushan, B. and Goldade, A.V. (2000b), Kelvin probe microscopy measurements of surface potential change under wear at low loads, Wear, 244, 104-117. Bhushan, B. and Koinkar, V.N. (1994a), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. Bhushan, B. and Koinkar V.N. (1994b), Nanoindentation hardness measurements using atomic force microscopy, Appl. Phys. Lett., 64, 1653-1655. Bhushan, B. and Kulkarni, A.V. (1996), Effect of normal load on microscale friction measurements, Thin Solid Films, 278, 49-56; 293, 333. Bhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction force microscopy: part II — application to magnetic media, ASME J. Tribol., 116, 389-396. Bhushan, B. and Sundararajan, S. (1998), Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy, Acta Mater., 46, 3793-3804.
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Bhushan, B., Koinkar, V.N., and Ruan, J. (1994), Microtribology of magnetic media, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, 17-29. Bhushan, B., Israelachvili, J.N., and Landman, U. (1995a), Nanotribology: friction, wear and lubrication at the atomic scale, Nature, 374, 607-616. Bhushan, B., Kulkarni, A.V., Koinkar, V.N., Boehm, M., Odoni, L., Martelet, C., and Belin, M. (1995b), Microtribological characterization of self-assembled and Langmuir–Blodgett monolayers by atomic and friction force microscopy, Langmuir, 11, 3189-3198. Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system in atomic force microscopy, Philos. Mag., 74, 1117-1128. Binnig, G., Quate, C.F., and Gerber, Ch. (1986), Atomic force microscopy, Phys. Rev. Lett., 56, 930-933. Binnig, G., Gerber, Ch., Stoll, E. Albrecht, T.R., and Quate, C.F. (1987), Atomic resolution with atomic force microscope, Europhys. Lett., 3, 1281-1286. Bowden, F. P. and Tabor, D. (1950), The Friction and Lubrication of Solids, Part 1, Clarendon Press, Oxford, U.K. DeVecchio, D. and Bhushan, B. (1997), Localized surface elasticity measurements using an atomic force microscope, Rev. Sci. Instrum., 68, 4498-4505. DeVecchio, D. and Bhushan, B. (1998), Use of a nanoscale Kelvin probe for detecting wear precursors, Rev. Sci. Instrum., 69, 3618-3624. Frisbie, C.D., Rozsnyai, L.F., Noy, A., Wrighton M.S., and Lieber, C.M. (1994), Functional group imaging by chemical force microscopy, Science, 265, 2071-2074. Guntherodt, H.J., Anselmetti, D., and Meyer, E. (1995), Forces in Scanning Probe Methods, Vol. E286, Kluwer Academic Pub., Dordrecht, Netherlands. Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391. Koinkar, V.N. and Bhushan, B. (1996c), Microtribological studies of Al2O3-TiC, polycrystalline and singlecrystal Mn–Zn ferrite and SiC head slider materials, Wear, 202, 110-122. Koinkar, V.N. and Bhushan, B. (1997a), Microtribological properties of hard amorphous carbon protective coatings for thin film magnetic disks and heads, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 211, 365-372. Koinkar, V.N. and Bhushan, B. (1997b), Effect of scan size and surface roughness on microscale friction measurements, J. Appl. Phys., 81, 2472-2479. Koinkar, V.N. and Bhushan, B. (1997c), Scanning and transmission electron microscopies of single-crystal silicon microworn/machined using atomic force microscopy, J. Mater. Res., 12, 3219-3224. Kulkarni, A.V. and Bhushan, B. (1996a), Nanoscale mechanical property measurements using modified atomic force microscopy, Thin Solid Films, 290-291, 206-210. Kulkarni, A.V. and Bhushan, B. (1996b), Nano/picoindentation measurements on single-crystal aluminum using modified atomic force microscopy, Materials Letters, 29, 221-227. Kulkarni, A.V. and Bhushan, B. (1997), Nanoindentation measurement of amorphous carbon coatings, J. Mater. Res., 12, 2707-2714. Li, W.B., Henshall, J.L., Hooper, R.M., and Easterling, K.E. (1991), The mechanism of indentation creep, Acta Metall. Mater., 39, 3099-3110. Maivald, P., Butt, H.J., Gould, S.A.C., Prater, C.B., Drake, B., Gurley, J.A., Elings, V.B., and Hansma, P.K. (1991), Using force modulation to image surface elasticities with the atomic force microscope, Nanotechnology, 2, 103-106. Makinson, K.R. (1948), On the cause of the frictional difference of the wool fiber, Trans. Faraday Soc., 44, 279-282. Mate, C.M., McClelland, G.M., Erlandsson R., and Chiang, S. (1987), Atomic-scale friction of a tungsten tip on a graphite surface, Phys. Rev. Lett., 59, 1942-1945.
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Meyer, E., Overney, R., Luthi, R., Brodbeck, D., Howald, L., Frommer, J., Guntherodt, H.J., Wolter, O., Fujihira, M., Takano, T., and Gotoh, Y. (1992), Friction force microscopy of mixed Langmuir–Blodgett films, Thin Solid Films, 220, 132-137. Persson, B.N.J. and Tosatti, E. (1996), Physics of Sliding Friction, Vol. E311, Kluwer Academic Pub., Dordrecht, Netherlands. Ruan, J. and Bhushan, B. (1993), Nanoindentation studies of fullerene films using atomic force microscopy, J. Mater. Res., 8, 3019-3022. Ruan, J. and Bhushan, B. (1994a), Atomic-scale friction measurements using friction force microscopy: part I — general principles and new measurement techniques, ASME J. Tribol., 116, 378-388. Ruan, J. and Bhushan, B. (1994b), Atomic-scale and microscale friction of graphite and diamond using friction force microscopy, J. Appl. Phys., 76, 5022-5035. Ruan, J. and Bhushan, B. (1994c), Frictional behavior of highly oriented pyrolytic graphite, J. Appl. Phys., 76, 8117-8120. Scherer, V., Bhushan, B., Rabe, U., and Arnold, W. (1997), Local elasticity and lubrication measurements using atomic force and friction force microscopy at ultrasonic frequencies, IEEE Trans. Magn., 33, 4077-4079. Scherer, V., Arnold W., and Bhushan, B. (1998), Active friction control using ultrasonic vibration, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic Pub., Dordrecht, Netherlands, 463-469. Scherer, V., Arnold, W., and Bhushan, B. (1999), Lateral force microscopy using acoustic friction force microscopy, Surface and Interface Anal., 27, 578-587. Schwarz, U.D., Zwoerner, O., Koester, P., and Wiesendanger, R. (1997), Friction force spectroscopy in the low-load regime with well-defined tips, in Micro/Nanotribology and Its Applications, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, Netherlands, 233-238. Singer, I.L. and Pollock, H.M. (1992), Fundamentals of Friction: Macroscopic and Microscopic Processes, Vol. E220, Kluwer Academic Pub., Dordrecht, Netherlands. Sundararajan, S. and Bhushan, B. (2000a), Development of a continuous microscratch technique in an atomic force microscope and its application to study scratch resistance of ultra-thin hard amorphous carbon coatings, J. Mater. Res., in press. Sundararajan, S. and Bhushan, B. (2000b), Topography-induced contributions to friction forces measured using an atomic force/friction force microscope, J. Appl. Phys., 88, 4825-4831. Zhao, X. and Bhushan, B. (1998), Material removal mechanism of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78.
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20 Computer Simulations of Friction, Lubrication, and Wear 20.1 20.2
Introduction ..................................................................... 717 Atomistic Computer Simulations ................................... 718 Model Potentials • Maintaining Constant Temperature • Imposing Load and Shear
20.3
Wearless Friction in Low-Dimensional Systems............ 722 Two Simple Models of Crystalline Surfaces in Direct Contact • Metastability and Static Friction in One Dimension • Metastability and Kinetic Friction • Tomlinson Model in Two Dimensions: Atomic Force Microscopy • Frenkel–Kontorova Model in Two Dimensions: Adsorbed Monolayers
20.4
Dry Sliding of Crystalline Surfaces................................. 734 Effect of Commensurability • Chemically Passivated Surfaces • Single Asperity Contacts
20.5
Flow Boundary Conditions • Phase Transitions and Viscosity Changes in Molecularly Thin Films • Submonolayer Lubrication • Corrugated Surfaces
Mark O. Robbins The Johns Hopkins University
Martin H. Müser Johannes Gutenberg-Universität
Lubricated Surfaces .......................................................... 740
20.6 20.7
Stick-Slip Dynamics......................................................... 752 Strongly Irreversible Tribological Processes ................... 755 Plastic Deformation • Wear • Tribochemistry
20.1 Introduction Computer simulations have played an important role in advancing our understanding of tribological processes. They allow controlled numerical experiments where the geometry, sliding conditions, and interactions between atoms can be varied at will to explore their effects on friction, lubrication, and wear. Unlike laboratory experiments, computer simulations enable scientists to follow and analyze the full dynamics of all atoms. Moreover, theorists have no other general approach to analyze processes like friction and wear, because there is no known principle like minimization of free energy that determines the steady state of nonequilibrium systems. Even if there were, simulations would be needed to address the complex systems of interest, just as in many equilibrium problems. Tremendous advances in computing hardware and methodology have dramatically increased the ability of theorists to simulate tribological processes. This has led to an explosion in the number of computational studies over the last decade, and allowed increasingly sophisticated modeling of sliding contacts. Although it is not yet possible to treat all the length scales and time scales that enter the friction coefficient of 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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engineering materials, computer simulations have revealed a great deal of information about the microscopic origins of static and kinetic friction, the behavior of boundary lubricants, and the interplay between molecular geometry and tribological properties. These results provide valuable input to more traditional macroscopic calculations. Given the rapid pace of developments, simulations can be expected to play an expanding role in tribology. In the following chapter we present an overview of the major results from the growing simulation literature. The emphasis is on providing a coherent picture of the field, rather than a historical review. We also outline opportunities for improved simulations, and high-light unanswered questions. We begin by presenting a brief overview of simulation techniques and focus on special features of simulations for tribological processes. For example, it is well known that the results of tribological experiments can be strongly influenced by the mechanical properties of the entire system that produces sliding. In much the same way, the results from simulations depend on how relative motion of the surfaces is imposed, and how heat generated by sliding is removed. The different techniques that are used are described, so that their influence on results can be understood in later sections. The complexities of realistic three-dimensional systems can make it difficult to analyze the molecular mechanisms that underlie friction. The third section focuses on dry, wearless friction in less complex systems. The discussion begins with simple one-dimensional models of friction between crystalline surfaces. These models illustrate general results for the origin and trends of static and kinetic friction, such as the importance of metastability and the effect of commensurability. Then two-dimensional studies are described, with an emphasis on the connection to atomic force microscope experiments and detailed measurements of the friction on adsorbed monolayers. In the fourth section, simulations of the dry sliding of crystalline surfaces are addressed. Studies of metal/metal interfaces, surfactant-coated surfaces, and diamond interfaces with various terminations are described. The results can be understood from the simple models of the previous chapter. However, the extra complexity of the interactions in these systems leads to a richer variety of processes. Simple examples of wear between metal surfaces are also discussed. The fifth section describes how the behavior of lubricated systems begins to deviate from bulk hydrodynamics as the thickness of the lubricant decreases to molecular scales. Deviations from the usual noslip boundary condition are found in relatively thick films. These are described and correlated to structures induced in the lubricant by the adjoining walls. As the film thickness decreases, the effective viscosity increases rapidly above the bulk value. Films that are only one or two molecules thick typically exhibit solid behavior. The origins of this liquid/solid transition are discussed, and the possibility that thin layers of small molecules are responsible for the prevalence of static friction is explored. The section concludes with descriptions of simulations using realistic models of hydrocarbon boundary lubricants between smooth and corrugated surfaces. The sixth section describes work on the common phenomenon of stick-slip motion and microscopic models for its origins. Atomic-scale ratcheting is contrasted with long-range slip events, and the structural changes that accompany stick-slip transitions in simulations are described. The seventh and final section describes work on friction at extreme conditions such as high shear rates or large contact pressures. Simulations of tribochemical reactions, machining, and the evolution of microstructure in sliding contacts are discussed.
20.2 Atomistic Computer Simulations The simulations described in this chapter all use an approach called classical molecular dynamics (MD) that is described extensively in a number of review articles and books, including Allen and Tildesley (1987) and Frenkel and Smit (1996). The basic outline of the method is straightforward. One begins by defining the interaction potentials. These produce forces on the individual particles whose dynamics will be followed, typically atoms or molecules. Next the geometry and boundary conditions are specified, and initial coordinates and velocities are given to each particle. Then the equations of motion for the
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particles are integrated numerically, stepping forward in time by discrete steps of size ∆t. Quantities such as forces, velocities, work, heat flow, and correlation functions are calculated as functions of time to determine their steady-state values and dynamic fluctuations. The relation between changes in these quantities and the motion of individual molecules is also explored. When designing a simulation, care must be taken to choose interaction potentials and ensembles that capture the essential physics that is to be addressed. The potentials may be as simple as ideal spring constants for studies of general phenomena, or as complex as electronic density-functional calculations in quantitative simulations. The ensemble can also be tailored to the problem of interest. Solving Newton’s equations yields a constant energy and volume, or microcanonical, ensemble. By adding terms in the equation of motion that simulate heat baths or pistons, simulations can be done at constant temperature, pressure, lateral force, or velocity. Constant chemical potential can also be maintained by adding or removing particles using Monte Carlo methods or explicit particle baths. The amount of computational effort typically grows linearly with both the number of particles, N, and the number of time-steps M. The prefactor increases rapidly with the complexity of the interactions, and substantial ingenuity is required to achieve linear scaling with N for long-range interactions or electronic density-functional approaches. Complex interactions also lead to a wide range of characteristic frequencies, such as fast bond-stretching and slow bond-bending modes. Unfortunately, the time step ∆t must be small (~2%) compared to the period of the fastest mode. This means that many time steps are needed before one obtains information about the slow modes. The maximum feasible simulation size has increased continuously with advances in computer technology, but remains relatively limited. The product of N times M in the largest simulations described below is about 1012. A cubic region of 106 atoms would have a side of about 50 nm. Such linear dimensions allow reasonable models of an atomic force microscope tip, the boundary lubricant in a surface force apparatus, or an individual asperity contact on a rough surface. However, 106 time steps is only about 10 nanoseconds, which is much smaller than experimental measurement times. This requires intelligent choices in the problems that are attacked, and how results are extrapolated to experiment. It also limits sliding velocities to relatively high values, typically meters per second or above. A number of efforts are under way to increase the accessible time scale, but the problem remains unsolved. Current algorithms attempt to follow the deterministic equations of motion, usually with the Verlet or predictor–corrector algorithms (Allen and Tildesley, 1987). One alternative approach is to make stochastic steps. This would be a nonequilibrium generalization of the Monte Carlo approach that is commonly used in equilibrium systems. The difficulty is that there is no general principle for determining the appropriate probability distribution of steps in a nonequilibrium system. In the following, we describe some of the potentials that are commonly used and the situations where they are appropriate. The final two subsections describe methods for maintaining constant temperature and constant load.
20.2.1 Model Potentials A wide range of potentials has been employed in studies of tribology. Many of the studies described in the next section use simple ideal springs and sine-wave potentials. The Lennard–Jones potential gives a more realistic representation of typical interatomic interactions, and is also commonly used in studies of general behavior. In order to model specific materials, more detail must be built into the potential. Simulations of metals frequently use the embedded atom method, while studies of hydrocarbons use potentials that include bond-stretching, bending, torsional forces, and even chemical reactivity. In this section we give a brief definition of the most commonly used models. The reader may consult the original literature for more detail. The Lennard–Jones (LJ) potential is a two-body potential commonly used for interactions between atoms or molecules with closed electron shells. It is applied not only to the interaction between noble gas atoms, but also to the interaction between different segments on polymers. In the latter case, one LJ particle may represent a single atom on the chain (explicit atom model), a CH2 segment (united atom
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model), or even a Kuhn’s segment consisting of several CH2 units (coarse-grained model). United atom models (Ryckaert and Bellemans, 1978) have been shown by Paul et al. (1995) to successfully reproduce explicit atom results for polymer melts, while Tschöp et al. (1998a,b) have successfully mapped chemically detailed models of polymers onto coarse-grained models and back. The 12-6 LJ potential has the form
12 6 σ σ U rij = 4 − rij rij
()
(20.1)
where rij is the distance between particles i and j, is the LJ interaction energy, and σ is the LJ interaction diameter. The exponents 12 and 6 used above are very common, but depending on the system, other values may be chosen. Many of the simulation results discussed in subsequent sections are expressed in units derived from , σ, and a characteristic mass of the particles. For example, the standard LJ time unit is defined as tLJ = mσ 2 ⁄ , and would typically correspond to a few picoseconds. A convenient time step is ∆t = 0.005tLJ for an LJ liquid or solid at external pressures and temperatures that are not too large. Most realistic atomic potentials cannot be expressed as two-body interactions. For example, bond angle potentials in a polymer are effectively three-body interactions, and torsional potentials correspond to four-body interactions. Classical models of these interactions (Flory, 1988; Binder, 1995) assume that a polymer is chemically inert and interactions between different molecules are modeled by two-body potentials. In the most sophisticated models, bond-stretching, bending, and torsional energies depend on the position of neighboring molecules, and bonds are allowed to rearrange (Brenner, 1990). Such generalized model potentials are needed to model friction-induced chemical interactions. For the interaction between metals, a different approach has proven fruitful. The embedded atom method (EAM), introduced by Daw and Baskes (1984), includes a contribution in the potential energy associated with the cost of “embedding” an atom in the local electron density ρi produced by surrounding atoms. The total potential energy U is approximated by
U=
∑ F˜ (ρ ) + ∑ ∑ φ (r ) i
i
i
ij
i
ij
(20.2)
j
where F˜i is the embedding energy, whose functional form depends on the particular metal. The pair potential φij(rij) is a doubly screened, short-range potential reflecting core–core repulsion. The computational cost of the EAM is not substantially greater than pair potential calculations because the density ρi is approximated by a sum of independent atomic densities. When compared to simple two-body potentials such as Lennard–Jones or Morse potentials, the EAM has been particularly successful in reproducing experimental vacancy formation energies and surface energies, even though the potential parameters were only adjusted to reproduce bulk properties. This feature makes the EAM an important tool in tribological applications, where surfaces and defects play a major role.
20.2.2 Maintaining Constant Temperature An important issue for tribological simulations is temperature regulation. The work done when two walls slide past each other is ultimately converted into random thermal motion. The temperature of the system would increase indefinitely if there were no way for this heat to flow out of the system. In an experiment, heat flows away from the sliding interface into the surrounding solid. In simulations, the effect of the surrounding solid must be mimicked by coupling the particles to a heat bath. Techniques for maintaining constant temperature T in equilibrium systems are well-developed. Equipartition guarantees that the average kinetic energy of each particle along each Cartesian coordinate is
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kBT/2 where kB is Boltzmann’s constant.* To thermostat the system, the equations of motion are modified so that the average kinetic energy stays at this equilibrium value. One class of approaches removes or adds kinetic energy to the system by multiplying the velocities of all particles by the same global factor. In the simplest version, velocity rescaling, the factor is chosen to keep the kinetic energy exactly constant at each time step. However, in a true constant temperature ensemble there would be fluctuations in the kinetic energy. Improvements, such as the Berendsen and Nosé–Hoover methods (Nosé, 1991) add equations of motion that gradually scale the velocities to maintain the correct average kinetic energy over a longer time scale. Another approach is to couple each atom to its own local thermostat (Schneider and Stoll, 1978; Grest and Kremer, 1986). The exchange of energy with the outside world is modeled by a Langevin equation → that includes a damping coefficient γi and a random force fi (t) on each atom i. The equations of motion for the α component of the position xiα become:
mi
d 2 xiα dx ∂ =− U − γ i iα + fiα t 2 ∂xiα dt dt
()
(20.3)
where U is the total potential energy and mi is the mass of the atom. To produce the appropriate temperature, the forces must be completely random, have zero mean, and have a second moment given by
()
fiα t
2
= 2kBT γ i ∆t
(20.4)
The damping coefficient γ must be large enough that energy can be removed from the atoms without substantial temperature increases. However, it should be small enough that the trajectories of individual particles are not perturbed too strongly. The first issue in nonequilibrium simulations is what temperature means. Near equilibrium, hydrodynamic theories define a local temperature in terms of the equilibrium equipartition formula and the kinetic energy relative to the local rest frame (Sarman et al., 1998). In d dimensions, the definition is
1 k BT = dN
∑
→ →
i
2 r dxi r r mi − v xi dt
( )
(20.5) →
where the sum is over all N particles and 〈v(x)〉 is the mean velocity in a region around x. As long as → → the change in mean velocity is sufficiently slow, 〈v(x)〉 is well-defined, and this definition of temperature is on solid theoretical ground. When the mean velocity difference between neighboring molecules becomes comparable to the random thermal velocities, temperature is not well-defined. An important consequence is that different strategies for defining and controlling temperature give very different structural order and friction forces (Evans and Morriss, 1986; Loose and Ciccotti, 1992; Stevens and Robbins, 1993). In addition, the distribution of velocities may become non-Gaussian, and different directions α may have different effective temperatures. Care should be taken in drawing conclusions from simulations in this extreme regime. Fortunately, the above condition typically implies that the velocities of neighboring atoms differ by something approaching 10% of the speed of sound. This is generally higher than any experimental velocity, and would certainly lead to heat buildup and melting at the interface. In order to mimic experiments, the thermostat is often applied only to those atoms that are at the outer boundary of the simulation cell. This models the flow of heat into surrounding material that is *This assumes that T is above the Debye temperature so that quantum statistics are not important.
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not included explicitly in the simulation. The resulting temperature profile is peaked at the shearing interface (e.g., Bowden and Tabor, 1986; Khare et al., 1996). In some cases the temperature rise may lead to undesirable changes in the structure and dynamics even at the lowest velocity that can be treated in the available simulation time. In this case, a weak thermostat applied throughout the system may maintain the correct temperature and yield the dynamics that would be observed in longer simulations at lower velocities. The safest course is to couple the thermostat only to those velocity components that are perpendicular to the mean flow. This issue is discussed further in Section 20.3.5. There may be a marginal advantage to local Langevin methods in nonequilibrium simulations because they remove heat only from atoms that are too hot. Global methods like Nosé–Hoover remove heat everywhere. This can leave high temperatures in the region where heat is generated, while other regions are at an artificially low temperature.
20.2.3 Imposing Load and Shear The magnitude of the friction that is measured in an experiment or simulation may be strongly influenced by the way in which the normal load and tangential motion are imposed (Rabinowicz, 1965). Experiments almost always impose a constant normal load. The mechanical system applying shear can usually be described as a spring attached to a stage moving at controlled velocity. The effective spring constant includes the compliance of all elements of the loading device, including the material on either side of the interface. Very compliant springs apply a nearly constant force, while very stiff springs apply a nearly constant velocity. In simulations, it is easiest to treat the boundary of the system as rigid, and to translate atoms in this region at a constant height and tangential velocity. However, this does not allow atoms to move around (Section 20.3.4) or up and over atoms on the opposing surface. Even the atomic-scale roughness of a crystalline surface can lead to order of magnitude variations in normal and tangential force with lateral position when sliding is imposed in this way (Harrison et al., 1992b, 1993; Robbins and Baljon, 2000). The difference between constant separation and constant pressure simulations of thin films can be arbitrarily large, since they produce different power law relations between viscosity and sliding velocity (Section 20.5.2). One way of minimizing the difference between constant separation and constant pressure ensembles is to include a large portion of the elastic solids that bound the interface. This extra compliance allows the surfaces to slide at a more uniform normal and lateral force. However, the extra atoms greatly increase the computational effort. To simulate the usual experiment ensemble more directly, one can add equations of motion that describe the position of the boundary (Thompson et al., 1990b, 1992, 1995), much as equations are added to maintain constant temperature. The boundary is given an effective mass that moves in response to the net force from interactions with mobile atoms and from the external pressure and lateral spring. The mass of the wall should be large enough that its dynamics are slower than those of individual atoms, but not too much slower, or the response time will be long compared to the simulation time. The spring constant should also be chosen to produce an appropriate response time and ensemble.
20.3 Wearless Friction in Low-Dimensional Systems 20.3.1 Two Simple Models of Crystalline Surfaces in Direct Contact Static and kinetic friction involve different aspects of the interaction between surfaces. The existence of static friction implies that the surfaces become trapped in a local potential energy minimum. When the bottom surface is held fixed, and an external force is applied to the top surface, the system moves away from the minimum until the derivative of the potential energy balances the external force. The static friction, Fs is the maximum force the potential can resist, i.e., the maximum slope of the potential. When this force is exceeded, the system begins to slide, and kinetic friction comes into play. The kinetic friction
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FIGURE 20.1 (a) Two ideal, flat crystals making contact at the plane indicated by the dashed line. The nearestneighbor spacings in the bottom and top walls are a and b, respectively. The Tomlinson model (b) and Frenkel–Kontorova model (c) replace the bottom surface by a periodic potential. The former model keeps elastic forces between atoms on the top surface and the center of mass of the top wall, and the latter includes springs of stiffness k between neighbors in the top wall. (From Robbins, M.O. (2000), Jamming, friction, and unsteady rheology, in Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, Liu, A.J. and Nagel, S.R. (Eds.), Taylor and Francis, London. With permission.)
Fk(v) is the force required to maintain sliding at a given velocity v. The rate at which work is done on the system is v · Fk(v) and this work must be dissipated as heat that flows away from the interface. Thus simulations must focus on the nature of potential energy minima to probe the origins of static friction, and must also address dissipation mechanisms to understand kinetic friction. Two simple ball and spring models are useful in illustrating the origins of static and kinetic friction, and in understanding the results of detailed simulations. Both consider two clean, flat, crystalline surfaces in direct contact (Figure 20.1a). The bottom solid is assumed to be rigid, so that it can be treated as a fixed periodic substrate potential acting on the top solid. In order to make the problem analytically tractable, only the bottom layer of atoms from the top solid is retained, and the interactions within the top wall are simplified. In the Tomlinson model (Figure 20.1b), the atoms are coupled to the center of mass of the top wall by springs of stiffness k, and the coupling between neighboring atoms is ignored (Tomlinson, 1929; McClelland and Cohen, 1990). In the Frenkel–Kontorova model (Figure 20.1c), the atoms are coupled to nearest-neighbors by springs, and the coupling to the atoms above is ignored (Frenkel and Kontorova, 1938). Due to their simplicity, these models arise in a number of different problems and a great deal is known about their properties. McClelland (1989) and McClelland and Glosli (1992) have provided two early discussions of their relevance to friction. Bak (1982) has reviewed the Frenkel–Kontorova model and the physical systems that it models in different dimensions.
20.3.2 Metastability and Static Friction in One Dimension Many features of the Tomlinson and Frenkel–Kontorova models can be understood from their onedimensional versions. One important parameter is the ratio η between the lattice constants of the two surfaces η ≡ b/a. The other is the strength of the periodic potential from the substrate relative to the spring stiffness k that represents interactions within the top solid. If the substrate potential has a single Fourier component, then the periodic force can be written as
2π f x = − f1 sin x a
()
(20.6)
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The relative strength of the potential and springs can be characterized by the dimensionless constant λ = 2πf1/ka. In the limit of infinitely strong springs (λ → 0), both models represent rigid solids. The atoms of the top wall are confined to lattice sites x l0 = xCM + lb, where the integer l labels successive atoms, and xCM represents a rigid translation of the entire wall. The total lateral or friction force is given by summing Equation 20.6 N
F = − f1
∑ sin 2aπ (lb + x )
(20.7)
CM
l =1
where N is the number of atoms in the top wall. In the special case of equal lattice constants (η = b/a = 1), the forces on all atoms add in phase, and F = –N f1 sin(2πxCM/a). The maximum of this restraining force gives the static friction Fs = N f1. Unless there is a special reason for b and a to be related, η is most likely to be an irrational number. Such surfaces are called incommensurate, while surfaces with a rational value of η are commensurate. When η is irrational, atoms on the top surface sample all phases of the periodic force with equal probability and the net force (Equation 20.7) vanishes exactly. When η is a rational number, it can be expressed as p/q where p and q are integers with no common factors. In this case, atoms only sample q different phases. The net force from Equation 20.7 still vanishes because the force is a pure sine wave and the phases are equally spaced. However, the static friction is finite if the potential has higher harmonics. A Fourier component with wavevector q2π/a and magnitude fq contributes N fq to Fs . Studies of surface potentials (Bruch et al., 1997) show that fq drops exponentially with increasing q and thus imply that Fs will only be significant for small q. As the springs become weaker, the top wall is more able to deform into a configuration that lowers the potential energy. The Tomlinson model is the simplest case to consider, because each atom can be treated as an independent oscillator within the upper surface. The equations of motion for the position xl of the l th atom can be written as
2π mx˙˙l = − γx˙ l − f1 sin xl − k xl − xl0 a
(
)
(20.8)
where m is the atomic mass and x 0l is the position of the lattice site. Here γ is a phenomenological damping coefficient, like that in a Langevin thermostat (Section 20.2.2), that allows work done on the atom to be dissipated as heat. It represents the coupling to external degrees of freedom such as lattice vibrations in the solids. In any steady state of the system, the total friction can be determined either from the sum of the forces exerted by the springs on the top wall, or from the sum of the periodic potentials acting on the atoms (Equation 20.7). If the time average of these forces differed, there would be a net force on the atoms and a steady acceleration (Thompson and Robbins, 1990a; Matsukawa and Fukuyama, 1994). The static . friction is related to the force in metastable states of the system where x¨ l = xl = 0. This requires that spring and substrate forces cancel for each l,
2π k xl − xl0 = − f1 sin xl a
(
)
(20.9)
As shown graphically in Figure 20.2a, there is only one solution for weak interfacial potentials and stiff solids (λ < 1). In this limit, the behavior is essentially the same as for infinitely rigid solids. There is static friction for η = 1, but not for incommensurate cases. Even though incommensurate potentials displace
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FIGURE 20.2 Graphical solution for metastability of an atom in the Tomlinson model for (a) λ = 0.5 and (b) λ = 3. The straight dashed lines show minus the force from the spring, k(xl – x l0), at different x l0, and the curved lines show the periodic substrate force. For λ < 1 there is a single intersection of the dashed lines with the substrate force for each value of x l0 and thus a single metastable state. For λ > 1 there are multiple intersections with the substrate force. Dotted portions of the force curve indicate unstable maxima, and solid regions indicate metastable solutions. As x l0 increases, an atom that started at xl = 0 gradually moves through the set of metastable states indicated by a thick solid line. At the value of x l0 corresponding to the third dashed line, this metastable state becomes unstable and the atom jumps to the metastable state indicated by the continuation of the thick region of the line. It then follows this portion of the line until this state becomes unstable at the x l0 corresponding to the rightmost dashed line.
atoms from lattice sites, there are exactly as many displaced to the right as to the left, and the force sums to zero. A new type of behavior sets in when λ exceeds unity. The interfacial potential is now strong enough compared to the springs so that multiple metastable states are possible. These states must satisfy both Equation 20.9 and the condition that the second derivative of the potential energy is positive: 1 + λ cos (2πxl /a) > 0. The number of metastable solutions increases as λ increases. As illustrated in Figure 20.2b, once an atom is in a given metastable minimum it is trapped there until the center of mass moves far enough away that the second derivative of the potential vanishes and the minimum becomes unstable. The atom then pops forward very rapidly to the nearest remaining metastable state. This metastability makes it possible to have a finite static friction even when the surfaces are incommensurate. If the wall is pulled to the right by an external force, the atoms will only sample the metastable states corresponding to the thick solid portion of the force from the substrate potential in Figure 20.2b. Atoms bypass other portions as they hop to the adjacent metastable state. The average over the solid portion of the curve is clearly negative and thus resists the external force. As λ increases, the dashed lines in Figure 20.2b become flatter and the solid portion of the curve becomes confined to more and more negative forces. This increases the static friction which approaches N f1 in the limit λ → ∞ (Fisher, 1985). A similar analysis can be done for the one-dimensional Frenkel–Kontorova model (Frank et al., 1949; Bak, 1982; Aubry, 1979, 1983). The main difference is that the static friction and ground state depend strongly on η. For any given irrational value of η there is a threshold potential strength λc . For weaker potentials, the static friction vanishes. For stronger potentials, metastability produces a finite static friction. The transition to the onset of static friction was termed a breaking of analyticity by Aubry (1979) and is often called the Aubry transition. The metastable states for λ > λc take the form of locally commensurate regions that are separated by domain walls where the two crystals are out of phase. Within the locally commensurate regions, the ratio of the periods is a rational number p/q that is close to η. The range of η where locking occurs grows with increasing potential strength (λ) until it spans all values.
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At this point there is an infinite number of different metastable ground states that form a fascinating “Devil’s staircase” as η varies (Aubry, 1979, 1983; Bak, 1982). Weiss and Elmer (1996) have performed a careful study of the one-dimensional Frenkel–Kontorova–Tomlinson model where both types of springs are included. Their work illustrates how one can have a finite static friction at all rational η and an Aubry transition at all irrational η. They showed that magnitude of the static friction is a monotonically increasing function of λ and decreases with decreasing commensurability. If η = p/q then the static friction rises with corrugation only as λq. Successive approximations to an irrational number involve progressively larger values of q. Since λc < 1, the value of Fs at λ < λc drops closer and closer to zero as the irrational number is approached. At the same time, the value of Fs rises more and more rapidly with λ above λc . In the limit q → ∞ one has the discontinuous rise from zero to finite values of Fs described by Aubry. Weiss and Elmer also considered the connection between the onsets of static friction, of metastability, and of a finite kinetic friction as v → 0 that is discussed in the next section. Their numerical results showed that all these transitions coincide. Work by Kawaguchi and Matsukawa (1998) shows that varying the strengths of competing elastic interactions can lead to even more complex friction transitions. They considered a model proposed by Matsukawa and Fukuyama (1994) that is similar to the one-dimensional Frenkel–Kontorova–Tomlinson model. For some parameters the static friction oscillated several times between zero and finite values as the interaction between surfaces increased. Clearly the transitions from finite to vanishing static friction continue to pose a rich mathematical challenge.
20.3.3 Metastability and Kinetic Friction The metastability that produces static friction in these simple models is also important in determining the kinetic friction. The kinetic friction between two solids is usually fairly constant at low center of mass velocity differences vCM. This means that the same amount of work must be done to advance by a lattice constant no matter how slowly the system moves. If the motion were adiabatic, this irreversible work would vanish as the displacement was carried out more and more slowly. Since it does not vanish, some atoms must remain very far from equilibrium even in the limit vCM → 0. The origin of this non-adiabaticity is most easily illustrated with the Tomlinson model. In the low velocity limit, atoms stay near to the metastable solutions shown in Figure 20.2. For λ < 1 there is a unique metastable solution that evolves continuously. The atoms can move adiabatically, and the kinetic friction vanishes as vCM → 0. For λ > 1 each atom is trapped in a metastable state. As the wall moves, this state becomes unstable and the atom pops rapidly to the next metastable state. During this motion the atom experiences very large forces and accelerates to a peak velocity vp that is independent of vCM. The value of vp is typically comparable to the sound and thermal velocities in the solid and thus cannot be treated as a small perturbation from equilibrium. Periodic pops of this type are seen in many of the realistic simulations described in Section 20.4. They are frequently referred to as atomic-scale stick-slip motion (Sections 20.4 and 20.6), because of the oscillation between slow and rapid motion (Section 20.6). The dynamic equation of motion for the Tomlinson model (Equation 20.8) has been solved in several different contexts. It is mathematically identical to simple models for Josephson junctions (McCumber, 1968), to the single-particle model of charge-density wave depinning (Grüner et al., 1981), and to the equations of motion for a contact line on a periodic surface (Raphael and DeGennes, 1989; Joanny and Robbins, 1990). Figure 20.3 shows the time-averaged force as a function of wall velocity for several values of the interface potential strength in the overdamped limit. (Since each atom acts as an independent oscillator, these curves are independent of η.) When the potential is much weaker than the springs (λ < 1), the atoms cannot deviate significantly from their equilibrium positions. They go up and down over the periodic potential at constant velocity in an adiabatic manner. In the limit vCM → 0 the periodic force is sampled uniformly and the kinetic friction vanishes, just as the static friction did for incommensurate walls. At finite velocity the kinetic friction is just due to the drag force on each atom and rises linearly with velocity. The same result holds for all spring constants in the Frenkel–Kontorova model with equal lattice constants (η = 1).
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FIGURE 20.3 Force vs. velocity for the Tomlinson model at the indicated values of λ. The force is normalized by the static friction N f1 and the velocity is normalized by v0 f1/γ where γ is the phenomenological damping rate. (From Robbins, M.O. (2000), Jamming, friction, and unsteady rheology, in Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, Liu, A.J. and Nagel, S.R. (Eds.), Taylor and Francis, London. With permission; adapted from Joanny, J.F. and Robbins, M.O. (1990), Motion of a contact line on a heterogeneous surface, J. Chem. Phys., 92, 3206-3212.)
As the potential becomes stronger, the periodic force begins to contribute to the kinetic friction of the Tomlinson model. There is a transition at λ = 1, and at larger λ the kinetic friction remains finite in the limit of zero velocity. The limiting Fk (v = 0) is exactly equal to the static friction for incommensurate walls. The reason is that as vCM → 0 atoms spend almost all of their time in metastable states. During slow sliding, each atom samples all the metastable states that contribute to the static friction and with exactly the same weighting. The solution for commensurate walls has two different features. The first is that the static friction is higher than Fk (0). This difference is greatest for the case λ < 1 where the kinetic friction vanishes, while the static friction is finite. The second difference is that the force/velocity curve depends on whether the simulation is done at constant wall velocity (Figure 20.3) or constant force. The constant force solution is independent of λ and equals the constant velocity solution in the limit λ → ∞. The only mechanism of dissipation in the Tomlinson model is through the phenomenological damping force, which is proportional to the velocity of the atom. The velocity is essentially zero except in the rapid pops that occur as a state becomes unstable and the atom jumps to the next metastable state. In the overdamped limit, atoms pop with peak velocity vp ~ f1 /γ – independent of the average velocity of the center of mass. Moreover, the time of the pop is nearly independent of vCM, and so the total energy dissipated per pop is independent of vCM. This dissipated energy is of course consistent with the limiting force determined from arguments based on the sampling of metastable states given above (Fisher, 1985; Raphael and DeGennes, 1989; Joanny and Robbins, 1990). The basic idea that kinetic friction is due to dissipation during pops that remain rapid as vCM → 0 is very general, although the phenomenological damping used in the model is far from realistic. A constant dissipation during each displacement by a lattice constant immediately implies a velocity independent Fk, and vice versa.
20.3.4 Tomlinson Model in Two Dimensions: Atomic Force Microscopy Gyalog et al. (1995) have studied a generalization of the Tomlinson model where the atoms can move in two dimensions over a substrate potential. Their goal was to model the motion of an atomic-force microscope (AFM) tip over a surface. In this case the spring constant k reflects the elasticity of the cantilever, the tip, and the substrate. It will in general be different along the scanning direction than along the perpendicular direction. The extra degree of freedom provided by the second dimension means that the tip will not follow the nominal scanning direction, but will be deflected to areas of lower potential energy. This distorts the
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image and also lowers the measured friction force. The magnitude of both effects decreases with increasing stiffness. As in the one-dimensional model there is a transition from smooth sliding to rapid jumps with decreasing spring stiffness. However, the transition point now depends on sliding direction and on the position of the scan line along the direction normal to the nominal scan direction. Rapid jumps tend to occur first near the peaks of the potential, and extend over greater distances as the springs soften. The curves defining the unstable points can have very complex, anisotropic shapes. Hölscher et al. (1997) have used a similar model to simulate scans of MoS2. Their model also includes kinetic and damping terms in order to treat the velocity dependence of the AFM image. They find marked anisotropy in the friction as a function of sliding direction, and also discuss deviations from the nominal scan direction as the position and direction of the scan line vary. Rajasekaran et al. (1997) considered a simple elastic solid of varying stiffness that interacted with a single atom at the end of an AFM tip with Lennard–Jones potentials. Unlike the other calculations mentioned above, this paper explicitly includes variations in the height of the atom and maintains a constant normal load. The friction rises linearly with load in all cases, but the slope depends strongly on sliding direction, scan position, and the elasticity of the solid. The above papers and related work show the complexities that can enter from treating detailed surface potentials and the full elasticity of the materials and machines that drive sliding. All of these factors can influence the measured friction and must be included in a detailed model of any experiment. However, the basic concepts derived from one-dimensional models carry forward. In particular, (1) static friction results when there is sufficient compliance to produce multiple metastable states, and (2) a finite Fk(0) arises when energy is dissipated during rapid pops between metastable states. All of the above work considers a single atom or tip in a two-dimensional potential. However, the results can be superimposed to treat a pair of two-dimensional surfaces in contact, because the oscillators are independent in the Tomlinson model. One example of such a system is the work by Glosli and McClelland (1993) described in Section 20.4.2. Generalizing the Frenkel–Kontorova model to two dimensions is more difficult.
20.3.5 Frenkel–Kontorova Model in Two Dimensions: Adsorbed Monolayers The two-dimensional Frenkel–Kontorova model provides a simple model of a crystalline layer of adsorbed atoms (Bak, 1982). However, the behavior of adsorbed layers can be much richer because atoms are not connected by fixed springs, and thus can rearrange to form new structures in response to changes in equilibrium conditions (i.e., temperature) or due to sliding. Overviews of the factors that determine the wide variety of equilibrium structures, including fluid, incommensurate and commensurate crystals, can be found in Bruch et al. (1997) and Taub et al. (1991). As in one dimension, both the structure and the strength of the lateral variation or “corrugation” in the substrate potential are important in determining the friction. Variations in potential normal to the substrate are relatively unimportant (Persson and Nitzan, 1996; Smith et al., 1996). Most simulations of the friction between absorbed layers and substrates have been motivated by the pioneering quartz crystal microbalance (QCM) experiments of Krim et al. (1988, 1990, 1991). The quartz is coated with metal electrodes that are used to excite resonant shear oscillations in the crystal. When atoms adsorb onto the electrodes, the increased mass causes a decrease in the resonant frequency. Sliding of the substrate under the adsorbate leads to friction that broadens the resonance. By measuring both quantities, the friction per atom can be calculated. The extreme sharpness of the intrinsic resonance in the crystal makes this a very sensitive technique. In most experiments the electrodes were the noble metals Ag or Au. Deposition produces fcc crystallites with close-packed (111) surfaces. Scanning tunneling microscope studies show that the surfaces are perfectly flat and ordered over regions at least 100 nm across. At larger scales there are grain boundaries
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and other defects. A variety of molecules have been physisorbed onto these surfaces, but most of the work has been on noble gases. The interactions within the noble metals are typically much stronger than the van der Waals interactions between the adsorbed molecules. Thus, to a first approximation, the substrate remains unperturbed and can be replaced by a periodic potential (Smith et al., 1996; Persson, 1998). However, the mobility of substrate atoms is important in allowing heat generated by the sliding adsorbate to flow into the substrate. This heat transfer into substrate lattice vibrations or phonons can be modeled by a Langevin thermostat (Equation 20.3). If the surface is metallic, the Langevin damping should also include the effect of energy dissipated to the electronic degrees of freedom (Schaich and Harris, 1981; Persson, 1991; Persson and Volokitin, 1995). With the above assumptions, the equation of motion for an adsorbate atom can be written as
mx˙˙α = − γ α x˙ α + Fαext −
∂ U + fα t ∂xα
()
(20.10)
where m is the mass of an adsorbate atom, γα is the damping rate from the Langevin thermostat in the α → direction, fα(t) is the corresponding random force, F ext is an external force applied to the particles, and U is the total energy from the interactions of the adsorbate atoms with the substrate and with each other. Interactions between noble gas adsorbate atoms have been studied extensively, and are reasonably well described by a Lennard–Jones potential (Bruch et al., 1997). The form of the substrate interaction is less well-known. However, if the substrate is crystalline, its potential can be expanded as a Fourier series in → the reciprocal lattice vectors Ql of the surface layer (Bruch et al., 1997). Steele (1973) has considered Lennard–Jones interactions with substrate atoms and shown that the higher Fourier components drop → off exponentially with increasing Q and height z above the substrate. Thus most simulations have kept only the shortest wavevectors, writing:
r
r U sub r , z = U 0 z + U1 z
( )
()
( ) ∑ cos[Q ⋅ rr] l
(20.11)
l
→
→
where r is the position within the plane of the surface, and the sum is over symmetrically equivalent Q l. For the close-packed (111) surface of fcc crystals there are six equivalent lattice vectors of length 4π/ 3a where a is the nearest neighbor spacing in the crystal. For the (100) surface there are four equivalent lattice vectors of length 2π/a. Cieplak et al. (1994) and Smith et al. (1996) used Steele’s potential with an additional four shells of symmetrically equivalent wavevectors in their simulations. However, they found that their results were almost unchanged when only the shortest reciprocal lattice vectors were kept. Typically the Lennard–Jones , σ, and m are used to define the units of energy, length and time, as described in Section 20.2.1. The remaining parameters in Equation 20.10 are the damping rates, external force, and the substrate potential, which is characterized by the strength of the adsorption potential U0(z), and the corrugation potential U1(z). The Langevin damping for the two directions in the plane of the substrate is expected to be the same and will be denoted by γ . The damping along z, γ⊥, may be different (Persson and Nitzan, 1996). The depth of the minimum in the adsorption potential can be determined from the energy needed to desorb an atom, and the width is related to the frequency of vibrations along z. In the cases of interest here, the adsorption energy is much larger than the Lennard–Jones interaction or the corrugation. Atoms in the first adsorbed layer sit in a narrow range of z near the minimum z0. If the changes in U1 over this range are small, then the effective corrugation for the first monolayer is U10 U1(z0). As discussed below, the calculated friction in most simulations varies rapidly with U10 but is insensitive to other details in the substrate potential. The simplest case is the limit of weak corrugation and a fluid or incommensurate solid state of the adsorbed layer. As expected based on results from one-dimensional models, such layers experience no
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static friction, and the kinetic friction is proportional to the velocity: Fk = –Γv (Persson, 1993a; Cieplak et al., 1994). The constant of proportionality Γ gives the “slip time” ts m/Γ that is reported by Krim and co-workers (1988, 1990, 1991). This slip time represents the time for the transfer of momentum between adsorbate and substrate. If atoms are set moving with an initial velocity, the velocity will decay exponentially with time constant ts. Typical measured values of ts are of order nanoseconds for rare gases. This is surprisingly large when compared to the picosecond time scales that characterize momentum transfer in a bulk fluid of the same rare gas. (The latter is directly related to the viscosity.) The value of ts can be determined from simulations in several different ways. All give consistent results in the cases where they have been compared, and should be accurate if used with care. Persson (1993a), Persson and Nitzan (1996), and Liebsch et al. (1999) have calculated the average velocity as a function → of F ext and obtained Γ from the slope of this curve. Cieplak et al. (1994) and Smith et al. (1996) used this approach and also mimicked experiments by finding the response to oscillations of the substrate. They showed ts was constant over a wide range of frequency and amplitude. The frequency is difficult to vary in experiment, but Mak and Krim (1998) found that ts was independent of amplitude in both fluid and crystalline phases of Kr on Au. Tomassone et al. (1997) have used two additional techniques to determine ts. In both cases they used no thermostat (γα = 0). In the first method all atoms were given an initial velocity and the exponential decay of the mean velocity was used to determine ts. The second method made use of the fluctuation–dissipation theorem, and calculated ts from equilibrium velocity fluctuations. A coherent picture has emerged for the relation between ts and the damping and corrugation in Equations 20.10 and 20.11. In the limit where the corrugation vanishes, the substrate potential is translationally invariant and cannot exert any friction on the adsorbate. The value of Γ is then just equal to γ . In his original two-dimensional simulations Persson (1993a) used relatively large values of γ and reported that Γ was always proportional to γ . Later work by Persson and Nitzan (1996) showed that this proportionality only held for large γ . Cieplak et al. (1994), Smith et al. (1996), and Tomassone et al. (1997) considered the opposite limit, γ = 0 and found a nonzero Γph that reflected dissipation due to phonon excitations in the adsorbate film. Smith et al. (1996) found that including a Langevin damping along the direction of sliding produced a simple additive shift in Γ. This relation has been confirmed in extensive simulations by Liebsch et al. (1999). All of their data can be fit to the relation
( )
Γ = γ + Γph = γ + C U10
2
(20.12)
where the constant C depends on temperature, coverage, and other factors. Cieplak et al. (1994) and Smith et al. (1996) had previously shown that the damping increased quadratically with corrugation and developed a simple perturbation theory for the prefactor C in Equation 20.12. Their approach follows that of Sneddon et al. (1982) for charge-density waves, and of Sokoloff (1990) for friction between two semi-infinite incommensurate solids. It provides the simplest illustration of how dissipation occurs in the absence of metastability, and is directly relevant to studies of flow boundary conditions discussed in Section 20.5.1. The basic idea is that the adsorbed monolayer acts like an elastic sheet. The atoms are attracted to regions of low corrugation potential and repelled from regions of high potential. This produces density → → modulations ρ(Ql) in the adsorbed layer with wavevector Ql . When the substrate moves underneath the adsorbed layer, the density modulations attempt to follow the substrate potential. In the process, some of the energy stored in the modulations leaks out into other phonon modes of the layer due to anharmonicity. The energy dissipated to these other modes eventually flows into the substrate as heat. The rate of energy loss can be calculated to lowest order in a perturbation theory in the strength of the corrugation if the layer is fluid or incommensurate. Equating this to the average energy dissipation rate given by the friction relation, gives an expression for the phonon contribution to dissipation. The details of the calculation can be found in Smith et al. (1996). The final result is that the damping rate is proportional to the energy stored in the density modulations and to the rate of anharmonic
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coupling to other phonons. To lowest order in perturbation theory the energy is proportional to the square of the density modulation and thus the square of the corrugation as in Equation 20.12. The density → modulation is experimentally accessible by measuring the static structure factor S(Q)
r SQ
( ) ≡ ρ(Qr ) N
2
(20.13)
ad
where Nad is the number of adsorbed atoms. The rate of anharmonic coupling is the inverse of an effective lifetime for acoustic phonons, tphon, that could also be measured in scattering studies. One finds
Γph m =
( )
cS Q
1 N ad t phon →
(20.14)
where c is half of the number of symmetrically equivalent Ql . For an fcc crystal, c = 3 on the (111) surface and c = 2 on the (100) surface. In both cases the damping is independent of the direction of sliding, in agreement with simulations by Smith et al. (1996). Smith et al. performed a quantitative test of Equation 20.14 showing that values of S(Q) and tphon from equilibrium simulations were consistent with nonequilibrium determinations of Γph . The results of Liebsch et al. (1999) provide the first comparison of (111) and (100) surfaces. Data for the two surfaces collapse onto a single curve when divided by the values of c given above. Liebsch et al. (1999) noted that the barrier for motion between local minima in the substrate potential is much smaller for (111) than (100) surfaces and thus it might seem surprising that Γph is 50% higher on (111) surfaces. As they state, the fact that the corrugation is weak means that atoms sample all values of the potential and the energy barrier plays no special role. The major controversy between different theoretical groups concerns the magnitude of the substrate damping γ that should be included in fits to experimental systems. A given value of Γ can be obtained with an infinite number of different combinations of γ and corrugation (Robbins and Krim, 1998; Liebsch et al., 1999). Unfortunately both quantities are difficult to calculate and to measure. Persson (1991, 1998) has discussed the relation between electronic contributions to γ and changes in surface resistivity with coverage. The basic idea is that adsorbed atoms exert a drag on electrons that increases resistivity. When the adsorbed atoms slide, the same coupling produces a drag on them. The relation between the two quantities is somewhat more complicated in general because of disorder and changes in electron density due to the adsorbed layer. In fact, adsorbed layers can decrease the resistivity in certain cases. However, there is a qualitative agreement between changes in surface resistivity and the measured friction on adsorbates (Persson, 1998). Moreover, the observation of a drop in friction at the superconducting transition of lead substrates is clear evidence that electronic damping is significant in some systems (Dayo et al., 1998). There is general agreement that the electronic damping is relatively insensitive to nad, the number of adsorbed atoms per unit area or coverage. This is supported by experiments that show the variation of surface resistivity with coverage is small (Dayo and Krim, 1998). In contrast, the phonon friction varies dramatically with increasing density (Krim et al., 1988, 1990, 1991). This makes fits to measured values of friction as a function of coverage a sensitive test of the relative size of electron and phonon friction. Two groups have found that calculated values of Γ with γ = 0 can reproduce experiment. Calculations for Kr on Au by Cieplak et al. (1994) are compared to data from Krim et al. (1991) in Figure 20.4a. Figure 20.4b shows the comparison between fluctuation–dissipation simulations and experiments for Xe on Ag from Tomassone et al. (1997). In both cases there is a rapid rise in slip time with increasing coverage nad . At liquid nitrogen temperatures, krypton forms islands of uncompressed fluid for nad < 0.055 Å–2 and the slip time is relatively constant. As the coverage increases from 0.055 to 0.068 Å–2, the monolayer is compressed into an incommensurate crystal. Further increases in coverage lead to an increasingly dense crystal. The slip time increases by a factor of seven during the compression of the monolayer.
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FIGURE 20.4 Slip times vs. coverage for (a) Kr on Au (Cieplak et al., 1994, Krim et al., 1991) and (b) Xe on Ag (Tomassone et al., 1997). Calculated values are indicated by symbols, and experimental results by solid lines. Experimental data for three different runs are shown in (b). The dashed lines in (a) indicate theoretical values obtained by fitting experiments with 1/3, 1/2, or 9/10 (from bottom to top) of the friction at high coverage coming from electronic damping. (From Robbins, M.O. and Krim, J. (1998), Energy dissipation in interfacial friction, MRS Bull., 23(6), 23-26. With permission.)
For low coverages, Xe forms solid islands on Ag at T = 77.4 K. The slip time drops slightly with increasing coverage, presumably due to increasing island size (Tomassone et al., 1997). There is a sharp rise in slip time as the islands merge into a complete monolayer that is gradually compressed with increasing coverage. Figure 20.4 shows that the magnitude of the rise in ts varies from one experiment to the next. The calculated rise is consistent with the larger measured increases. The simulation results of the two groups can be extended to nonzero values of γ , using Equation 20.12. This would necessarily change the ratio between the slip times of the uncompressed and compressed layers. The situation is illustrated for Kr on Au in Figure 20.4a. The dashed lines were generated by fitting the damping of the compressed monolayer with different ratios of γ to Γph . As the importance of γ increases, the change in slip time during compression of the monolayer decreases substantially. The comparison between theory and experiment suggests that γ is likely to contribute less than 1/3 of the friction in the compressed monolayer, and thus less than 5% in the uncompressed fluid. The measured increase in slip time for Xe on Ag is smaller, and the variability noted in Figure 20.4b makes it harder to place bounds on γ . Tomassone et al. (1997) conclude that their results are consistent with no contribution from γ . When they included a value of γ suggested by Persson and Nitzan (1996) they still found that phonon friction provided 75% of the total. Persson and Nitzan had concluded that phonons contributed only 2% of the friction in the uncompressed monolayer. Liebsch et al. (1999) have reached an intermediate conclusion. They compared calculated results for different corrugations to a set of experimental data and chose the corrugation that matched the change
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in friction with coverage. They concluded that most of the damping at high coverages is due to γ and most of the damping at low coverages is due to phonons. However, the data they fitted had only a factor of 3 change with increasing coverage, and some of the data in Figure 20.4b changes by a factor of more than 5. Fitting to these sets would decrease their estimate of the size γ . The behavior of commensurate monolayers is very different than that of the incommensurate and fluid layers described so far. As expected from studies of one-dimensional models, simulations of commensurate monolayers show that they exhibit static friction. Unfortunately, no experimental results have been obtained because the friction is too high for the QCM technique to measure. In one of the earliest simulation studies, Persson (1993a) considered a two-dimensional model of Xe on the (100) surface of Ag. Depending on the corrugation strength, he found fluid, 2×2 commensurate, and incommensurate phases. He studied 1/Γ as the commensurate phase was approached by lowering temperature in the fluid phase, or decreasing coverage in the incommensurate phase. In both cases he found that 1/Γ went to zero at the boundary of the commensurate phase, implying that there was no flow in response to small forces. When the static friction is exceeded, the dynamics of adsorbed layers can be extremely complicated. In the model just described, Persson (1993a,b, 1995) found that sliding caused a transition from a commensurate crystal to a new phase. The velocity was zero until the static friction was exceeded. The system then transformed into a sliding fluid layer. Further increases in force caused a first order transition to the incommensurate structure that would be stable in the absence of any corrugation. The velocity in this phase was also what would be calculated for zero corrugation, F = γ v (dashed line). Decreasing the force led to a transition back to the fluid phase at essentially the same point. However, the layer did not return to the initial commensurate phase until the force dropped well below the static friction. The above hysteresis in the transition between commensurate and fluid states is qualitatively similar to that observed in the underdamped Tomlinson model or the mathematically equivalent case of a Josephson junction (McCumber, 1968). As in these cases, the magnitude of the damping affects the range of the hysteresis. The major difference is the origin of the hysteresis. In the Tomlinson model, hysteresis arises solely because the inertia of the moving system allows it to overcome potential barriers that a static system could not. This type of hysteresis would disappear at finite temperature due to thermal excitations (Braun et al., 1997a). In the adsorbed layers, the change in the physical state of the system has also changed the nature of the potential barriers. Similar sliding-induced phase transitions were observed earlier in experimental and simulation studies of shear in bulk crystals (Ackerson et al., 1986; Stevens et al., 1991, 1993) and in thin films (Gee et al., 1990; Thompson and Robbins, 1990b). The relation between such transitions and stick-slip motion is discussed in Section 20.6. Braun and collaborators have considered the transition from static to sliding states at coverages near to a commensurate value. They studied one- (Braun et al., 1997b; Paliy et al., 1997) and two- (Braun et al., 1997a,c) dimensional Frenkel–Kontorova models with different degrees of damping. If the corrugation is strong, the equilibrium state consists of locally commensurate regions separated by domain walls or kinks. The kinks are pinned because of the discreteness of the lattice, but this Peierls–Nabarro pinning potential is smaller than the substrate corrugation. In some cases there are different types of kinks with different pinning forces. The static friction corresponds to the force needed to initiate motion of the most weakly pinned kinks. As a kink moves through a region, atoms advance between adjacent local minima in the substrate potential. Thus the average velocity depends on both the kink velocity and the density of kinks. If the damping is strong, there may be a series of sudden transitions as the force increases. These may reflect depinning of more strongly pinned kinks, or creation of new kink–antikink pairs. At high enough velocity, the kinks become unstable, and a moving kink generates a cascade of new kink–antikink pairs that lead to faster and faster motion. Eventually the layer decouples from the substrate and there are no locally commensurate regions. As in Persson (1995), the high velocity state looks like an equilibrium state with zero corrugation. The reason is that the atoms move over the substrate so quickly that they cannot respond. Although this limiting behavior is interesting, it would only occur in experiments between flat crystals at velocities comparable to the speed of sound.
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FIGURE 20.5 The effect of crystalline alignment and lattice constant on commensurability is illustrated by projecting atoms from the bottom (filled circles) and top (open circles) surfaces into the plane of the walls. In A through C the two walls have the same structure and lattice constant but the top wall has been rotated by 0°, 8.2°, or 90°, respectively. In D the walls are aligned, but the lattice constant of the top wall has been reduced by a small amount. Only case A is commensurate. The other cases are incommensurate, and atoms from the two walls sample all possible relative positions with equal probability. (From He, G., Müser, M.H., and Robbins, M.O. (1999), Adsorbed layers and the origin of static friction, Science, 284, 1650-1652. With permission. © 1999 American Association for the Advancement of Science.)
20.4 Dry Sliding of Crystalline Surfaces The natural case of interest to tribologists is the sliding interface between two three-dimensional objects. In this section we consider sliding of bare surfaces. We first discuss general issues related to the effect of commensurability, focusing on strongly adhering surfaces such as clean metal surfaces. Then simulations of chemically passivated surfaces of practical interest are described. The section concludes with studies of friction, wear, and indentation in single-asperity contacts.
20.4.1 Effect of Commensurability The effect of commensurability in three-dimensional systems has been studied by Hirano and Shinjo (1990, 1993). They noted that even two identical surfaces are likely to be incommensurate. As illustrated in Figure 20.5, unless the crystalline surfaces are perfectly aligned, the periods will no longer match up. Thus one would expect almost all contacts between surfaces to be incommensurate. Hirano and Shinjo (1990) calculated the condition for static friction between high symmetry surfaces of fcc and bcc metals. Many of their results are consistent with the conclusions described for lower dimensions. They first showed that the static friction between incommensurate surfaces vanishes exactly if the solids are perfectly rigid. They then allowed the bottom layer of the top surface to relax in response to the atoms above and below. The relative strength of the interaction between the two surfaces and the stiffness of the top surface plays the same role as λ in the Tomlinson model. As the interaction becomes stronger, there is an Aubry transition to a finite static friction. This transition point was related to the condition for multistability of the least stable atom. To test whether realistic potentials would be strong enough to produce static friction between incommensurate surfaces, Hirano and Shinjo (1990) applied their theory to noble and transition metals. Contacts between various surface orientations of the same metal (i.e., (111) and (100) or (110) and (111)) were tested. In all cases the interactions were too weak to produce static friction. Shinjo and Hirano (1993) extended this line of work to dynamical simulations of sliding. They first considered the undamped Frenkel–Kontorova model with ideal springs between atoms. The top surface was given an initial velocity and the evolution of the system was followed. When the corrugation was small, the kinetic friction vanished, and the sliding distance increased linearly with time. This “superlubric” state disappeared above a threshold corrugation. Sliding stopped because of energy transfer from the center of mass motion into vibrations within the surface. The transition point depended on the initial
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velocity, since that set the amount of energy that needed to be converted into lattice vibrations. Note that the kinetic friction only vanishes in these simulations because atoms are connected by ideal harmonic springs (Smith et al., 1996). The damping due to energy transfer between internal vibrations (e.g., Equation 20.14) is zero because the phonon lifetime is infinite. More realistic anharmonic potentials always lead to an exponential damping of the velocity at long times. Simulations for two-dimensional surfaces were also described (Shinjo and Hirano, 1993; Hirano and Shinjo, 1993). Shinjo and Hirano noted that static friction is less likely in higher dimensions because of the ability of atoms to move around maxima in the substrate potential, as described in Section 20.3.4. A particularly interesting feature of their results is that the Aubry transition to finite static friction depends on the relative orientation of the surfaces (Hirano and Shinjo, 1993). Over an intermediate range of corrugations, the two surfaces slide freely in some alignments and are pinned in others. This extreme dependence on relative alignment has not been seen in experiments, but strong orientational variations in friction have been seen between mica surfaces (Hirano et al., 1991) and between a crystalline AFM tip and substrate (Hirano et al., 1997). Hirano and Shinjo’s conclusion that two flat, strongly adhering but incommensurate surfaces are likely to have zero static friction has been supported by two other studies. As described in more detail in Section 20.4.3, Sørensen et al. (1996) found that there was no static friction between a sufficiently large copper tip and an incommensurate copper substrate. Müser and Robbins (2000) studied a simple model system and found that interactions within the surfaces needed to be much smaller than the interactions between surfaces in order to get static friction. Müser and Robbins (2000) considered two identical but orientationally misaligned triangular surfaces similar to Figure 20.5C. Interactions within each surface were represented by coupling atoms to ideal lattice sites with a spring constant k. Atoms on opposing walls interacted through a Lennard–Jones potential. The walls were pushed together by an external force (~3 MPa) that was an order of magnitude less than the adhesive pressure from the LJ potential. The bottom wall was fixed, and the free diffusion of the top wall was followed at a low temperature (T = 0.1/kB). For k ≤ 10σ –2, the walls were pinned by static friction for all system sizes investigated. For k ≥ 25σ –2, Fs vanished, and the top wall diffused freely in the long time limit. By comparison, Lennard–Jones interactions between atoms within the walls would give rise to k ≈ 200σ –2. Hence, the adhesive interactions between atoms on different surfaces must be an order of magnitude stronger than the cohesive interactions within each surface in order to produce static friction between the flat, incommensurate walls that were considered. The results described above make it clear that static friction between ideal crystals can be expected to vanish in many cases. This raises the question of why static friction is observed so universally in experiments. One possibility is that roughness or chemical disorder pins the two surfaces together. Theoretical arguments indicate that disorder will always pin low-dimensional objects (e.g., Grüner, 1988). However, the same arguments show that the pinning between three-dimensional objects is exponentially weak (Caroli and Nozieres, 1996; Persson and Tosatti, 1996; Volmer and Natterman, 1997). This suggests that other effects, like mobile atoms between the surfaces, may play a key role in creating static friction. This idea is discussed in Section 20.5.3.
20.4.2 Chemically Passivated Surfaces The simulations just described aimed at revealing general aspects of friction. There is also a need to understand the tribological properties of specific materials on the nanoscale. Advances in the chemical vapor deposition of diamond hold promise for producing hard protective diamond coatings on a variety of materials. This motivated Harrison et al. (1992b) to perform molecular-dynamics simulations of atomic-scale friction between diamond surfaces. Two orientationally aligned, hydrogen-terminated diamond (111) surfaces were placed in sliding contact. Potentials based on the work of Brenner (1990) were used. As discussed in Section 20.7.3, these potentials have the ability to account for chemical reactions, but none occurred in the work described here. The lattices contained ten layers of carbon atoms and two layers of hydrogen atoms, and each layer
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consisted of 16 atoms. The three outermost layers were treated as rigid units, and were displaced relative to each other at constant sliding velocity and constant separation. The atoms of the next five layers were coupled to a thermostat. Energy dissipation mechanisms were investigated as a function of load, temperature, sliding velocity, and sliding direction. At low loads, the top wall moved almost rigidly over the potential from the bottom wall, and the average friction was nearly zero. At higher loads, colliding hydrogen atoms on opposing surfaces locked into a metastable state before suddenly slipping past each other. As in the Tomlinson model, energy was dissipated during these rapid pops. The kinetic friction was smaller for sliding along the grooves between nearest-neighbor hydrogen terminations, [110], than in the orthogonal direction, [112], because hydrogen atoms on different surfaces could remain farther apart. In a subsequent study, Harrison et al. (1993) investigated the effect of atomic-scale roughness by randomly replacing 1/8 of the hydrogen atoms on one surface with methyl, ethyl, or n-propyl groups. Changing hydrogen to methyl had little effect on the friction at a given load. However a new type of pop between metastable states was observed: Methyl groups rotated past each other in a rapid turnstile motion. Further increases in the length of the substituted molecules led to much smaller Fk at high loads. These molecules were flexible enough to be pushed into the grooves between hydrogen atoms on the opposing surface, reducing the number of collisions. Note that Harrison et al. (1992b, 1993) and Perry and Harrison (1996, 1997) might have obtained somewhat different trends using a different ensemble and/or incommensurate walls. Their case of constant separation and velocity corresponds to a system that is much stiffer than even the stiffest AFM. Because they used commensurate walls and constant velocity, the friction depended on the relative displacement of the lattices in the direction normal to the velocity. The constant separation also led to variations in normal load by up to an order of magnitude with time and lateral displacement. To account for these effects, Harrison et al. (1992b, 1993) and Perry and Harrison (1996, 1997) presented values for friction and load that were averaged over both time and lateral displacement. Studies of hydrogenterminated silicon surfaces (Robbins and Mountain) indicate that changing to a constant load and lateral force ensemble allows atoms to avoid each other more easily. Metastability sets in at higher loads than in a constant separation ensemble, the friction is lower, and variations with sliding direction are reduced. Glosli and co-workers have investigated the sliding motion between two ordered monolayers of longer alkane chains bound to commensurate walls (McClelland and Glosli, 1992; Glosli and McClelland, 1993; Ohzono et al., 1998). Each chain contained six monomers with fixed bond lengths. Next-nearest neighbors and third-nearest neighbors on the chain interacted via bond bending and torsional potentials, respectively. One end of each chain was harmonically coupled to a site on the 6 × 6 triangular lattices that made up each wall. All other interactions were Lennard–Jones (LJ) potentials between CH3 and CH2 groups (the united atom model of Section 20.2.1). The chain density was high enough that chains pointed away from the surface they were anchored to. A constant vertical separation of the walls was maintained, and the sliding velocity v was well below the sound velocity. Friction was studied as a function of T, v, and the ratio of the LJ interaction energy between endgroups on opposing surfaces, 1, to that within each surface, 0. Many results of these simulations correspond to the predictions of the Tomlinson model. Below a threshold value of 1/0 (0.4 at kBT/0 = 0.284), molecules moved smoothly, and the force decreased to zero with velocity. When the interfacial interactions became stronger than this threshold value, “plucking motion” due to rapid pops between metastable states was observed. Glosli and McClelland (1993) showed that at each pluck, mechanical energy was converted to kinetic energy that flowed away from the interface as heat. Ohzono et al. (1998) showed that a generalization of the Tomlinson model could quantitatively describe the sawtooth shape of the shear stress as a function of time. The instantaneous lateral force did not vanish in any of Glosli and McClelland’s (1993) or Ohzono et al.’s (1998) simulations. This shows that there was always a finite static friction, as expected between commensurate surfaces. For both weak (1/0 = 0.1) and strong (1/0 = 1.0) interfacial interactions, Glosli and McClelland (1993) observed an interesting maximum in the T-dependent friction force. The position of this maximum coincided with the rotational “melting” temperature TM where orientational order at the interface
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was lost. It is easy to understand that F drops at T > TM because thermal activation helps molecules move past each other. The increase in F with T at low T was attributed to increasing anharmonicity that allowed more of the plucking energy to be dissipated.
20.4.3 Single Asperity Contacts Engineering surfaces are usually rough, and friction is generated between contacting asperities on the two surfaces. These contacts typically have diameters of order a µm or more (e.g., Dieterich and Kilgore, 1996). This is much larger than atomic scales, and the models above may provide insight into the behavior within a representative portion of these contacts. However, it is important to determine how finite contact area and surface roughness affect friction. Studies of atomic-scale asperities can address these issues, and also provide direct models of the small contacts typical of AFM tips. Sørensen et al. performed simulations of sliding tip–surface and surface–surface contacts consisting of copper atoms (Sørensen et al., 1996). Flat, clean tips with (111) or (100) surfaces were brought into contact with corresponding crystalline substrates (Figure 20.6). The two exterior layers of tip and surface were treated as rigid units, and the dynamics of the remaining mobile layers was followed. Interatomic forces and energies were calculated using semiempirical potentials derived from effective medium theory (Jacobsen et al., 1987). At finite temperatures, the outer mobile layer of both tip and surface was coupled to a Langevin thermostat. Zero temperature simulations gave similar results. To explore the effects of commensurability, results for crystallographically aligned and misoriented tip–surface configurations were compared. In the commensurate Cu(111) case, Sørensen et al. observed atomic-scale stick-slip motion of the tip. The trajectory was of zigzag form, which could be related to jumps of the tip’s surface between fcc and hcp positions. Similar zigzag motion is seen in shear along (111) planes within bulk fcc solids (Stevens and Robbins, 1993). Detailed analysis of the slips showed that they occurred via a dislocation mechanism. Dislocations were nucleated at the corner of the interface, and the moved rapidly through the contact region. Adhesion led to a large static friction at zero load. The static friction per unit area, or critical yield stress, dropped from 3.0GPa to 2.3GPa as T increased from 0 to 300K. The kinetic friction increased linearly with load with a surprisingly small differential friction coefficient µ˜ k ∂Fk /∂L ≈ .03. In the load regime investigated, µ˜ k was independent of temperature and load. No velocity dependence was detectable up to sliding velocities of v = 5 m/s. At higher velocities, the friction decreased. Even though the interactions between the surfaces were identical to those within the surfaces, no wear was observed. This was attributed to the fact that (111) surfaces are the preferred slip planes in fcc metals. Adhesive wear was observed between a commensurate (100) tip and substrate (Figure 20.6). Sliding in the (011) direction at either constant height or constant load led to interplane sliding between (111) planes inside the tip. As shown in Figure 20.6, this plastic deformation led to wear of the tip, which left a trail of atoms in its wake. The total energy was an increasing function of sliding distance due to the extra surface area. The constant evolution of the tip kept the motion from being periodic, but the sawtooth variation of force with displacement that is characteristic of atomic-scale stick-slip was still observed. Nieminen et al. (1992) observed a different mechanism of plastic deformation in essentially the same geometry, but at higher velocities (100m/s vs. 5m/s) and with Morse potentials between Cu atoms. Sliding took place between (100) layers inside the tip. This led to a reduction of the tip by two layers that was described as the climb of two successive edge dislocations, under the action of the compressive load. Although wear covered more of the surface with material from the tip, the friction remained constant at constant normal load. The reason was that the portion of the surface where the tip advanced had a constant area. While the detailed mechanism of plastic mechanism is very different than in Sørensen et al. (1996), the main conclusions of both papers are similar: When two commensurate surfaces with strong interactions are slid against each other, wear occurs through formation of dislocations that nucleate at the corners of the moving interface. Sørensen et al. (1996) also examined the effect of incommensurability. An incommensurate Cu(111) system was obtained by rotating the tip by 16.1° about the axis perpendicular to the substrate. For a small tip (5 × 5 atoms) they observed an Aubry transition from smooth sliding with no static friction at
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FIGURE 20.6 Snapshots showing the evolution of a Cu(100) tip on a Cu(100) substrate during sliding to the left. (From Sørensen, M.R., Jacobsen, K.W., and Stoltze, P. (1996), Simulations of atomic-scale sliding friction, Phys. Rev. B, 53, 2101-2113. With permission. © 1996 American Physical Society.)
low loads, to atomic-scale stick-slip motion at larger loads. Further increases in load led to sliding within the tip and plastic deformation. Finite systems are never truly incommensurate, and pinning was found to occur at the corners of the contact, suggesting it was a finite-size effect. Larger tips (19 × 19) slid without static friction at all loads. Similar behavior was observed for incommensurate Cu(100) systems. These results confirm the conclusions of Hirano and Shinjo (1990) that even bare metal surfaces of the same material will not exhibit static friction if the surfaces are incommensurate. They also indicate that contact areas as small as a few hundred atoms are large enough to exhibit this effect. Many other tip–substrate simulations of bare metallic surfaces have been carried out. Mostly, these simulations concentrated on indentation, rather than on sliding or scraping (see Section 20.7.2). Among the indentation studies of metals are simulations of a Ni tip indenting Au(100) (Landman et al., 1990), a Ni tip coated with an epitaxial gold monolayer indenting Au(100) (Landman et al., 1992), an Au tip indenting Ni(100) (Landman and Luedtke, 1989, 1991), an Ir tip indenting a soft Pb substrate (RaffiTabar et al., 1992), and an Au tip indenting Pb(110) (Tomagnini et al., 1993). These simulations have been reviewed in detail within this series by Harrison et al. (1999).
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0
A
(a)
Fz(nN)
Au / Ni
K I
-10
G
E
C
J
-20
H B
F
-30 D
-47230
Ep(eV)
(b)
-47300
0
4
0
dhs (A)
8
FIGURE 20.7 Normal force Fz and potential energy Ep of an Au tip lowered toward a Ni(001) surface as a function of separation dhs, which is defined to be zero after the jump to contact has occurred. As indicated by arrows, upper lines were obtained by lowering the tip; lower lines are obtained by raising the tip. The points marked C, E, G, I, and K correspond to ordered configurations of the tip, each containing an additional layer. (Data from Landman, U. and Luedtke, W.D. (1991), Nanomechanics and dynamics of tip–substrate interactions, J. Vac. Sci. Technol. B, 9, 414-423.)
In general, plastic deformation occurs mainly in the softer of the two materials, typically Au or Pb in the cases above. Figure 20.7 shows the typical evolution of the normal force and potential energy during an indentation at high enough loads to produce plastic deformation (Landman and Luedtke, 1991). As the Au tip approaches the Ni surface (upper lines), the force remains nearly zero until a separation of about 1 Å. The force then becomes extremely attractive and there is a jump to contact (A). During the jump to contact, Au atoms in the tip displace by 2 Å within a short time span of 1 ps. This strongly adhesive contact produces reconstruction of the Au layers through the fifth layer of the tip. When the tip is withdrawn, a neck is pulled out of the substrate. The fluctuations in force seen in Figure 20.7 correspond to periodic increases in the number of layers of gold atoms in the neck. Nanoscale investigations of indentation, adhesion and fracture of nonmetallic diamond (111) surfaces have been carried out by Harrison et al. (1992a). A hydrogen-terminated diamond tip was brought into contact with a (111) surface that was either bare or hydrogen-terminated. The tip was constructed by removing atoms from a (111) crystal until it looked like an inverted pyramid with a flattened apex. The model for the surface was similar to that described in Section 20.4.2, but each layer contained 64 atoms. The indentation was performed by moving the rigid layers of the tip in steps of 0.15 Å. The system was then equilibrated before observables were calculated. Unlike the metal/metal systems (Figure 20.7), the diamond/diamond systems (Figure 20.8) did not show a pronounced jump to contact (Harrison et al., 1992a). This is because the adhesion between diamond (111) surfaces is quite small if at least one is hydrogen-terminated (Harrison et al., 1991). For effective normal loads up to 200 nN (i.e., small indentations), the diamond tip and surface deformed elastically and the force distance curve was reversible (Figure 20.8A). A slight increase to 250 nN, led to plastic deformation that produced hysteresis and steps in the force distance curve (Figure 20.8B) (Harrison et al., 1992a).
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FIGURE 20.8 Total potential energy of a hydrogen-terminated diamond–diamond system as a function of separation during indentation to a maximum load of (A) 200 nN or (B) 250 nN. Arrows indicate the direction of the motion. (Data from Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1992a), Nanoscale investigation of indentation, adhesion and fracture of diamond (111) surfaces, Surf. Sci., 271, 57-67.)
20.5 Lubricated Surfaces Hydrodynamics and elastohydrodynamics have been very successful in describing lubrication by microthick films (Dowson and Higginson, 1968). However, these continuum theories begin to break down as atomic structure becomes important. Experiments and simulations reveal a sequence of dramatic changes in the static and dynamic properties of fluid films as their thickness decreases from microns down to molecular scales. These changes have important implications for the function of boundary lubricants. This section describes simulations of these changes, beginning with changes in flow boundary conditions for relatively thick films, and concluding with simulations of submonolayer films and corrugated walls.
20.5.1 Flow Boundary Conditions Hydrodynamic theories of lubrication need to assume a boundary condition (BC) for the fluid velocity at solid surfaces. Macroscopic experiments are generally well-described by a “no-slip” BC; that is that the tangential component of the fluid velocity equals that of the solid at the surface. The one prominent exception is contact line motion, where an interface between two fluids moves along a solid surface. This motion would require an infinite force in hydrodynamic theory, unless slip occurred near the contact line (Huh and Scriven, 1971; Dussan, 1979). The experiments on adsorbed monolayers described in Section 20.3.5 suggest that slip may occur more generally on solid surfaces. As noted, the kinetic friction between the first monolayer and the substrate can be orders of magnitude lower than that between two layers in a fluid. The opposite deviation from no-slip BC is seen in some Surface Force Apparatus experiments — a layer of fluid molecules becomes immobilized at the solid wall (Chan and Horn, 1985; Israelachvili, 1986). In pioneering theoretical work, Maxwell (1867) calculated the deviation from a no-slip boundary condition for an ideal gas. He assumed that at each collision molecules were either specularly reflected or exchanged momentum to emerge with a velocity chosen at random from a thermal distribution. The calculated flow velocity at the wall was nonzero, and increased linearly with the velocity gradient near the wall. Taking z as the direction normal to the wall and u as the tangential component of the fluid velocity relative to the wall, Maxwell found
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∂u u z 0 = S ∂z z
( )
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where z0 is the position of the wall. The constant of proportionality, S, has units of length and is called the slip length. It represents the distance into the wall at which the velocity gradient would extrapolate to zero. Calculations with a fictitious wall at this position and no-slip boundary conditions would reproduce the flow in the region far from the wall. S also provides a measure of the kinetic friction per unit area between the wall and the adjacent fluid. The shear stress must be uniform in steady state, because any imbalance would lead to accelerations. Since the velocity gradient times the viscosity µ gives the stress in the fluid, the kinetic friction per unit area is u (z0)µ/S. Maxwell found that S increased linearly with the mean free path and that it also increased with the probability of specular reflection. Early simulations used mathematically flat walls and phenomenological reflection rules like those of Maxwell. For example, Hannon et al. (1988) found that the slip length was reduced to molecular scales in dense fluids. This is expected from Maxwell’s result, since the mean free path becomes comparable to an atomic separation at high densities. However work of this type does not address how the atomic structure of realistic walls is related to collision probabilities and whether Maxwell’s reflection rules are relevant. This issue was first addressed in simulations of moving contact lines where deviations from noslip boundary conditions have their most dramatic effects (Koplik et al., 1988, 1989; Thompson and Robbins, 1989). These papers found that even when no-slip boundary conditions held for single fluid flow, the large stresses near moving contact lines led to slip within a few molecular diameters of the contact line. They also began to address the relation between the flow boundary condition and structure induced in the fluid by the solid wall. The most widely studied type of order is layering in planes parallel to the wall. It is induced by the sharp cutoff in fluid density at the wall and the pair correlation function g(r) between fluid atoms (Abraham, 1978; Toxvaerd, 1981; Nordholm and Haymet, 1980; Snook and van Megen, 1980; Plischke and Henderson, 1986). An initial fluid layer forms at the preferred wall-fluid spacing. Additional fluid molecules tend to lie in a second layer, at the preferred fluid–fluid spacing. This layer induces a third, and so on. Some of the trends that are observed in the degree and extent of layering are illustrated in Figure 20.9 (Thompson and Robbins, 1990a). The fluid density is plotted as a function of the distance between walls for a model considered in almost all the studies of flow BCs described below. The fluid consists of spherical molecules interacting with a Lennard–Jones potential. They are confined by crystalline walls containing discrete atoms. In this case the walls were planar (001) surfaces of an fcc crystal. Wall and fluid atoms also interact with a Lennard–Jones potential, but with a different binding energy wf . The net adsorption potential from the walls (Equation 20.11) can be increased by raising wf or by increasing the density of the walls ρw so that more wall atoms attract the fluid. Figure 20.9 shows that both increases lead to increases in the height of the first density peak. The height also increases with the pressure in the fluid (Koplik et al., 1989; Barrat and Bocquet, 1999a) since that forces atoms into steeper regions of the adsorption potential. The height of subsequent density peaks decreases smoothly with distance from the wall, and only four or five well-defined layers are seen near each wall in Figure 20.9. The rate at which the density oscillations decay is determined by the decay length of structure in the bulk pair-correlation function of the fluid. Since all panels of Figure 20.9 have the same conditions in the bulk, the decay rate is the same. The adsorption potential only determines the initial height of the peaks. The pair correlation function usually decays over a few molecular diameters except under special conditions, such as near a critical point. For fluids composed of simple spherical molecules, the oscillations typically extend out to a distance of order 5 molecular diameters (Magda et al., 1985; Schoen et al., 1987; Thompson and Robbins, 1990a). For more complex systems containing fluids with chain or branched polymers, the oscillations are usually negligible beyond ~3 molecular diameters (Bitsanis and Hadziianou, 1990; Thompson et al., 1995; Gao et al., 1997a, 1997b). Some simulations with realistic
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FIGURE 20.9 Panels (a) through (c) show density as a functions of position z relative to two walls whose atoms are centered at z/σ = ±6.4. Values of wf are indicated. Solid lines are for equal wall an fluid densities, and dotted lines are for ρw = 2.52ρ. Squares in panels (d) through (f) show the average velocity in each layer as a function of z, and solid and dotted lines are fits through these values for low- and high-density walls, respectively. For these data the walls were moved in opposite directions at speed U = 1σ/tLJ. The dashed line in (e) represents the flow expected from hydrodynamics with a no-slip BC (S = 0). As shown in (f), the slope (dashed line) far from the walls is used to define S. For this case, the first two layers stick, and S is negative. (Panels d through f from Thompson and Robbins, 1990a).
potentials for alkanes show more pronounced layering near the wall because the molecules adopt a rodlike conformation in the first layer (Ribarsky et al., 1992; Xia et al., 1992). Solid surfaces also induce density modulations within the plane of the layers (Landman et al., 1989; Schoen et al., 1987, 1988, 1989; Thompson and Robbins, 1990a, 1990b). These correspond directly to the modulations induced in adsorbed layers by the corrugation potential (Section 20.3.5), and can also be quantified by the two-dimensional static structure factor at the shortest reciprocal lattice vector Q of the substrate. When normalized by the number of atoms in the layer, Nl, this becomes an intensive variable that would correspond to the Debye–Waller factor in a crystal. The maximum possible value, S(Q)/Nl = 1, corresponds to fixing all atoms exactly at crystalline lattice sites. In a strongly ordered case such as ρw = ρ in Figure 20.9c, the small oscillations about lattice sites in the first layer only decrease S(Q)/Nl to 0.71. This is well above the value of 0.6 that is typical of bulk three-dimensional solids at their melting point and indicates that the first layer has crystallized onto the wall. This was confirmed by computer simulations of diffusion and flow (Thompson and Robbins, 1990a). The values of S(Q)/Nl in the second and third layers are 0.31 and 0.07, respectively, and atoms in these layers exhibit typical fluid diffusion. There is some correlation between the factors that produce strong layering and those that produce strong in-plane modulations. For example, chain molecules have several conflicting length scales that tend to frustrate both layering and in-plane order (Thompson et al., 1995; Gao et al., 1997a,b; Koike and Yoneya, 1998, 1999). Both types of order also have a range that is determined by g(r) and a magnitude that decreases with decreasing wf /. However, the dependence of in-plane order on the density of substrate atoms is more complicated than for layering. When ρw = ρ, the fluid atoms can naturally sit on the sites of a commensurate lattice, and S(Q) is large. When the substrate density ρw is increased by a factor of 2.52, the fluid atoms no longer fit easily into the corrugation potential. The degree of induced
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in-plane order drops sharply, although the layering becomes stronger (Figure 20.9). Sufficiently strong adsorption potentials may eventually lead to crystalline order in the first layers, and stronger layering. However, this may actually increase slip, as shown below. Figure 20.9 also illustrates the range of flow boundary conditions that have been seen in many studies (Heinbuch and Fischer, 1989; Koplik et al., 1989; Thompson and Robbins, 1990a; Bocquet and Barrat, 1994; Mundy et al., 1996; Khare et al., 1996; Barrat and Bocquet, 1999a). Flow was imposed by displacing the walls in opposite directions along the x-axis with speed U (Thompson and Robbins, 1990a). The average velocity Vx was calculated within each of the layers defined by peaks in the density (Figure 20.9), and normalized by U. Away from the walls, all systems exhibit the characteristic Couette flow profile expected for Newtonian fluids. The value of Vx rises linearly with z, and the measured shear stress divided by ∂Vx /∂z equals the bulk viscosity. Deviations from this behavior occur within the first few layers, in the region where layering and in-plane order are strong. In some cases the fluid velocity remains substantially less than U, indicating slip occurs. In others, one or more layers move at the same velocity as the wall, indicating that they are stuck to it. Applying Maxwell’s definition of slip length (Equation 20.15) to these systems is complicated by uncertainty in where the plane of the solid surface z0 should be defined. The wall is atomically rough, and the fluid velocity cannot be evaluated too near to the wall because of the pronounced layering. In addition, the curvature evident in some flow profiles represents a varying local viscosity whose effect must be included in the boundary condition. One approach is to fit the linear flow profile in the central region and extrapolate to the value of z* where the velocity would reach +U (Figure 20.9f). The slip length can then be defined as S = z* – ztw where ztw is the height of the top wall atoms. This is equivalent to applying Maxwell’s definition (Equation 20.15) to the extrapolated flow profile at ztw . The no-slip condition corresponds to a flow profile that extrapolates to the wall velocity at ztw as illustrated by the dashed line in Figure 20.9e. Slip produces a smaller velocity gradient and a positive value of S. Stuck layers lead to a larger velocity gradient and a negative value of S. The dependence of slip length on many parameters has been studied. All the results are consistent with a decrease in slip as the in-plane order increases. Numerical results for ρw = ρ and wf = 0.4 (Figure 20.9d) are very close to the no-slip condition. Increasing wf leads to stuck layers (Koplik et al., 1988, 1989; Thompson and Robbins, 1989, 1990a; Heinbuch and Fischer, 1989), and decreasing wf can produce large slip lengths (Thompson and Robbins, 1990a; Barrat and Bocquet, 1999a). Increasing pressure (Koplik et al., 1989; Barrat and Bocquet, 1999a) or decreasing temperature (Heinbuch and Fischer, 1989; Thompson and Robbins, 1990a) increases structure in g(r) and leads to less slip. These changes could also be attributed to increases in layering. However, increasing the wall density ρw from ρ to 2.52 ρ increases slip in Figure 20.9. This correlates with the drop in in-plane order, while the layering actually increases. Changes in in-plane order also explain the pronounced increase in slip when wf / is increased to 4 in the case of dense walls (Figure 20.9f). The first layer of fluid atoms becomes crystallized with a very different density than the bulk fluid. It becomes the “wall” that produces order in the second layer, and it gives an adsorption potential characterized by rather than wf . The observed slip is consistent with that for dense walls displaced to the position of the first layer and interacting with . Thompson and Robbins (1990a) found that all of their results for S collapsed onto a universal curve when plotted against the structure factor S(Q)/Nl. When one or more layers crystallized onto the wall, the same collapse could be applied as long as the effective wall position was shifted by a layer and the Q for the outer wall layer was used. The success of this collapse at small S(Q)/Nl can be understood from the perturbation theory for the kinetic friction on adsorbed monolayers (Equation 20.14). The slip length is determined by the friction between the outermost fluid layer and the wall. This depends only on S(Q)/Nl and the phonon lifetime for acoustic waves. The latter changes relatively little over the temperature range considered, and hence S is a single-valued function of S(Q). The perturbation theory breaks down at large S(Q), but the success of the collapse indicates that there is still a one-to-one correspondence between it and the friction.
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In a recent paper, Barrat and Bocquet (1999b) have derived an expression relating S and S(Q) that is equivalent to Equation 20.14. However, in describing their numerical results* they emphasize the correlation between increased slip and decreased wetting (Barrat and Bocquet, 1999a,b). In general the wetting properties of fluids are determined by the adsorption term of the substrate potential U0 (Equation 20.11). This correlates well with the degree of layering, but has little to do with in-plane order. In the limit of a perfectly structureless wall one may have complete wetting and yet there is also complete slip. The relation between wetting and slip is very much like that between adhesion and friction. All other things being equal, a greater force of attraction increases the effect of corrugation in the potential and increases the friction. However, there is no one-to-one correspondence between them. In earlier work, Bocquet and Barrat (1993, 1994) provided a less ambiguous resolution to the definition of the slip length than that of Thompson and Robbins (1990a). They noted that the shear rate in the central region of Couette flow depended only on the sum of the wall position and the slip length. Thus one must make a somewhat arbitrary choice of wall position to fix the slip length. However, if one also fits the flow profile for Poiseuille flow, unique values of slip length and the effective distance between the walls h are obtained (Barrat and Bocquet, 1999a). Bocquet and Barrat (1993, 1994) also suggested and implemented an elegant approach for determining both S and h using equilibrium simulations and the fluctuation–dissipation theorem. This is one of the first applications of the fluctuation–dissipation theorem to boundary conditions. It opens up the possibility of calculating flow boundary conditions directly from equilibrium thermodynamics, and Bocquet and Barrat (1994) were able to derive Kubo relations for z0 and S. Analytic results for these relations are not possible in general, but, as noted above, in the limit of weak interactions they give an expression equivalent to Equation 20.14 for the drag on the wall (Barrat and Bocquet, 1999b). Mundy et al. (1996) have proposed a nonequilibrium simulation method for calculating these quantities directly. In all of the work described above, care was taken to ensure that the slip boundary condition was independent of the wall velocity. Thus both the bulk of the fluid and the interfacial region were in the linear response regime where the fluctuation–dissipation theorem holds. This linear regime usually extends to very high shear rates (>1010s–1 for spherical molecules). However, Thompson and Troian (1997) found that under some conditions the interfacial region exhibits nonlinear behavior at much lower shear rates than the bulk fluid. They also found a universal form for the deviation from a linear stress/strain-rate relationship at the interface. The fundamental origin for this nonlinearity is that there is a maximum stress that the substrate can apply to the fluid. This stress roughly corresponds to the maximum of the force from the corrugation potential times the areal density of fluid atoms. The stress/velocity relation at the interface starts out linearly and then flattens as the maximum stress is approached. The shear rate in the fluid saturates at the value corresponding to the maximum interfacial shear stress and the amount of slip at the wall grows arbitrarily large with increasing wall velocity. Similar behavior was observed for more realistic potentials by Koike and Yoneya (1998, 1999).
20.5.2 Phase Transitions and Viscosity Changes in Molecularly Thin Films One of the surprising features of Figure 20.9 is that the viscosity remains the same even in regions near the wall where there is pronounced layering. Any change in viscosity would produce a change in the velocity gradient since the stress is constant. However, the flow profiles in panel (d) remain linear throughout the cell. The profile for the dense walls in panel (f) is linear up to the last layer, which has crystallized onto the wall. From Figure 20.9 it is apparent that density oscillations by at least a factor of 7 can be accommodated without a viscosity change. The interplay between layering and viscosity was studied in detail by Bitsanis et al. (1987), although their use of artificial flow reservoirs kept them from addressing flow BCs. They were able to fit detailed *They considered almost the same parameter range as Thompson and Robbins (1990a), but at a lower temperature (kBT/ = 0.7 vs. 1.1 or 1.4) and at a single wall density (ρ = ρw).
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flow profiles using only the bulk viscosity evaluated at the average local density. This average was taken over a distance of order σ that smeared out the rapid density modulations associated with layering, but not slower variations due to the adsorption potential of the walls or an applied external potential. In subsequent work, Bitsanis et al. (1990) examined the change in viscosity with film thickness. They found that results for film thicknesses h > 4σ could be fit using the bulk viscosity for the average density. However, as h decreased below 4σ, the viscosity diverged much more rapidly than any model based on bulk viscosity could explain. These observations were consistent with experiments on nanometer-thick films of a wide variety of small molecules. These experiments used the surface force apparatus (SFA), which measures film thickness with Å resolution using optical interferometry. Films were confined between atomically flat mica sheets at a fixed normal load, and sheared with a steady (Gee et al., 1990) or oscillating (Granick, 1992) velocity. Layering in molecularly thin films gave rise to oscillations in the energy, normal force, and effective viscosity (Horn and Israelachvili, 1981; Israelachvili, 1991; Georges et al., 1993) as the film thickness decreased. The period of these oscillations was a characteristic molecular diameter. As the film thickness decreased below seven to ten molecular diameters, the effective viscosity increased dramatically (Gee et al., 1990; Granick, 1992; Klein and Kumacheva, 1995). Most films of one to three molecular layers exhibited a yield stress characteristic of solid-like behavior, even though the molecules formed a simple Newtonian fluid in the bulk. Pioneering grand canonical Monte Carlo simulations by Schoen et al. (1987) showed crystallization of spherical molecules between commensurate walls separated by up to six molecular diameters. However, the crystal was only stable when the thickness was near to an integral number of crystalline layers. At intermediate h, the film transformed to a fluid state. Later work (Schoen et al., 1988, 1989) showed that translating the walls could also destabilize the crystalline phase and lead to periodic melting and freezing transitions as a function of displacement. However, these simulations were carried out at equilibrium and did not directly address the observed changes in viscosity. SFA experiments cannot determine the flow profile within the film, and this introduces ambiguity in the meaning of the viscosity values that are reported. Results are typically expressed as an effective viscosity . . µeff τs /γeff where τs is the measured shear stress and γeff v/h represents the effective shear rate that would be present if the no-slip condition held and walls were displaced at relative velocity v. Deviations from the no-slip condition might cause µeff to differ from the bulk viscosity by an order of magnitude. However, they could not explain the observed changes of µeff by more than five orders of magnitude or the even more dramatic changes by 10 to 12 orders of magnitude in the characteristic viscoelastic relaxation time determined from the shear rate dependence of µeff (Gee et al., 1990; Hu et al., 1991). Thompson et al. (1992) found very similar changes in viscosity and relaxation time in simulations of a simple bead-spring model of linear molecules (Kremer and Grest, 1990). Some of their results for the effective viscosity vs. effective shear rate are shown in Figure 20.10. In (a), the normal pressure P⊥ was fixed and the number of atomic layers, ml, was decreased from eight to two. In (b), the film was confined by increasing the pressure at fixed particle number. Both methods of increasing confinement lead to dramatic changes in the viscosity and relaxation time. The shear rate dependence of µeff in Figure 20.10 has the same form as in experiment (Hu et al., 1991). A Newtonian regime with constant viscosity µ0 is seen at the lowest shear rates in all but the uppermost . curve in each panel. Above a characteristic shear rate γc the viscosity begins to decrease rapidly. This shear thinning is typical of viscoelastic media and indicates that molecular rearrangements are too slow to . . respond to the sliding walls at γeff > γc . As a result, the structure of the fluid begins to change in a way that facilitates shear. A characteristic time for molecular rearrangements in the film can be associated . with 1/ γc . Increasing confinement by decreasing ml or increasing pressure, increases the Newtonian viscosity and relaxation time. For the uppermost curve in each panel, the relaxation time is longer than the longest simulation runs (>106 time steps) and the viscosity continues to increase at the lowest accessible shear rates. Note that the ranges of shear rate covered in experiment and simulations differ by orders of magnitude. However, the scaling discussed below suggests that the same behavior may be operating in both.
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FIGURE 20.10 Plots of µeff vs. γeff at (a) fixed normal pressure P⊥ = 4σ –3 and varying numbers of layers ml , and (b) fixed ml = 4 and varying P⊥ (Thompson et al., 1992). Dashed lines have slope –2/3. Panel (c) shows that this and other data can be collapsed onto a universal response function (Robbins and Baljon, 2000). Results are for decreasing temperature in bulk systems (circles), increasing normal pressure at a fixed number of fluid layers (triangles), or decreasing film thickness at fixed pressure with two different sets of interaction potentials (squares and crosses). The dotted line has a slope of –0.69. (Panels a and b from Thompson et al., 1992; panel c from Robbins and Baljon, 2000.)
For the parameters used in Figure 20.10, studies of the flow profile in four layer films showed that one layer of molecules was stuck to each wall and shear occurred in the middle layers. Other parameter sets produced varying degrees of slip at the wall/film interface, yet the viscoelastic response curves showed the same behavior (Thompson et al., 1995). Later work by Baljon and Robbins (1996, 1997) shows that lowering the temperature through the bulk glass transition also produces similar changes in viscoelastic response. This suggests that the same glass transition is being produced by changes in thickness, pressure or temperature. Following the analogy to bulk glass transitions, Thompson et al. (1993, 1995) have shown that changes . in equilibrium diffusion constant and γc can be fit to a free volume theory. Both vanish as exp(–h0 /(h – hc )) where hc is the film thickness at the glass transition. Moreover, at h < hc , they found behavior characteristic of a solid. Films showed a yield stress and no measurable diffusion. When forced to slide, shear localized . at the wall/film interface and µeff dropped as 1/ γ, implying that the shear stress is independent of sliding velocity. This is just the usual form of kinetic friction between solids. The close relation between bulk glass transitions and those induced by confinement can perhaps best be illustrated by using a generalization of time–temperature scaling. In bulk systems it is often possible to collapse the viscoelastic response onto a universal curve by dividing the viscosity by the Newtonian . value, µ0, and dividing the shear rate by the characteristic rate, γc . Demirel and Granick (1996a) found that this approach could be used to collapse data for the real and imaginary parts of the elastic moduli of confined films at different thicknesses. Figure 20.10c shows that simulation results for the viscosity of thin films can also be collapsed using Demirel and Granick’s approach (Robbins and Baljon, 2000). Data for different thicknesses, normal pressures, and interaction parameters taken from all parameters considered by Thompson et al. (1992, 1995) collapse onto a universal curve. Also shown on the plot (circles) are data for different temperatures that were obtained for longer chains in films that are thick enough
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to exhibit bulk behavior (Baljon and Robbins, 1996, 1997). The data fit well onto the same curve, providing a strong indication that a similar glass transition occurs whether thickness, normal pressure, or temperature is varied. The high shear rate region of the universal curve shown in Figure 20.10c exhibits power law shear . thinning: µeff ∝ γ –x with a best fit exponent x = 0.69 ± .02. In SFA experiments, Hu et al. (1991) found shear thinning of many molecules was consistent with x near 2/3. However, the response of some fluids followed power laws closer to 0.5 as they became less confined (Carson et al., 1992). One possible explanation for this is that these measurements fall onto the crossover region of a universal curve like Figure 20.10c. The apparent exponent obtained from the slope of this log-log plot varies from 0 to 2/3 as µeff drops from µ0 to about µ0 /30. Many of the experiments that found smaller exponents were only able to observe a drop in µ by an order of magnitude. As confinement was increased, and a larger drop in viscosity was observed, the exponent increased toward 2/3. It would be interesting to attempt a collapse of experimental data on a curve like Figure 20.10c to test this hypothesis. Another possibility is that the shear thinning exponent depends on some detail of the molecular structure. Chain length alone does not appear to affect the exponent, since results for chains of length 16 and 6 are combined in Figure 20.10c. Manias et al. (1996) found that changing the geometry from linear to branched also has little effect on shear thinning. In most simulations of simple spherical molecules, crystallization occurs before the viscosity can rise substantially above the bulk value. However, Hu et al. (1996) have found a set of conditions where spherical molecules follow a –2/3 slope over two decades in shear rate. Stevens et al. (1997) have performed simulations of confined films of hexadecane using a detailed model of the molecular structure and interactions. They found that films crystallized before the viscosity rose much above bulk values. This prevented them from seeing large power law scaling regimes, but the apparent exponents were consistently less than those for bead spring models. It is not clear whether the origin of this discrepancy is the inability to approach the glass transition, or whether structural changes under shear lead to different behavior. Hexadecane molecules have some tendency to adopt a linear configuration and become aligned with the flow. This effect is not present in simpler bead-spring models. Shear thinning typically reflects changes in structure that facilitate shear. Experiments and the above simulations were done at constant normal load. In bead-spring models the dominant structural change is a dilation of the film that creates more room for molecules to slide past each other. The dilations are relatively small, but have been detected in some experiments (Dhinojwala and Granick). When simulations are done at constant wall spacing, the shear-thinning exponent drops to x = 0.5 (Thompson et al., 1992, 1995; Manias et al., 1996). Kröger et al. (1993) find the same exponent in bulk simulations of these molecules at constant volume, indicating that a universal curve like that in Figure 20.10c might also be constructed for constant volume instead of constant pressure. Several analytic models have been developed to explain the power law behavior observed in experiment and simulations. All the models find an exponent of 2/3 in certain limits. However, they start from very different sets of assumptions, and it is not clear if any of these correspond to the simulations and experiments. Two of the models yield an exponent of 2/3 for constant film thickness (Rabin and Hersht, 1993; Urbakh et al., 1995) where simulations give x = 1/2. Urbakh et al. (1995) also find that the exponent depends on the velocity profile, while simulations do not. The final model (DeGennes) is based on scaling results for the stretching of polymers under shear. While it may be appropriate for thick films, it cannot describe the behavior of films which exhibit plug-like flow. It remains to be seen if the 2/3 exponent has a single explanation or arises from different mechanisms in different limits. The results described in this section have interesting implications for the function of macroscopic bearings. Some bearings may operate in the boundary lubrication regime where the separation between asperities decreases to molecular dimensions. The dramatic increase in viscosity due to confinement may play a key role in preventing squeeze-out of the lubricant and direct contact between asperities. Although the glassy lubricant layer would not have a low frictional force, the yield stress would be lower than that for asperities in contact. More important, the amount of wear would be greatly reduced by the glassy film. Studies of confined films may help to determine what factors control a lubricant’s ability to form
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a robust protective layer at atomic scales. As we now discuss, they may also help explain the pervasive observation of static friction.
20.5.3 Submonolayer Lubrication Physisorbed molecules, such as the short hydrocarbon chains considered above, can be expected to sit on any surface exposed to atmospheric conditions. Even in ultra-high vacuum, special surface treatments are needed to remove strongly physisorbed species from surfaces. Recent work shows that the presence of these physisorbed molecules qualitatively alters the tribological behavior between two incommensurate walls (He et al., 1999; Müser and Robbins, 2000) or between two disordered walls (Müser et al., 2000). As noted in Section 20.4, the static friction is expected to vanish between most incommensurate surfaces. Under similar conditions, the static friction between most amorphous, but flat, surfaces vanishes in the thermodynamic limit (Müser et al., 2000). In both cases, the reason is that the density modulations on two bare surfaces cannot lock into phase with each other unless the surfaces are unrealistically compliant. However, a submonolayer of molecules that form no strong covalent bonds with the walls can simultaneously lock to the density modulations of both walls. This gives rise to a finite static friction for all surface symmetries: commensurate, incommensurate, and amorphous (Müser et al., 2000). A series of simulations were performed in order to elucidate the influence of such “between-sorbed” particles on tribological properties (He et al., 1999; Müser and Robbins, 2000). A layer of spherical or short “bead-spring” (Kremer and Grest, 1990) molecules was confined between two fcc (111) surfaces. The walls had the orientations and lattice spacing shown in Figure 20.5, and results are labeled by the letters in this figure. Wall atoms were bound to their lattice sites with harmonic springs as in the Tomlinson model. The interactions between atoms on opposing walls, as well as fluid–fluid and fluid–wall interactions, had the LJ form. Unless noted, the potential parameters for all three interactions were the same. The static friction per unit contact area, or yield stress τs, was determined from the lateral force needed to initiate steady sliding of the surfaces at fixed pressure. When there were no molecules between the surfaces, there was no static friction unless the surfaces were commensurate. As illustrated in Figure 20.11a, introducing a thin film led to static friction in all cases. Moreover, all incommensurate* cases (B through D) showed nearly the same static friction, and τs was independent of the direction of sliding relative to crystalline axes (e.g., along x or y for case D). Most experiments do not control the crystallographic orientation of the walls relative to each other or to the sliding direction, yet the friction is fairly reproducible. This is hard to understand based on models of bare surfaces which show dramatic variations in friction with orientation (Hirano and Shinjo, 1993; Sørensen et al., 1996; Robbins and Smith, 1996). Figure 20.11 shows that a thin layer of molecules eliminates most of this variation. In addition, the friction is insensitive to chain length, coverage, and other variables that are not well controlled in experiments (He et al., 1999). The kinetic friction at low velocities is typically 15 to 25% lower than the static friction in all cases (He and Robbins). Of course experiments do observe changes in friction with surface material. The main factor that changed τs in this simple model was the ratio of the characteristic length for wall–fluid interactions σwf to the nearest-neighbor spacing on the walls, d. As shown in Figure 20.11b, increasing σwf /d decreases the friction. The reason is that larger fluid atoms are less able to penetrate between wall atoms and thus feel less surface corrugation. Using amorphous, but flat, walls produced a somewhat larger static friction. Note that τs rises linearly with the imposed pressure in all cases shown in Figure 20.11. This provides a microscopic basis for the phenomenological explanation of Amontons’ laws that was proposed by Bowden and Tabor (1986). The total static friction is given by the integral of the yield stress over areas of the surface that are in molecular contact. If τs = τ0 + αP, then the total force is Fs = αL + τ0Areal where – L is the load and Areal is the total contact area. The coefficient of friction is then µs = α + τ0 /P *Although perfectly incommensurate walls are not consistent with periodic boundary conditions the effect of residual commensurability was shown to be negligible (Müser and Robbins, 2000).
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FIGURE 20.11 Yield stress as a function of normal pressure for various systems. In (a) the letters correspond to the labels of wall geometries in Figure 20.5, and system D was slid in both x and y directions. Panel (b) shows the effect of increasing the wall/fluid coupling wf , decreasing or increasing the wall/fluid length σwf , and increasing the nearest-neighbor spacing d on the friction of system B. The unit of pressure and stress, σ –3 corresponds to about 30 to 50 MPa. (From He, G., Müser, M.H., and Robbins, M.O. (1999), Adsorbed layers and the origin of static friction, Science, 284, 1650-1652. With permission. © 1999 American Association for the Advancement of Science.) –
where P ≡ L/Areal is the mean contact pressure. Amontons’ laws say that µs is independent of load and – the apparent area of the surfaces in contact. This condition is satisfied if τ0 is small or if P is constant. The latter condition is expected to hold for both ideal elastic (Greenwood and Williamson, 1966) and plastic (Bowden and Tabor, 1986) surfaces. The above results suggest that adsorbed molecules and other “third-bodies” may prove key to understanding macroscopic friction measurements. It will be interesting to extend these studies to more realistic molecular potentials and to rough surfaces. To date, realistic potentials have only been used between commensurate surfaces, and we now describe some of this work. The effect of small molecules injected between two sliding hydrogen-terminated (111) diamond surfaces on kinetic friction was investigated by Perry and Harrison (1996, 1997). The setup of the simulation was similar to the one described in Section 20.4.2. Two sets of simulations were performed. In one set, bare surfaces were considered. In another set, either two methane (CH4) molecules, one ethane (C2H6) molecule, or one isobutane (CH3)3CH molecule was introduced into the interface between the sliding diamond surfaces. Experiments show that the friction between diamond surfaces goes down as similar molecules are formed in the contact due to wear (Hayward, 1991). Perry and Harrison found that these third bodies also reduced the calculated frictional force between commensurate diamond surfaces. The reduction of the frictional force with respect to the bare hydrogenterminated case was most pronounced for the smallest molecule, methane. The molecular motions were analyzed in detail to determine how dissipation occurred. Methane produced less friction because it was small enough to roll in grooves between the terminal hydrogen atoms without collisions. The larger ethane and isobutane collided frequently. As for the simple bead-spring model described above, the friction increased roughly linearly with load. Indeed, Perry and Harrison’s data for all third bodies correspond to α ≈ 0.1, which is close to that for
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commensurate surfaces in Figure 20.11a. One may expect that the friction would decrease if incommensurate walls were used. However, the rolling motion of methane might be prevented in such geometries. Perry and Harrison (1996, 1997) compared their results to earlier simulations (Harrison et al., 1993) where hydrogen terminations on one of the two surfaces were replaced by chemisorbed methyl (–CH3), ethyl (–C2H5), or n-propyl (–C3H7) groups (Section 20.4.2). The chemisorbed molecules were seen to give a considerably smaller reduction of the friction with respect to the physisorbed molecules. Perry and Harrison note that the chemisorbed molecules have fewer degrees of freedom, and so are less able to avoid collisions that dissipate energy.
20.5.4 Corrugated Surfaces The presence of roughness can be expected to alter the behavior of lubricants, particularly when the mean film thickness is comparable to the surface roughness. Gao et al. (1995, 1996) and Landman et al. (1996) used molecular dynamics to investigate this thin film limit. Hexadecane (n-C16H34) was confined between two gold substrates exposing only (111) surfaces (Figure 20.12). The two outer layers of the substrates were completely rigid and were displaced laterally with a constant relative velocity of 10 to 20m/s at constant separation. The asperities on both walls were modeled by flat-topped pyramidal ridges with initial heights of 4 to 6 atomic layers. The united atom model (Section 20.2.1) was used for the interactions within the film, and the embedded atom method was used for Au–Au interactions. All other interactions were modeled with suitable 6-12 Lennard–Jones potentials. The alkane molecules and the gold atoms in the asperities were treated dynamically using the Verlet algorithm. The temperature was kept constant at T = 350 K by rescaling the velocities every 50th time step. Simulations were done in three different regimes, which can be categorized according to the separation ∆haa that the outer surfaces of the asperities would have if they were placed on top of one another without deforming elastically or plastically. The cases were (1) large separation of the asperities ∆haa = 17.5 Å, (2) a near-overlap regime with ∆haa = 4.6 Å, and (3) an asperity-overlap regime with ∆haa = –6.7 Å. Some selected atomic and molecular configurations obtained in a slice through the near-overlap system are shown in Figure 20.12. In all cases, the initial separation of the walls was chosen such that the normal pressure was zero for large lateral asperity separations. One common feature of all simulations was the formation of lubricant layers between the asperities as they approached each other (Figure 20.12). This is just like the layering observed in equilibrium between flat walls (e.g., Figure 20.9), but the layers form dynamically. The number of layers decreased with decreasing lateral separation between the asperities, and the lateral force showed strong oscillations as successive layers were pushed out. This behavior is shown in Figure 20.13 for the near-overlap case. For large separation, case (1), four lubricant layers remained at the point of closest approach between the asperities, and no plastic deformation occurred. In case (2), severe plastic deformation occurred after local shear and normal stresses exceeded a limiting value of close to 4 GPa. This deformation led to direct intermetallic junctions, which were absent in simulations under identical conditions but with no lubricant molecules in the interface. The junctions eventually broke upon continued sliding, resulting in transfer of some metal atoms between the asperities. In this and the overlap case (3), great densification and pressurization of the lubricant in the asperity region occurred, accompanied by a significant increase in the effective viscosity in that region. For the near-overlap system, local rupture of the film in the region between the departing asperities was seen. A nanoscale cavitated zone of length scale ≈ 30 Å was observed that persisted for about 100 ps. The Deborah number D was studied as well. D can be defined as the ratio of the relaxation time of the fluid to the time of passage of the fluid through a characteristic distance l. D ≈ 0.25 was observed for the near-overlap system, which corresponds to a viscoelastic response of the lubricant. The increased confinement in the overlap system, resulted in D = 2.5, which can be associated with highly viscoelastic behavior, perhaps even elastoplastic or waxy behavior. Gao et al. (1996) observed extreme pressures of 150 GPa in the near-overlap case when the asperities were treated as rigid units. Allowing only the asperities to deform reduced the peak pressure by almost
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FIGURE 20.12 Atomic and molecular configurations obtained in a slice through the near-overlap system at times 156, 250, 308, 351, 400, 461, 614, and 766 ps. Time increases from top to bottom in the left column and then in the right. (From Gao, J., Luedtke, W.D., and Landman, U. (1995), Nano-elastohydrodynamics: structure, dynamics, and flow in non-uniform lubricated junctions, Science, 270, 605608. With permission. © 1995 American Association for the Advancement of Science.)
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FIGURE 20.13 Total force in driving direction fx and normal to the walls fz plotted vs. time. Solid lines correspond to the net force between lubricant and gold surface, dashed lines to direct forces between opposing gold surfaces. The numbers in panel A give the number of layers between the asperity ridges. (From Gao, J., Luedtke, W.D., and Landman, U. (1995), Nano-elastohydrodynamics: structure, dynamics, and flow in non-uniform lubricated junctions, Science, 270, 605-608. With permission. © 1995 American Association for the Advancement of Science.)
two orders of magnitude. However, even these residual pressures are still quite large, and one may expect that a full treatment of the elastic response of the substrates might lead to further dramatic decreases in pressure and damage. Tutein et al. (1999) have recently compared friction between monolayers of anchored hydrocarbon molecules and rigid or flexible nanotubes. Studies of elasticity effects in larger asperities confining films that are several molecules thick are currently in progress (Persson and Ballone, 2000).
20.6 Stick-Slip Dynamics The dynamics of sliding systems can be very complex and depend on many factors, including the types of metastable states in the system, the times needed to transform between states, and the mechanical properties of the device that imposes the stress. At high rates or stresses, systems usually slide smoothly. At low rates the motion often becomes intermittent, with the system alternately sticking and slipping forward (Rabinowicz, 1965; Bowden and Tabor, 1986). Everyday examples of such stick-slip motion include the squeak of hinges and the music of violins. The alternation between stuck and sliding states of the system reflects changes in the way energy is stored. While the system is stuck, elastic energy is pumped into the system by the driving device. When the system slips, this elastic energy is released into kinetic energy, and eventually dissipated as heat. The system then sticks once more, begins to store elastic energy, and the process continues. Both elastic and kinetic energy can be stored in all the mechanical elements that drive the system. The whole coupled assembly must be included in any analysis of the dynamics. The simplest type of intermittent motion is the atomic-scale stick-slip that occurs in the multistable regime (λ > 1) of the Tomlinson model (see Figure 20.2b). Energy is stored in the springs while atoms are trapped in a metastable state, and converted to kinetic energy as they pop to the next metastable state. This phenomenon is quite general and has been observed in several of the simulations of wearless
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FIGURE 20.14 Time profiles of the (a) frictional force per unit area F/A, (b) displacement of the top wall, xW , (c) wall spacing h, and (d) Debye–Waller factor S(Q)/N during stick-slip motion of spherical molecules that form two crystalline layers in the static state. Note that the system dilates (c) during each slip event. The coinciding drop in Debye–Waller factor shows a dramatic decrease from a typical crystalline value to a characteristic value for a fluid. (From Robbins, M.O. and Baljon, A.R.C. (2000), Response of thin oligomer films to steady and transient shear, in Microstructure and Microtribology of Polymer Surfaces, Tsukruk, V.V. and Wahl, K.J. (Eds.), American Chemical Society, Washington, DC, 91. With permission. © 2000 American Chemical Society.)
friction described in Section 20.4 as well as in the motion of atomic force microscope tips (e.g., Carpick and Salmeron, 1997). In these cases, motion involves a simple ratcheting over the surface potential through a regular series of hops between neighboring metastable states. The slip distance is determined entirely by the periodicity of the surface potential. Confined films and adsorbed layers have a much richer potential energy landscape due to their many internal degrees of freedom. One consequence is that stickslip motion between neighboring metastable states can involve microslips by distances much less than a lattice constant (Thompson and Robbins, 1990b; Baljon and Robbins, 1997; Robbins and Baljon, 2000). An example is seen at t/tLJ = 620 in Figure 20.14b. Such microslips involve atomic-scale rearrangements within a small fraction of the system. Closely related microslips have been studied in granular media (Nasuno et al., 1997; Veje et al., 1999) and foams (Gopal and Durian, 1995). Many examples of stick-slip involve a rather different type of motion that can lead to intermittency and chaos (Ruina, 1983; Heslot et al., 1994). Instead of jumping between neighboring metastable states, the system slips for very long distances before sticking. For example, Gee et al. (1990) and Yoshizawa and Israelachvili (1993), observed slip distances of many microns in their studies of confined films. This distance is much larger than any characteristic periodicity in the potential, and varied with velocity, load, and the mass and stiffness of the SFA. The fact that the SFA does not stick after moving by a lattice constant indicates that sliding has changed the state of the system in some manner, so that it can continue sliding even at forces less than the yield stress. Phenomenological theories of stick-slip often introduce an unspecified “state” variable to model the evolving properties of the system (Dieterich, 1979; Ruina, 1983; Batista and Carlson, 1998).
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One simple property that depends on history is the amount of stored kinetic energy. This can provide enough inertia to carry a system over potential energy barriers even when the stress is below the yield stress. Inertia is readily included in the Tomlinson model and has been thoroughly studied in the mathematically equivalent case of an underdamped Josephson junction (McCumber, 1968). One finds a hysteretic response function where static and moving steady-states coexist over a range of force between Fmin and the static friction Fs . There is a minimum stable steady-state velocity vmin corresponding to Fmin. At lower velocities, the only steady state is linearly unstable because ∂v/∂F < 0 — pulling harder slows the system. It is well-established that this type of instability can lead to stick-slip motion (Bowden and Tabor, 1986; Rabinowicz, 1965). If the top wall of the Tomlinson model is pulled at an average velocity less than vmin by a sufficiently compliant system, it will exhibit large-scale stick-slip motion. Confined films have structural degrees of freedom that can change during sliding, and this provides an alternative mechanism for stick-slip motion (Thompson and Robbins, 1990b). Some of these structural changes are illustrated in Figure 20.14, which shows stick-slip motion of a two-layer film of simple spherical molecules. The bounding walls were held together by a constant normal load. A lateral force was applied to the top wall through a spring k attached to a stage that moved with fixed velocity v in the x-direction. The equilibrium configuration of the film at v = 0 is a commensurate crystal that resists shear. Thus at small times, the top wall remains pinned at xW = 0. The force grows linearly with time, F = kv, as the stage advances ahead of the wall. When F exceeds Fs , the wall slips forward. The force drops . rapidly because the slip velocity xW is much greater than v. When the force drops sufficiently, the film recrystallizes, the wall stops, and the force begins to rise once more. One structural change that occurs during each slip event is dilation by about 10% (Figure 20.14c). Dhinojwala and Granick have recently confirmed that dilation occurs during slip in SFA experiments. The increased volume makes it easier for atoms to slide past each other, and is part of the reason that the sliding friction is lower than Fs. The system may be able to keep sliding in this dilated state as long as it takes more time for the volume to contract than for the wall to advance by a lattice constant. Dilation of this type plays a crucial role in the yield, flow, and stick-slip dynamics of granular media (Thompson and Grest, 1991; Jaeger et al., 1996; Nasuno et al., 1997). The degree of crystallinity also changes during sliding. As in Sections 20.3.5 and 20.5.1, deviations from an ideal crystalline structure can be quantified by the Debye–Waller factor S(Q)/N (Figure 20.14d), where Q is one of the shortest reciprocal lattice vectors of the wall and N is the total number of atoms in the film. When the system is stuck, S(Q)/N has a large value that is characteristic of a three-dimensional crystal. During each slip event, S(Q)/N drops dramatically. The minimum values are characteristic of simple fluids that would show a no-slip boundary condition (Section 20.5.1). The atoms also exhibit rapid diffusion that is characteristic of a fluid. The periodic melting and freezing transitions that occur during stick-slip are induced by shear and not by the negligible changes in temperature. Shear-melting transitions at constant temperature have been observed in both theoretical and experimental studies of bulk colloidal systems (Ackerson et al., 1986; Stevens and Robbins, 1993). While the above simulations of confined films used a fixed number of particles, Lupowski and van Swol (1991) found equivalent results at fixed chemical potential. Very similar behavior has been observed in simulations of sand (Thompson and Grest, 1991), chain molecules (Robbins and Baljon, 2000), and incommensurate or amorphous walls (Thompson and Robbins, 1990b). These systems transform between glassy and fluid states during stick-slip motion. As in equilibrium, the structural differences between glass and fluid states are small. However, there are strong changes in the self-diffusion and other dynamic properties when the film goes from the static glassy to sliding fluid state. In the cases just described, the entire film transforms to a new state, and shear occurs throughout the film. Another type of behavior is also observed. In some systems shear is confined to a single plane — either a wall/film interface, or a plane within the film (Baljon and Robbins, 1997; Robbins and Baljon, 2000). There is always some dilation at the shear plane to facilitate sliding. In some cases there is also in-plane ordering of the film to enable it to slide more easily over the wall. This ordering remains after sliding stops and provides a mechanism for the long-term memory seen in some experiments (Gee et al., 1990; Yoshizawa and Israelachvili, 1993; Demirel and Granick, 1996b). Buldum and Ciraci (1997) found
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stick-slip motion due to periodic structural transformations in the bottom layers of a pyramidal Ni(111) tip sliding on an incommensurate Cu(110) surface. The dynamics of the transitions between stuck and sliding states are crucial in determining the range of velocities where stick-slip motion is observed, the shape of the stick-slip events, and whether stickslip disappears in a continuous or discontinuous manner. Current models are limited to energy balance arguments (Robbins and Thompson, 1991; Thompson and Robbins, 1993) or phenomenological models of the nucleation and growth of “frozen” regions (Yoshizawa and Israelachvili, 1993; Heslot et al., 1994; Batista and Carlson, 1998; Persson, 1998). Microscopic models and detailed experimental data on the sticking and unsticking process are still lacking. Rozman et al. (1996, 1997, 1998) have taken an interesting approach to unraveling this problem. They have performed detailed studies of stick-slip in a simple model of a single incommensurate chain between two walls. This model reproduces much of the complex dynamics seen in experiments and helps to elucidate what can be learned about the nature of structural changes within a contact using only the measured macroscopic dynamics.
20.7 Strongly Irreversible Tribological Processes Sliding at high pressures, high rates, or for long times can produce more dramatic changes in the structure and even chemistry of the sliding interface than those discussed so far. In this concluding section, we describe some of the more strongly irreversible tribological processes that have been studied with simulations. These include grain boundary formation and mixing, machining, and tribochemical reactions.
20.7.1 Plastic Deformation For ductile materials, plastic deformation is likely to occur throughout a region of some characteristic width about the nominal sliding interface (Rigney and Hammerberg, 1998). Sliding-induced mixing of material from the two surfaces and sliding-induced grain boundaries are two of the experimentally observed processes that lack microscopic theoretical explanations. In an attempt to get insight into the microscopic dynamics of these phenomena, Hammerberg et al. (1998) performed large-scale simulations of a two-dimensional model for copper. The simulation cell contained 256 × 256 Cu atoms that were subject to a constant normal pressure P⊥. Two reservoir regions at the upper and lower boundaries of the cell were constrained to move at opposite lateral velocities ±up . The initial interface was midway between the two reservoirs. The friction was measured at P⊥ = 30 GPa as a function of the relative sliding velocity v. Different behavior was seen at velocities above and below about 10% of the speed of transverse sound. At low velocities, the interface welded together and the system formed a single work-hardened object. Sliding took place at the artificial boundary with one of the reservoirs. At higher velocities the friction was smaller, and decreased steadily with increasing velocity. In this regime, intense plastic deformation occurred at the interface. Hammerberg et al. (1998) found that the early time-dynamics of the interfacial structure could be reproduced with a Frenkel–Kontorova model. As time increased, the interface was unstable to the formation of a fine-grained polycrystalline microstructure, which coarsened with distance away from the interface as a function of time. Associated with this microstructure was the mixing of material across the interface.
20.7.2 Wear Large scale, two- and three-dimensional molecular dynamics simulations of the indentation and scraping of metal surfaces were carried out by Belak and Stowers (1992). Their simulations show that tribological properties are strongly affected by wear or the generation of debris. A blunted diamond tip was first indented into a copper surface and then pulled over the surface. The tip was treated as a rigid unit. Interactions within the metal were modeled with an embedded atom potential, and Lennard–Jones potentials were used between C and Cu atoms.
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In the two-dimensional simulation, indentation was performed at a constant velocity of about 1 m/s. The contact followed Hertzian behavior up to a load L ≈ 2.7 nN and an indentation of about 3.5 Cu layers. The surface then yielded on one side of the tip, through the creation of a single dislocation edge on one of the easy slip planes. The load needed to continue indenting decreased slightly until an indentation of about five layers. Then the load began to rise again as stress built up on the side that had not yet yielded. After an indentation of about six layers, this side yielded, and further indentation could be achieved without a considerable increase in load. The hardness, defined as the ratio of load to contact length (area), slightly decreased with increasing load once plastic deformation had occurred. After indentation was completed, the diamond tip was slid parallel to the original Cu surface. The work to scrape off material was determined as a function of the tip radius. A power law dependence was found at small tip radii that did not correspond to experimental findings for microscraping. However, at large tip radii, the power law approached the experimental value. Belak and Stowers found that this change in power law was due to a change in the mechanism of plastic deformation from intragranular to intergranular plastic deformation. In the three-dimensional simulations, the substrate contained as many as 36 layers or 72,576 atoms. Hence long-range elastic deformations were included. The surface yielded plastically after an indentation of only 1.5 layers, through the creation of a small dislocation loop. The accompanying release of load was much bigger than in two dimensions. Further indentation to about 6.5 layers produced several of these loading–unloading events. When the tip was pulled out of the substrate, both elastic and plastic recovery was observed. Surprisingly, the plastic deformation in the three-dimensional studies was confined to a region within a few lattice spacings of the tip, while dislocations spread several hundred lattice spacings in the two-dimensional simulations. Belak and Stowers concluded that dislocations were not a very efficient mechanism for accommodating strain at the nanometer length scale in three dimensions. When the tip was slid laterally at v = 100 m/s during indentation, the friction or “cutting” force fluctuated around zero as long as the substrate did not yield (Figure 20.15). This nearly frictionless sliding can be attributed to the fact that the surfaces were incommensurate and the adhesive force was too small to induce locking. Once plastic deformation occurred, the cutting force increased dramatically. Figure 20.15 shows that the lateral and normal forces are comparable, implying a friction coefficient of about one. This large value was expected for cutting by a conical asperity with small adhesive forces (Suh, 1986).
20.7.3 Tribochemistry The extreme thermomechanical conditions in sliding contacts can induce chemical reactions. This interaction of chemistry and friction is known as tribochemistry (Rabinowicz, 1965). Tribochemistry plays important roles in many processes, the best known example being the generation of fire through sliding friction. Other examples include the formation of wear debris and adhesive junctions, which can have a major impact on friction. Harrison and Brenner (1994) were the first to observe tribochemical reactions involving strong covalent bonds in molecular dynamics simulations. A key ingredient of their work is the use of reactive potentials that allow breaking and formation of chemical bonds. Two (111) diamond surfaces terminated with hydrogen atoms were brought into contact as in Section 20.4.2. In some simulations, two hydrogen atoms from the upper surface were removed, and replaced with ethyl (–CH2CH3) groups. The simulations were performed for 30 ps at an average normal pressure of about 33 GPa. The sliding velocity was 100 m/s along either the [110] or [112] crystallographic direction. Sliding did not produce any chemical changes in the hydrogen-terminated surfaces. However, wear and chemical reactions were observed when ethyl groups were present. For sliding along the [112] direction, wear was initiated by the shearing of hydrogen atoms from the tails of the ethyl groups. The resulting free hydrogen atoms reacted at the interface by combining with an existing radical site or abstracting a hydrogen from either a surface or a radical. If no combination with a free hydrogen atom occurred, the reactive radicals left on the tails of the chemisorbed molecules abstracted a hydrogen from
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FIGURE 20.15 Normal (bottom) and lateral (top) force on a three-dimensional, pyramidal diamond tip on a copper surface as a function of time. No plastic flow was reported up to 1000 time steps. The indentation stopped at about five layers after 2000 time steps (From Belak, J. and Stowers, I.F. (1992), The indentation and scraping of a metal surface: a molecular dynamics study, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, 511. With permission. © 1992 Kluwer Academic Publishers.)
the opposing surface, or they formed a chemical bond with existing radicals on the opposing surface (Figure 20.16). In the latter case, the two surface bonds sometimes broke simultaneously, leaving molecular wear debris trapped at the interface. It is interesting to note that the wear debris, in the form of an ethylene molecule CH2CH2, did not undergo another chemical reaction for the remainder of the simulation. Similarly, methane CH4, ethane C2H6, and isobutane (CH3)3CH were not seen to undergo chemical reactions when introduced into a similar interface composed of hydrogen-terminated (111) diamond surfaces (Section 20.5.3) at normal loads up to about 0.8 nN/atom (Perry and Harrison, 1996; 1997; Harrison and Perry, 1998). At higher loads, only ethane reacted. In some cases a hydrogen broke off of the ethane. The resulting free H atom then reacted with an H atom from one surface to make an H2 molecule. The remaining C2H5 could then form a carbon–carbon bond with that surface when dragged close enough to the nascent radical site. The C–C bond of the ethane was also reported to break occasionally. However, due to the proximity of the nascent methyl radicals and the absence of additional reactive species, the bond always reformed. Sliding along the (110) direction produced other types of reaction between surfaces with ethyl terminations. In some cases, tails of the ethyl groups became caught between hydrogen atoms on the lower surface. Continued sliding sheared the entire tail from the rest of the ethyl group, leaving a chemisorbed CH 2• group and a free CH 3• species. The latter group could form a bond with an existing radical site, it could shear a hydrogen from a chemisorbed ethyl group, or it could be recombined with the chemisorbed CH 2• .
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FIGURE 20.16 Adhesion of the two diamond surfaces via the formation of a carbon–carbon bond. The C atoms forming the bond originated from an ethyl group chemisorbed on the upper diamond surface. (From Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry: an atomic scale view of the wear of diamond, J. Am. Chem. Soc., 116, 10399-10402. With permission. © 1994 American Chemical Society.)
Acknowledgment Support from the National Science Foundation through Grants No. DMR-9634131 and DMR-0083286 and from the German–Israeli Project Cooperation, “Novel Tribological Strategies from the Nano to Meso Scales,’’ is gratefully acknowledged. We thank Gang He, Marek Cieplak, Miguel Kiwi, Jean-Louis Barrat, Patricia McGuiggan, and especially Judith Harrison for providing comments on the text. We also thank Jean-Louis Barrat for help in improving the density oscillation data in Figure 20.9, and Peter A. Thompson for many useful conversations and for his role in creating Figure 20.14.
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Barrat, J.-L. and Bocquet, L. (1999a), Large slip effect at a nonwetting fluid-solid interface, Phys. Rev. Lett., 82, 4671-4674. Barrat, J.-L. and Bocquet, L. (1999b), Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface, Faraday Discuss., 112, 1-9. Batista, A.A. and Carlson, J.M. (1998), Bifurcations from steady sliding to stick slip in boundary lubrication, Phys. Rev. E, 57, 4986-4996. Belak, J. and Stowers, I.F. (1992), The indentation and scraping of a metal surface: a molecular dynamics study, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, 511. Binder, K. (1995), Monte Carlo and Molecular Dynamics Simulations in Polymer Science, Oxford University Press, New York. Bitsanis, I. and Hadziioannou, G. (1990), Molecular dynamics simulations of the structure and dynamics of confined polymer melts, J. Chem. Phys., 92, 3827-3847. Bitsanis, I., Magda, J.J., Tirrell, M., and Davis, H.T. (1987), Molecular dynamics of flow in micropores, J. Chem. Phys., 87, 1733-1750. Bitsanis, I., Somers, S.A., Davis, H.T., and Tirrell, M. (1990), Microscopic dynamics of flow in molecularly narrow pores, J. Chem. Phys., 93, 3427-3431. Bocquet, L. and Barrat, J.-L. (1993), Hydrodynamic boundary conditions and correlation functions of confined fluids, Phys. Rev. Lett., 70, 2726-2729. Bocquet, L. and Barrat, J.-L. (1994), Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids, Phys. Rev. E, 49, 3079-3092. Bowden, F.P. and Tabor, D. (1986), The Friction and Lubrication of Solids, Clarendon Press, Oxford, U.K. Braun, O.M., Bishop, A.R., and Röder, J. (1997b), Hysteresis in the underdamped driven Frenkel–Kontorova model, Phys. Rev. Lett., 79, 3692-3695. Braun, O.M., Dauxois, T., Paliy, M.V., and Peyrard, M. (1997a), Dynamical transitions in correlated driven diffusion in a periodic potential, Phys. Rev. Lett., 78, 1295-1298. Braun, O.M., Dauxois, T., Paliy, M.V., and Peyrard, M. (1997c), Nonlinear mobility of the generalized Frenkel–Kontorova model, Phys. Rev. E, 55, 3598-3612. Brenner, D.W. (1990), Empirical potentials for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B, 42, 9458-9471. Bruch, L.W., Cole, M.W., and Zaremba, E. (1997). Physical Adsorption: Forces and Phenomena, Oxford, New York. Buldum, A. and Ciraci, S. (1997), Interplay between stick-slip motion and structural phase transitions in dry sliding friction, Phys. Rev. B, 55, 12892-12895. Caroli, C. and Nozieres, P. (1996), Dry friction as a hysteretic elastic response, in Physics of Sliding Friction, Persson, B.N.J. and Tosatti, E. (Eds.), Kluwer, Dordrecht, 27. Carpick, R.W. and Salmeron, M. (1997), Scratching the surface: fundamental investigations of tribology with atomic force microscopy, Chem. Rev., 97, 1163-1194. Carson, G.A., Hu, H., and Granick, S. (1992), Molecular tribology of fluid lubrication: shear thinning, Tribol. Trans., 35, 405-410. Chan, D.Y.C. and Horn, R.G. (1985), The drainage of thin liquid films between solid surfaces, J. Chem. Phys., 83, 5311-5324. Cieplak, M., Smith, E.D., and Robbins, M.O. (1994), Molecular origins of friction: the force on adsorbed layers, Science, 265, 1209-1212. Daw, M.S. and Baskes, M.I. (1984), Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B, 29, 6443-6453. Dayo, A., Alnasrallay, W., and Krim, J. (1998), Superconductivity-dependent sliding friction, Phys. Rev. Lett., 80, 1690-1693. De Gennes, P.G., unpublished. Demirel, A.L. and Granick, S. (1996a), Glasslike transition of a confined simple fluid, Phys. Rev. Lett., 77, 2261-2264.
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III Solid Tribological Materials Bharat Bhushan The Ohio State University
Ali Erdemir Argonne National Laboratory
Kenneth Holmberg VTT Manufacturing Technology 21 Metals and Ceramics Koji Kato and Koshi Adachi ......................................................... 771 Introduction • Pure Metals • Soft Metals and Soft Bearing Alloys • Copper-based Alloys • Cast Irons • Steels • Ceramics • Special Alloys • Comparisons Between Metals and Ceramics • Concluding Remarks
22 Solid Lubricants and Self-Lubricating Films
Ali Erdemir ............................................ 787
Introduction • Classification of Solid Lubricants • Lubrication Mechanisms of Layered Solids • High-Temperature Solid Lubricants • Self-Lubricating Composites • Soft Metals • Polymers • Summary and Future Directions
23 Tribological Properties of Metallic and Ceramic Coatings Kenneth Holmberg and Allan Matthews .............................................................................................................. 827 Introduction • Tribology of Coated Surfaces • Macromechanical Interactions: Hardness and Geometry • Micromechanical Interactions: Material Response • Material Removal and Change Interactions: Debris and Surface Layers • Multicomponent Coatings • Concluding Remarks
24 Tribology of Diamond, Diamond-Like Carbon, and Related Films Ali Erdemir and Christophe Donnet ......................................................................................................... 871 Introduction • Diamond Films • Diamond-like Carbon (DLC) Films • Other Related Films • Summary and Future Direction
25 Self-assembled Monolayers for Controlling Hydrophobicity and/or Friction and Wear Bharat Bhushan ................................................................................................ 909 Introduction • A Primer to Organic Chemistry • Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains • Tribological Properties • Conclusions
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26 Mechanical and Tribological Requirements and Evaluation of Coating Composites Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund ..... 931 Introduction • Design of Tribological Coatings • Design of Coated Components • Evaluation of Coating Composites • Visions and Conclusions
D
uring the industrial revolution, more importantly in the past 50 years, solid tribological materials and coatings have continued to play important roles in many engineering areas, mainly because mechanical systems rely on them for high performance, durability, and efficiency. In particular, the development of advanced coatings with low friction and high wear resistance has become a leading research activity in tribology and is now called “surface engineering.” The increasingly multifunctional needs and more stringent operating conditions envisioned for future mechanical systems will certainly make solid tribological materials and advanced coatings far more important in the near future. To meet the increasing tribological needs of these advanced systems, researchers are constantly exploring new materials and developing novel coatings. As a result, great strides have been made in recent years in the fabrication and diverse utilization of new tribomaterials and coatings that are capable of satisfying the multifunctional needs of more advanced mechanical systems. Major developments in solid tribological materials include coatings with superlow friction and extreme hardness, providing very long wear life to sliding or rolling contact surfaces. Some of these novel coatings are now available for key industrial applications with high thermal/mechanical loadings and harsh tribological environments. Overall, the state-of-the-art in advanced material and coating technologies has now reached the point at which a tribocomponent can be fabricated from bulk ceramics or coated with a hard ceramic film to provide improved tribological performance and durability. Progress in solid lubricants and self-lubricating films (such as transition-metal dichalcogenides, diamond, diamond-like carbon, and composites) has led to significant improvements in the wear lives of bearings, gears, seals, and cutting tools that typically operate under severe tribological conditions. With recent advances in fabrication methods, the cost of these new tribomaterials and coatings has become very affordable. This section focuses on the latest developments in solid tribological materials and coatings. Readers will find a wealth of information, ranging from mechanistic modeling and understanding of the friction and wear behavior of various materials and coatings to how, where, and when these materials and coatings can be used to solve a challenging tribological problem. Chapters in this section cover all aspects of the metals, alloys, ceramics, composites, solid lubricants, and novel materials and coatings developed, tested, and used for tribological purposes. Each chapter has been written by leading experts in the field. Tribological studies on traditional metals and alloys have continued at a steady pace during the last decade. The major research emphasis has been on further understanding the friction and wear mechanisms of these materials. During the same period, interest in ceramics and composites has increased tremendously, and these materials have become the major focus of tribological research, mainly because ceramics and composites offer perhaps the best prospect for realization of some new and advanced tribosystems (e.g., heat engines, high-speed bearings, high-temperature seals, and cutting tools). Obviously, ceramics and composites combine a wide range of attractive mechanical, thermal, and chemical properties that are not available in most metals and alloys. In-depth studies on ceramics have led to a better understanding of their friction and wear mechanisms, and this understanding has been used to design and develop a new generation of tribocomponents whose performance and durability far exceed that of traditional metal- and alloy-based tribocomponents. Koji Kato and Koshi Adachi provide an overview of the recent developments in the tribology of traditional metals and alloys, emphasizing the importance of advanced ceramic materials for demanding tribological applications (Chapter 21). Solid lubricants and self-lubricating films have been around for a long time and are used largely to combat friction and wear under severe tribological conditions in which liquid or grease lubricants cannot function. In recent years, great strides have been made in the processing, fabrication, and diverse utilization of solid lubricants. Chapter 22 by Ali Erdemir is devoted to solid lubricants and self-lubricating films. Recent progress in understanding the lubricating mechanisms of both traditional and new solid
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lubricants is presented. The state-of-the-art in advanced solid lubrication methods and application practices is discussed, with particular emphasis on synthesis and applications of solid lubricant films on tribological surfaces through advanced surface-engineering processes. Recent advances in surface engineering have led to the development of novel metallic and ceramic coatings that can meet the increasingly multifunctional needs of advanced mechanical systems. These advances were the result of dedicated research directed toward the modeling and mechanistic understanding of the tribological properties of these coatings. A chapter by Kenneth Holmberg and Allan Matthews is devoted to the recent progress made in tribological coatings and in understanding the friction and wear mechanisms of these coatings (Chapter 23). Special emphasis was placed on multilayered, compound, or gradient coatings used under both the dry and lubricated conditions. Diamond, diamond-like carbon, and other related coatings (such as carbon nitride and cubic boron nitride) are some of the hardest tribomaterials known and offer perhaps some of the lowest friction and wear coefficients under dry sliding conditions. A widespread application of diamond-like carbon coating is magnetic rigid disks and metal evaporated tapes used in magnetic storage devices. Chapter 24 by Ali Erdemir and Christophe Donnet provides an in-depth review of the recent progress made in the synthesis, tribology, and industrial uses of these coatings. Emphasis is on the state-of-the-art in understanding their friction and wear mechanisms, as well as on the uses of these coatings for diverse tribological applications. Referring to the structural and fundamental tribological knowledge gained during past decades, the authors stress the importance of surface physical and chemical effects on the friction and wear properties of these materials. Tribological issues associated with metal cutting and contact sliding are also addressed in detail. Self-assembled monolayers are organized, dense molecular-scale layers of long-chain organic molecules that are being developed for lubrication purposes. These films are synthesized such that the functional groups of the organic molecules chemisorb onto a solid surface, which results in the spontaneous formation of robust, highly ordered and oriented, dense monolayers chemically attached to the surface. The films with nonpolar end groups on the free end result in films with hydrophobic properties. These films have been successfully tried in the laboratory for microdevice applications. A chapter by Bharat Bhushan provides an in-depth review of the state-of-the-art of the science and technology of selfassembled monolayers (Chapter 25). Recent developments in deposition technologies have provided the flexibility needed for design and development of multifunctional coatings that afford low friction and long wear life under demanding tribological conditions. These exotic coatings with nanocomposite structures or multilayer architectures are quite tough and are resistant to cracking during sliding contact. They also work extremely well in aggressive environments. Chapter 26 by Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund focuses on tribological needs and design considerations for such multifunctional films. Important tribological issues addressed in this chapter include premature coating delamination, coating deformation, brittle fracture and spalling, abrasive scratching, material pickup or transfer, and coating wear due to abrasive, erosive, and tribochemical interactions. New techniques used in the mechanical, structural, and tribological characterization of multifunctional coatings are also discussed. Several examples are provided to highlight the effectiveness of these coatings in metal-cutting and -forming operations and other tribological fields. The use of thin surface coatings (such as diamond, diamond-like carbon, molybdenum disulfide, nitrides, carbides, and their composites and dopants) has substantially improved the tribological performance of rolling, rotating, or sliding mechanical parts and components in recent years. Specifically, friction and wear of sliding contact interfaces has decreased by orders of magnitude. Compared to any material combinations used in the past, some of these new coatings were able to reduce friction coefficients to as low as 0.001, and wear rates to levels that in some cases are almost impossible to measure. A key reason for these remarkable developments is that researchers are now better equipped and have a deeper understanding of the fundamental mechanisms that control friction and wear. A second factor is that the thin coatings are now applied on solid surfaces that are in perfect compliance with the chemical,
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mechanical, and thermal properties of the coating materials themselves, thus ensuring that premature failures due to thermal, mechanical, or chemical incompatibility are nonexistent. In short, while recent advances in new tribomaterials and coatings have been phenomenal, there remain several key challenges for future tribologists and surface engineers. In this field, there are almost unlimited numbers of material combinations, surface parameters, and application conditions that one can manipulate or use to his/her advantage in a tribological application to achieve better performance and longer durability. Pioneers and dedicated researchers in the tribology field have already made great strides in this respect, despite the very intricate and multifaceted nature of the field. Today, as we embrace a new millennium with great hopes and expectations, we should look forward to opening up new possibilities for a highly industrialized and modern society. To move forward in this direction, we must develop new surface-engineered materials and coatings, together with novel design concepts in tribology. Specifically, we need to devise new ways to build composite structures or systems that are based on multilayers or nanocomposites. We should also tailor or model the surface tribological properties of these structures and coating materials to achieve even higher performance and durability in future tribosystems. The tools (analytical, computational, and intellectual) for the successful execution of this task are now available. The greatest challenge for the future seems to be the formulation of new ideas and concepts and the integration of the vast knowledge base accumulated over the years in advanced tribological research and development. From the very beginning, mankind has been in search of new tribomaterials to achieve better and faster mobility. There should be no doubt that this trend will continue at a much accelerated pace in the new millennium, intensifying the need for new solid tribological materials and coatings.
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21 Metals and Ceramics
Koji Kato Tohoku University
Koshi Adachi Tohoku University
21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10
Introduction ..................................................................... 771 Pure Metals ....................................................................... 771 Soft Metals and Soft Bearing Alloys ............................... 772 Copper-based Alloys ........................................................ 774 Cast Irons.......................................................................... 774 Steels.................................................................................. 776 Ceramics ........................................................................... 778 Special Alloys.................................................................... 781 Comparisons Between Metals and Ceramics................. 782 Concluding Remarks ....................................................... 783
21.1 Introduction Friction and wear can be kept low if the contact interface is well-lubricated. Even when the contact interface is not supplied with lubricants, friction and wear are changed by adsorbed gasses (Bowden et al., 1954) or by frictional repetition. This means that tribological properties are responses of a tribosystem that is lubricated on purpose or is under the effects of surroundings. Therefore, material properties of only one of two contacting bodies cannot be independently related to the tribological properties in a direct way. At the frictional contact surfaces, there exist frictional heating, high flash temperature, severe plastic shear deformation under contact pressure, and the agglomeration of wear particles to form the tribolayer (Rigney et al., 1977). These produce new surface properties that are different from the bulk material properties. Friction and wear take place at the contact interface between such unsteady surfaces. Nevertheless, metal and ceramic materials can be classified into groups for different applicational purposes, and the tribological usefulness of each group in practice can be qualitatively explained, to a certain extent, by the bulk material properties. These explanations are described in the following sections, which can be guides in the first step of material selection for tribo-elements.
21.2 Pure Metals Pure metals are generally soft and ductile. Therefore, the contact junctions of asperities between them show large amounts of junction growth in sliding if the contact interface is not lubricated. Table 21.1 shows the friction coefficients µ observed with eight pure metals sliding on themselves in different atmospheres (Bowden et al., 1954). In air, oxygen, or water vapor, the friction coefficients of these eight frictional pairs vary from 0.8 to 3.0. Gold, nickel, platinum, and silver show relatively large values, which means that the adhesion is relatively strong at the contact interfaces of these metals and contact junctions grow sufficiently to generate such large values. In hydrogen or nitrogen, copper, gold,
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TABLE 21.1 Friction of Metals (Spectroscopically Pure) Outgassed in Vacuum (When clean, there is gross seizure.) Coefficient of Friction after Admitting Metals Aluminum on aluminum Copper on copper Gold on gold Iron on iron Molybdenum on molybdenum Nickel on nickel Platinum on platinum Silver on silver
H2 or N2
Air or O2
Water Vapor
— 4 4 — — 5 — —
1.9 1.6 2.8 1.2 0.8 3 3 1.5
1.1 1.6 2.5 1.2 0.8 1.6 3 1.5
Data from Bowden, F.P. and Tabor, D. (1954), Friction and Lubrication of Solids, I, Clarendon Press, Oxford.
FIGURE 21.1 Effect of hardness on the relative wear resistance of pure metals. (From Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., 655-659. With permission.)
and nickel show large µ values (between 4 and 5), which means adhesion is stronger in the inert gases than in air. The high friction of pure metals shown in Table 21.1 is applied in friction bonding of noble metals such as gold. Abrasive wear resistance of such pure metals linearly increases with hardness as shown in Figure 21.1 (Khruschov, 1957). On the other hand, adhesive wear does not show a clear relationship with hardness.
21.3 Soft Metals and Soft Bearing Alloys When hard metals such as steels slide on themselves without lubricants, high friction, gross seizure, and severe wear take place in air or vacuum. A soft-metal thin film at the sliding interface between hard materials can reduce friction to the level of µ = 0.1 to 0.2. Gold, silver, lead, and indium are representative soft metals whose hardness values vary from about 0.3 GPa to about 0.5 GPa. In practical cases of soft metal-lubricated tribosystems, sliding velocities are relatively small and soft metals are not expected to work in the molten state.
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FIGURE 21.2 Thin film lubrication of soft pure metals in sliding of an Si3N4 pin on SUS440C stainless steel disk in high vacuum. (From Kato, K., Kim, H., Adachi, K., and Furuyama, H. (1996), Basic study of lubrication by tribocoating for space machines, Trans. Japan Soc. Mech. Eng., 62(600), 3237-3243. With permission.)
Figure 21.2 shows the lubricating properties of Ag, Au, Bi, In, Pb, Sb, and Sn observed with the friction pair of an Si3N4 pin against an SUS440C stainless steel disk in a vacuum of 10–6 Pa (Kato et al., 1996). It is recognized that the soft-film thickness has its optimum value for the minimum friction coefficient (Bowden et al., 1954), but such optimum film thickness can be held during running only when the soft metal is supplied continuously to repair the worn parts of the film (Kato et al., 1990). When a soft-metal film of a certain thickness is precoated on a hard material substrate, the life of the tribocomponent is determined by the wear life of the film. Soft-metal film lubrication is, therefore, convenient for relatively small and replaceable tribocomponents such as ball bearings. When a bearing system is expected to run in a state of hydrodynamic lubrication with oil, an unexpected solid contact is generated by the introduction of hard abrasive particles, misalignment, high load, or slow speed at the sliding contact interface. Soft alloys such as lead- or tin-based babbitts and aluminum-based alloys work well as bearing materials in such contact conditions. Lead-based babbitts contain a high percentage (>80 wt%) of lead with 1 to 10 wt% tin and 10 to 15 wt% antimony, and have a hardness value of about 0.2 GPa. An Sb-Sn phase is distributed as fine cubes throughout the structure. This material has the weakness of low fatigue strength because of segregation of the Sb-Sn phase during solidification. Tin-based babbitts contain a high percentage (>85 wt%) of tin with 5 to 8 wt% antimony and 4 to 8 wt% copper, and have hardness values of about 0.2 GPa. They have the phase of Sb-Sn or Cu6Sn5, and the presence of either or both of these intermetallic phases increases fatigue strength below 130°C (Glaesure, 1992). These babbitts are soft enough to embed dirt or hard particles, but also provide good conforming under misalignment or high load. Even when the supply of oil is interrupted, babbitts flow or melt to protect the shaft from damage. The dry friction coefficient against steel remains at ~0.55 to 0.80 (Bowden et al., 1954). They are used below the contact pressure of 30 to 40 MPa and their fatigue strength is ~20 to 30 MPa. Aluminum-based alloys are used for bearings that require large fatigue strength and higher operating temperature than babbitt bearings. Aluminum-tin alloys show a fatigue strength three times larger than tin- or lead-based babbitts (Pratt, 1969) and provide better compatibility with steels. Aluminum-20 wt% lead alloy is less expensive and has fatigue strength almost equal to that of aluminum-20 wt% tin alloy and better wear resistance (Bierlein et al., 1969). Although these aluminum-based alloys exhibit better fatigue strength, corrosion resistance, wear resistance, and compatibility with steel than babbitts, their embeddability and seizure resistance are not as good as that of babbitts and a thin overlay of lead-tin becomes necessary. By considering all the tribological properties of babbitts and aluminum-based alloys, as well as the material costs, soft alloys are used for the oil-lubricated bearings. Because these alloys have relatively
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TABLE 21.2
Copper-based Alloys and Hardness Values
Alloy
Cu
Pb
Sn
P
Al
Be
Hardness BHN, GPa
Copper-lead alloy Lead bronze Tin bronze Phosphor bronze Aluminum bronze Beryllium copper
>60 >80 >80 >85 >78 99.5
25–35 1–10 — — — —
<1 4–6 5–15 9–15 — —
— — — 0.1–0.2 — —
— — — — 8–10 —
— — — — 1.8 —
280 650 750 800 1700 3000
small strength and elasticity, they are usually overlayed on strips of steel or copper alloys, which provide strength. Bearings for the crankshafts of internal combustion engines and reciprocating compressors, engine camshafts, and railroad car axles are good examples of the applications of these alloys.
21.4 Copper-based Alloys When journal bearings are oil lubricated and run under heavy load, bearing materials must have hardness and strength higher than that of babbitts or aluminum-based alloys. Copper-based alloys, known as bronze, have been used for such bearings for their strength and good compatibility with steels. Tin bronzes contain 5 to 13 wt% tin and 1 to 5 wt% zinc. The existence of a hard intermetallic compound of Cu31Sn8 increases the strength of the alloys, and gives a hardness value of about 0.75 GPa, which is useful for heavy loads. Leaded bronzes contain 4 to 6 wt% tin, 4 to 6 wt% zinc, and 1 to 10 wt% lead. Lead is insoluble in copper and forms free globules in the copper matrix. These free lead globules work as solid lubricants that transfer to the mating surface and form a coating of low shear strength. This lead coating reduces friction and seizure in boundary lubrication. The alloys have hardness values of ~0.65 GPa, and show good conforming against roughness and misalignment of the shaft. In addition to copper bronzes, aluminum bronzes, manganese bronze, silicon bronze, and phosphate bronze have been developed. Hardness values of some of these alloys are shown in Table 21.2. They are used for gears, seals, nonsparking contacts, and heavily loaded, slow-moving journal bearings.
21.5 Cast Irons Wheels, rails, brakes, clutches, crushers, piston rings, gears, and rollers are examples of machine elements that require higher bulk strength than bronzes to support heavy loads with small deformation and high wear resistance, even in unlubricated sliding. A hardness greater than 2 GPa is generally required for these purposes. Cast irons with a carbon content between 2.5 and 4.0 wt% are inexpensive structural materials with the required properties. There are five representative cast irons: grey iron, white iron, nodular iron, malleable iron, and high-alloy iron. They have hardness values between 2 and 6 GPa, as shown in Table 21.3. TABLE 21.3
Hardness and Carbon Content of Cast Irons
Cast Iron Grey iron White iron Nodular or ductile iron Malleable iron High-alloy iron
Flake graphite Iron carbides Graphite nodules Graphite nodules Chromium carbides
Hardness Hv (GPa)
Carbon Content (%)
2.00 4.25 3.50 2.48 5.60
<3.0 <3.0 2.5 ~ 4.0 2.5 ~ 3.2 ~3.0
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FIGURE 21.3 Abrasive wear weight loss of high-chromium iron pairs in abrasive wear tests. (From Diesburg, D.E. and Borik, F. (1974), Optimizing abrasion resistance and toughness in steels and irons for the mining industry, Symp. Materials for the Mining Industry, Climax Molybdenum Co., 15-41. With permission.)
Grey cast iron has flake graphite in a matrix of bainite or martensite. White iron has iron carbides in the matrix. Malleable iron is formed from white iron by heat treatment and has nodular graphite in the matrix. Nodular iron also has nodular graphite, which is formed by the addition of small amounts of magnesium or cerium for spheroidizing. These graphites in the matrix form a graphite layer at the sliding interface and reduce friction and wear. Steel shows a friction coefficient of 0.8 in sliding against steel; and cast iron shows a friction coefficient of 0.4 in sliding against the steel (Bowden et al., 1954). It is the result of graphite film formation at the sliding interface with graphite in the cast iron. In the case of rolling contact, fatigue wear is expected to take place, and the positive contribution of free graphite to fatigue is considered from the viewpoint of friction reduction. Nodular iron is preferable to grey iron from this viewpoint because it has more fatigue resistance than grey iron. White iron, on the other hand, contains large iron carbides and no free graphite, which gives it high abrasive resistance. When high wear resistance is required under heavy abrasion or high-temperature corrosion, high-phosphorous irons or high-chromium irons are used. High-silicon irons are used for combined abrasion and corrosion conditions. In the case of high-phosphorous irons, a hard phosphide eutectic network is formed and provides high abrasive resistance. When especially high abrasive wear resistance is required, cast irons of harder matrix structure and harder inclusions become necessary because abrasive wear resistance is proportional to the hardness of the wear material, as shown in Figure 21.1. Figure 21.3 shows the weight loss of a high-chromium pin in relation to its hardness HRC observed in an abrasive wear test (Diesburg et al., 1974). The hard matrix of austenite or martensite yields smaller amounts of wear. Hard chromium carbides in the matrix also work as abrasive wear-resistant parts. High phosphorous (>3 wt% phosphor) irons used for railroad cars include a hard phosphide eutectic network that gives high abrasive wear resistance by a similar mechanism. In general, the hardness of cast iron increases with increasing volume of carbides in the matrix. Figure 21.4 shows that the volume loss of high-chromium-molybdenum white irons decreases with increasing volume of carbides Cr7C3 in abrasive sliding against garnet, whose hardness is less than that of the carbides. But this protective property of carbides disappears when the abrasive is silicon carbide, which is much harder than carbides (Zum Gahr et al., 1980). This result is caused by the increased brittleness of carbides at higher content and their brittle fracture in abrasion against the harder silicon carbide.
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FIGURE 21.4 Volume loss (pin abrasion on 150 mesh garnet and 180 mesh SiC) of high-chromium-molybdenum white irons as a function of the volume % of massive carbides. (From Zum Gahr, K.H. and Eldis, G. (1980), Abrasive wear of white cast iron, Wear, 64, 175-194. With permission.)
21.6 Steels Steels are representative structural materials for almost all kinds of machines and structures because of their high strength, good machinability, and low cost. Their tribological applications are journals, gears, ball and roller bearings, tools, wheels, rails, fasteners, etc., which need to support heavy load with minimum elastic deformation and minimum clearance over a long period of time. The hardness of steels can be controlled by carbon content and heat treatment from ~1.0 GPa to ~3.0 GPa, which gives a choice of steels for each tribo-element. In many steel-made tribosystems, contact interfaces are lubricated with liquid lubricants and the properties of friction and wear are under the strong influence of operating conditions, which determine the state of lubrication. In the state of hydrodynamic lubrication, friction depends mainly on the viscosity of the liquid and the shape of clearance for the liquid film. In the state of boundary or mixed lubrication, lubrication film is penetrated by surface asperities in contact, and the friction coefficient is increased to about 0.1 and wear is generated as a result. Hard asperities act as abrasives to cause breakdown of the lubricant film, because the real contact pressure at each asperity contact is nearly equal to the hardness value of the asperity material. On the other hand, breakdown of lubricant film at the contact interface is caused more easily at surfaces of large roughness because real contacts of asperities at the interface are localized and the contact pressures there tend to be larger than those at smooth surface contacts. Therefore, the choice of an acceptable hardness of steel must be made in relation to the surface roughness of the tribo-elements and lubricant properties, especially in contact between steels. When steels have contacts with abrasive particles or abrasive surfaces without lubricants, their hardness is a good measure of abrasive wear resistance. The effect of hardness on abrasive wear of steels is shown in Figure 21.5, where the amount of abrasive wear of low alloy steels decreases with increasing original steel hardness (Borik, 1976). This result is similar to those in Figure 21.3. Thus, one can generally expect higher abrasive wear resistance with harder steels so long as brittle phases are not introduced into the matrix. There are some steel-made tribo-elements that are used without lubricants, such as wheels and rails, bolts and nuts, and fasteners. In such cases of unlubricated sliding between steels, work hardening, frictional heating, phase transition, and oxidization take place at the same time in a complicated way, and the original bulk hardness of the steels is not simply related to friction and wear, as in the case of abrasive wear.
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FIGURE 21.5 Relationship between the weight loss of various low alloy steels caused by abrasion of alumina particles and their hardness changed by carbon contents in the material. Numbers at data points indicate the carbon content in percent. (From Borik, F. (1976), Testing for abrasive wear, Selection and Use of Wear Test for Metals, Paper No. 3, ASTM Special Technical Publication 615, 30-40.)
FIGURE 21.6 Unlubricated wear rates of annealed plain carbon steel (0.52%, 268 DPN) as a function of the load. (From Archard, J.F. (1980), Wear theory and mechanisms, Wear Control Handbook, ASME, Peterson, M.B. and Winer, W.O. (Eds.), 35-80. With permission.)
Figure 21.6 shows the wear rate of a pin of annealed plain carbon steel rubbing against a ring of the same material (Archard, 1980). Below the transition load T1 in Figure 21.6, the wear rate is below about 10–5 mm3/m (10–6 mm3/Nm), and the wear mode is called “mild wear.” The dominant wear mechanism
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FIGURE 21.7 Wear patterns for high-chromium ferritic steel pins sliding on austenitic stainless steel disks at 0.23, 1.00, 2.00, and 3.30 m/s. (From Quinn, T.F.J. (1992), Oxidational wear modelling. I, Wear, 153, 179-200. With permission.) TABLE 21.4 Specific Wear Rates for High-Chromium Ferrite Steel Pins Specific Wear Rate (×10–5 mm3/Nm)
Sliding Velocity (m/s)
Below Transition
Above Transition
0.23 1.00 2.00 3.00
Not applicable 1.3 1.1 0.8
4.4 1.7 2.8 1.1
Data from Quinn, T.F.J. (1992), Oxidational wear modelling. I, Wear, 153, 179-200.
is oxidational wear. There is a change in the wear rate by more than 2 orders of magnitude above T1, where the wear mode is called “severe wear” and the dominant wear mechanism is adhesive wear. Above the load T2 , the wear rate is between those in mild wear and severe wear, and the wear mechanism is dominated again by the oxidational wear on the work-hardened wear surfaces. In the regime of oxidational wear, the wear rate changes within 1 order of magnitude, depending on the combination of load and sliding velocity. In Figure 21.7, mild oxidational wear is observed below the critical load of about 60 N at the sliding velocity of 1.0, 2.0, or 3.3 m/s; and severe oxidational wear is observed above the critical load or at the sliding velocity of 0.23 m/s (Queen, 1992). Wear rates obtained with these results are shown in Table 21.4, where it is confirmed that the change of specific wear rate is within the order of 10–5 mm3/Nm. Further comprehensive expressions about oxidational wear are introduced in the chapter on wear maps (Chapter 9).
21.7 Ceramics Ceramics such as Si3N4, SiC, Al2O3, and ZrO2 have high hardness between 15 and 20 GPa at room temperature and such high hardness is maintained up to high temperature. However, their toughness values are between 4 and 8 MPa(m)1/2, which are much lower than those of steels. These material properties suppress junction growth at asperity contacts in friction, and the friction coefficient in selfmated sliding is not increased to a value above 1.0 in many cases. Friction coefficients of these ceramics
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TABLE 21.5 Friction Coefficients of Ceramics in Self-mated Sliding Friction Coefficient Material
Vacuum
Air
Si3N4 SiC Al2O3 PSZ
0.85 0.84 0.98 —
0.75 0.80 0.70 0.90
Data from Kato, K., Furuyama, H., and Mizumoto, M. (1990), The fundamental properties of tribo-coating films in ultra high vacuum, in Proc. Japan Int. Tribology Conf., Nagoya, I, 261-266.
FIGURE 21.8 Effect of humidity on wear rate of Si3N4 sliding against itself. (From Fischer, T.E. and Tomizawa, H. (1985), Interaction of tribochemistry and microfracture in the friction and wear of silicon nitride, Wear, 105, 29-45. With permission.)
in self-mated sliding are between 0.7 and 0.9 in air and between 0.8 and 1.0 in vacuum, as shown in Table 21.5 (Kato, 1990). The high hardness of ceramics does not work positively for high wear resistance because their low toughness reduces wear resistance by easy introduction of microfracture at contact surfaces in sliding. The combined effect of hardness and toughness on abrasive wear resistance, which is given by the reciprocal of material removal rate, is shown for six different ceramics in Figures 23 and 24 in Evans and Marshall (1981), where abrasive wear resistance increases linearly with the parameter of (Hardness)5/8 × (Toughness)1/2 (Evans and Marshall, 1981). Although ceramics are considered chemically inert, Si3N4 and SiC react with oxygen and water in sliding in air and form soft surface layers of SiO2 and its hydride via tribochemical reaction. Hence, the wear rate of Si3N4 or SiC is sensitive to humidity in air and is reduced drastically from about 10–4 mm3/Nm to about 10–6 mm3/Nm by increasing the humidity, as shown in Figure 21.8 for Si3N4 (Fischer et al., 1985). A similar effect of humidity on wear is observed with Al2O3 sliding on itself, as shown in Figure 21.9 where aluminum hydroxide is formed by tribochemical reaction at higher humidity (Gee, 1992), and the wear rate is reduced from about 10–5 mm3/Nm to about 10–7 mm3/Nm. The friction coefficient, on the other hand, is insensitive to humidity and remains at ~0.7 in the case of Figure 21.9.
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FIGURE 21.9 Effect of humidity on wear of Al2O3 sliding against itself. (From Gee, M. (1992), The formation of aluminium hydroxide in the sliding wear of alumina, Wear, 153, 201- 227. With permission.)
FIGURE 21.10 Load dependent wear mode transition in unlubricated sliding contact of Al2O3/Al2O3. (From Hsu, S.M., Wang, Y.S., and Munro, R.G. (1989), Quantitative wear maps as a visualization of wear mechanism transitions in ceramic materials, Wear, 134, 1-11. With permission.)
Because of the brittleness of ceramics, their wear rate in sliding is increased by 1 or 2 orders of magnitude at a certain contact load, above which surface cracks are propagated drastically by the tensile stress in the contact region. The tensile stress at the contact region is further increased by the thermal stress induced by frictional heating. Figure 21.10 shows these effects of load and sliding speed on the transition of wear from mild to severe wear observed with Al2O3 in self-mated sliding, where wear increases by an order of magnitude at a certain critical load and the critical load becomes smaller at larger sliding speed (Hsu et al., 1989). The effect of sliding speed on wear mode transition is more clearly shown in Figure 21.11, where the wear rate increases from a low value of about 1 × 10–5 mm3/m (5 × 10–7 mm3/Nm) to a high value of about 4 × 10–4 mm3/m (2 × 10–5 mm3/Nm) at about 2.5 m/s (Blomberg et al., 1994). The tribochemical wear observed in Figures 21.8 and 21.9 with silicon nitride and alumina in humid air promises smooth wear surfaces in water and the possibility of useful water lubrication (Tomizawa et al., 1987). Figure 21.12 shows the Stribeck curves in water lubrication of SiC, Si3N4, and Al2O3 in selfmated sliding. The hydrodynamic lubrication observed in ηN/Pm > 0.2 × 10–7 means that the contact surfaces of ceramics are very smooth as a result of tribochemical wear, and a thin water film of low viscosity works well because of the high hardness of contact materials (Wong et al., 1995). It is impossible to get similar curves with steels in water. Ceramics with such tribological properties are used for seals and bearings in water pumps, ball bearings for high-speed guides, and rollers in heavy-duty manufacturing processes, and cylinder liners and valves of engines and cutting tools.
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FIGURE 21.11 Velocity-dependent wear mode transition in unlubricated sliding contact of Al2O3/Al2O3. (From Blomberg, A., Olsson, M., and Hogmark, S. (1994), Wear mechanisms and tribo mapping of Al2O3 and SiC in dry sliding, Wear, 171, 77-89. With permission.)
FIGURE 21.12 Stribeck curve in water lubrication of three different ceramics in self-mated sliding. η: viscosity, N: rotational speed, Pm: contact pressure. (From Wong, H.C., Umehara, N., Kato, K., and Nii, K. (1995), Fundamental study of water-lubricated ceramic bearings, Trans. Japan Soc. Mech. Eng., 61(509), C, 4027-4032. With permission.)
21.8 Special Alloys For usage in heavy-duty tribo-elements at high temperatures and/or highly corrosive environments, materials of both high hardness and high strength are required. Cermets are materials for such requirements. They have hard ceramic particles in a matrix of metals, which gives high toughness. The representative materials of hard ceramic particles are WC, TiC, TiN, Cr2C, and Al2O3, and those of binders are Co, Ni, and Cr. Different kinds of cermets are formed by combining some of these constituents. WC cermets have tungsten carbide bonded with cobalt. They have hardness values from 10 to 15 GPa and tensile strengths from 3 to 4 GPa, depending on the amount of cobalt (3 to 25 wt%). They are used as cutting tools for brittle metals such as cast irons. TiC cermets have titanium carbide bonded with cobalt and nickel, and have hardness values similar to those of WC cermets. Some TiC cermets have binders of cobalt, nickel, or chromium, which are extremely resistant to high-temperature oxidation. The WC-TiC cermet bonded with cobalt, which has about 15 wt% TiC, shows high wear resistance at high temperature and works well in machining steels. Cr3C2 cermets have chromium carbides bonded with nickel (10 to 15 wt%) and tungsten (–2 wt%), which are resistant to corrosion and oxidation. Figure 21.13 shows the specific wear rates of three kinds of cermets in relation to those of original ceramics and binding metals (Tsuya et al., 1989). It is obvious that high wear resistances of ceramics are well maintained in cermets, despite the existence of soft binding materials.
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FIGURE 21.13 The specific wear rates of cermets, and their original ceramics and binding metals observed in pinon-disk sliding. (From Tsuya, Y. and Ishii, S. (1989), Wear characteristics of ceramics and cermets, J. Japanese Soc. Tribologists, 34(5), 348-351. With permission.)
21.9 Comparisons Between Metals and Ceramics It is more useful to see the differences in tribological properties of metals and ceramics under the same contact conditions than to see them individually under different contact conditions. To see the differences in wear resistances of materials, fatigue wear and abrasive wear are appropriate wear modes because they can be compared without the strong influence of lubricants. In repeated rolling contact, silicon nitride balls show much longer fatigue life than bearing steel balls, as shown in Figure 21.14 (Fujiwara et al., 1988). If one remembers that silicon nitride has larger hardness and smaller toughness than steel, it is obvious that fatigue strength in rolling contact is determined by other functions. Figure 21.15 shows the effect of fracture toughness on abrasive wear resistance, which shows a maximum value at a certain fracture toughness (Diesburg et al., 1974). Abrasive wear resistance of ceramics
FIGURE 21.14 Fatigue strength of bearing steel and silicon nitride observed by rolling fatigue test. (From Fujiwara, T., Yoshioka, T., Kitahara, T., Koizumi, S., Takebayashi, H., and Tada, T. (1988), Study on load rating property of silicon nitride for rolling bearing material, J. Japan Soc. Lubrication Engineers, 33(4), 301-308. With permission.)
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FIGURE 21.15 Effect of material toughness on abrasive wear resistance. (From Diesburg, D.E. and Borik, F. (1974), Optimizing abrasion resistance and toughness in steels and irons for the mining industry, Symp. Materials for the Mining Industry, Climax Molybdenum Co., 15-41. With permission.)
increases with fracture toughness below ~10 MPa(m)1/2, and that of metals decreases with fracture toughness above ~15 MPa(m)1/2. This means that optimum material of optimum toughness must be carefully selected for high abrasive resistance. It is noted at the same time that hardness is not a measure to compare abrasive wear resistance between metals and ceramics. It is available only for the group of metals as shown in Figure 21.1 or for the group of ceramics as shown in Figures 23 and 24 in Evans and Marshall (1981). In modern, advanced machine systems, metal/ceramic combinations are being used for tribo-elements. It is clearly shown in Figures 21.16(a) and (b) that metal/ceramic combinations always show smaller wear rate than combinations of metal/metal or ceramic/ceramic (Iwasa, 1985). A similar effect is shown in Figure 21.17, where the largest value of critical contact pressure against seizure initiation is given by the combination of SiC/FC25, where FC25 is a cast iron (Asanabe, 1987). The excellent performances of metal/ceramic combinations in wear and seizure indicate the importance of material combination of elements. Therefore, it must be recognized that individual evaluation of a material for tribological needs can be useful only in some special cases.
21.10
Concluding Remarks
It has been generally recognized for a long time that dissimilar materials combination shows better tribological properties than similar materials combination for tribo-elements. Bearings of babbitts or bronzes for harder steel shafts with oil lubricants are traditionally established examples of this meaning. Figures 21.16 and 21.17 confirm the same empirical law for smaller wear and higher seizure resistance with metal/ceramic combinations. On the other hand, the Stribeck curves in Figure 21.12 and the successful applications of the SiC/SiC combination for water-lubricated journal bearings of a water pump (Kimura et al., 1996) suggest that higher performances of tribo-elements are attainable using hard similar materials combination with careful treatments. It is important, therefore, to enlarge the materials combination matrix for both dissimilar and similar materials combinations in selecting materials for tribo-elements.
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FIGURE 21.16 The effect of materials combination on wear rate in unlubricated sliding; (a) wear rates of Si3N4, SiC, AlN, and SUJ2 against an Si3N4 disk; (b) wear rates of Si3N4, SiC, AlN, and SUJ2 against an SUJ2 disk, where SUJ2 is bearing steel. (From Iwasa, M. (1985), Frictional properties of ceramics and measuring methods, Science of Machine, 12, 45-52. With permission.)
FIGURE 21.17 The effect of materials combination on critical contact pressure for seizure initiation in turbine oillubricated sliding. (From Asanabe, S. (1987), Applications of ceramics for tribological components, Tribol. Int., 20(6), 355-364. With permission.)
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References Archard, J.F. (1980), Wear theory and mechanisms, Wear Control Handbook, ASME, Peterson, M.B. and Winer, W.O. (Eds.), 35-80. Asanabe, S. (1987), Applications of ceramics for tribological components, Tribol. Int., 20(6), 355-364. Bierlein, J.C., DeHart, A.O., and Rosenberg, C. (1969), Performance Characteristics of the General Motors Aluminum-Babbitt Material, SAE publication 690113. Blomberg, A., Olsson, M., and Hogmark, S. (1994), Wear mechanisms and tribo mapping of Al2O3 and SiC in dry sliding, Wear, 171, 77-89. Borik, F. (1976), Testing for abrasive wear, Selection and Use of Wear Test for Metals, Paper No. 3, ASTM Special Technical Publication 615, 30-40. Bowden, F.P. and Tabor, D. (1954), Friction and Lubrication of Solids, I, Clarendon Press, Oxford. Diesburg, D.E. and Borik, F. (1974), Optimizing abrasion resistance and toughness in steels and irons for the mining industry, Symp. Materials for the Mining Industry, Climax Molybdenum Co., 15-41. Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439-452. Fischer, T.E. and Tomizawa, H. (1985), Interaction of tribochemistry and microfracture in the friction and wear of silicon nitride, Wear, 105, 29-45. Fujiwara, T., Yoshioka, T., Kitahara, T., Koizumi, S., Takebayashi, H., and Tada, T. (1988), Study on load rating property of silicon nitride for rolling bearing material, J. Japan Soc. Lubrication Engineers, 33(4), 301-308. Gee, M. (1992), The formation of aluminium hydroxide in the sliding wear of alumina, Wear, 153, 201- 227. Glaesure, W. (1992), Material for Tribology, Elsevier, 74. Pratt, G.C. (1969), New developments in bearing materials, SAE paper 690112. Hsu, S.M., Wang, Y.S., and Munro, R.G. (1989), Quantitative wear maps as a visualization of wear mechanism transitions in ceramic materials, Wear, 134, 1-11. Iwasa, M. (1985), Frictional properties of ceramics and measuring methods, Science of Machine, 12, 45-52. Kato, K. (1990), Tribology of ceramics, Wear, 136, 117–133. Kato, K., Furuyama, H., and Mizumoto, M. (1990), The fundamental properties of tribo-coating films in ultra high vacuum, in Proc. Japan Int. Tribology Conf., Nagoya, I, 261-266. Kato, K., Kim, H., Adachi, K., and Furuyama, H. (1996), Basic study of lubrication by tribo-coating for space machines, Trans. Japan Soc. Mech. Eng., 62(600), 3237-3243. Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., 655-659. Kimura, Y. (1996), Process hydrodynamic lubrication bearing and structure of its pump, Turbo Machine, 24(8), 41-46. Pratt, F.D. (1969), New developments in bearing materials, SAE paper 690112. Quinn, T.F.J. (1992), Oxidational wear modelling. I, Wear, 153, 179-200. Rigney, D.A. and Glaeser, W.A. (1977), The significance of near surface microstructure in the wear process, Proc. Wear of Materials, ASME, 41-46. Tomizawa, H. and Fischer, T.E. (1987), Friction and wear of silicon nitride and silicon carbide in water: hydrodynamic lubrication at low sliding velocity obtained by tribochemical wear, STLE Trans., 30, 41-46. Tsuya, Y. and Ishii, S. (1989), Wear characteristics of ceramics and cermets, J. Japanese Soc. Tribologists, 34(5), 348-351. Wong, H.C., Umehara, N., Kato, K., and Nii, K. (1995), Fundamental study of water-lubricated ceramic bearings, Trans. Japan Soc. Mech. Eng., 61(509), C, 4027-4032. Zum Gahr, K.H. and Eldis, G. (1980), Abrasive wear of white cast iron, Wear, 64, 175-194.
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22 Solid Lubricants and Self-Lubricating Films* 22.1
Introduction ..................................................................... 787 General Characteristics of Solid Lubricants • New Products, Practices, and Approaches in Solid Lubrication
22.2
Classification of Solid Lubricants ................................... 792
22.3 22.4
Lubrication Mechanisms of Layered Solids ................... 806 High-Temperature Solid Lubricants ............................... 808
Lamellar Solid Lubricants
Lubricious Oxides, Fluorides, and Sulfates • Composites • New Approaches to Solid Lubrication at High Temperatures
22.5
Self-Lubricating Composites ........................................... 813 Traditional Materials • New Self-lubricating Composite Coatings and Structures
Ali Erdemir Argonne National Laboratory
22.6 22.7 22.8
Soft Metals ........................................................................ 815 Polymers ........................................................................... 817 Summary and Future Directions .................................... 818
22.1 Introduction In most tribological applications, liquid or grease lubricants are used to combat friction and wear; but when service conditions become very severe (i.e., very high or low temperatures, vacuum, radiation, extreme contact pressure, etc.), solid lubricants may be the only choice for controlling friction and wear. Some of the key advantages of solid lubricants in tribological applications over liquid and grease lubricants are summarized in Table 22.1. A combination of solid and liquid lubrication is also feasible and may have a beneficial synergistic effect on the friction and wear performance of sliding surfaces. Solid lubricants can be dispersed in water, oils, and greases to achieve improved friction and wear properties under conditions of extreme pressures and/or temperatures (Barnett, 1977; Broman et al., 1978; Kimura et al., 1999; Erdemir, 1995). When present at a sliding interface, solid lubricants function the same way as their liquid counterparts. Specifically, they shear easily to provide low friction and to prevent wear damage between the sliding surfaces. Several inorganic materials (e.g., molybdenum disulfide, graphite, hexagonal boron nitride, *Work supported by U.S. Department of Energy, Office of Transportation Technology, under Contract W-31-109Eng-38. The submitted manuscript has been created by the University of Chicago as Operator of Argonne National Laboratory (“Argonne”) under Contract No. W-31-109-ENG-38 with the U.S. Department of Energy. The U.S. Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.
787
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TABLE 22.1
Modern Tribology Handbook
Comparison of Solid and Liquid Lubricants in Tribological Applications
Application Environment and/or Condition
Solid Lubricants
Liquid and Grease Lubricants
Vacuum
Some solids (i.e., transition-metal dichalcogenides) lubricate extremely well in high vacuum, have very low vapor pressure
Pressure
Can endure extreme pressures
Temperature
Relatively insensitive; can function at very low and high temperatures; low heat generation due to shear
Electrical conductivity Radiation Wear
Some provide excellent electrical conductivity Relatively insensitive to nuclear radiation Provide excellent wear performance or durability at slow speeds and under fretting conditions; lifetime is determined by lubricant film thickness and wear rate Extremely low friction coefficients are feasible
Most liquids evaporate, but perfluoropolyalkylethers (PFPE) and polyalfaolefins (PAO) have good durability May not support extreme pressures without additives May solidify at low temperatures and decompose or oxidize at high temperatures; heat generation varies with viscosity Mostly insulating May degrade or decompose over time Provide marginal performance and durability at slow speeds and under fretting conditions; need additives for boundary lubrication Depends on viscosity, boundary films, and temperature Good
Friction Thermal conductivity and heat dissipation capability Storage Hygiene
Compatibility with tribological surfaces Resistance to aqueous and chemically aggressive environments
Excellent for metallic lubricants; poor for most inorganic or layered solids Can be stored for very long times (dichalcogenides are sensitive to humidity and oxygen) Better industrial hygiene due to little or no hazardous emissions; since they are in solid state, there is no danger of spillage that can contaminate environment Compatible with hard-to-lubricate surfaces (i.e., Al, Ti, stainless steels, and ceramics) Relatively insensitive to aqueous environments, chemical solvents, fuels, certain acids and bases
May evaporate, drain, creep, or migrate during storage May release hazardous emissions; liquid lubricants may spill or drip and contaminate environment; fire hazard with certain oils and greases Not suitable for use on non-ferrous or ceramic surfaces May be affected or altered by acidic and other aqueous environments
boric acid) can provide excellent lubrication (Sutor, 1991; Klauss, 1972; Lancaster, 1984; Sliney, 1982; McMurtrey, 1985; Lansdown, 1999). Most of these solids owe their lubricity to a lamellar or layered crystal structure. A few others (e.g., soft metals, polytetrafluoroethylene, polyimide, certain oxides and rare-earth fluorides, diamond and diamond-like carbons, fullerenes) can also provide lubrication although they do not have a layered crystal structure. In fact, diamond-like carbon films are amorphous, but provide some of the lowest friction coefficients of all the solid materials (Erdemir et al., 2000). Because a special chapter (see Chapter 24) in this Handbook is devoted to the friction and wear behavior of diamond and diamond-like carbon, they will not be covered here. The solid lubricants with a layered crystal structure are graphite, hexagonal boron nitride, boric acid, and the transition-metal dichalcogenides MX2 (where M is molybdenum, tungsten, or niobium, and X is sulfur, selenium, or tellurium). Figure 22.1 shows the layered crystal structures of these solids. Certain monochalcogenides (e.g., GaSe and GaS) have lattice structures similar to those of dichalcogenides; hence, they can also provide low friction when present at a sliding interface (Erdemir, 1994). Major shortcomings of solid lubricants include: 1. Except for soft metals, most solid lubricants are poor thermal conductors and, hence, cannot carry away heat from sliding interfaces. 2. Depending on test environment and contact conditions, their friction coefficients may be high or fluctuate significantly.
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Carbon
3.35 A°
(a)
(b)
Sulfur Molybdenum
Oxygen Boron
Hydrogen 2.96 A°
3.18 A°
(c)
(d)
FIGURE 22.1 Schematic illustration of layered crystal structures of (a) graphite, (b) hexagonal boron nitride, (c) molybdenum disulfide (representing transition metal dichalcogenides), and (d) boric acid.
3. They have finite wear lives and their replenishment is more difficult than that of liquid lubricants. 4. Oxidation and aging-related degradation may occur over time and present some problems with transition-metal dichalcogenides. 5. Upon exposure to high temperatures or oxidative environments, they may undergo irreversible structural-chemistry changes that in turn lead to loss of lubricity and the generation of some abrasive, nonlubricious by-products.
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22.1.1 General Characteristics of Solid Lubricants Well-known solid lubricants (graphite, HBN, and transition-metal dichalcogenides) owe their lubricity to a unique layered structure. As illustrated in Figure 22.1, the crystal structures of these solids are such that while the atoms lying on the same layer are closely packed and strongly bonded to each other, the layers themselves are relatively far apart, and the forces that bond them (e.g., van der Waals) are weak. When present between sliding surfaces, these layers can align themselves parallel to the direction of relative motion and slide over one another with relative ease, thus providing low friction. In addition, strong interatomic bonding and packing in each layer is thought to help reduce wear damage. While this mechanism is largely responsible for low friction and is essential for long wear life, a favorable crystal structure in itself is not sufficient for effective lubrication. The presence or absence of certain chemical adsorbates is also needed for providing easy shear in most solids. For example, moisture or some other condensable vapors are needed for graphite and boric acid to lubricate (Rowe, 1960; Erdemir et al., 1999). In contrast, MoS2 and other transition-metal dichalchogenides work best in vacuum or dry running conditions, but degrade rather quickly in moist and oxidizing environments (Winer, 1967; Farr, 1975; Kanakia and Peterson, 1987). The friction coefficients of self-lubricating metal dichalcogenides are typically in the range of 0.002 to 0.05 in vacuum or dry and inert atmospheres, but increase rapidly to 0.2 in humid air. It is generally agreed that no solid can provide very low friction and wear, regardless of test environment and/or conditions. Soft metallic lubricants have crystal structures with multiple slip planes and do not work-harden appreciably during sliding contact. Dislocations and point defects generated during shear deformation are rapidly nullified by the frictional heat produced during sliding contact. Most high-temperature solid lubricants rely on thermal softening and/or limited chemical reaction with sliding surfaces that make them shear with relative ease; whereas self-lubricating polymers consist of long molecular chains with high chemical inertness and/or very low surface energy, making them non-stick or largely insensitive to chemical bonding. Ambient temperature has a strong influence on the lubricity of solid lubricants. Graphite can provide lubrication up to 400°C, while HBN can withstand temperatures up to 1000°C. Most transition metal dichalcogenides tend to oxidize at elevated temperatures, and thus lose their lubricity. MoS2 can provide lubrication up to 400°C, while WS2 endures up to 500°C (Sliney, 1982). In general, those with higher oxidation resistance or chemical/structural stability perform the best at elevated temperatures. Oxideand fluoride-based solid lubricants (e.g., CaF2, BaF2, PbO, and B2O3) (Sliney, 1993), as well as some soft metals (e.g., Ag, Au), function quite well at elevated temperatures (Erdemir et al., 1990c; Erdemir and Erck, 1996; Maillat et al., 1993), but all fail to provide low friction at room or lower ambient temperatures. The lubricity of these solids at elevated temperatures is largely controlled by their ability to soften and resist oxidation. Solid lubricants can be applied to a tribological surface in a variety of forms. The oldest and simplest method is to sprinkle, rub, or burnish the fine powders of solid lubricants on surfaces to be lubricated. Fine powders of certain solid lubricants were also used to lubricate sliding bearing surfaces with great success (Heshmat and Heshmat, 1999; and Higgs et al., 1999). Certain solid lubricants have been blended in an aerosol carrier and sprayed directly onto the surfaces to be lubricated. Powders of solid lubricants can be strongly bonded to a surface by appropriate adhesives and epoxy resins to provide longer wear life (Gresham, 1997). They can also be dispersed or impregnated into a composite structure. Certain solids (e.g., HBN and boric acid) have been mixed with oils and greases in powder form to achieve improved lubrication under extreme pressure and temperature conditions (Kimura et al., 1999; Erdemir, 1995). However, in most modern applications, thin films of solid lubricants are preferred over powders or bonded forms. They are typically deposited on surfaces by advanced vacuum deposition processes (e.g., sputtering, ion plating, and ion-beam-assisted deposition) to achieve strong bonding, dense microstructure, uniform thickness, and long wear life (Spalvins, 1969, 1971, 1980; Erdemir, 1993). Ion-beam deposition and mixing can also be used to enhance the durability of solid lubricant coatings (Bhattacharya
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et al., 1993; Erck et al., 1992). However, the lifetimes of most solid lubricants are still limited because of the finite lubricant film thickness. To increase their durability, a self-replenishment or resupply mechanism is needed but very difficult.
22.1.2 New Products, Practices, and Approaches in Solid Lubrication In recent years, several new lubricants and modern lubrication concepts have been introduced to achieve better lubricity and longer wear life in demanding tribological applications. Some of the traditional solid lubricants were prepared in the forms of metal, ceramic, and polymer-matrix composites and used successfully in a variety of engineering applications (Rohatgi et al., 1992; Prasad and McConnell, 1991; Gangopadhyay and Jahanmir, 1991; Friedrich, 1995). Carbonaceous films produced by catalytic cracking of carbon-bearing gases were also shown to provide good lubricity at elevated temperatures (Lauer and Bunting 1988; Blanchet et al., 1994). Recent developments in PVD and CVD deposition technologies have led to the synthesis of a new generation of adaptive, self-lubricating coatings with composite or multilayer architectures (Jayaram et al., 1995; Zabinski et al., 1992, 1995; Voevodin et al., 1999). These exotic architectures, based on layers of a self-lubricating dichalcogenide (e.g., MoS2, WS2, etc.) and a soft metallic or hard ceramic layer, were shown to work extremely well under demanding tribological conditions. Multifunctional nanocomposite films (consisting mainly of MoS2 and Ti) have also been produced by magnetron sputtering and are quite hard, moisture insensitive, and self-lubricating, thus raising the prospect for dry-sliding applications, as well as dry metal-cutting and -forming (Fox et al., 1999). Duplex/multiplex surface treatments and multilayer coatings with self-lubricating capabilities have also made their way into the commercial marketplace and have been meeting the ever-increasing performance demands of more severe applications. Recently, carbon and WS2 were prepared in the form of hollow nanotubes and demonstrated to provide high mechanical strength and very low friction coefficients under certain sliding conditions (Tenne, 1992; Falvo, 1999). Nanostructured ZnO films were also shown to be quite lubricious and relatively insensitive to variations in ambient pressure, environment, and temperature (Zabinski, 1997). A series of adaptive lubrication strategies has also been introduced in recent years and shown to be effective over a wide range of temperatures and pressures (Walck, 1997). Minute oxygen deficiency or sub-stoichiometry in rutile was shown to lead to the formation of low-shear crystallographic planes and hence high lubricity (Gardos, 1988, 1990, 1993). A series of plasma-sprayed composite coatings consisting of silver and alkaline halides (i.e., CaF2, BaF2) as the self-lubricating entities and CrC and/or Cr2O3 as the wear-resisting entities were also shown to provide excellent lubrication over a wide temperature range (DellaCorte, 1998; DellaCorte and Fellenstein, 1997). Furthermore, H3BO3 powders, films forming on B2O3, and B4C coatings were shown to be quite lubricious and highly effective under extreme sliding conditions (Erdemir, 1991; Erdemir et al., 1990b, 1991c, 1999). Thiomolybdates and oxythiomolybdates of Cs, Zn (i.e., Cs2MoO2S2, ZnMoO2S2), and a few other alkali metals were found to be effective in controlling friction and wear at elevated temperatures (King, 1990). These solids possess a lamellar structure like MoS2 but can endure much higher temperatures than MoS2. Furthermore, certain complex oxides and oxide-fluorides (i.e., ZnO/SnO/SrF 2 , NiO/BaTiO 3 , MgO/ZnO/CaF2, NiO/SrF2) were shown to be rather lubricious at elevated temperatures (Erdemir et al., 1998). Erdemir (1999) introduced a new crystal-chemical approach to the selection, classification, and mechanistic understanding of lubricious oxides used to combat friction and wear at elevated temperatures. Based on this approach, one can predict the shear rheology and hence lubricity of an oxide or oxide mixture at elevated temperatures. John and Zabinski (1999) investigated the lubrication properties of some sulfate-based (i.e., CaSO4 , BaSO4, and SrSO4) coatings at high temperatures as a potential replacement for alkaline halides (i.e., CaF2 , BaF2). They found that these sulfates became highly lubricious at 600°C and were able to provide friction coefficients of ≈0.15 to sliding surfaces. Structural studies revealed the presence of a carbonate crystal structure, along with a sulfate crystal structure after testing. The carbonate crystal structure
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consisted of alternating layers of alkali-earth atoms and carbonate ions. It was proposed that such a layered structure may have been responsible for the low-friction nature of these sulfates at high temperatures. The new lubricants and lubrication approaches mentioned above are some of the most notable developments in recent years and certainly have the potential to overcome difficult lubrication problems that may arise in the future. In this chapter, solids with self-lubricating capabilities are reviewed first and classified on the basis of their crystal structures, chemistry, and operational limits. A summary of the recent understanding of the lubrication mechanisms of both traditional and new solid lubricants is presented next. Then, the present state-of-the-art in advanced solid lubrication methods and practices is provided. Particular emphasis is placed on the synthesis and/or applications of solid lubricant films on tribological surfaces by means of advanced surface engineering processes such as ion-beam-assisted deposition, ion-beam mixing, and unbalanced magnetron sputtering. Traditional and new applications for self-lubricating composite solid lubricants are also emphasized. This chapter primarily focuses on developments evolved during the last decade because several excellent reviews, book chapters, and books cover the earlier developments (Sutor, 1991; Lancaster, 1984; Sliney, 1982, 1993; Singer, 1989, 1992, 1998; McMurtrey, 1985; Klauss, 1972; Miyoshi, 1996). Also, major emphasis is placed on inorganic solid lubricants with layered crystal structures and those that provide lubrication at high temperatures. Soft metals and polymers are briefly discussed because there are several excellent articles providing in-depth information on the properties and applications of these solid lubricants (Sliney, 1986; Dayson, 1971; Sherbiney and Halling, 1977; Wang et al., 1995; Briscoe, 1990; Zhang, 1997; Bahadur and Gong, 1992; Friedrich et al., 1995).
22.2 Classification of Solid Lubricants Solid lubricants can be categorized into several subclasses. Table 22.2 provides such a classification based on the chemistry, crystal structure, and lubricity of the most widely used and recently developed solid lubricants. As can be realized from Table 22.2, the range of friction coefficients is rather large for a given solid lubricant. This is mainly because friction is very sensitive to test environment, condition, and/or configuration. Ambient temperature and the type of counterface materials can also make a big difference in the frictional property of a given solid lubricant. The specific form or shape of the solid lubricants (i.e., thin films, powders, bulk, composite, and crystalline or amorphous states) can also play a major role. For example, the wide range of friction coefficients for MoS2 (i.e., 0.002 to 0.25) stems from several factors affecting its shear rheology and hence frictional properties. These factors include film microstructure and chemistry, test environment, ambient temperature, contact pressure, film thickness, stoichiometry, and purity. Deposition and/or lubricant application methods can also play a major role in frictional performance of MoS2 films. Due to their porous, columnar structure, MoS2 films deposited by conventional sputtering methods tend to exhibit higher friction and shorter wear lives than films produced by more robust ion-beam-assisted deposition and closed-field unbalanced magnetron sputtering techniques. The MoS2 films deposited by these advanced physical vapor deposition methods can have near-perfect stoichiometry, purity, and basal plane orientation parallel to the substrate surfaces. These highly optimized films can, in turn, provide friction coefficients as low as 0.002 in ultrahigh vacuum (Martin et al., 1994; Donnet et al., 1993). In general, no single lubricant can provide reasonably low and consistent friction coefficients over broad test conditions, temperatures, and environments. Each lubricant listed in Table 22.2 functions rather nicely under certain test conditions, but not under all conditions. Researchers have mixed two or more of these lubricants to broaden the operational range, but in most cases the improvements were either transitory or short-lived.
22.2.1 Lamellar Solid Lubricants Lamellar or layered solid lubricants are the class that is most studied by scientists and widely used by industry. Among the best-known examples are transition-metal dichalcogenides (e.g., MoS2), graphite,
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TABLE 22.2
Solid Materials with Self-lubricating Capability
Classification Lamellar solids
Soft metals
Mixed oxides
Single oxides
Halides and sulfates of alkaline earth metals Carbon-based solids
Organic materials/polymers
Bulk or thick-film (>50 µm) composites Thin-film (<50 µm) composites
Key Examples MoS2 WS2 HBN Graphite Graphite fluoride H3BO3 GaSe, GaS, SnSe Ag Pb Au In Sn CuO–Re2O7 CuO–MoO3 PbO–B2O3 CoO–MoO3 Cs2O–MoO3 NiO–MoO3 Cs2O–SiO2 B 2O 3 Re2O7 MoO3 TiO2 (sub-stoichiometric) ZnO CaF2, BaF2, SrF2 CaSO4, BaSO4, SrSO4 Diamond Diamond-like carbon Glassy carbon Hollow carbon nanotubes Fullerenes Carbon-carbon and carbon-graphite-based composites Zinc stearite Waxes Soaps PTFE Metal-, polymer-, and ceramic-matrix composites consisting of graphite, WS2, MoS2, Ag, CaF2, BaF2, etc. Electroplated Ni and Cr films consisting of PTFE, graphite, diamond, B4C, etc., particles as lubricants Nanocomposite or multilayer coatings consisting of MoS2, Ti, DLC, etc.
Typical Range of Friction Coefficienta 0.002–0.25 0.01–0.2 0.150–0.7 0.07–0.5 0.05–0.15 0.02–0.2 0.15–0.25 0.2–0.35 0.15–0.2 0.2–0.3 0.15–0.25 0.2 0.3–0.1 0.35–0.2 0.2–0.1 0.47–0.2 0.18 0.3–0.2 0.1 0.15–0.6 0.2 0.2 0.1 0.1–0.6 0.2–0.4 0.15–0.2 0.02–1 0.003–0.5 0.15 — 0.15 0.05–0.3 0.1–0.2 0.2–0.4 0.15–0.25 0.04–0.15 0.05–0.4 0.1–0.5 0.05–0.15
a Friction values given in this table represent friction measurements made on each solid lubricant over a wide range of test conditions, environments, and temperatures. The objective here is to show how friction varies depending on test conditions, as well as from one solid to another.
HBN, and H3BO3 . MoS2, graphite, and boric acid are natural minerals, extracted from deposits around the world. Other lamellar solids, such as WS2, fluorinated graphite, and transition-metal diselenides and ditellurides, are synthetic and are used at much smaller scales than graphite, HBN, and MoS2. MoS2 and WS2 are well-suited for aerospace and cryogenic applications, while HBN is preferred for lubrication at elevated temperatures. HBN is widely used as a release agent in high-temperature metal-forming operations. Graphite and H3BO3 work extremely well in moist air. The lubricity of graphite persists up to 400°C, while H3BO3 begins to decompose at about 170°C. These two solids do not provide lubrication in dry or vacuum environments. Graphite fluoride is produced by the fluorination of graphite. This
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process increases the spacing between the carbon-carbon layers in graphite from about 0.34 nm to values as high as 0.8 nm, resulting in easier shear and hence better lubricity, even in dry environments. Among the lamellar solids, MoS2 and WS2 have the best overall load-carrying capacity as thin films on rigid substrates. Most lamellar solids have good wetting capability or chemical affinity for ferrous surfaces. On a rough or porous sliding surface, they fill in the valleys between asperities and/or pores, thus providing a smoother surface finish and better support. When applied properly, these solids can also withstand extreme contact pressures without being squeezed out of the load-bearing surfaces. WS2 is preferred over MoS2 when applications involve relatively higher temperatures. However, WS2 is a synthetic lubricant and thus is expensive. Selenides of W, Nb, and Mo can provide even higher temperature capabilities than their sulfide analogs, but they too are expensive and are used on much smaller scales. Certain selenides and tellurides (e.g., V, Nb) provide excellent electrical conductivity. 22.2.1.1 Transition-Metal Dichalcogenides Transition-metal dichalcogenides, MX2 (where M is Mo, W, Nb, Ta, etc., and X is sulfur, selenium, or tellurium), are among the lowest-friction materials known in dry and vacuum environments (Winer, 1967; Farr, 1975; Kanakia and Peterson, 1987; Singer et al., 1990; Donnet, 1996). They are also well-suited for cryogenic applications. MoS2 and WS2 are the best-known examples and the most widely used dichalcogenides. MoS2 is a natural mineral known as molybdenite, whereas WS2 and other dichalcogenides are man-made and therefore expensive. The hardness values of these solids on the Mohs scale are 1.5 to 2 and their specific gravities lie between 4.7 and 5.5. They are chemically stable and resist attack by most acids, except aqua regia and hot and highly concentrated HCl, H2SO4, and HNO3. At room temperature in ultrahigh vacuum, these solid lubricants provide some of the lowest friction coefficients, but moisture in air has a detrimental effect on their lubricity (Peterson, 1953; Fusaro, 1978). Oxidation of MoS2 does not begin until the temperature reaches about 375°C. At approximately 500°C, rapid oxidation begins and MoO3 and SO2 are produced. The thermal and oxidative stability of WS2 is better than that of MoS2 (Sliney, 1982). 22.2.1.1.1 Preparation and Uses of Dichalcogenides MoS2 and other dichalcogenides are applied on tribological surfaces as thin, strongly bonded solid films providing very long wear lives and super-low friction coefficients. Depending on application conditions (load, speed, temperature, etc.) and the form (crystalline or amorphous), size, purity, stoichiometry, and film thickness, the friction coefficients of MoS2 and other dichalcogenides vary considerably. In moist air, the lifetimes of lubricant films are rather short and typical values for friction coefficients are 0.05 to 0.25. Burnished films tend to be short-lived and give higher friction than thin sputtered films (Spalvins, 1971; Fusaro, 1978; Peterson, 1953). Bonded and composite forms of MoS2 last much longer, but their friction coefficients are generally high (Gresham, 1977). The advanced physical vapor deposition (PVD) methods used in the deposition of high-quality MoS2 films include magnetron sputtering (Spalvins, 1969, 1971, 1980; Stupp, 1981), ion-beam-assisted deposition (IBAD) (Bolster, 1991; Wahl et al., 1995; Seitzman et al., 1995; Dunn et al., 1998), and ion-beam mixing (Kobs et al., 1986; Bhattacharya et al., 1993; Rai, 1997). A pulsed laser deposition (PLD) method can also be used to deposit high-quality MoS2 and other composite films with excellent tribological performance (Zabinski, 1992; Prasad, 1995). Sputtering has been and is still the most widely used method. Recently, closed-field unbalanced magnetron sputtering of MoS2 has become very popular and is highly effective in many tribological applications, including metal-forming and -cutting operations (Fox et al., 1999). Figure 22.2 compares the endurance lives of MoS2 films prepared by various methods. MoS2 films may also contain lattice and volume defects (i.e., large voids or porosities) in their microstructures (Spalvins, 1980; Lince and Fleischauer, 1987; Hilton and Fleischauer, 1991). Furthermore, some contain significant amounts of oxygen and carbon impurities that may have been present in the deposition chamber or introduced during film deposition. They may also come from the source or target material used during deposition. Depending on the level of contaminants, resultant MoS2 films may show
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Maximum Thrust Bearing Endurance of *1 µm* MoS2 Coatings burnished dc sputtered rf sputtered NRL S-modulated OSMC pure OSMC AuPd NRL Pb-alloyed 0
2
4
6
8
10
12
Revolutions to Failure (Millions)
FIGURE 22.2 Endurance lives of MoS2 films produced by various methods. (From Singer, I.L., Bolster, R.N., Seitzman, L.E., Wahl, K.J., and Mowery, R.L. (1994), Advanced Solid Lubricant Films by Ion-Beam Assisted Desposition., Naval Research Laboratory, NRL/MR/6170-94-7633.)
significant differences in their tribological properties (Suzuki, 1998). Crystalline films with porous columnar structures tend to wear out rather quickly. Tilting or bending of columnar grains with poor cohesion during sliding results in fracture of the top portions of each column; the remaining lower part is smeared on the surface and the basal planes of the MoS2 crystal are eventually oriented parallel to the sliding surfaces (Spalvins, 1980; Hilton, 1991). The rate and degree of reorientation appear to depend on the initial microstructure. Recent studies have indicated that films with dense morphology, preferred basal orientation, and high purity provided the best overall performance. In fact, the lowest friction coefficients (0.002 to 0.01) were reported on a phase-pure (oxygen-free) and stoichiometric MoS2 film (Donnet, 1993; Martin et al., 1993). These super-low friction coefficients are obtained in ultrahigh vacuum and are attributed to a combination of perfect basal orientation of the MoS2 layers and to the absence of any adsorbed species or contaminants on sliding surfaces. 22.2.1.1.2 Modern Practices Increasing demand for higher performance, longer wear life, and better efficiency in advanced mechanical systems that depend primarily on solid lubrication for safe operation has intensified interest in new and exotic lubrication practices in recent years. One of the major reasons for this interest was that conventional lubrication practices could no longer meet the performance and durability needs of advanced mechanical systems. Most studies have concentrated on MoS2 and have resulted in a better understanding of the friction and wear mechanisms of this solid lubricant. Such mechanistic understanding is, in turn, used to develop the new and better lubrication practices that are in wide use by industry today. With the advanced PVD methods mentioned earlier, MoS2 films can be grown at subzero, room, or elevated temperatures. At lower deposition temperatures or under high-energy ion bombardment, one can obtain amorphous and sub-stoichiometric films with relatively poor tribological properties. During sliding or upon annealing, the crystallinity, and hence the lubricity, of MoS2 may be restored (Zabinski et al., 1994). Ion-beam mixing of sputtered MoS2 or WS2 films (50 to 70 nm thick) with sapphire, Si3N4, and ZrO2 substrates can also result in an amorphous microstructure with a sub-stoichiometry of MoS1.8. In these studies, 2-MeV Ag+ ions at 5 × 1015 cm–2 dose were used. During tribological tests in dry N2,
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FIGURE 22.3 substrate.
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Friction performance and durability of sputtered and Ag+ ion-beam mixed MoS2 films on sapphire
friction coefficients of 0.03 to 0.04 were measured in both the as-deposited and ion-irradiated films. However, the sliding lives of Ag+ ion-irradiated films were found to increase 10- to 1000-fold over those of as-sputtered films on all ceramic surfaces studied. The improvements in wear lives were correlated with a significant improvement in film/substrate adhesion (Bhattacharya et al., 1993). Figure 22.3 shows the friction performance and durability of sputtered and Ag+ ion-beam mixed MoS2 films on sapphire substrates. Similar improvements in wear lives of WS2 film were found after ion-beam mixing (Rai et al., 1997). Recently, researchers have developed novel means to dope MoS2 films with certain metals (e.g., Au, Ni, Ti, Pb, C, etc.) and compounds (TiN, PbO, Sb2O3, etc.) (Zabinski et al., 1992, 1995; Spalvins, 1984; Stupp, 1981; Hilton et al., 1992, 1998; Wahl et al., 1995; Lince et al., 1995). Tribological studies have demonstrated that when doped properly and in the correct proportions, these dopants can substantially improve the mechanical and tribological properties of MoS2 films. For example, Au-doped MoS2 films were shown to have more stable frictional traces and lower friction than undoped sputtered MoS2 films, as shown in Figure 22.4. Figure 22.5 compares the friction and wear performance of conventional MoS2 with that of Ti-doped MoS2 in increasingly humid air. Furthermore, doping of MoS2 with Pb, Ti, Ni, Fe, Au, and Sb2O3 resulted in film amorphization or densification and in reduction of the crystallite size, which in turn reduced the mean and variance of the friction coefficients and substantially increased their wear lives (Zabinski et al., 1992, 1995; Wahl et al., 1995, 1999). The exact mechanisms responsible for lifetime improvements in doped MoS2 films are not yet fully understood. However, researchers have noticed that doping generally results in preferential alignments of basal planes parallel to the substrate surface and thus lower susceptibility of MoS2 to oxidation or moisture-induced degradation. It is speculated that such favorable alignment, together with increased resistance to oxidation, may have been responsible for increased wear life and lubricity. Films with duplex and/or alternating layers of MoS2 and metals or hard nitrides have also been produced in recent years and used in a variety of applications (Hilton et al., 1992; Jayaram, 1995; Seitzman et al., 1992). For example, MoS2 films prepared by RF magnetron sputtering on AISI 440C and 52100 steels, and multilayer coatings of MoS2 with either nickel or Au-(20%)Pd metal interlayers (with layer
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.05
MoS
COEFFICIENT OF FRICTION, µ
2
.04 Au-MoS2
.03 .02
.01
0
10000
20000
30000
40000
50000
SLIDING DURATION, cycles
FIGURE 22.4 Effect of Au doping on friction behavior of sputtered MoS2 films. (From Spalvins, T. (1984), Frictional and morphological properties of Au-MoS2 films sputtered from a compact target, Thin Solid Films, 118, 374-384. With permission.)
0.30 Pin-On-Disc Substrate: WC Counterpart: 6 mm dia. WC Ball Track Radius: 3.5 mm Speed: 500 rpm Load: 10 N
Friction Coefficient (µ)
0.25 0.20 0.15 0.10 0.05
MoS2 MoST™
0.00 0
20
40 60 % Relative Humidity
80
100
FIGURE 22.5 Friction performance of conventional and Ti-doped MoST films at different humidity levels. (Courtesy of Multi-arc, Inc.)
thicknesses ranging from 0.2 to 1.0 nm) on silicon substrates, had very dense microstructures that in some cases exhibited significant orientation of MoS2 basal planes parallel to the substrate. Some of the optimized films exhibited excellent endurance and friction coefficients of 0.05 to 0.08 in UHV (Hilton, 1992). Overall, these novel coating practices have led to favorable changes in crystallite size and film density and reduced edge orientation in growing films, which in turn resulted in increased coating endurance. Some dopants (Pb, Ti, PbO) resulted in an amorphous microstructure but with no detrimental effect on the low-friction and wear behaviors of the films. In fact, despite the formation of an amorphous microstructure, significant increases in wear lives are attained with Pb- and Ti-doped films (Fox et al., 1999; Wahl et al., 1995, 1999). However, the mechanism(s) responsible for such remarkable performance has not yet been resolved.
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In recent years, researchers have demonstrated that low-friction surface films can be formed in situ on the surfaces of Mo, W, and Mo- or W-containing metallic alloys by adding sulfur-bearing gases such as H2S and SO2 into the test chamber (Singer et al., 1996a,b; Sawyer and Blanchet, 1999). In a model experiment run in high vacuum, where a small amount of H2S was admitted to maintain an S partial pressure of 13 Pa, Singer et al. (1996) recorded a friction coefficient of 0.01 on the resulting films on Mo substrates. Recently, WS2 was prepared as nanoparticles having structures similar to those of nested carbon fullerenes and nanotubes. Preliminary test results showed that these nanoparticles are highly effective in reducing friction and wear and do outperform the solid and thin film forms of WS2 and MoS2 when tested under the same test conditions (Rapoport et al., 1997). For the excellent durability and performance of these nanoparticles, high chemical inertness and a hollow cage structure were proposed. Apparently, hollow structures are chemically very stable and do not interact with oxygen or water molecules in the environment. Because of their high rigidity, they impart high elasticity, which allows these particles to roll rather than slide. 22.2.1.2 Monochalcogenides Sulfides and selenides of gallium and tin (i.e., GaS, GaSe, SnSe) have crystal structures that resemble those of transition-metal dichalcogenides (i.e., MoS2, WS2, WSe2) which are well-known solid lubricants. Figure 22.6 shows the layered structure of GaSe. These solids are known as sandwich semiconductors in
FIGURE 22.6 (a) Crystal structure of GaSe, and (b) SEM photomicrograph of fractured GaSe pellet. (From Erdemir, A. (1994), Crystal chemistry and self-lubricating properties of monochalcogenides gallium selenide and tin selenide, Tribol. Trans., 37, 471-476.)
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solid-state physics and have been studied extensively for their electrical and optical properties (Phillips, 1969). Tin selenide represents a group of layered compounds that also comprise SnS and the sulfides and selenides of germanium, whereas GaSe belongs to a class that also includes the layered gallium sulfide and the sulfides and selenides of indium. Using a pin-on-disk machine, Erdemir (1994) performed friction tests on large crystalline pieces and compacts of GaSe and SnSe monochalcogenides against sapphire and 440C steel balls to assess their lubricity. For the specific test conditions explored, friction coefficients of the sapphire/GaSe and sapphire/SnSe pairs were ≈0.23 and ≈0.35, respectively. The friction coefficients of 440C pin/440C disk test pairs with GaSe and SnSe powders were ≈0.22 and ≈0.38, respectively. The friction data, together with the crystal-chemical knowledge and electron microscopy evidence, supported the conclusion that the lubricity and self-lubricating mechanisms of these solids are closely related to their crystal chemistry and the nature of their interlayer bonding. In a series of earlier studies, Boes and Chamberlain (1968) and Gardos (1984) explored the tribological and thermal oxidation properties of composite lubricants consisting of indium/gallium and WSe2. The principal goal of these studies was to achieve better oxidation resistance on WSe2 by alloying it with lowmelting-point indium and gallium. Upon curing the composite mixture at high temperatures, the investigators found that both indium and gallium underwent chemical reaction with WSe2 to form the selenides of these metals. Further studies by Gardos (1984) demonstrated that, compared to the parent WSe2, the new composite lubricant exhibited superior oxidation resistance over a wide range of ambient temperature. Also, the lubricating capability of this InSe/WSe2 composite was much superior to that of WSe2 alone, especially at elevated temperatures. Apparently, a protective film resulting mainly from the preferential oxidation of sub-stoichiometric indium selenides was primarily responsible for the superior oxidation resistance of this new lubricant. The protective film was thought to effectively shield the lubricating entities against oxidation. As discussed later, chalcogenides owe their low-friction nature to their lamellar structures in which strongly bonded atoms form extensive rigid sheets (see Figures 22.1 and 22.6). In the cases of dichalcogenides such as MoS2 or MoSe2, the crystal structure is composed of a monolayer of Mo ions sandwiched between layers of S or Se ions. However, in the case of monochalcogenides such as GaS or GaSe, the crystal structure is composed of double layers of Ga sandwiched between Se ions (Figure 22.6). 22.2.1.3 Graphite Graphite is another classic example of lamellar solids that provides low friction and high wear resistance to sliding surfaces. Because of its good lubricity, abundance, and low cost, it is used in many industrial applications. Like diamond, graphite is a polymorph of carbon. Both occur naturally and are recovered from deposits around the world; both can also be produced by synthetic means. Synthetic graphite is primarily produced by heating petroleum coke to about 2700°C. Chemically, both graphite and diamond are the same, but differ totally in their structures and properties. For example, graphite is perhaps one of the softest materials, while diamond is the hardest of all natural materials. Diamond has the highest thermal conductivity, whereas graphite is a relatively poor thermal conductor. However, graphite is a good electrical conductor, but diamond is an excellent electrical insulator. Graphite has a sheet-like crystal structure (see Figure 22.1) in which all of the carbon atoms lie in a plane and are bonded only weakly to the graphite sheets above and below. Each carbon atom in the plane joins to three neighboring carbon atoms at a 120° angle and at a distance of 0.1415 nm. The distance between atomic layers is 0.335 nm at room temperature, and the layers are held together by van der Waals forces. In moist air, the friction coefficient of graphite varies from 0.07 to 0.15, depending on test conditions, sliding contact configuration, form of graphite used (powder, bulk, thin film, purity, crystallite orientation), and test machine. The lowest friction coefficient of 0.01 was observed during a nanotribology experiment in which a W tip was slid against the cleaved graphite flakes (Mate, 1987). The dense and highly oriented pyrolitic graphite (HOPG) performs extremely well in humid air, giving friction coefficients of about 0.1. In dry air, inert atmospheres, or vacuum, graphite’s lubricity degrades rapidly, the friction coefficient increases to as high as 0.5, and it wears out quickly. Experimental studies carried out
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FIGURE 22.7 Effect of water vapor pressure on wear rate of graphite. (From Savage, R.H. (1948), Graphite lubrication, J. Appl. Phys., 19, 1-10. With permission.)
by research groups have confirmed that the lubricity of graphite is not due to its layered crystal structure alone, but depends strongly on the presence or absence of certain condensable vapors, water vapor being one. Research has shown that only a small amount of condensable vapor is needed to improve the lubricity of graphite (Rowe, 1960). Certain vapors appear to be more effective than others. For example, a test run by Savage (1948) showed that n-heptane and isopropanol are much more effective than water vapor in terms of increasing the lubricity of graphite. The beneficial effect of condensable vapors on the lubricity of graphite has been attributed to the saturation in its lattice of π-electrons, which otherwise make atomic layers slide with difficulty. Figure 22.7 shows the relationship between wear rate and water vapor pressure for graphite. Graphite can provide lubrication up to about 500°C in open air, although friction tends to increase as the temperature rises. At higher ambient temperatures, it begins to oxidize and lose its lubricity. In vacuum, the friction coefficient is initially high (i.e., 0.4), but decreases to about 0.2 at 1300°C. In most sliding experiments, thin transfer films are formed on the surfaces of sliding counterfaces. These transfer layers are thought to be important for achieving longer wear life and possibly even lower friction. When small amounts of sodium thiosulfate (Na2S2O3) or sodium molybdate (Na2MoO4) were added to graphite to improve the transfer film forming behavior, researchers observed longer wear life and lower friction against sliding steel counterfaces (Langlade et al., 1994). During these tests, transformations of the graphite structure to a turbostatic phase was observed as a thin layer by means of electron microscopy and X-ray diffraction. Graphite is inexpensive and readily available in various forms. It is resistant to both acids and bases. In practice, graphite is used in powder, colloidal dispersion, solid, and composite forms to combat friction and wear. It is a key ingredient of electrical brushes used in many motors. It can be dispersed in water, solvents, oils, and greases to achieve better lubricity under extreme application conditions, such as lubrication of molds and dies in metal-forming, as well as flange faces of rails and railcar wheels. Graphite is also used as a self-lubricating filler in various metal-, ceramic-, and polymer-matrix composites (Rohatgi et al., 1992; Prasad and McConnell, 1991; Gangopadhyay and Jahanmir, 1991). Carbon-graphite composites are rather common and widely used in various engine, aircraft, and seal applications.
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Graphite fluoride is prepared by fluorinating graphite at stoichiometries from X = 0.3 to 1.1 in CFx . It is prepared by direct reaction of graphite with fluorine gas at controlled temperatures and pressures and can be regarded as an intercalation compound of graphite. Fluorination increases the distance between atomic planes from about 0.34 nm to as high as 0.8 nm and, hence, results in easier shear and better lubricity (Fusaro and Sliney, 1970). It also causes basal planes of graphite to distort and lose their planar configuration. CFx is electrically insulating and nonwettable with water, but decomposes at about 450°C. Fluorination of graphite was shown by Fusaro and Sliney (1970) to substantially improve the lubricity and durability of this solid and make it less sensitive to variations in ambient humidity. Earlier studies indicated that burnished CFx was capable of providing friction coefficients of 0.1 or less up to about 480°C in open air. Compared to those of MoS2 and even HOPG under the same test conditions, such friction values were considerably lower. It is possible to prepare composite structures and resin-bonded films of CFx in order to achieve longer life; however, due to its high cost, CFx is rarely used by industry. In a recent study, CFx was used as an additive to WS2 thin films to reduce their sensitivity to moisture (Zabinski et al., 1995). These films were produced on AISI 440C steel substrates by a pulsed laser deposition method. Substrate temperature and CFx concentration were varied to control film microstructure and chemistry. Tribological tests were conducted over a wide range of relative humidities (i.e., <1 to 85% RH). Coatings with a low concentration of CFx exhibited ultra-low friction in dry air (friction coefficients <0.01), but the coefficients increased with increasing relative humidity. Films grown at elevated temperatures (300°C) or with higher concentrations of CFx showed insensitivity to humidity, but the friction coefficients were relatively high (0.04 in dry air). 22.2.1.3.1 Modern Practices Graphitic lubricious precursors can also result from catalytic cracking of certain carbon-bearing gases and can be used to lubricate surfaces, especially at high temperatures (Ashley, 1992; Lauer and Bunting, 1988; Blanchet et al., 1994). This is done by injecting a stream of hydrocarbon-bearing gases into the test chamber where hot ceramic or metal surfaces are maintained and slid against one another. The hydrocarbons in the gas turn into a thin coating of graphite-like carbon that is responsible for lubrication. In recent years, a few attempts were made to lubricate sliding surfaces by other carbon forms, such as bucky-balls (C60) (Bhushan et al., 1993) and hollow nanotubes of carbon (Falvo, 1999). In addition to the powder form, sublimation or thermal evaporation methods were used to deposit C60 as strongly bonded and dense films on metallic and ceramic substrates. Depending on the form, density, and adhesion of these films to their substrates, friction coefficients of 0.15 to 0.5 were obtained. Ion irradiation of such films with 2 MeV Ag+ and B+ ions at various doses resulted in partly crystalline to amorphous films that were able to provide friction coefficients of <0.1 (Bhattacharya et al., 1996). Recently, a series of new boron-doped and partially graphitized carbon composites were developed to achieve better lubricity at elevated temperatures. Long-duration friction and wear tests were run as a function of both increasing and decreasing temperatures to assess the durability and the friction and wear performance of the composites. As shown in Figure 22.8, the friction coefficients of the borondoped carbon composite against a ceramic counterface were in the range of 0.05 to 0.1 at temperatures up to 500°C. Based on analytical studies, it was concluded that the boron doping was essential for achieving higher oxidation resistance on these graphitic materials. Vitreous or glassy carbon materials are made by pyrolysis of thermosetting polymers. Structurally, they are different from graphite, but the interatomic bonding and local arrangement at nanoscale are more graphitic than diamond. They are extremely hard and, hence, more wear resistant than graphite, which is very soft. Just like graphite, the friction coefficient of glassy carbon shows high sensitivity to relative humidity of the test environment. Glassy carbon materials have very low fracture toughness, but can be reinforced with metallic/nonmetallic fibers to achieve improved toughness. Copper-containing glassy carbon composites have high electrical conductivity and can be used for electrical contacts or brushes (Burton and Burton, 1989).
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FIGURE 22.8
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Friction performance of boron-doped carbon composite at temperatures to 525°C.
Quite recently, researchers have produced highly disordered graphitic carbon layers on silicon carbide by reaction with chlorine and chlorine/hydrogen gas mixtures at 1000°C. The thickness of the graphitic layer can vary from a few to 100 µm, depending on process time. When such a graphitized surface is subjected to sliding friction tests, very low (0.1 to 0.15) friction coefficients are achieved (Gogotsi et al., 1997). It is possible that such graphitic layers on rigid SiC substrates can be used to control friction and wear of microelectromechanical systems, sliding bearings (e.g., mechanical seals), electrical contacts, and biomedical implants. 22.2.1.4 Hexagonal Boron Nitride (HBN) HBN is a synthetic solid lubricant with high refractory and lubricity qualities at elevated temperatures. Below 1000°C, oxidation is negligible. It is chemically inert and resists attack by molten metals, oxides, glasses, slags, and fused salts. Its crystal structure is similar to that of graphite as shown in Figure 22.1. The atomic planes are made of two-dimensional arrays of boron and nitrogen atoms, configured in a honeycomb pattern (Rowe, 1960). As in graphite, the bonding between the atoms of HBN in each layer is covalent and very strong, while bonding between the layers is of the weak van der Waals type. HBN is typically produced by reacting B2O3 with urea or ammonia gases at high temperatures. Unlike graphite, HBN has a white color. Its cubic analog (i.e., cubic boron nitride) is like diamond and is extremely hard and resistant to wear. HBN is generally produced in powder form. Depending on manufacturing conditions, different grades (i.e., turbostatic, quasi-turbostatic, meso-graphitic, and graphitic) of HBN are obtained. In terms of lubrication performance, the graphitic grade provides the best results. Purity and powder size of final products can also affect lubrication performance. The presence of boron oxide in the structure or as a binder makes a significant difference in the tribological performance of HBN. HBN can be compacted into dense, solid pieces or parts by hot-pressing and can also be prepared as a composite structure. It can be plasma-sprayed with other ceramics to obtain a self-lubricating coating. Recently, very fine particles of HBN were incorporated into electroplated Ni coatings to provide superior friction and wear properties under unlubricated and high-load, high-temperature sliding conditions (Funatani and Kurosawa, 1994; Pushpavanam and Natarajan, 1995). HBN can also be used as a selflubricating phase in ceramic composites. Such materials will be very attractive for mechanical face seal applications. In a recent study, Westergard et al. (1998) investigated the tribological performance of Si3N4 /SiC composites containing 0 to 8 wt% HBN. All specimens were produced by hot isostatic pressing. The results indicated that the presence of HBN in the composite body lowered the friction coefficients of test pairs from a range of 0.4 to 0.9 to a range of 0.02 to 0.1. Analytical studies revealed that sliding surfaces were covered by a thin, well-adhering tribofilm, which may have been responsible for the improved tribological performance. HBN has also been used as an additive in oils and greases. Recent tests by Kimura et al. (1999) showed that addition of HBN in concentrations as little as 1 wt% results in an order of magnitude reduction in
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TABLE 22.3 Effect of Various Gases at Various Pressures on Friction Behavior of HBN Sliding Against Itself Environment UHV, 10–8 Pa CO, C3H8, H2O, air (50% RH); 10–3 Pa CO, N2, O2; 10 Pa Air (50% RH); 10 Pa C3H8; 10 Pa Air (50% RH); 105 Pa Air (50% RH), atmospheric pressure
Steady-state Friction Coefficient 0.6–0.7 0.6–0.7 0.6–0.7 0.4 0.4 0.2 0.1
Data from Martin, J.M., LeMogne, T., Chassagnette, C., and Gardos, M.N. (1992), Friction of hexagonal boron nitride in various environments, Tribol. Trans., 35, 463-472.
wear of bearing steels sliding against each other in line contacts. At higher concentrations, the reduction in wear is even greater. Similar improvements in antiwear and antifriction properties were reported for HBN-containing greases by Denton and Fang (1995). HBN has high thermal and chemical stability and does not appreciably oxidize up to about 1000°C. Typical friction coefficients of HBN in air are 0.2 to 0.3 up to about 700°C. It has been used as a release agent in metalworking operations involving high temperatures (Golubus, 1970). In high vacuum, HBN loses its lubricity. Buckley (1978) reported a friction coefficient of 1 for HBN sliding against itself in ultrahigh vacuum. Much earlier tests by Deacon and Goodman (1958), Rowe (1960), and Haltner (1966) gave friction coefficients of 0.4 to 0.7 in high vacuum in the outgassed states. Admission of certain organic vapors into the test chamber reduced friction coefficients to the 0.2 level. Recent fundamental studies by Martin et al. (1992) in ultrahigh vacuum (10–8 Pa) and under partial pressures of CO, C3H8 , H2O, air with 50% humidity, N2, and O2 resulted in friction coefficients of 0.1 to 0.7; Table 22.3 summarizes their experimental results. These experiments further reinforced the initial assertion that HBN is not only similar to graphite in its crystal structure, but also in its lubrication behavior (Rowe, 1960; Rabinowicz, 1964). Thus, one can understand why HBN is often referred to as “white graphite.” 22.2.1.5 Boric Acid Boric acid is a lamellar solid lubricant (Figure 22.9) with a crystal structure similar to those of graphite and HBN (Erdemir, 1991). It has a triclinic unit cell in which boron, oxygen, and hydrogen atoms are arrayed to form extensive atomic layers parallel to the basal plane of the crystal (see Figure 22.1). Because of the triclinic crystal structure, the c-axis is inclined to the basal plane at an angle of 101° (see Figure 22.1). This inclination causes shifting of alternate layers along the c-axis. Bonding between the atoms lying on
FIGURE 22.9
SEM photomicrograph of lamellar structure of boric acid.
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0.09
0.07
µ
0.05
0.03
0.01 1N SAPPHIRE BALL
2N
5N ALUMINA BALL
10N STEEL BALL
FIGURE 22.10 Variation of friction coefficient of boric acid films under different loads during sliding against steel and ceramic balls. (Adapted from Erdemir, A. (1991), Tribological properties of boric acid and boric-acid-forming surfaces. I. Crystal chemistry and mechanism of self-lubrication of boric acid, Lubr. Eng., 47, 168-172.)
the same plane is of the covalent/ionic and hydrogen type; the layers are 0.318 nm apart and held together only by weak van der Waals forces. Boric acid exists in two major crystalline forms: metaboric acid (H2O·B2O3 or HBO2) and orthoboric acid (3H2O·B2O3 or H3BO3). Furthermore, metaboric acid has been reported to crystallize in three different forms: orthorhombic or α-metaboric acid, monoclinic or β-metaboric acid, and cubic or Γ-metaboric acid. Among these, orthoboric and orthorhombic metaboric acids exhibit layered-crystal structures and thus can provide low friction. Orthoboric acid exists as a natural mineral known in mineralogy books as sassolite. It is stable up to about 170°C. Due to its layered-crystal structure, H3BO3 is a self-lubricating solid. To demonstrate its lubricity, Erdemir (1991) performed extensive friction tests with solid compacts of H3BO3 on a pin-on-disk machine. Cylindrical rods with a nominal diameter of 1.27 cm were compacted from 99.8 wt% H3BO3 powders by cold-pressing at about 35 MPa. To establish point contact during friction tests, one end of the rod-shaped compacts was finished with a hemispherical cap of 5-cm radius. Subsequently, the boric acid pin was attached to the pin holder of a pin-on-disk machine and rubbed against a 50-cm-diameter AISI 52100 steel disk. The friction coefficient of the pin/disk pair described above was measured as a function of sliding distance. The initial friction coefficient of this tribosystem was approximately 0.2; it then decreased steadily with distance and eventually reached a steady-state value of 0.1 after sliding about 20 m. H3BO3 can spontaneously form on the surfaces of boron and B2O3 films. Erdemir et al. (1990b) investigated the formation and tribological characteristics of such boric acid films formed on the surfaces of vacuum-evaporated B2O3 layers. They found that H3BO3, which formed spontaneously on the surfaces of B2O3 coatings, is remarkably lubricious. For a sliding pair of sapphire ball/B2O3-coated Al2O3 disk, they reported friction coefficients ranging from 0.02 to 0.05 in open air with 50% relative humidity, depending on applied force. Figure 22.10 presents the friction coefficients of various balls sliding against a B2O3-coated Al2O3 disk under different contact loads. The use of a harder, more rigid ball (e.g., sapphire) results in a lower friction coefficient because the true contact area between a hard, rigid ball will be smaller than that between a soft, less-rigid ball. Friction force, which is a product of the true contact area multiplied by the shear strength of the contact interface, will be much lower when hard, rigid balls are used in sliding contact. Based on surface and structure analytical studies, it was concluded that low friction is a direct consequence of the layered crystal structure of H3BO3 films forming on the exposed surfaces of the B2O3 coating by the spontaneous chemical reaction:
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(
)
(
)
1 2 B2O 3 coating + 3 2 H2O moisture → H 3BO3 ∆H298 = −45.1 kJ mol The above reaction occurs naturally, and a thin layer of H3BO3 forms everywhere on the exposed surface of B2O3 coatings. Formation of such self-lubricating and self-replenishing films was later demonstrated on VB2, B4C, and borided steel surfaces, affording very low friction coefficients to sliding metal and ceramic surfaces (Erdemir et al., 1991, 1996b,d, 1998, 1999; Bindal and Erdemir, 1996). As described previously, H3BO3 crystallizes in a triclinic crystal structure essentially made of atomic layers parallel to the basal plane. The atoms lying on each layer are closely packed and strongly bonded to each other. The bonds between the boron and oxygen atoms are mostly covalent, with some ionic character. Hydrogen bonds strongly hold the planar boron/oxygen groups together. The atomic layers are widely spaced (e.g., 0.318 nm apart) and held together by weak forces (e.g., van der Waals). Because of the ionic character of interatomic bonds, boric acid can dissolve in water and some other solvents. With its layered crystal structure, H3BO3 resembles other layered solids well-known for their good lubrication capabilities (e.g., MoS2, graphite, and HBN). Erdemir (1990) proposed that under shear stresses, plate-like crystallites of H3BO3 can align themselves parallel to the direction of relative motion. Once so aligned, they can slide over one another with relative ease and thus impart the low friction coefficients shown in Figure 22.10. Boric acid films were shown to bond strongly to the surface of aluminum and its alloys and provide excellent lubricity when used as a metal-forming lubricant (Erdemir and Fenske, 1998). Used as a filler in polymers, boric acid and boron oxide can substantially lower friction and increase the wear resistance of base polymers (Figure 22.11) (Erdemir, 1995). It was demonstrated that sub-micrometer size powders of boric acid can be dispersed in oils and greases to impart better lubricity and extreme pressure capability (Erdemir, 1995, 2000b). For applications at elevated temperatures, the use of H3BO3 is not recommended for several reasons. First, above about 170°C, H3BO3 tends to decompose and eventually turn into B2O3, thus losing its layered crystal structure and hence its lubricity. Second, at temperatures greater than about 450°C, B2O3 becomes liquid-like and tends to react with underlying substrates. For metals, the chemical reaction is negligible,
FIGURE 22.11
Friction performance of polyimide and boron oxide-filled polyimide.
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L
INTRAFILM FLOW V
L
INTERFACE SLIDING V
L
INTERFILM SLIDING V
FIGURE 22.12 Schematic representation of three ways by which sliding can be accommodated between an uncoated and a coated surface. (From Singer, I.L. (1992), Solid Lubrication Processes, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), NATO-ASI Series, Vol. 220, Kluwer Academic, London, 237-261. With permission.)
and low friction can be reinstated by viscous-flow lubrication. However, for ceramics — especially for the oxides — the situation is different. Liquid B2O3 can react with these ceramics and lead to high corrosive wear. Friction can also be very high because of the highly viscous nature of the reaction products.
22.3 Lubrication Mechanisms of Layered Solids In general, the lubricity and durability of a solid lubricant are controlled by a mechanism that involves interfilm sliding, intrafilm flow, and film/substrate or interface slip, as illustrated in Figure 22.12. It has been found that the lamellar solid lubricants discussed above provide lubrication by an interlayer shear mechanism, mainly because the crystal structures of these solids are such that while the atoms lying on the same layer are closely packed and strongly bonded to each other, the layers themselves are relatively far apart and the forces that bond them (e.g., van der Waals) are weak (see Figure 22.1). Strong interatomic bonding and packing in each layer give these solids the very high in-plane strength that is essential for longer wear life or reduced wear damage during sliding. When present on a sliding surface, crystalline layers of these solids align themselves parallel to the direction of relative motion and slide over one another with relative ease to provide lubrication. Furthermore, the formation of a smooth transfer film on the sliding surfaces of counterface materials is also important for long wear life and the accommodation of sliding velocity, as well as for dissipation of frictional energy. Recent electron microscopy studies of H3BO3-lubricated rubbing surfaces of steel test pairs clearly revealed some plate-like crystallites exhibiting a preferred alignment parallel to the sliding direction (Figure 22.13). Similar observations were made by TEM on sputtered MoS2 films after sliding tests. Several other studies used X-ray diffraction to further verify that indeed some crystalline orientation occurs on most lamellar solids during sliding tests (Wahl et al., 1995, 1999; Martin et al., 1994; Moser and Levy, 1993). Crystalline layers can be made of single or several atomic planes. For example, in graphite, H3BO3 , and HBN, the layers are made of a single atomic plane; while in MoS2 and other transition-metal dichalcogenides, the layers consist of three atomic planes (see Figure 22.1); in monochalcogenides, there are four atomic planes in each layer (see Figure 22.6).
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FIGURE 22.13 cated surface.
807
Physical evidence for preferred crystalline orientation and intercrystallite slip on boric acid-lubri-
The electronic states of atoms in each layer play a major role in the lubricity of each solid. Graphite and HBN are similar in electronic states. The only major difference between the bonding configuration of these two solid lubricants is that the π-bonding and π-antibonding bands overlap weakly at the Brillouin-zone boundary in graphite, which is responsible for the fairly good electrical conductivity of graphite; whereas these bands are separated by an energy gap of several electron-volts in stoichiometric BN, causing it to be an insulator. In both cases, if residual π attractions between atomic layers are not eliminated or reduced, high friction and wear may result. In graphite, π-bond interactions are generally reduced or eliminated by intercalation. Both donor (e.g., alkali metals) and acceptor (metal chlorides) type intercalants can be used for this purpose (Levy, 1979; Dresselhaus, 1996). As a result, the interlayer shear properties of graphite are markedly improved. However, attempts to find effective intercalation species for HBN were mostly unsuccessful. Within the layered-crystal structure of transition-metal dichalcogenides, metal atoms are sandwiched between the chalcogen atoms in a planar array of S-Mo-S, while the layers in monochalcogenides consist of four atomic layers. For example, each layer of GaSe consists of strongly bonded Ga and Se atoms in the sequence Se-Ga-Ga-Se (see Figure 22.6). The Ga atoms are paired to form the two atomic planes inside, while the chalcogen atoms form the top and bottom planes. Note that the removal of one layer of Ga atoms in the GaSe crystal structure would have produced the exact crystal structure of MoS2, as illustrated in Figure 22.1(c); this suggests that mono- and dichalcogenides are indeed closely related. The interatomic bonding within the layers of mono- and dichalcogenides is strong and mainly of the covalent type, whereas the bonding between adjacent layers is weak and of the van der Waals type. Within the rigid two-dimensional layers of MoS2 crystals, the S atoms have a trigonal prismatic coordination around the Mo atoms, while the Ga atoms in the GaSe structure are tetrahedrally coordinated. Previous studies have clearly demonstrated that the lubricity of a solid lubricant is controlled by a number of intrinsic and extrinsic parameters. For example, intrinsically, both graphite and MoS2 have layered crystal structures, but the extent of their lubricity and durability is largely controlled by extrinsic factors such as the presence or absence of vapors or gaseous species in the test environment. Graphite functions best in humid air, while MoS2 lubricates best in dry and vacuum environments. As mentioned earlier, the lubrication behavior of HBN and H3BO3 is similar to that of graphite. This contrasting behavior of self-lubricating solids has been — and still is — the subject of numerous fundamental studies. Thus far, suggestions have been made that the enhanced lubricity of graphite and HBN in a humid environment may be related to the weakening effect of water molecules on the residual π-bonds between the layers of their crystals. As for the poor lubricity of MoS2 in a humid environment, it has been suggested that water molecules react directly or indirectly with MoS2 and thus alter the interatomic array and
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bonding, which in turn increase friction. When tested in open air, MoS2 and other dichalcogenides were found to react with oxygen and form MoO3 or other types of complex oxides. It has been speculated that the chemical reactions leading to MoO3 formation occur predominantly at the prismatic edges where reactive dangling bonds exist. Another intrinsic parameter that can affect the lubricity of a layered solid is the interlayer-to-intralayer bond-length ratio. It has been reported that this ratio is a crude but revealing indicator of the lubricity of a lamellar solid (Jamison, 1972, 1978). In general, it was found that the greater the interlayer-tointralayer bond-length ratio, the weaker the interlayer bonding with respect to the intralayer bonds, and thus the higher the lubricity. For MoS2 and GaSe crystals, the interlayer-to-intralayer bond-length ratios are 1.5 and 1.6, respectively (Zallen and Slade, 1974). The presence or absence of electrostatic attractions between the layers of mono- and dichalcogenides constitutes yet another intrinsic parameter that can affect the lubricity of these solids. For example, of the numerous metal dichalcogenides, only a few can impart low friction to sliding tribological interfaces. Previous research has shown that despite their layered crystal structures, NbS2, TiS2, VS2, TaS2, etc., are not as lubricious as MoS2 or WS2 (Clauss, 1972; Jamison, 1978). Based on the molecular orbital and valence bond theories, Jamison (1972, 1978) proposed the following explanation for the poor lubricating performance of NbS2, TiS2, VS2, TaS2, etc. In the layered crystal structure of these solids, there is a region of negative electrical charge that not only concentrates above the chalcogen atoms of a given layer, but also extends well into the pockets between the chalcogen atoms of neighboring layers. Because the bottoms of the pockets are positively charged (due to the exposed ion cores of the surrounding atoms), an electrostatic attraction exists between the layers, making the layers of these solids shear with difficulty. As for the excellent solid-lubricating capacities of MoS2 and WS2, the region of negative electrical charge is contained within the layers. Thus, the surfaces of the chalcogen atoms are positively charged, creating an electrostatic repulsion between the layers and making interlayer slippage exceedingly easy (Jamison, 1978). Relatively greater interlayer separation in MoS2 and WS2 crystals is thought to result from the same electrostatic repulsion between successive layers. In general, previous studies have clearly demonstrated that the friction and wear performance of solid lubricants are strongly affected by both the intrinsic (crystal-specific) and extrinsic (operating-environment-specific) factors. Therefore, no single solid lubricant can provide low friction and wear in all environments. Furthermore, not all layered solids are good solid lubricants. The type and magnitude of interlayer bonds are also important.
22.4 High-Temperature Solid Lubricants For applications in open air and at temperatures above 500°C, most of the lamellar solids mentioned above lose their lubricity and become useless. Furthermore, most sliding interfaces (including metals and non-oxide ceramics) become oxidized (Quinn and Winer, 1985). Thin oxide films that form on the sliding surfaces may, in turn, dominate the friction and wear behavior of these interfaces. In particular, wear debris particles trapped at sliding interfaces could be very abrasive and cause high wear. If the sliding bodies differ chemically or if there is a third or fourth body at the sliding interface, two or more oxides may form on the sliding surface and control friction and wear. In past years, significant research has been carried out to study the shear rheology of such oxides and to formulate alloys or composite structures that can lead to the formation of oxides with very low shear strength (Peterson et al., 1994). These are often referred to as lubricious oxides.
22.4.1 Lubricious Oxides, Fluorides, and Sulfates Certain oxides (e.g., Re2O7, MoO3, PbO, B2O3, NiO, etc.), fluorides (e.g., CaF2, BaF2, SrF2, LiF, and MgF2), and sulfates (e.g., CaSO4, BaSO4, and SrSO4) become soft and highly shearable at elevated temperatures and hence can be used as lubricants (Sliney et al., 1965; Sliney, 1969; John and Zabinski, 1999). When applied as thin or thick coatings (by means of PVD, plasma spraying, fusion bonding, etc.), these solids
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0.6 Friction Coefficient
25 C 0.5 300 C
0.4 0.3 0.2
600 C
0.1 1.3 kg
0 0
1000
2000
3000
Sliding Cycle
FIGURE 22.14 Effect of test temperature on friction coefficient of an ion-beam-deposited Cu-Mo film; lower friction coefficients at high temperatures are attributed to formation of CuO-MoO3 films. (From Wahl, K.J., Seitzman, L.E., Bolster, R.N., Singer I.L., and Peterson, M.B. (1997), Ion-beam deposited Cu-Mo coatings as high temperature solid lubricants, Surf. Coat. Technol., 89, 245-251. With permission.)
can provide acceptable levels of friction coefficients and long wear life. They can also be mixed with other solid lubricants to obtain lubrication over much wider temperature ranges. Major drawbacks of oxidebased lubricants are that they are inherently brittle and thus may fracture easily and wear out quickly. Furthermore, most oxide-based lubricants do not provide lubrication down to room temperature. Potential applications for lubricious oxides include high-temperature seals, bearings, and gears, valves and valve seats, variable stator vanes, and foil bearings. Recent systematic studies have demonstrated that the oxides of Re, Ti, Ni, W, Mo, Zn, V, B, etc., become highly lubricious and can provide fairly low friction at elevated temperatures (Kanakia et al., 1984; Kanakia and Peterson, 1987; Peterson et al., 1960, 1982, 1994). Mixed oxides (e.g., CuO-Re2O7, CuOMoO3, PbO-B2O3, PbO-MoO3, CoO-MoO3, Cs2O-MoO3, NiO-MoO3) can also provide wider operational ranges and can be prepared as alloys or composite structures to provide longer durability. The lubricious layers that form by oxidation of alloy surfaces are very desirable and exceptionally advantageous when compared with the solid lubricant coatings with finite lifetimes. At high temperatures, as the oxide layer is depleted from the surface by wear, the alloying ingredients diffuse toward the surface where the oxygen potential is higher; they oxidize again to replenish the consumed lubricious layers that have low shear strength and/or surface energy to decrease friction (Peterson et al., 1982, 1994). Figure 22.14 shows the frictional performance of CuO-MoO3 at different temperatures (Wahl et al., 1997). In a series of fundamental studies, Gardos (1988) demonstrated that at a very narrow range of anion vacancies and at high temperatures, crystalline TiO2 (rutile) and rutile-forming surfaces can provide very low friction coefficients to sliding tribological interfaces. Further work by Gardos (1993) and Woydt et al. (1999) demonstrated the formation of Magneli phases on sliding surfaces containing titanium-based alloys and compounds. Their findings suggested that Magneli phases are principally the result of tribooxidation and that once formed, they can dominate the tribological behavior of sliding ceramic interfaces, mainly because of their unique shear properties. However, TiOx-based solid lubricants have not yet found wide use, mainly because of the difficulty in achieving and maintaining the very narrow range of oxide stoichiometry needed for good lubricity. A new breed of lubricious zinc oxide films was recently synthesized by pulsed-laser deposition, and their tribological properties were explored over a wide range of test conditions (Zabinski et al., 1997). The stoichiometry and microstructure of these films were found to have profound effects on lubricity and were controlled by adjusting substrate temperature and oxygen partial pressure during deposition. Zinc oxide films with oxygen deficiency and nanoscale structure were found to provide low friction coefficients and long wear lives at room temperature. However, as the chemical stoichiometry and crystal structure approached those of the bulk zinc oxide, the tribological properties and load/speed sensitivity
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Cycles
1.00
PLD ZnO Film
0.80
One-Million-Cycle Test 0.60
µ
0.40
µ=0.2
0.20
Cycles
1x106
FIGURE 22.15 Variation of friction coefficient of pulsed-laser deposited ZnO film with number of sliding cycles. (From Zabinski, J.S., Saunders, J.H., Nainaparampil, J., and Prasad, S.V. (2000), Lubrication using a microstructurally engineered oxide: performance and mechanisms, Tribol. Lett., 103-116. With permission.)
of the films degraded. Figure 22.15 shows the variation of friction coefficient of a pulsed-laser-deposited ZnO film during sliding against an AISI 440C steel ball.
22.4.2 Composites Plasma-sprayed self-lubricating composites and adaptive lubricants were recently engineered to combat friction and wear problems at high temperatures. The composite coatings consist of silver and alkaline halides (i.e., CaF2, BaF2) as the self-lubricating entities and chrome carbide and/or oxide as the wearresisting entities (DellaCorte and Sliney, 1987, 1990; Sliney, 1993; DellaCorte and Fellenstein, 1997). Thick plasma sprayed coatings (0.1 to 0.2 mm) and bulk powder metallurgy composite forms of these solid lubricants provide friction coefficients ranging from 0.2 to 0.5, depending on ambient temperature, load, and speed. Over the years, these solid lubricants have been highly optimized and carefully formulated and the latest formulations are capable of providing lubrication over much broader temperature ranges than their earlier versions. Figure 22.16 shows the friction performance of PS-304 (consisting of 20 wt% Cr2O3, 10 wt% Ag, 10 wt% BaF2/CaF2 eutectic composition, and NiCr as the binder) against an alumina ball at temperatures up to 870°C. Recent studies have also demonstrated that these lubricants are very
FIGURE 22.16
Friction performance of PS-304 self-lubricating composite coating at temperatures to 870°C.
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suitable for high-speed sliding bearing surfaces and provide excellent durability and frictional performance, especially when used in foil bearing applications (DellaCorte, 1998). To achieve low friction from room temperature to very high temperature, a series of adaptive solid lubricants has recently been developed. A good adaptive lubricant is made of several ingredients that provide low friction at low temperatures, and as the temperature increases, these lubricious ingredients react with each other and/or oxygen in air to form a high-temperature solid lubricant phase providing low friction. The lubricating entities in this case were selected from those metals that can react with the environment to form the kind of lubricious layers needed (Wlack et al., 1997; Zabinski et al., 1992). One problem is that the oxidation is not reversible, so when the temperature returns to low values, the friction may increase. To solve this problem, researchers have used very thin diffusion-barrier layers to limit the extent of oxidation to the very top surface rather than to the bulk or over a thick layer. Another approach was to use capsules of high-temperature adaptive lubricants in a low-temperature matrix. While the lowtemperature matrix provides lubricity at lower temperatures, the capsules with a protective shell on the surface react with oxygen and become lubricious, thus providing the needed level of lubricity.
22.4.3 New Approaches to Solid Lubrication at High Temperatures Recently, a crystal-chemical approach was introduced by Erdemir (2000a) to classify lubricious oxides on the basis of lubrication performance and operational limits. This approach was proposed to serve as a guide for determining the kind(s) of lubricious oxides needed on a sliding surface at high temperatures. Apparently, the crystal chemistry of certain oxides that form on sliding surfaces relates strongly to their shear rheology and hence their lubricity at high temperatures. The principle of the crystal-chemical approach is based essentially on the ionic potential of an oxide and is defined as γ = Z/r, where Z is the cationic charge and r is the radius of the cation. Erdemir (1999) proposed that using this principle, one can establish model relationship(s) between the quantum-chemical characteristics and the lubricity of oxides at high temperatures. Specifically, it is possible to establish a correlation between the ionic potential or the cationic field strength of an oxide and its shear rheology, and hence its lubricity. Apparently, ionic potential controls several key physical and chemical phenomena in oxides. In general, the higher the ionic potential, the greater the extent of screening of a cation in an oxide by surrounding anions such as B2O3 or Re2O7. Oxides with highly screened cations are generally soft and their melting points are low. Their cations are well-separated and completely screened by anions; hence, they have little or no chemical interaction with other cations in the system. Most of their bonding is with surrounding anions. Conversely, oxides with lower cationic field strengths or ionic potentials (e.g., Al2O3, ZrO2, MgO, and ThO2) are very strong, stiff, and difficult to shear, even at high temperatures, because their cations interact with each other and form strong bonds. The crystal-chemical approach can be used to predict the extent of adhesive interactions between two or more oxides at a sliding interface; hence, it can be used to predict frictional performance. Extensive research by previous investigators has already identified several lubricious oxides that afford fairly low (≈0.2) friction coefficients at elevated temperatures (Kanakia et al., 1984; Kanakia and Peterson, 1987; Peterson et al., 1960, 1982, 1994). Some of these oxides and their friction coefficients at high temperatures are shown in Figure 22.17. As can be deduced from this figure, the higher the ionic potential, the lower the friction coefficient. This means that oxides with higher ionic potentials appear to shear more easily and thus exhibit lower friction at high temperatures. As mentioned earlier, the higher the ionic potential, the greater the screening of a cation in an oxide by surrounding anions. The highly screened cations in an oxide will interact very little with other cations in their surroundings, and this will allow them to shear more easily at elevated temperatures. In most tribological situations, two or more dissimilar solid bodies may be rubbing against each other, and often the sliding surfaces are covered by more than one kind of oxide. The crystal-chemical approach introduced in this chapter can also be used to predict the lubricity of such complex binary oxide systems. Specifically, crystal chemistry can be used to estimate the solubility, chemical reactivity, number of
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FIGURE 22.17 Relationship between ionic potentials and friction coefficients of single oxides. (Adapted from Erdemir, A. (2000a), A crystal chemical approach to lubrication by solid oxides, Tribol. Lett., 8, 97-102.)
compounds formed, and eutectic temperature or lowering of the melting point of an oxide when a second oxide is present. For example, the eutectic temperature and compound-forming tendencies of two oxides are closely related to the cationic field strengths or ionic potentials of the involved elemental species. The ability of an oxide to dissolve in or react with other oxides or to form complex oxides is estimated from the difference in relative ionic potentials of the oxides in the system. In general, the greater the difference in ionic potential, the lower the eutectic temperature and the greater the tendency to form complex oxides. Figure 22.18 shows several cases in which two oxides (CuO-Re2O7, CuO-MoO3, PbO-B2O3, PbO-MoO3, CoO-MoO3, and NiO-MoO3, etc.) were either present at or purposely introduced to the sliding interfaces to achieve low friction at high temperatures. Most of these data were extracted from papers and progress reports authored by Peterson et al. (Peterson, 1987; Peterson et al., 1960, 1982, 1994), who have had extensive experience with lubricious oxides. Nickel-based superalloys, because of their relevance to hightemperature applications, were used as substrates in most of their studies. The specially formulated nickel alloys contained Ti, Ta, W, Re, B, and Mo as potential lubricious oxide formers. Note that the scatter in the friction values shown in Figures 22.17 and 22.18 is large; this is not unusual in the field of tribology because test machines, conditions, or parameters vary greatly from study to study. Recently, Cs-based oxides were reported to be very promising for lubricating Si-based ceramic components at high temperatures. At 600°C, 0.02 to 0.1 friction coefficients have been reported for Cs2Olubricated Si3N4 ceramics (Strong and Zabinski, 1999). During sliding at high temperature, a mixed oxide layer consisting of Cs2O and SiO2 was found and believed to be responsible for low friction. As can be seen from Figure 22.18, such a combination would result in a large difference in the ionic potentials of these two oxides. From Figure 22.18, it can be seen that as the difference in ionic potential increases, the lubricity of the oxide species also increases. There are two fundamental reasons for this phenomenon. One is that as the difference in ionic potential increases, the ability of oxides to form a low-melting-point or readily shearable compound improves; hence, oxides tend to exhibit lower hardness and shear strength at elevated temperatures because the anions are able to better shield or screen the cations and thus make them less likely to interact with neighboring cations. The second reason for the phenomenon is that the ability or affinity of ionic species to form highly stable compounds (that exert very little chemical or electrostatic
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FIGURE 22.18 Relationship between friction coefficient and difference in ionic potentials of double oxides. (From Erdemir, A. (1999), A crystal chemical approach to lubrication by solid oxides, Tribol. Lett., 8, 97-102.)
attraction) improves as the difference in ionic potential increases. Lower attraction between sliding surfaces means lower adhesive forces across the sliding contact interfaces, and hence lower friction (Erdemir, 2000a).
22.5 Self-Lubricating Composites 22.5.1 Traditional Materials Self-lubricating composites have been available for a long time and are used rather extensively by industry to combat friction and wear in a variety of sliding, rolling, and rotating bearing applications. They are generally prepared by dispersing appropriate amounts of a self-lubricating solid (as fillers, preferably in powder form) with a polymer, metal, or ceramic matrix. With powder metallurgy techniques, fillers and matrix materials can be thoroughly mixed, compacted, and then sintered (if necessary) to obtain the desired shape. They can also be extruded, rolled, or hot/cold-pressed into useful shapes. Recently, compositionally and functionally gradient self-lubricating composite structures were also manufactured and offered for industrial use. While the core is made of nearly pure matrix material to provide high strength, hardness, and toughness, the near-surface regions where sliding will occur are enriched in selflubricating powders to achieve lubricity. Composite structures prepared in this fashion are used for a wide range of tribological applications, such as bushings, bearings, and a variety of gears and traction devices. For example, copper-graphite and silver-graphite composites are used in electrical brushes and contact strips, while aluminum-graphite composites are well-suited for bearings, pistons, and cylinder liners in engines and a host of other mechanical systems (Kumar and Sudarshan, 1996). Recent tribological studies have demonstrated that when mixed at correct concentrations with optimal particle sizes, self-lubricating filler materials can have a substantial beneficial impact on the mechanical and tribological properties of matrix materials. For example, it was shown that graphite, MoS2, and boric acid fillers tend to increase the wear resistance of nylon and polytetrafluoroethylene (PTFE)-type polymers (Blanchet and Kennedy, 1992; Fusaro, 1990). Aluminum-graphite composites exhibit excellent lubricity, durability, and resistance to galling under both dry and lubricated conditions (Rohatgi et al.,
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1992). When the graphite content in aluminum-matrix composites exceeds ≈20 vol%, the friction coefficient approaches that of pure graphite and becomes highly independent of the matrix alloy. AluminumWS2 composites were also found to be very effective in reducing galling and in providing excellent lubricity and durability, especially in high-vacuum environments (Prasad and Mecklenburg, 1994). The presence of WS2 particles in the matrix results in significantly increased resistance to seizure and enables the composite body to operate under very high loads without galling. Recent studies concluded that improved tribological behavior was mainly due to the formation of a thin transfer layer on the sliding surfaces of counterface materials. In the case of polymers, a significant increase in mechanical strength was also observed and thought to be responsible for high wear resistance. It was found that, initially, transfer films were not present but formed as a result of surface wear and subsurface deformation. They are continuously replenished by embedded graphite particles dispersed in the matrix (Rohatgi et al., 1992). In addition to metal-matrix composites, a series of self-lubricating polymer and ceramic matrix composites have also been developed, tested, and offered for industrial use in recent years (Gangopadhyay and Jahanmir, 1991; Prasad and Mecklenburg, 1994; Fredrich et al., 1995). These composites are emerging as an important class of tribological materials, offering new means to combat friction, wear, and galling under extreme conditions. In a recent study, tribological properties of fine-grain alumina (20%)-graphite composites were explored as potential candidates for advance sealing applications. Pin-on-disk wear tests showed that friction coefficients can be reduced from 0.5 for alumina-on-alumina to ≈0.25 for aluminagraphite composite (Yu and Kellett, 1996). In another study, ceramic-matrix composites were fabricated by drilling a series of small holes in alumina and silicon nitride ceramics and then filling the holes with NiCl2-intercalated graphite under high pressure. Addition of graphite to silicon nitride considerably reduced the friction coefficient, but the alumina-graphite composites exhibited only a marginal reduction in friction coefficient compared to that of the alumina. The reduction in friction coefficient for silicon nitride-graphite composite can be explained by the formation of transfer films consisting of a mixture of materials from both contacting surfaces. However, for the alumina-graphite composites, the graphite regions were completely covered with steel wear particles, inhibiting the formation of graphite-containing transfer films (Gangopadhyay and Jahanmir, 1991). Mixing of Sb2O3 with MoS2 was shown to act synergistically to improve the friction and wear behavior of MoS2. Specifically, the tribological behavior improves because only the thin layers of MoS2 residing on top are exposed to the environment, while the MoS2 at the bottom is protected against thermal or environmental degradation by Sb2O3, which also acts as a beneficial support for MoS2. The proposed mechanism suggests that composite structures containing Sb2O3 were also found to be more resistant to tribo-oxidation than was pure MoS2 alone (Zabinski et al., 1993).
22.5.2 New Self-lubricating Composite Coatings and Structures Recent advances in PVD and CVD technologies have led to the development of a new generation of selflubricating nanocomposite films and multilayer coatings. One such film is based on the MoS2 and Ti system and is produced by closed-field unbalanced magnetron sputtering. This film is much harder and more wear-resistant than conventional MoS2 coatings, yet it still has the low friction characteristics of conventional MoS2 films. Its friction coefficient against a steel ball is ≈0.02 in humid air and <0.01 in dry N2. The Vickers hardness value could be >1500 HV (Teer et al., 1997; Fox et al., 1999). Furthermore, this coating is not greatly affected by moisture in the test environment. It is proposed for use in a variety of dry sliding and machining applications (e.g., milling, drilling, tapping, cold-forming dies and punches, stamping, bearings, and gears for aerospace and vacuum applications). New coating architectures based on layers of a self-lubricating solid (e.g., MoS2, WS2, etc.) and a metal, ceramic, or hard metal nitride or carbide (i.e, Ti, TiN, TiC, Pb, PbO, ZnO, Sb2O3) were also produced in recent years and were shown to work extremely well under demanding tribological conditions. These coatings can be prepared by co-sputtering of MoS2 and TiN or TiB2 targets, or a single target composed
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of TiN and MoS2. The resultant coatings may consist of distinct TiN and MoSx phases in the form of a nanodispersive system. The hardness of these coatings could be as high as 20 GPa, while their friction coefficients are generally low (i.e., ≈0.1), even in open-air environments. Because of high hardness and low friction, they can be used in both sliding and machining applications (Gilmore et al., 1998a,b). Recently, researchers have also produced multilayers of MoSX/Pb and MoSX/Ti (with individual layer thickness in the 4 to 100 nm range) by magnetron sputtering at room temperature. Sliding wear tests in 50% relative humidity showed great improvements in wear life over that of pure MoSx coatings (Simmonds et al., 1998). The three-dimensional design of adaptive coatings based on a multicomponent MoS2/TiC/DLC coating architecture resulted in improved tribological properties over broad ranges of environmental humidity and other test parameters (Voevodin et al., 1998). While the hard coatings of TiC and DLC provided high strength and resistance to wear, solid lubricants DLC and MoS2 provided low friction at the sliding surface. The coating had friction coefficients of 0.15 in humid air and 0.02 in dry nitrogen, thus increasing the prospects for use in space mechanisms. PbO/MoS2 and ZnO/WS2 nanocomposite films were also produced in recent years and tested for their lubricity and durability in a variety of environments. The volume fraction of WS2 decreased with increasing depth from the surface (Wlack et al., 1994). Composite films perform significantly better during tribotesting than films composed entirely of MoS2 or PbO and ZnO. In addition, the composite films demonstrate the properties of “adaptive” lubricants. MoS2 provides lubrication at room temperature; however, when the films are exposed to oxidizing environments at elevated temperatures, they adapt by forming PbMoO4. This compound has been noted to display lubricant properties at high temperature. Thus, there is significant potential for tailoring film compositions so that the components react to produce lubricious wear debris and lubrication over extended temperature ranges (Wlack et al., 1997; Zabinski et al., 1992). Electroless nickel, chromium, nickel-phosphorus coatings containing small amounts of graphite, MoS2, PTFE, and diamond particles were also developed in recent years and used to achieve relatively thick films with self-lubricating properties. The deposition of MoS2 containing Ni-P composite coatings (containing ≈3 wt% MoS2) resulted in significant improvements in wear resistance and reduced the friction coefficient of the base Ni coatings (Moonir-Vaghefi et al., 1997).
22.6 Soft Metals Mainly because of their low shear strengths and rapid recovery as well as recrystallization, certain pure metals (e.g., In, Sn, Pb, Ag, Au, Pt, Sn, etc.) can provide low friction on sliding surfaces (Wells and De Wet, 1988; Sherbiney and Halling, 1977). They are used chiefly as solid lubricants because the attractive properties they combine are unavailable in other solid lubricants. For example, in addition to its soft nature, silver has excellent electrical and thermal conductivity, oxidation resistance, good transfer-filmforming tendency, and a relatively high melting point; thus, it has been commercially used to lubricate the high-speed ball bearings of rotating anode X-ray tubes for many years. The Mohs hardness values of soft metals are generally between 1 and 3. Reported friction coefficients of soft metals range from 0.1 to 0.4, depending on the metal and test conditions. Pb, In, and Sn provide better lubricity at room temperature than Ag, Au, and Pt. At elevated temperatures, Pb, Sn, and In melt and undergo oxidation. Ag, Au, and Pt have fairly high melting points, do not oxidize appreciably, and hence are preferred for high-temperature lubrication purposes (Erdemir and Erck, 1996; Maillat et al., 1993; Seki et al., 1995). Au remains in metallic form regardless of the temperature, while Ag2O decomposes as the temperature increases and Pt oxidizes only slightly. Bronze and babbitts prepared by alloying some of these soft metals with Al, Zn, Cu, have been used as bushings, bearings, and other tribological applications for a number of years. Soft metals are generally produced as thin films on surfaces to be lubricated. Simple electroplating and vacuum evaporation can be used to deposit most of these metals as self-lubricating films, but dense and highly adherent films are produced by ion plating, sputtering, or ion-beam-assisted deposition techniques (Erdemir et al., 1990a). Film-to-substrate adhesion is extremely critical for achieving long
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FIGURE 22.19 Variation of friction coefficient of indium films as a function of film thickness. (From Sherbiney, M.A. and Halling, J. (1977), Friction and wear of ion-plated soft metallic films, Wear, 45, 211-220. With permission.)
wear life or durability, especially on the surfaces of ceramic tribomaterials (Spalvins and Sliney, 1994; Spalvins, 1998). The thickness of the soft metallic films also plays a major role in both friction and wear. The lowest friction coefficients and wear rates are usually obtained with thinner films (i.e., 0.5 to 1 µm thick) and under higher contact pressures (Dayson, 1971; El-Sherbiny and Salem, 1986). Figure 22.19 shows the variation of friction coefficient of an indium film with thickness (Sherbiney and Halling, 1977). However, too thin a film tends to wear out quickly. Also, the friction coefficients of most soft metals tend to decrease as the ambient temperature increases, mainly because of additional softening and rapid recovery from strain hardening. Thick films result in large contact areas and hence high friction. The combination of very high thermal conductivity with low shear strength and chemical inertness makes silver and gold coatings ideal for applications involving high frictional or ambient heating, such as sliding ceramic interfaces. As can be seen in Figure 22.20, thin Ag films can lower wear rates of zirconia balls and disks by factors of 2 to 3 orders of magnitude. Reduction in wear is more dramatic at higher sliding speeds. This is mainly because of the fact that zirconia has a very poor thermal conductivity, and thus suffers severe thermomechanical wear at high sliding velocities. However, when a highly thermally
FIGURE 22.20 Wear performance of uncoated and silver-coated zirconia (calcia-partially stabilized) test pairs at sliding velocities up to 2 m/s. (Adapted from Erdemir, A., Busch, D.E., Erck, R.A., Fenske, G.R., and Lee, R.H. (1991b), Ionbeam-assisted deposition of silver films on zirconia ceramics for improved tribological behavior, Lubr. Eng., 47, 863-867.)
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FIGURE 22.21 zirconia ball.
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Physical condition of a wear track formed on silver-coated zirconia disk during sliding against
conductive film like silver is present at the sliding interface, the wear rate decreases dramatically, mainly because frictional heat is dissipated rapidly from the sliding interface. The low friction coefficient of silver also helps in reduced frictional heating. Figure 22.21 shows the condition of a wear track formed on a silver-coated zirconia disk. Overall, the film is still intact; only the tips of substrate asperities are exposed, but the base zirconia is well-protected against wear. Figure 22.21 also reveals some physical evidence for shear deformation experienced by soft silver film during contact sliding. Silver is used as a lubricant in X-ray tubes, certain satellite parts, ball bearings, bolts, and other sliding parts in nuclear reactors. When applied as a dense and adherent coating on the surfaces of these components, it can effectively dissipate frictional heat that can otherwise cause thermomechanical and tribochemical wear. Used on ceramic surfaces, it shears easily, thereby reducing the friction and microfracture-induced wear of the sliding ceramic surfaces (Erdemir et al., 1990a, 1991). Silver and other soft metallic coatings can also protect the sliding surfaces against environmental and/or tribochemical degradation under dry and oil-lubricated sliding contact conditions (Ajayi et al., 1993; Erdemir et al., 1992; DellaCorte et al., 1988). Under lubricated sliding conditions, thin silver films were extremely effective in reducing friction and wear at temperatures up to 300°C (Ajayi et al., 1993, 1994; Erdemir et al., 1992, 1996a). One of the major shortcomings of metallic solid lubricants is that most of them react with sulfur and chlorine (if present in the operating environment) and may undergo rapid corrosive wear.
22.7 Polymers Polymers in various forms are widely used in tribology. They are lightweight, relatively inexpensive, and easy to fabricate. They can easily be blended with other solids to make self-lubricating composite structures. Certain polymers (polytetrafluoroethylene [PTFE], polyimide, nylon, ultra-high-molecular-weight polyethylene [UHMWPE], etc.) are self-lubricating when used in both the bulk and thin-film forms, or as binders for other solid lubricants (Lancaster, 1984; Fusaro, 1988, 1990; Gresham, 1994; Jamison, 1994). Coatings can be produced on a tribological surface by first spraying or sprinkling the powders, then consolidating and curing them at high temperatures. The most common polymer-based solid lubricant is PTFE, which is widely known as Teflon (an E.I. DuPont de Nemours Co. trade name). It is a “nonstick” surfacing agent used in cookware, seals, and gaskets to facilitate release. It is also used in various other forms (powder, composite, colloidal dispersion in oils and greases) to achieve low friction. Its friction coefficient ranges from 0.04 to 0.2, depending on test conditions. PTFE can be used at temperatures up to about 250°C. Polyimide and its coatings can also provide low friction. It can also be composited with a self-lubricating inorganic filler to enhance its mechanical and tribological properties, especially at
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elevated temperatures (Fusaro and Sliney, 1973; Blanchet and Kennedy, 1992). Fine PTFE powders have also been used as additives in various oils and as thickeners in greases (Willson, 1992). UHMWPE is another popular polymer used widely in total joint replacements (Kurtz et al., 1999). Because of the very long molecules and highly entangled molecular chains, it provides better wear resistance than PTFE. However, wear of this polymer still poses a major obstacle for the longevity of the total joint replacements. Recent efforts to solve these problems have increased interest in the structure, morphology, and mechanical properties of the UHMWPE and in various surface and structural treatment processes (such as crosslinking, carbon-fiber reinforcing, recrystallization). It was reported that crosslinked UHMWPE has much better wear properties and thus is a promising alternative for total joint replacements. There are several excellent review articles and book chapters devoted to the tribological uses of UHMWPE and other polymers in various applications. It is impossible to cover all of them here, but readers can refer to the references provided here for further information (Wang et al., 1995; Briscoe, 1990; Zhang, 1997; Bahadur and Gong, 1992; Friedrich et al., 1995).
22.8 Summary and Future Directions This chapter further demonstrates that solid lubricants have much to offer for demanding tribological applications. Their use in advanced tribosystems is expected to increase in the near future, mainly because the operating conditions of future tribosystems are becoming more and more demanding. One major problem is that there exists no such lubricant that is capable of providing reasonably low and consistent friction coefficients over broad test conditions, temperatures, and environments. The results of previous studies demonstrate that the performance of layered solid lubricants are very much dependent on tribological and environmental conditions. For example, the lubricity of transition-metal dichalcogenides is adversely affected by moisture, while graphite depends on moisture for good lubricity. Layered solid lubricants can be doped or intercalated with a number of metals and compounds to achieve lesser sensitivity to ambient humidity and temperature. Nowadays, most solid lubricants are produced as thin solid films on sliding surfaces. They are also used as fillers in self-lubricating metallic, ceramic, and polymeric composites. In most cases, a transfer film is found on the sliding surfaces. In general, formation of such a film at sliding interfaces seems to be key to achieving low friction and long wear lives in most solid-lubricated surfaces. For solid lubricant films, strong adhesion is key for long service life. Modern sputtering techniques and ion-beam processes are quite capable of imparting strong adhesion between solid lubricant films and their substrates. Ionbeam mixing of conventional solid lubricants, such as MoS2, with ceramics is also feasible and appears promising for severe tribological applications. For materials with poor thermal conductivity, Ag and Au films combining high thermal conductivity with low shear strength and good chemical inertness should be considered. Silver is primarily used as a lubricant in ball bearings of rotating anode X-ray tubes. A unique solid lubricant, boric acid, which forms naturally on the surfaces of boric oxide- and boron-containing ceramics, has recently been discovered. It was shown that this lubricant can impart remarkably low friction coefficients (e.g., 0.02) to sliding interfaces in moist environments where MoS2 is known to be ineffective. For applications involving high temperatures, most layered solid lubricants appear ineffective. A combination of solid and liquid lubrication may provide short-term solutions to this problem; but for a long-term solution, the development of effective lubricious oxides, fluorides, and other compounds is essential. Recently, a crystal-chemical approach was introduced to classify lubricious oxides on the basis of their lubrication performance and operational limits at high temperatures. This approach may serve as a basis for determining the kind(s) of lubricious oxides needed on a sliding surface at high temperatures. Lubrication from vapor phases and by catalytic cracking of carbonaceous gases also appears promising. Recently, sulfates of Ca, Ba, and Sr were shown to provide quite a low friction coefficient at high temperatures. A series of adaptive lubrication strategies was also introduced in recent years and shown to be effective in achieving lubrication at broader temperature ranges.
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Certain polymers are also used as solid lubricants because the attractive properties they combine are unavailable in other solid lubricants. Polymers are particularly favored for applications where cost, weight, corrosion, and biocompatibility are the major considerations. In short, solid lubricants have been around for a long time and they have been meeting some very important and critical tribological needs. They are expected to be in high demand for many more years to come.
References Ahsley, S. (1992), Lubricating ceramic engines with exhaust, Mechanical Eng., 114, 72-73. Ajayi, O.O., Erdemir, A., Hsieh, J.H., Erck, R.A., Fenske, G.R., and Nichols, F.A. (1993), Boundary film for structural ceramic materials, Wear, 164, 1150-1155. Ajayi, O.O., Erdemir, A., Fenske, G.R., Erck, R.A., Hsieh, J.H., and Nichols F.A. (1994), Effect of metalliccoating properties on the tribology of coated and oil-lubricated ceramics, Tribol. Trans., 37, 656-661. Barnett, R.S. (1977), Molybdenum disulfide as an additive for lubricating greases, Lubr. Eng., 33, 308-313. Bahadur, S. and Gong, D. (1992), The action of fillers in the modification of the tribological behavior of polymers, Wear, 158, 41-59. Bhattacharya, R.S., Rai, A.K., McCormick, A.W., and Erdemir A. (1993), High-energy (MeV) ion-beam modifications of sputtered MoS2 coatings on ceramics, Tribol. Trans., 36, 621-626. Bhattacharya, R.S., Rai, A.K., Zabinski, J.S., McDevitt, N.T., and Neil, T. (1994), Ion beam modification of fullerene films and their frictional behavior, J. Mat. Res., 9, 1615-1618. Bhushan, B., Gupta, B.K., Van Cleef, G.W., Capp, C., and Coe, J.V. (1993), Sublimed C60 films for tribology, Appl. Phys. Lett., 62, 3253-3255. Bindal C. and Erdemir, A. (1996), Ultralow friction behavior of borided steel surfaces after flash-annealing, Appl. Phys. Lett., 68, 923-926. Blanchet, T.A. and Kennedy, F.E. (1992), Sliding wear mechanism of polytetrafluoroethylene (PTFE) and PTFE composites, Wear, 153, 229-243. Blanchet, T.A., Lauer, J.L., Liew, Y.-F., Rhee, S.J., and Sawyer, W.G. (1994), Solid lubrication by decomposition of carbon monoxide and other gases, Surf. Coat. Technol., 68-69, 446-452. Boes, D.J. and Chamberlain, B. (1968), Chemical interactions involved in the formation of oxidationresistant solid lubricant composites, ASLE Trans., 11, 131-139. Bolster, R.N., Singer, I.L., Wegand, J.C., Fayeulle, S., and Gossett, C.R. (1991), Preparation by ion-beamassisted deposition, analysis and tribological behavior of MoS2 films, Surf. Coat. Technol., 46, 207-216. Briscoe, B.J. (1990), Materials aspects of polymer wear, Scripta Met. Material., 24, 839-844. Broman, V.E., DeJovine, J., DeVries, D.L., and Keller, G.H. (1978), Testing of Friction Modified Crankcase Oils for Improved Fuel Economy, SAE Reprint No. 780597. Buckley, D. (1978), Friction and transfer behavior of pyrolytic boron nitride in contact with various metals, ASLE Trans., 21, 118-124. Burton, R.A. and Burton, R.G. (1989), Friction and wear experiments on glassy carbon based materials, Proc. 35th Meet. IEEE Holm Conf. on Electrical Contacts, IEEE, New York, 31-34. Clauss, F.J. (1972), Solid Lubricants and Self-lubricating Solids, Academic Press, New York. Dayson, C. (1971), The friction of very thin solid film lubricants on surfaces of finite roughness, ASLE Trans., 14, 105-115. DellaCorte C. and Fellenstein, J.A. (1997), The effect of compositional tailoring on the thermal expansion and tribological properties of PS300: a solid lubricant composite coating, Tribol. Trans., 40, 639-645. DellaCorte, C., Sliney, H.E., and Deadmore, D.L. (1988), Sputtered silver films to improve chromium carbide based solid lubricant coatings for use to 900°C., STLE Trans., 31, 329-334. DellaCorte, C. and Sliney, H.E. (1987), Composition optimization of self-lubricating chromium-carbide based composite coatings for use to 760°C, ASLE Trans., 30, 77- 83. DellaCorte, C. (1998), The Evaluation of a Modified Chrome Oxide Based High Temperature Solid Lubricant Coating for Foil Bearings, NASA/TM-1998-208660.
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23 Tribological Properties of Metallic and Ceramic Coatings 23.1 23.2
Introduction ..................................................................... 827 Tribology of Coated Surfaces .......................................... 828 Contact Mechanisms and Stresses in the Surface • Tribological Contact Mechanisms in Coated Surfaces • Macromechanical Friction and Wear Mechanisms • Micromechanical Tribological Mechanisms • Tribochemical Mechanisms of Coated Surfaces • Nanophysical Contact Mechanisms
23.3
Macromechanical Interactions: Hardness and Geometry .......................................................................... 835 Soft Coating on Hard Substrate • Hard Coating on Softer Substrate • Load-Carrying Capacity of Coated Surfaces
23.4
Micromechanical Interactions: Material Response........ 839 Material Response • Energy Accommodation in the Surface • The Influence of Fracture Toughness in Material Response
23.5
Kenneth Holmberg VTT Manufacturing Technology
Surface and Subsurface Cracks • Tribological Influence of Wear Debris • Debris Agglomeration • Transfer Layers • Reaction Layers
23.6
Multicomponent Coatings .............................................. 852 Multilayer Coatings • Nanocomposite Coatings • Functionally Graded Coatings • Adaptive Coatings
Allan Matthews The University of Hull
Material Removal and Change Interactions: Debris and Surface Layers ........................................................... 844
23.7
Concluding Remarks ....................................................... 858
23.1 Introduction The physical and chemical phenomena that govern both the friction and wear in moving contacts take place at the surfaces of the solids in relative motion. Usually, the interaction mechanisms at the outermost surfaces are the most crucial for tribological performance. The introduction of a fluid between the surfaces has long been the most common way to change the tribological behavior of two surfaces moving relative to each other. Another increasingly popular possibility is to apply a thin surface layer or coating on one or both of the surfaces. This approach is promoted by the new coating techniques that have been developed over the last few decades. In particular, physical vapor deposition (PVD) and chemical vapor deposition (CVD) offer considerable possibilities to tailor the thin surface layers with regard to their material and structure as well as their mechanical and chemical properties. These deposition techniques are presented in Chapter 24.
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The first major commercial application of tribological thin surface coatings was the use of titanium nitride and titanium carbide coatings on cutting tools. Other early applications were the use of lead coatings for dry lubrication of rolling bearings in near-vacuum conditions in space, and gold coatings for electrical contacts. Following the early rapid adoption of advanced coatings on cutting tools, there has been a gradual but accelerating interest in the use of vapor deposition technologies in other applications sectors (e.g., automotive and aerospace) and in other branches of manufacturing industry (e.g., food processing) (Leyland and Matthews, 1994; Cselle and Barimani, 1995; Bull and Jones, 1996; Zabinski et al., 1996; Enomoto and Yamamoto, 1998; Theunissen, 1998; Verkammen et al., 1999). Two issues that have constrained their wider adoption include their relatively higher cost and concern over repeatability of properties such as thickness, composition, hardness, and adhesion. Such reliability issues are now being solved through improvements in process monitoring and control. Also, developments in continuous and semicontinuous high-throughput coating equipment have reduced the coating cost per component and opened up high-volume markets such as automotive parts. These include components used in fuel injection systems, air conditioning units, engines and even transmission systems in high-performance vehicles. Thus, the nature of the tribological contacts to be protected by the coatings is becoming ever more wide-ranging and demanding. Hence, there is a need for a full and systematic understanding of both the mechanisms occurring and the response behavior of coatings to these challenging applications. Today, there is a huge variety of metallic and ceramic coatings available and used for tribological applications, as well as soft polymer coatings, lamellar coatings such as molybdenum disulfide, and extremely hard coatings such as diamond and cubic boron nitride that are receiving research attention. This chapter focuses on the tribological behavior and properties of metallic and ceramic coatings, as the others are covered in elsewhere in this book. Another constraint applied is to focus on thin tribological coatings, that is, those that are sufficiently thin that the substrate material plays a role in determining the friction and wear performance. Thus, coatings that are so thick that there is little or no substrate influence on the tribological behavior — the coating in effect acts as a bulk material — are excluded. The tribology of bulk materials is presented in Section I of this Handbook. This chapter primarily concerns the tribology of dry contacts. The addition of a lubricant will, in many cases, lead to a lessening of the severity of the tribological mechanisms, but it may also change the friction and wear mechanisms involved, for example, through its influence on the formation of surface layers. This aspect has received little attention in the literature. The authors’ purpose is to review the present understanding of tribological mechanisms of metallicand ceramic-coated surfaces, as well as to deepen the understanding of the crucial micromechanical interactions by introducing a new energy accommodation concept that includes elastic, plastic, and fracture mechanics considerations. The approach is to try to explain in qualitative terms the tribological mechanisms and interactions, as it has been difficult to produce precise quantitative generic data, due to the large scatter in reported experimental methods and conditions in the literature. This chapter focuses primarily on the most recent literature published, as the earlier works can be found in previous reviews of the subject, such as Holmberg and Matthews (1994) and Holmberg et al. (1998).
23.2 Tribology of Coated Surfaces 23.2.1 Contact Mechanisms and Stresses in the Surface The phenomena that take place in a tribological contact are influenced by the force pressing the two surfaces together. Calculation methods for the stress fields and deformations in a coated surface have been reviewed in the references cited above. A useful approach to calculating the coating/substrate interface stresses has been used by Ramalingam and Zheng (1995) to assess the problems that can be encountered when hard coatings are applied on
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substrates with lower or higher compliance than the coating. Numerical solutions are obtained for different stress distributions on the coated surface. They show how tensile stresses in the wake of the contact tend to separate the coating from the substrate, and how this can be solved by adjusting the film thickness and choice of coating conditions to ensure that the coating-to-substrate adhesion strength can withstand the stresses. The calculations were later extended to also include interface stresses and multilayer coatings (Zheng and Ramalingam, 1995, 1996). In the analysis of interfacial stresses, it is necessary to include the influence of parameters such as coating thickness, interface topography, and elastic mismatch, as well as the effects induced by pores, edges, or scratches (Wiklund et al., 1999). Coatings that are thin compared to the interface topography have been found to be less sensitive to residual stress-induced failure. At a critical coating thickness, the stress across the interface can be of a magnitude sufficient to initiate coating delamination. However, residual stresses can also be beneficial; for example, the influence of high compressive stresses in hard and smooth diamond coatings has been studied by Gunnars and Alaheliste (1996) and Gåhlin et al. (1996). They found that highly stressed coatings correspond with smoother surfaces and wear rates, which are only 5 to 20% of those of the stress-free coatings. The internal stresses were shown to influence the crack propagation direction in diamond coatings. For other coatings, such as TiN, it should be noted that the process parameters that control film stresses (e.g., ion current density, temperature, and bias voltage) also influence other properties such as crystallographic structure, density, and even the texture. It is not usually possible to separate out the specific effect of the residual stress on performance. Nevertheless, it is generally believed that the residual compressive stresses in the plane of the coatings, which are usually produced by plasma-assisted PVD methods, are beneficial to tribological performance. The surface profiles, both undeformed and deformed, the contact pressures, and the von Mises stresses beneath the surface for a rough sphere in contact with a smooth plane are shown in Figure 23.1. Finiteelement methods have been applied to evaluate the stress field in the hard coating and the substrate under frictional loads (Diao et al., 1994a; Wong and Kapoor, 1996; Wong et al., 1997; Bouzakis et al., 1998; Lowell, 1998; Njiwa et al., 1998a,b). Diao and Kato analyzed the von Mises stress distributions in hard coatings and in elastic sliding (Diao and Kato, 1994a,b; Diao et al., 1994a). An elliptical distribution of normal and traction contact pressures was assumed for the analysis of von Mises stress for different coating thicknesses, friction coefficients, and elastic moduli of the coating and the substrate. The position of yield could be calculated and they introduced a local yield map showing the yield strength ratio in relation to the ratio of the coating thickness to the contact half-width. The local yield maps showed that yield at the coating-substrate interface on the substrate side is the most common case under a wide range of contact conditions. The surface roughness is an important parameter influencing the contact stresses, especially at the coating-substrate interface. This was first shown by Sainsot et al. (1990), who also concluded that in hard coatings with thicknesses less than 15 µm on softer substrates, the maximum von Mises stresses both in the coating and in the substrate will be located just at their interface. This clearly confirms the importance of analyzing the stresses at the coating-substrate interface and comparing them to the coating adhesion strength. In rolling contact fatigue situations (e.g., rolling bearings), the surface roughness will result in small-scale contact stress spikes that initiate cracks and result in failure (Polonsky et al., 1997; Nélias et al., 1999). A numerical technique, including integral transform and finite-element methods for solving contact problems in layered rough surfaces, has been developed by Mao et al. (1994; 1995) and Bell et al. (1998). They apply their numerical model for the two-dimensional dry sliding contact of two elastic bodies on real rough surfaces, where an elastic body contacts with a multilayer surface under both normal and tangential forces. Of special interest is that their model uses surface profile data directly recorded with a stylus-measuring instrument. They analyze the contact pressure distribution for layers with different coefficients of friction, thicknesses, and elastic moduli. The magnitude of internal stresses can vary but, for example, for TiN coatings on steel deposited by different PVD techniques, they are compressive. Hardness and bonding strength have an obvious effect on internal stresses in TiN coatings (Daming et al., 1998) and this influences their tribological behavior.
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FIGURE 23.1 (a) Profiles of a rough sphere, undeformed, and deformed loaded against a plane surface. (b) Normalized contact pressures for a smooth and a rough sphere loaded against a plane surface. (c) Lines of constant normalized von Mises stresses for a rough sphere loaded against a smooth plane surface with no friction. (a = Hertzian contact radius, h = height, z = depth, p = pressure, po = maximum Hertzian contact pressure.) (Adapted from Lee, S.C. and Ren, N. (1994), The subsurface stress field created by three-dimensionally rough bodies in contact with traction, Tribol. Trans., 37, 615-621.)
FEM modeling of a TiN-coated steel substrate subject to rolling with a surface crack perpendicular to the surface shows that the stress intensities at the surface increased with layer thickness and crack length (Eberhardt and Kim, 1998). Crack face friction reduced the stress intensity more significantly for thicker layers and longer cracks, and for higher coating/substrate stiffness ratios.
23.2.2 Tribological Contact Mechanisms in Coated Surfaces The tribology of a contact involving surfaces in relative motion can be understood as a process with certain input and output data (Holmberg and Matthews, 1994). Input data that are used as a starting
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FIGURE 23.2 The tribological process in a contact between two surfaces includes mechanical and tribochemical changes as well as material transfer. The changes are determined by material and energy input parameters and result in a similar set of partly changed output parameters.
point for the analysis of a tribological contact include the geometry of the contact, both on a macroand microscale, the material properties based on the chemical composition and structure of the different parts involved, and the environmental parameters, as shown in Figure 23.2. Other input data include the energy parameters such as normal load, velocity, tangential force, and temperature. The tribological process takes place as the two surfaces are moving in relation to each other, and both physical and chemical changes occur in accordance with the physical and chemical laws with respect to the input data. As a function of time, the tribological process causes changes in both the geometry and the material composition and results in energy-related output effects: friction, wear, velocity, temperature, sound, and dynamic behavior. The complete tribological process in a contact in which two surfaces are in relative motion is very complex because it simultaneously involves friction, wear, and deformation mechanisms at different scale levels and of different types. To achieve a holistic understanding of the complete tribological process taking place and to understand the interactions, it is useful to separately analyze the tribological changes of four different types: the macro- and microscale mechanical effects, the chemical effects, and the material transfer taking place, as shown in Figure 23.3. In addition, there has recently been an increasing interest in studying tribological behavior on a molecular level; that is, nanophysical effects (Bhushan, 1995, 1999). A better and more systematic understanding of the mechanisms involved in a tribological contact is necessary for the optimization of the properties of the two contacting surfaces in order to achieve the required friction and wear performance. Approaches to the tribological optimization of surfaces have been presented by Matthews et al. (1993) and Franklin and Dijkman (1995), who introduce eight wear design rules in an expert system for assisting the selection of metallic materials, surface treatments, and coatings during the initial stages of engineering design.
23.2.3 Macromechanical Friction and Wear Mechanisms The macromechanical tribological mechanisms describe the friction and wear phenomena and are influenced by the stress and strain distribution in the entire contact, the total elastic and plastic deformations they result in, and the total wear particle formation process and its dynamics. In contacts between two surfaces of which one or both are coated, four main parameters can be defined that control the tribological contact behavior. They are:
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FIGURE 23.3 Tribological contact mechanisms: (a) macromechanical, (b) material transfer, (c) micromechanical, (d) tribochemical, and (e) nanophysical.
1. 2. 3. 4.
coating-to-substrate hardness relationship thickness of the coating surface roughness size and hardness of any debris in the contact, which may originate from external sources or be produced by the surface wear interactions themselves
The relationship between these four parameters will result in a number of different contact conditions characterized by specific tribological contact mechanisms. Figure 23.4 shows schematically 12 such very typical tribological contacts, with different mechanisms influencing friction, when a hard spherical slider moves on a coated flat surface (Holmberg, 1992). The corresponding wear mechanisms have been described in a similar way (Holmberg et al., 1993). The macromechanical influencing parameters are discussed in more detail in Section 23.3.
23.2.4 Micromechanical Tribological Mechanisms The origins of the friction and wear phenomena observed on the macrolevel are found in the mechanisms that take place at the microlevel. The micromechanical tribological mechanisms describe the stress and strain formation at an asperity-to-asperity level, the crack generation and propagation, material liberation, and particle formation, as shown in Figure 23.3(c). In typical engineering contacts, these phenomena are at a size level of about 1 µm or less, down to the nanometer range.
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FIGURE 23.4 Macromechanical contact conditions for different mechanisms that influence friction when a hard spherical slider moves on a coated flat surface
Shear and fracture are two basic mechanisms for the first nucleation of a crack and for its propagation until it results in material liberation and formation of a wear scar and a wear particle. These mechanisms have been discussed by, for example, Argon (1980) and Suh (1986), but still today there is only a poor understanding of these quite fundamental phenomena. Another approach is to study the tribological micromechanical mechanisms using the velocity accommodation concept developed by Berthier et al. (1989). This chapter presents a new energy accommodation approach to the micromechanical tribological mechanisms, which is described in Section 23.4.
23.2.5 Tribochemical Mechanisms of Coated Surfaces The chemical reactions taking place at the surfaces during sliding contact, and also during the periods between repeated contacts, change the composition of the outermost surface layer and its mechanical properties. This has a considerable influence on both friction and wear because they are determined to a great extent by the properties of the surface, where phenomena such as shear, cracking, and asperity ploughing take place (Gee and Jennett, 1995). The chemical reactions on the surfaces are strongly influenced by the high local pressures and the flash temperatures, which can be over 1000°C, at spots where asperities collide. Very low coefficients of friction, down to 0.1, have been reported for a hard titanium nitride coating sliding against itself (Mäkelä and Valli, 1985) and even lower values, down to about 0.01 but more typically 0.05, have been measured for diamond-like carbon (DLC) coatings sliding against different counterface materials (Donnet, 1995; Holmberg et al., 1994; Donnet et al., 1994; Donnet, 1996) and diamond coatings sliding against diamond and ceramics (Erdemir et al., 1996b; Hayward et al., 1992; Zuiker et al., 1995; Habig, 1995; Gardos, 1994). This can be explained by the formation of low-shear microfilms on the hard coating or perhaps only on the asperity tips of the coating. Thus, if one considers such a contact on a microscale, there is effectively a soft coating on a hard substrate (see Figure 23.3(d)), although now the coating (e.g., TiN or diamond) plays the role of hard substrate, and the soft microfilm formed plays the role of a coating. It is obviously advantageous if the substrate under the hard coating is as hard as possible, to avoid fracture of the brittle coating by deformation, to improve the load support, and to decrease the real area of contact. The very low coefficients of friction of polished diamond and diamond-like coatings are further explained by the
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extreme smoothness of the surface, excluding effects such as interlocking and asperity ploughing, as well as the hard coating reducing the ploughing component of friction. The chemical reactions and the chemically formed reaction layers are treated in more detail in Section 23.5.5.
23.2.6 Nanophysical Contact Mechanisms Emerging technologies such as atomic force microscopy and other surface force methods (Israelachvili and Tabor, 1972; Bhushan, 1999) have opened the possibility to study friction and wear phenomena on a molecular scale and to measure frictional forces between contacting molecules at the nano-Newton level. Increased computational power has made it possible to study friction and associated phenomena by molecular dynamic simulations of sliding surfaces and to investigate the atomic-scale contact mechanisms, as shown in Figure 23.3(e). Only some aspects of these complex nanophysical phenomena have thus far been investigated; an example is the friction that arises from slippage between solid-to-solid interfaces (Thompson and Robbins, 1989) and between closely packed films in sliding contact (McClelland and Glosli, 1992). The atomic-scale mechanisms of friction when two hydrogen-terminated diamond surfaces are in sliding contact has been studied and the dependence of the coefficient of friction on load, crystallographic sliding direction, and roughness have been investigated (Harrison et al., 1992, 1993). Work on molecular-scale viscoelastic effects and viscous flow has been reported (Wahl and Unertl, 1998; Zhang and Tanaka, 1998). The present understanding of nanoscale tribology is presented in Section II of this Handbook. The increased understanding of the origin of friction at the atomic scale and even why friction exists has resulted in an examination of the relationship between the commonly used laws of friction at a macroscale and the molecular frictional behavior on a nanoscale. There have been suggestions that friction arises from atomic lattice vibrations occurring when atoms close to one surface are set into motion by the sliding action of atoms on the opposing surface. Thus, some of the mechanical energy needed to slide one surface over the other would be converted to sound energy, which is then eventually transformed into heat (Krim, 1996). In an interesting investigation, Tervo (1998) found that friction correlates to some extent with Rayleigh surface waves. This would suggest that friction arises primarily from the elastic interactions (i.e., lattice vibrations) on the surfaces due to sliding motion. The velocity of a Rayleigh surface wave is dependent on the Poisson ratio, shear modulus, and density. Tervo found that nitrogen alloying of stainless steel slightly increases the friction. In a molecular-level study of Amontons’ law, Berman et al. (1998) found that at the molecular level, the projected area is not necessarily proportional to the load and that the shear strength is not constant. Despite this, Amontons’ laws are obeyed and the friction force is still proportional to load on a macrolevel. They offer a physical model, based on intermolecular forces and thermodynamic considerations, that explains why the friction force is proportional to the applied load, and why the case of adhering surfaces — where the friction force is found to be proportional to the molecular contact area — is quite different from that of nonadhering surfaces. Today, we are only at the very beginning of the understanding of the nanomechanical tribological contact effects that explain the origin of friction and wear, and there is no doubt that in the near future many new theories and explanations for the origin of tribological phenomena will become available. The scaling up of the nanomechanical explanations of contact mechanisms to practically useful conclusions on a macroscale is a most challenging and complex task and will take many years. There already are practical applications on a nanoscale where the increasing knowledge of tribological nanomechanisms can be used. This has resulted in the development of Micro Electro Mechanical Systems (MEMS) such as motors, transducers, gears, and bearings of sizes in the micrometer range (Bhushan, 1998a). For these extremely small components, silicon has been used in the early applications for production reasons, but studies have shown that tribological improvements can be achieved using polycrystalline diamond or MoS2 thin coatings or hydrogenated diamond-like carbon coatings (Donnet et al., 1995; Beerschwinger et al., 1995; Gardos, 1996).
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FIGURE 23.5 Macromechanical contact conditions for different mechanisms that influence wear when a hard spherical slider moves on a coated flat surface.
23.3 Macromechanical Interactions: Hardness and Geometry The macromechanical tribological mechanisms describe the friction and wear phenomena by considering the stress and strain distributions in the entire contact, the total elastic and plastic deformations they result in, and the total wear particle formation process and its dynamics. In contacts with one or two coated surfaces, four main parameters that control the tribological process must be defined (Holmberg and Matthews, 1994). They are the coating and bulk hardness, coating thickness, surface roughness, and debris and tribolayers in the contact. The effects of these parameters are further discussed. The influence on the macromechanical friction mechanisms of coating and substrate hardness, coating thickness, surface roughness, and debris present in the contact is illustrated in Figure 23.4 and the corresponding wear mechanisms in Figure 23.5. The mechanisms involved are very different, depending on whether the coating and/or the substrate is soft or hard (Holmberg and Matthews, 1994; Donnet, 1995; Ramalingam and Zheng, 1995). Consider first the case of soft coatings on harder substrates.
23.3.1 Soft Coating on Hard Substrate 23.3.1.1 Decreased Friction by Shear in Soft Top Layer For soft coatings, the thickness of the coating influences the ploughing component of friction. When the film is thin enough, the effect of ploughing on the film is small (see Figure 23.4(b)). The friction is thus determined by the shear strength of the film and the contact area, which is related to the deformation properties of the substrate (Roberts, 1989, 1990). The formation of grooves in the coated surface by plastic deformation (see Figure 23.5(a)) is the main wear effect; but with thinner films, continuous sliding can result in coating compaction as well as adhesive and fatigue wear (see Figure 23.5(b)). Using a low cycle fatigue model, Tangena and co-workers correlated the wear volume with the calculated von Mises stresses averaged over the contact width and the depth of a gold surface layer (Tangena, 1987, 1989; Tangena and Wijnhoven, 1988; Tangena et al., 1988). The effect of decreased shear stress at the contact due to a soft film was investigated by Erdemir et al. (1991a). They applied a thin 2-µm-thick silver film on a hard ceramic plate sliding against a hard ceramic ball; the coefficient of friction decreased
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from 0.8 to 0.4 and the wear of both the coating and the counter-surface decreased by several orders of magnitude. A soft coating not only reduces the coefficient of friction, but can also reduce the surface tensile stresses that contribute to undesirable subsurface cracking and subsequently to severe wear (Spalvins and Sliney, 1994). 23.3.1.2 Ploughing Friction The friction usually increases with coating thickness for soft coatings, due to plastic or elastic deformation of the film and to the increased contact area at the interface between the sliding counterface and the coating where the shear takes place (see Figure 23.4(a)). This increase in friction has been experimentally demonstrated for lead films (Tsuya and Takagi, 1964; Sherbiney and Halling, 1977); for gold films (Takagi and Liu, 1967); for silver films (El-Sherbiny and Salem, 1986; Yang et al., 1999); and for MoS2 films (Aubert et al., 1990; Wahl et al., 1998). For very thick soft coatings, the mechanism of ploughing will be very similar to that of soft bulk materials scratched by a hard indenter. These tribological mechanisms have been described by several authors, for example, Hokkirigawa and Kato (1988), who in addition to the ploughing mechanism, also identify a wedge-forming and a cutting mechanism, depending on the degree of penetration and the shear strength of the contact interface. 23.3.1.3 Influence of Surface Roughness The substrate surface roughness has an almost negligible influence on friction if the roughness is considerably smaller than the thickness of the soft coating and the coating is stiff enough to carry the load, as shown in Figure 23.4(e). However, when the roughness of the slider is higher than the coating thickness, coating penetration will take place (Figure 23.4(f)) and the friction is considerably increased due to scratching of the substrate material. This has been described both experimentally and theoretically by Sherbiney and Halling (1977), Halling and El-Sherbiny (1978), and El-Sherbiny (1984). A model for predicting the wear rate when hard asperities penetrate the soft coating and produce grooves in the substrate (see Figure 23.5(c)) was developed by El-Sherbiny and Salem (1984).
23.3.2 Hard Coating on Softer Substrate The use of hard thin coatings on softer substrate materials is currently very popular in many tribological applications. The hard coating can provide good wear protection and, with a suitable choice of material and surface layer design, the friction can be very low as well. 23.3.2.1 Hard Coating Can Reduce Wear With a very thin hard layer on top of a softer substrate (see Figure 23.5(e)), it may be that neither the coating nor the substrate is able to support the load. However, the function of the coating is to separate the substrate from the counter-surface and to prevent ploughing by increasing the hardness of the top layer of the surface. The latter effect has been considered to be very important by Shepard and Suh (1982), Suh (1986), and Bull and Rickerby (1990). For very thin carbon nitride layers with thicknesses of 10 to 200 nm on a silicon substrate, Wang and Kato (1999a,b) reported an increase in nano-indentation hardness with increasing coating thickness. The increase in wear resistance with increased coating hardness has recently been reported by Kodali et al. (1997) and Wiklund (1999). Increased substrate hardness results in decreased contact area, where the shear takes place, and decreased friction, which is indicated in the results obtained by Ronkainen et al. (1999a). 23.3.2.2 Hard Coatings Without Microfilm Can Have High Friction The prevention of ploughing reduces both friction and wear; however, the higher shear strength introduced at the contact interface by the hard coating can, on the other hand, have the effect of increasing friction in sliding if no microfilms are formed as described above (see Figure 23.3(d)). That is why very high coefficients of friction often occur in sliding contacts with hard coatings (Holmberg and Matthews, 1994; Voevodin et al., 1995d). The increase in friction caused by increased shear strength generally seems
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FIGURE 23.6 Fracture of a hard brittle coating on a soft substrate takes place in the contact area and at the material pileup area around the contact. Directions of material flow are indicated by arrows.
to be more dominant than the reduction in friction due to decreased ploughing. Here, the recently developed diamond and diamond-like carbon coatings are an exception. The friction may then be extremely low because of the graphitic microfilm produced, as described in Section 23.6. 23.3.2.3 Deflection Influence on Stresses and Cracks For very soft substrates, the indentation deformation will be considerable and this will thus add a ploughing or hysteresis effect on friction (see Figure 23.4(d)). The deflection increases the stresses in the coating and also at the interface between the coating and the substrate, possibly resulting in fracture or fatigue cracks that may harm the coating or the substrate material. With a soft substrate, cracks may occur in the coating, both within the contact area and outside at the substrate material pile-up area, as shown in Figure 23.6 (Burnett and Rickerby, 1987b; Miyoshi,1989; Page and Knight, 1989; Bull et al., 1994; Guu et al., 1996a,b; Lin et al., 1996a,b; Lee and Jedong, 1998; Yuan and Hayashi, 1999). The harder the substrate, the higher the loading that the coating can resist without failure by fracture (Hedenqvist et al., 1990). 23.3.2.4 Thick Hard Films Are Better Able to Carry the Load Increased loads can also be resisted with thicker hard coatings because of their load-carrying capacity, which reduces deflection, as shown in Figure 23.4(c) (Rabinowicz, 1967; Roth et al., 1987). A thick hard coating will have a modifying effect on the size and shape of the stress zone beneath the coating, as has been shown for a hardness indenter by Burnett and Rickerby (1987a). 23.3.2.5 Cracks Generated by the Deflection When a loaded sphere is sliding on a hard coating, the friction originating from both shear and ploughing will result in tensile stresses behind the sphere and compressive stresses and material pile-up in front of the sphere. This can result in several different cracking patterns, depending mainly on the geometry and hardness relationships (Buckley, 1981; Je et al., 1986; Hedenqvist et al., 1990; Hills et al., 1990). The contact response of a coated system with large deflections has been modeled by Ramsey et al. (1991), showing the nonlinear contribution that stretching of the coating has on stiffness of the surface when the deflections are of the order of the coating thickness or greater. 23.3.2.6 Fatigue Life of Coatings The fatigue life of a thin coating may be considerably longer than that of a thick coating for several reasons. Under similar deformation conditions, the thicker coating will experience higher bend stress levels. Because coatings typically have columnar growth morphologies, any crack normal to the surface will be large in a thick coating, and may exceed the critical crack length; whereas in a thin coating, this may not be the case. It has been shown experimentally that in rolling contact fatigue tests, hard TiN coatings with a film thickness well below 1 µm have up to 2 orders of magnitude longer lifetime than 2- to 3-µm-thick similar coatings (Erdemir and Hochman, 1988; Chang et al., 1990, 1992; Erdemir, 1992). In a more recent paper, Polonsky et al. (1997) claim, without giving experimental details, that they have been able to demonstrate that the rolling contact fatigue life increase achieved with less than 1-µm TiN coatings was entirely due to polishing of the steel loading balls by the significantly harder TiN coating.
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They changed the test procedure and eliminated the polishing effect and observed a somewhat negative effect of the TiN coating on the rolling contact fatigue life. In their paper, they present a theoretical model of near-surface rolling contact fatigue initiation in coated rolling contact elements and conclude that a truly effective hard coating that can resist near-surface rolling contact fatigue must be relatively thick (>3 µm), adherent to the substrate, and have a fine microstructure to resist cohesive fatigue failure in the coating. This has not been experimentally verified but they report that such work is ongoing. 23.3.2.7 Stresses at the Coating-Substrate Interface It has been shown by Sainsot et al. (1990) and others that high stresses are concentrated at the interface between the hard coating and the soft substrate (see Figure 23.1). The ability to resist the high stresses at the interface depends on the strength of adhesion between the two. Single or repeated loading can result in breaking of the adhesive bonds and liberation of parts of the coating in flake-like wear debris (Miyoshi, 1989; Hedenqvist et al., 1990).
23.3.3 Load-Carrying Capacity of Coated Surfaces The term “load-carrying capacity,” or load-bearing capacity, has been used to express the ability of a coated surface to withstand the action of a loaded tribological contact without failure. More specifically, the load-carrying capacity of a coating/substrate system has been determined as the ability of the system to bear the normal and tangential forces applied on the coated surface without losing the functional properties of the system (Ronkainen et al., 1998b). There is no standardized or generally agreed and defined method to measure the load-carrying capacity. Even its definition is still a subject for scientific discussion. However, many investigators have used the scratch test method (Valli, 1986; Valli et al., 1986) for this purpose, ostensibly to assess the effective adhesion of the coating under conditions in which bulk plastic deformation occurs. Experiments have shown that the load-carrying capacity of a coated surface can be improved by increased substrate hardness and increased coating thickness, in the coating thickness range of 0.5 to 9 µm (Bell et al., 1998; Lee and Jeong, 1998; Ronkainen et al., 1999; Wang and Kato, 1998, 1999a,b), as shown in Figure 23.7. Correlating results of TiN coating breakdown with softer substrates in fretting tests have been reported (Shima et al., 1999). In a microscale scratch and wear resistance test, Sundararajan and Bhushan (1999) showed that very hard diamond-like carbon coatings can have a reasonable loadcarrying capacity and wear resistance at a coating thickness even down to 5 nm. A thinner, 3.5-nm-thick coating had poor load-carrying capacity. Lee and Jedong (1998) concluded from Rockwell hardness test results that the load-carrying capacity is improved by decreased surface roughness, but these results should not be generalized because they were not in correlation with scratch test results. The mechanism when the load-carrying capacity is exceeded and the coating fails can be very different, depending on the materials involved and surface parameters. Wang and Kato (1998) have shown that when a diamond tip slides over very thin carbon nitride coatings (h = 10–200 nm) on a bare silicon substrate, this will result in a “no-grooving” mode at low loads, a “grooving with no material removal” mode at higher loads, and finally in a “grooving with material removal” mode at high load (up to 300 mN) with a linear sliding speed of 10 µm/s. In this case, the failure occurs as grooves in the coating due to plastic deformation. In more severely loaded situations, the failure may be more due to brittle fracture of the coating (Lee and Jedong, 1998; Kodali et al., 1997) and flaking of the coating. The pattern of coating fracture and failure due to exceeding the load-carrying capacity has been explained and classified by Olsson (1989), Hedenqvist (1991), and Wiklund (1999). Scratch testing is a fast and easy way of evaluating the load-carrying capacity of a substrate/coating combination that gives reasonably relevant results. One should be very careful when using the Rockwell indentation test for this purpose because it has been found that the results can be contradictory to the scratch test results (Lee and Jedong, 1998; Ronkainen et al., 1998b, 1999a). It has been suggested by Bennet et al. (1994) that a more lightly loaded multipass scratch testing method gives better correlation with practical situations than single-pass testing and would thus be more suitable as a quality assurance method for coatings. Ronkainen et al. point out that the stress situation under the diamond tip in a
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FIGURE 23.7 Influence of (a) substrate hardness, (b) coating thickness, and (c) surface roughness on load-carrying capacity measured by scratch test critical load for TiN coating on a steel substrate. (Data from Lee, Y.Z. and Jeong, K.H. (1998), Wear-life diagram of TiN-coated steels, Wear, 217, 175-181.)
scratch test is much more severe than generally observed in practice and thus a more suitable method for evaluating the load-carrying capacity of a coated surface would be a ball-on-disc configuration, as typically used in sliding tests.
23.4 Micromechanical Interactions: Material Response The micromechanical tribological mechanisms describe the friction and wear phenomena by considering the stress and strain at the asperity level, the crack generation and propagation, material liberation, and single particle formation. In typical engineering contacts, these phenomena are at the size level of about 1 µm or less, down to the nanometer level.
23.4.1 Material Response In a tribological contact, one surface moves over another, typically by a sliding, rolling, cutting, or impacting kind of motion. The interactions between the surfaces and the resultant material changes will govern the friction and wear behavior. Friction can be generated by adhesion between the two surfaces, by ploughing, or by asperity deformation, as shown in Figure 23.8. In a rolling contact situation, the friction is induced by the hysteresis of the repeatedly elastically deformed rolling component (Holmberg and Matthews, 1994). The elasticity, hardness, and fracture toughness of the material influence friction and wear, both on a macroscale and on a microscale. On a macroscale, the rough surface of an elastic material deforms with the applied load and the load is thus spread more widely over the two surfaces, resulting in a lower surface pressure for the materials to respond to, as shown in Figure 23.9(a) and (b). When the load is removed, the surface will return to its original shape.
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a) Adhesion
b) Ploughing
c) Asperity deformation
FIGURE 23.8 The three components of sliding friction are (a) adhesion, (b) ploughing, and (c) asperity deformation.
FIGURE 23.9 The deformation and contact pressure for a rough sphere on a rough plane in the case when both are (a) rigid and (b) elastic. The substrate deformation when a hard sphere is sliding on (c) a hard substrate and (d) a soft substrate.
In sliding and rolling, the hardness of the material indicates its ability to carry a load. When a counterface such as a sphere slides on a soft flat surface, indentation and ploughing may take place, with high friction and wear as a result. For a harder material the ploughing action decreases, with less friction and wear as a result, as shown in Figures 23.9(c) and (d). It was previously suggested that the E:H ratio should be used as a parameter for estimating the relative wear rate of materials, and in several cases this correlates well with results from experimental wear tests (Oberle, 1951). It has been reported that in an abrasive wear situation, the wear is inversely proportional to the elastic moduli (Spurr, 1957; Lancaster, 1963). However, this may be true only for surfaces with preexisting flaws or cracks because, in general, tough and elastic materials (i.e., with low E) are able to resist abrasion very effectively. If flaws are present, then a stiffer (i.e., higher E) surface may resist crack-opening forces, and this is the reason why brittle fracture mechanics models prescribe high E values to produce “tougher” surfaces. However, the balance of evidence now suggests that a coating with a lower E value will be more wear resistant than one with a similar hardness but higher E (Leyland and Matthews, 2000; Matthews and Leyland 2000a,b). Coatings with a higher H/E ratio have a longer elastic strain to failure, and are thus more able to deform (without yielding) as the substrate deforms.
23.4.2 Energy Accommodation in the Surface When one surface is loaded against another, the two surface geometries interact and influence the pressures on the surfaces and the stresses generated in the two solids close to their surfaces. The mechanisms taking place related to friction and wear have been reviewed by Holmberg and Matthews (1994).
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FIGURE 23.10 The three modes of energy accommodation in a sliding contact are elastic deformation, plastic deformation, and brittle fracture.
Godet (1989) presented a velocity accommodation approach in which he pointed out that the elastic, plastic, fracture, and rolling behavior in the contact are important for friction and wear. The following develops and presents a new energy accommodation concept for the wear behavior of coated metallic or ceramic surfaces, which emphasizes the parameters of elasticity, plasticity, and fracture toughness. The basic wear mechanisms can be described by studying the material response effects in a simplified situation when a sphere is sliding over a flat surface, as in Figure 23.10. At stage 1, point A on the upper surface is in contact with point B at the lower flat surface. When the upper surface moves to stage 2 some distance to the right, point B will follow point A because of the adhesion or interlocking between the surfaces. This movement of point B is allowed by the material response in the lower surface. This material response can be split up into three components: elastic deformation, plastic deformation, and brittle fracture. In the elastic case, B will follow A; and when the contact is released, B will elastically move back to its original position. The work in this process, the load × distance moved, has been transferred to heat. The main parameter indicating the material response is the Young’s modulus of elasticity, (also called the elastic modulus, E). In the situation of plastic behavior, point B will follow point A in the same way, but after the contact release, the deformation of the flat surface will not return to its original shape but remain deformed. The work of the rubbing process has been transferred to heat and permanent material modification. In this case, a key parameter indicating the material response is the shear strength, τ. Third, in the situation of brittle fracture behavior, point B again moves with point A and now the movement is allowed by the material cracking on the left-hand side of the contact. The moving contact has created a crack in the surface. The work of the process has now been transferred to heat and surface energy needed for the formation of new surfaces in the crack. The parameter indicating the material response is the fracture toughness or, more specifically, the critical stress intensity for microstructurally short cracks, KIc. The fracture toughness can more conveniently be expressed in the form of critical strain energy release rate, Gc . Thus far, it has been assumed that both materials are homogenous and defect-free. Now assume that the flat material is not defect-free, but has cracks at the surface perpendicular to the surface, created, for example, from earlier sliding situations that are now repeated. Figure 23.11 shows how the surface in the elastic case is modified and returns after each contact to its original shape. However, after a certain number of repeated contacts, fatigue cracks will be created in the surface that result in material release. A load that is sufficiently large to cause plastic deformation in the early cycles of the loading may accommodate purely elastic deformation in the later stages due to a shake-down material effect of the surface (Wong et al., 1997).
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FIGURE 23.11 Material release and particle formation mechanisms in the elastic, plastic, and brittle energy accommodation modes.
FIGURE 23.12
Energy accommodation geometry in (a) sliding and (b) rolling, with curved surfaces or asperities.
In the fully plastic situation, the contact will result in a modified surface; and when this is repeated, the modification will continue, and finally this process will also result in material release from the surface. In the brittle fracture situation, the repeated contacts will result in more new cracks. One can see that in all three cases, material will be released from the surface and wear particles will be formed. The discussion has thus far been limited to a sphere sliding on a smooth surface. The situation is basically the same even if the lower surface is not considered flat due to surface roughness, curvature, or ploughing, as shown in Figure 23.12. In the case of rolling, the situation will be similar, but now the tangential friction force will be much lower and the stress field in the surface will have a different shape. The authors’ conclusion from this discussion is that the Young’s modulus of elasticity, shear strength, and fracture toughness are basic important material parameters influencing the friction and wear behavior of the contact. To control the wear and friction situation, one needs to know the values of these parameters in the coating, at the asperities, and in the bulk of the substrate, as illustrated in Figure 23.13.
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FIGURE 23.13 Basic material response parameters in energy accommodation are the Young’s modulus of elasticity (E), the shear strength (τ), and the fracture toughness (indicated by KIc or Gc) in the coating (c), at the asperities (a) and in the bulk of the substrate (b).
23.4.3 The Influence of Fracture Toughness in Material Response The influence of elasticity on wear has been recognized in several papers. The plasticity effect has also been widely studied (Bowden and Tabor, 1950, 1964; Oberle, 1951; Lancaster, 1963; Halling and Arnell, 1984). Hardness, H, is a measure of the contact pressure needed to cause yield and material flow in a surface, that is, plastic deformation. The commonly used parameter indicating the response of brittle materials to loading is the fracture toughness or, more specifically, the critical stress intensity ψ factor, KIc. The fracture toughness can be more conveniently expressed in the form of critical strain energy release rate, Gc. Gc is a measure of the fracture toughness of a material and, as such, it is a material property just like Young’s modulus and the yield stress (Anderson et al., 1985). Gc can be expressed as:
Gc = K c2 E
(
for plane stress and
)
Gc = K c2 1 − ν E where Kc is the critical stress intensity factor, E the Young’s modulus of elasticity, and ν the Poisson ratio. The models and measurement methods developed in fracture mechanics, such as the linear elastic fracture mechanics (LEFM) techniques for expressing the fracture toughness of a material, are in most cases applicable for large cracks longer than 1 mm, or with special modifications for physically short cracks in the range of 100 µm to 1 mm. Cracks less than 100 µm are considered microstructurally short cracks because their dimensions are on the order of the grain size in metals. At these scales, the material no longer behaves as a homogenous continuum because the crack growth is strongly influenced by microstructural features. In this region, crack growth is influenced by grain size and boundaries, inclusion spacing, precipitation spacing, microasperities, macro-asperities, etc. The crack growth is often very sporadic, such that it may grow rapidly in certain intervals and then be followed by crack arrest when it meets barriers such as grain boundaries and second-phase particles (Haddad et al., 1979; Meguid, 1989; Anderson, 1995). Microstructurally short cracks in a plain specimen may not affect its fatigue limit. Fracture mechanical aspects on short cracks and their behavior have been collated by Miller and de los Rios (1986). The three regions of crack growth are illustrated in a diagram with log stress range, log ∆σ, as a function of log crack lengths (log a), as first suggested by Kitagawa and Takahashi (1976) and shown in Figure 23.14. In contrast to long fatigue crack propagation, there exists no adequate definition of the growth mechanism, the crack tip stress/strain fields, or the interaction with microstructural features for short fatigue crack propagation, which is the more likely case in thin metallic or ceramic coatings.
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FIGURE 23.14 The Kitagawa–Takahashi curve, illustrating the regions for different crack propagation mechanisms. (Adapted from Meguid, S.A. (1989), Engineering Fracture Mechanics, Elsevier Applied Science, London. 397 p.)
The different features that can influence how short cracks are initiated and subsequently grow in metallic components are shown in Figure 23.15. The process is influenced by the material parameters, the geometrical features, and the state of stress, both applied and residual. The three fundamental mechanical properties — the elastic modulus, hardness, and fracture toughness — can be measured using a sharp indenter (Pharr, 1998). If they are to be measured close to the surface, as is relevant when evaluating tribological properties, a low-load nano-indenter should preferably be used. In indentation measurements, the effects of temperature, environment, and geometrical scale (Ramsey and Page, 1988), as well as mechanisms like the pile-up effect (Bolshakov and Pharr, 1998), should be considered.
23.5 Material Removal and Change Interactions: Debris and Surface Layers The process of wear and friction results in both geometrical and structural changes in the surfaces of the contacting bodies. These changes will influence future contact conditions and friction and wear generated in the same contact. The changes range from nanoscale to macroscale. At the nanoscale, outer surface molecules are released and they react chemically with adjacent molecules; at the microscale, cracks are initiated and debris released; and at the macroscale, wear products are agglomerated and surface layers formed and deformed.
23.5.1 Surface and Subsurface Cracks The initiation of cracks at the surface or in the material is the starting point of a process that may result in material detachment, debris generation, and the formation of transfer layers. In most wear situations, in addition to hardness, the ability to elastically recover from deformation and the fracture toughness of the material are very important parameters (Zum Gahr, 1998; Wiklund, 1999). The modern fracture mechanics approach to the initiation and generation of cracks is presented by Andersson (1995). For the case of a loaded, very thin coated surface, there does not exist any general theory or model for crack initiation or generation.
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FIGURE 23.15 Classification of different sources for short crack initiation and propagation. (Adapted from Meguid, S.A. (1989), Engineering Fracture Mechanics, Elsevier Applied Science, London. 397 p.)
Based on macroscale experimental observations in rolling contact tests with bearing steel materials, Nélias et al. (1999) report that the cracks are either initiated from subsurface inclusions or surface microcracks. They claim that the initiation and propagation of inclusion-initiated cracks is the main mode of sub-surface-originated cracks in rolling bearings. Under the load is a stress concentration built up around inhomogeneities like inclusions and primary carbides. This is due to the elasto-plastic mismatch between these inhomogeneities and the martensitic matrix. Once the yield stress is reached, a plastic strain is induced in a small volume surrounding the inclusion. Under repeated action, the dislocations will move back and forth and accumulate. This process leads to localized changes in the steel microstructure and a crack is nucleated in this domain once a critical density is reached. Surface microcracks are typically generated in the discontinuities of the surface topography, such as at grinding marks or large-wavelength surface roughnesses (Nélias et al., 1999). The process of initiation of surface microcracks and formation of microspalls along grinding marks is shown schematically in Figure 23.16(a). Microcracks can also propagate parallel to the surface at a few micrometers depth along the machining direction, leading to the formation of microspalls, as shown in Figure 23.16(b). These processes have mainly been observed in pure rolling. Sliding may play a significant role, as it produces transverse microcracks at an angle of 30° to 40° to the friction direction. The cracks are located mainly on the top of large roughness peaks, as shown in Figure 23.16(c). There are indications that the local
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5 µm
5 µm a)
b) 40 µm
10 µm c)
400 µm d)
FIGURE 23.16 Schematic stages of (a) microspall formation along grinding marks (transverse cut), (b) microspall formation below longitudinal roughness of large wavelength (transverse cut), (c) microcrack and microspall formation (longitudinal cut), and (d) surface initiated deep spall formation (longitudinal cut). (Adapted from Nélias, D., Dumont, M.L., Champiot, F., Vincent, A., Girodin, D., Fougères, R., and Flamand, L. (1999), Role of inclusions, surface roughness and operating conditions on rolling contact fatigue, J. Tribol., Trans. ASME, 121, 240-251.)
friction coefficient at the top of asperities may be large enough to initiate transverse microcracks. Such microcracks are at the origin of microspalls, usually wider and deeper than those observed under pure rolling conditions. Depending on the combination of load movement, friction direction, and crack orientation, a lubricant may help propagate surface cracks by hydraulic pressure effects. Recent studies of the stress intensity factor at the tip of a surface breaking crack in a layered surface indicate that compressive stresses may tend to prevent crack propagation (Eberhardt and Peri, 1994). The crack patterns of ceramic coatings in indentation have been analyzed and correlated to coating thickness and load, and the critical normal loads have been estimated by considering the deformation of the substrate (Diao et al., 1994b). There is a strong influence on both the fracture load and the fracture pattern by the mismatch of elastic properties between the layer and the substrate (Oliveira and Bower, 1996). Variations in coating properties and coating thickness may change the fracture loads by up to a factor of ten. In ceramic coatings, the thickness and grain size are important parameters for crack propagation. In indentation tests of 1- to 10-µm-thick Al2O3 coatings on cemented carbide substrates, Yuan and Hayashi (1999) found that the critical load for generation of radial cracks decreases with increasing coating thickness, and that the grain size of the coatings decreases with the thickness. A more coarse-grained microstructure generally displays a lower cohesive strength as compared with a fine-grained microstructure. Thus, the fracture strength of the coating increases with decreasing grain size and thickness. Nanocrystalline-amorphous TiC-amorphous carbon (a-C) composite coatings have been produced by Voevodin and Zabinski (1998a,b) with a combination of high hardness and fracture toughness. In their coating design, nanocrystals of 10 to 50 nm size were encapsulated in an amorphous phase, the nanocrystals being separated from each other by 5 nm. This permitted generation of dislocations and grain boundary microcracks and nanocracks, which terminated in the surrounding amorphous matrix. This surface design achieved a self-adjustment in composite deformation from hard elastic to plastic at loads exceeding the elastic limit, as opposed to deformation from hard elastic to brittle fracture.
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For amorphous diamond-like carbon (DLC) coatings in the thickness range of 0.7 to 2 µm, it was shown that the hardness and apparent fracture toughness of the coating/substrate combination, measured by Vickers indentation, depend on the thickness of the coating (Kodali et al., 1997). The hardness and the apparent fracture toughness of the coating (both of which influence the wear) increased with increasing coating thickness. The hardness and the thickness influenced the initiation of cracks, whereas the residual stress in the film influenced the propagation of cracks. In a study of very thin DLC coatings in the thickness range of 3.5 to 20 nm, Sundarajan and Bhushan (1999) conclude that the formation of cracks depends on the hardness and fracture toughness of the coating. They suggest that the observed nonuniform failure depends on spatial variation in the coating properties. Surface cracks are developed in weaker regions with lower fracture toughness. As cracks propagate, they are forced to expand within the weak region, as the neighboring strong regions inhibit extensive lateral crack growth. Because of this, cracks propagate down to the interface, where, aided by interfacial stresses, they get diverted along the interface just enough to cause local delamination of the coating. Simultaneously, the weakened regions experience excessive ploughing. Thus, weaker regions fail while stronger regions remain wear-resistant. The propagation of cracks along the coating/substrate interface is suppressed due to the strong adhesion of the coatings because, otherwise, coating delamination would take place. There have been a number of papers published wherein the crack pattern has been experimentally demonstrated and studied both by indentation and scratch testing. Such studies have been published by Olsson (1989), Hedenqvist (1991), Prasad and Zabinski (1997) for nanocrystalline ZnO, Sundararajan and Bhushan (1998) for SiC, Sue and Kao (1998) for TiN/TiC multilayer coatings, Wiklund et al. (1999) for TiN and CrN coatings, and Yuan and Hayashi (1999) for Al2O3 coatings.
23.5.2 Tribological Influence of Wear Debris Debris that has been generated by the wear process or loose particles originating from the surrounding environment may be present in a tribological contact. It has been observed that the coefficient of friction rises significantly once wear particles are formed at the sliding surface, and particles present in the contact affect the instantaneous coefficient of friction and the wear. The coefficient of friction can be altered by removing wear particles or by inserting particles in the interface, as shown by Hwang et al. (1999), who also found that the particle size influences friction but not so much the number of particles present in the contact. In experiments with sliding surfaces of materials with different hardnesses (Pb, Zn, Al, Cu, Ni, Ti, and AISI 1045 steel), they found a clear difference between soft and hard surfaces. Soft and ductile surfaces produced larger wear particles with a stronger tendency to agglomerate, while hard surfaces produced smaller wear particles with weaker agglomeration tendency. For coated surfaces, the influence of debris in the contact on friction and wear is, under some conditions, considerable, depending on the particle size and shape; coating thickness and surface roughness relationship; and the particle, coating, and substrate hardness relationship (Holmberg and Matthews, 1994). 23.5.2.1 Particle Embedding In the sliding situation shown in Figure 23.4(i), hard particles are present in the contact, the particles having a diameter considerably smaller than the thickness of the soft coating on a hard substrate. The particles are pressed into the soft coating and embedded into it without any further contact with the slider as long as the soft coating remains thicker than the particle diameter. In this case, the particles have no great effect on friction, which is primarily controlled by the ploughing mechanisms described earlier. The slider will produce a main groove by ploughing in the soft coating, and the surface asperities or trapped debris may cause microploughing and microgrooves within the main groove (Hwang et al., 1999). El-Sherbiny and Salem (1979) showed with a theoretical model that the wear appears to be dependent on the surface texture of the system rather than on material properties during the initial wear when hard conical asperities are ploughing a soft surface coating.
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23.5.2.2 Particle Entrapping For thin surface coatings where the dimensions of the particles are of the same magnitude or larger than the coating thickness and the surface roughness, as shown in Figure 23.4(j), their influence on friction can be considerable. If the particles are harder than the coating but softer than the substrate, then they are easily caught by the roughness of the counterface or partly sink into it and scratch grooves in the soft coating, as in the case of asperity penetration. The friction will increase because of particles ploughing the coating (Hwang et al., 1999). The influence of ploughing wear particles on friction in sliding wear contacts has been shown to be considerable (Kim and Suh, 1991; Komvopoulos, 1991a,b). An increase in friction may follow if the slider and the substrate are of equal hardness and the loose particles in the contact have a higher hardness (Suh, 1986). Then the particles may partly sink through the coating into the substrate, as well as into the counterface by a kind of anchoring mechanism resist motion. Even if the particles are fairly spherical in shape, it is not probable that they will decrease friction by rolling because they will be stuck into the soft coating. Sin et al. (1979) have shown that the contribution of ploughing on the friction coefficient is very sensitive to the ratio of the radius of curvature of the particle to the depth of penetration. The particles are free to rotate in the contact and they are often considerably sharper than the asperity angles of engineering surfaces. The wear rate depends on the particle size. If the particles in the contact are soft, then their tribological effect is quite different. Soft particles with low shear stress trapped in the contact can carry part of the load and inhibit direct substrate-tocountersurface contact, thus reducing both wear and friction (Grill, 1997; Voevodin et al., 1999d). A similar effect has been observed by Yamada et al. (1990), who found that polymer particles can act very effectively to reduce wear and friction. In contacts with MoS2 coatings or when Mo and S are present, MoO2 wear debris is produced that has a very low shear stress and thus can act as a solid lubricant, reducing the friction and wear (Donnet et al., 1995; Wahl and Singer, 1995; Singer et al., 1996a,b; Donnet, 1996, 1998; Grossiord et al., 1998; Singer, 1998; Xu et al., 1999; Wahl et al., 1999). The tribological behavior of molybdenum disulfide coatings is treated in detail in Chapter 22. 23.5.2.3 Particle Hiding The introduction of small particles into the sliding contact of a hard and rough surface, as shown in Figure 23.4(k), does not necessarily make the tribological contact more severe. The particles can be hidden in the valleys formed by the asperities, while the sliding takes place at the asperity tops. Thus, the particles will have no great effect on either friction or wear. It is important to notice that reduced surface roughness can increase both friction and wear if the particles cannot hide in the valleys and instead interact with the surfaces by scratching and interlocking. 23.5.2.4 Delamination In the very common sliding situation when a hard rough slider moves over a hard rough surface, as shown in Figure 23.5(g), the sliding action takes place at the top of the contacting asperities. They mainly deform plastically, although the overall contact stress may be less than the yield stress of the contacting materials, because the local stresses at the small asperity areas are much higher. High contact stresses can generate dislocations, pile-up of dislocations, and crack nucleation very near the surface, as described by Suh (1973, 1986) in the delamination theory of wear and shown in Figure 23.17. Because of the small plastic deformation of the surface, a large number of cracks must be nucleated before a loose particle can form. The delamination particles are flake-like and may be some hundred micrometers long. This kind of flake-like wear debris has been observed in the sliding contact between a steel slider and a hard titanium nitride coating by Sue and Troue (1990) after about 200 sliding cycles, agglomerated particles being observed after 500 cycles. This behavior correlates with the observations of Fu et al. (1998) for plasma-sprayed Ni,Cr coatings sliding against a steel ball. The generation of flake-like wear debris, probably by some kind of delamination mechanism, has also been observed for softer materials like polyimide polymers (Yamada et al., 1990). The wear rate in delamination can be
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FIGURE 23.17 The initial stage of the delamination process of wear particle formation by shear deformation of voids in the material near the surface. (Adapted from Suh, N.P. (1973), The delamination theory of wear, Wear, 25, 111-124.)
calculated from the equation developed by Suh (1986) where it is given as a function of hardness, contact length, depth, average crack propagation rate, load, spacing of asperity contacts, and crack spacing. 23.5.2.5 Particle Crushing When particles, large in relation to the surface roughnesses, are introduced between two hard surfaces, the result can be particle crushing, scratching, or rolling, as shown in Figure 23.4(i). If the particles have lower hardness than the surfaces, then they will be crushed and destroyed under the load of the contact, with smaller debris and some increase in friction as a result. If the particles have a higher hardness than the surfaces, they will be caught by the roughness of the surfaces, resulting in ploughing and scratching. The scratching particles carry part of the load, which results in concentrated pressure peaks on both surfaces as they try to penetrate them. The high pressure peaks may well be the origin of crack nucleation in the coating (De Wit et al., 1998). The presence of hard particles between hard surfaces may in some cases even reduce the coefficient of friction. If the particles are fairly round in shape, hard enough to carry the load, and at least one of the surfaces is smooth, the particles may act as rollers and reduce the friction (Blomberg, 1993; Fu et al., 1998). The debris in the contact can also change in its properties during the sliding action. In the sliding contact of a TiN coating against a corundum ball, De Wit et al. (1998) observed that the wear debris produced by fretting was transformed during the sliding from amorphous debris into nanocrystalline rutile-like particles with a drop in the friction as a result. Wear debris formed in a contact with a multilayer (Ti,Al)N/TiN coating on steel substrate sliding reciprocatingly against a corundum ball was observed to become progressively lubricious with increasing humidity. The alumina debris produced was originally quite abrasive, but increasing humidity lowered the abrasiveness of the alumina particles, probably due to the formation of hydrated oxides (Huq and Celis, 1999). The sliding process will have an influence on the material properties of the counterface surface material. Because of work hardening, phase transitions, or third-body formation, the microhardness of a steel wear surface can be about 3 times larger than the initial bulk hardness. In sliding abrasive contacts with uncoated steel surfaces, most of the wear particles are often less than 1 µm in size (Kato, 1992). Abrasive wear and oxidative wear have been observed in steady-state sliding of a steel slider against a hard TiN coating by Sue and Troue (1990), Malliet et al. (1991), Franklin and Beuger (1992), and Xu et al. (1999).
23.5.3 Debris Agglomeration Particles that have been liberated from a surface by wear may still have an influence on the future friction and wear behavior of the contact. In sliding contacts with materials of different hardness (lead, zinc, aluminum, copper, nickel, titanium, and steel), Hwang et al. (1999) observed different wear particle agglomeration behavior, depending on hardness and sliding direction. Smaller wear particles had a stronger tendency to join together and form larger ones, and particles of soft and ductile metals had a
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stronger tendency to agglomerate than those of hard and brittle metals. There was a difference in agglomeration behavior, depending on whether the sliding was unidirectional or reciprocating, and lower friction and wear were measured in the cases of reciprocating sliding. Particle agglomeration was not just limited to one location but occurred simultaneously over a distributed area, and the observed particle or flake sizes were in the range of 100 to 600 µm. The mechanism of agglomeration is complicated and probably due to adhesion and/or mechanical interlocking. The agglomerated particles can act as larger particles in the contact, detach to either of the surfaces, or be rejected from the contact (Yuan et al., 1999).
23.5.4 Transfer Layers The material transfer mechanism (Figure 23.3b) is well-known for polymers (e.g., polytetrafluoroethylene [PTFE]), sliding on steel. Surface material from the polymer will wear off and attach by adhesion to the steel counterface to form an extensive PTFE film. This means that after some time of sliding, the tribological pair is actually PTFE sliding against a thin PTFE film on steel, which has very low friction. Similar mechanisms have been observed for sputtered, <1-µm-thick PTFE coatings on steel substrates, resulting in film-like PTFE wear debris transfer to the steel counterface; and for sputtered polyimide (PI)-coated steel, resulting in fine flake-like wear debris transfer to form a polymer layer on the steel counterface (Yamada et al., 1990). In rolling contact bearings in different gas environments, PTFE films have transferred from the retainer onto CaF2 layers on the races and balls, effectively protecting them from wear and increasing the endurance life (Nosaka et al., 1999). A typical building-up process of a transferred surface layer in contacts with steel and hard coatings such as TiN, CrN, and (TiAl)N has been described by Huang et al. (1994). As a result of the ploughing action of hard coating asperities, slider material fragments were first removed and then adhered to some preferential sites on the sliding track of the coating. The preferential sites were the highest asperities that made earliest contact with the counter-surface. Repeated sliding resulted in accumulation of fragments, which then united and formed discontinuous layers on the coating surface. After some sliding, the highest asperities were covered with transferred material, which was deformed and flattened under continuous sliding and a transferred layer built up. Similar processes of transfer layer buildup have been observed and reported for different ceramic and steel contacts (e.g., by Andersson and Holmberg, 1994). Depending on the contact condition, the formation of transfer films in the sliding contact of a titanium nitride coating against a steel slider may be very complex. Sue and Troue (1990) have described the process of minute wear fragments adhering to both surfaces, plastic deformation and strain hardening of the transferred layers and patches, cracking and oxidation of the layers, removal of the layers and patches by fracture, and finally the formation of very thin films, possibly oxides, on both surfaces. In pin-on-disk experiments with a steel ball sliding on TiN coatings, Wilson and Alpas (1998) observed a load effect. At low loads of about 20 N, transfer and buildup of oxidized counterface material on the coating surface and minimal damage to the coating took place; at higher loads up to 100 N, increased debris transfer, polishing, and brittle spallation occurred; but at higher loads, plastic deformation and ductile ploughing or smearing of the TiN coating prevailed. The material transfer layers generated in sliding coated contacts are generally some few micrometers in thickness, but may vary in the range of 0.01 to 50 µm (Ko et al., 1992; Blomberg, 1993). The excellent tribological properties of molybdenum disulfide coatings, often in combination with other materials as a compound, is basically also due to a process of MoS2 debris generation and transfer layer formation. This process has been described by several authors (Fayelle et al., 1990; Donnet et al., 1995; Wahl and Singer, 1995; Donnet, 1996; Singer et al., 1996a,b; Grossiord et al., 1998; and Singer, 1998) and is treated in detail in this book in Chapter 22.
23.5.5 Reaction Layers In a tribological contact, the sliding process brings energy and often high local temperatures into the contacts and at the same time the wear process results in exposure of pure uncontaminated material
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surfaces to the environment. This situation is very favorable for chemical reactions to take place on the newly formed or deformed surfaces. The chemical reactions are dependent on what kind of additional material is brought to the contact in gaseous or liquid form (Ruff et al., 1995; Singer et al., 1996c, Ronkainen et al., 1998a). Based on observations from sliding contacts with MoS2 and TiN coatings, Singer (1998) presents a three-stage nanoscale model for the formation of reaction layers and for the buildup of transfer layers. First, a thin layer is removed from the coating and transferred to the counterface. Meanwhile, both the surface and the transfer layer can react with possible surrounding gases, forming new compounds. The first films to be transferred to the counter-surface may be very thin, of only molecular dimensions. As the transfer film thickens, it is extruded from the contact area and may break up to form new wear debris. This process is then repeated and a layer-by-layer buildup takes place. It has been observed for MoS2 coatings that particle detachment appears to be preceded by deformation, reorientation, and sometimes crack propagation within the first 20 to 50 nm of the coating. In environments containing oxygen, such as air, a thin (about 1- to 10-nm-thick) oxide layer is formed very quickly on most metal surfaces. Some oxide layers (e.g., copper oxide) are sheared more easily than a metal, while others (e.g., aluminium oxide) form a very hard layer. Erdemir et al. (1998) have studied the shear properties and lubricity of a number of oxides for high-temperature tribosystems. They concluded that a complex system, including the kinetics of oxidation and cation diffusion rates, heats of formation, electrostatic electronegativity, surface energy, and other fundamental crystallochemical properties may influence the adhesion and shear rheology of an oxide film forming on a sliding surface. Mechanistically, the crystallochemical properties relate strongly to the melting point of an oxide and its viscosity, the lowering of the surface energy and melting point of an oxide when a second oxide is present in the system, and the solubility, chemical interactions, and compound-forming tendencies between two or more oxides. Tribologically, these phenomena can play a significant role in shear rheology, adhesive interactions, and hence the frictional properties in a sliding contact. There are a number of reports describing studies on different aspects of oxide layer formation on tribological properties. In contacts with alumina (Al2O3) surfaces, Gee and Jennett (1995) found that the tribologically formed hydroxide films are much softer than the remaining alumina, and that the films are liable to fracture under concentrated loading conditions. The hydroxide films were composed of small particles, about 20 to 50 nm in size. Erdemir et al. (1995, 1997) investigated the formation and selflubricating mechanism of thin boron oxide (B2O3) and boric acid (H2BO3) films on the surfaces of boron oxide substrates. They developed a short-duration annealing procedure resulting in the formation of a glass-like boron oxide layer for which they measured very low coefficients of friction (down to 0.05) when sliding against a steel ball. The tendency of formation of an oxide layer on the surface of different (Ti, Al, Zr, Si)N coatings has been reported by Rebouta et al. (1995). The formation of environmentally stable and smooth third-body films on the wear surface was believed to be responsible for the improvement in room-temperature tribological performance of nanocrystalline zinc oxide (ZnO) films observed by Prasad and Zabinski (1997). The friction coefficient of the ZnO films against a steel ball was between 0.16 and 0.34. Friction, in the beginning, was sensitive to load and sliding speed; but once a smooth wear scar was formed, it was very stable and the test conditions had no significant effect on it. Experiments with steel sliding against a chromium nitride (CrN) coating resulted in the formation of a chromium oxide (Cr2O3) surface film with very good wear resistance (Lin et al., 1996b). Increases in the applied load or the sliding velocity helped to form a thicker Cr2O3 film, thus reducing the wear. However, the growth of a thick TiO2 surface film in a TiN-coated contact under the same conditions did not help reduce the wear loss. Additional material, active in the chemical surface reaction, may also be brought to the contact in liquid form. Li et al. (1998) investigated the sliding contact of a plasma-sprayed Cr3C2-NiCr surface against a TiO2 coating under water and ethanol lubricated conditions in a block-on-ring test. They found that water deteriorated the tribological properties of both surfaces by accelerating cracking and fracture. Ethanol reduced the friction coefficient and wear of the Cr3C2-NiCr surface, which could be attributed
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to the formation of a smooth surface film consisting mainly of Cr2O3. However, ethanol also increased the wear coefficient of the TiO2 coating by adsorption-induced cracking as a result of the low fracture toughness of the coating. Surface chemistry considerably influences the surfaces in sliding contacts involving hard carbon coatings such as diamond films or amorphous diamond-like carbon layers. The extremely low friction and the wear properties observed are partly explained by grafitization of the top layer of the surface (Jahanmir et al., 1989; Erdemir et al., 1991b; Donnet et al., 1994; Ronkainen et al., 1994; Schouterden et al., 1995; Erdemir et al., 1995; Pimenov et al., 1995; Voevodin et al., 1996a; Liu et al., 1996; Erdemir et al., 1996a,b; Schmitt et al., 1998; Ronkainen et al., 1999b). The tribological mechanisms involved have been explained by several authors (Gardos, 1994; Holmberg et al., 1994; Donnet et al., 1995; Voevodin et al., 1995b; Donnet, 1996; Hogmark et al., 1996; Voevodin et al., 1996a; Grill et al., 1997; Huu et al., 1998; Singer, 1998; Voevodin et al., 1999d).
23.6 Multicomponent Coatings It has been known for many years that it can be tribologically beneficial to mix together different materials and phases in a coating to achieve enhancements in frictional behavior, as achieved by the addition of PTFE or MoS2 to metallic coatings, or the wear behavior, as achieved by using mixed-phase ceramics such as TiAlN (Knotek et al., 1986; Jehn et al., 1986; Bienk et al., 1995), TiCN (Bienk et al., 1995; Sproul, 1994), TiBN (Gissler, 1994), etc. The concept of utilizing mixed phases is now being taken forward using three main approaches: multilayer coatings, nanocomposite coatings, and functionally graded coatings.
23.6.1 Multilayer Coatings The idea to use a laminated structure to enhance the toughness of materials frequently occurs in nature, for example, in the shells that protect animals. In man-made bulk materials, it has been used for many decades, for example, in the pearlite structure in carbon steels or the “sandwich” construction of laminated glass. The multilayering concept applied to coatings is now regarded as one of the most promising means of performance enhancement. The mechanism of that enhancement can take many forms, including: 1. The use of one interlayer or several interlayers to reduce the mismatch in mechanical or chemical properties between coating and substrate, in order to enhance the adhesion of the coating 2. Multilayered structures to control the residual strain and therefore the stress within coatings, most commonly to enhance the effective adhesion 3. Alternating layers that can act as crack-stoppers either by introducing layer boundaries to stop cracks or providing a tough medium through which propagation is curtailed 4. Compliant alternate layers that allow harder and more brittle layers to slide over each other during bending, thereby avoiding the occurrence of the significant stresses which can occur with thick hard coatings when they deflect under load 5. Extremely thin nanoscale multilayers that constrain dislocation movement — and thereby impart extreme mechanical properties to the coating 6. Layers that provide distinct individual physical properties, such as a diffusion barrier or a thermal barrier Often, a number of the above enhancement mechanisms are combined in a single coating. Some of the key historical developments in this field are outlined below. Work on PVD multilayers was carried out in the late 1970s and early 1980s by Springer and Catlett (1978) and Springer and Harford (1982). They attempted to build on the earlier models of Koehler (1970), which predicted that high-yield-strength materials could be fabricated by alternating thin layers of high-shear-modulus material with thin layers of low shear modulus. The model was based on the inhibition of dislocation formation and mobility. They investigated Al/AlαOγ films deposited by a pulsed gas process in an electron beam gun system, and showed that a Hall-Petch type relationship was obeyed
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Tribologically important properties in different zones of the coated surface.
for yield stress based on the layer spacings. Bunshah and co-workers also deposited microlaminate coatings by evaporation techniques, both metal/metal (Bunshah et al., 1984) and metal/ceramic (Sans et al., 1983) couples being studied. In general, an improvement in mechanical properties was observed for decreasing layer thicknesses. In recent years, the literature and, at a certain level, the theoretical understanding of multilayer films has grown, in particular with regard to compositionally modulated superlattice thin films (Barnett, 1993; Barnett and Shinn, 1994). However, many of the theories developed are applicable to highly epitaxial or single-crystal layers; and while considerable progress has been made in understanding the theoretical aspects of superlattice hardening and strengthening mechanisms, their value in practical tribological systems is somewhat limited. There are several reasons for this, not the least of which is the difficulty in growing true superlattices (i.e., epitaxial layers) on real polycrystalline engineering components. A more practical approach is to consider how the requirements of a surface differ at different locations within it — that is, at the interface with the substrate, within the coating itself, and at its surface, as shown by Figure 23.18. Multilayer coatings offer the possibility of designing the surface according to such requirements (Holleck, 1986, 1990; Holleck and Schier, 1995; Voevodin et al., 1996b). This is the concept behind the functionally graded coatings discussed in Section 23.6.3. Holleck tended to use multilayers of different ceramic materials (e.g., TiC and TiB2), selected on the basis of their dominant bonding mechanism (i.e., metallic, covalent, or ionic). He demonstrated improvements in hardness, indentation toughness, adhesion, and wear performance under optimized layer thickness conditions (Holleck et al., 1990), and attributed this, in part, to the crack deflection and stress relaxation mechanisms for the TiC/TiB2 system. This will pertain to many kinds of contact, especially where cyclic, fatigue-inducing conditions prevail. The benefits are no longer defined in terms of the early Koehler-type arguments based on the maximization of yield strength. Rather, they relate to the macro behavior of the multilayer stack. However, the concept of the alternation of high- and low-shear-modulus layers does seem to provide benefits beyond those described even by Holleck. One can cite, for example, the considerable benefits exhibited by multilayer diamond-like carbon and metal carbide films (Matthews and Eskildsen, 1994) or multilayer TiN/Ti films (Leyland and Matthews, 1994; Bull and Jones, 1996; Ensinger et al., 1992). In these cases, a different argument must be developed to fully explain the benefits observed. One way to consider the behavior of these films is to model the coating under a normal force, which can be a point or distributed load, causing the coating to deflect. This will be accompanied by deformation of the substrate, which ideally should remain elastic. If one considers the bending stresses induced in the coating under such a normal load, the level of maximum stress will increase with thickness for a given deflection and radius of curvature; see Figure 23.19.
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FIGURE 23.19 (a) Thin hard coatings on soft substrate generate lower stresses in the coating and at the coatingsubstrate interface, compared with (b) a thick hard coating with the same deflection.
Load H = hard layer S = soft layer H S H S H S
Substrate
FIGURE 23.20 A multilayer coating with alternate hard and soft layers can allow deflection to occur under load without yielding of the harder layers. They effectively slide over each other, with shear occurring in the soft layer. The pattern of shear is illustrated by the line through the film, which was initially straight in the unloaded condition.
The diagram is highly schematic and treats the coating in two dimensions as a beam, taking no account of the influence of the substrate on the stress distribution. Nevertheless, it is illustrative because it shows that many multilayers, if bent to a similar radius, would individually see a much lower stress than one thick layer. This concept only works if the layers can effectively slide over each other, that is, in the manner of a sheaf of paper or a paperback book being bent. In effect, one sees another benefit of multilayer coatings; that is, that the role of one of the sets of alternate layers can be to offer a shear zone to permit the harder and more brittle layers to deflect under load without fracture. Thus, a straight line scribed on such a cross-section would deflect as shown in Figure 23.20. This ensures that each of the hard layers will be subject to a much lower maximum bending stress than would be the case for a thick film bent to the same radius, although clearly the deflection under the same load would be greater due to the lower stiffness of the surface coating. That is not necessarily an issue, because for many tribological contacts with thin surface coatings, it is the substrate that provides the main load support; the coating is present to provide a hard, low-friction outer layer to reduce abrasive and/or adhesive wear. Thus, one can now see why multilayer coatings based on Ti/TiN and DLC/WC, for example, have proved successful in many practical contact conditions. The former have shown promise in erosive conditions (Leyland and Matthews, 1994), while the latter are now used on gears and bearing surfaces that see cyclic contact conditions (Matthews and Eskildsen, 1994). Because this concept is relatively new, the development of models to permit layer optimization in terms of relative thickness and mechanical properties has been limited. The constraint on both the hard and soft layers may be that the elastic limit should not be exceeded, although this criterion seems more important for the hard layers because if they yielded, then rapid fracture would ensue. The softer layers will be present to give an easy shear; that is, they should have a low shear modulus, which equates to a low elastic modulus. Also, these layers should have a long elastic strain to failure, meaning that yield should not occur. Although in this case plastic yielding is to be avoided, especially in contacts subject to cyclic loading and fatigue, the main purpose will be to prevent the harder layers from exceeding their yield stress. There are some interdependent variables in the optimization of layer thicknesses. For example, because the layers also carry a load normal to the surface, they will be subject to
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compressive stresses, which will tend to squash the layers, in particular the softer ones. This will have the effect of limiting their maximum thickness; otherwise, they may collapse and provide inadequate support for the harder layers within the coating. While an increase in the thickness of the layers will increase the relative sliding distance of one hard layer over another, it will not necessarily increase the shear strain — which is a ratio between the sliding distance of one hard layer over the next and the thickness. The ideal seems to be to incorporate a large number of thin layers, thereby ensuring that the load support is not compromised. In the case of DLC/WC coatings produced commercially, layer thicknesses of 20 nm are typical for sliding and rolling contacts, while for Ti/TiN films, layers 1 and 2 µm thick have proved effective in erosion conditions (Leyland and Matthews, 1994). The optimization of layer thickness will thus depend on the application and the loading conditions. In erosive or abrasive contacts, for example, a greater overall coating thickness is often needed, especially for coarse and hard third bodies. The benefits of the multilayering of relatively hard and relatively elastic layers has recently been demonstrated in a specially developed cyclic impact test (Bantle and Matthews, 1995; Voevodin et al., 1995c). In that work, a relatively soft substrate (316 stainless steel) was used. This deformed plastically under repeated loads of 900 N applied at a frequency of 8 Hz by a 6-mm-diameter tungsten carbide ball, while coatings comprising multilayer stacks of Ti, TiN, TiCN, TiC, Ti/DLC, TiC, and Ti/DLC showed good wear performance, although not optimized for adhesion. Further tests using machines such as this, which apply the kinds of impact load often encountered in machine applications, will allow the full benefit of multilayered coatings to be achieved through further optimization.
23.6.2 Nanocomposite Coatings As mentioned earlier, the most significant driver in the development of new tribological coatings has been the realization that increased hardness should not be the sole goal when seeking to optimize coatings for enhanced wear performance (Leyland and Matthews, 2000). It is now clear that in most tribological contacts, the elastic modulus, hardness, and fracture toughness should be considered together in defining the likely material response of a surface to a loading condition. This is, in fact, the secret behind the success of many of the multilayered coatings previously discussed; that is, they provide a means of combining hardness with an ability to deform under load without cracking — they are tough. Another key route to the production of coatings that combines toughness characteristics with hardness is to control their grain size. Several researchers have, in recent years, concentrated on this aspect of coating development (Veprek, 1999; Musil, 1999; Niedorfer et al., 1999; Mitterer et al., 1999; Hauert et al., 1999; Vaz et al., 1999; Musil et al., 1999a,b; Musil et al., 1998; Musil and Vlcek, 1999; Musil and Regent, 1998; Benda and Musil, 1999; Misina et al., 1998; Zeman et al., 1999). Thus, the understanding of nanocomposite coatings represents both a challenge and an opportunity, not only to coating process developers, but also to those involved in modeling the deformation and failure behavior of such films. Veprek (1999) and Musil (1999) have produced comprehensive review papers on the subject of superhard and nanocomposite coatings. According to Veprek, superhard refers to materials whose hardness exceeds 40 GPa, and these can be divided into those with intrinsic hardness, such as diamond (70 to 100 GPa), cubic boron nitride (~48 GPa); and those with extrinsic hardness, which is determined by their microstructure. One group of these consists of the multilayer and superlattice structures discussed previously. The other group comprises the nanocrystalline (nc) composites. Examples are nc-MnN/aSi3N4 (where M is Ti, W, V, and other transition metal nitrides, and a-Si3N4 is an amorphous silicon nitride), nc–TiN/BN, nc–TiN/TiB2, and others with a hardness over 50 GPa. In the case of nc-TiN/SiNα , the hardness is claimed to reach 105 GPa (Veprek, 1999). While Veprek has tended to emphasize the nc-metal nitride/amorphous nitride route to the production of superhard nanocomposites, Musil has concentrated on the nc-metal nitride/metal coating approach. Examples of coatings in this latter category are ZrCuN (Musil et al., 1999c) and TiAlN (Musil and Hruby, 1999). To date, much of the research on the ceramic/metal and ceramic/ceramic nanocomposite coatings has emphasized investigations of their grain size and microstructure (e.g., through X-ray diffraction techniques)
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and the evaluation of hardness using nanoindentation. Comparatively little work has been done on their tribological properties. That is not the case for the nanocomposite coatings based on metal carbides and amorphous carbon, which have been extensively researched by Voevodin and co-workers (e.g., Voevodin et al., 1997a,b; Voevodin et al., 1998a,b; Voevodin et al., 1999a,b,c). In dry ball-on-disk tests, nanocrystalline TiC-amorphous DLC composites showed a friction coefficient of 0.15 against steel, compared to 0.5 to 0.6 for TiN and CrN, and 0.3 to 0.4 for TiC. The coating was also tough and withstood static loading tests without cracking much more effectively than the single-phase TiC and even DLC (Voevodin and Zabinski, 1998b). Similarly, nanocrystalline WC/amorphous DLC composites showed low wear rates and friction coefficients of about 0.2 against steel. A particularly encouraging feature of these coatings was that the pulse laser deposition process used allowed them to be produced at less than 300°C. WC2 coatings with an extremely fine grain size of 1 to 3 nm could be obtained (Voevodin et al., 1999c). As pointed out by Mitterer and co-workers (Mitterer et al., 1999), it is not only the nanoscale grain size that is important in providing the advantageous properties of nanocomposite materials. The interfacial strength between the grains will also be important. To avoid unstable crack propagation, an interface of high cohesive strength is needed. Mitterer et al. state that this can be obtained from those compounds that show a high miscibility gap in the solid state, but a certain chemical affinity to each other to form high-strength grain boundaries. This can be achieved, for example, with the quasi-binary systems TiNTiB3 and TiC-TiB2, both showing a eutectic type, as well as for other similar transition-metal nitride/boride or carbide/boride films. Various authors have examined the Ti-B-C-N system for nanocomposite coating production. Further to the early work of Holleck (1986) and Holleck and Schultz (1988), other authors (Mitterer et al., 1990; Ronkainen et al., 1990, 1991, 1992; Gissler, 1994) have also investigated nanograined coating production based on the TiN/TiB2 and TiC/TiB2 quasi-binary phase systems, using both magnetron sputtering and electron-beam PVD, with promising results in various tribological applications. While the recent work of Mitterer et al. (1998, 1999) has shown the importance of cohesive interfacial strength, other studies by Rebholz et al. (1998, 1999b,d) of aluminum in the Ti-B-N phase system have demonstrated that coatings with high hardness (≥ 30 GPa) but relatively low elastic modulus (≤ 300 GPa) can be produced, which have a high H:E ratio. Thus, the toughness is improved through better coating/substrate elastic property matching, showing enhanced tribological behavior in both laboratory wear tests and practical cutting applications, where a life twice that of TiN can be observed (Rebholz et al., 1999b). Further work by these authors (Rebholz et al., 1999a) on adding small amounts of boron (≤ 5 at%) to TiN coatings to reduce coating grain size, and on metallic/intermetallic/ceramic Ti-Al-B coatings (Rebholz et al., 1999c) to reduce coating elastic modulus, has shown excellent results in laboratory wear tests.
23.6.3 Functionally Graded Coatings In some ways, functionally graded coatings can be regarded as the logical progression from multilayered coatings. In effect, the multilayer stack described at the end of Section 23.6.1 represents an excellent example of a functionally graded coating — where the coating is designed to utilize specific layers to impart desired properties at specific levels within the coating. This is illustrated in Figure 23.21. Such a concept can even be achieved with just two layers; for example, an electroless nickel coating can be used as a load supporting layer for a hard PVD TiN or CrN coating, that improves the abrasive wear performance and enhances the corrosion resistance (Vetter et al., 1993; Leyland et al., 1993; Bin-Sudin et al., 1996). It is even possible to include within this approach the concept of pretreating a substrate surface to produce a hardened outer layer, which can then support the coating more effectively. Such approaches have been termed hybrid or duplex coatings (Matthews et al., 1995; Matthews, 1997; Bell, 1997). Many research groups are now examining the possibility of grading the composition, and even the structure, of coatings to meet the needs of specific applications. For example, Savan et al. (1999) have developed a coating that combines a relatively hard TiAlN phase and a relatively soft MoS2 phase with increasing MoS2 toward the outer surface, a coating that might have benefits in dry machining applications.
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FIGURE 23.21 (a) A functionally graded multilayer coating design to utilize specific layers for distinct properties. (b) A particular multilayer coating tested by Voevodin et al. (1996).
Goller et al. (1999) have reported that TiN coatings with small amounts of MoSα (up to 8 at%) can extend coating drill lifetimes compared to TiN coatings alone. One of the benefits of grading the composition of coatings has been shown to be the ability to enhance the effective adhesion of DLC-based coatings that contain metal additions. Improvements have been measured under local high contact loads (Voevodin et al., 1997a) or even under repetitive impact conditions (Bantle and Matthews, 1995), as well as under loaded sliding conditions (Voevodin et al., 1995b; Voevodin et al., 1996b).
23.6.4 Adaptive Coatings The concept of “intelligent” materials is one that is gaining increasing attention in the research community, and this is equally true among those who are developing coatings. An intelligent coating can be defined as one that adapts to its operating environment. While appearing at first sight to be a rather exaggerated “blue-skies” concept, such adaptability is in fact a property that has existed in many coatings for some decades. For example, coatings designed to resist high-temperature corrosion in gas turbine engines are designed to form a stable oxide on their surface during operation. A similar observation could be made for some of the most recently developed cutting tool coatings, based on, for example, TiAlN, which produces a stable oxide during high-temperature cutting operations. This effect has been further enhanced in TiAlN coatings that contain additions of yttrium and/or chromium to help to further stabilize the oxide film (Munz 1997; Savan et al., 1999). In some ways, the diamond and DLC films discussed in Chapter 24 can also be regarded as adaptive in the sense that the formation of a temperature-induced graphite-like layer in the contact is thought to be the source of the low friction demonstrated by such coatings. One of the main advocates of adaptive coatings that can provide advantageous properties across a range of operating temperatures and environments has been Zabinski who, together with co-workers, has been working on solid lubricant coatings capable of operating at temperatures from ambient up to 600°C and beyond, even up to 800°C. At such temperatures, conventional oils and greases cannot be used, and graphite and metal dichalcogenides such as MoS2 and WS2 have historically been used as alternatives. Their lubricious nature is generally attributed to weak interplanar bond strength; this condition may not prevail at higher temperatures at which the materials may oxidize. Zabinski et al. (1995a,b) have reported that this oxidation may become a problem at 350°C, and have carried out research into the deposition of coatings with additives such as graphite fluoride (CFα) in order to extend the permissible operating temperature up to 450°C. They utilized a laser-pulsed deposition method and showed that the films were less sensitive to moisture than pure WS2, achieving friction coefficients of 0.01 to 0.04 against a stainless steel counterface in dry air. Although not adaptive in the usual sense of the word, these coatings point the way toward coating materials and processes that can achieve a wider operating range.
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To provide lubricity in the 500 to 800°C temperature range, other materials must be considered (John et al., 1999). Oxides such as ZnO, along with fluorides such as CaF2 and BaF2, are lubricious in this regime, due to their low shear strength and high ductility. The oxides and, to a lesser extent, the fluorides are also chemically stable in air at high temperatures. At ambient temperatures, however, these materials are brittle and subject to cracking and high wear rates. According to John et al., no single material is known to be lubricious over the entire range from ambient temperature to 800°C. Thus, the obvious answer to producing a lubricant coating that can operate over a broad temperature range is to combine low- and high-temperature lubricant materials into either a composite or layered structure. The objective is for the properties of both materials to be manifested in their respective temperature ranges. John et al. (1999) examined both composite and layered structures of CaF2 and WS2 grown by pulsed-laser deposition on steel and TiN-coated steel substrates, and found that the films were lubricious at up to 500°C. They found that the CaF2 and WS2 materials interacted to form CaSO4, among other compounds. Thus, the coatings, in effect, adapted to their environment by forming a low-friction outer layer. The concept of combining coating materials to extend the operating range using several other compounds has been applied; for example, MoS2 with PbO, and WS2 with ZnO, to provide lubrication over a wide temperature range (Donley and Zabinski, 1992; Zabinski et al., 1996; Zabinski et al., 1992; Walck et al., 1994; Zabinski et al., 1995a,b: Walck et al., 1997; Zabinski and Donley, 1994). In these cases, the metal dichalcogenides reacted with the oxides to form PbMoO2 and ZnWO4, which were found to be lubricious at high temperatures. The problem with these coatings was that they were adaptive only on heating; that is, the low-temperature lubricant materials reacted to form a high-temperature lubricant — but the reaction was irreversible. After returning to room temperature, the lubricious properties had disappeared. Work is proceeding to control the reactions using layered structures with diffusion barrier coatings, and thereby to develop coatings that will function through multiple temperature cycles.
23.7 Concluding Remarks This chapter began by setting the scene on the present state-of-play regarding advanced metallic and ceramic coatings and their applications. The macroscopic and microscopic responses of surfaces to loading conditions were discussed, and, in the latter case, the energy accommodation concept was introduced as a means of understanding the critical property requirements that the surfaces of bulk materials and also coatings must exhibit in order to have adequate functionality. This highlighted the importance of toughness, in addition to the usually emphasized property — hardness. When a surface has a coating applied, the coating and substrate act together as a composite and this allows each to provide specific benefits. For example, the coating can add a low friction layer, or a diffusion or thermal barrier, while the substrate can impart a load-supporting function or a bulk toughness, which a monolithic component made just of the coating material might not possess. In effect, with new developments in tribological understanding and in coating production methods, we are now at the dawn of a new era in effective tribological design, in which concepts and practices that were previously only theoretically possible can now be applied — giving enhanced and predictable levels of reliability and therefore well-controlled and optimized life-cycle costs for coated components.
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Voevodin, A.A., Rebholz, C., and Matthews, A. (1995b), Comparative tribology studies of hard ceramic and composite metal-DLC coatings in sliding friction conditions, Tribol. Trans., 38, 829-836. Voevodin, A.A., Rebholz, C., Schneider, J.M., Stevenson, P., and Matthews, A. (1995c), Wear resistant composite coatings deposited by electron enhanced closed field unbalanced magnetron sputtering, Surf. Coat. Technol., 73, 185-197. Voevodin, A.A., Phelps, A.W., Zabinski, J.S., and Donley, M.S. (1996a), Friction induced phase transformation of pulse laser deposited diamond-like carbon, Diamond Rel. Mater., 5, 1264-1269. Voevodin, A.A., Schneider, J.M., Rebholz, C., and Matthews, A. (1996b), Multilayer composite ceramicmetal-DLC coatings for sliding wear applications, Tribol. Int., 29, 559-570. Voevodin, A.A., Walck, S.D., and Zabinski, J.S. (1997a), Architecture of multilayer nanocomposite coatings with super-hard diamond-like carbon layers for wear protection at high contact loads, Wear, 203/204, 516-527. Voevodin, A.A., Prasad, S.V., and Zabinski, J.S. (1997b), Nanocrystalline carbide/amorphous carbon composites, J. Appl. Phys., 82, 855-858. Voevodin, A.A. and Zabinski, J.S. (1998a), Load-adaptive crystalline-amorphous nanocomposites, J. Mater. Sci., 33, 319-327. Voevodin, A.A. and Zabinski, J.S. (1998b), Superhard functionally gradient, nanolayered and nanocomposite diamond-like carbon coatings for wear protection, Diamond Rel. Mater., 7, 463-467. Voevodin, A.A., O’Neill, J.P., Prasad, S.V., and Zabinski, J.S. (1999a), Nanocrystalline WC and WC/a-C composite coatings produced from intersected plasma fluxes at low deposition temperatures, J. Vacuum Sci. Technol., A17, 986-992. Voevodin, A.A., O’Neill, J.P., and Zabinski, J.S. (1999b), WC/DLC/WS2 nanocomposite coatings for aerospace tribology, Tribol. Lett., 6, 75-78. Voevodin, A.A., O’Neill, J.P., and Zabinski, J.S. (1999c), Nanocomposite tribological coatings for aerospace applications, Surf. Coat. Technol., 116/119, 36-45. Voevodin, A.A., O’Neill, J.P., and Zabinski, J.S. (1999d), Tribological performance and tribochemistry of nanocrystalline WC/amorphous diamond-like carbon composites, Thin Solid Films, 342, 194-200. Wahl, K.J. and Singer, I.L. (1995), Quantification of a lubricant transfer process that enhances the sliding life of a MoS2 coating, Tribol. Lett., 1, 59-66. Wahl, K.J. and Unertl, W.N. (1998), Formation of nanometer-scale contacts to viscoelastic materials, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, London, 261-271. Wahl, K.J., Belin, M., and Singer, I.L. (1998), A triboscopic investigation of the wear and friction of MoS2 in a reciprocating sliding contact, Wear, 214, 212-220. Wahl, K.J., Dunn, D.N., and Singer, I.L. (1999), Wear behaviour of Pb-Mo-S solid lubricating coatings, Wear, 230, 175-183. Walck, S.D., Donley, M.S., Zabinski, J.S., and Dyhouse, V.J. (1994), Characterisation of pulsed laser deposited PbO/MoS2 by transmission electron microscopy, J. Mater. Sci., 9, 236-245. Walck, S.D., Zabinski, J.S., McDevitt, N.T., and Bultman, J.E. (1997), Characterisation of air-annealed, pulse laser deposited ZnO-WS2 solid film lubricants by transmission electron microscopy, Thin Solid Films, 305, 130-143. Wang, D.F. and Kato, K. (1998), Coating thickness effect on surface damage mode transitions for an ion beam assisted carbon nitride coating subject to sliding contact with a spherical diamond, Wear, 223, 167-172. Wang, D.F. and Kato, K. (1999a), Dynamic evaluation of surface damage mode transitions in carbon nitride coatings due to sliding contact with a spherical diamond, Wear, 225/229, 104-110. Wang, D.F. and Kato, K. (1999b), Effect of coating thickness on friction variations in sliding between CN0.1 coated Si(111) and a diamond pin, Wear, 224, 113-117. Wiklund, U. (1999), Mechanics and Tribology of Micro- and Nanolayered PVD Coatings, Ph.D. thesis, Acta Universitatis Upsaliensis, Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 428, Uppsala, Sweden. 47 p.
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Wilson, S. and Alpas, A.T. (1998), TiN coating wear mechanisms in dry sliding contact against high speed steel, Surf. Coat. Technol., 108/109, 369-376. Wong, S.K. and Kapoor, A. (1996), Effect of hard and stiff overlay coatings on the strength of surfaces in repeated sliding, Tribol. Int., 29, 695-702. Wong, S.K., Kapoor, A., and Williams, J.A. (1997), Shakedown limits of coated and engineered surfaces, Wear, 203/204, 162-170. Xu, G., Zhou, Z., Liu, J., and Ma, X. (1999), An investigation of fretting behavior of ion-plated TiN, magnetron-sputtered MoS2 and their composite coatings, Wear, 225/229, 46-52. Yamada, Y., Tanaka, K., and Saito, K. (1990), Friction and damage of coatings formed by sputtering polytetrafluoroethylene and polyimide, Surf. Coat. Technol., 43/44, 618-628. Yuan, F. and Hayashi, K. (1999), Influence of the grain size of the aluminium coating on crack initiation in indentation, Wear, 225/229, 83-89. Yang, S.H., Kong, H., Yoon, E.S., and Kim, D.E. (1999), An experimental study of the rolling resistance of bearings coated by pure silver, Wear, 225/229, 119-126. Zabinski, J.S. and Donley, M.S. (1994), Lubricant Coatings, U.S. Patent 5, 282, 985. Zabinski, J.S. and Prasad, S.V. (1996), Advanced solid lubricant coatings for aerospace systems. Proc. AGARD Conf. ‘Tribology of Aerospace Systems,’ Sesimbra, Portugal, AGARD-CP-589. Zabinski, J.S., Donley, M.S., Dyhouse, V.J., and McDevitt, N.T. (1992), Chemical and tribological characterisation of PbO-MoS2 films grown by pulsed laser deposition, Thin Solid Films, 214, 156-163. Zabinski, J.S., Donley, M.S., Walck, S.D., Schneider, T.R., and McDevitt, N.T. (1995a), The effects of dopants on the chemistry and tribology of sputter-deposited MoS2 films, Tribol. Trans., 36, 894-904. Zabinski, J.S., Florkey, J.E., Walck, S.D., Bultman, J.E., and McDevitt, N.T. (1995b), Friction properties of WS2/graphite fluoride thin films grown by pulsed layer deposition, Surf. Coat. Technol., 76/77, 400-406. Zabinski, J.S., Prasad, S.V., and McDevitt, N.T. (1996), Advanced solid lubricant coatings for aerospace systems, in Tribology for Aerospace Systems, Proc. of NATO AGARD SMP Conference, 6-7 May 1996, Sesimbra, Portugal, AGARD-CP-589. Zeman, P., Mitterer, C., Mayrhofer, P.H., and Musil, J. (1999), A novel type of nanocomposite coating — magnetron sputtered ZrN/Cu films, Proc. 14th Int. Symp. Plasma Chemistry, Prague, Czech Republic. Zhang, L. and Tanaka, H. (1998), Atomic scale deformation in silicone monocrystals induced by twobody and three-body contact sliding, Tribol. Int., 31, 425-433. Zheng, L. and Ramalingam, S. (1995), Stresses in a coated solid due to shear and normal boundary tractions, J. Vac. Sci. Technol., A13, 2390-2398. Zheng, L. and Ramalingam, S. (1996), Multi-layer and composite structures for advanced coatings, Surf. Coat. Technol., 81, 52-71. Zuiker, C., Krauss, A.R., Gruen, D.M., Pan, X., Li, J.C., Csencsits, R., Erdemir, A., Binal, C., and Fenske, G. (1995), Physical and tribological properties of diamond films grown in argon-carbon plasmas, Thin Solid Films, 270, 154-159. Zum Gahr, K.-H. (1998), Wear by hard particles, Tribol. Int., 31, 587-596.
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24 Tribology of Diamond, Diamond-Like Carbon, and Related Films* 24.1 24.2
Introduction ..................................................................... 871 Diamond Films ................................................................ 872 Microcrystalline Diamond Films • Nanocrystalline Diamond Films • Tribology of Diamond Coatings • Tribological Applications
24.3 Argonne National Laboratory
Christophe Donnet École Centrale de Lyon
Diamond-like Carbon (DLC) Films ............................... 888 Background on DLC Films • Tribology of DLC Films • Applications of DLC Films
Ali Erdemir 24.4
Other Related Films ......................................................... 897 Cubic Boron Nitride (CBN) • Carbon Nitride Films
24.5
Summary and Future Direction...................................... 899
24.1 Introduction Diamond, diamond-like carbon (DLC), and other related materials (i.e., carbon nitride and cubic boron nitride [CBN]) are some of the hardest materials known and offer several other outstanding properties, such as high mechanical strength, chemical inertness, and very attractive friction and wear properties, that make them good prospects for a wide range of tribological applications, including rolling and sliding bearings, machining, mechanical seals, biomedical implants, microelectromechanical systems (MEMS), etc. The dry sliding friction and wear coefficients of these materials are among the lowest recorded to date (Brookes and Brookes, 1991; Feng and Field, 1991; Field, 1992; Miyoshi, 1995; Erdemir, 2001a,b). In fact, if they were inexpensive and readily available, they would undoubtedly be the materials of choice for a wide range of applications. Besides their exceptional mechanical and tribological properties, most of these superhard materials offer broad optical transparency, high refractive index, wide bandgap, low or negative electron affinity, transparency to light from deep UV through visible to far infrared, excellent thermal conductivity, and extremely low thermal expansion. Briefly, these exceptional qualities make diamond, DLC, and other related materials ideal for numerous industrial applications in addition to tribology. * The submitted manuscript has been created by the University of Chicago as Operator of Argonne National Laboratory (“Argonne”) under Contract No. W-31-109-ENG-38 with the U.S. Department of Energy. The U.S. Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. Work supported by U.S. Department of Energy, Office of Energy Research, under Contract W-31-109-Eng-38.
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The purpose of this chapter is to provide an overview of the tribology of diamond and related coatings that have attracted overwhelming interest in recent years. Emphasis is placed on the current state-of-theart of our understanding of the friction and wear mechanisms of these films as well as on their uses for demanding tribological applications. Referring to the structural and fundamental tribological knowledge gained during the past decade, this chapter emphasizes the importance of surface physical and chemical effects on friction and wear of these materials and describes new deposition procedures that can lead to the production of novel films that afford ultralow friction and very long wear life to sliding tribological interfaces. Tribological issues associated with metal cutting and contact sliding are also addressed. By referring to recent tribological studies, one observes that the surface roughness of these materials plays a major role in their friction and wear performance. Smooth diamond films obtained by polishing and by controlling grain size hold promise for future tribological applications, including mechanical seals and MEMS. The chapter is divided into three main subject areas. The first area is devoted to the synthesis, tribology, and applications of diamond films. The second deals with DLC films and their tribology; and the third is devoted to the tribology and applications of other related films such as CBN and carbon nitride.
24.2 Diamond Films Natural diamonds are expensive and difficult to machine into useful wear parts for large-scale industrial applications. Except for a few cases (e.g., diamond-studded rotary drill bits, dressers, diamond-tipped glass cutters, and fine powders as superabrasives in grinding wheels), natural diamond is rarely used for tribological purposes. However, synthetic polycrystalline diamonds (PCDs) have been available for more than 30 years and they are widely used in many industrial applications. PCDs are produced in large quantities by a high-pressure/high-temperature (HPHT) method in which diamond is crystallized from a graphitic or carbonaceous precursor at pressures of 50 to 100 kbar and temperatures of 1600 to 2000°C. The end product is a fine diamond powder that is used mostly as a superabrasive in grinding and polishing media. The phase diagram in Figure 24.1 indicates the stability ranges of diamond, graphite, and other
FIGURE 24.1 indicated.
Carbon diagram in which the stability ranges of diamond, graphite, and other forms of carbon are
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forms of C. It is possible to sinter these diamond powders with metallic or ceramic binders (e.g., Co, Ni, TiC, etc.) at high pressures and temperatures and then use them as tool bits or sharp blades in metalcutting or machining operations.
24.2.1 Microcrystalline Diamond Films The prospects for inexpensive and large-scale production of diamond increased tremendously in the 1970s, when researchers discovered that diamond can be grown as a thin film at low deposition pressures (102 to 103 Pa) from a hydrocarbon/hydrogen mixture by chemical vapor deposition (CVD). Early attempts to produce diamond by CVD date to when HPHT synthesis of diamond was being explored. The tube oven experiments of Eversole (1962) and Angus (1994) and low-pressure synthesis of diamond from hydrocarbon gas mixtures by Deryagin and Fedoseev (1975) and Fedoseev (1994) can be regarded as the earliest attempts to produce synthetic diamond by CVD. In fact, Eversole of Union Carbide was able to produce diamond phases by a thermal pyrolysis method in 1962 (Eversole, 1962). Progress slowed thereafter until Angus of Case Western University found a more efficient method in which graphite is etched simultaneously with atomic H in the deposition system (Angus, 1994). His work motivated Deryagin and co-workers to focus on the uses of H/hydrocarbon mixtures for low-pressure diamond growth (Deryagin and Fedoseev, 1975). Since these studies, there has been an explosion in research on diamond and related materials, with the expectation that low-pressure methods will allow faster, less expensive, and easier production of synthetic diamonds. During the past 2 decades, great strides have been made in both the production and industrial applications of diamond films. At present, several techniques can be used to produce high-quality diamond films with micro- and nanocrystalline structures at fairly high deposition rates over reasonably large surface areas (Banholzer, 1992; Gruen et al., 1994; Hatta and Hiraki, 1998; Komplin and Hauge, 1998). The most widely used methods are plasma-enhanced CVD, hot-filament CVD, microwave CVD, DC-arc jet, combustion flame, and laser-assisted CVD (Haubner and Lup, 1992; Anthony, 1992; Butler and Windischmann, 1998). These methods have greatly reduced the unit production cost of diamond and increased the prospects for large-scale industrial applications in tribological and other fields. In fact, several commercial companies now offer diamond-coated products at reasonable cost. The high-quality diamond coatings produced by CVD methods exhibit most of the desired mechanical and tribological properties of natural diamonds (Field, 1992; Miyoshi, 1995; Lux et al., 1997). Low-pressure synthesis of diamond coatings involves the use of hydrogen (H) and methane (CH4) gas mixtures. Typical deposition pressures in these syntheses are 102 to 103 Pa, and the gas mixture primarily consists of H and very little CH4. In the case of microwave CVD, 0.5 to 5% CH4 is mixed with H gas and introduced into the deposition reactor. Small amounts of O and N can also be blended. In the case of microwave CVD, a 2.45-GHz power source is used to initiate and maintain a gas discharge plasma in which the substrate material is immersed. At very high plasma temperatures, electrons intensely interact with the H-rich gas mixture, and the ionic species that are created during this interaction lead to the formation of diamond nuclei on the surface of a suitable substrate (i.e., Si, SiC, W, Mo). Plasma conditions in deposition reactors are tailored to control the film microstructure and chemistry, as well as growth rates and orientation. Typical substrate temperatures for high-quality diamond deposition can range from 700 to 1000°C. Deposition of diamond at temperatures below 700°C has also been demonstrated but growth rates are reduced significantly and the amount of non-diamond precursors in these coatings is increased (Hatta and Hiraki, 1998). Hydrogen is extremely important for the synthesis of high-quality diamond coatings in most CVD processes. It plays a critical role in the stabilization of the sp3 bond character of the growing diamond surfaces. It also controls the size of the initial nuclei, dissolution of C and generation of condensable C radicals in the gas phase, abstraction of H from hydrocarbons attached to the surfaces, and production of vacant surface sites where sp3-bonded C precursors can be inserted. It etches most of the double or sp2-bonded C from the surface, and thus hinders the formation of graphitic and/or amorphous C (Banholzer, 1992). Hydrogen also continuously etches out the smaller diamond grains and suppresses
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continuous renucleation. Only those grains that attain a certain critical ratio of bulk-to-surface atoms survive. Consequently, these diamond coatings consist primarily of large grains with highly faceted surface finishes that exhibit a surface roughness value of ≈10% of the film thickness. During the initial stage of film growth, nucleation starts at preferred sites; eventually, independent nuclei form. As these nuclei grow larger, they close the gaps between them and merge to form a continuous film. Thereafter, the growth process and growth rates are dominated by nearby neighbors and growth orientation. Grains with more favorable growth orientation grow most quickly and overshadow the grains with less favorable growth orientation. Grains with less favorable growth orientation will be buried between the large grains. Figure 24.2 shows initial, intermediate, and final growth stages of a diamond film on an Si substrate. High-quality microcrystalline diamond coatings are rough and often nonuniform in thickness or slightly bowed because of internal stresses and differences in deposition rate from the edges to the center of the samples. The generally rough surface finish of these coatings precludes their immediate use for most tribological applications. As discussed in detail later, when used in sliding-wear applications, such rough coatings cause high friction and very high wear losses on mating surfaces. The rough diamond coatings can be polished by laser beams, mechanical lapping with fine diamond powders, ion-beam or plasma etching, and thermomechanical polishing with hot Fe or Ni plates (Zaitsev et al., 1998; Ramesham and Rose, 1998; Erdemir et al., 1997a; Bhushan et al., 1994; Gupta et al., 1994; Pimenov et al., 1996). Mechanical lapping and polishing with hot Fe plates, the most widely used methods, allow polishing of large areas. Depending on the polishing method, one can achieve mirror finish surfaces with an rms surface roughness of 10 nm or less. As demonstrated by numerous investigators, the polished diamond coatings can provide friction coefficients comparable to that of natural diamond (Erdemir et al., 1997a; Bhushan et al., 1993; Gupta et al., 1994; Pimenov et al., 1996). However, the polishing processes are tedious, time-consuming, and, in the case of complex geometries, highly impractical. Depending on the desired film thickness or the degree of original roughness, it may be necessary to remove large amounts of material before a smooth surface is obtained. Figure 24.3 shows the surface morphology of a rough microcrystalline diamond film before and after laser polishing.
24.2.2 Nanocrystalline Diamond Films The very rough nature of the above-described microcrystalline diamond films renders them useless for most tribological applications. Recently, new methods have been developed for the deposition of finegrained or nanocrystalline diamond (NCD) films with a very smooth surface finish. In these methods, a higher than normal C:H ratio is used in a microwave plasma, or a DC bias is applied to the substrates (Hollman et al., 1998; Hogmark et al., 1996; Cappelli et al., 1998; Bhusari et al., 1998). The methane fraction in the source gas, substrate temperature, and substrate pretreatment were also shown to exert a strong effect on the crystallinity and grain size of these films (Gilbert et al., 1998; Erz et al., 1993; Hogmark et al., 1996). Although growth rates are somewhat reduced and the amount of non-diamond phase is somewhat increased, the surface finish of the resultant coatings is very smooth (i.e., 25 nm, rms). Deposition of NCD coatings has also been achieved by microwave CVD in the near absence of H. The source gas consists of mostly Ar, with either C60 or CH4 as the C precursor (Gruen et al., 1994; Gruen, 1998; Zuiker et al., 1995; Erdemir et al., 1996b,c). The CVD reactor used in this process is essentially a modified version of a conventional microwave CVD reactor, details of which are schematically depicted in Figure 24.4. To introduce C60 into the reactor, a quartz transpirator, also shown in Figure 24.4 is attached. Fullerene-rich soots that contain ≈10% C60 are placed in the transpirator. The soot is heated to 200°C under vacuum for 2 h to remove residual gases and hydrocarbons. The tube furnace and transport tube are heated to between 550 and 600°C to sublime C60 into the gas phase. Argon gas is passed through the transpirator to carry the C60 vapor into the plasma. To ensure that C60 is transported into the chamber, an Si wafer is placed in front of the transport tube while maintaining a 14-sccm Ar flow. With the reactor pressure at 100 torr and the transpirator at 600°C, a 1.7-mg brown film was deposited on the wafer in 1 h. The film displayed only strong C60 infrared absorption features. The measured Raman
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FIGURE 24.2 (a) Initial, (b) intermediate, and (c) final growth stages of a microcrystalline diamond film produced in a microwave CVD reactor.
spectrum was also attributable to C60. Based on these measurements, the transpirator is considered an effective source of C60 for diamond growth. The NCD coatings can also be grown under similar low-Hcontent conditions, with CH4 instead of C60 as the C source. The NCD coatings can be grown on various substrates, including single-crystal Si wafers, sintered SiC, W, WC, Si3N4, etc. Initially, a bias of –150 V is applied to enhance diamond nucleation density. Film growth is monitored in situ by laser reflectance interferometry to determine growth rate and to stop growth at the desired film thickness. The substrate temperature can vary between 700 and 950°C, and
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FIGURE 24.3
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Surface morphology of a rough diamond film (a) before and (b) after laser polishing.
the total gas flow rate is ≈100 sccm. A typical gas composition for NCD diamond film can be 97% Ar, 2% H2, and 1% C60 or CH4 at a total pressure of 1.33 × 104 Pa and a microwave power of 800 W. Figure 24.5 shows atomic force microscopy (AFM) and scanning electron microscopy (SEM) images of the surface of an NCD film produced by the method depicted in Figure 24.4. The growth mechanism of NCD differs radically from that of a microcrystalline diamond film. Specifically, extraction of a C dimer (C2) from C60 and CH4 molecules and its subsequent insertion into the diamond surface has been proposed for the growth of these coatings (Gruen, 1998). The resultant coatings are phase-pure NCD, with an average grain size of ≈15 nm. The C dimer growth mechanism is unique in that it is capable of producing a continuous diamond coating that can be as thin as 30 to 60 nm.
24.2.3 Tribology of Diamond Coatings In addition to being the hardest material known to mankind, diamond provides some of the lowest friction coefficients to sliding tribological interfaces when tested in open air. This combination of extreme hardness (and hence wear resistance) and ultralow friction in one material is very rare in the field of tribology and it renders diamond ideal for a wide range of tribological applications. However, recent fundamental studies have confirmed that there are several factors that can adversely affect the friction and wear performance of bulk diamond and thin diamond films (Bowden and Tabor, 1950; Bowden and Young, 1951; 1964; Bowden and Hanwell, 1966; Tabor, 1979; Enomoto and Tabor, 1981; Feng and Field, 1992; Hayward and Field, 1987; Gardos 1994; Chandrasekar and Bhushan, 1992; Miyoshi et al., 1993; Kohzaki and Noda, 1994). Most previous studies have confirmed the finding that the friction coefficient
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Fullerene Transpiration Source
2.45 GHz
Plasma
Substrate Heater Stages
Quartz Frit 10µm Pore Size
Platinum Heating Wires
Carrier Gas inlet Fullerene Rich Soot
Tube Furnace
Quartz Tubing
FIGURE 24.4 Schematic illustration of a modified microwave CVD reactor used for deposition of nanocrystalline diamond films. (From Zuiker, C., Krauss, A.R., Gruen, D.M., Pan, X., Li, J.C., Csencsits, R., Erdemir, A., Bindal, C., and Fenske, G. (1995), Physical and tribological properties of diamond films grown in argon-carbon plasmas, Thin Solid Films, 270, 154-159. With permission.)
of bulk diamond sliding against itself in open air is 0.02 to 0.05. However, when tested in ultrahigh vacuum (UHV) or at high temperatures, the friction coefficient of diamond increases by more than 1 order of magnitude (Hayward and Field, 1987; Chandrasekar and Bhushan, 1992; Miyoshi et al., 1993; Dugger et al., 1992). Some of the other factors that influence the friction and wear behavior of diamond are contact pressure, surface roughness, crystallographic orientation, and the presence or formation of gaseous, liquid, or solid third-body and/or transfer film on the sliding surface. In addition to the early studies that were performed at micro-to-meso scales, recent fundamental tribological studies at atomic-to-nano scales have greatly increased our understanding of the influence of each of the above-mentioned factors on friction and wear of diamond. In particular, with the advent of new experimental tools (e.g., AFM) and computer simulation methods (e.g., molecular dynamic simulation), it is now possible to visualize and better understand the extent of chemical, physical, and mechanical events that occur at atomic or molecular levels and hence gain a better understanding of the mechanisms that govern the friction and wear behavior of diamonds. 24.2.3.1 Early Studies Early tribological studies have led to the conclusion that the low-friction property of diamond is largely due to the highly inert or very passive nature of its sliding contact surfaces (Bowden and Young, 1951; Bowden and Hanwell, 1966). Specifically, it has been proposed that the low friction of diamond was associated with the lack of adhesive forces between sliding diamond surfaces. Gaseous adsorbates in the surrounding atmosphere, such as H, O, or water molecules, can attach to and effectively passivate the dangling σ-bonds of diamond surfaces, and hence lead to reduced adhesion and/or friction. This hypothesis for the low-friction mechanism of diamond has existed for a long time. More recent work by Gardos (1999), Gardos and Ravi (1994), Miyoshi et al. (1993), Dugger et al. (1992), and Chandrasekar and Bhushan (1992) has confirmed that the presence or absence of surface contaminants in the test chamber
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FIGURE 24.5 (a) AFM and (b) SEM images of the surface morphology of nanocrystalline diamond film produced by microwave CVD in Ar-C60 plasma.
makes a huge difference in the friction and wear performance of bulk diamond and/or thin diamond films. When tested in ultraclean and ultradry test environments (i.e., UHV) or at high ambient temperatures, sliding diamond surfaces always exhibit high friction and wear, mainly because surface contaminants are desorbed or mechanically removed from the sliding surfaces and hence are not available to passify the dangling σ-bonds of the sliding diamond surfaces. 24.2.3.2 Friction and Wear Mechanisms Carbon atoms in bulk diamond crystals are held together by strong covalent bonds in a tetrahedral bond configuration. However, C atoms on diamond surfaces can only establish three covalent bonds with their near neighbors, while the fourth bond is left open and dangling out of the surface. Gaseous species in the surrounding air such as water molecules, O, and H, can chemisorb and effectively passivate these dangling surface bonds (Figure 24.6) (Holmberg, 1998; Pate et al., 1982; Derry et al., 1983; Wei et al., 1995). When dangling bonds are tied up and passivated, the extent of adhesion and hence friction between sliding diamond surfaces is drastically reduced. The extent of interaction between passive diamond surfaces that are sliding against each other drops to the level of very weak van der Waals attractions. Knowing the critical role that dangling bonds play on friction, researchers have developed more effective means to passivate them with, for example, F atoms, and have thus achieved extremely low friction and wear coefficients for bulk diamond and diamond films (Miyake et al., 1994; Smentkowski et al., 1996, 1997; Molian et al., 1993). Recent fundamental studies have shown very clearly that, when adsorbed gases are removed from the sliding surfaces of diamond by thermal desorption at high temperatures, the friction coefficient increases
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Dangling bond orbital Free electron Shear plane
C
C
C
-C-C-C-C-C-C-C-C-C-CI I I I I I I I I I H H H H H H H H H H H H H H H H H H H H I I I I I I I I I I -C-C-C-C-C-C-C-C-C-C-
C C
C
C
C
C
0.8
µ
0.6
UHV
air, 55% RH
1.0
air, 52% RH
FIGURE 24.6 Schematic illustration of dangling surface bonds of diamond and weak shear plane between hydrogenterminated diamond surfaces. (From Holmberg, K. (1998), Tribology of diamond and diamond coatings — A review, Tribologia, 12, 33-62. With permission.)
0.4 0.2
0
100
200
300
400
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Cycles FIGURE 24.7 Friction coefficient vs. number of sliding passes for a CVD-coated SiC pin sliding against a CVD diamond-coated Si wafer in air and UHV environments. (From Dugger, D., Peebles, E., and Pope, L.E. (1992), Counterface material and ambient atmosphere: role in the tribological performance of diamond films, in Surface Science Investigations in Tribology, Experimental Approaches, Chung, Y.-W., Homolo, A.M., and Street, G.B. (Eds.), ACS Symposium Series 485, American Chemical Society, Washington, D.C., 72-102. With permission.)
rapidly; presumably, the dangling surface bonds are reactivated and are available to form strong adhesive bonds with the surface atoms of the counterface materials (Gardos, 1994; Dugger et al., 1992). Conversely, if the surface of diamond is exposed to gaseous contaminants or open air again, the friction coefficient drops precipitously, presumably because of the repassivation of the dangling surface bonds, as shown in Figure 24.7 (Dugger et al., 1992). Most of the vacuum tribological studies on diamond were performed by Gardos and co-workers. Using an SEM tribometry test device, they have explored the effects of surface chemistry-induced changes on friction and wear of self-mated sliding diamond surfaces as a function of ambient temperature. As summarized in a recent review article by Gardos (1999), their studies provide circumstantial evidence for the effect of surface dangling bonds on friction (in the absence of shear-induced phase transformation and/or graphitization). Specifically, their studies show that the lowest friction is achieved under conditions where complete passivation of dangling bonds of diamond surfaces is feasible (i.e., by atomic or molecular adsorbates such as H2O, H, or O). However, reconstructed diamond surfaces provide relatively reduced friction and, finally, the incipient linking of the sliding diamond surfaces by totally unsaturated dangling bonds (created by thermal desorption) causes the highest friction. The repassivation of dangling bonds by atomic or molecular adsorbates during cooling or exposure to gaseous species causes reduced adhesion and hence low friction. Figure 24.8 illustrates the frictional behavior of diamond films in the passive,
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FIGURE 24.8 Variation of friction coefficient of CVD diamond films sliding against themselves in vacuum at temperatures to 850°C. (From Gardos, M.N. (1999), Tribological fundamentals of polycrystalline diamond films, Surf. Coat. Technol., 113, 183-200. With permission.)
active, and reconstructed regimes of sliding. Apparently, as the temperature increases, surface adsorbates begin to desorb and leave some of the dangling surface bonds exposed and available for strong adhesive interactions. As the extent of adhesive interactions increases, the friction coefficient increases sharply and reaches values ≈0.7 until some of them reconstruct and reduce the extent of adhesion and hence friction. Among all of the surface adsorbates, H provided the lowest friction (Gardos and Gabelish, 1999). Because of its extreme hardness, bulk diamond and thin diamond film hardly wear under normal sliding conditions (i.e., open air, room temperature, low velocity). However, under certain test conditions, diamond may experience some wear by shear or ambient-induced phase transformation. For example, a few studies have indicated that micrographitization of sliding diamond surfaces can occur at high temperatures or at high sliding velocities, and the surfaces of diamond films begin to act like graphite; that is, they give low friction in moist air, but relatively high friction in dry, inert, or vacuum environments (Gardos et al., 1997; Gardos and Ravi, 1994; Erdemir et al., 1997b). Natural diamond is chemically very stable and does not appreciably oxidize until the temperature reaches 600°C. The oxidation behavior of diamond films is also similar to that of natural diamond but, because they contain some non-diamond phases, high levels of structural defects, and grain boundaries, they tend to oxidize at relatively lower temperatures (Tankala, 1990; Johnson et al., 1990). When tribotested at elevated temperatures, bulk diamond and thin diamond films tend to gradually oxidize and transform to graphite in open air (Erdemir et al., 1996d; Erdemir et al., 1997c; Kohzaki et al., 1992). However, in inert test environments or under high vacuum, diamond films are more stable and do not undergo oxidation or graphitization. Briefly, diamond films are not suitable for use at high temperatures in open air. In addition to the effects of surface chemistry and/or environment, which largely control the adhesion component of friction, the effects of crystal orientation and surface roughness on friction and wear of diamond have also been studied rather extensively in previous years. It has been shown that surface roughness profoundly influences the friction and wear performance of thin diamond films. As mentioned above, the surface rms roughness of synthetic diamond films can vary from 10 to >1000 nm, depending on deposition conditions, growth orientation, grain size, and film thickness. As demonstrated by Casey and Wilks (1973), and Samuels and Wilks (1988), the extent of interaction between sliding-surface asperities of diamond may contribute to the amount of total energy being dissipated in the form(s) of phonons and/or vibrations. In general, higher surface roughness leads to higher levels of vibration and, hence, high friction. Recent systematic studies by Hayward (1991), and Hayward et al. (1992), Bhushan et al. (1993), Miyoshi et al. (1993), and Erdemir et al. (1996b) further confirm the results of above-mentioned studies
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FIGURE 24.9 Relationship between rms surface roughness of CVD diamond films and their friction coefficients. (Data from Bhushan, B., Subramanian, V.V., Malshe, A., Gupta, B.K., and Ruan, J. (1993), Tribological properties of polished diamond films, J. Appl. Phys., 74, 4178-4185; Erdemir, A., Halter, M., Fenske, G.R., Krauss, A., Gruen, D.M., Pimenov, S.M., and Konov, V.I. (1997a), Durability and tribological performance of smooth diamond films produced by Ar-C60 microwave plasmas and by laser polishing, Surf. Coat. Technol., 94/96, 537-541; Erdemir, A., Halter, M., Fenske, G.R., Zuiker, C., Csencsits, R., Krauss, A.R., and Gruen, D.M. (1997b), Friction and wear mechanisms of smooth diamond films during sliding in air and dry nitrogen, Tribol. Trans., 40, 667-673; Erdemir, A., Fenske, G., and Wilbur, P. (1997c), High-temperature durability and tribological performance of diamond and diamondlike carbon films, in Protective Coatings and Thin Films: Synthesis, Characterization and Applications, Pauleau, Y. and Barna, B. (Eds.), NATO ASI-High Technology Series, Vol. 21, Kluwer Academic, London, 169-184. With permission.)
in that the diamond films with high surface roughness always lead to high friction and wear. Conversely, when polished or NCD coatings are used in sliding-contact experiments, very low friction coefficients are attained (Erdemir et al., 1997a; Erdemir et al., 1999; Miyoshi et al., 1993) (Figure 24.9). Reported friction values typically range from 0.03 (for ultra-smooth nanocrystalline or polished diamond films) to >0.5 (for very rough microcrystalline films). In all cases, friction tends to be higher initially, but decreases substantially as sliding continues in open air. The trend appears to be the opposite during tests in UHV environments where, regardless of the counterface materials, the friction coefficients are initially low but go up significantly as sliding continues (Miyoshi et al., 1993). The type of counterface material used during friction tests also makes a substantial difference in the measured friction coefficients of bulk diamond and/or diamond films. Usually, diamond-against-diamond or diamond films give lower friction than diamond-against-nondiamond counterfaces (Hayward et al., 1992; Miyoshi et al., 1993). When bulk diamond or diamond films are slid against relatively softer metals, alloys, or ceramic counterfaces, the steady-state friction and wear are largely controlled by the extent of surface roughness of the sliding diamond side and by the tendency of the counterface material to form a transfer layer (Hayward et al., 1992; Gangopadhyay et al., 1993; Erdemir et al., 1997b). Rougher diamond surfaces usually cause greater plowing and abrasive wear on the softer metallic or ceramic counterfaces and also facilitate the transfer of worn debris particles to its sliding surface. Fine debris particles can easily fill in the valleys between sharp asperities of diamond films and, eventually, sliding contact largely occurs between the transferred and original material of the non-diamond counterfaces. Previous research has demonstrated that growth orientation of microcrystalline diamond films can significantly affect friction and wear. Films with large grains and highly faceted surface finish usually cause high friction and wear (Hayward, 1991; Blau et al., 1990; Yee et al., 1995; Erdemir et al., 1996b). In recent years, researchers have developed special procedures to control growth orientation and, hence, the surface roughness of diamond films. From a tribological standpoint, 〈100〉 type growth orientation is very desirable and can be achieved by controlling deposition conditions and by pretreatment of the substrate surfaces (Yee et al., 1997; Wolden et al., 1997; Wolter et al., 1996). Diamond films with coarse
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FIGURE 24.10 Friction coefficients of Si3N4 balls sliding against diamond films with 〈111〉 and 〈100〉 type growth orientations. (From Erdemir, A., Bindal, C., Fenske, G.R., and Wilbur, P. (1996a), Tribological properties of hard carbon films on zirconia ceramics, Tribol. Trans., 39, 735-741. With permission.)
grains and 〈111〉 type growth orientation tend to be very rough and can cause severe abrasive wear (Erdemir et al., 1996b). Figure 24.10 shows the frictional performance of two films with 〈111〉 and 〈100〉 growth orientation. These films were grown in an H2/CH4 plasma. After an initial run-in period, the friction coefficients of both coatings decreased. The friction coefficients of the film with 〈100〉 growth orientation stabilized at ≈0.1, whereas the friction coefficient of the film with 〈111〉 growth orientation and micropyramidal asperities remained high and unsteady but continued to decrease steadily during successive sliding passes. The high friction coefficients of rough diamond coatings with 〈111〉 orientation can be attributed to the abrasive cutting and ploughing effects of sharp surface asperities on the softer counterface pins. If a favorable 〈100〉 growth orientation is present, such coatings can also afford low friction coefficients to sliding surfaces, despite relatively higher measured surface roughness. In general, previous studies confirmed that regardless of the grain size, diamond coatings with a smooth surface finish provide very low friction to sliding counterfaces. Apart from physical roughness and chemical passivation effects, phase transformation or structural changes can also play a major role in the friction and wear performance of diamond coatings. The extent of such changes can be dominated by environmental species or by ambient temperature (Jahanmir et al., 1989; Gardos and Ravi, 1994; Erdemir et al., 1997). Phase transformation can readily occur even in natural diamond (see Gogotsi et al., 1998) when extreme contact pressures and/or high frictional heating are present at local asperity levels. Real contact occurs first between these asperities, and their tips can either fracture or undergo phase transformation because of the extreme pressures and high frictional heating. Thermodynamically, graphite is the most stable form of C, whereas diamond is metastable. It is also known that when excited thermally or by ion bombardment, diamond can transform to a graphitic form (Lee et al.,1993). The graphitic debris particles can gradually accumulate at the sliding contact interface and then begin to dominate the long-term sliding friction and wear performance of these coatings.
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Previous research by Erdemir et al. (1997b) and Jahanmir et al. (1989) revealed that most of the debris particles derived from sliding diamond surfaces exhibited a graphitic microstructure. Raman spectroscopy, electron diffraction, EELS, and transmission electron microscopy have concurrently confirmed the presence of highly disordered graphitic debris particles at sliding contact interfaces (Erdemir et al., 1997b). 24.2.3.3 Tribology of Diamond at Nanoscale Recent fundamental studies on nanometer and molecular scales with new experimental tools (e.g., friction force microscopy, surface force apparatus, and quartz crystal microbalance) and computational methods (e.g., molecular dynamics simulation) have allowed friction studies on very fine scales (Mate, 1993; Bhushan, 1998; Germann et al., 1993; Harrison et al., 1992a,b; 1993; Harrison and Brenner, 1994; Miyake et al., 1995). These studies have greatly increased our fundamental knowledge base of the tribology of diamond. Superhigh-speed computers with high memory and processing capability have allowed simulation and real-time visualization of atomic-scale phenomena that occur at sliding diamond surfaces. For the most part, results from fundamental nanoscale experimental studies are consistent with those from earlier micro- to mesoscale studies, in which standard tribology test machines were used. The nanoscale studies have revealed that surface adsorbates, ambient temperature, and gaseous, liquid, or solid debris particles that are present or generated at the sliding diamond interfaces play critical roles in the friction and wear of diamond. For example, it was shown that when adsorbed gases are removed from sliding diamond surfaces, friction increases rapidly, because the dangling surface bonds are free and highly activated to form strong bonds across the sliding contact interface (Harrison et al., 1992a; Harrison and Brenner, 1994). Despite a large discrepancy in time and length scales, molecular dynamics simulation has provided significant insight into the extent of physical, chemical, and mechanical interactions that occur at sliding diamond interfaces on the atomic scale.
24.2.4 Tribological Applications Over the years, great strides have been made in the deposition, characterization, and industrial utilization of diamond films (Seal, 1995; Ravi, 1994; Lux and Haubner, 1993; Murakawa, 1997). Our fundamental understanding of the structure, properties, and performance of these coatings has increased tremendously in recent years and this understanding has been used to optimize, design, and customize new diamond coatings that can meet the increasingly stringent needs of advanced tribological applications. While some uses are still in the exploratory stage and require further development, others have been fully established and are offered on a commercial scale. In particular, cutting tools (e.g., inserts, end mills, microdrills, push pins, tab tools, etc.) are offered commercially by several industrial manufacturers. Recent laboratory and field tests confirm that these coated tools provide much improved performance during metal-cutting operations by allowing high-speed machining at increased feed rates. Some of the advantages that diamond provides in these applications include extreme hardness and wear resistance; good fatigue strength; high chemical inertness; excellent resistance to abrasion, erosion, and corrosion; high thermal conductivity; low friction; and excellent environmental compatibility. The current market share of diamond-coated cutting tools is relatively small, and the widespread utilization of diamond coatings in other tribological fields has not yet been fully realized. Some of the major reasons for the slow progress in large-scale utilization of diamond coatings are high fabrication cost, limitations on the type and size of substrate materials, oxidation when used at elevated temperatures, insufficient reliability and reproducibility, high surface roughness of finished products, somewhat poor adhesion, high deposition temperatures, and slow growth rates. Diamond-coated tool inserts cannot be used to machine pure Fe and Fe-base materials and the alloys of groups IVa, Va, VIa, VIIa, and VIIIa of the Periodic Table, which represent the largest segment of industrial machining. Diamond can chemically react with and/or dissolve in these materials at the high temperatures generated during machining, and thus it wears out rather quickly. Also, diamond coatings cannot be produced on the surfaces of tools that are made of materials such as high-speed steels, which are widely used in the tooling industry. Thus far,
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diamond films can only be deposited on certain refractory metals (e.g., W and Mo) and a few ceramics (e.g., WC, Si, SiC, and Si3N4) that can endure the high deposition temperatures of the CVD process. Among others, WC-based tools have been coated successfully with diamond and made available for commercial machining. Although prototypes of other tribological parts (e.g., mechanical seals; Hollman et al., 1998) have also been demonstrated, their large-scale utilization has not yet been realized because of high fabrication costs and insufficient reliability in actual operation. Other potential applications for diamond coatings include sliding bearings, MEMS, wire-drawing dies, and various wear parts that are used against erosion and abrasion (e.g., jet nozzles). 24.2.4.1 Industrial Machining Diamond has been used for machining purposes in three distinct forms. One is based on the use of synthetic diamond powders produced by HPHT methods. Specifically, fine diamond powders are first sintered into the shape of a tool tip and then brazed directly onto the cutting edges of the tool inserts. The second form is based on the CVD of a relatively thick (i.e., 0.5 to 1 mm thick) diamond film on an Si wafer from which small bits are laser-cut into a desired cutting-edge shape. Subsequently, the Si substrate is etched out and the cut diamond tips are recovered. As a last step, the freestanding diamond tips are bonded or brazed onto the cutting edges of the tool inserts or end mills. The third form is the direct deposition of diamond onto cutting tools by various CVD methods. There are some fundamental differences between brazed and coated diamond tool bits. First, diamondcoated tools can be tailor-made to meet the specific machining needs of an application, whereas the brazed diamond tips come in a strict geometric form and cover only the sections of the sharp tips of tool inserts. Second, the entire functional surface of a tool insert can be coated with diamond, and it can be prepared in any style or geometry to provide better efficiency and overcome limitations on depth of cuts — always a problem with brazed tool bits. Finally, the shape and area of a coated carbide insert can be prepared in such a way that it will allow better chip handling and breaking capability than the very small brazeable diamond tips. CVD diamond coatings perform equally well or even better than PCD diamonds in cutting and turning operations. However, edge chipping or deterioration due to easy cleavage of highly oriented needle-like diamond grains of CVD diamond films can occasionally occur and limit the lifetime of the coated tools. Figure 24.11 shows the morphology of the cutting edge of a diamondcoated tool insert. As mentioned above, diamond-coated tools are primarily used in the machining of nonferrous metals, alloys, and composite materials that are inherently very difficult to cut or machine. In particular, diamond
FIGURE 24.11
Cutting-edge morphology of a CVD diamond-coated tool insert.
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has been the material of choice for machining of high-Si-content Al alloys for automotive applications. Hypereutectic Al-Si alloys are increasingly being used in this industrial sector, mainly because of their light weight, relatively high strength, and high resistance to wear (Deuerler et al., 1996; Keipke et al., 1998; Prengel et al., 1998; Shen, 1996, 1998; Trava-Airoldi et al., 1998). The major applications for Al-Si alloys include pistons, engine blocks and heads, wheels and chassis, and some transmission parts. The increased use of lightweight materials in the automotive industry is likely to continue and, hence, the need for diamond-coated tools will increase. Other engineering materials suitable for machining by diamond-coated tools include alloys of Mg, Cu, Pb, and Mn, as well as various composites (e.g., fiberreinforced plastics, fiberglass composites, C-C composites, and metal-matrix composites), bulk graphite, plastics, epoxy resins, green ceramic, concrete, and various mining and rock-drilling operations (Kubel, 1998; Lux and Haubner, 1998; Komanduri and Nandyal, 1993; Inspektor et al., 1997; Karner et al., 1996). Another key application for diamond coatings is in woodworking tools. The most important factor that governs the success of a diamond-coated tool insert in cutting operations is strong bonding between diamond coating and substrate insert (i.e., WC-Co). If bonding is not intimate and strong, diamond coatings can easily be removed from the cutting edges, which thus lose their cutting performance and effectiveness. In fact, premature delamination of the diamond film in early trials represented the biggest challenge and most common mode of tool failure. Residual stresses are inherent in all CVD-diamond coatings, and these stresses can significantly affect the film/substrate adhesion (Olson and Dawes, 1996; Gunnars and Alahelisten, 1996). Diamond coatings are often deposited at high temperatures, and a large mismatch in thermal-mechanical properties between the diamond coating and the underlying substrate leads to large compressive stresses. The presence of a high stress in the coating can lead to various undesirable failure modes that can cause the film to delaminate, crack, or blister and thus destroy the entire structure. Other factors, such as film thickness, film roughness, substrate preparation, and substrate grain size, also affect film/substrate adhesion, and they must be considered along with the residual stresses whenever the quality of a diamond coating is evaluated. Two other problems can occur when diamond films are used in machining operations. One is oxidation; the other is fracture or chipping. Despite its extreme hardness, diamond is brittle and will readily fracture, especially when forced in the direction of relatively weak columnar grains. Currently, diamond coatings are primarily produced on WC-Co-based cemented carbide tool inserts, mainly because of their excellent toughness, hardness, and high-temperature durability. Co serves as a binder and controls the toughness of these materials. In addition to strict process control during deposition, the selection and pretreatment of the substrate materials are extremely important for achieving strong adhesion between the diamond coating and the substrate material. In particular, the selection of the correct types of WC-Co material is a must for achieving strong bonding and, hence, long wear life. In principle, a low Co content (<5%) in cemented carbide is highly desired. Higher Co contents can adversely affect the adhesion of diamond coatings to carbide inserts. Specifically, during deposition at high temperatures, Co can play a catalytic role in the formation of non-diamond phases and complex Co carbides that are highly undesirable. It also slows the nucleation process and reduces nucleation density. Interfaces with a high proportion of non-diamond phases and low nucleation density suffer from poor adhesion. Too much Co can also increase the difference in thermal expansion coefficient between diamond and substrate; hence, during cooling, very high compressive stresses can build up at the interface region. When these stresses are combined with the stresses associated with cutting action, premature adhesive failures can occur at or near the cutting edges. Briefly, it is important to use carbide substrates with low Co content or to etch the Co out completely from the near surface; otherwise, the coatings will not stick to the tools (Menningen et al., 1994; Cappelli et al., 1998; Toenshoff et al., 1998). Several methods are used by industry to remove surface Co from cemented carbide tool inserts. Most of the methods involve selective etching of Co by chemical means. Some of the chemicals that have proved to be effective in etching Co are HNO3, HCl, and CH3COOH. In one case, tool inserts are dipped in a nitric acid and water solution (mixed 1:1 by volume) and ultrasonically agitated for 15 min. They are then rinsed and ultrasonically cleaned in ultrapure water for 5 min. In another case, researchers have heat treated WC-Co substrates at very high temperatures for an extended period of time in a protective
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FIGURE 24.12 Cutting performance of an uncoated and CVD diamond-coated insert while machining a cast aluminum alloy containing 7% Si (cutting conditions: speed, 150 to 2500 m/min; depth of cut, 0.5 to 3 mm; feed rate, 0.25 to 0.8 mm/rev). (From Karner, J., Pedrazzini, M., Reineck, I., Sjostrand, M.E., and Bergmann, E. (1996), CVD diamond-coated cemented carbide cutting tools, Mater. Sci. Eng., A209, 405-413. With permission.)
environment. Heat treatment causes grain growth in WC and hence roughens the surface; it also evaporates Co and thus reduces the amount of Co at or near the surface. Increased surface roughness provides better mechanical interlocking between diamond and WC grains, whereas the absence of Co ensures higher nucleation density and better adhesive bonding. Because Co is the binder that holds the tool’s WC grains together, Co removal must be done with great care. If too much Co is removed from the surface, the tool will become weakened and its integrity near the surface will be impaired. Formation of stable Co borides and silicides that can endure the high deposition temperatures of diamond has also been used in the past to prevent Co-associated problems (Kupp et al., 1994; Kubelka et al., 1994). Various bond layers (i.e., W, Si, SiC, and Si3N4) have also been tried on tool inserts to achieve strong bonding. The effectiveness of bond layers is very much dependent on the exact composition and thickness of the bond layer material. Few other procedures have been developed by industry to achieve strong adhesion, but they are considered highly proprietary; hence, very little is known about them. Published case studies indicate that, depending on the material cut and cutting conditions, tools coated with CVD diamond can exhibit tool life improvements that range from 25% to more than a factor of 40. Greater improvements in tool life are reported when cutting Al-Si alloys, green ceramics, and fiberreinforced composites. Figure 24.12 shows the performance of uncoated and CVD-diamond-coated carbide inserts during machining of an Al-Si alloy for a truck wheel application. Figure 24.13 demonstrates the effectiveness of a nanocrystalline diamond-coated carbide insert in preventing edge wear and loss of sharpness after machining of a high-Si-content Al alloy. CVD diamondcoated tools were proven to be as good as or better than the PCD tool inserts when used during turning of Al-Si alloys and graphite. The market share of coated tools is expected to increase steadily because prices are declining while performance and reliability are improving. Better quality and reliability will certainly result in diamondcoated tools that last longer, cost less, and increase productivity. Several companies are engaged in the production of CVD diamond-coated tool inserts. DeBeers, Mitsubishi, Nachi-Fujikoshi, Norton, Kennametal, Sandvik, and Sumitomo are the major firms. Kennametal and Sandvik provide diamond-coated tools commercially. As discussed above, CVD diamond-coated inserts are primarily targeted for machining applications that involve high-Si-Al alloys. The projected growth of Al use in automobiles indicates
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FIGURE 24.13 Extent of wear damage on (a) uncoated and (b) nanocrystalline diamond-coated tool inserts after machining of a hypereutectic aluminum-silicon alloy.
that the growth of the diamond-coated tool insert market will be significant. When the performance and price of CVD tools compare favorably with those of PCD tools, CVD tools may displace PCD in some applications. Woodworking tools represent another major market segment for diamond coatings. Tungsten carbide blades already comprise a large part of the woodworking tool market. CVD diamond-coated tools have yet to be used in woodworking and, thus, they offer an excellent business opportunity. 24.2.4.2 Mechanical Seals After cutting tools, mechanical seals represent the next best application possibility for CVD diamond films. The mechanical-seals market is rather large, ranging from the very simple seals used in automotive water pumps to higher-end seals that are used at high temperatures and in aggressive environments. Coated seals would be especially attractive in applications where high chemical stability and resistance to corrosion, erosion, and abrasion is needed. Because of its low friction, a diamond-coated seal can also be very useful in applications where a liquid lubricant is not permissible, for example, in pharmaceutical and food processing plants. Over 3 million higher-end pumps rely on the tribological performance of SiC seals, and SiC is an ideal substrate for diamond film growth. Improper use of or leakage in mechanical pump systems can be very costly and may lead to environmental disasters. Total energy losses due to high friction and wear can be very high. Because properly applied diamond coatings afford very low friction to the sliding surfaces of seal components, they can extend the useful life of these components and also reduce energy losses. Recent studies by Hollman et al. (1998a,b) have demonstrated that smooth diamond films can result in substantial reductions in frictional torque and wear rates of shaft seals. Rough diamond coatings cannot be used in seal applications. One of the sealing faces (inserts) is made of soft graphite or C composite. When rubbed against a rough and superhard surface, these inserts wear out rather quickly. Hard SiC inserts can also be used, but they are much more expensive and, when rubbed against rough diamond, they too suffer major wear losses. Polished or smooth nanocrystalline diamond coatings will be more desirable for seal applications. 24.2.4.3 Other Applications Microelectromechanical systems represent a new class of moving mechanical assemblies that can be used for a wide range of applications, including sensors, actuators, high-precision positioning devices,
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microelectronics, etc. MEMS devices such as gear assemblies and micromotors have been largely fabricated by Si micromachining technology; however, Si exhibits very poor mechanical and tribological properties. When these microdevices are used in very high-speed applications, they suffer from unacceptably high friction and wear losses and thus are unsuitable for applications that involve high speeds and realistic loads. Researchers have developed alternative fabrication methods that allow production of MEMS devices from SiO2, Si3N4, or SiC-type materials. However, the tribological performance of these materials is also very poor; hence, they may not function well in a dynamic MEMS application. Because of its excellent properties, researchers have recently been exploring possible uses of diamond coatings for MEMS applications (Bjorkman et al., 1998; Aslam and Schulz, 1995; Mao et al., 1995; Ramesham, 1999; Gardos, 1998; Cagin et al., 1999). However, there have been some difficulties in fabricating diamond coatings and/or components with a morphology suitable for MEMS. The NCD films discussed previously appear to be better suited because of their very small grain size (i.e., 10 to 30 nm). With these films, it will be possible to attain film coverage at very small thicknesses (as thin as 50 nm) and hence preserve the fine structural features of MEMS devices. Conventional CVD films with thicknesses of 0.5 to 10 µm may not achieve complete coverage on the surface of Si-based MEMS devices. Other tribological applications for CVD diamond coatings include woodworking tools, tab tools, push pins, high-precision microdrills, surgical blades, wire-drawing dies, and various wear parts that are used against erosion and abrasion (e.g., jet nozzles).
24.3 Diamond-like Carbon (DLC) Films DLC films represent a noteworthy example of thin films whose properties can be varied over a wide range of structures and compositions. The tribological behavior of these films strongly depends on the deposition technique. Consequently, the first part of this discussion is dedicated to a background on DLC, highlighting the relationships between the deposition process, the film structure, and some film properties. The second part summarizes the tribological behavior of DLC films, through a description of the friction and wear mechanisms, successively at the macroscopic, microscopic, and nanometer scales.
24.3.1 Background on DLC Films 24.3.1.1 Classification of DLC Films Diamond-like carbon coatings have been the subject of intensive studies for the last 20 years. The general term “DLC” describes hydrogenated and hydrogen-free metastable amorphous carbon materials, prepared by a wide variety of PVD and CVD techniques. The films exhibit a wide range of structure, composition, and attractive mechanical, optical, electrical, chemical, and tribological properties. The film structure and properties are determined by the H content and the relative ratio of the two sp2 and sp3 carbon hybridizations, the sp1 C hybridization being negligible. Hydrogen in DLC is important for obtaining a wide optical gap and a high electrical resistivity, removing midgap defect states, stabilizing the random network, and preventing its collapse into a graphitic phase. As proposed by Robertson (1998), the wide range of DLCs is conveniently displayed on a ternary phase diagram in Figure 24.14. The sp2-bonded amorphous C lies in the lower left corner. Phases with an H content that is too high, lying at the far right of the diagram, cannot form an interconnected network and form gas or liquid molecules. The nonhydrogenated films are classified either as sputtered amorphous C (Sputtered C) with a predominance of the sp2 hybridization, or as tetragonal amorphous C (ta-C), with a predominance of the sp3 hybridization of up to 85%. The most common type of DLC is the hydrogenated a-CH film, with only moderate sp3 content and a rather high H content of up to ≈50 at%. A lightly hydrogenated analogue of ta-C, termed ta-CH (Weiler et al., 1996), is also shown. Donnet (1998) attempted to modify some DLC properties by the addition of alloying elements, mainly Si, F, N, and various metals.
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FIGURE 24.14 Ternary “phase diagram” showing the various forms of diamond-like carbon. (From Robertson, J. (1998), Deposition mechanism of diamond-like carbon, in Amorphous Carbon: State of the Art, Silva, S.R.P., Robertson, J., Milne, W.I., and Amaratunga, G.A.J. (Eds.), World Scientific Publishing, Singapore, 32-45. With permission.)
Such a wide range of film structures and composition and the diversity of methods used for DLC film deposition provide the flexibility to tailor their properties according to specific needs and applications. The study of hydrogenated DLC and the state of our knowledge concerning its properties and practical applications have apparently matured. The study of hydrogen-free DLCs has not yet reached this state and practical applications for it have yet to be found. 24.3.1.2 Influence of Deposition Methods on Film Microstructure and Composition From the point of view of optimizing the routine production of DLC films, the primary need is for effective process control, primarily the tailoring of adhesion properties. Indeed, the adhesion of DLC films varies widely, depending on the nature of the substrate. To be used as tribological coatings, DLC films must adhere well to the substrate material, and the adhesive forces must overcome the high internal stresses that would otherwise cause film delamination (Holmberg and Matthews, 1994). Adhesion can be affected by the deposition method, in combination with the nature of the substrate. Good adhesion of DLC films is observed on carbide- and silicide-forming substrates. The adhesion of DLC coatings to silicide-forming metals can be improved by depositing a 2- to 4-nm-thick interfacial layer of amorphous Si between the metal and the C film, thus forming an interfacial silicide layer promoted by the plasma, even at relatively low substrate temperatures. The use of Ti-based, functionally gradient films intercalated between the substrate and the DLC top layer has also been studied (Voevodin et al., 1997). The deposition of adhesion and interface layers is ideally achieved in the same reactor as the deposition of the DLC films, by multiplex processes that minimize the introduction of defects and impurities between the superimposed layers and allow precise control of the entire deposition methodology. Whatever the deposition conditions, DLC films are generally smooth to the level of tenths of a nanometer and are therefore referred to as nanosmooth. The roughness thus conforms to the underlying topography. All methods for the deposition of DLC are nonequilibrium processes characterized by the interaction of energetic species with the surface of the growing film. The growth and properties of DLC films are controlled by the substrate temperature and the energy of the species impinging on the surface during the deposition process, the latter exerting dominant control. A wide literature survey on the deposition procedures has been assembled by Grill and Meyerson (1994). The following discussion is limited to the techniques that are most commonly used to deposit DLC films, with emphasis on the relationships between deposition conditions and film structure. The deposition of ta-C films is summarized prior to a discussion of the deposition of a-CH films. Today, the main processes used to deposit nonhydrogenated DLC films are magnetron sputtering, mass-selected ion beam, cathodic vacuum arc, and laser plasma. Whatever the technique, the fraction of sp3 bonding is maximized for ion-dominated processes with ion energies ≈100 eV. The specific properties of ta-C films are achieved by the high energies of the impinging particles, with film growth governed by
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a subplantation process instead of conventional condensation as in a-CH films (Robertson, 1998). Consequently, the temperature during the deposition process is also a crucial parameter. Above a transition temperature of 250°C, a noticeable decrease in the high sp3 content and density is generally observed. This transition temperature, which is much lower than the thermal stability temperature of ta-C films (which can reach relatively high values approaching 600°C), decreases with increasing ion energy. Magnetron sputtering is probably the most commonly used industrial method for depositing DLC films. In the unbalanced configuration, the substrate is bombarded with Ar ions, thus increasing the sp3 content of the films. Ar/H mixtures allow the production of hydrogenated DLC films. With the massselected ion-beam technique, it is possible to obtain ta-C films that contain up to 80% sp3-hybridized C by varying the acceleration, mass, and energy selection of a C ion beam that is condensing onto the substrate. ta-C films can also be obtained by a cathodic vacuum process on both the laboratory and industrial scales. An arc is struck on a graphite cathode, creating an intense, 30%-ionized plasma that expands through the deposition chamber and condenses onto the substrate. The filtered cathodic vacuum arc configuration avoids degradation of the growing film by particulates produced in the arc along with the desired reactive species. Laser plasma deposition is a versatile method used to deposit many materials; it is widely used for DLC film deposition by creating a plasma plume similar to the cathodic arc produced by UV laser ablation of a graphite target. Plasma-enhanced CVD, in which any gaseous hydrocarbon species is used as precursor, is probably the most popular means to deposit a-CH films. The chamber is configured with cathode and anode plates, with the substrate attached to the cathode to maximize ion bombardment. Parallel plate reactors are preferred because they allow the deposition of uniform films over large areas. RF power can be capacitively coupled to retain the ability to deposit the films on a wide variety of substrates, including insulators. Because the film structure is a strong function of the energy of the impacting species, this ability depends on several plasma parameters — primarily the bias and the gas pressure. The bias is indirectly controlled by the RF power and the gas pressure in the RF configuration. The sp3 and H content are strongly controlled by the average impact energy. More precisely, at the lowest impact energies, the gaseous precursor is not sufficiently decomposed, and polymer-like C films with a predominance of CH2 groups are generally obtained. At intermediate impact energies, the H content has declined sufficiently so the C–C sp3 bonding has reached a maximum, thus leading to the so-called diamond-like qualities. However, if the impact energies become too high, graphite-like C structures are generally deposited because of an increase of disordered sp2-like bonding, at the expense of a decline of C–C sp3 bonding. From characterization by Fourier transform infrared (FTIR) combined with forward recoil elastic scattering experiments, a significant amount of H in a-CH films has been unbound to C (Grill and Patel, 1992). This free H, optically inactive by FTIR, should be trapped in some voids of the carbonaceous network. Free H fraction increases when the impact energy, and hence the dissociation of precursor, is increased. This also leads to higher C network crosslinking. Consequently, the nature of the precursor plays a direct role in the fraction of H bonded to C. However, based on recent comparisons between FTIR and 13C/1H NMR experiments performed on typical DLC films obtained under various conditions (Donnet et al., 1999), the absolute quantification of the fraction of H that is bonded to C remains ambiguous. As with ta-C films, temperature during deposition is another parameter that generally affects the DLC structure. Deposition should be carried out below 250°C to stabilize a significant sp3 content. The increase of diamond-like qualities of a-CH films has been achieved using a plasma beam source with acetylene to reduce the amount of incorporated H, and by operating at lower gas pressure to increase plasma ionization (Weiler et al., 1996). The resultant films are called ta-CH, by analogy to ta-C. The sp3 content can reach a maximum near 80% and H content in the range of 25 to 30%, with an effect of deposition temperature that is more complex than that for ta-C films. Metal- and/or nonmetal-doped diamond-like films are deposited by the same techniques as the regular films, by introducing into the reactor species or precursors that contain the modifying elements.
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TABLE 24.1
Range of DLC Structure, Composition, and Properties
Variable Hydrogen content, at% sp3, % Density, g/cm3 Thermal stability, °C Optical gap, eV Electrical resistivity, Ω/cm Index of refraction Compressive stress, GPa Hardness, GPa Young’s modulus, GPa a b
a-Ca
a-CHb
<5 5–90 1.9–3.0 <600 0.4–1.5
20–60 20–65 0.9–2.2 <400 0.8–4.0 102–1016 1.8–2.4 0.5–5
<80 <900
<60 <300
a–C = amorphous carbon. aCH = amorphous carbon, hydrogenated.
24.3.1.3 Influence of Film Structure and Composition on Some Typical Properties As described in Section 24.3.1.2, the structure and composition of the films (H content, fraction of H bonded to C, C hybridizations, nature of bonds, alloying elements) are strongly influenced by the average impact energy of the particles that impinge on the growing surface and by the deposition temperature. Thus, most film properties depend on key structural parameters that are related to specific deposition processes and conditions. Table 24.1 summarizes the range of various typical properties that depend on the presence or lack of H in the film. Nonhydrogenated films exhibit generally higher hardness, Young’s modulus, density, thermal stability, and compressive stress; and lower index of refraction, resistivity, and bandgap, when compared with hydrogenated films. For each category of film, the property variation is directly related to the structure, as controlled by the deposition process. The relationships between the structure and the properties of DLC films have been more extensively studied on a-CH than on ta-C films. In hydrogenated DLC films, an increase in H content is generally associated with a decrease in hardness, Young’s modulus, stress, thermal stability, density, and index of refraction, and an increase in the gap and electrical resistivity. A more accurate discussion remains impossible because most of these properties also depend on the fraction of H that is bonded to C, which remains difficult to investigate for the reasons mentioned previously. The difficulties in generalizing the structure/property relationships are due to a lack of systematic and unambiguous standardized characterization of DLC films, the wide range of structures and compositions, and the experimental difficulties encountered when thin metastable amorphous films are accurately probed. Differing models, such as the graphitic cluster, the random covalent network, or the defective graphite network reviewed by Grill and Meyerson (1994), constitute interesting guidelines to improve our current knowledge about structure/property relationships. Various C-based materials, similar in structure to a-CH or ta-C, include elements such as Si, F, N, and various metals. The introduction of dopants generally brings about a decrease in compressive stress, due to fewer interconnections in the random carbonaceous network. Grischke et al. (1995) have shown that the specific chemical composition of the modified films strongly influences the surface energy, depending on the nature of the dopant, and may modify various physical properties, making some doped DLCs suitable for various applications — for example, to improve field emission characteristics. As highlighted in Section 24.3.2, the introduction of alloying elements into DLC affects many properties, including tribological behavior.
24.3.2 Tribology of DLC Films Much effort has been invested in the characterization of the tribological behavior of DLC films, mainly because of the very low friction coefficients and high wear resistance of these materials. Thus, the tribology of DLC coatings has been discussed extensively in the literature, and has been summarized in recent
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reviews such as those of Holmberg and Matthews (1994), Grill and Meyerson (1994), Grill (1997a), Donnet (1995, 1998), and Erdemir (1998). Friction and wear of DLC coatings are strongly affected by the nature of the films, as controlled by the deposition process, and by the tribotesting conditions, including material parameters (nature of the substrate), mechanical parameters (contact pressure), kinematic parameters (nature of motion, speed), physical parameters (temperature during friction), and chemical parameters (nature of the environment). An exhaustive presentation of the tribological behavior of DLC is thus impossible. A more interesting and useful method of presentation will be used here, in which a top-down approach to DLC tribology is used to focus on the various phenomena occurring at three different scales. The macroscopic scale allows the establishment of relationships between the nature of the films and friction levels and wear rates under various testing conditions. The microscopic scale focuses on the accommodation modes, in terms of interfacial shearing mechanisms, transfer film buildup, and friction-induced wear-particle formation. The nanometric scale focuses on the chemical reactivity of the top surface in relationship to the environment that surrounds the contact spot, and the surface chemistry of the films deposited under differing conditions. Below, the current knowledge at these three complementary scales is summarized. 24.3.2.1 Tribology of DLC at the Macroscopic Scale: Friction and Wear Behavior The friction data on DLC films show that their sliding friction coefficients, µ, span the range of 0.003 to 0.6, which probably represents the widest range of friction behavior in any category of coatings. Wear rates are less systematically investigated and are often recorded in nonstandard units, thus increasing the difficulty of comparing results. DLC films that are easily scratchable with no wear resistance at all, as well as films with normalized wear rates as low as 10–8 mm3/N-m, can be produced. Friction and wear control can be achieved, primarily by considering the nature of the DLC films, together with the environmental conditions. In ambient humid air (typically 20% < Relative Humidity < 60%), friction generally ranges between 0.05 and 0.3, with wear rates strongly depending on the nature of the films. Hydrogen-free films generally exhibit lower friction (<0.15) when compared with a-CH coatings. This finding is consistent with the expected role of H in stabilizing the random covalent network and preventing its collapse into a graphitic network. In ta-C films, friction easily causes a local shearinduced graphitization at the microscopic scale, as described in Section 24.3.2.2. Consequently, it is not surprising to observe a decrease in the friction of ta-C films with increasing humidity (Voevodin et al., 1996), because water molecules are known to intercalate between graphite layers and ease their slip over each other. On the other hand, friction of a-CH films generally increases with humidity (Franks et al., 1990). The role of water vapor at both the microscopic and nanometric scales is highlighted in Sections 24.3.2.2 and 24.3.2.3. Unlike friction, wear resistance performance is not so easy to discuss by simply discriminating between the two previous categories of DLC films. Extremely low wear rates can be achieved for both ta-C and a-CH coatings. In the case of H-containing films deposited by PECVD, Grill (1997b) has correlated wear resistance (down to 0.1 nm for 1000 rotations in ambient air) with deposition conditions (precursor, bias, and pressure). Polymer-like films obtained at low average impact energy (controlled through low DC bias) are less wear resistant than diamond-like films. Thus, based on the accumulated knowledge described in the previous sections on deposition/structure/property relationships, this finding shows that the optimization of the wear resistance of DLC films requires strong attention to the control of the deposition procedure. In inert environments, including dry N and vacuum, friction coefficients can reach either ultralow values (down to 0.01 or less [Erdemir et al., 2000a,b]) or high values (>0.5). Donnet and Grill (1997) have shown that this binary friction behavior, under UHV conditions during tribological tests, can be controlled by the H content of the films. Hydrogen concentrations lower than 34 at% systematically lead to high friction, similar to the friction level of diamond or graphite in the same UHV environment. Ultralow friction is achieved with films that contain at least 40 at% H. The effect of H on the friction level is highlighted in the chapter section dedicated to the tribology of DLC at the nanometric scale (Section 24.3.2.3).
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A compilation of the tribology of doped DLC and C alloy coatings has been recently prepared by Donnet (1998). Silicon incorporation into the DLC structure is shown to affect most film properties (including a decrease in surface energy and internal stress) and its tribological behavior. Friction appears to be significantly reduced (<0.1), where compared with that of conventional undoped DLC in ambient humid air, with comparably high wear resistance. However, this tribological behavior appears to be observed when the contact pressure remains below 1 GPa. At higher contact pressures, conventional ta-C and a-CH films cannot be surpassed. Consequently, ta-CHSi films can be used in applications that require both low friction (<0.1) and high wear resistance (<10–7 mm3/N-m) under moderate mechanical conditions, for the protection of low-stress aerospace or automotive components, precision ball bearings and gears, sliding bearings, and magnetic recording media. The incorporation of Si and F into the DLC structure affects the surface properties. The reduction of stress, when compared with conventional DLC, is in the same range as that in a-CHSi. However, the reduction of the surface energy is higher with F than with Si. Highly fluorinated DLC (F/[F+C] > 0.4) appears to be soft, with no wear resistance. Moderate fluorination (F/[F+C] < 0.2) can be controlled by deposition conditions to obtain films with comparable wear resistance and friction levels of conventional a-CH films, but with lower stress and surface energy. Less research has been performed on the tribological investigation of N-containing DLC films because of their recent discovery when compared with conventional DLC and other doped DLC. A review of the tribological behavior of C nitride films is presented elsewhere in this chapter (Section 24.4.2). The range of composition and structures attainable with metal-containing DLC coatings appears to be enormous. One should keep in mind that the optimization of the material combination and deposition parameters is a challenging subject for each element or combination of elements. When optimization is achieved, metal-containing DLC films can exhibit promising tribological properties in terms of steadystate friction levels and wear rates for various applications. Dimigen and Klages (1991) observed friction coefficients in the range of 0.02 to 0.04 in ambient air when a significant amount of Ta or W was incorporated in a-CH films. 24.3.2.2 Tribology of DLC at the Microscopic Scale: Accommodation Modes Most experimental observations indicate that for the low friction and reasonably long life of DLC, a transfer film buildup that is followed by an interfilm sliding mechanism is the most frequently observed velocity accommodation mode (Figure 24.15). The kinetics of transfer film formation, together with its thickness, strongly depend on the nature of the counterfaces and the environmental conditions. The interfilm sliding mechanism occurs when the DLC film adheres strongly to both contacting surfaces, but separates into two distinct layers that slide across one another. The resultant shear strength is that of the two layers sliding against one another. Neither of the two original surfaces is in contact, except if the film is completely worn. At this scale, the behavior of ta-C and a-CH is rather similar, and DLC films are generally considered to slide according to this accommodation mode. One should keep in mind that the initial formation of a transfer film is associated with significant wear of the initial coated part. Consequently, this initial running-in wear may be crucial to ensure low friction and wear over long periods, and wear does not systematically vary linearly with time.
FIGURE 24.15 coatings.
Interfilm sliding mechanism consecutive to transfer film formation, frequently observed with DLC
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The nature of the counterfaces can significantly influence the size and nature of the transfer layer (both of which sometimes differ from the initial composition of the film). The transfer layers may become a mixture of the original carbon film and elements from the counterface, indicating a strong triboreactivity with the initial pin counterface. Such a mixture has already been observed by secondary ion mass spectroscopy (SIMS) analysis of inside wear tracks of DLC-coated steels (Ronkainen et al., 1993). The analysis revealed a transfer film composed of a mixture of C, Fe, Cr, H, and O. A lower wear rate of the pin, associated with a modification of the transfer composition, was observed by SIMS analysis at high loads and high speeds. The authors also investigated, with Al2O3 pins, the coatings and experimental setup that had been studied earlier with metal counterfaces. The thickness of the transfer increases with higher loads and sliding velocities; this is associated with a drastic decrease in friction coefficient from 0.13 to 0.02. Alumina was transferred to the surface of the disc wear track. These results were observed both on H-free and hydrogenated DLC films. Thus, similar mechanisms are generally observed when ceramic materials are used. Transfer layers are also formed on ceramic counterfaces such as Si3N4, with composition strongly depending on the environment during friction (Kim et al., 1991; Miyoshi et al., 1992). This can be explained in terms of tribochemical reactions, as described in Section 24.3.2.3. The structure of the transfer layer can also be modified by the friction process, as frequently observed in a wear-induced graphitization mechanism (Erdemir et al., 1991, 1993, 1995, 1996; Liu et al., 1996). Lower humidity generally increases the graphitization rate, more than likely because the effect of water molecules is reduced. A decreased graphitization rate is also observed at lower temperatures and higher humidity during friction, and can be attributed to the suppression of temperature rises at hot spot. Moreover, the environment, controlled by the partial pressure of pure water vapor (pH2O), strongly affects the transfer film thickness, which appears to influence the friction level. This effect has been observed in hydrogenated DLC film deposited on an Si substrate and tested against a steel pin counterface in UHV at various pH2O values (Donnet et al., 1998). A transition between ultralow friction (10–2 range) and higher friction (10–1 range) is observed within a water vapor pressure range between 0.1 hPa (RH = 0.4% at 23°C) and 1 hPa (RH = 4% at 23°C). Ultralow friction at the lowest pH2O values is associated with a homogeneous C-based transfer, as shown by in situ Auger electron spectroscopy (AES) performed inside the transfer film. Higher humidity values are associated with a thinner transfer film, so that AES detects the substrate elements that underlie this transfer, and friction rises to higher values. The transfer is thus impeded at high humidity values. Consequently, the nature of the counterface and the tribotesting parameters, together with the nature of the environment, play a crucial role in the kinetics of formation and composition of the transfer film, and thus strongly influence the friction levels and wear rates. Tribochemical reactions between the transfer film and the counterface can induce the formation of complex structures and compositions on the top surface of the film. Moreover, the nature and thickness of contaminant or passivation layers will probably play a role, but this kind of assumption can be checked only by tribological tests under UHV conditions and sliding in situ on fresh surfaces. An exception to this conventional transfer film formation mechanism can be found when DLC-coated steel slides slowly against PTFE (Yang et al., 1991). Without the DLC film, very little PTFE is directly transferred onto the steel counterface and friction remains between 0.15 and 0.20. With the DLC film, friction decreases to 0.04, without any transfer film formation, because of the low adhesion between PTFE and the DLC coating. 24.3.2.3 Tribology of DLC at the Nanometric Scale: Tribochemistry and Molecular Interactions During a sliding process, interfacial rheology is associated with exposure of the top surfaces and interfaces (third body) to one another and, except for UHV tribotests, to the surrounding atmosphere. Therefore, the chemical composition of the first layers is of paramount importance in understanding the tribochemistry of DLC coatings.
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TABLE 24.2
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Friction Mechanism of Carbonaceous Compounds at the Molecular Scale
Friction range Nature of the interaction Energy (eV/bond) Schematic of the interaction (environment)
< 0.02 van der Waals 0.08 a-C:H (UHV)
0.1–0.2 Hydrogen 0.2 a-C:H or a-C (RH > 4%)
>0.5 σ or π 0.4–0.8 Diamond, graphite, DLC with low H content (UHV)
Note: Energy values are indicated by Gardos (1994), and experimental friction ranges have been compiled by Donnet (1997; 1998b) and Gardos (1994). UHV means ultrahigh vacuum.
The role of the H content and sp2/sp3 hybridizations in a-CH films is discussed first. The discussions are based on Table 24.2. With this approach, it should be possible to explain the role of the high H content in lowering the friction of DLC in UHV from high values that are in the same range as values related to diamond or graphite under the same environmental conditions. When transfer film buildup during the running-in period is taken into account, steady-state sliding with DLC films is accommodated between the two counterfaces by interfilm sliding of C-covered smooth surfaces. Under UHV conditions, the contaminant topcoats are removed and sliding occurs between the two carbonaceous fresh surfaces. In the case of diamond/diamond or graphite/graphite, as with poorly hydrogenated a-CH films, the UHV friction coefficient is initially in the 0.1 to 0.2 range, as long as the surface sites are saturated by H, O, or H2O molecules. Steady-state friction of diamond and un-intercalated graphite is generally very high (>0.5), as reviewed by Gardos (1994). Desorption of adsorbates upon rubbing in vacuum creates σ dangling bonds on diamond surfaces. If these free bonds do not reconstruct or are not activated by any adsorbates, they interact with high energies and thus contribute to the high friction. In the case of un-intercalated graphite, the π-π* orbitals (i.e., sub-bands of the graphite band structure) overlap at selected sites of the Brillouin zone. The overlap of these sub-bands can lead to attractive interactions that range from 0.4 eV (37 kJ/mol) to 0.8 eV (66 kJ/mol). The actual interaction force is somewhere within this range, depending on how the band parameters influence the net inter- and intraplanar attraction of a family of imperfect graphitic planes of particles interacting in a solid lubricant layer. Gardos (1994) indicates that the 0.4 to 0.8 eV binding energy between the basal planes is enough to render pristine highly oriented graphite, a high friction and wear material. The discussion related to a-CH films is more complex in that it considers the wide distribution of H content and C hybridizations, and determines various degrees of C crosslinking. The ultralow friction of highly hydrogenated DLC films in UHV is consistent with the predominance of hydrocarbon polymerlike topcoats mutually interacting through weak van der Waals interactions (Table 24.2). As observed by Donnet and Grill (1997), this mechanism appears to be predominant if the H content is higher than ≈40 at%, whereas DLC with H content lower than 34 at% behaves in UHV as graphite or diamond. The exact origin of the threshold between ultralow friction and high friction observed with a difference limited to 6 at% is not completely understood. Others have already observed that aliphatic-type hydrocarbon chains with high flexibility undergo easy friction-induced orientation along the sliding direction, as shown by polarized infrared microscopy performed on inside wear tracks of hydrogenated DLC after a UHV friction test (Sugimoto and Miyaki, 1990).
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The tenfold increase in friction from <0.02 to >0.1 caused by humidity and oxidation indicates that the increase in bond strength from 0.08 eV/bond to 0.2 eV/bond (H bonding at CO sites by water molecules) associated with a progressive friction-induced graphitization should be the main cause of the change in friction (Table 24.2). However, such a description fails to account for the modification of the rheology of the contact by triboreactivity between the transfer layer and the counterface, and by the formation of friction-induced wear particles. This modification of the rheology has been shown by Kim et al. (1991) by performing FTIR microprobe tests to identify the debris and film structures observed on various interfacial films formed by a Si3N4 ball rubbed against DLC-coated Si in dry Ar, dry air, and moist air conditions. Humidity caused a tribochemical reaction and led to a transfer film composed of oxidized hydrocarbon and hydrated silica (from the ball). Consequently, friction was rather low, but wear was significantly high. The opposite tribological behavior was observed in dry air, where the transfer layer and debris were composed of a carbonyl compound formed by the tribo-oxidation of hydrocarbons in the DLC films. The triboreactivity was reduced in dry Ar, thus lowering both friction and wear, with a transfer film and debris whose composition was similar to that of the initial film.
24.3.3 Applications of DLC Films The unique properties of DLC films and their modifications, together with the possibility of adjusting the properties by choosing the right deposition parameters, make them suitable for various applications. The exploited properties thus far include high wear resistance and low friction coefficients, chemical inertness, infrared transparency, high electrical resistivity, and, potentially, field emission and low dielectric constant. Although ta-C has properties similar to or (in some instances) better than those of conventional DLC (i.e., a-CH), thus far, only conventional DLC films have been used for practical applications (see extensive reviews by Grill and Meyerson, 1994; Grill, 1997a). Because DLC is IRtransparent, it can be used as an antireflective and scratch-resistant, wear-protective coating for IR optics (at wavelengths of 8 to 13 µm) made of Ge, ZnS, and ZnSe (Grill, 1999). The low deposition temperature of DLC allows its use as a wear-protective layer on products made of plastic; therefore, it is used to protect polycarbonate sunglass lenses from abrasion. The most widespread use of DLC films is in wear and corrosion protection of magnetic storage media. Nanosmooth and very thin (even <5 nm) DLC films are now used as corrosion and wear protective coatings for both magnetic disks and magnetic heads (Bhushan, 1999). Video recording or magnetic data storage tapes, in which ferromagnetic metal is a recording medium, and the metallic capstans in contact with the tapes are also being protected with DLC coatings to reduce wear and friction, thus extending both the life of the tapes and their reliability. The announcements of the latest MACH3 razor blades by Gillette underscore the use of DLC as a coating to improve the quality and performance of the blades. DLC seems also to have found its uses in tribological coatings for metal bearings, gears, and seals. Its potential use for phase-shift masks for DUV lithography has also been demonstrated. DLC films appear to be biocompatible, and applications are being developed for their use in biological environments. Because they are chemically inert and impermeable to liquids, DLC coatings could protect biomedical implants against corrosion and serve as diffusion barriers. DLC is being considered for coating metallic and polymeric-substrate biocomponents, such as polyurethane, polycarbonate, and polyethylene, to improve their compatibility with body tissues. DLC deposited on stainless steel and Ti alloys, which are components of artificial heart valves, has been found capable of satisfying both the mechanical and biological requirements and improving the performance of these components. The same properties may make DLC useful as a protective coating for hip joint implants. Improvement of carbon/carbon composite prosthetics by DLC coatings has also been demonstrated. Currently, DLC and its modifications are being considered as low-dielectric materials for the interconnect structures of ultra-large-scale integrated circuits (ULSI). A better understanding of the means to control the thermal stability and other integration problems of DLC and its modifications will potentially expand their use in ULSI chips. Nonhydrogenated ta-C films have yet to find such widespread application. The most promising application appears to be for cathodes in field-emission-based flat-panel displays or as pixel elements in large outdoor displays.
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24.4 Other Related Films 24.4.1 Cubic Boron Nitride (CBN) Like diamond, CBN exhibits many exceptional properties that render it far superior to other hard nitrides and carbides used by industry today. It is the second hardest material known. Unlike diamond, it does not dissolve in or interact with Fe-based alloys, and thus can be used to machine ferrous materials (which account for 80% of all cutting and machining operations). Because CBN has a very high melting point, is chemically very stable, and exhibits excellent hot hardness and strength, it can provide excellent resistance to wear and oxidation at elevated temperatures. CBN can also work very well under dry machining conditions. In addition to its excellent thermal and chemical stability and high wear resistance, CBN offers high thermal conductivity and a very large band gap (≈6 eV). It can be doped with both pand n-type elements; hence, like diamond, CBN can also be used in various optical and electrical applications. Like diamond, CBN can be synthesized by the HPHT method in the powder form and can be deposited in thin films on various metallic and ceramic substrates by both PVD and CVD methods. The most widely used deposition methods include magnetron sputtering, plasma-enhanced CVD, ion plating, pulse laser deposition, ion-beam-assisted deposition, etc. (Murakawa and Watanabe, 1990; Chiang et al., 1997; Smeets et al., 1997; Konyashin et al., 1997). The deposition temperatures needed for the formation of the CBN phase are substantially lower than those required for diamond films. Also, the surface finish of CBN films is much smoother; hence, there is no need for post-deposition polishing (Watanabe et al., 1999). Several factors can affect the synthesis of high-quality CBN films during deposition. First, achieving and maintaining a 1:1 stoichiometry between B and N atoms tends to be rather difficult. Most films are slightly N-deficient and, hence, are not perfectly crystalline. Increases in B above stoichiometry and concomitant formation of vacancies on the N sublattice lead to distortions and significant changes in crystal structure. These changes can adversely affect the mechanical, thermal, and other important properties of CBN. Depending on deposition temperature, ion energy, and current density, resultant films may contain appreciable amounts of amorphous or hexagonal BN phases. For example, the formation of an sp3-hybridized CBN phase is largely controlled by the substrate temperature and the energy of N and Ar ions in sputtering and ion-beam deposition. The presence or absence of H in the plasma can also affect film quality. For higher quality CBN films, moderate ion energies are needed (Schaffnit et al., 1996). Growing CBN films tend to accumulate increasingly high compressive stresses in their microstructures and this represents a major problem in attaining films that are thick enough (at least 3 to 5 µm) for machining operations. The lack of suitable tool substrates with a good lattice and thermal expansion match is a major part of this problem. During deposition, compressive stress within the film tends to increase with increasing thickness and eventually becomes so high that CBN film delaminates prematurely or fractures severely (Murakawa and Watanabe, 1990). Currently, safe film thickness for crystalline CBN films is in the range of 0.2 to 0.5 µm. For most machining and other tribological applications, films thicker than this are needed. Deposition of such thick films is quite possible with diamond, but not with CBN. In recent years, approaches have been tried to achieve strong bonding between CBN and various substrate materials. In one approach, CBN was produced over a graded Ti interlayer. In another approach, annealing of the CBN films both during and after deposition was tried. Annealing is thought to relieve some of the residual stresses, and hence reduce the amount of stress buildup at the coating-substrate interface. The use of a Ti layer or first layer, followed by a second layer of graded BN, was shown to be quite effective in achieving strong adhesion between CBN and several tool materials (i.e., WC-Co alloy and high-speed steel). Furthermore, it was shown that CBN can be directly grown on diamond films without using a bond or a graded BN layer (Murakawa and Watanabe, 1990; Murakawa et al., 1991); hence, a duplex coating of the two hardest materials can be obtained. Despite some incremental improvements in achieving strong adhesion between CBN and various substrate materials, high residual stresses in these films still hinder the deposition of very thick films with good adhesion.
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24.4.1.1 Tribology of CBN Films Because of its excellent mechanical properties, chemical inertness, and high-temperature durability, CBN holds significant promise for various tribological applications, including wear parts, cutting tools, dies, seals, bearings, etc. Accordingly, it has been the subject of several tribological studies in recent years. Specifically, the friction, wear, and usefulness of CBN for extreme machining operations have been explored. Tribological studies have indicated that the friction and wear performance of CBN is highly dependent on the test environment and counterface materials. In a search of self-lubricating materials for space applications, Miyoshi (1999) performed comprehensive tests with diamond, DLC, and CBN in UHV environments. Surprisingly, it was found that CVD diamond films against CBN exhibited the lowest coefficients of friction. Such impressive results led Miyoshi to the conclusion that a combination of these two hardest materials may serve as an effective self-lubricating, wear-resistant couple for UHV or space applications. Tribological tests by Watanabe et al. (1999) have revealed that CBN exhibited much better wear performance than amorphous BN and TiN or TiC films. When CBN is slid against steel in air or under water, wear is low; but in high vacuum, it is high. Sliding CBN against Al led to high friction and wear in air and vacuum; but in water, wear was almost zero. Studies by Miyake et al. (1992) and Watanabe et al. (1991) demonstrated that the crystallinity of CBN coatings strongly affects the friction and wear properties of ion-plated CBN films. In their tests, highly crystalline CBN films provided the best wear resistance and lubrication, whereas films with an amorphous structure exhibited good frictional properties but very short wear lives. Poor adhesion of hexagonal BN led to premature debonding and hence poor wear performance. In the end, these authors concluded that perhaps an ideal film should contain a mixture of CBN (for high wear resistance) and amorphous BN (for good lubricity) phases. To test this idea, they prepared a duplex film that consisted of both CBN and amorphous BN. More specifically, an initial layer of CBN was deposited onto an Si substrate by ion plating, followed by a second layer of amorphous BN on top of the CBN layer with a gradient interlayer formed between the two BN layers. The results of tribological tests showed that this composite film exhibited significantly lower friction coefficients and much longer wear life than the single-layer CBN film. Compared to other hard nitride and carbide coatings, CBN provides very low friction coefficients during sliding in air. Comprehensive studies by Murakawa (1997) and Watanabe et al. (1991, 1995) have demonstrated that the friction coefficients of high-quality CBN films are in the range of 0.1 to 0.2, whereas those of TiC, TiN, and TiCN films are 0.3 to 0.5 under the same test conditions. Because of their excellent tribological properties, CBN films were deposited on WC-Co drills and tool inserts and subjected to cutting operations. Except for partial delamination in a few cases, CBN coatings reduced torque while drilling 440C steel work pieces. Large-scale applications of CBN films have not yet been realized. Despite its many attractive properties (i.e., high thermal stability, low reactivity with ferrous alloys, smooth surface finish, excellent resistance to corrosion and high-temperature oxidation, and low-to-moderate deposition temperatures), CBN suffers from poor adhesion, limited film thickness, high internal stresses, and poor reproducibility of structure and properties. Currently, researchers are concentrating on overcoming these problems. Except for a few case studies where superior machining and lower torque were demonstrated while cutting or drilling steels, CBN films have not yet been offered for large-scale applications.
24.4.2 Carbon Nitride Films First-principles calculations by Cohen (1985) and Liu and Cohen (1989, 1990) have predicted a new form of carbon nitride (i.e., cubic beta carbonitride β-C3N4) that exhibits an extremely low compressibility and superhigh hardness that exceed those of natural diamond. The unique crystal structure of cubic β-C3N4 is based on the β-Si3N4 structure, in which C is substituted for Si to achieve an atomic bond configuration that favors extreme hardness and elastic modulus. Because hardness is inversely proportional to the bond length and hence to the radii of the atoms that form that bond, Cohen predicted that such compounds based on C and N, which have very small atomic radii and the strongest bonds,
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will exhibit the highest hardness. Since these initial theoretical studies, many researchers have attempted to synthesize β-C3N4 in both the bulk and thin-film forms by various methods, with the expectation that this will lead to new possibilities in the fields of superhard and wear-resistant materials. In addition to its extreme mechanical properties, researchers have predicted that β-C3N4 will provide excellent thermal conductivity and wide bandgap (Cohen, 1995; Wang, 1997). During the past decade, several new methods have been developed and used to synthesize crystalline β-C3N4 films. Despite intense research efforts around the world, successful synthesis of crystalline β-C3N4 has not yet been fully realized. Most PVD and CVD methods (such as laser ablation, RF and DC magnetron sputtering, ion-beam deposition, ion implantation, plasma arc deposition, UV-assisted chemical synthesis, and hot-filament CVD) have produced amorphous carbon nitride films with a relatively low N content (≈20 to 30%), mainly because of an extremely high bond dissociation energy for N in gas discharge plasmas or ion fluxes. Occasionally, within the predominantly amorphous structure of these films, some researchers have reported the presence of small crystallites with electron diffraction patterns that match the pattern of β-C3N4 (Chen et al., 1997; Yu et al., 1997; Yu et al., 1994). Frustrated by slow progress in producing β-C3N4 in the bulk or thin-film forms, a few researchers have tried to stabilize the crystalline phase in a pseudomorphic state using appropriate structural templates such as TiN or ZrN(111), which can provide the correct unit cell geometry and lattice match. Specifically, using crystalline ZrN(111) as the structural template, Li et al. (1995) and Wu et al. (1997, 1998) have recently produced a multilayer film that consists of very thin β-C3N4 (1 to 2 nm thick) and ZrN films with a hardness value above 40 GPa and an elastic modulus of 400 GPa. Most research groups have been able to successfully produce amorphous C nitride coatings. Although these coatings are much softer than diamond, they still provide excellent tribological performance, especially when used as a protective overcoat for computer hard drive systems (Cutiongco et al., 1996; Khurshudov and Kato, 1996). Primarily because of a large variation in their microstructure and chemical stoichiometry (i.e., C:N ratio), amorphous C nitride films produced by various research groups exhibit large variations in mechanical properties and tribological performance. Reported friction values range from 0.05 to >0.5 in air. In dry environments or high vacuum, much higher friction coefficients were observed. Such a large scatter in friction has been mainly attributed to the differences in N content, extent of sp3 and/or sp2 hybridization, deposition methods and conditions, and, ultimately, the mechanical properties of the films. Kusano et al. (1998) have found that CNx films deposited with >70% N in the sputtering gas exhibit higher friction and wear coefficients than films grown in the presence of lower N content. Czyzniewski et al. (1998), Hajek et al. (1997), and Fendrych et al. (1998) have also found a very close relationship between friction and wear properties of CNx films, C:N ratio, and deposition conditions (i.e., temperature, ion energy, ion current density, etc.). Li et al. (1994) have observed that in dry sliding contacts, CNx gives an initial friction coefficient of 0.1 against a 52100 steel ball, but this value increases to ≈0.5 in steady states. Zou et al. (1999) reported steady-state friction coefficients of 0.08 to 0.14 for CNx films produced by a reactively ionized cluster beam technique. As far as tribological applications are concerned, amorphous C nitride films are currently used as protective coatings in magnetic hard disks. Khurshudov and Kato (1996) reported that the wear rates of the carbon nitride-coated disks were 10 times lower than those of disks coated with a commercial DLC film of the same thickness. These C nitride coatings also provided ≈3 to 30-times longer wear life than commercial C coatings. Carbon nitride coatings can also be used in other tribological fields where conventional DLC films have already been exploited, but the progress in implementation has been rather slow.
24.5 Summary and Future Direction Over the last 2 decades, great strides have been made in the deposition, characterization, and tribological utilization of diamond, DLC, and related films, which represent some of the hardest materials known. In addition to their exceptional mechanical properties, these coatings incorporate several other attractive
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properties that can be very useful for some demanding tribological applications. The current state-ofthe-art in diamond, DLC, and other related films allows many tribocomponents to be coated with these films and offered for practical applications. Although some applications are still in the exploratory stage and require further refinement, prototypes of others have been successfully produced and are currently being evaluated for endurance and reliability. As a true reflection of the growing interest in these films, the number of publications that deal with them has steadily increased over the years. It is not possible to refer to all of them in this chapter, but even a simple literature survey will yield several key publications for those who are interested in more in-depth information about these films. In addition to some archival journals, several technical/scientific books and book chapters, as well as conference proceedings, are now available. These publications have led to a better understanding of the microstructure and chemistry of these films and, hence, have led to their greater utilization by industry. The relatively high cost of diamond and poor adhesion and reliability of CBN are delaying their wider applications in industry. Until now, only tool inserts and drills have been coated successfully with diamond and CBN and been made available for limited commercial use. However, these superhard coatings have much to offer future tribological applications. It is anticipated that their use in the cutting-tool industry will further increase if and when their reliability is improved and their unit cost is further reduced. Although prototypes of other tribological parts (e.g., mechanical seals) with diamond coatings have also been prepared, their large-scale utilization has not yet been realized. Some of the reasons for the slow progress in the commercialization of diamond and CBN coatings are rough surface finish (in the case of diamond), problems with adhesion (CBN), high fabrication cost (both diamond and CBN), and most important, insufficient reliability and reproducibility in actual application. DLC and C nitride films are more cost-effective and much easier to produce than diamond and CBN; hence, they are now used in various tribological applications. The combination of high wear resistance (due to high mechanical hardness) and low friction makes diamond, DLC, and related films very unique and ideal for demanding tribological applications. However, the results of previous studies suggest that, depending on the tribological and environmental constraints, tribochemical and thermomechanical interactions can occur at the sliding interfaces of these films and control their friction and wear performance. Existing data suggest that, with proper control of their microstructure, chemistry, and surface topography, these films may live up to their promise. The high surface roughness of microcrystalline diamond films presents serious problems in many tribological applications. These microcrystalline films can be polished by various methods or, alternatively, nanocrystalline diamond films with a very smooth surface finish can be used to achieve low friction and wear in sliding tribological applications. These smooth films are particularly suitable for mechanical shaft seals and MEMS applications. As with other types of hard coatings, strong bonding between these films and their substrates is an important prerequisite for long service life in most tribological applications. Field and laboratory test results confirm the notion that diamond coatings can afford excellent life improvement to cutting tool inserts when they are used to machine Al-Si alloys and graphite, whereas CBN is more suitable for machining ferrous and nonferrous alloys. When compared to diamond, CBN has not yet found large-scale applications in the industrial world. Poor adhesion, insufficient thickness, high internal stresses, and difficulties in attaining and maintaining 1:1 stoichiometry between B and N atoms in a cubic crystalline structure during deposition are some of the major problems that hinder further use of CBN in tribological fields. With recent advances in deposition technology, the quality and reliability of these coatings are expected to improve in the near future and, hence, increase their chances for large-scale applications. Briefly, the future of diamond, DLC, and related coatings in tribological applications looks promising because the industrial need for materials with unusual properties is constantly increasing.
Acknowledgment This work is supported by the U.S. Department of Energy, Office of Energy Research, under Contract W-31-109-Eng-38.
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Erdemir, A., Fenske, G., and Wilbur, P. (1997c), High-temperature durability and tribological performance of diamond and diamondlike carbon films, in Protective Coatings and Thin Films: Synthesis, Characterization and Applications, Pauleau, Y. and Barna, B. (Eds.), NATO ASI-High Technology Series, Vol. 21, Kluwer Academic, London, 169-184. Erdemir, A., Nichols, F.A., Pan, X., Wei, R., and Wilbur, P. (1993), Friction and wear performance of ionbeam-deposited diamondlike carbon films on steel substrates, Diamond Rel. Mater., 3, 119-124. Erdemir, A., Switala, M., Wei, R., and Wilbur, P. (1991), A tribological investigation of the graphite-todiamond-like behaviour of amorphous carbon films ion beam deposited on ceramic substrates, Surf. Coat. Technol., 50, 17-23. Erdemir, A., Eryilmaz, O.L., and Fenske, G. (2000a), Synthesis of diamondlike carbon films with superlow friction and wear properties, J. Vacuum Sci. Technol., 18, 1987-1992. Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., and Fenske, G. (2000b), Effect of source gas chemistry on tribological performance of diamondlike carbon films, Diamond Rel. Mater., 9, 632-637. Erdemir, A., Fenske, G.R., Krauss, A.R., Gruen, D.M., McCauley, T., and Csencsits, R. (1999), Tribological properties of nanocrystalline diamond films, Surf. Coat. Technol., 121, 589-593. Erz, R., Doetter, W., Jung, K., and Ehrhardt, H. (1993), Preparation of smooth and nanocrystalline diamond films, Diamond Rel. Mater., 2, 449-453. Eversole, W.G. (1962), U.S. Patents 3,030,187, and 3,030,188. Fedoseev, D.B. (1994), Summary of Research on Diamond Growth from the Gas Phase in Russia, in Synthetic Diamond: Emerging CVD Science and Technology, Spear, K.E. and Dismukes, J.P. (Eds.), John Wiley & Sons, New York, 41-56. Fendrych, F., Jastrabik, L., Pajasova, L., Chvostova, D., Soukup, L., and Rusnak, K. (1998), Mechanical tribological and optical properties of CN2 coatings prepared by sputtering methods, Diamond Rel. Mater., 7, 417-421. Feng, Z. and Field, J.E. (1992), The friction and wear of diamond sliding on diamond, J. Phys. D. Appl. Phys., 25, A33-A37. Feng, Z. and Field, J.E. (1991), Friction of diamond and chemical vapor deposited diamond coatings, Surf. Coat. Technol., 47, 631-645. Field, J.E. (1979), The Properties of Diamond, Field, J.E. (Ed.), Academic Press, London, 281-324. Field, J.E. (1992), The Properties of Natural and Synthetic Diamond, Academic Press, London. Franks, J., Enke, K., and Richardt, A. (1990), Diamond-like carbon — Properties and applications, Met. Mater., November, 695-700. Gangopadhyay, A.K. and Tamor, M.A. (1993), Friction and wear behavior of diamond films against steel and ceramics, Wear, 169, 221-29. Gardos, M.N. (1994), Tribology and wear behavior of diamond, in Synthetic Diamond: Emerging CVD Science and Technology, Spear, K.E. and Dismukes, J.P. (Eds.), John Wiley & Sons, New York, 419-504. Gardos, M.N. (1998), Silicon and diamond for MEMS bearing applications in extreme environments, Electrochem. Soc. Proc., 97, 465-481. Gardos, M.N. (1999), Tribological fundamentals of polycrystalline diamond films, Surf. Coat. Technol., 113, 183-200. Gardos, M.N., Davis, P.S., and Meldrum, G.R. (1997), Crystal-structure-controlled tribological behavior of carbon-graphite seal materials in partial pressures of helium and hydrogen. II. SEM tribometry, Tribol. Lett., 3, 185-198. Gardos, M.N. and Gabelich, S.A. (1999), Atmospheric effects of friction, friction noise and wear with silicon and diamond. III. SEM tribometry of polycrystalline diamond in vacuum and hydrogen, Tribol. Lett., 6, 103-112. Gardos, M.N. and Ravi, K.V. (1994), Surface chemistry controlled friction and wear behavior of Si (100) vs. textured polycrystalline diamond film tribocontacts, Diamond Films Technol., 4, 139-165. Germann, G.J., Cohen, S.R., Neubauer, G., McClelland, G.M., and Seki, H. (1993), Atomic scale friction of a diamond on diamond (100) and (111) surface, J. Appl. Phys., 73, 163-176.
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Gilbert, D.R., Lee, D.-G., and Singh, R.K. (1998), Novel in situ production of smooth diamond films, J. Mater. Res., 13, 1735-1737. Gogotsi, Y.G., Kailer, A., and Nickel, K.G. (1998), Pressure-induced phase transformations in diamond, J. Appl. Phys., 84, 1299-1304. Grill, A. (1997a), Property control of diamondlike carbon coatings by selection of precursor bias and dilutant, in Protective Coatings and Thin Films, Pauleau, Y. and Berna, P.B. (Eds.), Kluwer Academic, New York, 243-253. Grill, A. (1997b), Tribology of diamondlike carbon and related materials, Surf. Coat. Technol., 94/95, 507-513. Grill, A. (1999), Electrical and optical properties of diamondlike carbon, Thin Solid Films, 356, 189-193. Grill, A. and Meyerson, B.S. (1994), Development and status of diamondlike carbon, in Synthetic Diamond: Emerging CVD Science and Technology, Spear, K.E. and Dismukes, J.P. (Eds.), John Wiley & Sons, New York, 91-141. Grill, A. and Patel, V. (1992), Characterization of diamondlike carbon by infrared spectroscopy, Appl. Phys. Lett., 60, 2089-2091. Grischke, M., Bewilogua, K., Trojan, K., Dimigen, H. (1995), Application-oriented modifications of deposition processes for diamond-like-carbon-based coatings, Surf. Coat. Technol., 74/75,739-745. Gruen, D.M. (1998), Nucleation, growth, and microstructure of nanocrystalline diamond films, MRS Bull., 23, 32-35. Gruen, D.M., Liu, S., Krauss, A.R., Luo, J., and Pan, X. (1994), Fullerenes as precursors for diamond film growth without hydrogen or oxygen additions, Appl. Phys. Lett., 64, 1502-1504. Gruen, D.M., Liu, S., Krauss, A.R., and Pan, X. (1994), Buckyball microwave plasmas: fragmentation and diamond-film growth, J. Appl. Phys., 75, 1758-1763. Gruen, D.M., Zuiker, C., and Krauss, A.R. (1995), Diamond films grown from fullerene precursors, Fullerenes Photonics, 25/30, 1-13. Gunnars, J. and Alahelisten, A. (1996), Thermal stresses in diamond coatings and their influence on coating wear and failure, Surf. Coat. Technol., 80, 303-312. Gupta, B.K., Malshe, A., Bhushan, B., and Subramanian, V.V. (1994), Friction and wear properties of chemomechanically polished diamond films, J. Tribol., 116, 445-453. Hajek, V., Rusnak, K., Vlcek, J., Martinu, L., and Hawthorne, H.M. (1997). Tribological study of CN2 films prepared by reactive DC magnetron sputtering, Wear, 213, 80-89. Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry. An atomic-scale view of the wear of diamond, J. Am. Chem. Soc., 116, 10399-10402. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1992a), Molecular-dynamics simulations of atomic-scale friction of diamond surfaces, Phys. Rev. B, 46, 9700-9708. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1992b), Nanoscale investigation of indentation, adhesion, and fracture of diamond (111) surfaces, Surf. Sci., 271, 57-67. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1993), Effects of chemically bound, flexible hydrocarbon species on the frictional properties of diamond surfaces, J. Phys. Chem., 97, 6573-6576. Hatta, A. and Hiraki, A. (1998), Low temperature diamond deposition, in Low-Pressure Synthetic Diamond, Dischler, B. and Wild, C. (Eds.), Springer-Verlag, Berlin, 103-117. Haubner, R. and Lux, B. (1993), Diamond growth by hot-filament chemical vapor deposition: state of the art, Diamond Rel. Mater., 2, 1277-1294. Hayward, I.P. (1991), Friction and wear properties of diamonds and diamond coatings, Surf. Coat. Technol., 49, 554-559. Hayward, I.P. and Field, J.E. (1987), Friction and wear of diamond, Int. Conf. On Tribol., 50 Years on, IMechE, C159/87, 205-209. Hayward, I.P., Singer, I.L., and Seitzman, L.E. (1992), Effect of roughness on the friction of diamond on CVD diamond coatings, Wear, 157, 215-227. Hogmark, S., Hollman, P., Alahelisten, A., and Hedenqvist, P. (1996), Direct current bias applied to hotflame diamond deposition produces smooth low friction coatings, Wear, 200, 225-232.
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Hollman, P., Wanstrand, O., and Hogmark, S. (1998a), Friction properties of smooth nanocrystalline diamond coatings, Diamond Rel. Mater., 7, 1471-1477. Hollman, P., Bjorkman, H., Alahelisten, A., and Hogmark, S. (1998b), Diamond coatings applied to mechanical face seals, Surf. Coat. Technol., 105, 169-174. Holmberg, K. (1998), Tribology of diamond and diamond coatings — A review, Tribologia, 12, 33-62. Holmberg, K. and Matthews, A. (1994), Coatings Tribology, Elsevier, Amsterdam. Inspektor, A., Oles, E.J., and Bauer, C.E. (1997), Theory and practice in diamond coated metal-cutting tools, Int. J. Ref. Met. Hard Mater., 15, 49-56. Jahanmir, S., Deckman, D.E., Ives, L.K., Feldman, A., and Farrabaugh, E. (1989), Tribological characteristics of synthesized diamond films on silicon carbide, Wear, 133, 73-81. Johnson, C.E., Hasting, M.A.S., and Weimer, W.A. (1990), Thermogravimetric analysis of the oxidation of CVD diamond films, J. Mater. Res., 5, 2320-2325. Karner, J., Pedrazzini, M., Reineck, I., Sjostrand, M.E., and Bergmann, E. (1996), CVD diamond-coated cemented carbide cutting tools, Mater. Sci. Eng., A209, 405-413. Keipke, R., Buchkremer-Hermanns, H., Weiss, H., and Ren, H. (1998), Machining of hypereutectic AlSi alloy with CVD diamond-coated Si3N4 inserts, Mat. Manufact. Process., 13, 603-610. Khurshudov, A.G. and Kato, K. (1996), Tribological properties of carbon nitride overcoat for thin-film magnetic rigid disks, Surf. Coat. Technol., 86/87, 664-671. Kim, D.S., Fischer, T.E., and Gallois, B. (1991), The effects of oxygen and humidity on friction and wear of diamond-like carbon films, Surf. Coat. Technol., 49, 537-542. Kohzaki, M., Higuchi, K., Noda, S., and Uchida, K. (1992), Tribological characteristics of polycrystalline diamond films produced by chemical vapor deposition, J. Mater. Res., 7, 1769-1777. Kohzaki, M. and Noda, S. (1994), Tribological properties of CVD diamond films in various environments, Diamond Films Technol., 3, 135-148. Komanduri, R. and Nandyal, S. (1993), Low-pressure diamond synthesis of polycrystalline diamond abrasive, Int. J. Machine Tools Manuf., 33, 285-296. Komplin, N.J. and Hauge, R.H. (1998), Other CVD methods for diamond production, in Low Pressure Synthetic Diamond, Dischler, B. and Wild, C. (Eds.), Springer-Verlag, Berlin, 119-136. Konyashin, I., Bill, J., and Aldinger, F. (1997), Plasma-assisted CVD of cubic boron nitride, Adv. Mater., 9, 239-255. Kubel, E. (1998), Coating crank up tool performance, Manufact. Eng., 120, 40-46. Kubelka, S., Haubner, R., Lux, B., Steiner, R., Stingeder, G., and Grasserbauer, M. (1994), Influences of WC-Co hard metal substrate pre-treatments with boron and silicon on low pressure diamond deposition, Diamond Rel. Mater., 3, 1360-1369. Kupp, E.R., Drawl, W.R., and Spear, K.E. (1994), Interlayers for diamond-coated cutting tools, Surf. Coat. Technol., 68-69, 378-383. Kusano, Y., Evetts, J.E., Somekh, R.E., and Hutchings, I.M. (1998), Properties of carbon nitride films deposited by magnetron sputtering, Thin Solid Films, 332, 56-61. Lee, E.H., Hembree, D.M., Rao, G.R., and Mansur, L.K. (1993), Raman scattering from ion-implanted diamond, graphite, and polymers, Phys. Rev., 48, 15540-15551. Leyendecker, Y., Lemmer, O., Esser, S., and Frank, M. (1995), Wear mechanism of diamond coated cutting tools, Proc. 3rd Int. Conf. on Appl. Diam. Films and Rel. Mater., Feldman, A., Tzeng, Y., Yarhrough, W.A., Yoshikawa, M., and Murakawa, M. (Eds.), NIST SP-885, Washington, D.C., 183-190. Li, D., Chung, Y.-W., Wong, M.S., and Sproul, W.D. (1994), Nano-indentation and tribological studies of ultrahigh strength carbon nitride thin films, Tribol. Trans., 37, 479-482. Li, D., Chu, X., Cheng, S.C., Lin, X.W., Dravid, V.P., Chung, Y.W., Wong, M.S., and Sproul, W.D. (1995), Synthesis of superhand carbon nitride composite coatings, Appl. Phys. Lett., 67, 203-205. Liu, A.Y. and Cohen, M.L. (1989), Prediction of new low-compressibility solids, Science, 245, 841-845. Liu, A.Y. and Cohen, M.L. (1990), Structural properties and electronic structure of low-compressibility materials: β-Si3N4 and Hypothetical β-C3N4, Phys. Rev. B, 41, 10727-10734.
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Liu, Y., Erdemir, A., and Meletis, E.I. (1996), A study of the wear mechanism of diamond-like carbon films, Surf. Coat. Technol., 82, 48-56. Lux, B. and Haubner, R. (1993), Diamond as a wear-resistant coating, diamond films and coatings, Davis, R.F. (Ed.), NOYES Publications Park Ridge, NJ, 184-243. Lux, B. and Haubner, R. (1998), CVD diamond for cutting tools, in Low-Pressure Synthetic Diamond, Dischler, B. and Wild, C. (Eds.), Springer-Verlag, Berlin, 223-242. Lux, B., Haubner, R., Holzer, H., and DeVries, R.C. (1997), Natural and synthetic polycrystalline diamond, with emphasis on Ballas, Int. J. Ref. Met. Hard Mater., 15, 263-288. Mao, M.Y., Wang, T.P., Xie, J.F., and Wang, W.Y. (1995), Fine patterning of diamond thin films, Proc. IEEE Micro Electro Mechanical Systems, ASME-IEEE, 392-393. Mate, M. (1993), Nanotribology studies of carbon surfaces by force microscopy, Wear, 168, 17-20. Menningen, K.L., Childs, M.A., Toyoda, H., Anderson, L.W., and Lawler, J.E. (1994), Evaluation of a substrate pretreatment of hot-filament CVD of diamond, J. Mater. Res., 9, 915-920. Miyake, S. (1994), Tribological improvements of polished chemically vapor-deposited diamond film by fluorination, Appl. Phys. Lett., 65, 1109-1111. Miyake, S., Miyamoto, T., Kaneko, R., and Miyazaki, T. (1995), Macro- and micro-tribological properties of polished CVD diamond films and trial processing diamond, IEICE Trans. Electron., E78, 180-185. Miyake, S., Watanabe, S., Murakawa, M., Kaneko, R., and Miyamoto, T. (1992), Tribological study of cubic boron nitride film, Thin Solid Films, 212, 262-266. Miyoshi, K. (1995), Structures and mechanical properties of natural and synthetic diamonds, Diamond Films Technol., 8, 153-172. Miyoshi, K. (1999), Surface Design Engineering Toward Wear-Resistant, Self-lubricating Diamond Films and Coatings, NASA TM-208905, 1-17. Miyoshi, K., Wu, R.L.C., and Garscadden, A. (1992), Friction and wear of diamond and diamondlike carbon coatings, Surf. Coat. Technol., 54/55, 428-434. Miyoshi, K., Wu, R.L.C., Garscadden, A., Barnes, P.N., and Jackson, H.E. (1993), Friction and wear of plasma-deposited diamond films, J. Appl. Phys., 74, 4446-4450. Molian, P.A., Janvrin, B., and Molian, A.M. (1993), Laser chemical vapor deposition of fluorinated diamond thin films for solid lubrication, Wear, 165, 133-140. Murakawa, M. (1997), Surface coating of superhard materials for tool applications, Mater. Sci. Forum, 246, 1-28. Murakawa, M. and Watanabe, S. (1990). Possibility of coating cubic BN films on various substrates, Surf. Coat. Technol., 43, 145-153. Murakawa, M., Watanabe, S., and Miyake, S. (1991), Manufacture of c-BN films with improved adhesion, Mater. Sci. Eng., A140, 753-758. Olson, J.M. and Dawes, M.J. (1996), Examination of the material properties and performance of thindiamond film cutting tool inserts produced by arc-jet and hot-filament chemical vapor deposition, J. Mater. Res., 11, 1765-1775. Pate, B.B., Waclawski, B.J., Stefan, P.M., Binns, C., Ohta, T., Hecht, M.H., Jupiter, P.J., Shek, M.L., Pierce, D.T., and Swanson, N. (1982), Diamond (111) surface: a dilemma resolved, Physica B, 117/118, 783-785. Pimenov, S., Smolin, A.A., Obraztsova, E.D., Konov, V.I., Bogli, U., Blatter, A., Loubnin, E.N., Maillat, M., Leijala, A., Burger, J., and Hintermann, H.E. (1996), Tribological properties of smooth diamond films, Appl. Surf. Sci., 92, 106-114. Prengel, H.G., Pfouts, W.R., and Santhanam, A.T. (1998), State of the art in hard coatings for carbide cutting tools, Surf. Coat. Technol., 102, 183-190, 93. Ramesham, R. (1999), Fabrication of diamond microstructures for microelectromechanical systems (MEMS) by a surface micromachining process, Thin Solid Films, 340, 1-6. Ramesham, R. and Rose, M.F. (1998), Polishing of polycrystalline diamond by hot nickel surface, Thin Solid Films, 320, 223-227.
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25 Self-assembled Monolayers for Controlling Hydrophobicity and/or Friction and Wear 25.1 25.2
Introduction ..................................................................... 909 A Primer to Organic Chemistry ..................................... 912 Electronegativity/Polarity • Classification and Structure of Organic Compounds • Polar and Nonpolar Groups
25.3
Bharat Bhushan The Ohio State University
25.4 25.5
Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains ..... 917 Tribological Properties..................................................... 921 Conclusions ...................................................................... 924
25.1 Introduction Reliability of microdevices, also commonly referred to as microelectromechanical systems (MEMS), as well as magnetic storage devices (which include magnetic rigid disk drives, flexible disk drives, and tape drives), require the use of molecularly thick films for protection of sliding surfaces (Bhushan et al., 1995a; Bhushan, 1996, 1998a, 1999a). A solid or liquid film is generally necessary for acceptable friction and wear properties of sliding interfaces. A small quantity of liquid present between some surfaces can substantially increase the static friction as a result of formation of menisci or adhesive bridges (Bhushan, 1999b). Smooth surfaces in contact, and in the presence of a small amount of liquid, generally tend to adhere or stick strongly and can exhibit high static friction (Bhushan, 1996). It becomes a major concern in devices operating at ultralow loads as the liquid-mediated adhesive force may be on the same order as the external load and may lead to high friction and wear. The source of the liquid film can be either a preexisting film of liquid and/or capillary condensates of water vapor from the environment. If the liquid wets the surface (0 ≤ θ < 90°, where θ is the contact angle* between the liquid-vapor interface and the liquid-solid interface at the solid-liquid-vapor threephase contact line and surface (Figure 25.1(a)), the liquid surface is thereby constrained to lie parallel with the surface (Ulman, 1995), and the complete liquid surface must therefore be concave in shape (Figure 25.1(b)). Surface tension results in a pressure difference across any meniscus surface, referred to *The direct measurement of contact angle is most widely made from sessile drops. The angle is generally measured by aligning a tangent with the drop profile at the point of contact with the solid surface using a telescope equipped with a goniometer eyepiece.
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FIGURE 25.1 (a) Schematic of a sessile drop on a solid surface and the definition of contact angle; and (b) formation of meniscus bridges as a result of liquid present at an interface.
as capillary pressure or Laplace pressure, and is negative for a concave meniscus (Bhushan, 1999b). The negative Laplace pressure results in an intrinsic attractive (adhesive) force that depends on the interface roughness (local geometry of interacting asperities and number of asperities), surface tension, and contact angle. During sliding, frictional effects — due not only to external load but also to intrinsic adhesive force — need to be overcome. High measured static friction force contributed largely by liquid-mediated adhesion (meniscus contribution) is generally referred to as stiction. One of the ways to minimize the effect of liquid-mediated adhesion, in addition to an increase in surface roughness, is to select hydrophobic (water-fearing) rather than hydrophilic (water-loving) surfaces. If a liquid lubricant film needs to be applied for control of friction, stiction, and wear, it should be thin (about half of the composite roughness of the interface) to minimize the stiction contribution (Bhushan, 1998b, 1999b). Thus, for ultra-smooth surfaces with RMS roughness on the order of a few nanometers, molecularly thick liquid films are required for liquid lubrication. If the interface requires significant sliding (e.g., in micromotors, microactuators, and magnetic disk drives), the interface should exhibit low friction and wear properties. High static friction or high adhesion is also one of the major problems, because the devices are used over a range of humidities. Some devices may require little relative motion but the surfaces may come in close proximity, in which case stiction can be a major issue. An example is an optical switch using oscillating mirrors to switch optical fibers; oscillating mirrors sometimes contact the substrate and stiction can be an issue. In these cases, hydrophobicity of the surface is the major requirement. Silicon used in the construction of microdevices can be treated to make it hydrophobic or hydrophilic. A hydrophilic surface is desirable if a hydrophobic film is to be anchored on it. Bulk silicon and polysilicon film are dipped in hydrofluoric acid (HF) or hydrogen peroxide (H2O2) to generate either a hydrophobic or hydrophilic surface, respectively (e. g., Maboudian, 1998; Scherge and Schaefer, 1998). In HF etching of silicon, hydrogen passivates the silicon surface by saturating the dangling bonds and results in a hydrogen-terminated silicon surface that is responsible for less adsorption of water. However, after exposure of the treated surface to the environment, it re-oxidizes, which can adsorb water and thus the surface again becomes hydrophilic. H2O2 treatment generates a thin oxide layer (Si-Ox) that is receptive to water.
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The surfaces can be either treated or coated with a liquid of low surface tension or a certain solid film to make them hydrophobic and/or to control friction, stiction, and wear. The classical approach to lubrication uses freely supported multimolecular layers of liquid lubricants (Bowden and Tabor, 1950; Bhushan, 1996, 1999a,b; Bhushan and Zhao, 1999). Boundary lubricant films are formed either by physisorption, chemisorption, or chemical reaction. The physisorbed films can be either monomolecular or polymolecular thick. The chemisorbed films are monomolecular, but stoichiometric films formed by chemical reaction can be multilayered. In general, the stability and durability of surface films decrease in the following order: chemically reacted films, chemisorbed films, and physisorbed films. A good boundary lubricant should have a high degree of interaction between its molecules and the sliding surface. As a general rule, liquids are good lubricants when they are polar and thus able to grip solid surfaces (or be adsorbed). Polar lubricants contain reactive functional end groups. Boundary lubrication properties are also dependent on molecular conformation and lubricant spreading. It should be noted that liquid films with a thickness on the order of a few nanometers may be discontinuous and may deposit in an island form with nonuniform thickness and lateral resolution on the nanometer scale. Solid films are also commonly used for controlling hydrophobicity and/or friction and wear. Hydrophobic films have nonpolar terminal groups (to be described later) that repel water. These films have low surface energy (15 to 30 dyn/cm) and high contact angle (θ ≥ 90°), which minimize wetting (e.g., Zisman, 1959; Schrader and Loeb, 1992; Neumann and Spelt, 1996). It should be noted that these films do not totally eliminate wetting. Multimolecularly thick (few tenths of a nanometer) films of conventional solid lubricants have been studied. Hansma et al. (1992) reported the deposition of multimolecularly thick, highly oriented PTFE films from the melt or vapor phase, or from solution by a mechanical deposition technique, by dragging the polymer at controlled temperature, pressure, and speed against a smooth glass substrate. Scandella et al. (1994) reported that the coefficient of nanoscale friction of MoS2 platelets on mica, obtained by exfoliation of lithium intercalated MoS2 in water, was a factor of 1.4 less than that of mica itself. However, MoS2 is reactive to water, and its friction and wear properties degrade with an increase in humidity (Bhushan, 1999b). Amorphous diamond-like carbon (DLC) coatings can be produced with extremely high hardness and are commercially used for wear applications (Bhushan, 1999c). Their largest application is in magnetic storage devices (Bhushan, 1996). Doping of the DLC matrix with elements such as silicon, fluorine, oxygen, and nitrogen (Dorfman, 1992; Grischke et al., 1995) influences the contact angle (or surface energy) and tribological properties. Oxygen and nitrogen reduce the contact angle (or increase the surface energy), due to the strong polarity formed when these elements are bonded to carbon. On the other hand, silicon and fluorine increase the contact angle from 70 to 100° (or reduce the surface energy from 20 to 40 dyn/cm), making them hydrophobic (Butter et al., 1997; Grischke et al., 1998). Nanocomposite coatings with a diamond-like carbon (a-C:H) network and a glass-like (a-Si:O) network are deposited using a PECVD (plasma-enhanced chemical vapor deposition) technique in which plasma is formed from a siloxane precursor using a hot filament. For a fluorinated DLC, CF4 as the fluorocarbon source is added to an acetylene plasma. In addition, fluorination of DLC can be achieved by the post-deposition treatment of DLC coatings in a CF4 plasma. Fluorine- and siliconcontaining DLC coatings mainly reduce their polarity due to the loss of sp2-bonded carbon (polarization potential of the involved π electrons) and dangling bonds of the DLC network. Silicon and fluorine are unable to form double bonds, so they force carbon into an sp3 bonding state (Grischke et al., 1998). Friction and wear properties of both silicon-containing and fluorinated DLC coatings have been reported to be superior to that of conventional DLC coatings (Donnet et al., 1997; Kester et al., 1999). These films may not be well-organized or uniform, and are too thick for microdevices. Organized and dense molecular-scale layers of, preferably, long-chain organic molecules are known to be superior lubricants on both macro- and microscales as compared with freely supported multimolecular layers (Bhushan et al., 1995b; Bhushan, 1999a). Common methods to produce monolayers and thin films are by Langmuir–Blodgett (LB) deposition and by chemical grafting of organic molecules to realize self-assembled monolayers or SAMs (Ulman, 1991, 1996). In the LB technique, organic molecules from suitable amphiphilic molecules are first organized at the air-water interface and then transferred to a solid surface to form mono- or multilayers (Zasadzinski et al., 1994). In the case of SAMs, the
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functional groups of molecules chemisorb onto a solid surface, which results in the spontaneous formation of robust, highly ordered and oriented, dense monolayers chemically attached to the surface (Ulman, 1996). In both cases, the organic molecules used have well-distinguished amphiphilic properties (hydrophilic functional head and a long hydrophobic, aliphatic tail) so that adsorption of such molecules on an active inorganic substrate leads to their firm attachment to the surface. Direct organization of SAMs on the solid surfaces allows coating in the tight areas, such as the bearing and journal surfaces in an assembled bearing. The weak adhesion of classical LB films to the substrate surface restricts their lifetimes during sliding, but certain SAMs of films can be very durable (Bhushan et al., 1995b). As a result, SAMs are of great interest in tribological applications. An overview of unbonded and chemically bonded multimolecular layers of liquid lubricants can be found in various references (Bhushan, 1996, 1999a,b; Bhushan and Zhao, 1999). This chapter focuses on SAMs for low friction and wear and/or low stiction (with high hydrophobicity). SAMs are produced by various organic precursors. First, a primer to organic chemistry is presented, followed by an overview of suitable substrates, organic molecules, and end groups in the organic chains for SAMs, and then an overview of tribological properties and some concluding remarks.
25.2 A Primer to Organic Chemistry All organic compounds contain the carbon (C) atom. Carbon, in combination with hydrogen, oxygen, nitrogen, and sulfur results in a large number of organic compounds. The atomic number of carbon is 6, and its electron structure is 1s2 2s2 2p2. Two stable isotopes of carbon, 12C and 13C, exist. With four electrons in its outer shell, carbon forms four covalent bonds, with each bond resulting from two atoms sharing a pair of electrons. The number of electron pairs that two atoms share determines whether or not the bond is single or multiple. In a single bond, only one pair of electrons is shared by the atoms. Carbon can also form multiple bonds by sharing two or three pairs of electrons between the atoms. For example, the double bond formed by sharing two electron pairs is stronger than a single bond and also shorter than a single bond. An organic compound is classified as saturated if it contains only the single bond, and unsaturated if the molecules possess one or more multiple carbon-carbon bonds.
25.2.1 Electronegativity/Polarity When two different kinds of atoms share a pair of electrons, a bond is formed in which electrons are shared unequally: one atom assumes a partial positive charge and the other a negative charge with respect to each other. This difference in charge occurs because the two atoms exert unequal attraction for the pair of shared electrons. The attractive force that an atom of an element has for shared electrons in a molecule or polyatomic ion is known as its electronegativity. Elements differ in their electronegativities. A scale of relative electronegatives, in which the most electronegative element, fluorine, is assigned a value of 4.0, was developed by L. Pauling. Relative electronegativities of the elements in the Periodic Table can be found in most undergraduate chemistry textbooks (e.g., Hein et al., 1997). The relative electronegativity of the nonmetals is high as compared to that of metals. The relative electronegativities of selected elements of interest here with high values are presented in Table 25.1. The polarity of a bond is determined by the difference in TABLE 25.1 Relative Electronegativity electronegativity values of the atoms forming the bond. If the of Selected Elements electronegativities are the same, the bond is nonpolar and the Element Relative Electronegativity electrons are shared equally. In this type of bond, there is no F 4.0 separation of positive and negative charge between atoms. If O 3.5 the atoms have greatly different electronegativities, the bond is N 3.0 very polar. A dipole is a molecule that is electrically asymmetCl 3.0 rical, causing it to be oppositely charged at two points. As an C 2.5 S 2.5 example, both hydrogen and chlorine need one electron to form P 2.1 stable electron configurations. They share a pair of electrons in H 2.1 hydrogen chloride, HCl. Chlorine is more electronegative and
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FIGURE 25.2
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Schematic representation of the formation of a polar HCl molecule.
therefore has a greater attraction for the shared electrons than does hydrogen. As a result, the pair of electrons is displaced toward the chlorine atom, giving it a partial negative charge and leaving the hydrogen atom with a partial positive charge (Figure 25.2). However, the entire HCl molecule is electrically neutral. The hydrogen atom with a partial positive charge (exposed proton on one end) can be easily attracted to the negative charge of other molecules, and this is responsible for the polarity of the molecule. A partial charge is usually indicated by δ, and the electronic structure of HCl is given as: δ+
..
δ−
H : Cl : ..
Similar to the HCl molecule, HF is polar and both behave as a small dipole. On the other hand, methane (CH4), carbon tetrachloride (CCl4), and carbon dioxide (CO2) are nonpolar. In CH4 and CCl4 , the four C-H and C-Cl polar bonds are identical; and because these bonds emanate from the center to the corners of a tetrahedron in the molecule, the effects of their polarities cancel each other. CO2 (OCO) is nonpolar because carbon-oxygen dipoles cancel each other by acting in opposite directions. Symmetric molecules are generally nonpolar. Water (H-O-H) is a polar molecule. If the atoms in water were linear, as in CO2, two O-H dipoles would cancel each other, and the molecule would be nonpolar. However, water has a bent structure with an angle of 105° between the two bonds; this is responsible for water being a polar molecule.
25.2.2 Classification and Structure of Organic Compounds Table 25.2 presents selected organic compounds grouped into classes. 25.2.2.1 Hydrocarbons Hydrocarbons are compounds that are composed entirely of carbon and hydrogen atoms bonded to each other by covalent bonds. Saturated hydrocarbons (alkanes) contain single bonds. Unsaturated hydrocarbons that contain carbon-carbon double bonds are called alkenes, and those with triple bonds are called alkynes. Unsaturated hydrocarbons that contain an aromatic ring (e.g., the benzene ring) are called aromatic hydrocarbons. 25.2.2.1.1 Saturated Hydrocarbons: Alkanes Alkanes, also known as paraffins, are saturated, straight- or branched-chain hydrocarbons, with only single covalent bonds between the carbon atoms. The general molecular formula for alkanes is CnH2n+2 ,
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TABLE 25.2(a)
Names and Formulae of Selected Hydrocarbons
Name Saturated hydrocarbons Straight-chain alkanes: e.g., Methane Ethane Alkyl groups: e.g., Methyl Ethyl Unsaturated hydrocarbons Alkenes: e.g., Ethene Propene Alkynes: e.g., Acetylene Aromatic hydrocarbons e.g., Benzene
Formula CnH2n+2 CH4 C2H6 or CH3CH3 CnH 2n+1 –CH3 –CH2CH3 (CH2)n C2H4 or CH2CH2 C3H6 or CH3CHCH2 HCCH
where n is the number of carbon atoms in the molecule. Each carbon atom is connected to four other atoms by four single covalent bonds. These bonds are separated by angles of 109.5° (the angle by lines drawn from the center of a regular tetrahedron to its corners). Alkane molecules contain only carboncarbon and carbon-hydrogen bonds, which are symmetrically directed toward the corners of a tetrahedron. Therefore, alkane molecules are essentially nonpolar. Common alkyl groups have the general formula Cn H2n+1 (one hydrogen atom less than the corresponding alkane). The missing H atom can be detached from any carbon in the alkane. The name of the group is formed from the name of the corresponding alkane by replacing -ane with the -yl ending. Some examples are shown in Table 25.2(a). 25.2.2.1.2 Unsaturated Hydrocarbons Unsaturated hydrocarbons consist of three families of compounds that contain fewer hydrogen atoms than the alkane with the corresponding number of carbon atoms, and contain multiple bonds between carbon atoms. These include alkenes (with carbon-carbon double bonds), alkynes (with carbon-carbon triple bonds), and aromatic compounds (with benzene rings that are arranged in a six-membered ring with one hydrogen atom bonded to each carbon atom and three carbon-carbon double bonds). Some examples are shown in Table 25.2(a). 25.2.2.2 Alcohols, Ethers, Phenols, and Thiols Organic molecules with certain functional groups are synthesized for their desirable properties. Alcohols, ethers, and phenols are derived from the structure of water by replacing the hydrogen atoms of water with alkyl groups (R) or aromatic (Ar) rings. For example, phenol is a class of compounds having a hydroxyl group attached to an aromatic ring (benzene ring). Organic compounds that contain the -SH group are analogs of alcohols, and known as thiols. Some examples are shown in Table 25.2(b).
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TABLE 25.2(b) Names and Formulas of Selected Alcohols, Ethers, Phenols, and Thiols Name
Formula
Alcohols: e.g., Methanol Ethanol Ethers: e.g., Dimethyl ether Diethyl ether Phenols Thiols: e.g., Methanethiol
R–OH CH3OH CH3CH2OH R–O–R′ CH3–O–CH3 CH3CH2–O–CH2CH3 OH C6H5OH or –SH CH3SH
Note: The letters R- and R′- represent an alkyl group. The R- groups in ethers can be the same or different and can be alkyl or aromatic (Ar) groups.
TABLE 25.2(c) and Ketones
Names and Formulas of Selected Aldehydes
Name
Formula O
Aldehydes:
RCHO or
R–C–H O
e.g., Methanal or formaldehyde Ethanal or acetaldehyde Ketones:
ArCHO or Ar–C–H HCHO CH3CHO O
RCOR′ or R–C–R′ O
RCOAr or R–C–Ar O
e.g., Butanone or methyl ethyl ketone
ArCOAr or Ar–C–Ar CH3COCH2CH3
Note: The letters R and R′ represent an alkyl group, and Ar represents an aromatic group.
25.2.2.3 Aldehydes and Ketones Both aldehydes and ketones contain the carbonyl group, CO, a carbon-oxygen double bond. Aldehydes have at least one hydrogen atom bonded to the carbonyl group, whereas ketones have only alkyl or aromatic groups bonded to the carbonyl group. The general formula for the saturated homologous series of aldehydes and ketones is CnH2nO. Some examples are shown in Table 25.2(c). 25.2.2.4 Carboxyl Acids and Esters The functional group of carboxylic acids is known as a carboxyl group and represented as -COOH. Carboxylic acids can be either aliphatic (RCOOH) or aromatic (ArCOOH). The carboxylic acids with even numbers of carbon atoms, n, ranging from 4 to about 20 are called fatty acids (e.g., n = 10, 12, 14, 16, and 18 are called capric acid, lauric acid, myristic acid, palmitic acid, and stearic acid, respectively).
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TABLE 25.2(d) Names and Formulae of Selected Carboxylic Acids and Esters Name
Formula O
Carboxylic acida :
RCOOH or
e.g., Methanoic acid (formic acid) Ethanoic acid (acetic acid) Octadecanoic acid (stearic acid) Estersb :
ArCOOH or Ar–C–OH HCOOH CH3COOH CH3(CH2)16COOH O
R–C–OH O
{
R–C–O–R′
{
RCOOR′ or
acid alcohol
e.g., Methyl propanoate
CH3CH2COOCH3
a The letter R represents an alkyl group and Ar represents an aromatic group b The letter R represents a hydrogen, alkyl group, or aromatic group; and R′ represents an alkyl or aromatic group.
TABLE 25.2(e) Names and Formulae of Selected Organic Nitrogen Compounds (Amides and Amines) Name
Formula O
Amides: e.g., Methanamide (formamide) Ethanamide (acetamide)
RCONH2 or HCONH2 CH3CONH2
Amines:
RNH2
R–C–NH2
H or R–N H
e.g., Methylamine Ethylamine
R2NH R 3N CH3NH2 CH3CH2NH2
Note: The letter R represents an alkyl or aromatic group.
Esters are alcohol derivates of carboxylic acids. Their general formula is RCOOR′, where R can be hydrogen, an alkyl group, or an aromatic group, and R′ can be an alkyl or aromatic group, but not a hydrogen. Esters are found in fats and oils. Some examples are shown in Table 25.2(d). 25.2.2.5 Amides and Amines Amides and amines are organic compounds containing nitrogen. Amides are nitrogen derivates of carboxylic acids. The carbon atom of a carbonyl group is bonded directly to the nitrogen atom of an -NH2, -NHR, or -NR2 group. The characteristic structure of amide is RCONH2 . An amine is a substituted ammonia molecule that has the general formula RNH2, R2NH, or R3N, where R is an alkyl or aromatic group. Some examples are shown in Table 25.2(e).
25.2.3 Polar and Nonpolar Groups Table 25.3(a) summarizes polar and nonpolar groups commonly used in the construction of hydrophobic and hydrophilic molecules. Table 25.3(b) lists the relative polarity of selected polar groups (Mohrig et al., 1998). Thiol, silane, carboxylic acid, and alcohol (hydroxyl) groups are the most commonly used polar
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TABLE 25.3(a) Some Examples of Polar (hydrophilic) and Nonpolar (hydrophobic) Groups Name
Formula
Polar: Alcohol (hydroxyl) Carboxyl Aldehyde Ketone
–OH –COOH –COH O
Ester Carbonyl Ether Amine Amide
R–C–R –COO– CO R–O–R –NH2 O
–C–NH2 Phenol Thiol Trichlorosilane Nonpolar: Methyl Trifluoromethyl
OH –SH SiCl3 –CH3 –CF3
Aryl (benzene ring) Note: The letter R represents an alkyl group.
TABLE 25.3(b) Organic Groups Listed in Increasing Order of Polarity Alkanes Alkenes Aromatic hydrocarbons Ethers Trichlorosilanes Aldehydes, ketones, esters, carbonyls Thiols Amines Alcohols, phenols Amides Carboxylic acids
anchor groups for attachment to surfaces. Methyl and trifluoromethyl are commonly used end groups for hydrophobic film surfaces.
25.3 Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains Much of the research in preparation of SAMs has been carried out for the so-called soft lithographic technique (Tien et al., 1998; Xia and Whitesides, 1998). This is a nonphotolithographic technique. Photolithography is based on a projection-printing system used for projection of an image from a mask to a thin-film photoresist, and its resolution is limited by optical diffraction limits. In soft lithography, an elastomeric stamp or mold is used to generate micropatterns of SAMs by contact printing (known as microcontact printing or µCP (Kumar and Whitesides, 1993), by embossing (imprinting) (Chou et al., 1996), or by replica molding (Xia et al., 1996), all of which circumvent the diffraction limits of
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FIGURE 25.3
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Schematic of a self-assembled monolayer on a surface and the associated forces.
photolithography. The stamps are generally cast from photolithographically generated patterned masters, and the stamp material is generally polydimethylsiloxane (PDMS). In µCP, the ink is a SAM precursor to produce nanometer-thick resists with lines thinner than 100 nm. Although soft lithography requires little capital investment, it is doubtful that it would ever replace well-established photolithography. However, µCP and embossing techniques can be used to produce microdevices that are substantially cheaper and more flexible in choice of material for construction than conventional photolithography (e.g., SAMs and non-SAM entities for µCP and elastomers for embossing). Other applications for SAMs are in the areas of bio/chemical and optical sensors, for use as drugdelivery vehicles, and in the construction of electronic components (Ulman, 1991; Service, 1994). Bio/chemical sensors require the use of highly sensitive organic layers with tailored biological properties that can be incorporated into electronic, optical, or electrochemical devices. Self-assembled microscopic vesicles are being developed to ferry potentially lifesaving drugs to cancer patients. By getting organic, metal, and phosphonate molecules (complexes of phosphorous and oxygen atoms) to assemble themselves into conductive materials, these can be produced as self-made sandwiches for use as electronic components. The application of interest here is an application requiring hydrophobicity and/or low friction and wear. SAMs are formed as a result of spontaneous self-organization of functionalized, long-chain organic molecules onto the surfaces of appropriate substrates into stable, well-defined structures (Figure 25.3). The final structure is close to or at thermodynamic equilibrium; as a result, it tends to form spontaneously and rejects defects. SAMs are named based on the terminal group, followed by the backbone chain and the head group (or type of compound formed at the surface). For a SAM to control friction, wear, and hydrophobicity, it should be strongly adherent to the substrate, and the terminal group (tail group or the group at the free end) of the organic molecular chain should be nonpolar. For strong attachment of the organic molecules to the substrate, the other end of the molecular chain (head group) should contain a polar end group. The head group provides the more exothermic process (energies on the order of tens of kcal/mol); that is, it results in an apparent pinning of the head group to a specific site on the surface through a chemical bond. Thus, the organic molecule of a SAM should contain a nonpolar end group on one end and polar end group on the other. Furthermore, molecular structure and any crosslinking will have a significant effect on friction and wear performance. The substrate surface should have a high surface energy, so that there will be a strong tendency for molecules to adsorb to the surface. The surface should be highly functional, with polar groups and dangling bonds (generally unpaired electrons), so that they can react with organic molecules and provide a strong bond. Because of the exothermic head
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TABLE 25.4
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Selected Substrates and Precursors Commonly Used for SAMs Formation
Substrate Au Au Au Au Si/SiO2, glass Si/Si-H Metal oxides (e.g., Al2O3, SnO2, TiO2)
Precursor R SH (thiol) Ar SH (thiol) RSSR′ (disulfide) RSR′ (sulfide) R SiCl3 (trichlorosilane) RCOOH (carboxyl) RCOOH (carboxyl)
Binding with Substrate RS-Au ArS-Au RS-Au Si-O-Si (siloxane) R-Si RCOO-….MOn
Note: R represents alkane (CnH2n+2) and Ar represents aromatic hydrocarbon. It consists of various surface active headgroups, mostly with methyl terminal group.
group-substrate interactions, molecules try to occupy every available binding site on the surface; and during this process, they generally push together molecules that have already adsorbed. The process results in the formation of crystalline molecular assemblies. The interactions between molecular chains are van der Waals or electrostatic in nature, with energies on the order of a few (<10) kcal/mol, and exothermic. The molecular chains in SAMs are not perpendicular to the surface; the tilt angle depends on the anchor group as well as on the substrate and the spacer group. For example, the tilt angle for alkanethiolate on Au is about 30 to 35° with respect to substrate normal. The requirement is that the space be filled optimally. SAMs are usually produced by immersing a substrate in the solution containing precursor (ligand) that is reactive to the substrate surface, or by exposing the substrate to the vapor of the reactive chemical species (Ulman, 1991). Table 25.4 lists selected systems that have been used for the formation of SAMs (Xia and Whitesides, 1998). The backbone of a SAM is usually an alkyl chain (CnH2n+1) or a derivatized alkyl group. By attaching different terminal groups at the surface (or surface group), the film surface can be made to attract or repel water. The commonly used terminal group of a hydrophobic film with low surface energy, in the case of a single alkyl chain, is the nonpolar methyl (CH3) group; the other is trifluoromethyl (CF3). For a hydrophilic film, the commonly used terminal groups are alcohol (OH) or carboxyl acid (COOH) groups. Surface-active head groups most commonly used are thiol (SH), silane (e. g., trichlorosilane or SiCl3), and carboxyl (COOH) groups. The substrates most commonly used are gold, silver, platinum, copper, hydroxylated (activated) surfaces of SiO2 on Si, Al2O3 on Al and glass, and hydrogen-terminated single-crystal silicon (H-Si). Hydroxylation of oxide surfaces is important to make them hydrophilic. For example, thermally grown silica can be activated by sulfochromic treatment. The sample is dipped in a solution consisting of 100 mL of concentrated H2SO4 , 5 mL water, and 2 g potassium bichromate for 3 to 15 min (Bhushan et al., 1995b). The sample is then rinsed with flowing pure water. This results in a surface with silanol groups (-Si-OH), resulting in a surface that is hydrophilic (Figure 25.4). Bulk silicon, polysilicon film, or SiO2 film surfaces can also be treated to produce an activated silica surface by immersion in about three parts H2SO4 and one part H2O2 at temperatures ranging from ambient to 80°C. For organic molecules to pack together and provide a better ordering, a
FIGURE 25.4 treatment.
Schematic showing the hydroxylation process occurring on a silica surface through a sulfochromic
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FIGURE 25.5
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Schematic of a methyl-terminated, n-alkylsiloxane monolayer on Si/SiO2.
substrate for given molecules should be selected such that the cross-sectional diameter of the backbone of the molecule is equal to or smaller than the distance between the anchor groups attached to the substrate. Epitaxial Au film on glass, mica, or single-crystal silicon produced by e-beam evaporation is commonly used because it can be deposited on smooth surfaces as a film that is atomically flat and defect-free. For the case of alkanethiolate film, the advantage of Au substrate over SiO2 substrate is that it results in better ordering because the cross-sectional diameter of the alkane molecule is slightly smaller than the distance between sulfur atoms attached to the Au substrate (~0.53 nm). The thickness of the film can be controlled by varying the length of the hydrocarbon chain, and the properties of the film surface can be modified by the terminal group. Some of the SAMs have been widely reported. SAMs of long-chain fatty acids CnH2n+1COOH or (CH3) (CH2)nCOOH (n = 10, 12, 14, or 16) on glass or alumina are one class of films studied since the 1950s (Bowden and Tabor, 1950; Zisman, 1959). Probably the most studied SAMs to date are n-alkanethiolate* monolayers CH3(CH2)nS-prepared from adsorption of alkanethiol -(CH2)nSH solution onto an Au film (Xia and Whitesides, 1998) and n-alkylsiloxane** monolayers produced by adsorption of n-alkyltrichlorosilane -(CH2)nSiCl3 solution onto hydroxylated Si/SiO2 substrate (Wasserman et al., 1989) with siloxane (Si-O-Si) binding (Figure 25.5). SAMs of n-alkyltrichlorosilanes such as methyl-terminated, octadecyltrichlorosilane (OTS) CH3(CH2)17SiCl3 compound on hydroxylated SiO2 on silicon wafer are also a commonly studied film. Jung et al. (1998) have produced organosulfur monolayers-decanethiol (CH3)(CH2)9SH, didecyl disulfide CH3(CH2)9S-S(CH2)9CH3, and didecyl sulfide CH3(CH2)9-S(CH2)9CH3 on Au films. Geyer et al. (1999) have produced monolayers of 1,1′-biphenyl-4-thiol (BPT) on Au film surface, in which the backbone of the film consists of two phenyl rings with a hydrogen end group (Figure 25.6). Rings are expected to be stiff; therefore, their tribological properties are expected to be superior to that of linear molecular structures. Crosslinking by low-energy electrons may further improve mechanical and tribological properties.
*n-Alkyl and n-alkane are used interchangeably. **Siloxane (Si-O-Si) refers to the bond and silane (SinX2n+2 which includes a covalently bonded compounds containing the elements Si and other atoms or groups such as H and Cl to form SiH4 and SiCl4, respectively) refers to the head group of the precursor. These terms are used interchangeably.
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FIGURE 25.6 Schematic of biphenylthiol (BPT) monolayer on Au and after electron-induced crosslinking. (From Geyer, W. Stadler, V., Eck, W., Zharnikov, M., Golzhauser, A. and Grunze, M. (1999), Electron-induced crosslinking of aromatic self-assembled monolayers: negative resists for nanolithography, Appl. Phys. Lett., 75, 2401-2403. With permission.)
25.4 Tribological Properties Friction and wear properties have been studied on the macro- and microscales. Macroscale tests are conducted using a so-called pin-on-disk test apparatus in which a ceramic (typically alumina or sapphire) ball is slid against a lubricated specimen (Bhushan, 1999b). Microscale tests are conducted using an atomic force/friction force microscope or AFM/FFM (Bhushan, 1999a). In AFM/FFM experiments, a sharp tip of radius ranging from about 5 to 50 nm is slid against a lubricated specimen. An Si3N4 tip is commonly used for friction studies, and a natural diamond tip is commonly used for wear and indentation studies. In early studies, the effect of chain length of the carbon atoms of fatty acid monolayers on the coefficient of friction and wear using macroscale tests was studied by Bowden and Tabor (1950) and Zisman (1959). Zisman (1959) reported that for the monolayers deposited on a glass surface sliding against a stainless steel surface, there was a steady decrease in friction with increasing chain length. At a significantly long chain length, the coefficient of friction reaches a lower limit (Figure 25.7). He further reported that monolayers having a chain length below 12 carbon atoms behaved as liquids (poor durability); those with a chain length of 12 to 15 carbon atoms behaved like a plastic solid (medium durability); and those with chain lengths above 15 carbon atoms behaved like a crystalline solid (high durability).
FIGURE 25.7 Effect of chain length (or molecular weight) on coefficient of microscale friction of stainless steel sliding on glass lubricated with a monolayer of fatty acid and contact angle of methyl iodide on condensed monolayers of fatty acid on glass. (From Zisman, W.A. (1959), Friction, durability and wettability properties of monomolecular films on solids, in Friction and Wear, Davies, R. (Ed.), Elsevier, Amsterdam, 110-148. With permission.)
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FIGURE 25.8 Effect of chain length of methyl-terminated, n-alkanethiolate over Au film AuS(CH2)nCH3 on the coefficient of microscale friction and peak bandwidth at half maximum (∆ν1/2) for the bandwidth of the methylene stretching mode [νa(CH2)]. (From McDermott, M.T., Green, J.B.D., and Porter, M.D. (1997), Scanning force microscopic exploration of the lubrication capabilities of n-alkanethiolate monolayers chemisorbed at gold: structural basis of microscopic friction and wear, Langmuir, 13, 2504-2510. With permission.)
McDermott et al. (1997) studied the effect of alkyl chain length on the frictional properties of methylterminated n-alkylthiolate CH3(CH2)nS- films chemisorbed on Au(111) using an AFM. Through an examination of the influence of the alkyl chain length with monolayers slid against Si3N4 tips, they reported that the longer chain monolayers exhibited a markedly lower friction (Figure 25.8) and a reduced propensity to wear than shorter chain monolayers. They conducted infrared reflection spectroscopy to measure the bandwidth of the methylene stretching mode [νa(CH2)], which exhibits a qualitative correlation with the packing density of the chains. It was found that the chain structures of monolayers prepared with longer chain lengths are more ordered and more densely packed in comparison to those of monolayers prepared with shorter chain lengths (Figure 25.8). They further reported that the ability of the longer chain monolayers to retain molecular scale order during shear leads to a lower observed friction. Monolayers having a chain length more than 12 carbon atoms, preferably 18 or more, are desirable for tribological applications. (Monolayers with 18 carbon atoms, octadecanethiol or ODT, films are commonly studied.) Joyce et al. (1992) reported that these films have negligible adhesive film(tungsten) tip interaction and complete passivation (hydrophobicity). Xiao et al. (1996) and Lio et al. (1997) also studied the effect of the length of the alkyl chains on the frictional properties of n-alkanethiolate films on gold and n-alkylsilane films on mica. Friction was found to be particularly high with short chains of less than eight carbon atoms. Thiols and silanes exhibit similar friction force for the same n when n > 11; while for n < 11, silanes exhibit higher friction, larger than that for thiols by a factor of about 3 for n = 6. The increase in friction was attributed to the large number of dissipative modes in the less-ordered chains that occurs when going from a thiol to a silane anchor or when increasing n. Longer chains (n > 11), stabilized by van der Waals attraction, form more compact and rigid layers and act as better lubricants. Srinivasan et al. (1998) also reported that octadecyltrichlorosilane (C18) films deposited on oxidized (activated) polysilicon films reduced static friction by a factor of 20 with respect to the oxide films. Fluorinated carbon (fluorocarbon) molecules are commonly used for lubrication (Bhushan, 1996b). Kim et al. (1997, 1999) studied frictional properties of fluorinated n-alkanethiolate films adsorbed on single-crystal gold film. They reported a factor of 3 increase in the friction in going from a hydrogenated (methyl-terminated) SAM (contact angle of 82° with methylene iodide) to the fluorinated (trifluoromethyl) SAM (contact angle of 78° with methylene iodide). The latter type of SAM surfaces can be produced as “Teflon-like” to have low surface energies. They suggested that fluorinated monolayers exhibit higher frictional properties due to tighter packing at the interface, which arises from the larger van der Waals
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FIGURE 25.9
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Schematic of a methyl-terminated octadecyldimethylchlorosilane monolayer on Si/SiO2.
radii of the fluorine atoms. Subsequent steric and rotational factors between adjacent terminal groups give rise to long-range multimolecular interactions in the plane of the CF3 groups. When these energetic barriers are overcome in the film structure, more energy is imparted to the film during sliding and results in higher friction for the fluorinated films. Liu et al. (1996) studied the effect of humidity on SAMs with hydrophobic surfaces (dihexadecyldimethylammonium, including two C16 substituents) and hydrophilic surfaces [(16, 16′-dihydroxydihexadecyl)dimethylammonium, including two HOC16]. They reported that the friction force of the hydrophobic film (contact angle = 62°) is an order of magnitude lower than that of a hydrophilic film (contact angle = 7°). NH2- and SO3H-terminated silane-based SAMs were deposited on activated single-crystal silicon and polysilicon films by Tsukruk et al. (1998). They used various polymer molecules for the backbone, and reported that these films exhibited high adhesion and friction in AFM experiments. Cappings of NH2-modified surfaces (3-aminopropyltriethoxysilane) with rigid and soft polymer layers resulted in a significant reduction in adhesion to a level lower than that of untreated surface. Liu et al. (1996) also studied the effect of velocity on the coefficient of friction of these films. They found that a peak in the friction vs. velocity measurements exists. Shearing on a surface monolayer of certain organic films may induce local phase transition in the film, which is related to its structure and bulk chain melting. Bhushan et al. (1995a,b) conducted detailed micro- and macroscale friction and wear studies on SAMs and LB films and their underlayers. The SAMs used were methyl-terminated octadecyldimethylchlorosilane (C18) films onto an Si(100) wafer covered with a thermally grown hydroxylated SiO2 layer (Figure 25.9). In these films, two of the chlorine atoms of trichlorosilane were replaced by methyl groups. This kind of silane still becomes bound to the silica surface, but crosslinking of the chains by siloxane (Si-O-Si) bond does not take place. This increases the space between the chains for more ordered layers. The structure of the LB film consists of an octadecylthiol (ODT)-coated gold sample (gold films thermally evaporated onto single-crystal silicon) on top of which a single, upper inverted bilayer of zinc arachidate (C20, ZnA) was deposited by the LB technique (Figure 25.10). Note that ZnA is weakly bonded by van der Waals forces to the ODT underlayer. Macro- and microscale friction and microwear data are summarized in Table 25.5 and Figure 25.11. Note that the C18 film exhibits the lowest coefficient of microscale friction of 0.018 as compared with other samples measured in this study (the coefficient of friction of ZnA film is ~0.03). The coefficient of microscale friction for ZnA film is comparable to that of the ODT layer and lower than that of the Au film. The microwear resistance of C18 film is much better than ZnA
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FIGURE 25.10
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Schematic of the zinc arachidate LB film on ODT with a gold underlayer.
TABLE 25.5 Typical RMS Roughness and Coefficients of Microscale and Macroscale Friction Values of Various Samples Sample Si(100) SiO2/Si C18/SiO2/Si Au/Si ODT/Au/Si ZnA/ODT/Au/Si
RMS Roughness (nm)a
Coefficient of Microscale Frictionb
Coefficient of Macroscale Frictionc
0.12 0.21 0.16 1.16 0.92 0.55
0.03 0.03 0.018 0.04 0.03 0.03
0.33 0.19 0.07 0.13 0.14 0.16
Measured on 1 µm × 1 µm scan area using AFM. Si3N4 tip with a radius of about 30 to 50 nm at normal load in the range of 10 to 200 nN and scanning speed of 4 µm/s on a 1 µm × 1 µm scan area. c Alumina ball with 3-mm radius at normal loads of 0.1 N and average sliding speed of 0.8 mm/s. a
b
and Au films, and is comparable with that of SiO2 film. The C18 films can withstand much higher than normal load of 40 µN as compared with 200 nN for the case of ZnA films (Figure 25.12). Nanomechanical studies on SAMs have been conducted using an AFM (Salmeron et al., 1993; Bhushan et al., 1995b; Liu et al., 1998). Nanoindentation studies conducted by Bhushan et al. (1995b) showed that C18 films are more rigid than ZnA films, which may be responsible for the high wear resistance of C18 films. For comparison, macroscale friction and wear data on C18 and ZnA films are next presented (Bhushan et al., 1995b). The coefficient of friction values after they reach a steady-state value are presented in Table 25.5. Representative profiles of the coefficient of friction as a function of sliding distance (time) are presented in Figure 25.13. A significant increase in the coefficient of friction during sliding suggests that the interface has degraded and the inflection point in the friction curves is taken as the end of life. Note that C18 film exhibits the longest durability, as compared to ZnA and ODT films. Trends in macroscale friction and wear data are comparable to that in microscale data.
25.5 Conclusions Exposure of microdevices to a humid environment results in condensates of water vapor from the environment. Condensed water or a preexisting film of liquid forms concave meniscus bridges between the mating surfaces. The negative Laplace pressure present in the meniscus results in an intrinsic attractive
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FIGURE 25.11 Microwear depth (a) as a function of normal load after one scan cycle, and (b) as a function of number of scan cycles at the normal load indicated for various films using a square-pyramidal natural diamond tip with a radius of about 100 nm in an AFM. (From Bhushan, B., Kulkarni, A.V., Koinkar, V.N., Boehm, M., Odoni, L., Martelet, C., and Belin, M. (1995b), Microtribological characterization of self-assembled and Langmuir-Blodgett monolayers by atomic and friction force microscopy, Langmuir, 11, 3189-3198. With permission.)
(adhesive) force that depends on the interface roughness, surface tension, and contact angle. The adhesive force can be significant in an interface with ultrasmooth surfaces and it can be on the same order as the external load if the latter is small, such as in magnetic storage devices and microdevices. Surfaces with high hydrophobicity can be produced either by surface treatment or by the application of hydrophobic films. In many applications, these films are expected to provide low friction and wear. To minimize high static friction (stiction), and/or because of small clearances, these films should be molecularly thick. Liquid films of low surface tension or certain hydrophobic solid films can be used. Ordered molecular assemblies with high hydrophobicity can be engineered using chemical grafting of various polymer molecules with suitable functional head groups and nonpolar terminal end groups. A class of selfassembled monolayers (or SAMs) with a polar group chemically attached to an activated substrate have been produced. Many of these films exhibit high hydrophobicity and low friction and wear. One of the most extensively studied SAM films is made of alkanethiol molecules, long hydrocarbon chains with a sulfur atom at one terminus and a methyl group at another terminus for a hydrophobic film. A substrate of a gold (or silver) film is dipped into a solution of alkanethiol; the sulfur atoms attach to the gold. The distance between the sulfur atoms adsorbed on the surface is about the same as the cross-sectional diameter of the alkane molecule, resulting in a well-packed film. The film thickness can be controlled by the length of the hydrocarbon chain and the properties of the film can be modified by the terminal group. Flexibility in choosing the backbone chain length, functional head groups, and nonpolar terminal group enables the adaptability of the grafting process for lubrication purposes. Based on limited tribological studies of SAM films, these films exhibit attractive hydrophobic and tribological properties. SAM films should find many tribological applications, including use in microdevices.
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FIGURE 25.12 Surface profiles showing the worn regions (center, 1 µm × 1 µm) after one scan cycle (in Figure 25.11) for C18 and ΖnA films. Normal load and wear depths are indicated in the figure.
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FIGURE 25.13 Coefficient of macroscale friction as a function of sliding distance for a 3-mm radius alumina ball sliding against (a) C18 and SiO2 films and Si(100); and (b) ZnA, ODT, and Au films at a normal load of 0.1 N and above-average sliding speed of 0.8 mm/s.
References Bhushan, B. (1996), Tribology and Mechanics of Magnetic Storage Devices, 2nd ed., Springer-Verlag, New York. Bhushan, B. (1998a), Tribology Issues and Opportunities in MEMS, Kluwer Academic, Dordrecht, The Netherlands. Bhushan, B. (1998b), Contact mechanics of rough surfaces in tribology: multiple asperity contact, Tribol. Lett., 4, 1-35. Bhushan, B. (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. Bhushan, B. (1999b), Principles and Applications of Tribology, Wiley, New York. Bhushan, B. (1999c), Chemical, mechanical and tribological characterization of ultra-thin and hard amorphous carbon coatings as thin as 3.5 nm: recent developments, Diamond Rel. Mater., 8, 1985-2015. Bhushan, B. and Zhao, Z. (1999), Macro- and microscale tribological studies of molecularly thick boundary layers of perfluoropolyether lubricants for magnetic thin-film rigid disks, J. Info. Storage Proc. Syst., 1, 1-21.
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Bhushan, B., Israelachvili, J.N., and Landman, U. (1995a), Nanotribology: friction, wear and lubrication at the atomic scale, Nature 374, 607-616. Bhushan, B., Kulkarni, A.V., Koinkar, V.N., Boehm, M., Odoni, L., Martelet, C., and Belin, M. (1995b), Microtribological characterization of self-assembled and Langmuir-Blodgett monolayers by atomic and friction force microscopy, Langmuir, 11, 3189-3198. Bowden, F.P. and Tabor, D. (1950), The Friction and Lubrication of Solids. Part I, Clarendon Press, Oxford, U. K. Butter, R.S., Waterman, D.R., Lettington, A.H., Ramos, R.T., and Fordham, E.J. (1997), Production and wetting properties of fluorinated diamond-like carbon coatings, Thin Solid Films, 311, 107-113. Chou, S.Y., Krauss, P.R., and Renstrom, P.J. (1996), Imprint lithography with 25-nanometer resolution, Science, 272, 85-87. Donnet, C., Fontaine, J., Grill, A., Patel, V., Jahnes, C., and Belin, M. (1997), Wear-resistant fluorinated diamondlike carbon films, Surface and Coatings Technol., 94/95, 531-536. Dorfman, V.F. (1992), Diamond-like nanocomposites (DLN), Thin Solid Films, 212, 267-273. Geyer, W. Stadler, V., Eck, W., Zharnikov, M., Golzhauser, A. and Grunze, M. (1999), Electron-induced crosslinking of aromatic self-assembled monolayers: negative resists for nanolithography, Appl. Phys. Lett., 75, 2401-2403. Grischke, M., Bewilogua, K., Trojan, K., and Dimigan, H. (1995), Surf. Coat. Technol. 74/75, 739-745. Grischke, M., Hieke, A., Morgenweck, F., and Dimigan, H. (1998), Variation of the wettability of DLC coatings by network modification using silicon and oxygen, Diamond Rel. Mater., 7, 454-458. Hansma, H., Motamedi, F., Smith, P., Hansma, P., and Wittman, J. C. (1992), Molecular resolution of thin, highly oriented poly (tetrafluoroethylene) films with the atomic force microscope, Polymer Commun., 33, 647-649. Hein, M., Best, L.R., Pattison, S., and Arena, S. (1997), Introduction to General, Organic, and Biochemistry, 6th ed., Brooks/Cole Publishing Co., Pacific Grove, CA. Joyce, S.A., Thomas, R.C., Houston, J.E., Michalske, T.A., and Crooks, R.M. (1992), Mechanical relaxation of organic monolayer films measured by force microscopy, Langmuir 68, 2790-2793. Jung, C., Dannenberger, O., Xu, Y., Buck, M., and Grunze, M. (1998), Self-assembled monolayers from organosulfur compounds: a comparison between sulfides, disulfides, and thiols, Langmuir, 14, 1103-1107. Kester, D.J., Brodbeck, C.L., Singer, I.L., and Kyriakopoulos, A. (1999), Sliding wear behavior of diamondlike nanocomposite coatings, Surf. Coat. Technol., 113, 268-273. Kim, H.I., Koini, T., Lee, T.R., and Perry, S.S. (1997), Systematic studies of the frictional properties of fluorinated monolayers with atomic force microscopy: comparison of CF3- and CH3-terminated groups, Langmuir, 13, 7192-7196. Kim, H.I., Graupe, M., Oloba, O., Koini, T., Imaduddin, S., Lee, T.R., and Perry, S.S. (1999), Molecularly specific studies of the frictional properties of monolayer films: a systematic comparison of CF3-, (CH3)2CH-, and CH3-terminated films, Langmuir, 15, 3179-3185. Kumar, A. and Whitesides, G.M. (1993), Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching, Appl. Phys. Lett., 63, 2002-2004. Lio, A., Charych, D.H., and Salmeron, M. (1997), Comparative atomic force microscopy study of the chain length dependence of frictional properties of alkanethiol on gold and alkylsilanes on mica, J. Phys. Chem. B, 101, 3800-3805. Liu, Y., Evans, D.F., Song, Q., and Grainger, D.W. (1996), Structure and frictional properties of selfassembled surfactant monolayers, Langmuir, 12, 1235-1244. Liu, G.Y., Xu, S., Cruchon-Dupeyrat, S. (1998), Atomic force microscopy studies of self-assembled monolayers of thiols, Thin Films, 24, 81-110. Maboudian, R. (1998), Surface processes in MEMS technology, Surf. Sci. Rep., 30, 209-269.
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McDermott, M.T., Green, J.B.D., and Porter, M.D. (1997), Scanning force microscopic exploration of the lubrication capabilities of n-alkanethiolate monolayers chemisorbed at gold: structural basis of microscopic friction and wear, Langmuir, 13, 2504-2510. Mohrig, J.R., Hammond, C.N., Morrill, T.C., and Neckers, D.C. (1998), Experimental Organic Chemistry, W.H. Freeman, New York. Neumann, A.W. and Spelt, J.K. (Eds.) (1996), Applied Surface Thermodynamics, Marcel Dekker, New York. Salmeron, M., Neubauer, G., Folch, A., Tomitori, M., Ogletree, D.F., and Sautet, P. (1993), Viscodestic and electrical properties of self-assembled monolayers on Au(111) films, Langmuir, 9, 3600-3611. Scandella, L., Schumacher, A., Kruse, N., Prins, R., Meyer, E., Luethi, R., Howald, L., and Guentherodt, H.J. (1994), Tribology of ultra-thin MoS2 platelets on mica: studies by scanning force microscopy, Thin Solid Films, 240, 101-104. Scherge, M. and Schaefer, J.A. (1998), Surface modification and mechanical properties of bulk silicon, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 529-537. Schrader, M.E. and Loeb, G.I. (Eds.) (1992), Modern Approaches to Wettability, Plenum Press, New York. Service, R.F. (1994), Self-assembly comes together, Science, 265, 316-318. Srinivasan, U., Howe, R.T., and Maboudian, R. (1998), Lubrication of polysilicon micromechanisms with alkylsiloxane self-assembled monolayers: coefficient of static friction measurements, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 597-606. Tian, J., Xia, Y., and Whitesides, G. M. (1998), Microcontact printing of SAMs, in Thin Films — SelfAssembled Monolayers of Thiols, Ulman, A. (Ed.), Vol. 24, Academic Press, San Diego, 227-254. Tsukruk, V.V., Nguyen, T., Lemieux, M., Hazel, J., Weber, W.H., Shevchenko, V.V., Klimenko, N., and Sheludko, E. (1998), Tribological properties of modified MEMS surfaces, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 607-614. Ulman, A. (1991), An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-assembly, Academic Press, San Diego, CA. Ulman, A. (Ed.) (1995), Characterization of Organic Thin Films, Butterworth-Heineman, Boston. Ulman, A. (1996), Formation and structure of self-assembled monolayers, Chem. Rev., 96, 1533-1554. Wasserman, S.R., Tao, Y.T., and Whitesides, G.M. (1989), Structure and reactivity of alkylsiloxane monolayers formed by reaction of alkylchlorosilanes on silicon substrates, Langmuir, 5, 1074-1089. Xia, Y. and Whitesides, G.M. (1998), Soft lithography, Angew. Chem. Int. Ed., 37, 550-575. Xia, Y., Kim, E., Zhao, X.M., Rogers, J.A., Prentiss, M., and Whitesides, G.M. (1996), Complex optical surfaces formed by replica molding against elastomeric masters, Science, 273, 347-349. Xiao, X., Hu, J., Charych, D.H., and Salmeron, M. (1996), Chain length dependence of the frictional properties of alkylsilane molecules self-assembled on mica studied by atomic force microscopy, Langmuir, 12, 235-237. Zasadzinski, J.A., Viswanathan, R., Madsen, L., Garnaes, J., and Schwartz, D.K. (1994), Langmuir-Blodgett films, Science, 263, 1726-1733. Zisman, W.A. (1959), Friction, durability and wettability properties of monomolecular films on solids, in Friction and Wear, Davies, R. (Ed.), Elsevier, Amsterdam, 110-148.
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26 Mechanical and Tribological Requirements and Evaluation of Coating Composites 26.1
Introduction ..................................................................... 931 Coating Composites • Typical Mechanisms of Coating Composite Failure • Tribological Coatings of Today
26.2
Design of Tribological Coatings ..................................... 938 Current Designs of Coating Structures • Coatings of Tomorrow
Sture Hogmark
26.3
Staffan Jacobson Uppsala University
26.4
Evaluation of Coating Composites ................................. 949 Important Parameters • Adhesion to the Substrate • Basic Coating Properties • Intrinsic Mechanical Properties • Tribological Properties • Tribological Response of Coated Components • Failure Analysis of Coating Composites
Mats Larsson Balzers Sandvik Coating AB
Urban Wiklund Uppsala University
Design of Coated Components....................................... 945 General Design Considerations • Design Considerations for Cutting Tools • Design Considerations for Forming Tools and Machine Components
Uppsala University
26.5
Visions and Conclusions ................................................. 959
26.1 Introduction Coatings are increasingly being used to improve the tribological properties of mechanical components such as tools for metal cutting and forming, and machine elements such as sliding bearings, seals, and valves. This chapter presents tribological requirements and design considerations in the development of coating composites, and recommends methods and techniques for their evaluation. It is aimed both for those involved in development of coatings and for the practicing tribology engineer. Current concepts of coating composites used in cutting tools, forming tools, and machine elements are reviewed, and the respective requirements addressed within each category are summarized. Concepts of coatings designed for tools and machine elements are exemplified. Further, it is demonstrated how the tribological properties of coating composites are related to the fundamental coating properties (chemical, thermal, mechanical); the general coating characteristics such
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FIGURE 26.1
Types of composite materials and the functional improvements addressed.
as composition and microstructure, topography, and thickness; and different aspects of the substrate material. The important tribological phenomena discussed include: • premature failures such as coating detachment, permanent surface deformation, cracking and spalling, occasional scratching, and material pickup • gradual coating removal, including abrasive, erosive, and tribochemical wear. Techniques to evaluate some of the more important fundamental and tribological properties are presented, and several examples are given, mainly with thin physical vapor deposition (PVD) coatings. The evaluation techniques can be utilized both in coatings selection and development of future coatings. The chapter concludes with some recent trends and speculations about the future.
26.1.1 Coating Composites In the development of modern materials, the functionality is often improved by combining materials of different properties into composites. Many classes of composites exist, most of which address improved mechanical properties such as stiffness, strength, toughness, and resistance to fatigue. Coating composites (i.e., surface-engineered materials) are designed to specifically improve functions such as tribological, electrical, optical, electronic, chemical, and magnetic (Figure 26.1). It is thus natural to select the bulk of a component to meet the demands for stiffness, strength, formability, cost, etc., and then modify or add another material as a thin surface layer, which is the location of virtually all other functional properties. Application of coatings on tools and machine elements is therefore a very efficient way of improving their friction and wear resistance properties. The obvious aim of applying tribological coatings is to obtain increased lifetime. There are, however, several other positive effects, including: 1. The improved wear resistance of coated metal cutting tools is usually utilized to increase the feed rate and cutting speed and thereby the productivity, rather than to give prolonged tool life. 2. Reduced friction often means reduced energy consumption. In some cases, a lowered friction may permit the exclusion of lubrication or of cooling stages. 3. Increased or controlled friction can be a beneficial effect in applications such as brakes, bolted joints, and safety connectors.
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4. Reduced tendency to sticking and material pickup from the countersurface is crucial for the performance of forming tools and in many sliding applications. Antisticking agents can be omitted in forming tool applications. 5. Components of reduced weight can be designed by application of coatings. Reduced weight means, for example, an increased ratio of power to weight of car engines, which in turn can give lower fuel consumption. There are also some limitations in thin coating application: 1. The coating process often involves significant heating of the substrate. This restricts the number of potential substrate materials. 2. There is always a risk of galvanic corrosion associated with applying a coating to a metallic substrate. 3. Good tribological performance often requires high levels of hardness and stiffness of the substrate material, because the thickness of PVD and CVD coatings is so limited that they normally need firm support. 4. The PVD process has a limited ability to coat complicated geometries because it, in principle, is a line-of-sight method. 5. Finally, it should be noted that premature coating failure due to poor adhesion to the substrate or cracking and spalling of the coating material can be disastrous because loose coating fragments in many applications can aggravate the wear. Examples of components that may be at high risk to these phenomena include journal bearings, ball bearings, gears, and piston/cylinder systems. The rapid development of new coating technologies thus has led to an accelerated increase in the use of coated tools and other components during the last couple of decades. This chapter is primarily restricted to thin (1 to 10 µm) physical vapor deposited (PVD) and chemical vapor deposited (CVD) coatings.
26.1.2 Typical Mechanisms of Coating Composite Failure It is important to realize that the mechanical contact between solids is localized to a number of microscale contact spots that together form the real area of contact. Irrespective of the nominal (or geometrical) contact area, a good estimate of the real contact area is obtained by dividing the normal load by the hardness of the softer of the two mating surfaces. In other words, the contact pressure in these tiny areas is of the order of their hardness. Bearing this in mind, it is not surprising that damage can occur, even in apparently very mildly loaded tribological contacts. One such example is the damage that occurs when sliding ceramic seals against each other despite the nominal contact pressure being 100,000 times lower than their hardness (Blomberg et al., 1994; Hogmark et al., 1992b). The wear resistance of a coated component is mainly determined by the coating as long as it covers the contact area. As soon as the coating is partly worn through, or the substrate is exposed due to adhesive failure or cracking and spalling, the wear resistance of the substrate material becomes important. An indepth description of the large number of wear mechanisms found in the applications of coated components is given in Holmberg and Matthews (1994). Characteristic of coating composites as to their modes of failure is the inhomogeneity of the surface layer due to the presence of the coating. There is often a large difference in mechanical, thermal, and chemical properties between the coating and substrate materials, and the interface between them often represents a steep discontinuity in these properties. There are principally two modes by which a coating composite may fail: 1. premature failure 2. failure due to gradual wear If the wear resistance of the coating is high and the coating wears down gradually, a considerable prolongation in life can be experienced as compared to that of an uncoated reference, even if the coating
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FIGURE 26.2 Illustration showing how the life of a component can be prolonged by application of a thin coating. A hypothetical life-limiting wear depth is denoted by wc and the coating thickness by fc. A denotes an uncoated reference component; B denotes the same component supplied with a coating that experiences slow, gradual wear; and C refers to an undesired situation of premature coating failure.
is thin (Figure 26.2). On the other hand, if the coating fails prematurely due to poor adhesion or cracking and spalling, the lifetime may even be shortened, because coating wear debris entrapped in the contact interface can aggravate the wear of the substrate material. It is clear from Figure 26.2 that increasing the coating thickness will prolong the lifetime as long as the wear rate is gradual and steady. However, as will be further elucidated in Section 26.4.4.2, the thickness of PVD and CVD coatings is restricted by their internal stresses, which build up in the coating during deposition. Therefore, the coating is often very thin compared with the tolerable wear depth. Consequently, in addition to displaying sufficient adhesion and resistance against cracking and spalling, the coating must be extremely wear resistant in order to considerably improve the tribological properties of the coating composite. Often, premature coating failure ends the life of well-functioning components after a period of gradual wear. In contrast to failure due to gradual coating wear, premature coating failure is very difficult to predict — both experimentally and theoretically. Some of the more important mechanisms of coating failure are summarized in Figure 26.3. 26.1.2.1 Premature Failure Premature failure designates a situation where the full tribological potential of the coating is not gained (see Figures 26.2 and 26.4). Instead, the component fails due to one or several of the following reasons: 1. 2. 3. 4.
coating detachment permanent deformation of the coating composite cracking and spalling of the coating pickup of material from the countersurface
In general, tribological applications put higher demands on the coating adhesion than any other area of application, although the demands can differ substantially from one tribological situation to the other. It is instructive to distinguish between the actual adhesive forces (the strength of the physical adhesion or atomic bonding that acts between coating and substrate), and the practical adhesion by which is understood the ability of the coating composite to resist interfacial failure in its practical application. Naturally, the upper limit of the practical adhesion is correlated to the atomic bond strength, but this parameter cannot be directly measured (see Section 26.4.2). Cracking and spalling of the coating may be the result of occasional or repeated excessive mechanical or thermal loading. A brittle coating on too soft a substrate can fracture and spall off, as exemplified in
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FIGURE 26.3 Common failure mechanisms of coating composites. (a) Initial state. (b)–(e): Premature failures due to coating detachment (b), cracking and spalling (c), coating and substrate deformation (d), and coating and substrate deformation including coating fracture (e). (f) Pickup of material from the countersurface. (g) Gradual coating wear. (h) Initial gradual wear followed by premature coating detachment; see C in Figure 26.2. (i) Coating detachment followed by accelerated wear of the substrate material.
(a)
(b)
(c)
FIGURE 26.4 (a) Excessive mechanical loads have caused cracking and spalling of a brittle electroless nickel coating applied to a gear wheel made of quenched and tempered steel. (b) Topography of a TiN-coated, high-speed steel milling tool for which the coating has fractured. (c) Cross-section of the tool in (b), revealing thermal softening of the substrate due to severe cutting conditions.
Figure 26.4(a). Frictional heat may soften the substrate, making it unable to support a hard and brittle coating (see Figure 26.4b). Once the coating has fractured, coating fragments are peeled off, typically by the shearing action of the countersurface. When the coating is partially removed, the rate of detachment often increases due to excessive contact pressure at the edge of the scar. Critical parameters to resist coating cracking and spalling include coating thickness and toughness, and substrate hardness. Applying thin, hard coatings to rolling element bearings always puts the detachment, cracking, and spalling mechanisms at high risk.
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Permanent deformation of the coating composite basically involves permanent changes in component geometry and/or in surface topography. Decisive parameters for a change in geometry are Young’s modulus and the hardness of coating and substrate, and coating toughness (see Section 26.4.4). Tiny scratches or cracks may disqualify a forming tool used to, for example, press compact disks. Coating hardness is the crucial parameter for scratch resistance, and coating toughness or fracture resistance for the resistance to surface cracking. Work material locally adhered to, for example, the surface of a sheet forming tool used in the automotive industry will inevitably produce indentations or scratches in the surface of the product. Material transfer between the contact surfaces of sliding machine elements is a similar problem, often named galling, scuffing, or seizure. Pickup of material from the countersurface is typical of many situations of sliding contact, and by no means unique to coating composites. It is generally reduced or avoided by giving the surface a smooth topography and making sure that the chemical affinity to the countersurface is low. This is often accomplished by applying a proper coating. Tribochemical layers may form when, for example, machining certain work materials at high cutting speeds. They are the result of mechanical smearing of or chemical reactions with constituents in the work material, and may have the positive effect of protecting the coating from excessive damage (Nordgren and Melander, 1994; Palmai, 1984). 26.1.2.2 Failure Due to Gradual Wear This category of failure includes regular wear; that is, gradual material loss mainly determined by the intrinsic coating properties. When thin PVD or CVD coatings are involved, gradual wear often means mild wear due to abrasion, erosion, chemical dissolution, etc., and does not, in principle, deviate from the mechanisms causing wear of homogeneous materials. Suitable evaluation techniques are given in Section 26.4.5. Because the wear rate of thin coatings in most applications is extremely low, oxidation and other types of chemical degradations often play a significant role. In typical applications of bulk materials, the wear mechanisms are normally characterized as mechanical. The resistance against abrasive wear of coatings increases with coating hardness, which preferably should be higher than that of the counter material (at the relevant contact temperature) (Khruschov, 1974). High Young’s modulus and hardness of both coating and substrate, combined with a sufficient coating thickness, are also important in avoiding cracking caused by deformation of the substrate (see Section 26.3). Resistance to particle erosion (i.e., wear due to mechanical attack by liquid or gas-borne particles) requires a coating that combines high hardness, fracture toughness, and corrosion resistance. The toughness is usually the most decisive parameter if the erosion results in a mechanically dominated material removal mechanism. Adhesive wear of today’s coating materials rarely occurs unless the strength of the coating material is weakened by thermal softening and/or chemical attack from the counter material or the environment. A high contact temperature facilitates chemical degradation and dissolution. In some instances, the selection of coating material has to be performed in consideration of the ability of the counter material (e.g., work material in a forming operation) or environment (e.g., lubricant of a machine component) to react (or not react) chemically with the coating. Sometimes, protective layers are formed by such reactions; but more often, they promote the gradual coating wear.
26.1.3 Tribological Coatings of Today 26.1.3.1 General Overview Application of surface coatings for tribological uses may require deposition temperatures ranging from room temperature up to more than 1000°C (Figure 26.5). The coating thickness ranges from microns to several millimeters. Typically, the atomistic methods produce the thinnest coatings. For some methods,
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Atomistic deposition Particular deposition
Process temperature[°C]
Full-thickness deposition
1000
Overlay welding
CVD
800 600 400
Electrochemical plating
PVD
Chemical (electroless) plating
200
Thermal spraying
0,1
1
10
100
1000
10000
Layer thickness [µm] FIGURE 26.5 Typical values of coating thickness and process temperature (temperature at the substrate surface) of today’s tribological coating methods.
PVD WC/C M oS2 DLC Cr N
Coating deposition
Application
Components
Al al l oys
Substrate material
Cu al l oys M g al l oys
RT
1%C steel QT- steel Car bon steel
200
CVD
( Ti ,Al ) N Ti ( C,N) Ti N
Forming tools Col d wor k steel "D1"
HSS "H13" Hot wor k steel
500 Temperature °C
Di amond Si C Al2 0 3 Ti C Ti N
Metal Cutting tools
CC Al 2 0 3 Si C Si3N4
1000
FIGURE 26.6 Limited heat resistance often excludes materials from different applications and coating processes. This figure illustrates typical temperature limits of potential substrate materials compared with typical working temperatures of applications and deposition temperatures of PVD and CVD coating processes.
high deposition temperatures can cause undesired phase transformations, softening, or shape changes of the coated component. An important benefit of PVD and CVD processes is the high flexibility as to composition and structure of the coating. These coatings are today successfully utilized to coat a large variety of mechanical components (Figure 26.6). Most of today’s PVD and CVD coating materials consist of nitrides (TiN, CrN, etc.), carbides (TiC, CrC, W2C, WC/C, etc.), oxides (e.g., alumina), or combinations of these. Important exceptions are molybdenum disulfide (MoS2), diamond-like carbon (DLC), and diamond. MoS2, WC/C, and DLC can be classified as low-friction coatings because they often display friction coefficients ranging from 0.05 to 0.25 in dry sliding (Holmberg and Matthews, 1994; Hirvonen et al., 1996). Their wear resistance is
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FIGURE 26.7 (a) Comparative friction values recorded during dry sliding in a ball-on-disk geometry (Hollman et al., 1997a). A water-lubricated diamond/Al value is added for comparison. (b) Intrinsic abrasive wear resistance of diamond and TiC coatings obtained by micro abrasion against diamond abrasives (see Section 26.4.5.2). The wear resistance of cemented carbide (CC) and high-speed steel (HSS) is also shown. (From Hollman, P. (1997a), Microand Nanocrystalline Diamond Coatings with Extreme Wear Resistance and Ultra Low Friction, Acta Universitatis Upsaliensis Dissertation in Science and Technology 325, ISBN 91-554-4084-3. With permission.)
generally inferior to that of nitrides, carbides, and oxides. On the other hand, nitrides, carbides, and oxides normally give friction values between 0.4 and 0.9 in dry sliding. In this context, they are referred to as wear-resistant coatings. A very important exception to this simple classification is the CVD diamond coating, which in many applications combines an ultralow friction with very high wear resistance (Figure 26.7). Friction values below 0.05 have been recorded for diamond in nonconformal dry sliding. A further reduction in friction down to 0.02 can be obtained by water lubrication. This makes diamond a very strong coating candidate, in particular when environmental considerations have to be met (Hogmark et al., 1996). Figure 26.6 indicates that the deposition temperature and heat resistance of the substrate materials strongly limit the number of possible coating/substrate combinations. All types of PVD and CVD coatings can be applied to most ceramic materials and cemented carbides (CC). The most heat-resistant steels, such as high-speed steel (HSS) and some of the forming tools, can be coated by all types of PVD and some low-temperature CVD processes; whereas progress in PVD or CVD coating of low-alloy steel, copper-based alloys, and light metals like aluminum and magnesium remains very limited. In addition to the restricted number of coating candidates, this last category of substrate materials has a relatively low hardness in comparison with ceramics, CCs, and tool steels. This fact must be considered when designing coating composites, as further discussed in Section 26.3. 26.1.3.2 Materials, Properties, and Applications of Some Common Coatings The number of commercially successful tribological CVD and PVD coatings is still rather limited. They are briefly summarized in Table 26.1, together with some of their most important tribological properties, substrate materials, and applications. The four categories of tribological components — metal cutting tools, hot forming tools, cold forming tools, and machine elements — all put specific demands on the coating composite, as generalized in Table 26.2. From Tables 26.1 and 26.2 general conclusions can be drawn on how to design coated components for specified applications (see Section 26.3).
26.2 Design of Tribological Coatings A tribological coating composite is primarily designed to offer two types of functions: 1. a specified friction behavior (including low, high, or just stable friction level) 2. a high wear resistance
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TABLE 26.1 Commercially Successful Combinations of PVD and CVD Coatings and Substrate Materials, Common Tribological Applications and Typical Ranges of Deposition Temperature, Hardness Levels, and Friction Coefficients Against Steel Coating (Deposition Technique)
Substrate Material
TiC (CVD) Al2O3 (CVD) TiN (CVD) TiN (PVD) CrN (PVD) CrC (PVD) Ti(CN) (PVD) TiAlNb (PVD) DLC (CVD) DLC (PVD) W2C (CVD) WC/C (PVD) MoS2 (PVD) Diamond (CVD) Duplexc
Deposition Temperature (°C)
Hardness (GPa)
Dry Friction vs. Steel
CC, HSSa
500–1100
28–35
0.1–0.3
CC CC CC, HSS HSS, forming tool steels Tool steels
700–900 500–1100 250–500 300–400
18–23 16–20 20–24 18–20
0.5–0.8 0.3–0.7 0.3–0.7 0.6–0.8
200–400
15–20
0.20–0.5
HSS, CC
300–600
30
0.15–0.4
HSS, CC
300–500
28
0.7–0.9
CC, tool steels Tool steel and lowalloyed steels CC, tool steelsa HSS, tool steels
300–800 RT–400
5–30 5–30
0.05–0.15 0.05–0.15
700 250
25–30 12–18
0.20–0.30 0.10–0.30
HSS, tool steels
100–400
0.6–15
0.03–0.20
CC, SiC
800–1000
80–100
0.05–0.10
Forming tool steels
500–550
Given by the coating
Given by the coating
Applications Tools for metal cutting and forming Metal cutting tools Metal cutting tools Metal cutting tools Tools for metal cutting and forming Forming tools, machine elements Metal cutting tools Metal cutting tools Machine elements Machine elements, magnetic hard disks Forming tools Machine elements Metal cutting tools, machine elements Cutting tools for aluminum alloys Forming tools, machine elements
a
Heat treatment is often performed subsequent to coating deposition by quenching from the process temperature. Processes combining the chemistry and physics of PVD and CVD are normally used. c Duplex treatment combines ion nitriding with PVD coating in one process. Successful top coatings applied in duplex treatment include TiN and CrN. b
To fulfill these functional demands, a sufficient adhesion between coating and substrate, plus a sufficient load-carrying capacity, are both necessary prerequisites. The load-carrying capacity is the ability of the composite to resist tribological loads without premature failure. Usually, premature failure is characterized by cracking or delamination of the coating or by subsurface plastic deformation.
26.2.1 Current Designs of Coating Structures Today, three types of coating structures are frequently found: single-layer coatings, sandwich coatings, and graded coatings. One of the first — and today one of the most common — thin coatings to be used in tribological applications is hard chromium (Cr). This coating is electrolytically deposited, for example, to improve the wear resistance of piston rings, hydraulic pistons, bearing shafts, chain saw teeth, etc. Most commercial PVD and CVD coatings consist of one single layer, often containing one structure phase. Among the most common are TiC (commercially introduced by Sandvik Coromant [1969] on cemented carbide metal-cutting tools); TiN (introduced in 1978 on high-speed steel metal-cutting tools [Figure 26.8]), CrN; alumina (Al2O3), and diamond-like carbon (DLC). All these coatings are usually applied directly to the surface of a homogeneous substrate material. Consequently, to ensure a high load-carrying capacity of the coating composite, the substrate must possess high hardness and Young’s modulus.
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TABLE 26.2 Four Important Coating Application Areas, and the Prevailing Contact Conditions and Desired Properties of the Substrate and Coating Material Component
Conditions of Application
Metal cutting tools
High static and dynamic (intermittent cutting) mechanical loading, high surface temperatures (500–1400°C), high shear stresses, chemically reactive work material often including abrading particles, and often presence of cutting fluid. High contact temperatures (300–1100°C), chemically reactive work material, often including abrasive particles, thermal cycling due to water cooling, presence of antisticking agent High contact pressure, presence of abrasive particles, high shear stresses, often presence of lubricant Friction and wear properties of both mating surfaces often of equal interest; the contact temperatures and often also pressures are moderate; often presence of lubricant and sometimes also abrasive particles
Hot forming tools
Cold forming tools
Machine elements
Desired Properties of Substrate Material
Desired Properties of Coating Material
High levels of hot hardness, fracture toughness, wear, and fatigue resistance; the substrate material is supposed to work reasonably well also if the coating is locally removed
High chemical and thermal resistance, high hardness and toughness at the high contact temperature; very good adhesion to the substrate and low solubility in the work material
High Young’s modulus, yield stress, and hot hardness to resist macroscopic deformation, high resistance to thermal fatigue, and chemical reactions
High chemical and thermal resistance, including resistance to thermal fatigue (heat checking) and low tendency to stick to the work material (low chemical potential between coating and work material); low friction, high hot hardness and toughness to resist abrasive wear Low chemical potential between coating and work material give low friction and avoids work material pickup; high hardness and toughness to resist abrasive wear Low friction properties, combined with good resistance to surface damage; a certain amount of running in wear is sometimes desirable to conform the sliding surfaces and reduce the asperity contact stress peaks; an ability to accommodate permanent substrate deformation, combined with a relatively high hardness to resist any abrasives are other desired properties
High Young’s modulus and yield stress to resist macroscopic deformation, high fracture toughness, and high hardness to support the coating Sufficiently high Young’s modulus, yield stress, and, in rolling contact and lubricated sliding, a good fatigue strength to resist the cyclic loads; high hardness to support the coating (hardened low- and mediumgrade steels dominate)
(a)
(b)
FIGURE 26.8 (a) Typical morphology of a PVD-TiN coating, and (b) transmission electron microscopy image revealing the initial Ti layer normally used to enhance the adhesion of the TiN coating.
Thin coatings of alumina have been manufactured for more than 20 years using CVD; and today, CVD alumina on cemented carbide inserts represents one of the largest industrial applications. Like CVD TiN, alumina is normally deposited on an intermediate layer of TiC.
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FIGURE 26.9 Sandwich coating composed of TiC, Al2O3, and Ti(CN) on a CC metal cutting insert intended for machining austenitic stainless steel. The Ti(CN) coating consists of several layers with different carbon:nitrogen ratios. (Courtesy of Seco Tools.)
Several successive layers of different composition are often applied to form a sandwich coating for demanding applications. Metal cutting inserts for machining austenitic stainless steel are typically CVD coated with three layers, namely, TiC-Al2O3-TiN starting from the substrate (Figure 26.9). TiC accounts for good bonding to the CC material; Al2O3 provides good wear resistance at elevated temperatures; and, in addition to its attractive color, TiN gives a clear visual indication of which edges of the insert have been used. In addition, TiN often reduces the problem with sticking of the work material. Another example of a sandwich layered coating is found in the reader head in computers (see Hedenqvist et al., 1992). A graded coating composition or structure improves the load-carrying capacity by offering smoother transitions in mechanical properties from those of the hard and stiff coating to those of the softer and more flexible substrate. In this way, the contact load can be distributed over larger areas, which reduces the maximum contact stresses and the stress at the coating-substrate interface. Successful graded surface layers on steel have been produced by nitriding or carburizing for many decades, and the examples of forming tools and machine components taking advantage of these treatments are abundant (Bell, 1975; Dingremont et al., 1995a,b). Today, graded compositions are also utilized in commercial PVD coatings such as Ti(CN) (Bergmann et al., 1990).
26.2.2 Coatings of Tomorrow 26.2.2.1 Materials and Strengthening Structures There seems to be an almost universal relationship between hardness and toughness of all materials, as illustrated in Figure 26.10. Improving the hardness of a material will almost always be at the expense of reducing the toughness (Courtney, 1990; Allen and Thomas, 1998). There are two important exceptions, however. By reducing the grain size or by introducing a fiber structure, both hardness and toughness can be raised. The fracture toughness of state-of-the-art bulk ceramics is typically within the range of 3 to 8 MPam1/2. PVD or CVD coatings of the same materials usually display much lower toughness, in the range of 0.1 to 1.0 MPam1/2. Consequently, much of today’s development in tribological coatings focuses on improving their toughness. Several phases and layers can be combined into sandwich coatings, graded coatings, duplex coatings, multilayer, superlattice, nanocrystalline, and multicomponent coatings, etc. (Figure 26.11) (Holmberg
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Modern Tribology Handbook
Deformation Solid solution Hard phase
Grain refinement (Hall-Petch) Composite structure
Pure state Toughness
FIGURE 26.10 The general hardness vs. toughness relationship of materials, and the effect on this relationship from the most commonly used metallographic strengthening mechanisms.
FIGURE 26.11
Possible structures of tribological coatings.
and Matthews, 1994; Sproul, 1994). Obviously, the strengthening mechanisms known to metallurgists for many decades are now being introduced to tribological coatings, which also offer numerous new combination possibilities. 26.2.2.2 New Coating Materials Diamond coatings have recently been introduced on inserts for aluminum cutting (Figure 26.12) (Karner et al., 1996). Diamond offers a unique combination of high hardness, high wear resistance, low friction properties, high thermal conductivity, and environmental friendliness. The latter applies both to processing and application. Diamond will probably become one of the most versatile coating materials once it can be deposited at a more moderate temperature and ways of improving its toughness have been established. Up to now, the PVD techniques have not allowed deposition of tribological quality alumina coatings. However, recent advances in process technology have made reactive deposition of high-quality alumina coatings possible (Sproul et al., 1995). Cubic boron nitride (CBN) cutting edges are currently produced by conventional hot isostatic pressing and brazed onto the tip of cemented carbide cutting tools. CBN is second to diamond, the hardest material, 5200 HV, and it is very effective in cutting hardened steels and other difficult-to-machine alloys. Applying CBN directly to the tool in the form of a coating would of course be very attractive. The current restriction is that CBN coatings produced by PVD normally exhibit excessively high compressive stresses (Sproul, 1996a). Carbon nitride (C3N4) would theoretically be harder than diamond if it could be given the same structure as Si3N4. Although there have been reports of producing crystalline carbon nitride coatings, to date no one has presented fully crystalline C3N4 coatings. The carbon nitrides produced thus far, often denoted CxNy , have shown extreme elastic properties combined with relatively high hardness values (15 to
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(b)
FIGURE 26.12 Characteristic topographies of diamond coatings: (a) top view of a 10-µm CVD diamond coating (Ra = 430 nm); (b) smooth (Ra = 25 nm) diamond coating as deposited with 400 V negative bias on the substrate. Note that the partially removed coating is significantly smoother than the substrate revealed in the lower part of the micrograph. (From Hogmark, S., Hollman, P., Alahelisten, A., and Hedenqvist, P. (1996), Direct current bias applied to hot flame diamond deposition produces smooth low friction coatings, Wear, 200, 225-232. With permission.)
(b) (a)
FIGURE 26.13 (a) Process layout, and (b) microstructure of PVD-TiC. (From Wiklund, U. and Larsson, M. (1999a), Low friction PVD titanium-carbon coatings, Wear, 241, 234-238. With permission.)
60 GPa) (Sjöström et al., 1996). A limitation of CxNy is its low thermal stability. It loses nitrogen and softens at 300°C, (Hellgren 1999; Sproul, 1996b). Recently, TiC coatings have been produced by argon plasma-activated PVD, comprising simultaneous electron beam evaporation of Ti and sputtering of carbon. The substrates are rotated at a sufficient speed above the two sources to allow for the deposited constituents to react chemically (Figure 26.13) (Wiklund and Larsson, 1999a). 26.2.2.3 Duplex Coatings Because many of the wear-resistant PVD and CVD coatings are relatively brittle, they can be successfully applied only to hard and stiff substrate materials such as hardened steel, cemented carbides, or structural ceramics. On softer substrates, an intermediate layer acting as a mechanical support for the coating is usually required (see Section 26.3.3). For steel and titanium alloys, this support is preferably achieved by nitriding (Dingremont et al., 1995a,b; Johansson, 1993). If nitriding and PVD coating are performed in sequence within one coating system, the process is called duplex treatment. 26.2.2.4 Multilayered Coatings Multilayered coatings are distinguished from sandwich layers by their periodically repeated structure of lamellae of two or more materials. The lamella thickness can vary from a few nanometers to a few tenths of a micrometer. Coatings made of multilayered structures have proven harder and significantly tougher than homogeneous coatings of the same materials. One possible mechanism for this improvement would
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FIGURE 26.14 The superior toughness of a multilayered Ti/TiN coating (a) compared with a homogeneous TiN coating (b), as demonstrated by 500 gf Vickers indents. The corresponding coating structures are shown in (c) and (d).
be that the lamellae structure obstructs dislocation glide and also crack propagation (Figure 26.14 and Section 26.4.4.4) (Gunnars, 1997; Sugimura et al., 1995). 26.2.2.5 Superlattice Coatings Multilayered coatings of materials with similar crystal structures tend to form columnar crystals that extend through the entire coating, provided that the thickness of the individual lamellae is sufficiently thin, typically 5 to 25 nm. Such coatings are referred to as superlattice coatings. Some of the first examples of superlattice coatings were obtained by combining TiN/VN and TiN/NbN (Todorova et al., 1987; Chu et al., 1993; Shinn et al., 1992; Larsson et al., 1996). Several authors have shown that this type of multilayered coating structure can improve the hardness as well as the toughness, compared to single layers of the same materials (see Sections 26.4.4.3 and 26.4.4.4) (Chu et al., 1993; Nordin et al., 1998). Superlattice strengthening is well-known from classical metallurgy, where it is sometimes referred to as substructure strengthening or order hardening (Courtney, 1990; Allen and Thomas, 1998). By selecting a suitable combination of materials for the multilayered structure, it is possible to improve resistance against wear, corrosion, oxidation, high friction, etc. For example, superlattice coatings with thin lamellae of TiN and TaN (Figure 26.15), have shown very good results in cutting of stainless steel. This is believed to be a result of a very good toughness, combined with the low affinity of TaN to the work material (Selinder et al., 1998). 26.2.2.6 Nanocrystalline Coatings The yield strength, hardness, and toughness of polycrystalline materials all generally improve with decreasing grain size, in accordance with the well-known Hall-Petch relation. A similar phenomenon appears to be valid for thin coatings down to nanometer-sized grains. In addition to improved mechanical properties, nanocrystalline materials can exhibit higher thermal expansion, lower thermal conductivity, unique optical, magnetic and electronic properties, etc. (Suryanarayana, 1995; Sproul, 1996b). Currently, nanocrystalline structures (of bulk materials as well as thin coatings) are being explored for tribological applications (Voevodin et al., 1997; Veprek and Reprich, 1995). 26.2.2.7 Multicomponent Coatings Multicomponent coatings are composed of two or more constituents in the form of grains, particles, or fibers. Although many of today’s single-layer coatings have a multicomponent structure, this is still a rather unexplored means for coating strengthening.
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FIGURE 26.15 A cross-section of a TiN/TaN polycrystalline superlattice coating on HSS: (a) fine-grained columnar structure revealed by SEM; (b) the superlattice structure revealed by TEM. (From Nordin, M., Larsson, M., and Hogmark, S. (1998), Mechanical and tribological properties of multilayered PVD TiN/CrN, TiN/NbN, TiN/MoN and TiN/TaN, Surf. Coat. Technol., 106, 234-241. With permission.)
26.3 Design of Coated Components 26.3.1 General Design Considerations As mentioned, the load-carrying capacity is the ability of the composite to resist tribological loads without premature failure due to subsurface plastic deformation, cracking, or delamination of the coating. The primary consideration in the design of coated components should be to avoid such premature failure by achieving a sufficient load-carrying capacity. Second, when this is achieved, attention is turned to increasing the intrinsic wear resistance of the coating in the application. The tools in the toolbox for design of coated components include coating thickness, coating material, coating microstructure, state of residual stress, and roughness. All these parameters are determined by the choice of deposition process and process parameters, but they are also often influenced by the material and topography of the substrate (see Section 26.4.1). The choice of design settles the intrinsic coating properties, including resistance to different wear mechanisms, hardness, modulus, toughness (improved by residual compressive stresses), high-temperature properties, and friction performance. 26.3.1.1 Stresses in Tribology of Coatings At least two types of contact stress patterns must be considered in the design of coatings: 1. Hertzian contact stresses related to the macroscopic contact geometry 2. stresses associated with the microscopic asperity contacts In static contact, rolling contact, or sliding contact with very low friction, the maximum shear stresses occur at a depth roughly equal to half the Hertzian contact radius. For a ball bearing with 10-mm balls, this typically corresponds to 0.1 to 0.3 mm. The group of components that may fail by sub-surface fatigue due to excessively high cyclic Hertzian stresses at a depth below the surface includes ball bearings, gears, and other machine elements with nonconforming contact surfaces. Here, the maximum shear stress typically appears well below the thickness of a PVD or CVD coating. Consequently, applying a thin coating is seldom effective in reducing these problems. In sliding contact between conformal surfaces, such as those of journal bearings, face seals, piston/cylinders, and cutting and forming tools, the load is distributed over a large nominal contact area. The detrimental contact stresses are localized to the areas of asperity contact. In these microscopical contact zones, the highest stresses usually appear within a few microns of the contact interface (Figure 26.16). Here, the prognosis of improving the friction and wear properties by applying a thin coating is significantly better.
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FIGURE 26.16 Normal stress distribution at different levels below the contact surface. The discrete, localized elastic and plastic normal load distributions associated with asperity contacts are gradually smoothed below the surface. The pressure peaks at the coating interface can lead to local plastic deformation of the substrate, despite the average stress level being rather low.
In all sliding contacts, the location of the maximum shear stress approaches the surface when the friction increases. For a friction coefficient of about 0.3 or higher, it is confined to the contact surface (Mao et al., 1994) and, consequently, thin coatings could be efficient in reducing wear and improving the load-carrying capacity of the composite. 26.3.1.2 Topography of Coated Components Several aspects have to be considered when designing for the optimum topography of thin, hard coatings. To minimize the maximum contact stresses on the asperity level, the coating surface should be as smooth as possible (see Figure 26.16). Because most thin coatings inherit the substrate topography, the final step in substrate surface preparation should be a careful polishing or a very mild blasting; this is also recommended to increase the practical adhesion of coatings with high residual stresses (see Section 26.4.4.2). However, all coating processes introduce some surface irregularities, and it may also be necessary to polish the coating or use a superficial layer with good running-in properties (see Section 26.3.3). In most tooling applications, the surface finish of the tool is replicated on the product, and the requirement on the coating topography is related to that of the product. In many metal cutting operations, however, constituents in the work material can form protective tribochemical layers on the tool (Palmai, 1984; Nordgren and Melander, 1988). This mechanism can be facilitated by a reasonably rough topography. A certain roughness can also be beneficial for oil retention of sliding bearings, etc. 26.3.1.3 Primary Design Goal: Improving the Load-Carrying Capacity The primary goal of improving the load-carrying capacity can be reached by a number of design choices. At least three coating approaches lead to a reduced risk for sub-surface plastic deformation (Figure 26.17). 1. A hard coating can relieve the substrate by “hosting” the maximum shear stress, provided it is thicker than the depth to the location of maximum stress. 2. A thin, high modulus coating can spread the load over a larger area on the substrate by a drum skin effect. 3. A soft coating yields and thus gives a flatter, less concentrated load distribution over the substrate.
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(a)
(b)
(c)
(d)
FIGURE 26.17 Mechanisms of improving the load-carrying capacity of a coating composite by load spreading. The concentrated elastic load distribution on an uncoated substrate (a) can be spread out by using a harder coating thick enough to accommodate the location of maximum shear stress (b), by using a thin, high-modulus coating that widens the load bearing area of the substrate by a drum skin effect (c), and by using a softer coating that yields and thus flattens out the stress distribution on the substrate (d).
Of course, the substrate properties are also decisive in avoiding plastic deformation: • Substrates with a high hardness resist plastic deformation up to higher levels of stress. • Substrates with a high hot hardness retain their deformation resistance up to high temperatures. • Substrates with a high thermal conductivity reduce the risk of thermal softening induced by friction heating. • Substrates with a low modulus get large nominal contact areas and thus reduce the level of subsurface stress (the modulus of the substrate is normally not a design criterion because it cannot be varied by modifying the microstructure, but is practically a constant for the chosen material). The risk for premature failure by cracking and delimitation of the coating can be reduced by proper design choices, including: • Tough coatings can accommodate more deformation without fracturing. The toughness (measured as critical component strain to coating fracture) is improved by high compressive residual stresses in the coating (see Section 26.4.4.4). • Smooth coatings avoid detrimental contact stress concentrations, thus reducing the risk for both cracking and plastic deformation. • For coating processes yielding high residual stresses, the risk for delamination is lower for thin coatings because the load exerted on the interface from the stress in the coating is proportional to the coating thickness (see Section 26.4.4.2). 26.3.1.4 Secondary Design Goal: Improving the Wear Resistance of the Coating The intrinsic wear resistance of a coating generally does not differ from that of the same materials in bulk form. Thus, the same design criteria as for bulk materials apply. Some of the exceptions were mentioned in Section 26.1.2.2.
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26.3.2 Design Considerations for Cutting Tools Cutting tools will probably continue to be a leading application of modern tribological coatings. They are relatively small so that batch coating can keep the cost within reasonable limits, even for high-tech coatings of, for example, nanocrystalline and nanolayered multicomponent layers. Today, there are two obvious trends in cutting tool developments. Dry machining is desirable to avoid the extra costs and environmental problems associated with cutting fluids. High-speed machining of hardened steel has the potential of giving sufficiently high quality of the machined surface to make finishing operations such as grinding or polishing unnecessary. In both cases, the heat generation along the tool surfaces will be even more intense than with today’s contact conditions and, consequently, the tools must possess further improved hot hardness, thermal and chemical stability, etc.
26.3.3 Design Considerations for Forming Tools and Machine Components Forming tools and machine components constitute much larger industrial sectors than do cutting tools, and application of thin tribological coatings on forming tools and machine components thus has enormous potential. There are several reasons why the use of coatings in these applications remains relatively scarce. Many forming tools and machine elements are too large to be economically coated by today’s processes. Further, the substrate materials of most forming tools and machine elements cannot resist the currently used deposition temperatures. In addition, these components often have complicated and narrow sections that are difficult — or even impossible — to coat. Finally, the high tool cost often makes the user restrictive against applying new, unexplored coatings. The automotive industry encourages research on new concepts of surface engineering, with the general aim to substitute traditional steel components with components made of lighter materials, typically aluminum, titanium, and magnesium alloys. The ultimate aim is to reduce fuel consumption. The application of thin, wear-resistant, and/or low-friction coatings on inherently soft materials requires a supporting, intermediate layer to achieve a sufficient load-carrying capacity. Electroless nickel, hard chrome, laser cladded or thermally sprayed hard coatings, and nitrided and carburized layers, are all candidates for providing this property. The primary design parameters of the supporting layer are thickness and the Young’s modulus, and the aim is to avoid plastic deformation and to minimize elastic deformation of the substrate. An additional, softer low-friction coating may have to be applied on top of the wear-resistant coating (Figure 26.18). This layer serves to spread the load, thereby reducing the stress peaks indicated in Figure 26.16, and simultaneously ensuring a mild running-in wear. Future coatings for forming tools and machine components are thus expected to be multilevel composites. The base material of, for example, a hardened steel is typically a particle composite; the base material plus coating constitute the coating composite; and finally, the coating is of sandwich type, and one or more of its layers may possess various substructures.
FIGURE 26.18 materials.
Suggested structure and materials of a multilevel composite coating designed for soft substrate
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FIGURE 26.19 Illustration of how the coating deposition parameters influence the tribological response of coating composites through the coating characteristics, which in turn determine the basic tribological properties. The influence from the substrate is also indicated.
Currently, plasma-assisted PVD processes are being evaluated for production of duplex coatings (see Section 26.2.2.3). The functional PVD coating is typically CrN or TiN or a wear-resistant, low-friction coating (e.g., DLC or WC/C) (Farges et al., 1989; Bell, 1997).
26.4 Evaluation of Coating Composites 26.4.1 Important Parameters A general theory of the relations illustrated in Figure 26.19, starting from the coating deposition parameters and predicting the tribological response of coated components, is still far from being realized (Hogmark et al., 1997b). Such a theory would involve the relationships between the deposition parameters (substrate temperature, plasma characteristics, etching time, gas pressure, etc.); the substrate characteristics (e.g., composition, microstructure, topography); and the coating characteristics (thickness, chemical composition, microstructure, topography, etc.). The influence from the substrate is primarily related to the nucleation and growth of the coating, and to the coating topography. Consequently, the substrate material and surface preparation prior to deposition are crucial to the coating adhesion, and, in turn, to the performance of the coating composite. Further, the coating characteristics consequently govern the basic coating properties (chemical, thermal, mechanical, etc.) (Hogmark et al., 1997c). By tribological properties, one can understand resistance against deformation, abrasion, erosion, adhesive contact, repeated impact, and material pickup of the coating composite. These properties are determined by the basic properties of the coating and, assuming that the coating is thin, also directly by the basic properties of the substrate (see Figures 26.1 and 26.3). Finally, the tribological response of a coated component in operation is estimated from the tribological properties necessary to sustain the actual tribological situation, that is, conditions such as geometry, contact pressure, sliding velocity, temperature, lubrication, etc. Those involved in coatings development and production usually assess some of the relevant coating characteristics and basic properties, whereas end users pay direct attention to the tribological response of the coated component in the actual application. Knowledge of the entire chain of properties is important for the general understanding of the behavior of coating composites, even if the correlation
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illustrated by the arrows in Figure 26.19 can only be given qualitatively. Because different applications put different demands on the coating composites, the set of most decisive parameters will vary.
26.4.2 Adhesion to the Substrate Obviously, a good adhesion of the coating to the substrate is a crucial property of most applications of coated components. However, any adhesion test will, inevitably, superimpose a stress field over the coating-substrate interface. This stress field will depend on the type of tribological loading (indentation, scratching, sliding, abrasion, impact, etc.), as well as on the elastic and plastic parameters of the coating and substrate. Important parameters include the nature, magnitude, and homogeneity of coating residual stresses, the shape, flatness, and roughness of the interface, etc. Thus, any test value of adhesion will only be representative of the particular test from which it has been obtained. Because the situation in the test most likely deviates significantly from that of the intended application, the result must be handled with caution. In fact, the relationships between the above parameters are so complicated that a general theory to predict practical adhesion does not exist. One has to be very careful when trying to correlate results from indentation or scratching performed with, for example, spherical diamond tips with the situation of sliding contact in actual components like tools and machine elements. On the other hand, scratch tests can be very useful for obtaining qualitative measures of the mechanical strength (adhesion, cohesion, toughness, etc.) of coating composites (see Section 26.4.5.1). To evaluate the practical adhesion of coated components, the advice is to use, if not field tests, tribological tests with the closest possible resemblance to the actual situation.
26.4.3 Basic Coating Properties Basic coating properties such as thickness, composition, structure, morphology, and topography are best studied by modern imaging and analytical techniques (see Table 26.3) (Hogmark et al., 1997b). Coating thickness and morphology of thin PVD or CVD coatings are often easy to reveal from fractured cross-sections (see Figures 26.8, 26.12, and 26.14). Compositional depth profiles of coatings 1 µm in thickness or less can be obtained by XPS or AES. These techniques combine alternating ion etching and analysis. Due to a larger information depth, EDS gives the average coating composition, and often also signals from the substrate material. Thicker coatings can be profiled without prior sample preparation by GDOES (Figure 26.20). Alternatively, EDS or AES can give the corresponding information by analyzing polished cross-sections or tapered sections.
26.4.4 Intrinsic Mechanical Properties Some of the intrinsic mechanical properties are of particular interest. These are the Young’s modulus and residual stress, that is, properties related to elastic deformation, hardness (i.e., property related to plastic deformation), and toughness or fracture resistance (i.e., properties related to fracture). 26.4.4.1 Young’s Modulus The intrinsic Young’s modulus (elastic modulus) of the coating (Ec) is a useful parameter in the measurements and calculations of the stress state and the cracking and delamination behavior of coating composites. It is possible to obtain Ec through a number of techniques, but the uniaxial tensile test is the most straightforward (Hollman et al., 1997b). The Young’s modulus of a coating can be obtained from
(
Ec = k − Es t s w − k g
) tw c
(26.1)
where k is the slope of the tensile curve, kg is the slope of force vs. strain for a strain gage glued to the coated sample (determined separately), Es is the Young’s modulus of the substrate material (known), w is the width of the coated sample, and tc and ts are the thicknesses of coating and substrate, respectively.
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TABLE 26.3
Common Techniques Used to Assess Basic Coating Properties
Technique Scanning electron microscopy (SEM) Transmission electron microscopy (TEM) Energy dispersive X-ray spectroscopy (EDS) X-ray diffraction (XRD) X-ray photo-electron spectroscopy (XPS) Auger electron spectroscopy (AES) Rutherford backscattering (RBS) Glow discharge optical emission spectroscopy (GDOES) Secondary ion mass spectrometry (SIMS) Raman spectroscopy Atomic force microscopy (AFM) Profilometryc
Type of Information Surface topography and defects, coating thickness, porosity and structure morphology, fractography, etc. Grain size, morphology and defects by imaging, phase composition and orientation by electron diffraction, elemental composition by electron energy loss spectroscopy (EELS) Elemental composition with good relative quantitative accuracy (0.5 to 5%); sensitivity 0.1% Phase structure, texture and composition, chemical modulation period of multilayers, strain in surface layers Elemental and chemical composition through the nature of the chemical bonds; depth profiling down to 1 µm; relative quantitative accuracy (10 to 30%) Elemental composition, especially the light elements C, N, O; some chemical information; depth profiling down to 1 µm; sensitivity 0.2%, relative quantitative accuracy (10 to 20%) Composition, including all elements (except H); depth profiling down to 50 µm Composition, including all elements (even H); depth profiling down to 50 µm depth; sensitivity down to 0.01% Composition, including all elements (even H); depth profiling down to 10 µm; sensitivity 0.1 ppm!; relative quantitative accuracy (10 to 50%) Often used to analyze the proportion of sp2 (graphite) and sp3 (diamond) bonds of carbon coatings Quantified surface topography and friction recordings down to atomic scale Quantified surface topography
Lateral Resolution (µm)
Information Deptha (µm)
0.1–0.01 0.0003
1–0.001b
1
1000
0.01–2
20
0.002
1–0.05
0.002
500
2
2.000
100
1–0.05
0.002
5
2
1–0.001
5c
1–0.05
1000d
a The information always represents an average composition of a surface layer, the thickness of which depends on the depth of penetration of the activating radiation and the absorption of the measured signal. b Used in SEM, the resolution is about 1 µm. In TEM, a lateral resolution down to about 0.001 µm can be obtained due to a limited specimen thickness (1 to 20 nm). c Includes stylus and optical profilometry. d Refers to the maximum surface profile height/depth.
FIGURE 26.20 GDOES elemental depth profile of a coating aimed for machine elements. A superficial DLC layer has been deposited on top of a Ti/TiN multilayer coating.
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The intrinsic elastic modulus of thin coatings can also be determined by nanoindentation (see Section 26.4.4.3), vibrating reed tests, bulge tests, beam bending tests, ultrasonic wave propagation, etc. (Brown et al., 1993; Rouzaud et al., 1995; Blakely, 1964; Hoffman, 1989; Schultrich et al., 1984). 26.4.4.2 Residual Stresses Residual stresses (σres) are usually generated in PVD and CVD coatings during deposition and subsequent cooling from the deposition temperature. During deposition, structural misfits in epitactic coating nucleation and growth, and simultaneous ion bombardment, can generate stresses of tensile or compressive nature. On top of these, stresses due to mismatch in thermal contraction between coating and substrate materials, and possible phase transformations during cooling, are superimposed (Nix, 1989). The actual stress during application (σ) is given by:
σ = σ res + σ app
(26.2)
where σapp denotes any stress field induced by external forces during application, including the consequence of frictional heating and thermal mismatch. Excessively high compressive stresses can result in spontaneous coating detachment (e.g., during cooling from the process temperature) or detachment when the component is externally loaded (see Figure 26.21(a)) (Hogmark et al., 1997a). The risk for detachment depends on the geometry and topography of the coating-substrate interface, as well as the interfacial stresses induced by the tribological loading, as described by Wiklund et al. (1999b). The magnitude of the interfacial normal or shear stress generated by the residual stress in the coating can, for unfavorable shapes, exceed 50% of the residual stress level. For coatings on a rough substrate, they can amount to 25% of the residual stress, if the roughness is of the same order as the coating thickness (see Figure 26.21(b)). Even if the adhesion is optimized, there remains a high risk that the induced interfacial stresses will reach the yield stress of the substrate material. Because most wear-resistant PVD and CVD coatings are quite brittle, a compressive σres will usually improve their apparent cohesion and toughness. During PVD deposition, the compressive stress state can be controlled by varying the bias voltage applied to the substrate. The common techniques used for residual stress measurements are based either on measurements of the elastic strains in the film (using X-ray diffraction), or on the deflection of thin coated substrates. The two approaches yield comparable accuracy. X-ray techniques can yield information of all strain components in the coating (Rickerby et al., 1987; Sue, 1992), and also give information about the strain distribution through the thickness of the coating
(a)
(b)
FIGURE 26.21 A compressive residual stress of 4 GPa in a TiN coating on a rough HSS substrate generates normal stresses across the interface in convex areas. A tensile residual stress state would give similar stresses of opposite sign. (a) Coating detachment along a sharp ridge as a result of combined excessively high residual stress and external loading by scratching; (b) maximum tensile stress max σn across the interface vs. radius R of surface ridges for four coating thicknesses.
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(Venkatraman et al., 1992). To obtain the residual stress using X-rays, the elastic constants of the coating must be known. The substrate deflection techniques determine the coating residual stress by measuring the curvature of the thin coating composite, caused by the stressed coating (Townsend and Barnett, 1987; Röll, 1976; Stoney, 1909). The deflection is often measured using laser scanning techniques or profilometry (Nix, 1989). Coating to substrate thickness ratios in the range of 1:100 to 1:1000 are required for best accuracy, which means that substantial thinning is often necessary prior to deflection measurement of actual components. Deflection techniques can also be used in situ during coating deposition, if sufficiently thin substrates are used. Usually, the residual stress is obtained by the “thin-film approximation” technique (the coating is much thinner than the substrate). This technique has the advantage of not requiring data of the elastic properties of the coating material to calculate the residual stress. This is done by applying the so-called Stoney equation (Stoney, 1909):
σ res = −
Es t s2 1 1 − 6 1 − νs t c ra rb
(
)
(26.3)
where Es /(1 – νs) is the biaxial modulus of the substrate; ts and tc are the substrate and coating thickness, respectively; ra is the radius of curvature after coating deposition on an originally flat substrate; and rb is the radius of curvature for the substrate prior to coating. The deflection technique assumes that the residual stresses are homogeneously distributed throughout the coating. The accuracy of the X-ray and deflection techniques is comparable. The nature of the residual stress of PVD coatings is generally compressive due to the ion bombardment during deposition. The nature and magnitude of the residual stresses in CVD coatings are primarily a result of the difference in thermal contraction between coating and substrate material. 26.4.4.3 Hardness To assess coating quality and to predict the coating performance in various applications, coating developers often use hardness measurements. However, the importance of a high intrinsic coating hardness should not be exaggerated. It is only in pure two-body abrasive wear that the wear resistance is very closely coupled to hardness. This also requires that the abrasives or abrasive surface is harder than the wearing surface. Almost all abrasive materials — except for coated components — are softer than 20 GPa, a value that is exceeded by many of today’s PVD and CVD coatings (see Table 26.1). When the hardness of the coating exceeds that of the wearing, surface properties such as toughness, chemical stability, and fatigue resistance become more important. The intrinsic hardness of thin coatings can be directly measured by conventional microhardness testing if the indentation depth does not exceed 10% of the coating thickness. Consequently, conventional Vickers indentation is restricted to coatings thicker than about 5 µm. It is possible to use microhardness values obtained from thinner coatings if models that take the substrate deformation into account are applied (Jönsson and Hogmark, 1984; Vingsbo et al., 1986; Burnett and Rickerby, 1987). During the last decade, however, nanoindentation has become the most common technique to obtain intrinsic mechanical properties of thin coatings. In nanoindentation, the applied load is typically 0.01 to 5 g, as compared to 5 to 1000 g for microhardness testing. In nanoindentation, the load and tip displacement are continuously recorded (Figure 26.22). The hardness is obtained from load/displacement curves using different theoretical approaches (e.g., as proposed by Oliver and Pharr, 1992). 26.4.4.4 Toughness Coating cracking or fracture often precedes severe damage of PVD and CVD coatings. Thus, the ability of the coating composite to accommodate deformation in tension or compression without crack nucleation and propagation is crucial. Critical situations are found in applications of nonconforming sliding or rolling (see Sections 26.4.5.4 and 26.4.5.5).
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FIGURE 26.22 Nanoindentation curves for three different PVD coatings: TiB2, TiN, and CrN. The obtained hardness values and Young’s moduli [GPa] were 53/566 (TiB2), 30/450 (TiN), and 25/330 (CrN), respectively. (a)
(c) (b)
FIGURE 26.23 (a) Photograph of a four-point, beam-bending device suitable for operation in an SEM. A indicates the coated test specimen, B the load cell, and C the acoustic detector. (b) A representative plot of crack density (o) and acoustic emission (line) vs. coating and composite strain, respectively, for a 4-µm PVD TiN-coating on ASP2030 HSS. The insert shows a top view of a coating stressed beyond the fracture limit. (c) Critical strains of multilayered TiN/TaN coatings compared with those of the single TiN and TaN layers. The light bars represent the composite strain, while the dark bars represent the coating strain for which the residual stress has been subtracted. (From Wiklund, U., Hedenqvist, P., and Hogmark, S. (1997), Multilayer cracking resistance in bending, Surf. Coat. Technol., 97, 773-778. With permission.)
Several investigators have used beam bending to assess the deformability of coatings and to obtain numerical estimates of their fracture resistance and toughness (Ramsey et al., 1991; Oettel and Wiedemann, 1995; Wiklund et al., 1997). In the device of Figure 26.23(a), the bending load is continuously
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increased and the critical strain to initiation of the first crack can be recorded acoustically or in situ in the SEM (see Figure 26.23(b)). Multilayered coatings generally exhibit a higher critical strain to fracture than do homogeneous coatings (see Figure 26.23(c)). Because cracking is initiated by tensile stresses, any compressive residual stress must be overcome before cracking will commence. Consequently, high compressive residual stresses in the coating increase the critical strain of the component to coating fracture. The critical composite strain is thus a more important parameter than the critical intrinsic tensile strain of the coating. Note also that the true fracture strain of the coating materials is very low compared to that of homogeneous bulk ceramics, which usually is around 1%. This indicates a great potential of improving the coating toughness once the weak columnar structure can be avoided.
26.4.5 Tribological Properties Tribological properties here refer to the general tribological properties of the coating composite, for thin coatings involving influence from both coating and substrate. With relevant information on the general friction and wear properties, and supporting knowledge of basic coating and substrate properties, it is possible to recommend applications for given coating composites. As discussed in Section 26.4.6, the end user may, however, not be satisfied until a confirming field test has been performed. Below, five tribological properties are identified and simple tests for their assessment are demonstrated. 26.4.5.1 Scratch Resistance Scratch testing has, together with hardness measurements, become the most common way of assessing the mechanical quality of coating composites (Steinmann and Hintermann, 1989). Most often, the scratch test utilizes a spherical diamond tip of Rockwell C geometry. The tip loading is increased either stepwise or continuously, and critical loads for coating failure are determined by friction and acoustic emission (AE) recording. The critical load can be defined as the load for first crack appearance or first induced cohesive or interfacial fracture. Optical microscopy or SEM should be used to confirm the results (Steinmann et al., 1987), and can give detailed information about various modes of coating failure (Figure 26.24). A general rule of thumb says that a critical load of 30 N (using a diamond tip of 25-µm radius) is sufficient for sliding contact applications. Critical loads of 60 to 70 N are frequently recorded for PVD coatings on hardened HSS. It should be pointed out that the critical load usually increases with substrate hardness and coating thickness, and decreases with increasing surface roughness (Larsson, 1996a). Originally, the scratch test was developed for evaluation of adhesion, and adhesive failures are often associated with a sudden increase in friction force and acoustic emission. However, many of today’s PVD and CVD coatings either deform to accommodate to the substrate deformation or fail by cohesive rather than interfacial fracture. 26.4.5.2 Resistance to Abrasive Wear In situations of mild abrasion, the coating material can determine the wear resistance of a coating composite. Standard abrasive wear tests are usually not capable of generating the intrinsic wear resistance of thin coatings.
(a)
(b)
FIGURE 26.24 Typical information revealed by SEM of scratch tested coating composites: (a) local cohesive failure at the edge of a scratch in a TiN coating on HSS; and (b) extensive coating failure along the scratch in a multilayered TiN/NbN coating on HSS.
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FIGURE 26.25 (a) Schematic view of the dimple grinder. A grinding wheel rotating about horizontal axes is loaded against the horizontally positioned specimen, which is also rotated. In this way, a spherical crater is obtained in the specimen surface. Any suitable abrasive medium can be used. (b) Representative Vc vs. (SL – Vs/κs) plot (TiN on HSS). (From Gåhlin, R., Larsson, M., Hedenqvist, P., Jacobson, S., and Hogmark, S. (1997), The crater grinder method as a means for coating wear evaluation — an update, Surf. Coat. Technol., 90, 107–114. With permission.) (c) Typical plot of intrinsic abrasive wear resistance of some PVD coatings. The particle erosion wear is also indicated. (From Nordin, M., Larsson, M., and Hogmark, S. (1999), Evaluation of the wear resistance of multilayered PVD TiN/TaN coatings, accepted for publication in Surface and Coatings Technology.) (d) Localized adhesive failure detected by SEM of a wear crater made by dimple grinding.
However, thin coatings can be evaluated in the micro-abrasion test originally proposed by Kassman et al. (1991) and further developed by Rutherford and Hutchings (1996, 1997), and Gåhlin et al. (1997). This technique makes it possible to distinguish the abrasive wear resistance of a thin coating material from that of the substrate, and also in situations where the coating is worn through. A small grinding wheel (dimple grinding) or ball (ball cratering) is used to produce a spherical crater in the surface of the coating composite (Figure 26.25(a)). The contact area is immersed in an abrasive medium. The test is interrupted at regular intervals; and the crater volume is estimated either from measuring the diameter, or directly by using three-dimensional surface profilometry. By assuming Archard’s law to be valid for both coating and substrate, one arrives at:
SL =
Vc Vs + κc κ s
(26.4)
where S is the sliding distance, L is the applied load, Vc and Vs are the wear volumes, and κc and κs are the specific wear rates of the coating and substrate, respectively (Figure 26.25(b)). Intrinsic abrasive wear resistance of some PVD coatings obtained as 1/κc are given in Figure 26.25(c). Not only does the micro-abrasion test supply information about the coating and substrate wear resistance, but inspection of the test craters in the SEM reveals any content of coating defects such as
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pores and cracks. A poor adhesion can be detected by the presence of spallings in the coating substrate interface (see Figure 26.25(d)). Micro-abrasion test results must be handled with caution. Two-body abrasive wear of the coated surface dominates if the abrasives stick to the surface of the grinding wheel or ball. This is likely to be the case if the wheel or ball is softer than the tested material. If any constituent in the tested material is softer, the abrasives preferentially stick to the test material surface and wear the rotating ball or wheel. In a situation where both surfaces are of equal hardness, the particles may roll rather than slide, and the wear is dominated by three-body abrasion (Axén et al., 1994). Other parameters that must be kept under control are size distribution and volume fraction of the abrasive particles, and viscosity and wetting angle of the liquid medium. 26.4.5.3 Resistance to Particle Erosion Surface damage caused by impinging hard particles is usually referred to as particle erosion. For a thin coating to be effective in erosion protection, the strain fields of the individual impacts must not penetrate into the substrate material. Particle erosion can also be used as a means to test intrinsic coating properties — primarily the toughness, provided that the particle size, velocity, and angle of impact are chosen to limit the deformation energy transfer involved when the particle hits the surface. Resistance to particle erosion is rewarded by a combination of hardness and toughness, with the toughness being the dominant parameter. 26.4.5.4 Resistance to Sliding Wear Sliding wear is here referred to as wear in a tribological system where the coated component slides against a relatively smooth countersurface, free from hard particles or hard asperities. Naturally, it constitutes a very large group of tribological situations. After a sliding wear test, the mass loss of typical PVD or CVD coatings is too small to be resolved by weighing. The situation has, however, recently been improved by the introduction of accurate surface profilometers and by atomic force microscopes (AFM), by which very small wear volumes can be detected, mapped, or measured (Gåhlin and Jacobson, 1998). Apart from this, there is no principal difference in evaluating the sliding wear resistance of thin coatings and bulk materials. A new test for evaluation of friction and load-carrying capacity of coating composites has recently been suggested (Hogmark et al., 1998). Two elongated specimens slide axially against each other in a way similar to that of the contact between the edges of a pair of scissors. If the load is gradually increased, as in the scratch test, each contact spot along the wear track will experience a unique load. Unidirectional as well as multipass sliding can be applied, and critical loads for coating failure can be obtained as for the scratch test. The main advantage over the scratch test is that the contact situation is very much closer to practical applications of sliding contact. In addition, the counter material, as well as the contact geometry (radius of contacting rods), can be selected to represent the intended application. 26.4.5.5 Resistance to Wear in Rolling Contact The stress distribution in rolling contact between smooth surfaces can be estimated according to Hertz (Figure 26.17). Because the maximum shear stress is generated below the contact surface, the intrinsic wear resistance of the surface material is usually not the main concern. Strong adhesion and ability to deform elastically with the substrate are the two most important coating requirements in rolling contact (Figure 26.26). If a small, permanent deformation is accumulated in each contact event (ratchetting), the fracture limit of the coating will sooner or later be achieved. Rolling element bearings are currently being considered for application of coatings. Use in railway wheels is a larger-scale application which, of course, requires relatively thick coatings for wear protection. Pure rolling usually gives negligible wear. A small proportion of sliding in dry or boundary lubricated rolling contacts may give a mild wear. In slowly rotating roller bearings, such mild wear may gradually concentrate the contact pressure to the unworn regions of pure rolling and, eventually, cause catastrophic surface fatigue (Andersson, 1999). A wear-resistant coating can solve this problem.
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FIGURE 26.26 (a) Test designed to simulate the tribological situations in rolling contact. The cylindrical test pin is rotated against two normally loaded disks. (b) Typical coating wear after rolling contact simulation of TiN-coated HSS. The original grinding topography is seen at the left in the figure. Initially, the surface is smoothed due to a very mild wear mechanism. After a critical number of revolutions, the coating starts to spall.
The stress distribution in sliding between nonconforming surfaces resembles that of rolling contact, if the friction coefficient is below 0.3. Practical examples include the cam and tappet contact of a car engine, or the contact between gear teeth, both of which are designed to operate in the boundary lubrication regime. This means that the friction coefficient typically amounts to 0.10 to 0.15, and the maximum shear stress is not confined to the contact surface. Consequently, good adhesion and the ability to deform elastically with the substrate are required for coatings in this kind of application, as it is for rolling element bearings.
26.4.6 Tribological Response of Coated Components The end users of coated components are recommended to make the final evaluation of the tribological response in field tests or in component tests (i.e., tests where the actual component is evaluated under realistic conditions). Any simplified laboratory test can deviate from the actual situation as to nominal and real contact pressure, sliding speed, heat conductivity and capacity, ambient cooling, etc., and correlation to the real case is hazardous. Examples of components that can be field-tested relatively easily are cutting tools and other relatively small components with limited life. Large and expensive forming tools, for example, may have to be evaluated in simplified tests, preferably through smaller model tools used in a pilot plant. It is sometimes possible to design a large component incorporating small inserts that can be easily exchanged and act as test surfaces. In carefully designed tests, these inserts will experience the same tribological conditions as the actual component.
26.4.7 Failure Analysis of Coating Composites Premature failure of coating composites almost always involves local or extensive coating detachment. Given the task to analyze the cause of a premature failure of a coated component and suggesting means to improve it, the following questions should be addressed: 1. Substrate condition: Is the hardness, chemical composition, etc., of the substrate that which is desired? 2. Substrate surface preparation: Is the substrate too rough? Has the grinding been too severe, thus generating, for example, untempered martensite, decarburization, or thermal softening? Are there any residual impurities in the interface? 3. Type of coating failure: Has the failure been initiated mechanically, thermally, or chemically?
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Of course, these three causes require different remedies. Mechanical failure has been thoroughly treated in Section 26.4. If thermal softening or decomposition of coating and/or substrate is suspected, the mechanical properties at elevated temperatures should be emphasized. A chemical cause of coating detachment can be related to galvanic corrosion in the interface. A corrosion-resistant coating on a corrosion-resistant material can form a galvanic cell if chemical potentials deviate. In such a case, it is important that the coating is free from pin holes or cracks, running down to the substrate. If the coating/substrate material combination can be changed, increasing the coating thickness or introducing a multilayered coating structure might improve the situation (Wiklund et al., 1996). In the case of excessively rapid coating wear, again start by making sure if the dominant wear mechanism is mechanical or chemical. This is suitably done in the SEM, looking for any scratches, indentations, fracture surfaces, or any other sign of mechanical damage. It may be useful to also study metallographic cross-sections, because mechanical damage is accompanied by sub-surface deformation. Absence of such features indicates that chemical attack is dominant.
26.5 Visions and Conclusions The evolution of surface engineering has just begun. Sandvik Coromant introduced the first tribological CVD coating (TiC) in 1969 to protect cemented carbide cutting tools, and the first PVD coating (TiN) was applied to high-speed steel in the late 1970s for the same reason. These two are still considered to be among the very best tribological coating materials, even though new improved PVD and CVD coatings have evolved and proved superior in specific applications. During the last decade, the number of new coating materials, structures, combinations, and applications has increased exponentially. We have only seen the very beginning of an evolution which in the future probably will encompass virtually all mechanical components. Research will soon succeed in applying coatings to vital machine components of lightweight materials, thereby reducing the weight of machinery while maintaining or even improving performance and lifetime. Furthermore, many low-friction coatings may offer the same low-friction levels as those of boundary lubricated contacts (0.10 to 0.20). Thus, the need for lubrication of tools and machine components will decrease, which will help to relieve some of today’s environmental stresses. The current aim to coat light materials such as alloys based on Al, Ti, and Mg was pointed out in Section 26.3.3. Because these materials cannot resist the temperatures of most of today’s PVD and CVD processes (see Figure 26.6), there is an urgent need to develop deposition processes that involve considerably lower temperatures. Metal alloying has proved successful in increasing the toughness of other coatings and bulk ceramics, and should be explored also for diamond. The columnar structure of current PVD and CVD coatings makes them sensitive to stresses parallel to the plane of the coating. The fracture toughness of the best PVD coatings of today is only about one tenth that of the corresponding bulk ceramic material. However, there has been some pioneering work to overcome this drawback, reported by Veprek and Reprich (1995), by introducing second-phase particles. It would be even more challenging to design coatings with grains elongated to fibers preferably oriented in the plane of the coating. Such a structure should have the potential of being very tough. Finally, there is a need for models that can predict the tribological response of coated components. This is most urgent for machine components (see Section 26.3.3). Given relevant information of the application, these models should preferentially consider the load-carrying capacity of the composite, and generate recommendations of the coating thickness and of coating and substrate materials properties in terms of Young’s modulus, hardness, and toughness. However, while awaiting analytical tools for coatings selection and design, one will have to rely on selective testing (see Hogmark and Jacobson, 1992a). Thus, the development of versatile and reliable techniques for evaluation of coated components will continue to be important for the tribological assessment and development of new coating composites and their applications.
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Acknowledgments The authors gratefully acknowledge support from the Swedish Research Council for Engineering Sciences (TFR); the National Swedish Board for Technical and Industrial Development (NUTEK); the Swedish Board for Strategic Research (SSF); Sandvik Coromant; Erasteel; Seco Tools; Balzers Sandvik; Tixon; Volvo; Scania; ABB; Duroc; SKF; and staff at the Tribomaterials Group at the Ångström Laboratory, Uppsala University.
References Allen, S.M. and Thomas, E.L. (1998), The Structure of Materials, Wiley, New York. Andersson, S., (1999), Prediction of wear in rolling and sliding contacts, Proc. 21 IRG-OECD Meeting on Wear of Engineering Materials, Amsterdam, March 25-26. Axén, N., Jacobson, S., and Hogmark, S. (1994), Influence of the hardness of the counterbody in threebody abrasive wear — an overlooked hardness effect, Tribol. Int., 27, 233–241. Bell, T. (1975), Heat Treat. Met., 2, 39-49. Bell, T. (1997), New Directions in Tribology, Mech. Eng. Publication Ltd., World Trib. Congress, London, 121. Bergmann, E., Kaufmann, H., Schmid, R., and Vogel, J. (1990), Ion-plated titanium carbonitride films, Surf. Coat. Technol., 42, 237-251. Blakely, J.N. (1964), Mechanical properties of vacuum-deposited gold films, J. Appl. Phys., 35, 1736. Blomberg, A., Olsson, M., and Hogmark, S. (1994), Wear mechanisms and tribo mapping of Al2O3 and SiC in dry sliding, Wear, 171, 77-89. Brown, G.C. and Pryputniewicz, R.J. (1993), Measurement of Young’s modulus on thin films under static and dynamic loading conditions, 302/SPIE, 2004 Interferometry, VI: Applications, 302. Chu, X., Barnett, S.A., Wong, M.S., and Sproul, W.D. (1993), Reactive unbalanced magnetron sputter deposition of polycrystalline TiN/NbN superlattice coatings, Surf. Coat. Technol., 57, 13-18. Courtney, T.H. (1990), in Mechanical Behavior of Materials, McGraw-Hill, New York. Dingremont, N., Bergmann, B., and Collignon, P. (1995a), Application of duplex coatings for metal injection moulding, Surf. Coat. Technol., 72, 157-162. Dingremont, N., Bergmann, B., Collignon, P., and Michel, H. (1995b), Optimisation of duplex coatings built from nitriding and ion plating with continuous and discontinuous operation for construction and hot working steels, Surf. Coat. Technol., 72, 163-168. Farges, G., Bosch, J.P., and Bergmann, E. (1989), Friction and adhesive wear behavior of W-C coatings against steel and titanium nitride, Wear, 135, 1-14. Gåhlin, R. and Jacobson, S. (1998), A novel method to map and quantify wear on a micro-scale, Wear, 222, 93–102. Gåhlin, R., Alahelisten, A., and Jacobson, S. (1996), The effects of compressive stresses on the abrasion of diamond coatings, Wear, 196, 226–233. Gåhlin, R., Larsson, M., Hedenqvist, P., Jacobson, S., and Hogmark, S. (1997), The crater grinder method as a means for coating wear evaluation — an update, Surf. Coat. Technol., 90, 107–114. Gunnars, J. (1997), On Fracture of Layered Materials, Ph.D. thesis No. 37, Luleå University of Technology, Sweden. Hedenqvist, P., Olsson, M., and Hogmark, S. (1992), Tribological studies of various magnetic heads and thin-film rigid disks, Wear, 153, 65-78. Hellgren, N. (1999), Sputtered Carbon Nitride Thin Films, Ph.D. thesis No. 604, Linköping University, Sweden. Helmersson, U., Sundgren, J.-E., and Greene, J.E. (1986), Microstructure evolution in TiN films reactively sputter deposited in multiphase substrates, J. Vac. Sci. Technology, A4, 500. Hirvonen, J.-P., Koskinen, J., Jervis, J.R., and Nastasi, M. (1996), Present progress in the development of low friction coatings, Surf. Coat. Technol., 80, 139.
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Hoffman, R.W. (1989), Nanomechanics of thin films: Emphasis: Tensile properties, Mat. Res. Soc. Proc., 130, 295. Hogmark, S. and Jacobson, S. (1992a), Hints and guidelines for tribotesting and evaluation, JSTLE, May, 401-409. Hogmark, S., Jacobson, S., and Vingsbo, O. (1992b), In Friction Lubrication and Wear Technology, ASM Handbook 18, 176. Hogmark, S., Hollman, P., Alahelisten, A., and Hedenqvist, P. (1996), Direct current bias applied to hot flame diamond deposition produces smooth low friction coatings, Wear, 200, 225-232. Hogmark, S., Hedenqvist, P., and Jacobson, S. (1997a), Tribological properties of thin hard coatings — Demands and evaluation, Surf. Coat. Technol., 90, 247-257. Hogmark, S., Jacobson, S., Hedenqvist, P., and Olsson, M. (1997b), Surface Characterisation, A User’s Sourcebook, Brune, Hellborg, Whitlow and Hunderi (Eds.), Wiley-VCH, Weinheim, Germany, 624–644. Hogmark, S., Jacobson, S., and Wänstrand, O. (1998), Universal test for friction, wear and lubrication, Swedish patent DNR 9802017-5. Hollman, P. (1997a), Micro- and Nanocrystalline Diamond Coatings with Extreme Wear Resistance and Ultra Low Friction, Acta Universitatis Upsaliensis Dissertation in Science and Technology 325, ISBN 91-554-4084-3. Hollman, P., Larsson, M., Hedenqvist, P,. Hogmark, S. (1997b), Tensile testing as a method for determining the Young’s modulus of thin hard coatings, Surf. Coat. Technol., 90, 234-238. Holmberg, K. and Matthews, A. (1994), Coatings Tribology, Tribology series, 28, Elsevier. Johansson, E. (1993), Surface modification in tribology, Acta Universitatis Upsaliensis Dissertation in Science and Technology 433 ISBN 91-554-3061-6, Paper VII. Jönsson, B. and Hogmark, S. (1984), Hardness measurements of thin films, Thin Solid Films, 114, 257-269. Karner, J., Pedrazzini, M., Reineck, I., Sjöstrand, M.E., and Bergmann, E. (1996), CVD diamond coated cemented carbide cutting tools, Mater. Sci. Eng. A: (Structural Materials: Properties, Microstructure and Processing), A209, 402-410. Kassman, Å., Jacobson, S., Erickson, L., Hedenqvist, P., and Olsson, M. (1991), A new test method for the intrinsic abrasion resistance of thin coatings, Surf. Coat. Technol., 50, 75–84. Khruschov, M.M. (1974), Principles of abrasive wear, Wear, 28, 68-88. Larsson, M. (1996a), Ph.D. thesis, Acta Universitatis Upsaliensis Dissertation No. 191, Uppsala University, Sweden. Larsson, M., Hollman, P., Hedenqvist, P., Hogmark, S., Wahlström, U., and Hultman, L. (1996b), Deposition and microstructure of PVD TiN-NbN multilayered coatings, Surf. Coat. Technol., 86/87, 351-356. Mao, K., Sun, Y., and Bell, T. (1994), Contact mechanics of engineering surfaces: state of the art, Surf. Eng., 10, 297-306. Nix, W.D. (1989), Mechanical properties of thin films, Metallurgical Trans., 20a, 2225. Nordgren, A. and Melander, A. (1988), Tool wear and inclusion behavior during turning of a Ca-treated quenched and tempered steel using coated cemented carbide tools, Proc. 1st Int. Conf. on the Behaviour of Materials in Machining, Stratford-upon-Avon, U.K., Nov., paper 20. Nordin, M., Larsson, M., and Hogmark, S. (1998), Mechanical and tribological properties of multilayered PVD TiN/CrN, TiN/NbN, TiN/MoN and TiN/TaN, Surf. Coat. Technol., 106, 234-241. Nordin, M., Larsson, M., and Hogmark, S. (1999), Wear resistance of multilayered PVD TiN/TaN coatings on HSS, Surf. Coat. Technol., 120-121, 528-534. Oettel, H. and Wiedemann, R. (1995), Residual stresses in PVD hard coatings, Surf. Coat. Technol., 76/77, 265–273. Oliver, W.C. and Pharr, G.M. (1992), An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments J. Mater. Res., 7, 1564-1583. Palmai, Z. (1984), Formation of non-metallic protective layers on high speed tools, Met. Technol., 11, 34-37.
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Ramsey, P.M., Chandler, H.W., and Page, T.F. (1991), Bending tests to estimate the through-thickness strength and interfacial shear strength in coated systems, Thin Solid Films, 201, 81-89. Rickerby, D.S., Bellamy, B.A., and Jones, A.M. (1987), Internal stress and microstructure of titanium nitride coatings, Surf. Eng., 3, 138. Rickerby, D.S. and Bull, S.J. (1989), Engineering with surface coatings. The role of coating microstructure, Surf. Coat. Technol., 39/40, 315. Rickerby, D.S. and Burnett, P.J. (1987), The wear and erosion resistance of hard PVD coatings, Surf. Coat. Technol., 33, 191-211. Röll, K. (1976), Analysis of stress and strain distribution in thin films and substrates, J. Appl. Phys., 47, 3224. Rouzaud, A., Barbier, E., Ernoult, J., and Quesnel, E. (1995), A method for elastic modulus measurements of magnetron sputtered thin films dedicated to mechanical applications, Thin Solid Films, 270, 270. Rutherford, K.L. and Hutchings, I.M. (1996), A microabrasive wear test with particular application to coated systems, Surf. Coat. Technol., 79, 231-239. Rutherford, K.L. and Hutchings, I.M. (1997), Theory and application of a micro-scale abrasive wear test, J. Testing Eval., 25, 250-260. Schultrich, B., Scheibe, H.-J., Grandremy, G., and Schneider, D. (1984), Elastic modulus of amorphous carbon films, Phys. Stat. Sol. (a), 145, 385. Selinder, T.I., Nordin, M., Larsson, M., Hedenqvist, P., Östlund, Å., Hogmark, S., and Sjöstrand, M.E. (1998), Performance of PVD TiN/TaN and TiN/NbN superlattice coated cemented carbide tools in stainless steel machining Surf. Coat. Technol., 105, 51-55. Shinn, M., Hultman, L., and Barnett, S.A. (1992), Growth, structure and microhardness of epitaxial TiN/NbN superlattices, J. Mater. Res., 7, 901-911. Sjöström, H., Hultman, L., Sundgren, J.-E., Hainsworth, S.V., and Page, T.F. (1996), Structural and mechanical properties of L. carbon nitride CNx (0.2 ≤ x ≤ 0.35) films, Theunissen-GSAM, J. Vac. Sci. Technol., 14, 56-62. Sproul, W.D. (1994), Multilayer, multicomponent, and multiphase physical vapor deposition coatings for enhanced performance, J. Vac. Sci. Technol., A12, 1595. Sproul, W.D., Graham, M.E., Wong, M.S., Lopez, S., Li, D., and Scholl, R.A. (1995), Reactive direct current magnetron sputtering of aluminium oxide coatings, J. Vac. Sci. Technol., 13 1188. Sproul, W.D. (1996a), Physical vapor deposition tool coatings, Surf. Coat. Technol., 81, 1. Sproul, W.D. (1996b), Reactive sputter deposition of superhard polycrystalline nanolayered coatings, layered materials for structural applications, Symp. Mater. Res. Soc., Pittsburgh, PA, ix+314, 47-55. Steinmann, P.A. and Hintermann, H.E. (1989), A review of the mechanical tests for assessment of thinfilm adhesion, J. Vac. Sci. Technol., A7, 2267-2272. Steinmann, P.A., Tardy, Y., and Hintermann, H.E. (1987), Adhesion testing by the scratch test method: the influence of intrinsic and extrinsic parameters on the critical load, Thin Solid Films, 154, 333-349. Stoney, G.G. (1909), The tension of metallic films deposited by electrolysis, Proc. R. Soc. London, A82, 172. Sue, J.A. (1992), X-ray elastic constants and residual stress of textured titanium nitride coating, Surf. Coat. Technol., 54/55, 154. Sugimura, Y., Lim, P.G., Shih, C.F., and Suresh, S. (1995), Fracture normal to a bimaterial interface: effects of plasticity on crack-tip shielding and amplification, Acta Metall. Mater., 43, 1157. Suryanarayana, C. (1995), Nanocrystalline materials, Int. Mat. Rev., 40, 41. Todorova, S., Helmersson, U., Barnett, S.A., Sundgren, J.-E., and Greene, J.E. (1987), TiN-VN strained layer superlattice hard coatings, IPAT 87. 6th Int. Conf. on Ion and Plasma Assisted Techniques, CEP Consultants, Edinburgh, U.K., xi+481,248. Townsend, P.H. and Barnett, D.M. (1987), Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate, J. Appl. Phys., 62, 4438. Venkatraman, R., Besser, P.R., Brennan, S., and Brauman, J. (1992), Determination of strain distributions in aluminium thin films as a function of temperature by the use of synchrotron grazing incidence X-ray scattering, Mat. Res. Soc. Symp. Proc., 239, 227.
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Veprek, S. and Reprich, S. (1995), A concept for the design of novel superhard coatings, Thin Solid Films, 268, 64. Vingsbo, O., Hogmark, S., Jönsson, B., and Ingemarsson, A. (1986), A., Microindentation Techniques in Materials Science and Engineering, Blau, P.J. and Lawn, B.R. (Eds.), ASTM publication 889, 257-271. Voevodin, A.A., Donley, M.S., and Zabinski, J.S. (1997), Pulsed laser deposition of diamond-like carbon wear protective coatings: a review, Surf. Coat. Technol., 92, 42-49. Voevodin, A.A., O’Neill, J.P., and Zabinski, J.S. (1998), Tribological performance and tribochemistry of nanocrystalline WC/amorphous diamond-like carbon composites, Thin Solid Films, 342, 194-200. Wiklund, U., Hedenqvist, P., Hogmark, S., Stridh, B., and Arbell, M. (1996), Multilayer coatings as corrosion protection of Zircalloy, Surf. Coat. Technol., 86-87, 530-534. Wiklund, U., Hedenqvist, P., and Hogmark, S. (1997), Multilayer cracking resistance in bending, Surf. Coat. Technol., 97, 773-778. Wiklund, U. and Larsson, M. (1999a), Low friction PVD titanium-carbon coatings, Wear, 241, 234-238. Wiklund, U., Gunnars, J., and Hogmark, S. (1999b), Influence of residual stresses on fracture and delamination of thin hard coatings, Wear, 232, 262-269. Windischmann, H. (1992), Intrinsic stress in sputter-deposited thin films, Crit. Rev. Solid State and Mater. Sci., 17, 547.
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IV Tribology of Industrial Components and Systems Bharat Bhushan The Ohio State University
Stephen M. Hsu National Institute of Standards and Technology
27
Slider Bearings David E. Brewe ..................................... 969 Introduction • Self-acting Finite Bearings • Failure Modes • Slider Bearing Materials
28
Rolling Element Bearings Xiaolan Ai and Charles A. Moyer ................................................................................. 1041 Introduction • Rolling Element Bearing Types • Bearing Materials • Contact Mechanics • Bearing Internal Load Distribution • Bearing Lubrication • Bearing Kinematics • Bearing Load Ratings and Life Prediction • Bearing Torque Calculation • Bearing Temperature Analysis • Bearing Endurance Testing • Bearing Failure Analysis
29
Gears
Herbert S. Cheng ................................................. 1095
Introduction • Gear Types • Tribological Failure Modes • Full-Film Lubrication Performance • Mixed Lubrication Characteristics • Modeling of Tribological Failures in Gears • Failure Tests • Conclusions
30
Rotary Dynamic Seals
Richard F. Salant .................... 1131
Introduction • Mechanical Seals • Rotary Lip Seal • Nomenclature • Defining Terms
31
Space Tribology William R. Jones, Jr. and Mark J. Jansen ................................................................................ 1159 Introduction • Lubrication Regimes • Mechanism Components • Liquid Lubricants and Solid Lubricants • Liquid Lubricant Properties • Accelerated Testing and Life Testing • Summary
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Automotive Tribology Ajay Kapoor, Simon C. Tung, Shirley E. Schwartz, Martin Priest, and Rob S. Dwyer-Joyce ....................................................................... 1187 Introduction • The Engine • Transmission and Drive Line • The Tire • The Brakes • Windshield Wipers • Automotive Lubricants
33
Diesel Engine Tribology Malcolm G. Naylor, Padma Kodali, and Jerry C. Wang ................................... 1231 Introduction • Power Cylinder Components • Overhead Components • Engine Valves • Bearings and Bushings • Turbomachinery • Fuel System • Fuels, Lubricants, and Filtration • Future Trends
34
Tribology of Rail Transport Ajay Kapoor, David I. Fletcher, F. Schmid, K.J. Sawley, and M. Ishida .............. 1271 Introduction • Wheel/Rail Contact • Diesel Power for Traction Purposes • Current Collection Interfaces of Trains • Axle Bearings, Dampers, and Traction Motor Bearings • New Developments and Recent Advances in the Study of Rolling Contact Fatigue • Conclusion
35
Tribology of Earthmoving, Mining, and Minerals Processing Jeffrey A. Hawk and R.D. Wilson .............. 1331 Introduction • Wear Processes in Mining and Minerals Processing • Equipment Used in Earthmoving Operations • Equipment Used in Mining and Minerals Processing • General Classification of Abrasive Wear • Tribological Losses in the Mining of Metallic Ores, Coal, and Non-metallic Minerals • Financial Cost of Wear in Earthmoving, Mining, and Minerals Processing • Concluding Remarks
36
Marine Equipment Tribology Steven R. Schmid and Karl J. Schmid ............................................................ 1371 Introduction • Marine Oil Properties and Chemistry • Diesel Engine Lubrication • Steam and Gas Turbines • Ancillary Equipment
37
Tribology in Manufacturing Steven R. Schmid and William R.D. Wilson ......................................................... 1385 Introduction • Unique Aspects of Manufacturing Tribology • Metal Cutting • Finishing Operations • Bulk Forming Operations
38
Macro- and Microtribology of Magnetic Storage Devices Bharat Bhushan ............................................... 1413 Introduction • Magnetic Storage Devices and Components • Friction and Adhesion • Interface Temperatures • Wear • Lubrication • Micro/Nanotribology and Micro/Nanomechanics • Closure
39
Macro- and Microtribology of MEMS Materials Bharat Bhushan ................................................................ 1515 Introduction • Experimental Techniques • Results and Discussion • Closure
40
Mechanics and Tribology of Flexible Media in Information Processing Systems Richard C. Benson and Eric M. Mockensturm ................................... 1549 Introduction • Introduction to Foil Bearings • A Simple Foil Bearing Model • Other Foil Bearing Models • Air Reversers • Introduction to Wound Rolls • Air Entrainment in Wound Rolls • Nip-Induced Tension and J-line Slip in Web Winding • Web Tenting Caused by High Asperities • Mechanisms that Cause a Sheet to Jam, Stall, or Roll Over in a Channel • Micro-slip of Elastic Belts • Transport of Sheets Through Roller/Roller and Roller/Platen Nips
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Biomedical Applications John Fisher .......................... 1593 Introduction • Tribology in the Human Body • Tribology of Artificial Organs and Medical Devices • Natural Synovial Joint and Articular Cartilage • Total Replacement Joints • Wear and Wear Debris Induced Osteolysis • Joint Replacement and Repair in the Next Millennium
42
Technologies for Machinery Diagnosis and Prognosis Richard S. Cowan and Ward O. Winer ....... 1611 Introduction • Failure Prevention Strategies • Condition Monitoring Approaches • Tribo-Element Applications • Equipment Asset Management
T
ribology is an applied science and, as such, many industrial components are designed based on tribological principles. Reliability and durability are the two most important criteria for tribological industrial components. Broadly speaking, tribological components are used to transmit power, achieve desired direction, machining, removing materials, shaping materials, etc. Therefore, a large variety of components are designed, including: gears, axles, pistons and cylinder liners, bearings, and seals. At the same time, tiny moving parts that enable electronic and electrical components to work (e.g., printers, scanners, actuators, hard disks, and satellites) all depend on successful tribological components. In short, any components that have contacting moving parts call for designs based on successful application of the science and engineering of tribology. As such, tribological components permeate throughout the industrial sectors, from aerospace to microelectronics, from manufacturing to earthmoving equipment, from automobiles to railroad transportation, from power generation to metal forming. Tribology is truly a basic building block of modern industries. For a given design, materials, lubricants, and environment need to be integrated to produce a reliable and durable component. Due to the numerous applications, many materials and environments are encountered. There are mechanical design considerations such as load, speed, and materials selection. Then there are lubricant and environmental considerations to avoid corrosion, pitting, and other undesirable side effects. The variety produces specialization. Specialization leads to empirical practice based on experience. When this phenomenon is multiplied a thousand times due to the large number of variations, confusion reigns. To avoid unforeseen failure and side effects, it is a common practice to first test any new tribological components in the field for a period of time before commercialization. Therefore, the development cost for engines, lubricants, transmission fluids, etc., becomes very high. Associated with this high cost of entry, maintenance and diagnostic tools for existing equipment is another area that is important in industrial component applications. Some critical components such as large stationary turbines used in electricity generation or pumps used in nuclear power generation are constantly monitored. The technology of monitoring, failure prediction, and diagnostic analysis becomes part of the industrial tribology practice. In this section, tribological components are classified by component types which include bearings, gears, and seals. They are also classified by industry, such as automotive, space, diesel engine, and railroad. Others include earth-moving, manufacturing, data storage devices, computer peripherals, and biomedical components. Finally, a chapter on diagnostic and failure prediction rounds out the section. By the very nature of the subject, it is not possible to cover all the applications. This section describes the notable components in different industries and by different components. Readers are urged to seek additional references for other areas. One theme that dominates throughout the section is durability. Reliable design makes the components suitable for the specific applications in the first place. The issues of how long a component will last and what is the failure mode that causes it to fail underline the knowledge base in current tribology. Most industrial components are seeking the goals of maintenance-free and lubricated-for-life. This is true for diesel engines, human joint replacements, space components, printer heads, computer hard disks, etc. How to get there is the challenge that the tribological community is currently facing. When one focuses on this goal, gaps in our knowledge translate into gulfs in practice.
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New materials are becoming available every day. Advances in coatings, thin films, and powder metallurgy allow unprecedented choices in design. Yet the lack of understanding of how these materials react, corrode, lubricate, and fail prevent widespread application of the material technology into our designs. Lubricant technology, however, lags behind. Also, system design and integration do not progress fast enough to produce rapid advancements. These are common issues that readers will find in the various chapters underlining the technology described.
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27 Slider Bearings 27.1
Introduction ..................................................................... 969 Slider Bearing Types • Compressible Lubrication • Compressible vs. Incompressible • Advantages and Disadvantages for Bearing Types
27.2
Self-acting Finite Bearings............................................... 977 Fixed-Geometry Thrust Bearings • Pivoted (Tilting) Pad Thrust Bearings • Journal Bearings
27.3
Failure Modes ................................................................. 1019
27.4
Slider Bearing Materials ................................................ 1027
Cavitation Erosion Damage • Wear Due to Contaminants
David E. Brewe NASA Glenn Research Center
27.1
Materials for Liquid-Film Applications • Bearing Materials for Gas-Film Applications
Introduction
The vast number of industrial slider bearing designs initially evolved from a desire to create a bearing having better load-carrying capacity and/or reduced friction and wear. Thus, a great deal of emphasis was placed on the effectiveness of the bearing geometry to generate pressure (self-acting bearings) and thus increase load capacity. To illustrate how geometry affects the pressure-generating mechanism in a bearing, first consider the one-dimensional inclined slider in Figure 27.1. If one assumes the “no slip” condition, fluid is dragged into the converging wedge region by the moving runner. Since the exit is smaller than the entrance, a pressure is created to open up the exit so as to balance the flow into and out of the slider. If the two surfaces are restrained by a force (load), then pressure created within the bearing surfaces will resist the amount of fluid trying to enter (i.e., reverse flow) and will push more fluid out the exit so that the actual flow entering equals the flow exiting the slider.* For a finite bearing, one must take into account the fluid exiting along the sides as well (i.e., side-leakage). The slope of the inclined slider in Figure 27.1 is greatly exaggerated for bearing applications. To put it in perspective, Fuller (1984) considers the extreme case of a bearing pad having the length of a football field. The rise**, based upon a slope known for good load capability (3 mils/ft), was calculated to be 0.9 in. (2.28 cm). With respect to the slope of the inclined slider, another question arises: For the converging wedge geometry, is there an optimum slope that provides a maximum load-carrying capacity? Pinkus and Sternlicht (1961) calculated load capacity and friction, and plotted them against h1/h2 (see Figure 27.2). In the plot, Cp and Cf are functions of h1/h2, representing the dimensionless coefficients for load W and friction F, respectively. That is: *Hamrock (1994) provides a more detailed account of this process. **The difference in elevation between the entrance, h1, and exit, h2, of the inclined slider, i.e., h1 – h2 as viewed in Figure 27.1.
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x1
Runner
x2
U h2
tan-1m
h1 _ B
W Tapered land
B
FIGURE 27.1 Slider bearing configuration. (From Anderson, W.J. (1964), Hydrostatic lubrication, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, National Aeronautics and Space Administration, Washington, D.C.)
0.20 0.18
1.0
cf
0.9
cp 0.16
0.8 0.14 0.7 0.12 0.6 c p 0.10 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 a = h1/h2
cf
FIGURE 27.2 Load capacity and friction in plane sliders. (From Pinkus, O. and Sternlicht, B. (1961), Theory of Hydrodynamic Lubrication, McGraw-Hill, New York. With permission.)
W=
µ ⋅U ⋅ L ⋅ B2 ⋅ Cp h22
(27.1)
F=
µ ⋅U ⋅ B ⋅ L ⋅ Cf h2
(27.2)
and
where µ is the lubricant viscosity, U is the linear velocity, B is the breadth of the bearing (parallel to the direction of motion), and L is the bearing length (normal to the direction of motion). They showed that the maximum load capacity is achieved if h1/h2 = 2.2, at which value the load coefficient Cp was calculated to be 0.1602. Frene et al. (1997) plotted the dimensionless pressure profiles for three values of h1/h2 (see Figure 27.3). The figure illustrates the pronounced effect that geometry has on the pressure development for the one-dimensional inclined slider. Note that the profile producing the maximum pressure supports the optimization performed by Pinkus and Sternlicht. Note further from Equation 27.1 that aside from geometry, one can increase the load-carrying capacity of the bearing by increasing the fluid viscosity or the relative velocity of the runner. From Figures 27.2 and 27.3, one can see how the angle of inclination affects the one-dimensional inclined slider bearing. However, Lord Rayleigh (1918) recognized that other bearing profiles were as effective as or were more effective than the inclined slider in generating pressure. His analysis of several bearing profiles revealed that the shape for maximum load capacity was simply two parallel surfaces — one having a rectangular cross-sectional dam. This geometry eventually became known as the Rayleigh step bearing, which is shown in Figure 27.4, along with the corresponding pressure profile. Pinkus and
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FIGURE 27.3 Pressure distribution for various ratios of a = h1/h2. (From Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: Bearings and Thrust Bearings, Tribology Series 33, Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. With permission.) y for region 1
y for region 2
1
2
u
x
B2
B1
h2
h1
B
p
Pmax
FIGURE 27.4 Rayleigh step bearing and corresponding pressure profile, after Archibald (1950). (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
Sternlicht (1961) calculated the load coefficient for the step bearing to be 0.2052. Using the calculus of variations, one can verify that the stepped bearing is the optimum geometry for a one-dimensional slider. Frene et al. (1997) plot dimensionless load vs. h1/h2 (Figure 27.5) for both the inclined slider and the step bearing. Again, the plot supports the conclusion by Pinkus and Sternlicht (1961).
27.1.1
Slider Bearing Types
An overall view of industrial-type bearings can be presented expediently by first considering an assortment of possible one-dimensional configurations (e.g., Figure 27.6). Regardless of the specific geometry, the pressure-generating mechanism works basically in the same way as described previously for the simplest case, as seen in Figure 27.6b. The geometry in Figure 27.6a is characteristic of a partial arc bearing and/or journal bearing in which the upper member represents the shaft and the lower member the housing. Here, the housing is shown as the moving surface although the application dictates the motion. In the case in which there exists only normal motion relative to the two members, the geometry would be representative of a squeeze-film damper. Extending this geometry to three dimensions, in which the upper member is spherical and the lower member is a conforming cup-shaped surface, the geometry would represent a spherical bearing. The wedge-shaped configuration shown in Figure 27.6b is used in the classical Kingsbury (1950) and Michell (1905) thrust bearings, which will also be discussed in the context of tilting-pad thrust bearings
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FIGURE 27.5 Dimensionless load vs. ratio h1/h2. (From Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: Bearings and Thrust Bearings, Tribology Series 33, Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. With permission.)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
FIGURE 27.6 Eight typical geometries that have been analyzed for the formation of hydrodynamic films. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
(Figure 27.7). The same geometry and variations thereof are employed in the “flying heads” used for computer hard drives. The heads are tilting-pad sliders that are supported above the spinning magnetic disk by a hydrodynamic air film. Fuller (1984), at that time, reported films on the order of 5.0 × 10–7 m (20 millionths of an inch) and less. According to Van der Stegen (1997), the development of the hard disk slider has enabled gas film spacing on the order of 25 nm (9.84 × 10–7 in.) and less. Bao and Li (1998) reported studies on liquid films an order of magnitude less, i.e., ~ 2.0 to 3.0 nm (7.87 × 10–8 to 11.81 × 10–8 in.). Figure 27.6 includes geometries [(c) through (h)] that Purday (1949) had analyzed for pressure generation. His conclusion was in agreement with Rayleigh’s; which was that one geometry was about as effective in generating pressure as the other, and that the step bearing geometry in Figure 27.6h generated the maximum peak pressure. Furthermore, friction forces were larger for a step bearing than
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Motion of the runner
Wp Runner h
Pad leading edge
Pivot
Film-pressure profile
FIGURE 27.7 Tilting-pad slider bearing and generated pressure distribution. (From Anon. (1983), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded, Off-Set Pivot, Tilting-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 83004, Institution of Mechanical Engineers, London, England.)
for a plane inclined slider, but the flow was smaller. Also, the moment of pressure (i.e., center of pressure) was independent of h1/h2. The idea of using the step bearing was advanced by Archibald (1950) when he applied it to a sector-shaped thrust bearing and then later to a journal bearing. The stepped bearing design is easier to fabricate than the tapered land bearings shown in Figures 26.6e and f (Fuller, 1984). Self-acting bearings sometimes required additional help (via external pressurization) to keep the bearing surfaces separated during start and stop conditions to avoid surface wear and reduce frictional energy loss. Thus, hybrid bearings were the result of occasionally combining the two pressure-generating schemes to provide greater load-carrying capacity and/or a stiffer bearing to improve stability. Externally pressurized bearings without relative motion between the bearing surfaces are commonly referred to as “hydrostatic bearings.”* The consideration of industrial bearings herein is limited to those having relative motion, that is “pure sliding,” “relative rotation,” and/or “normal motion” described by Szeri (2001) in self-acting and hybrid applications. As industrial applications increased, it became apparent that the bearing designer often did not have the option of choosing the lubricant. For example, launch vehicles and power generation systems are better suited for space exploration if one can eliminate conventional oil lubrication systems. This cuts down on the size and weight and reduces the hazard of leakage which could result in a chemical/physical interaction of the working fluid with the oil. Furthermore, the design of the pump and/or power generator is simplified by elimination of several seals normally required for conventional lubricants and bearings. In the foregoing applications, hydrodynamic fluid-film-lubricated bearings were preferred to rolling element bearings because of the flexibility in choosing materials compatible with many of the highly reactive/corrosive working fluids (e.g., liquid-oxygen, liquid-hydrogen, and liquid-sodium). However, the extremely low absolute viscosity of cryogenic fluids (about one fifth that of water) used in launch vehicle applications severely limits the hydrodynamic load capacity of such bearings. For extended space travel, the bearings used for power generation operate under zero-gravity conditions and load capacity is not so much a concern as bearing instability. The bearing instability referred to here is the so-called “half-frequency whirl.” This is the tendency of the journal center to orbit about the bearing center at an angular velocity slightly less than or equal to one half the angular velocity of the journal around its own center. Various types of bearing designs are discussed with regard to their effectiveness in reducing tendencies for this type of instability. *The principles of hydrostatic bearings are treated in detail in Chapter 11 of this handbook by A. Szeri.
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The study of gas bearings was noticeably accelerated following the Manhattan Project during World War II. According to Fuller (1992), gaseous diffusion plants were used to provide an enriched fuel by pumping uranium hexafluoride gas through a cascade of successive diffusion stages. Several thousand stages in series were needed to achieve the required composition. The bearings and seals in the pumps could not be oil-lubricated because of the high power losses and concerns for contamination of the lubricant. The natural choice became the working fluid (i.e., gaseous uranium hexafluoride) and a concerted design effort helped contribute to the success of the project.
27.1.2
Compressible Lubrication
For a compressible lubricant, one needs to consider how the pressure depends on the density of the fluid, that is, the equation of state. For a perfect gas, the equation of state is:
(
)
p = ρ ⋅ℜ⋅T = ρg c p − c v T
(27.3)
where ρ is the density; ℜ, the gas content; T, the temperature; cp , the specific heat per unit weight for constant pressure; cv , the specific heat for constant volume per unit weight; and g, the gravitational constant. Because temperature is a function of pressure, the conservation of energy equation has to be linked with the Reynolds equation to calculate pressure. Fortunately, most gas lubricating films are nearly isothermal* due to the fact that bearing materials generally dissipate heat much faster than gases generate heat. Therefore, according to the ideal gas law (Equation 27.3), the pressure is directly proportional to the density, so the energy equation can be bypassed. Gas-lubricated bearings are used in a wide variety of applications (Fuller, 1992; van der Stegen, 1997): 1. High-speed grinding spindles 2. A high-speed spindle for laser copiers and printers is shown in Figure 27.8. The figure reveals a fixed shaft with straight grooves for the aerodynamic bearing, and a rotating hollow shaft, which is driven by the rotor. The rotor is suspended vertically by magnetic thrust bearings and positioned horizontally by the aerodynamic bearings. The mirror has ten flat surfaces for the reflection of a laser beam (Vliestra, 1987; cited in van der Stegen, 1997). 3. Sliding ways on machine tools, for avoiding stick-slip vibration 4. Bearings for precise linear and rotational indexing metrology devices 5. Hermetically sealed high-speed blowers and compressors that use the working fluid as the lubricant. Typical applications include gas-cooled reactors, cryogenic and pyrogenic turbomachinery where great temperature extremes are encountered. 6. High-precision inertial guidance instruments such as gyroscopes and accelerometers 7. Foil-type gas bearings for auxiliary power units in aircraft and power-generating components used in space 8. Computer peripheral devices, such as hard/floppy disk drives, consisting of slider-bearing readwrite heads. Figure 27.9 presents a rotating disk with an arm-slider assembly of a hard disk; and Figure 27.10 a video recording tape consisting of a rotating drum with heads and tape. 9. High-speed dental and orthopedic drills and cutters that operate with quiet, oil-free performance 10. Membrane bearings, that are used to support and position large machine tools, heavy die blocks, full-scale railroad cars, or a grandstand in a football stadium
*Although the literature contains many references to adiabatic gas lubricating films, a gas lubricating film that is not virtually isothermal has not been shown to exist (Gross, 1962).
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6
5 7 4 1 3 2
FIGURE 27.8 Spindle in a copier. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.)
arm with slider
disk FIGURE 27.9 Computer hard disk with arm-slider assembly. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.)
27.1.3
Compressible vs. Incompressible*
The advantages of gas-lubricated bearings over liquid-lubricated fluid-film bearings are now well-understood. These include: • Cleanliness: elimination of contamination caused by more traditional lubricants • Reduction (often elimination) of the need for bearing seals
*The list of advantages and disadvantages of gas bearings is given in Fuller (1992).
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drum video tape
head
FIGURE 27.10 Videotape with head. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.)
• Lubricant stability: no vaporization, cavitation*, solidification, decomposition, or phase change over extreme ranges of temperature, from cryogenic (–270°C or –450°F) up to approximately 1650°C (3000°F). Operation at these extremes of temperature is a current research goal. • Permits practical attainment of high speeds (700,000 rpm) at low friction** and heating, with little or no cooling generally required. Disadvantages of gas-lubricated bearings are recognized as resulting from the relatively low viscosity*** and damping of gas films. Thus, • Gas-lubricated bearings have a reduced load-carrying capacity compared to liquid-lubricated bearings, especially with self-acting or hydrodynamic bearings. Consequently, for a given load, gas bearings operate with thinner hydrodynamic films than their liquid-lubricated counterparts. As the films become thinner, the possibility of surface scoring, wear, and eventual bearing failure is a real concern. Tighter manufacturing tolerances and improved surface finishes are required. In addition, careful bearing alignment is necessary as well as consideration of possible loss of clearance due to thermal effects. However, compliant surface bearings (i.e., foil bearings and membrane bearings) are more forgiving and do not require the rigid specifications regarding design and manufacture of the bearings. The membrane bearing, for example, operates very satisfactorily over a typical factory floor. • The gas film in a slider bearing behaves as a cushion of air providing very little damping. If a critical speed or instability is encountered, there may not be enough damping to suppress or control it. This makes it necessary to carefully analyze the dynamics of the system so that by design one can preclude severe rubbing sand /or failure of the bearing. *While cavitation causes damage in liquid-lubricated journal bearings, it can, on the other hand, be beneficial because cavitation stabilizes the behavior of liquid-lubricated journal bearings (van der Stegen, 1997). Calculations by Brewe (1986) show that the occurrence of vapor cavitation in a journal bearing undergoing circular whirl can increase load capacity by as much as 20%. **Gross (1962) points out “… that both the load carrying capacity and the friction of a gas film must be much less than that of a liquid film. Interestingly, though, the ratio of friction to load, the coefficient of friction, must always be greater for a self-acting gas film than for a similar liquid film.” ***Approximately 2 × 10–5 Pa s (2.9 × 10–9 lbf · sec/in.2) for air under room conditions compared with oil, approximately 2 × 10–2 Pa s (2.9 × 10–6 lbf · sec/in.2) (van der Stegen, 1997).
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• Pressure buildup in a slider bearing is limited by the gas compressibility. As the velocity of the runner is increased, the effectiveness to build pressure and carry load is decreased. Eventually, the most important parameter to generate pressure depends on the minimum to maximum film thickness ratio (van der Stegen, 1997). • Because of a lack of boundary lubricating properties, additional surface treatments are necessary. Otherwise, when there is not sufficient lift to keep the surfaces separated during starts and stops, damage can occur easily. Even after a sufficient film has formed, vibrations can cause the gas to compress enough so that the surfaces touch (van der Stegen, 1997). While this should be helpful if one is confronted with the choice of using a liquid or gas lubricant, the following section provides a more global viewpoint, which includes a broader class of bearings.
27.1.4
Advantages and Disadvantages for Bearing Types
Tables 27.1 and 27.2 from the Engineering Sciences Data Unit (1965, 1967) illustrate the advantages and disadvantages of bearings (including rolling element bearings) for both thrust and journal (radial) bearing applications.
27.2
Self-acting Finite Bearings
Self-acting bearings all operate on the principle that pressures are generated via relative motion between the surfaces to produce load support. The mechanism in which pressures are generated is discussed in the Introduction in the context of infinitely wide bearings (i.e., no side leakage) and in more detail by Hamrock (1994). In designing finite bearings, side-leakage becomes an important issue. It determines the effectiveness of the bearing to generate pressure and thus carry loads. Consequently, one can increase load capacity of a step bearing by including side-rails, hence shrouded-step bearings and pocket bearings. In the case of recording air bearing sliders used in computer hard disk drives, rails are designed to be the load-bearing area.
27.2.1
Fixed-Geometry Thrust Bearings
Several configurations of fixed-geometry sliders are shown in Figure 27.11 as rectilinear and sector thrust bearings. However, these geometries are also suitable for journal bearing applications as well as conical and spherical geometry bearings. Sector thrust bearings are used specifically to take loads in the axial direction for rotating machinery. A typical thrust bearing arrangement illustrating the main components of a fixed-inclined-pad thrust bearing is shown in Figure 27.12. The upper configuration in Figure 27.13 illustrates a side view of the wedge-shaped pad with land, along with the pressure distribution. The bearing support plate contains several such pads distributed evenly around the axial plate, as shown in the bottom half of the figure. 27.2.1.1 The Dynamics of Fixed-Geometry Thrust Bearings Bearing instability is a problem peculiar to thrust bearings having a fixed-geometry. To understand the instability of the fixed pads, refer back to Equation 27.1 and Figure 27.2, which illustrates the optimization of the load coefficient (Pinkus and Sternlicht, 1961). The outlet (minimum) film thickness can be solved from Equation 27.1; that is:
µU ⋅ C P h2 = B W L
(27.4)
Attention to differential expansions and starting torques necessary Attention to the possibility of fretting damage necessary (except hydrostatic bearings)
Low temperature
Rolling Bearings
Hydrostatic Liquid Film Bearings
Normally satisfactory, Sealing important scaling advantageous Excellent Lubricant may impose limitations
Dirty or dusty conditions
Wet and humid Attention to the Normally satisfactory Normally Normally satisfactory, but Satisfactory conditions possibility of metallic depending upon satisfactory, sealing special attention to corrosion necessary material advantageous sealing perhaps necessary Radiation Satisfactory Lubricant may impose limitations
Satisfactory filtration of lubricant is important
Bearings of many different Small radial extent but total space proportions, small axial requirement depends on the extent lubrication feed system
Small radial extent
Excellent
Externally Pressurized Gas Bearings
Excellent
Satisfactory
Not normally applicable
Sealing important
Small radial extent
Normally satisfactory
Not applicable when vacuum has to be maintained
Small radial extent but total space requirement depends on the gas feed system Satisfactory
Excellent
Excellent, thorough drying of gas necessary
Excellent
Self-acting Gas Bearings
978
Vacuum
Hydrodynamic Liquid Film Bearings
Normally satisfactory Attention to Up to 100°C (212°F) no Attention to oxidation resistance of depending upon oxidation limitations; from 100°C lubricant necessary material resistance of to 250°C (212 to 482°F), lubricant necessary stabilized bearings and special lubrication procedures probably required Lubricant may Below minus 30°C (–22°F) Lubricant may Lubricant impose limitations, special lubricants impose limitations, may impose consideration of required, consideration considerations of limitations starting torque of starting torque starting torque necessary necessary necessary Normally satisfactory except when peak of May impose limitations; Satisfactory Excellent impact load exceeds load capacity consult manufacturer
Rubbing Bearings
Oil-Impregnated Porous Metal Bearings
Space requirements
External vibration
Attention to differential expansions and their effect upon fits and clearances necessary
General Comments
Advantages and Limitations of Thrust Bearings
High temperature
Environmental Conditions
TABLE 27.1a
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Good for steady loading Excellent
Combination of axial and radial load carrying capacity Silent running
Good
Satisfactory
Good
Rolling Bearings
Excellent
Excellent
Hydrostatic Liquid Film Bearings
Good
Excellent
Satisfactory
Self-acting Gas Bearings
Excellent
Good to excellent Excellent depending upon type Improved performance Normally satisfactory, but attention to sealing necessary, except where a process liquid Excellent can be obtained by can be used as a lubricant allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations
Simplicity of lubrication
Availability of standard parts Prevention of contamination of the product and surroundings
Usually Excellent Excellent, Excellent satisfactory, except for consult possible manufacturer pump noise Excellent with self- Self-contained assemblies Auxiliary high- Excellent contained grease can be used with certain pressure or oil lubrication limits of load, speed and pump diameter. Beyond this, necessary oil circulation necessary Good Not available
Theoretically infinite, but Theoretically affected by filtration and infinite number of stops and starts
Satisfactory
Satisfactory
Hydrodynamic Liquid Film Bearings
Excellent
Excellent
Externally Pressurized Gas Bearings
Excellent, except for possible compressor noise Pressurized supply of dry clean gas necessary
Theoretically Theoretically infinite, but infinite affected by number of stops and starts A thrust face must be provided to carry the Most types capable A thrust face must be provided to carry the axial loads axial loads of dual duty
Poor
Not normally recommended
Rubbing Bearings
Oil-Impregnated Porous Metal Bearings
Finite, but predictable
General Comments
Advantages and Limitations of Thrust Bearings
Low starting torque Low running torque Accuracy of radial location Life
Requirements
TABLE 27.1b
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General Comments
Very low
Excellent
Rubbing Bearings
Generally good
Good
Oil-Impregnated Porous Metal Bearings
Advantages and Limitations of Thrust Bearings
Excellent
Rolling Bearings
Excellent
Hydrostatic Liquid Film Bearings
Poor
Self-acting Gas Bearings
Depends upon complexity Cost of Nil of lubrication system lubricant supply has to be considered
Generally good
Good
Hydrodynamic Liquid Film Bearings
Cost of gas supply has to be considered
Excellent
Externally Pressurized Gas Bearings
980
From Anonymous (1965), General Guide to the Choice of Thrust Bearing Type, Engineering Sciences Data Unit, Item 67033, Institution of Mechanical Engineers, London, England.
Frequent stopstart Frequent change of direction of notation Running costs
Requirements
TABLE 27.1b (continued)
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Self-acting Gas Bearings
Externally Pressurized Gas Bearings
Excellent
Not normally applicable
Sealing important
Small axis extent
Not applicable when vacuum has to be maintained
Small axis extent but total space requirement depends on the gas feed system Satisfactory
Slider Bearings
Radiation
Normally Normally Normally satisfactory, Satisfactory satisfactory satisfactory, but special attention to depending upon sealing sealing perhaps material advantageous necessary Satisfactory Lubricant may impose limitations
Satisfactory, filtration of lubricant important
Small axis extent but total space requirement depends on the lubrication feed system
Wet and cold conditions
Bearings of many different proportions available
Normally satisfactory, sealing Sealing important advantageous Excellent Lubricant may impose limitations
Attention to the possibility of metallic corrosion necessary
Hydrostatic Liquid Film Bearings
Up to 100°C (212°F) no Attention to oxidation resistance of Excellent limitations; from 100°C lubricant necessary to 250°C (212 to 482°F) stabilized bearings and special lubrication procedures probably required Below minus 30°C Lubricant may Lubricant may Excellent, thorough drying of gas necessary (–22°F) special impose impose lubricants required, limitations, limitations consideration of consideration of starting torque starting torque necessary necessary May impose limitations, Satisfactory Excellent Normally satisfactory Excellent consult manufacturer
Rolling Bearings
Hydrodynamic Liquid Film Bearings
Dirty or dusty conditions Vacuum
Space requirements
External vibration
Lubricant may impose limitations, consideration of starting torque necessary Attention to the Normally satisfactory except when possibility of fretting peak of impact load exceeds load damage necessary capacity (except hydrostatic bearings) Small axial extent
Attention to differential expansions and starting torque necessary
Low temperature
Rubbing Bearings
Attention to Normally Attention to differential satisfactory oxidation expansions and their depending upon resistance of effect upon axial material lubricant clearance necessary necessary
General Comments
Oil-Impregnated Porous Metal Bearings
Advantages and Limitations of Journal Bearings
High temperature
Environmental Conditions
TABLE 27.2a
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General Comments Satisfactory
Excellent with selfcontained grease lubrication. With large sizes or high speeds, oil lubrication might be necessary
Usually, satisfactory; consult manufacturer
Good for steady loading Excellent
Excellent
Some types capable of dual duty
Good
Rolling Bearings
A journal bearing surface must be provided to carry the radial loads
Finite but can be estimated
Good
Not normally recommended
Rubbing Bearings
Oil-Impregnated Porous Metal Bearings
Advantages and Disadvantages of Journal Bearings
Excellent
Excellent
Hydrostatic Liquid Film Bearings
Good
Excellent
Satisfactory
Self-acting Gas Bearings
Excellent
Excellent
Externally Pressurized Gas Bearings
Excellent Excellent except for possible pump noise Self-contained assemblies Auxiliary can be used with certain high limits of load, speed, and pressure diameter. Beyond this, oil pump circulation necessary necessary
Excellent
Excellent except for possible compressor noise Pressurized supply of dry clean gas necessary
Theoretically Theoretically Theoretically infinite infinite, but infinite affected by number of starts and stops A journal bearing surface must be provided to carry the radial loads
Theoretically infinite, but affected by filtration and number of starts and stops
Satisfactory
Satisfactory
Hydrodynamic Liquid Film Bearings
982
Simplicity of lubrication
Combination of axial and radial load carrying capacity Silent running
Low starting torque Low running torque Accuracy of axial location Life
Requirements
TABLE 27.2b
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Very low
Oscillatory Running costs
Good
Satisfactory
Suitable
Excellent
Satisfactory
Unsuitable Depends upon complexity Cost of of lubrication system lubricant supply has to be considered
Suitable Some type suitable
Good
Poor
Normally satisfactory, but attention to sealing necessary, except where a process liquid can be used as a lubricant
Excellent
Some types suitable Unsuitable Nil
Poor
Excellent
Not available
Cost of gas supply has to be considered
Suitable
Excellent
Satisfactory
From Anonymous (1965), General Guide to the Choice of Journal Bearing Type, Engineering Sciences Data Unit, Item 65007, Institution of Mechanical Engineers, London, England.
Excellent
Suitable
Good to excellent depending upon type Improved performance can be obtained by allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations Good
Tolerance to manufacturing and assembly inaccuracies Type of Motion Frequent start-stops Unidirectional Bidirectional
Availability of standard parts Prevention of contamination of the product and surroundings
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U
U
Taper
U
Taper-flat
Pocket
Step
Spiral groove
Herringbone
FIGURE 27.11 Examples of self-acting thrust bearings. (From Ausman, J.S. (1964), Gas-lubricated bearings, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, 109–138.)
W DR Runner
t Pad Bearing support plate ds
FIGURE 27.12 View showing relative position of bearing components for an axial thrust bearing. (From Anon. (1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England.)
Using the fact that h2 is directly proportional to C 1/2 P , and h1/h2 is a function of CP , according to Figure 27.2, one can account for the occurrence of a bearing instability. Further, the ratio h1/h2 is equal to (δ/h2 + 1), where δ is the rise of the slider (h1 – h2). For bearings with fixed inclination, the rise is established during manufacture.* If the bearing is operating so that the value of h1/h2 yields the maximum load coefficient, then any increase in load will cause a decrease in minimum film thickness. This will, in turn, cause CP to decrease because it is proportional to h2. However, according to Figure 27.2, as CP drops, the value of h1/h2 increases, causing h2 to decrease. Mathematically, the bearing is stable only when ∂CP /∂H ≥ 0. Although this poses a serious limit to the stable operation of fixed-pad bearings, other concerns may be more potently dangerous that affect competing type bearings as well. For example, temperatureviscosity effects may well be a greater concern when loads are increased because they can lead to an increase in shear heating, raising the temperature of the lubricant and decreasing the viscosity. This would result in a decreased minimum film thickness. 27.2.1.2 Tapered-land Slider The tapered-land thrust bearing is shown in Figure 27.14, illustrating the lubricant flow between successive pads. Here, the lubricant source is provided at the inside diameter of the pad support plate and is *Cameron (1966) points out that tilting-pad bearings have the most important feature (which fixed inclination pads do not have): that the inlet and outlet gaps vary together, so that h1/h2 always remains constant.
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Runner
Wp
MOTION
h
β
Pad
Typical pressure pattern generated Section through a thrust pad
Pad
Trailing edge Outer side
L
b
d dm D
dm
Land Inner side Leading edge
Individual pad
FIGURE 27.13 Sectional view of thrust plate and layout of pads. (From Anon. (1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England.)
MOTION Side leakage Side leakage Qi
Pad
Pad Side leakage
Side Leakage
Qf
Groove
FIGURE 27.14 Flooded or oil-bath system of lubrication. (From Anon. (1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England.)
expelled at the inner and the outer diameter. Referred to as an oil-bath or flood-feed system, a disadvantage of this supply type is that oil is caught in the large space between pads and causes a drag (or churning) loss. This loss can be considerable, especially for large bearings and high-speed applications. One means of reducing the power loss is by including an orifice between each pad to direct the lubricant into the pad inlet as shown in Figure 27.15. In this way, the space between each pad does not have to be flooded to assure adequate lubrication in the inlet. A land at the trailing edge of the taper provides load support upon starting and stopping. This can be effective without any assistance from external pressure (hydrostatic jacking), provided the land pres-
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MOTION
Side leakage
Side leakage
Ql
Qf
Pad
Pad Side leakage Groove
Side leakage
FIGURE 27.15 Individual pad feed system of lubrication. (From Anon. (1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England.)
sures remain less than 0.7 MN/m2 (Anon., 1982). Harrison (1913) optimized the one-dimensional tapered thrust bearing with regard to the extent of the land and the slope parameter δ/h2. For optimum load capacity, the extent of the land was determined to be 20% of the breadth of the bearing with a value of δ/h2 = 1.25. For a pad having fixed inclination, this optimum condition can be achieved only at a single value of applied load (or minimum film thickness h2). The value of δ/h2 will change as the value of applied load changes, as discussed in the section on dynamics. No significant errors should arise for land lengths within the range of 10 to 30% (Anon., 1982). The use of rectangular pad data for the design and analysis of bearings with sector-shaped pads does not lead to errors of practical significance with sector angles up to 45°. Tapered-land bearings have been used in large thrust bearings for hydroelectric turbines with some success. Hall and de Guerin (1957) and Linn and Shepard (1938) described their performance (Cameron, 1966). 27.2.1.3 Rayleigh Step Bearing A typical axial Rayleigh step sector thrust bearing is shown in Figure 27.16. Even though Lord Rayleigh (1918) showed that the infinitely wide step bearing gave a 20% greater load capacity than infinitely wide tilling-pad bearings, Kingsbury and Michell had captured the marketplace with the tilting-pad bearing, causing the step bearing to be neglected until about 1950. At that time, Archibald (1950) calculated the load capacity for a square step bearing, including side flow:
W=
0.0725 ⋅µ ⋅U ⋅ B 2 h22
, per unit width
(27.5)
If one calculates the load capacity per unit width for the corresponding square tilting-pad bearing:
ro ri
T
∆
σg h
FIGURE 27.16
Rayleigh step sector thrust bearing.
hs
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FIGURE 27.17 Shrouded step bearings. (a) Semicircular step bearing; (b) triangular step bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York. With permission.)
W=
0.0704 ⋅µ ⋅U ⋅ B 2 h22
, per unit width
(27.6)
The difference between the two bearings, including side flow, is now much smaller than before. Numerous studies have been performed to retard the side flow with shrouded designs in order to maximize load capacity and/or stiffness. Johnston and Kettleborough (1956) conducted experiments using straight and shrouded steps. Wildmann et al. (1965) studied gas-lubricated step thrust bearings extensively. In an earlier study, Ausman (1961) optimized sector-shaped pad geometries based upon maximum load capacity for low compressibility numbers (near-incompressible lubrication). Hamrock (1972) extended the range of compressibility using a similar analysis for rectangular pads. In 1983, Bagci and Singh extensively analyzed the effects of side flow for finite bearings. 27.2.1.3.1 Semicircular Step Bearing Typically, results from Cameron (1966) show that a bearing with a semicircular step of radius equal to B/2 and a ratio of h1/h2 of 1.7, had a load coefficient of 0.105 (see Figure 27.17a). Thus,
W=
0.105 ⋅µ ⋅U ⋅ B 2 h22
, per unit width
(27.7)
27.2.1.3.2 Triangular Step Bearing A triangular step bearing (Figure 27.17b) with h1/h2 of 2.12 had a load coefficient of 0.121:
W=
0.121⋅µ ⋅U ⋅ B 2 h22
, per unit width
(27.8)
This represents a considerable increase in load capacity due to retardation of side flow. Note that in all of the above shrouded step bearings, the height of the step (h1 – h2), Figure 27.4, is usually much less than 0.025 mm (0.001 in.). Such a small step height can be difficult to fabricate. During operation, especially starts and stops where the runner is prone to touch the bearing, a small amount of wear may wipe away the step. In spite of the disadvantages listed, step bearings are widely used as gas bearings because they are less expensive to make than the attractive tilting-pad bearings. 27.2.1.3.3 Pocket Step Bearing Wilcock (1955) demonstrated that one could combine some of the advantages of hydrostatic-type pocket bearings with a hydrodynamic-type thrust bearing to achieve a thrust bearing having low power loss and high load-carrying capability without the disadvantage of maintaining an external high-pressure pump. The hydrodynamic pocket thrust bearing, as it was originally, conceived, is illustrated in Figure 27.18.
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h
y δ
U
x
OIL IN b
L b
E
B b
FIGURE 27.18 Diagram of hydrodynamic-pocket thrust bearing. (From Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGraw-Hill, New York. With permission.)
The upper side-view in the figure shows oil being introduced at the inlet of an inclined pumping land (hydrodynamic slider bearing). The pumping action in this region provides lubricant to help fill the pocket and establish high pressure. Oil leakage out of the pocket and pump land occurs through the clearance between the rails and runner. The clearance height adjusts itself until the oil leakage out of the bearing is exactly equal to the flow into the bearing. At this point, the pocket pressure is sufficient to support the external load. Wilcock provided further analysis to show that for maximum film thickness at a given load and speed the taper of the pumping land must be zero. In other words, a Rayleigh step with a pocket at the end of the step provides the best performance. Wilcock and Booser (1957) compared the performance of a hydrodynamic-pocket-step thrust bearing with the tapered-land and the tilting-pad thrust bearings. The results are shown in Table 27.3. TABLE 27.3 Comparison of the Pocket-Step Thrust Bearing with Two Hydrodynamic Thrust Bearings Tapered Land Bearing Load W Size, D1 /D2 Nos. of pads Pad slope Operating viscosity Avg. unit load hmin Power loss Oil flow, Q Film temp. rise, ∆T a
Tilting Pad Bearing
Pocket-Step Bearing
70,000 lbs 311.37 kN 7/15 6 0.00105a 18 cP 2.61 µReyns
70,000 lbs 311.37 kN 7/15 6 0.00049 18 cP 2.61 µReyns
70,000 lbs
18 cP
2.61 µReyns
555 psi 0.0015 in. 76 hp 15.7 gpm 58°F
614 psi 0.0016 in. 86 hp 23.9 gpm 44°F
565 psi 0.00185 in. 45 hp 17.5 gpm 31°F
3.90 MPa 47.0 µm 35.56 kW 11.0 × 10–4 m3/s 17.22°C
3.83 MPa 38.1 µm 56.67 kW 9.91 × 10–4 m3/s 32.22°C
4.23 MPa 40.6 µm 64.13 kW 15.1 × 10–4 m3/s 24.44°C
311.37 kN 7/15 4 0
Average of inner and outer slopes.
Some of the advantages indicated in the table are lower power loss for the same high load capacity. Consistent with lower power loss, the film temperature rise during operation is significantly less for roughly the same hydrodynamic oil flow. Disadvantages of the hydrodynamic pocket step-bearing are: (1) that it is sensitive to misalignment, (2) it can’t carry a heavy thrust load for low speed conditions, and (3) at high Reynolds number, turbulence in the pockets becomes a serious issue and was shown by Wilcock (1955) to reverse the trend of decreasing power loss with increasing speed. To address the misalignment, Wilcock (1955) devised a frictionless pressurized ball seat mounting that was self-aligning.
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B
θ h2 h1
Pocket
B
bB
0.1B FIGURE 27.19 Pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York. With permission.)
And if high loads must be carried at low speed, high-pressure oil can be fed to the pocket so that it operates as a hydrostatic bearing at low speeds. But the issue of turbulence in the pockets at high speed remains a concern. Wilcock and Booser (1957) hypothesized that decreasing pocket depth might have a beneficial effect but concluded there is virtually no advantage in reducing the pocket depth to avoid turbulence. Kettleborough (1961) analyzed the pocket step bearing having the geometry shown in Figure 27.19. The distinguishing geometric features of this bearing over that studied by Wilcock (1955) and shown in Figure 27.18 are the shape of the side rails and the absence of a lubricant supply hole at the inlet. The speckled region (Figure 27.19) having film thickness h1 and length bB (i.e., pumping length) is the inlet of the Rayleigh step. The step height is the difference between h1 and the minimum film thickness h2. Upon having chosen h1 /h2 to be 1.76 and the angle of the inside rail wall relative to the outside wall θ to be 18.5°, Kettleborough optimized this bearing based upon minimum friction and maximum load capacity for a wide range of pumping lengths (i.e., 0 ≤ b ≤ 1.0). The value of b that resulted in maximum dimensionless load
W B h2 µ ⋅U B
2
was b = 0.6 where W is load, U is the speed of the runner, and µ is the absolute viscosity, while the minimum dimensionless friction f/(h2/B) is 5.3 where b = 0.3 and f is the friction coefficient. Naturally the choice of b depends upon the importance the designer places on minimum friction or maximum load. Giving them equal weight, a reasonable compromise would be to assign b = 1/2 . Cameron (1966) points out that the dimensionless load
W B h2 µ ⋅U B
2
very nearly equals that of the optimum square tilting pad, just less than 0.1 (Figure 27.20). 27.2.1.4 Recurrent-Grooved Thrust Bearings 27.2.1.4.1 Spiral Grooved Thrust Bearing An annular plate, spiral grooved thrust bearing is shown in Figure 27.21. The operating principle of the spiral grooved thrust bearing is based on the fact that a viscous lubricant (oil, grease, or air) is dragged into a slot or groove by a moving runner. If the flow is inhibited at the end of the groove by a dam or restrictor, pressure builds up and the bearing is able to support a load. The direction of rotation
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0.12
12 Load
10 8
0.08 Friction
0.06
6
0.04
4
0.02
2
0
0.1
0.2
0.3
0.4
0.5 b
0.6
0.7
0.8
0.9
µ ho/L
W/L h02 ηU L2
0.10
0 1.0
FIGURE 27.20 Load and friction for pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York.)
Wt
ω hc
h2 h o h1
a2 a1 Groove Ridge r1 r2
α
FIGURE 27.21 Flat spiral grooved thrust bearing without transverse flow (no net flow from r1 to r2). (From Muijderman, E.A. (1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands. With permission.)
determines whether fluid is pumped inward to, or outward from the center of rotation. Muijderman (1966) describes how bearing performance can be improved by considering the relationship between pressure development and leakage as a consequence of the pumping action. Increasing the groove depth δ increases the pumping action and hence the lift as a result of the increase in pressure generation. If the grooves are too deep, the leakage will become excessive. If the groove depth is reduced to zero, the pumping effect naturally ceases. Here, the groove depth can be optimized so as to continue to support the constant bearing load and/or the rotating disk. The shape of the spiral grooves should be optimized to achieve the most effective pumping. This would result in a maximum pressure buildup. Muijderman calculated the value of α required to produce maximum pressure for a basic element (see Figure 27.22). → → This can be done by ensuring that the angle α between the local velocity vector (ω × r ) and the tangent to the groove at all times produces maximum pressure. Muijderman deduced that the shape of the groove is a logarithmic spiral. In polar coordinates, the shape of the groove is defined as
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ωxr
Tangent
α C
α
β
r Radius vector
r =f (θ)
θ
0
A
r1
FIGURE 27.22 The logarithmic spiral, r = r1eθtanα. (From Muijderman, E.A. (1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands.)
r = r1e θ ⋅ tan α
(27.9)
as the lubricant. Cameron (1966) points out that bearing flatness is most important if air is used. The flatness is checked by optical interference. It is found that, as the front (frictional) surface gets hot, the bearing “hogs” and so it is usually made initially slightly hollow to allow for this bifilar-type expansion. The grooves can be made by vapor blasting, sandblasting, or etching. Pressure: The pressure above ambient at radius r1 (where pr2 = pambient) for the spiral groove thrust bearing without transverse flow is derived by Muijderman (1966) as:
pr1 =
3µωr22 h22
(1 − λ ) ⋅ g (α, H , γ )C (α, H , γ , λ, k) 2
1
(27.10)
1
where λ = r1/r2, H = h2/h1, γ = α2/α1, k = number of grooves, µ = viscosity, and C1 is:
(
)
C1 α, H , γ , λ, k =
−
e
π α 2 1 + γH 3 ⋅ 1 − tan α k 90° 1 + γ 1+ H 3
(
)
− λ2 ⋅ e
+
π α 2 1 + γH 3 ⋅ 1 − tan α k 90° 1 + γ 1+ H 3
(
)
(27.11)
1 − λ2
and g1 is:
(
)
g 1 α, H , γ =
(
)(
)(
γH 2 cot α 1 − H 1 − H 3
)
(1 + γH ) ⋅ (γ + H ) + H (cot α)(1 + γ ) 3
3
3
2
2
(27.12)
Load-carrying capacity: Muijderman calculates the load-carrying capacity of the spiral groove bearing without transverse flow to be:
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Wtsgb. =
3πµωr24 2h22
(1 − λ ) ⋅ g (α, H , γ )C (α, H , γ , λ, k) 4
1
(27.13)
2
where −
(
)
C2 α, H , γ , λ , k =
e
α 2π 2 1 + γH 3 ⋅ 1 − tan α k 90° 1+ γ 1 + H 3
(
)
− λ4 ⋅ e
+
α 2π 2 1 + γH 3 ⋅ 1 − tan α k 90° 1+ γ 1 + H 3
(
)
(27.14)
1 − λ4
Frictional torque: In this case, the frictional torque from the inner chamber is neglected because hc h2. Thus, for the case without transverse flow,
M tsgb. =
(
) (
πµωr24 1 − λ4 ⋅ g 2 α, H , γ 2 h2
)
(27.15)
Coefficient of friction: The coefficient of friction for the inward pumping spiral grooved bearing without transverse flow is given as:
ftspg. =
( ) ) (
g 2 α, H , γ h2 ⋅ 3r2 g 1 α, H , γ C2 α, H , γ , λ, k
(
(27.16)
)
27.2.1.4.2 Herringbone Grooved Thrust Bearing Figure 27.23 shows a herringbone annular thrust bearing configuration where the fluid is pumped into the grooves from both outside edge and the inside edge. This bearing operates properly when the grooves are not closed off at the inner or outer diameter. However, this bearing can operate without transverse flow (no net flow across the inner and outer radius) if rh is chosen so that the inner and outer grooves build up equal pressures at a distance r = rh from the center. Pressure: For the inner (r1 < r < rh) and outer (rh < r < r2) grooves, respectively, the pressure buildup was determined by Muijderman to be: 2 1 + γH 3 π α° ⋅ ⋅ 1 − ⋅ ( tan α ) 3µω 2 k 90° 1+ γ 1 + H 3 2 pr = 2 r − r1 ⋅ e ⋅ g 1 α, H , γ h2
(
)
(27.17)
and 2 1 + γH 3 π α° 3µω 2 − k ⋅ 1 − 90° ⋅ (tan α ) 1 + γ ⋅ 1 + H 3 2 pr = 2 r2 ⋅ e − r ⋅ g 1 α, H , γ h2
(
)
(27.18)
In practice, the expression for rh is often approximated as:
(
1 rh ≈ ⋅ r12 + r22 2
)
(27.19)
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Wt ω
h2 ho h1
a2 a1 groove ridge
α
r1 rh inner grooves
r2
outer grooves
FIGURE 27.23 Herringbone spiral-grooved bearing, with no net flow between r2 and r1. (From Muijderman, E.A. (1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands. With permission.)
U hmin 1.45hmin
PIVOT
B
b
D2
0 58 B
D1
B
FIGURE 27.24 Diagram of a tilting-pad bearing (one shoe), showing the optimum pivot location and the resultant shoe inclination. (From Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGraw-Hill, New York. With permission.)
Load-carrying capacity: Muijderman calculates the load-carrying capacity of the herringbone thrust bearing with no transverse flow to be
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Wtherr. =
3πµωr24 4 h22
(1 − λ ) ⋅ g (α, H , γ )C (α, H , γ , λ, k) 2
2 1
1
(27.20)
Frictional torque: For the frictional torque, he obtained
M therr. =
(
) (
πµωr24 1 − λ4 ⋅ g 2 α, H , γ 2 h2
)
(27.21)
Coefficient of friction:
( (
) ) (
( ) ) (
2 g 2 α, H , γ 2 ⋅ h2 1 + λ ftherr. = ⋅ 3r2 1 − λ2 g 1 α, H , γ C12 α, H , γ , λ, k
27.2.2
)
(27.22)
Pivoted (Tilting) Pad Thrust Bearings
27.2.2.1 Basic Features* The tilting-pad thrust bearing (Kingsbury-type bearing) differs from the tapered-land thrust bearing in that each pad is an individual plate which is free to pivot. The pivot line is radial so that each pad can be inclined in a circumferential direction in order to provide a tapered oil film. Figure 27.24 shows the geometry of one tilting pad. Such bearings usually have three or more pads and are enclosed in a housing. Lubricating oil is normally fed to the center of the housing near the shaft and expelled at the outer edge because of the pumping action of the bearing. A large portion of the oil flowing through a tilting-pad bearing does not flow over the working bearing surfaces, because of the spaces necessarily left free around each pad. For this reason, oil flow is normally controlled by an orifice. When the runner is stationary, the pads will lie with their surfaces parallel to the runner face. As the bearing is started and an oil film is created between the pad and runner, each pad will tilt to the angle that will generate the proper distribution of film pressures (Figure 27.24). In setting out to design a tilting-pad bearing, the designer will normally know the total load W to be carried, the shaft speed N, the shaft diameter D, the inlet-oil temperature T1, the desired oil-temperature rise ∆T, and the oil-viscosity grade. In addition, a minimum film thickness, usually 0.001 in., is stipulated. The designer must then determine the number of pads and the size of each pad that will give the desired values of temperature rise and minimum film thickness. Another variable to be determined is the location of the pivot.** If rotation is always to be in one direction, the optimum pivot location is 58% of the distance from the leading edge to the trailing edge of the pad. The design procedure given in this section is based on this pivot location. If the shaft is to rotate in either direction, the pivot location must be at the mid-point, or 50% point. Experience has shown that there is usually enough crown to the pad as manufactured to give pads pivoted at the mid-point an equivalent performance. This is discussed in more detail in Wilcock and Booser (1957). Use of a 58% pivot point not only gives maximum load capacity and minimum friction, but also greatly simplifies the calculation procedures. 27.2.2.2 Michell and Kingsbury Bearings Tilting-pad bearings were first introduced in 1905 by Michell and Kingsbury, almost simultaneously. Michell had been seeking an efficient thrust bearing that could withstand the demands of the newly *This section is taken from Wilcock and Booser (1957). **A brief discussion of the basic equations can be found in Wilcock and Booser (1957); Chap. 7, Sec. 7-4, pp. 195–197.
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FIGURE 27.25 Tilting-pad thrust bearing with multiple segmented pads mounted on pivots. (From Hamrock, B.J. (1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. With permission.)
FIGURE 27.26 Kingsbury pivoted pad thrust bearing incorporating load equalizer “leveling plates.” (From Michell, A.G.M. (1950), Lubrication: Its Principles and Practice, Blackie and Son Limited, London. With permission.)
Collar Shoe
Leveling plate
Base ring
Joint in base ring
FIGURE 27.27 Developed section of bearing showing the leveling plates to distribute the load equally among the six shoes of the thrust bearing. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
emerging steam turbine applications. In 1897, ships were being powered by turbines and required thrust bearings that would take up the loading transmitted from the propellers to the ship’s hull. A typical tilting-pad thrust bearing with several segmented pads is shown in Figure 27.25. The earlier Kingsbury thrust bearings were operated in a bath of oil that was circulated by the pumping action of the rotating element. Kingsbury bearings commonly used three, six, or eight pads per bearing. The number of segmented pads depended on the application. To obtain maximum load-carrying, each pad
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FIGURE 27.28 Kingsbury LEG® thrust bearing illustrating lubricant flow path. (Courtesy of the Kingsbury Bearing Co.)
should carry the same load. In actual practice, the bearings can expect to be subjected to a certain amount of misalignment, which causes uneven loading. The Kingsbury Machine Works addressed this problem by developing a system of “leveling plates.” This consisted of an annular series of equalizing levers on which the pads were supported. Figure 27.26 illustrates the Kingsbury thrust bearing with leveling plates. A section view is shown in Figure 27.27. The leveling plates leave each pad free to move up or down to take an equal share of the load regardless of the misalignment. As mentioned above, the earlier designs ran submerged in a bath of oil. But, as pointed out in the discussion on fixed-geometry sector thrust bearings, this leads to unnecessary churning of the oil and high power loss. By placing a groove at the leading edge of each pad, the bearing can run with less lubricant between pads. This effectively reduces the power loss of the bearing. Further, cool oil is introduced at the leading edge, displacing the hot-oil carryover, and thus providing a cooler load- bearing film. This enables the bearing to carry more load. Brockwell, Dmochowski, and DeCamillo (1994) reported a significant reduction in both power loss and oil flowrate compared to a conventional pivoted pad bearing. Figure 27.28 shows the flow path of the oil over the pad surface for a tilting-pad load equalizer bearing with grooves at the leading edge of the bearing.
27.2.3
Journal Bearings
27.2.3.1 Plain Journal Bearings A plain journal bearing, a true circular bearing without grooves, is shown in Figure 27.29. Application of a vertical load on the shaft displaces the shaft in the direction of the load. This creates a tapered wedge in the bearing, establishing a pressure on the inlet side so as to establish a flow balance into and out of the bearing. The hydrodynamic pressure also reacts to support the load. A moment is exerted on the inlet side of the shaft by the buildup in pressure that causes the shaft to be displaced in a direction normal to the load. When the applied load and the hydrodynamic forces balance each other, the measure of the eccentrically displaced shaft along the line of centers settles at an angle ψ from the load line. This is referred to as the attitude angle of the bearing for a particular load, speed, and lubricant condition. A typical pressure distribution around the circumference of the bearing is shown in Figure 27.29b. Along the axial direction, the pressure peaks at the center, thus creating a pressure flow to the ambient sides. The axial pressure distribution is shown in Figure 27.29c.
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FIGURE 27.29 Hydrodynamic journal bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
In dynamically loaded bearings, the relative normal motion of the shaft to the bearing through the line of centers (Figure 27.30b) creates an additional contribution to the load capacity. The pressures depicted in this figure are a result of the squeezing action caused by the normal approach of shaft and bearing. Conversely, negative pressures are created if the shaft and the bearing are receding from each other. If the negative pressure reaches the saturation pressure of the liquid, dissolved gases can be released from the liquid to form gaseous cavitation. If the pressure decreases to the vapor pressure of the fluid before the gases have time to be released, then vapor cavitation will occur.
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W
Fluid
(a) Plane surfaces.
Bearing Cavitation
Journal
Fluid
W
Housing
(b) Cylindrical journal bearing.
Load, W
+
0
Time (c) Loading.
FIGURE 27.30 Dynamically loaded squeeze film bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
27.2.3.1.1 Steady-state Pressure Distribution Steady-state operation occurs when the bearing and shaft centers remain fixed relative to each other during operation. To obtain the pressures, the film shape must first be defined and appropriate boundary conditions applied upon integration of the Reynolds equation. From Figure 27.29, the film thickness, h, can be expressed as:
(
h = c ⋅ 1 + ε ⋅ cos θ
)
(27.23)
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x:
0
prb
¿:
0
p
2prb
rw b
2p
h
FIGURE 27.31 Film thickness around the circumference of the bearing. (From Hamrock, B.J. (1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. With permission.)
27.2.3.1.2 Flow Balance and Cavitated Flow Characteristics Making a cut at the line of centers where the maximum film thickness occurs results in a plot of the film thickness along the circumference of the unwrapped bearing (Figure 27.31). The film is convergent for 0 < θ < π and divergent for π < 0 < 2π. As described earlier, pressure builds up in the convergent region because fluid is being convected into a constricting space. This pressure buildup reaches a maximum near the minimum film thickness and within the convergent region. As a result, a pressure flow away from the peak pressure is created, leading to some side-flow leakage out of the bearing as well as some flow into the divergent region (see Figure 27.32). This extra pressure flow together with the convective flow into the divergent region helps fill the increasing available space until there is insufficient fluid to complete the film. The film ruptures and, depending on the load, speed, viscosity, and surface tension at the bearing/journal surfaces, either (1) it breaks up into small filmlets similar to those shown in Figure 27.32, or (2) fluid is transported through the cavity in the form of a sheet having a free surface and attached to the faster moving surface. The latter condition occurs if the surfaces are sufficiently separated so as to preclude the possibility of fluid attaching itself to both surfaces. This is more apt to occur for very light loads and/or higher (viscosity × speed) applications. Coyne and Elrod (1971) demonstrated the start of film striations and their sensitivity to load. In heavily loaded applications, the filmlets extend to both surfaces and are separated by gas, vapor, and/or foam. The fluid within the filmlets is convected downstream either until it encounters a fresh supply from a groove or until pressure flow from the high-pressure region helps to reestablish a full film. For a submerged bearing, unless the pressures in the divergent region are subambient to draw fluid back into the bearing, the fluid would
FIGURE 27.32 Plan view of unwrapped bearing illustrating direction of fluid flow out of and into bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
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soon be pumped out from the high-pressure region, causing starvation and subsequent failure. Fluids, in particular oil, are known to sustain negative pressure (i.e., tensile stress) relative to atmospheric pressure (Sun et al., 1993). The extent to which oil can sustain tension depends on the availability of cavitation nucleation sites. These sites can consist of tiny gas bubbles and/or wear particles within the fluid. In practice, most lubricants contain an abundance of nucleation sites so that the fluid cavitates at either its gas saturation pressure or vapor pressure. If the fluid is relatively free of gas, vapor cavitation can occur during steady-state conditions. Under dynamic conditions, the content of the cavitation region should be oil vapor rather than gas liberated from solution. Evaporation liberates dissolved gases much faster than does diffusion (Sun and Brewe, 1990), and the conditions that caused cavitation would have disappeared before gases could be liberated from the fluid. 27.2.3.2 Lubricant Supply Arrangements In the foregoing discussion of the submerged plain circular journal bearing, it was mentioned that unless the pressure along the sides of the bearing is greater than the cavitation pressure there wouldn’t be a natural mechanism to draw fluid into the bearing. Consequently, one either pressurizes the fluid at the sides of the bearing or replenishes the lubricant in the bearing with oil holes and/or grooves. Supply holes and grooves are preferred because they improve the distribution of oil and are more effective in cooling. In order to ensure an easy entrance for the lubricant to the bearing, the oil holes and grooves should be well rounded or chamfered. They should not be placed in the loaded area of the bearing where they will tend to disrupt the formation of high fluid pressure. By providing an amount in excess of that required to lubricate, the lubricant can provide additional cooling. Fuller (1984) discusses a variety of lubricant supply schemes; but only the simplest schemes will be discussed here. These include the hole/orifice-, the circumferential groove-, and the axial groove-supply. The ring bearing offers a different means of bringing the lubricant to the journal bearing without requiring pressurization and is included to illustrate its effectiveness. 27.2.3.2.1 Single Oil Supply Hole In the case of a unidirectional loading, lubricant is commonly supplied through a hole or holes in the bearing housing. From the experiments of Boyd and Robertson (1948), it was found that in the case of a single hole, the most desirable position to place the supply hole is opposite the area of load application where the pressure is least. For rotating loads, oil can be supplied through a hole in the journal. Thus the source will rotate with the journal and is usually quite satisfactory. A case in point is the radial-engine crankpin bearing discussed in Shaw and Macks (1949). The oil can be supplied through a hole in the crankpin at a location that is always in the unloaded region. Although, in some engine bearings the load vector periodically traverses the complete periphery of the journal and so the oil inlet hole cannot always be in the unloaded portion of the bearing. A circumferential groove is often used in this case. 27.2.3.2.2 Bearing with a Circumferential Groove One widely used practice is to place a circumferential groove at the center of the bearing. The oil is fed under pressure to this groove. This method is very effective as far as cooling is concerned, but it does have the disadvantage that the groove interrupts the active length of the bearing and splits the bearing in half, each half having a much lower l/d ratio than the original bearing. Despite this disadvantage, however, such a groove generally lowers the oil temperature sufficiently to permit the bearing to carry more load, even with the circumferential groove in place. Without such a groove, the bearing might overheat so badly that it could carry very little load. The circumferential groove configuration is shown in Figure 27.33. 27.2.3.2.3 Axial-Grooved Bearing The same rule that applies to positioning of a lubricant supply hole applies to the axial groove arrangement. The groove needs to be placed at a position that is least disruptive to oil pressure generation. A
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FIGURE 27.33 Circumferential groove in journal bearing. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York.)
good choice would be at the opposite area of load application where the pressure is the least. In the case of a split bearing, location of the groove or grooves at the split line (which is assembled normal to the load line) is convenient and causes very little problem to pressure generation (Figure 27.34). The groove should extend across the major portion of the bearing as shown in the figure. In most applications adequate lubrication can be assured if the axial extent is nominally 80% of the bearing length, and a circumferential extent roughly 25% of the diameter. To avoid significant restriction of the inlet flow, the depth of the grooves should not be less than 20 times the diametral clearance (Anon., 1984). When axial grooves are indiscriminately placed in the bearing, the groove can act as a scraper and interrupt the film. Figure 27.35 shows the effect of improper groove location on pressure generation for both the axial and the circumferential groove. The dashed line represents the pressure generated without the groove. The groove in that location bleeds off the hydrodynamic film that would have otherwise been established there and the pressure falls to the value of the groove pressure. It wouldn’t be unusual for the groove pressure to be an order of magnitude lower than the hydrodynamic film pressure.
FIGURE 27.34 Example of 2-axial groove bearing with load mid way between grooves. (From Neale, M.J. (1993), Steady load pressure fed journal bearings, in Bearings: A Tribology Handbook, Neale, M.J. (Ed.), ButterworthHeinemann, Oxford. With permission.)
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W
N
Groove With groove (a) Axial groove
Without groove
W
N
Groove With groove
Without groove
(b) Circumferential groove
FIGURE 27.35 Modification of hydrodynamic film pressure due to introduction of groove in load-carrying area. (From Shaw, M.C. and Macks, F.E. (1949), Analysis and Lubrication of Bearings, McGraw-Hill, New York. With permission.)
27.2.3.2.4 Ring Bearings One important use of oil-ring bearings is to provide a fresh supply of lubricant to a rotating journal as shown in the schematic in Figure 27.35. The lubricant is supplied from the sump by the ring. The ring drags against the top of the rotating journal. The imparted rotational motion to the ring enables it to pick up oil on its sides and underside of the ring from the sump. It is then carried to the top of the journal where it is distributed for lubrication. This is a case in which it is desirable to maintain high friction between the ring/journal interface so that the ring will rotate at higher speed and deliver more oil to the bearing. A sectioned view of an oil-ring bearing for an industrial application is shown in Figure 27.36. “At low ring speed, oil is delivered to the journal by the inside of the ring and by the sides of the ring. The oil adhering to the inner surface of the ring is the most important potential source of oil supply to the journal. It is partly squeezed out on the shaft at the point of contact between the ring and the shaft. At low speeds, additional oil is supplied by gravity from the oil that adheres to the sides of the ring. Thus, at low speeds, the radial depth of the ring probably has more effect on ring oil delivery than the axial width of the ring. Figure 27.37a and b indicates in a general way this mechanism of oil delivery. At high ring speeds the oil is thrown off by the rotational effect in the form of a spray. This spray should be collected in the crown of the bearing by collector scoops and directed back to the journal. Otherwise, it will flow down the inside of the bearing housing, directly back into the oil sump. A typical curve of delivery is shown in Figure 27.38. At high speeds, the transmission rate of oil from the ring is roughly proportional to its width. Baildon (1937) indicates that the demarcation between high-speed and low-speed ring
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(b)
(a)
Ring
Shaft
Oil
FIGURE 27.36 (a) Representation of oil-ring bearing; (b) detail of film formation between ring and shaft. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
FIGURE 27.37 Oil-ring journal bearing, in cross-section. (Courtesy of Mobil Oil Corp.) (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
Oil
Oil Oil
Oil
Shaft low speed
Shaft high speed
(a)
(b)
FIGURE 27.38 General mechanism of oil delivery. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
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Oil from propulsive film (underside of ring)
Oil from sides of ring
Journal speed FIGURE 27.39 Typical oil delivery curve. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
operation occurs at 250 rpm of a 3-in.-diameter journal, and 120 rpm of a 12-in.-diameter journal (7.62 and 30.48 cm)’’ (Fuller, 1984, p. 473). 27.2.3.3 Helical-Grooved Journal Bearings Journal bearings made with spiral grooves or with herringbone grooves belong to a class of bearings more generally referred to as helical-grooved bearings. The principle of operation is fundamentally the same as that described for the recurrent groove thrust bearing. 27.2.3.3.1 Spiral-Grooved Journal Bearing In the case of the spiral-grooved configuration, oil (viscous fluid) is dragged into the mouth of the grooves due to the relative sliding motion of the surfaces. Because of the spiral groove geometry, there is a net axial flow through the bearing. If there is some restriction to flow, a pressure will build up, thus supplying a source of pressurized flow as well as load support. This type of device has been successfully used as a viscous pump. The chemical processing industry uses the viscous pump as a feeder of molten polymers through extrusion dies. Christopherson and Naylor (1955) performed an excellent study on the application of the viscous pumping action to wire drawing. In that application, a wire was drawn through a reducing die along a tube with a small clearance filled with oil. 27.2.3.3.2 Herringbone-Grooved Journal Bearings One can obtain higher pressure development in the center and higher load capacity with a shaft (or bearing) having a right-hand screw on one end and a left-hand screw on the other. In this herringbone configuration, fluid is pumped inwardly from both ends to the middle. Fuller (1984) points out that this also can be used as a very strong pump in which fluid is bled away from the central high-pressure zone. Pressures have been recorded as high as 44,000 psi (303 MPa). By increasing the land width of this configuration, the device can be used as a very stable type of herringbone journal bearing (Figure 27.40). Herringbone journal bearings are effective at providing load capacity and stability without requiring a source of pressurized fluid. Unlike externally pressurized bearings, there is no load capacity at zero speed, but at high speed the herringbone-grooved bearing’s load capacity and stability may exceed those of the externally pressurized bearing. According to Schuller (1973), most of the studies on herringbone grooved journals dealt with compressible lubricants. Low load capacity and poor stability characteristics are two of the biggest problems in using gas-lubricated bearings. Another means of increasing load capacity and stability simultaneously is by including external pressurization of the bearing. Figure 27.41 shows an externally pressurized journal bearing in which high-pressure gas is introduced into the central land area of the bearing. The external pressurization tends to stiffen the bearing and to push the shaft of a loaded bearing back to the central
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0 0
1
CM 2.5
Plain bearing
10 Partial grooves
20 Partial grooves
10 Full grooves
20 Full grooves
40 Partial grooves
40 Full grooves
FIGURE 27.40 Herringbone-grooved journals. (From Schuller, F.T. (1973), Design of Various Fixed-Geometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
Bearing length, L Lf/2 Lg/2
Orifice radius, a
Orifice Recess Orifice Recess diameter, d
Rotation
Bearing radius, R
Groove angle, β
Clearance at zero eccentricity, C Axial coordinates z, ς
FIGURE 27.41 Externally pressurized herringbone journal bearing. (From Fleming, D.P. (1970), Steady-State and Stability Analysis of Externally Pressurized Gas-Lubricated Journal Bearings with Herringbone Grooves, NASA TN D-5870, Washington, D.C.)
position. This decreases its tendency to whirl and thus increases its stability. External pressurization also precludes rubbing contact and wear during starts and stops by providing load support at zero speed. 27.2.3.4 Foil Journal Bearings The foil bearing concept was originally developed by Blok and Van Rossum (1953). Later work by Eshel and Elrod (1965); Licht and Branger (1973); Licht, Branger, and Anderson (1973); Heshmat, Walowit, and Pinkus (1983); Saville, Gu, and Capaldi (1991); Heshmat, (1991a,b, 1994); Heshmat and Hermel
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(1992); Ku and Heshmat (1992, 1993); Gilbrech, Gu, Rigney, Saville, and Rossoni (1993); Ping and Carpino (1993); Braun, Choy, Dzodzo, and Hsu (1994); and others have done much to advance foil bearing technology for commercial application (Brewe, Fleming, Dimofte, and Hendricks, 1997). The types of foil bearings that exist are either a tension-dominated type or bending-dominated type. With the bending-dominated type, Fuller (1984) makes an additional distinction, that is, whether the foil is continuous or segmented. The tension-dominated foil bearings are suitable only for journal bearings. The bending-dominated designs can be applied to either journal bearings or thrust bearings. 27.2.3.4.1 Tension Dominated A tension-dominated foil bearing consists of a single foil wrapped around the entire journal (see Figure 27.42). Tension in the foil sufficiently exceeds the stiffness so that the stiffness of the foil membrane may be neglected. The tensioned foil bearing shown in the figure was designed and tested by Licht and Branger (1973) for a Brayton-cycle unit to function in the low gravity of space. They were able to eliminate the effects of gravitational loading by running the bearing in the vertical position. The 10-kg (22-lb.), 44-mm (1.75-in.) rotor ran to 43,000 rpm on a foil with a 4-mm (0.16-in.) thick molybdenum disulfide film and for 100 hours at 36,000 rpm with nominal wear. Ampex Corporation have also developed tension-dominated foil bearings to be used primarily for data-processing equipment where they provided support for magnetic tape traveling over guides, heads, and vacuum columns in tape transport.
Clamp Guide
Foil o
90
Guide
Journal
Lock Foil
FIGURE 27.42 Vertically oriented, tensioned foil bearing for space application. (From Licht, L. and Branger, M. (1973), Design, fabrication, and performance of foil journal bearings for the Brayton rotating unit, NASA CR-2243.)
27.2.3.4.2 Bending Dominated (Segmented) As the name implies, the bearing is broken into overlapping foil segments (Figure 27.43) that may or may not be supported on a corrugated bump foil shown in Figure 27.44. Part of each foil fits into a groove in the bearing housing. Each foil has a defined radius of curvature and thickness. Depending on the bearing and the fit, generally foil thickness can vary from 0.1 to 0.3 mm (0.004 to 0.011 in.). The bearing fits over the shaft as a single unit having a radial clearance ratio c/R normally from 0.001 to 0.02, approximately. This is 100 times greater than conventional bearings that have film thicknesses ranging from 100 to 200 µm (0.004 to 0.008 in.). Bearing stiffness is achieved by the pressure distribution generated in the convergent fluid film wedge and the mechanical design of the leaves and foil bumps. The leaves and foil bumps are usually separated by a distance of 0.025 to 0.075 mm (0.001 to 0.003 in.), which results in a nonlinear stiffness. Damping is provided both by the fluid film and the friction characteristics of the foil and/or bumps (Brewe, Fleming, Dimofte, and Hendricks, 1997, p. 550).
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Housing Foil segment Journal
FIGURE 27.43 Bending-dominated segmented foil journal bearing. (From Suriano, F.J., Dayton, R.D., and Woessner, F.G. (1983), Test Experience with Turbine-End Foil Bearing-Equipped Gas Turbine Engines, Paper 83-GT-73, American Society of Mechanical Engineers.)
Top foil (lifted)
Bump foil
(a) Construction of bearing.
U
Shaft Top foil Spacer block
Thickness of foil
h
s
Bump foil l
(b) Basic element of bearing.
FIGURE 27.44 Corrugated bump foil bearing design. (From Heshmat, H., Walowit, J.A., and Pinkus, O. (1983), Analysis of gas-lubricated foil journal bearings, J. Lubr. Technol., 105(4), 647–655. With permission.)
27.2.3.4.3 Bending Dominated (Continuous) This type of bearing is shown in Figure 27.45. The identifying feature of this bearing is the continuous top foil that is attached to the bearing housing at one end and wraps around the entire circumference of the bearing. Here it is shown elastically supported by a bump foil strip that is resilient and controls the stiffness of the bearing. The top foil provides the frictional damping which offers a stabilizing effect on the dynamics of the rotor. This configuration was developed by Mechanical Technology, Inc., with the trade-name HYDRESIL. Significant accomplishments have been recorded for the HYDRESIL bearings. Some of these reported by Fuller (1984) are: 1. 2. 3. 4. 5.
Three years of operation in automotive-type gas turbines at 60,000 rpm and 500°F (250°C) 120,000 rpm in product hardware Bearing shock resistance to 25 g at 100,000 rpm Tests at 1200°F bearing temperature (649°C) Bearing pressures for hydrodynamic air operation up to 50 psi (345 kPa) based on projected area (under laboratory conditions)
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Restrained end Free end Housing Journal
Top foil strip Bump foil strip
FIGURE 27.45 Bending-dominated continuous foil journal bearing. (From Heshmat, H., Walowit, J.A., and Pinkus, O. (1983), Analysis of gas-lubricated foil journal bearings, J. Lubr. Technol., 105(4), 647–655. With permission.)
Heshmat, the inventor of this bearing, has since made improvements. According to Heshmat (1994), the improved bearing successfully demonstrated “major advances in aerodynamic foil bearing speed and load performance … over a speed range to 2200 cps (132,000 rpm) or 4.61 × 106 DN. The current load capacity of 727.8 N (163.6 lb.) corresponded to a projected area pressure of 673.5 kPa (97.68 psi) at an operating speed of 995 cps (59,700 rpm). The corresponding bearing temperature was 40°C (104°F), with a peak film temperature of 175°C (347°F) in an ambient-pressure environment. The improved foil bearings used to support the rotor shared the center bearing loading and were stable throughout the load testing. The load on these two bearings varied between 7.6 and 371.4 N (1.7 and 83.5 lb.). These bearings with a variable stiffness gradient demonstrated excellent whirl stability characteristics. A higher unbalance level (by an order of magnitude higher than standard level) was introduced to the test rotor. The bearings operated in a stable manner up to the full achievable speed of the test spindle. In addition, the thermal and centrifugal growth of the test journal surpassed the bearing initial clearance by some 18% under full load and speed operation.” 27.2.3.4.4 Advantages of Foil Bearings* Foil bearings have the following advantages over rigid bearings: 1. Accommodations to distortions and misalignments. No strict tolerances are needed on journal diameter or roundness because the foil conforms. Because the foil can deflect, relatively large excursions can be accommodated without rupturing the fluid film. Foil bearings can operate at elevated temperatures in the presence of appreciable temperature gradients, producing large thermal distortion. They have been demonstrated at speeds above 5 million DN (upper DN limits have not been established). 2. Stability. Self-excited vibrations do not occur. 3. Low wear. Foil bearings have excellent wipe-wear, start-stop, and longevity characteristics. No external pressure source is required for starting or stopping, and long life is anticipated. 4. Resistance to particle damage. The large film thickness and the ability of the foil to conform provide relative immunity from the effects of abrasive particles and foreign matter entering the bearing clearance. Foil bearings can also be advantageous with liquids, especially with particle-laden lubricants and in machines using contaminated process fluids as lubricants. 5. High load capacity and low torque. Foil bearings carry heavier loads than similar-size rigid geometry bearings and have generally low power losses. 6. Simple construction, lower weight, and smaller envelope than conventional bearings.
*Taken from Brewe, Fleming, Dimofte, and Hendricks (1997).
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27.2.3.4.5 Disadvantages of Foil Bearings The disadvantages relative to rigid bearings are: 1. 2. 3. 4. 5.
Supporting foil wear can lead to catastrophic fracture. Few analytical tools or design charts are available. Damping mechanism is not well understood. Starting and stopping friction wear can be large. Starting torques are high.
27.2.3.4.6 Foil Bearing Materials The materials that have been used for foil bearings are Inconel, beryllium copper, and various stainless steels. Also, under consideration are superalloys such as MA-2000 for temperature applications as high as 1100°C (2012°F). Solid lubricant coatings and other coatings extend foil life. 27.2.3.4.7 Applications “Foil gas bearings have been applied successfully to a wide range of high-speed aerospace rotating machinery such as air cycle machines (ACMs), auxiliary power units (APUs), and even cryogenic turbocompressors” (Heshmat, 1991a, 1993). “The use of these bearings reduces system complexity and maintenance costs, and increases efficiency and operating life. Since the early 1970s, the development of various classes of bending dominated foil bearings has taken an aggressive path toward improving bearing speed and load capability. Because a self-acting foil bearing surface will deform as hydrodynamic pressure is generated, the bearings can be constructed to deform in an advantageous manner with respect to the application, whether it be for high-load capability or for high-speed operation. Frictional damping can also be introduced through rubbing as deformation takes place and by selecting material combinations and an elastic foundation design that will optimize the internal frictional damping effect and bearing operating stiffness coefficients” (Heshmat and Hermel, 1992). Foil bearings are presently employed in naval APUs and in ACMs for numerous aircraft engines (e.g., Boeing 747, 757, and 767, DC-10, F-15, F-16, and Falcon 2000). Also, their use in automotive gas turbine engines has been investigated. These bearings are now being developed for high-temperature applications in limited-life, expendable, gas turbine engines under the DOD/NASA/Industry Integrated High-Performance Turbine Engine Technology (IHPTET) initiative. The goal of the present IHPTET foil gas bearing effort is to develop a new class of foil bearings capable of operating at temperatures to 815°C (1500°F) that provide increased levels of vibrational damping for smoother, more durable operation (Heshmat, 1994). 27.2.3.5 Reciprocating-Load Journal Bearings Journal bearings subjected to reciprocating loads are found in automobile engines, diesel engines, steam engines, reciprocating compressors, and poorly balanced high-speed rotors. In this discussion, a few select examples of bearing types used in diesel engine applications are presented along with some related information on imposed bearing conditions and environment.* 27.2.3.5.1 Diesel Engine Bearings Figure 27.46 illustrates a typical V-block diesel engine exposing a view of the big-end connecting-rod bearing in situ. These bearings are typically split for assembly purposes. Figure 27.47 shows a connecting rod with a conventional big-end bearing and a unique spherical joint piston bearing. Connecting-rod big-end bearing: The bearing shape is often made elliptical by increasing the clearance along the direction of the split. An elliptically shaped bearing tends to run cooler than a cylindrical bearing with the same minor rod axis clearance but larger clearance along the direction of the split. Also, the elliptical shape has a tendency to suppress the “half-frequency whirl” phenomenon. The elliptical shape is accomplished by inserting a thin-walled bearing liner in the housing with a slight interference
*For a more in-depth discussion of these bearing types, the reader should refer to Wilcock and Booser (1957) and Shaw and Macks (1949).
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9
10
11
12 8
13 7 14 6
5 15 4 16 3
17 18
2 19
1
20
FIGURE 27.46 Cross-section of a V-block diesel engine. (Cummins Inc.) (From Gunther, R.C. (1971), Lubrication, Chilton Book Company, Philadelphia. With permission.)
FIGURE 27.47 Connecting rod illustrating typical con-rod bearing but with unique spherical-piston-bearing design. (Courtesy of Cummins Inc., Yonushonis et al. (1989), NASA/CR-1999-209163.)
fit (several mils) or “crush.” The liner is made slightly thinner at the split line (~1/2 mil). If the crush is excessive, it can lead to an undesirable inward pinching at the split due to bearing distortion. Oil supply for large con-rod bearings used for heavy-duty diesel engines is normally introduced via a circumferential groove. Figure 27.48 shows the slotted circumferential groove used by Yonushonis et al. (1999) in a DOE/NASA study. The upper half of the bearing liner was slotted from the split to the oil drilling leading to the spherical joint piston bearing. The slot was not continued around the entire upper bearing liner to maximize the bearing area in the high load region. Not only do the slots provide better distribution of oil to the connecting-rod bearing, but they also increase the oil flow to the oil drilling. Spherical joint piston bearing: The reason for the spherical geometry is that it provides a larger load bearing area (16 to 29% more) as compared to a conventional wrist-pin bearing (Figure 27.49). Another
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FIGURE 27.48 Slotted connecting-rod big end bearing. (From Yonushonis, T.M., Wiczynski, P.D., Myers, M.R., Anderson, D.D., McDonald, A.C., Weber, H.G., Richardson, D.E., Stafford, R.J., and Naylor, M.G. (1999), Development of Advanced In-Cylinder Components and Tribological Systems for Low Heat Rejection Diesel Engines, NASA/CR-1999-209163, DOE/NASA/0375-2, ARL-CR-442.)
FIGURE 27.49 Typical piston-pin bushings, for four-cycle engines (left) and two-cycle engines (right). (Courtesy of General Motors Corp.) (From Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGrawHill, New York. With permission.)
reason for this geometry is that it permits the piston to rotate. By inducing rotation of the piston, thermal gradients can be avoided that are set up by the cooler inlet gases on one side of the chamber and the hotter exhaust gases on the other side. Thus, rotation results in uniform thermal growth. 27.2.3.5.2 Dynamic Loading* Piston engines generate an external dynamic load on their oil-lubricated, connecting-rod journal bearings (Figure 27.50). Mass acceleration and unbalanced fluid forces cause the journal center to move within the bearing clearance circle (Figure 27.51). The theoretical methods for predicting the journal trajectory *Taken from Brewe, Fleming, Dimofte, and Hendricks (1997).
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Peak firing load
222.5kN (50 000 lbf)
Crank angle, deg 360 540 180
lnertia loop
450 90
270 630
89kN (20 000 lbf)
89kN (20 000lbf)
lnertia loop
13305kN (30 000lbf)
0/720
FIGURE 27.50 Representative polar load-vs.-load-angle diagram for piston engine connecting-rod bearing relative to connecting-rod axis. (From Vijayaraghavan, D., Brewe, D.E., and Keith, T.G., Jr. (1992), Effect of Out-of-Roundness on the Performance of a Diesel Engine Connecting-Rod Bearing, NASA TM-105600.) Rod half lnstant of peak firing load 180
540
εmax = 0.932 (occurred during inertia load period)
450 270 530 360
Crank angle, deg 90
0/720 Clearance circle Cap half
FIGURE 27.51 Representative journal center locus plot for connecting-rod journal bearing (relative to connectingrod axis). (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
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during the load cycle range from such quick computational methods as the short-bearing theory (DuBois and Ocvirk, 1953), the mobility method (Booker, 1971), and the semi-analytical method (Ritchie, 1975), to more rigorous methods that use finite bearing analysis and incorporate oil film history (Jones, 1983) and inertia effects (Holmes and Craven, 1971). Campbell et al. (1967), Martin (1983), and later Vijayaraghavan et al. (1992), have extensively discussed and compared theoretical predictions, experimental results, and operational experiences with engine bearings. They have not only pooled the available information about these bearings but have also encouraged researchers and designers to improve the modeling and/or the performance prediction methods for these bearings. 27.2.3.6 Vibrational Loading Even if the bearing is subjected to a constant applied load, the bearing can experience dynamic loading through machine vibrations. Depending on how the frequency of the vibration relates to the speed of the shaft, these vibrations are either sub-synchronous, synchronous, or super-synchronous. 27.2.3.6.1 Synchronous Resonant Shaft Whirl In fluid film journal bearings, one can treat the shaft as a rigid mass suspended in a spring-like fluid film. this mass-spring system will have an inherent natural frequency of vibration that can be excited by external forces. These forces can be the result of residual unbalances in the system such as caused by a blade loss in a turbine engine. Under these circumstances the natural frequency or resonant vibration produced by the system would occur at the shaft rotational speed. The resulting motion of the shaft center within the clearance circle of the bearing has been commonly observed as a precession or orbiting of the shaft center about the bearing center. This is called “synchronous whirl” and can lead to very large excursions of the shaft center relative to the bearing center resulting in rubbing and likely failure. Synchronous whirl can manifest itself in a variety of motions, for example, translatory whirl or conical whirl. Translatory whirl occurs when the centerline of the shaft describes the locus of a cylinder. Conical whirl occurs when the ends of the shaft are orbiting out of phase with each other and the midpoint between the shaft ends remains fixed. Other complications can arise if the housing is elastically supported because it can vibrate in either of these modes as well. Hagg (1947) has analyzed these situations in considerable detail. 27.2.3.6.2 Sub-synchronous Whirl Instabilities from sub-synchronous vibrations can be caused by the journal interacting with the working fluid (e.g., half-frequency whirl), friction rubs, and internal friction due to stress reversals in parts that were assembled with a shrink-fit. One of the most serious forms of instability is the first mentioned here, i.e., half-frequency whirl. This condition occurs when the center of the journal orbits around the bearing center at a frequency equal to one half of the journal rotational speed. Under these conditions, the net entrained flow through the bearing is zero. The film cannot generate pressure and hence support a load or provide stiffness. the journal continues to whirl at one-half of the journal speed or less, having no ability to resist. This is more apt to set up and occur under lightly loaded conditions at high speeds. Unlike an ordinary critical speed that one might encounter with the resonant synchronous whirl, one cannot increase the shaft speed to pass through the critical to attain a region of stability at higher speeds. 27.2.3.6.3 Super-synchronous Whirl Misalignment, which normally creates a response at twice the shaft speed, would be a good example of a super-synchronous vibration. Any number of these vibrational sources can occur in a rotating machine, thus complicating the procedures one must go through to achieve a smooth operating machine. 27.2.3.7 Bearing Designs that Inhibit Whirl Under high-speed and lightly loaded conditions, the plain circular journal bearings are especially prone to half-frequency whirl. The bearing has a strong tendency to whirl and go unstable if the attitude angle
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becomes large. There are numerous design features that can be built into the bearing that enable a bearing to run at more favorable attitude angles, thereby inhibiting whirl tendencies. 27.2.3.7.1 Steps and Grooves For example, introduction of axial grooves can have a mildly stabilizing effect by disrupting the flow pattern and breaking up the pressure distribution, as shown in Figure 27.52. With the grooves judiciously placed relative to the load line, this tends to reduce the attitude angle from what it otherwise would assume if it were a plain bearing. Sternlicht and Winn (1964) demonstrated a higher half-frequency whirl threshold with lower attitude angle. Rayleigh step and herringbone-grooved bearings: Bearings designed to create a pumping action circumferentially around the bearing with the use of steps or grooves are known to be more stable than plain journal bearings. Boeker and Sternlicht (1956) demonstrated the effectiveness of using a Rayleigh step bearing with plain bearings to inhibit whirl. Hamrock and Anderson (1968a,b) analyzed an incompressibly lubricated concentric Rayleigh step bearing (Figure 27.53) for the optimal step configuration that would provide a maximum load. The fact that this bearing would carry a substantial load although the bearing and shaft were concentric prompted Schuller (1971) to study stability characteristics of several Rayleigh step designs. One of the most promising designs for stability is shown in Figure 27.54. Vohr and Chow (1965) analyzed the special case of a herringbone-grooved, gas-lubricated, cylindrical journal bearing using a narrow groove theory (i.e., the number of grooves is large enough so that local
FV1 FH1
+ +
FH2 FV2 FIGURE 27.52 Three-groove bearing. (From Pinkus, O. and Sternlicht, B. (1961), Theory of Hydrodynamic Lubrication, McGraw-Hill, New York. With permission.)
L/2 _ y
Cst
+y
Cr
+
+
R U
U
FIGURE 27.53 Concentric Rayleigh step bearing. (From Hamrock, B.J. and Anderson, W.J. (1968a), Incompressibly Lubricated Rayleigh Step Journal Bearing. I. Zero-Order Perturbation Solution, NASA TN D-4839.)
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pressure variations across the groove width pair can be ignored). In contrast to a plain bearing, they concluded that the load capacity of a herringbone-grooved journal bearing continues to increase without limit with increasing speed. In addition, their analysis suggested that the grooved bearings may not suffer the half-frequency whirl instability that is associated with the unloaded, plain bearing. Malanoski (1967) studied a pair of partial herringbone-grooved journal bearings (Figure 27.55) for stability using air as the lubricant. The bearings were run to 60,000 rpm and showed no signs of being unstable under load and no-load conditions. Fleming, Cunningham, and Anderson (1968) verified that inward-pumping bearings showed promise for stable operation at high speeds. These are effective anti-whirl bearings even when the shaft is in the central or unloaded position. The mechanism that holds it in place involves the positive forces generated by the separate sets of pumping grooves. If the shaft is perturbed from its equilibrium position, the forces generated by the multiple sets of grooves tend to press the shaft directly back to its equilibrium position. Further, the tangential component of force that drives it into whirl is less with steps and grooves than with plain bearings (Whitley, 1964, p. 102).
A
Feed groove Ridge region C Rotation
Step Shroud
ζ
Step region
γ
S φ
Shroud
Cs
Pad
A
Section A-A (a) One-segment, three-pad shrouded Rayleigh step journal bearing.
(b) Rayleigh step bearing geometry. Ridgeto pad-arc ratio ψ = γ/(γ + ϕ + ζ); film thickness ratio kr = Cs/C.
FIGURE 27.54 One segment Rayleigh step bearing. (From Schuller, F.T. (1973), Design of Various Fixed-Geometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
Ridge width Groove width Bearing length, L
Helix angle Ridge Groove Rotation
L 3
Radial clearance
Land
Journal Bearing
FIGURE 27.55 Herringbone-partial-grooved journal bearing. (From Schuller, F.T. (1973), Design of Various FixedGeometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
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Pressure dam bearing: Another type of step bearing used to improve the stability of rotating machinery is the pressure dam bearing, shown in (Figure 27.56). These bearings are composed of a plain journal or two axial-grooved bearings in which a dam is cut in the top pad. As the fluid rotates into the dam region, a large hydrodynamic pressure is created on top of the shaft. The resulting hydrodynamic force adds to the static load on the bearing, making the shaft appear to weigh much more than it actually does. This has the effect of making the bearing appear much more heavily loaded and thus more stable. Pressure dam bearings are extremely popular with machines used in the petrochemical industry and are often used for replacement bearings in this industry (Allaire and Flack, 1980, p. 120).
DAM R+c+cd R+c R
FIGURE 27.56 Pressure dam bearing. (From Allaire, P.E. and Flack, R.D. (1980), Journal bearing design for highspeed machinery, in Bearing Design-Historical Aspects, Present Technology and Future Problems; Proceedings of the International Conference, Anderson, W.J. (Ed.), American Society of Mechanical Engineers, New York, 111–159. With permission.)
27.2.3.7.2 Preloaded Non-circular Bearings Another effective means of inhibiting whirl is to design the bearing with a more strongly converging wedge so as to increase the stiffness of the bearing. Elliptical (lemon) bearing: One relatively simple way to create a more strongly converging-diverging geometry is to make the bearing elliptical in shape by splitting the bearing and moving each half in toward the bearing center by some fraction of the pad clearance. This is otherwise known as a lemon bearing or two-lobe bearing. When the shaft rotates, hydrodynamic clamping pressures (Figure 27.57) are generated, which inhibits whirl. Another reason for using the lemon bearing is that for the same minor vertical clearance, it runs cooler than a cylindrical plain bearing because of the larger horizontal clearance. The fraction of pad clearance that the pads are moved in is called the preload factor, m, and is defined as:
m=
C − Cb C
(27.24)
where C represents the original clearance of the bearing and Cb represents the clearance after assembly. Figure 27.58b shows the pad centers of curvature coinciding with the bearing center resulting in a zero preload configuration. While a preload factor of 1.0 corresponds to having all of the pads touching the shaft as shown in Figure 27.58c. In both cases, the shaft radius and pad clearance are held constant. Offset elliptical bearing: One can increase the clamping pressures by horizontally offsetting the elliptical bearing so as to make each pad totally converging (Figure 27.59), because only the converging wedge region of the lobe generates pressure to support a load. Chadbourne, Dobler, and Rottler (1966) showed
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FIGURE 27.57 Elliptical (lemon) shaped bearing bore illustrating hydrodynamic clamping pressures. (From Neale, M.J. (1993), High speed bearings and rotordynamics, Bearings: A Tribology Handbook, Neale, M.J. (Ed.), ButterworthHeinemann, Oxford. With permission.)
R + cb
a) LARGEST SHAFT WHICH FITS IN BEARING
x
R+c R+c R
b) TWO LOBE BEARING WITH PRELOAD m = 0.0, LARGEST SHAFT = R + c, BEARING CLEARANCE cb = c.
xR
R+c
c) TWO LOBE BEARING WITH PRELOAD m = 1.0, LARGEST SHAFT = R BEARING CLEARANCE cb = 0.
FIGURE 27.58 Effect of preload on two-lobe bearing. (From Allaire, P.E. and Flack, R.D. (1980), Journal bearing design for high-speed machinery, in Bearing Design-Historical Aspects, Present Technology and Future Problems; Proceedings of the International Conference, Anderson, W.J. (Ed.), American Society of Mechanical Engineers, New York, 111–159. With permission.)
that tilting the lobe toward the shaft at the trailing edge results in a more favorable converging wedge region resulting in greater load capacity, and improved stability. A measure of the fraction of the full pad arc length that the converging wedge assumes is called the “offset factor” α (Figure 27.60). That is, α is defined as:
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FIGURE 27.59 Horizontal offset bearing bore hydrodynamic clamping pressures. (From Neale, M.J. (1993), High speed bearings and rotordynamics, Bearings: A Tribology Handbook, Neale, M.J. (Ed.), Butterworth-Heinemann, Oxford. With permission.)
β θ=β
θ = 0.6 β
Sector
Sector
Leading edge
Leading edge
RL
RL
C
R
PC
R PC R
R
C
P
RP a
R a Shaft
Shaft
(a) Converging-diverging configuration. Offset factor α = θ/β = 0.6.
(b) Wholly converging configuration. Offset factor α = θ/β = 1.0.
FIGURE 27.60 Lobed sector illustrating offset factor, α = θ/β. (From Schuller, F.T. (1973), Design of Various FixedGeometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
α=
θ β
(27.25)
where θ represents the arc length of the converging wedge portion of the full pad length, β. Three- and Four-Lobe Bearings: Further, by increasing the number of converging-diverging regions around the bearing, whirl can be suppressed by the clamping effect it produces. Still more effective in inhibiting whirl than the elliptical bearing are the three-lobe bearing (Marsh, 1964; Lund, 1968) and the four-lobe bearing. All these bearings provide built-in oil wedges even when there is not external load. Both the three-lobe (Figure 27.61) and four lobe bearings (Figure 27.62) have an offset factor of α = 0.5. By machining the pad’s surface radius so that it is greater than the radius of the shaft, the bearing becomes more stable. Under this condition, each lobe is under load and stabilizing forces are directed toward the
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Bearing housing
Bearing
Shim
Rotation
Shaft
Identification mark
FIGURE 27.61 Three-central-lobe bearing. (From Schuller, F.T. (1973), Design of Various Fixed-Geometry WaterLubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
center of the bearing. Pinkus and Sternlicht (1961) discuss the performance of these bearings for various geometrical arrangements. 27.2.3.7.3 Stability Comparison of Five Fixed-geometry Bearings Whirl onset speed is plotted against clearance C/R in Figure 27.63 for five different fixed-geometry journal bearings with an L/D of unity. The data for these curves were obtained from optimum locus curves for each bearing. Figure 27.63 shows that the five fixed-geometry bearings considered can be generally rated in order of diminishing stability as follows: (1) three tilted-lobe bearing (offset factor of 1.0); (2) herringbone journal mated with a plain bearing; (3) one-segment, three-pad, shrouded Rayleigh step bearing; (4) three-tilted-lobe journal with grooves (offset factor of 1.0) mated with a plain bearing; and (5) three-central-lobe bearings with grooves. 27.2.3.7.4 Summary of Anti-whirl Bearing Types Numerous bearing configurations having anti-whirl characteristics have been discussed very briefly to give a broad view of the wide range of bearing designs that are available to the designers and users of rotating machinery. These bearings ranged from very simple plain journal bearings to very complex tilting pad bearings. As one would expect, the simple plain bearings are much easier to make and lower in cost. The ease of manufacture and cost considerations must be weighed with the necessity to suppress vibration and the particular circumstances in the application. Some of the advantages and disadvantages of various bearing types to suppress whirl are given in Table 27.4.
27.3
Failure Modes
27.3.1
Cavitation Erosion Damage*
The experiences discussed in the paper “Cavitation Erosion Damage in Engine Bearings: Theory and Practice” by Garner, James, and Warriner (1980) still reflect much of the current view on the subject. A *This topic in the following subsections is an excerpt from “Current Research in Cavitating Fluid Films,” STLE SP-28 by F. Martin (1990), Tribology Consultant to the Glacier Metal Company, Limited, Middlesex, England.
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Bearing
a
P
R P
r
Q P Shaft
P FIGURE 27.62 Four-lobe bearing geometry. (From Fuller, D.D. (1956), Theory and Practice of Lubrication for Engineers, 1st Ed., John Wiley & Sons, New York. With permission.)
few selected extracts from that paper are presented here. These include examples of typical cavitation erosion damage, together with suggested mechanisms of damage. Commonly applied palliatives and their effectiveness, based on engine experience, are also discussed. “Cavitation erosion in engine bearings is a phenomenon which has assumed increasing significance during the past … years, probably as result of the design trends toward higher rotational speeds and, in some cases, higher rates of change of cylinder pressure…. “… Damage is seen predominantly in diesel engine bearings, and on the rare occasions when damage occurs in gasoline engines, it is normally as a result of operating under [incorrect conditions]. “In many cases the damage is restricted to local attack of the overlay and the performance of the bearing is virtually unaffected…. However, in more extreme cases extensive loss of overlay and interlayer material occurs, and the consequential adverse effects upon oil film conditions will reduce the service reliability and life of the bearings…. “The fact that diesel engine bearings are more prone to cavitation erosion damage is attributed to the more severe combustion conditions, and, additionally, to the necessity for more complex oil feeding arrangements with greater chance of flow discontinuities.” Garner et al. (1980) state that cavitation erosion damage is associated with the collapse of vaporous cavities near to the bearing surface, and suggest that the mechanism is the impingement by micro-jets of fluid. They describe a possible sequence of events in the collapse of vaporous cavities leading to the formation of high intensity micro-jets (Figure 27.64). Now look at the result of this in terms of actual damaged bearings. 27.3.1.1 Large End Bearing Damage Predominantly Associated with Oil in Connecting Rod Drilling “The commonest form of damage occurring in large end bearings appears at first sight to be due more to flow erosion than to cavity collapse, but detailed examination of the damage confirms a cavitation effect. This can occur in either fully grooved or partially grooved bearings. “In fully grooved bearings, the damage occurs predominantly at the groove edges, but can ultimately spread into the bearing lands. There is strong evidence that the damage is caused by inertia effects on the column of oil in the connecting rod drilling which is supplied from the large end bearing groove to provide top end lubrication and piston cooling….” The damage may be cured by restricting the back flow from the rod drilling into the bearing (fitting a non-return valve has been one solution). In other cases, “the damage was diminished when the groove
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TABLE 27.4
Comparison of Whirl Suppression Journal Bearing Designs
Bearing Type
Advantages
Disadvantages
Comments
Plain journal
1. Easy to make 2. Low cost
1. Very subject to oil whirl
Round bearings are nearly always “crushed” to make elliptical bearings
Axial groove
1. Easy to make 2. Low cost
1. Subject to oil whirl
Round bearings are nearly always “crushed” to make elliptical or multi-lobe
Elliptical
1. Easy to make 2. Low cost 3. Good damping at critical speeds
1. Subject to oil whirl at high speeds 2. Load direction must be known
Probably most widely used bearing at low or moderate speeds
Three and four lobe (tapered land, etc.)
1. Good suppression of whirl 2. Overall good performance 3. Moderate cost
1. Some types can be expensive to make properly 2. Subject to whirl at high speeds
Currently used by some manufacturers as standard bearing design
Pressure dam (single dam)
1. 2. 3. 4.
1. Goes unstable with little warning 2. Dam may be subject to wear or buildup over time 3. Load direction must be known
Very popular with petrochemical industry; easy to convert elliptical over to pressure dam
Offset half (with horizontal split)
1. Excellent suppression of whirl at high speeds 2. Low cost 3. Easy to make
1. Fair suppression of whirl at moderate speeds 2. Load direction must be known
Has high horizontal stiffness and low vertical stiffness; may become popular; used outside U.S.
Hydrostatic
1. Good suppression of oil whirl 2. Wide range of design parameters 3. Moderate cost
1. Poor damping at critical speeds 2. Requires careful design 3. Requires high-pressure lubricant supply
Generally high stiffness properties used for high-precision rotors
Tilting pad
1. Will not cause whirl (no cross coupling) 2. Wide range of design parameters
1. 2. 3. 4.
Widely used bearing to stabilize machines with sub-synchronous non-bearing excitations
Good suppression of whirl Low cost Good damping at critical speeds Easy to make
High cost Requires careful design Poor damping at critical speeds Hard to determine actual clearances 5. High horsepower loss
From Allaire, P.E. (1979), Fundamentals of the Design of Fluid Film Bearings, Rhode, S.M., Maday, C.J., and Allaire, P.E. (Eds.), American Society of Mechanical Engineers, New York, 77. With permission.
cross-sectional areas in both the main and large end bearings were increased, thus allowing the oil column fluctuations to be better absorbed by the oil in the grooves…. “On partially grooved large end bearings damage frequently occurs at the groove run-out, either at the end of the partial groove, or at the side of the run-out (Figure 27.65). The problem occurs at the end of the partial groove in the direction of shaft rotation, regardless of the position of the oil feed connection to the rod drilling. In the example shown in Figure 27.65, in which the damage had occurred within 400 hours, the oil feed to the rod was adjacent to the damaged groove ending. The problem was overcome by the simple expedient of drilling a radial hole in the run-out section, as shown by the lower bearing in Figure 27.65, which had run for 1500 hours. Several other cases of similar damage have been successfully treated, … either by provision of a radial hole or by terminating the groove conveniently at the end of a bridge-piece slot.”
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Journal
10000 8000
Bearing
Offset From factor, fig. α
Plain 1.0 Three-tilted-lobe Herringbone-groove Plain Plain Rayleigh step (onesegment, threepad shrouded) Three-tilted-lobe Plain 1.0 with grooves Plain .5 Three-central-lobe with grooves
43 17 29 50 36
Unstable operation
6000
Whirl onset speed, NW, rpm
4000
2000
1000 800 600 400 Stable operation 200
100 .6
1.0 1.5 Clearance ratio, C/R
2.0
2.5 3.0x10-3
FIGURE 27.63 Stability of five fixed-geometry bearings. (From Schuller, F.T. (1973), Design of Various FixedGeometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333.)
Original bubble shape
Depression on side opposite solid surface
Fluid flows into growing depression
Formation of micro-jet
FIGURE 27.64 Mechanism of micro-jet formation. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
FIGURE 27.65 Cavitation damage associated with groove run-out in large-end bearing, together with effective solution. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
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27.3.1.2 Main Bearing Damage Predominantly Associated with Oil in Crankshaft Drilling “The majority of modern medium-speed diesel engines use partially grooved main bearings in which the ungrooved arc is symmetrically placed in the bottom half, and is approximately 120° in extent. Such bearings provide an acceptable oil film thickness within the narrow confines dictated by the overall design, but, at today’s high ratings, are those most likely to suffer from cavitation erosion damage. This occurs downstream of, but usually close to, the groove run-out and typically takes the form shown in Figure 27.66. “In this instance, the damage was found after only 400 hours of operation, and was restricted to the soft overlay plated surface of the bearing, which was of the order of 0.03 mm thick. The stronger bearing lining underneath had not been attacked. This form of damage is characterized by a crescent form. In the particular example shown, after the initial short-term damage, further progression was slow. Bearings in this condition after several thousand hours operation may quite safely be refitted. However, in some instances, the damage can be much more severe. “It is probable that as the oil drilling in the shaft traverses the groove run-out, cavities are formed at the intersection of groove run-out edge and the oil hole blend radius, as depicted diagrammatically in Figure 27.67. “Various palliatives have been tried on different engine types to alleviate this type of damage. These have usually consisted of modifications to the end of the partial groove. The most effective palliative so far adopted has been a tangential blend from groove to bearing surface with a square profile” (Figure 27.68).
FIGURE 27.66 Mild overlay damage in partially grooved main bearing. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
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(a)
(c)
(b) Cavities formed
Cavities collapsed
FIGURE 27.67 Cavity formation associated with interaction between journal drilling and partial groove. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
r tte Cu ter e m dia
90o
Tangential groove runout
FIGURE 27.68 Design detail of successfully applied modification to groove ending. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
27.3.1.3 Main and Large End Bearing Damage Predominantly Associated with Rapid Shaft Motion Cavitation damage of the type shown in Figure 27.69 (commonly referred to as suction cavitation erosion) occurs in the center of the lands in some fully grooved bearings. It is due to rapid shaft movement away from the bearing surface and is worse with large clearances. It occurs in the upper half of high-speed diesel main bearings (and also in a large end bearing during a series of development tests on a mediumspeed, two-stroke engine). Prediction of the journal orbit and examination of the hydrodynamic conditions within the bearing helps to pinpoint the area of likely damage. It also enables the designer to quickly examine the relative merits and disadvantages of various designs. “For the purposes of balancing loads and integrated pressures, that is, in predicting the journal center orbit, it has been assumed, as is common practice, that negative pressures cannot be sustained by the lubricant. However, it is considered that predicted negative pressures will indicate the position and intensity of any cavity formation.” This method was used to examine the hydrodynamic conditions of a center main bearing showing the same type of damage as shown in Figure 27.69. “The load diagram and resulting orbit are shown in
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FIGURE 27.69 Suction damage in large-end bearing associated with large clearance. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
Figure 27.70a and it can be seen that a rapid journal movement takes place between points B and C. Whilst such movements, the initial plot of rupture zones within the bearing (Figure 27.70b) failed to show anything significant at the top of the bearing (0° or 360°) where damage occurred. It was only when the time step of the solution was refined (from 10° to 1° crank angle) that intense “negative” pressure zones were predicted” (Figure 27.70c). The position of the maximum negative pressure corresponded to the position of cavitation damage on the bearing surface, thus indicating that the cause of the damage was cavity formation (and subsequent collapse). The palliative here was to reduce the bearing clearance, which alleviated the damage. However, it may be necessary in other instances to modify the polar load diagram. For example, the counter-weights could be changed. 27.3.1.4 Concluding Remarks Cavitation erosion damage in diesel engine bearings appear to fall broadly into three categories, associated with: • Oil in crankshaft drillings and bearing oil feed features • Effects of the oil within the connecting rod drillings • Journal movements within the bearing clearance space leading to adverse oil film conditions Relatively simple modifications to the detailed design of the bearing and its associated components can usually obviate problems from the first two categories, but often not from the third. However, these more intractable problems do seem to show some correlation with predicted oil film conditions. A more detailed theory than that considered here will probably be needed before damage can be reliably predicted at the design stage.
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Journal center locus
Polar load diagram B
D
A C Ruptured regions (a)
0 an gl e
180 Cr
an
k
0 180 0 0
180
360
Bearing angle Ruptured regions (b)
Cr
an
k
an
gl
e
265 255 245 235 225 215 0
180 Bearing angle
360
(c)
FIGURE 27.70 Predicted hydrodynamic conditions associated with occurrence of cavity damage. (From Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. With permission.)
27.3.2
Wear Due to Contaminants*
Contaminants in both fluid-film- and gas-film-lubricated systems can significantly affect bearing performance, life, and reliability. Figure 27.70 compares various contaminant sizes and presents a typical operating film thickness in a fluid film bearing…. These particles can brinell the shaft (journal) and bearing surfaces, causing stress raisers that can act as nuclei for surface pitting (spalling). Hard particles act as an abrasive medium and wear the softer surface. The particles can also act to clog lubricant orifices and jets, resulting in lubricant starvation of the bearing surfaces.
*Taken from Brewe, Fleming, Dimofte, and Hendricks (1997).
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ω
Journal
Lint or dust Smoke particle (6-µm diameter)
Fingerprint smudge
Human hair (100-µm diameter)
Oxide film (5 µm thick) Hydrodynamic fluid film (2.5 µm thick)
Fluid film bearing
FIGURE 27.71 Various contaminant sizes in fluid film bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
Even in systems that are initially clear, multiple startups and shutdowns cause metal-to-metal contact, resulting in wear debris. This debris with time can cause damage. As a result, good filtration is required in the lubrication system for long life and reliability.
27.4
Slider Bearing Materials
27.4.1
Materials for Liquid-Film Applications*
E.R. Booser (1970) summarized the materials requirements for fluid-film bearing applications. Bearings operating with full film lubrication theoretically never touch the shaft. However, bearings do start and stop, and some are required to operate with boundary lubrication, or no lubrication at all, for short periods. Hence, successful use of a fluid-film bearing material depends on matching its properties to the demands of the application. Operating factors to be considered include load, speed, contamination, life required, temperature, and the type and quantity of lubrication available. No bearing material is equally good with respect to all requirements. Booser (1970) states that proper selection is a matter of judgment based on the following factors: 1. Compatibility — a measure of the anti-weld and anti-scoring characteristics of a bearing material when operated with a given mating material. All journal bearings experience some metal-to-metal contact, if only during starting. During metal-to-metal contact, the sliding surfaces rub on microscopic high spots. The friction developed at these points can produce localized welding, causing a seizing damage that resembles scoring. Therefore, a good bearing material will not weld easily to the shaft material. Liquid cadmium, for instance, will not wet a steel shaft. 2. Conformability — the ability to compensate for misalignment and to conform to other geometric errors. Good conformability is characteristic of soft metals with a low modulus of elasticity. 3. Embeddability — the ability to absorb dirt and other foreign particles to avoid scoring and wear. Usually, in metallic bearing materials, good embeddability is found in materials with good conformability. This is not true in nonmetallic materials. Carbon graphite has a low modulus and good conformability, but its hardness gives it a poor ability to absorb dirt. 4. Load capacity — largely, this is an experience factor related equally to design and lubrication, as well as to the strength and other performance properties of the material. It is a measure of the maximum hydrodynamic pressure that a material can be expected to endure. *Taken from Brewe, Fleming, Dimofte, and Hendricks (1997).
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5. Fatigue resistance — this factor is particularly important in applications where the load changes direction, such as in reciprocating automotive and aircraft engines. When a bearing material experiences a fatigue failure, cracks begin just below the surface of the material at the points of maximum shear stress. In babbitt, these cracks propagate at a right angle to the surface down to the bond with the backing material. Then they progress along the backing material and join other similar fatigue cracks. When sufficiently weakened, the bearing material begins to flake loose. (Low-modulus materials are often used as thin overlays on strip steel to improve fatigue resistance.) 6. Corrosion resistance — this factor is important where uninhibited industrial lubricating oils are used. Oxidation products from some lubricating oils can attack and corrode cadmium, lead, zinc, and some copper bearing alloys. Corrosion effects can be minimized by such modifications as applying a thin flash of indium over cadmium or lead alloys or by adding tin to lead babbitt. Both tin and aluminum alloys are usually unaffected by oxidized oils. 7. Cost factors — overall costs are frequently the deciding factor in selecting a bearing material. Some materials cost more than others. Frequently, however, a thin layer of a high-cost material can supply the necessary bearing characteristics while a low-cost substrate provides the necessary structural strength. Performance characteristics of common fluid film bearing alloys are indicated in Table 27.5. For instance, the babbitts and cadmium-base materials are rated highest on compatibility for operation against steel shafts. Babbitts, which are soft, low-melting-point alloys, are best in conformability and in embedding dirt. The harder, higher strength materials, such as the bronzes, aluminum, and silver, carry heavier loads and offer better fatigue strength (Booser, 1970). 27.4.1.1 Babbitts Tin- and lead-base babbitts are probably the best known of all bearing materials. With their ability to embed dirt and excellent compatibility properties under boundary lubrication conditions, babbitt bearings are used in a wide range of applications. In small bushings for fractional-horsepower motors and in automotive engine bearings, the babbitt is generally used as a thin coating over a steel strip. For larger bearings in heavy-duty equipment, a thicker babbitt is cast on a rigid backing of steel or cast iron. After machining, the babbitt layer is usually 3 to 6 mm (1/8 to 1/4 in.) thick (Booser, 1970). Relative to other bearing materials, babbitts generally have lower load capacity and fatigue strength, are a little higher in cost, and require a more complicated design. Also, their strength decreases rapidly with increasing temperature. These shortcomings can often be avoided by using an intermediate layer of high-strength, fatigue-resisting material between a steel backing and a thin babbitt surface layer. Such composite bearings frequently eliminate any need for using alternative materials with poorer compatibility characteristics (Booser, 1970). Specifications established by the Society of Automotive Engineers (SAE) for babbitt compositions are given in Table 27.6. Grades 11 and 12 are tin-base babbitts and grades 13 to 15 are lead base. The American Society for Testing and Materials (ASTM) had adopted similar specifications (B23). ASTM grades 1 to 5 are tin base and grades 6 to 19 are lead base (Booser, 1970). 27.4.1.2 Bronzes and Copper Alloys Dozens of copper alloys are available as bearing materials. Most can be grouped into four classes: copperlead, leaded bronze, tin-bronze, and aluminum-bronze. Characteristics of typical copper alloy cast bearing materials are listed in Table 27.7. The alloys at the top of this listing have higher lead content and correspondingly better compatibility properties. Thus, copper-lead and leaded bronzes are generally the best bearing alloys despite their lower physical properties. Load capacity, strength, hardness, wear
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resistance, and fatigue strength increase as other alloying elements (such as tin, aluminum, and iron) are added. Costs vary widely. Simple bronze bushings are usually cheaper than babbitt bearings; copperlead bearings are more expensive. Copper alloy bearings provide greater load capacity than the softer babbitts, better high-temperature operation, and greater wear resistance, but poorer anti-scoring properties (Booser, 1970). 27.4.1.3 Aluminum and Aluminum Alloys With their high capacity, fatigue strength, and thermal conductivity, excellent corrosion resistance, and low cost, aluminum alloys are used extensively in connecting-rod and main bearings in internal combustion engines, in roll-neck bearings in steel mills, and in reciprocating compressors and aircraft equipment. Aluminum has not replaced babbitt for industrial equipment operating under a steady unidirectional load. Aluminum alloys require hardened shafts and improved surface finish. They have relatively poor compatibility characteristics and lack embeddability and conformability. For automotive use, anti-scoring characteristics and embeddability are considerably improved by using a thin lead babbitt or an electrodeposited lead-tin overlay (Booser, 1970). The most common aluminum bearing material is the SAE 770 listed in Table 27.8. In this casting alloy, 6.5% tin is included for improved compatibility. The small amounts of copper and nickel increase strength, hardness, and scuff resistance. A wrought alloy is available of almost the same composition with the addition of 1.5% silicon (SAE 780). This alloy can be used to form bimetal bearings of SAE 780 sheet, 0.76 mm (0.030 in.) thick, bonded by hot rolling to nickel-plated, low-carbon steel (Booser, 1970). A second major type of aluminum alloy, such as SAE 781, contains 1 to 3% cadmium for improved bearing properties. Varying amounts of silicon, copper, and nickel may be used. This type of alloy is used in making steel-back bearings with a 0.013-mm (0.0005-in.) overlay containing approximately 90% lead and 10% tin. This thin layer of babbitt improves the surface properties of composite bearings during break-in (Booser, 1970). A third type of aluminum bearing alloy is a 20 to 30% tin alloy containing up to 3% copper. This reticular tin-aluminum is used extensively in Great Britain (Booser, 1970).
27.4.2
Bearing Materials for Gas-Film Applications
The following criteria were developed for selecting gas-lubricated bearing materials and coatings for sliding compatibility. 1. Hard, wear-resistant material combinations, such as solid members or coatings or ceramic or carbide material, nitrided or “malcomized” alloys, and hardened tool steels. 2. Self-lubricating materials mated against a hard, lapped shaft. These materials can be carbon graphite, or sintered bronze on a thin steel backing with an impregnated surface of PTFE and lead. 3. Soft-phase materials melted against a hard, lapped shaft. The materials are leaded bronze and powder compresses containing an infiltrated phase. 4. Solid lubricant films melted against a hard, lapped shaft. These can be resin or ceramic bonded or applied in any other acceptable manner. For operation in an inert environment, consideration should be given to the following material combinations: hard material combinations, particularly oxides such as chromium oxide: self-lubricating materials, which depend on PTFE for sliding properties; and solid lubricant films containing MoS2. Results of tests with different material combinations are summarized in Table 27.9. Table 27.10 contains suggested material combinations for use at various temperatures.
200–250 200 300 300–400 200–300 300–400
10.3–13.8 10.3–17.2 20.7–27.6 27.6+ 34.5+ 34.5+
5.5–10.3 5.5–8.3 13.8–35.4+
MPa
1500–2000 1500–2500 3000–4000 4000+ 5000+ 5000+
800–1500 800–1200 2000–5000+
psi
Load Capacity
Arbitrary scale with 1 being the best material and 5 the worst. From Booser, E.R. (1970), Machine Design, 42(15), 14–20. With permission.
30–40 20–30 40–70 60–80 45–50 25
15 20–23 40–60 60–70 40–45 25
130–170 130–170 200–300
Minimum Shaft
260 177 232 260+ 121 260
149 149 149
°C
500 350 450 500+ 250 500
300 300 300
°F
Maximum Operating Temperature
1 2 3 5 4 2
1 1 1
Compatibilitya
2 2 4 5 3 3
1 1 2
Conformability and Embeddabilitya
5 5 4 2 1 1
1 3 2
Corrosion Resistancea
4 3 2 1 2 1
5 5 2
Fatigue Strengtha
1030
a
20–30 15–20 —
At 149°C (300°F)
6–12 6–12 —
At Room Temperature
Brinell Hardness
Performance Characteristics of Fluid Film Bearing Alloys
Tin-base babbitt Lead-base babbitt Three-component bearings, babbitt surfaced Cadmium base Copper-lead Lead bronze Tin bronze Aluminum alloy Silver (overplated)
Alloy
TABLE 27.5
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86.0 min 6.0–7.5 0.50 5.0–6.5 0.08 0.10 0.08 0.005 0.005 — 0.20
Tin Antimony
Lead Copper
Iron Arsenic
Bismuth Zinc
Aluminum Cadmium
Others, total
0.20
0.005 —
0.08 0.005
0.08 0.10
0.50 3.0–4.0
88.25 min 7.0–8.0
SAE 12 (ASTM 2) Composition,a %
Tin Base
All values not given as ranges are maximum except as shown. From Booser, E.R. (1970), Machine Design, 42(15), 14–20. With permission.
a
SAE 11
Composition of Babbitts
Element
TABLE 27.6
0.20
0.005 0.05
0.10 0.005
— 0.25
Remainder 0.50
5.0–7.0 9.0–11.0
SAE 13
0.20
0.005 0.05
0.10 0.005
— 0.60
Remainder 0.50
9.25–10.75 14.0–16.0
SAE 14 (ASTM 7)
Lead Base
0.20
0.005 0.02
0.10 0.005
— 0.80–1.20
Remainder 0.50
0.9–1.25 14.0–15.5
SAE 15 (ASTM 15)
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— — 5 6 5 7 10 10 8 10 (a)
Sn 35 30 25 16 5 7 10 — — 2 —
Pb — — — — 5 3 — 2 4 — —
Zn
4 Fe, 11 Al. From Booser, E.R. (1970), Machine Design, 42(15), 14-20. With permission.
65 70 70 78 85 83 80 88 88 88 85
Cu 25 28 48 55 60 60 63 65 68 70 195
Hardness (Brinell) 55 60 170 210 240 240 240 310 280 280 620
MPa 8000 8500 25,000 30,000 35,000 35,000 35,000 45,000 40,000 40,000 90,000
psi
Tensile Strength
180 180 200+ 230 230 230+ 230+ 260+ 260 260 260+
°C
350 350 400+ 450 450 450+ 450+ 500+ 500 500 500+
°F
Maximum Operating Temperature
14 14 21+ 21+ 24 28 28 28 28+ 28+ 31+
MPa
2000 2000 3000+ 3000+ 3500 4000 4000 4000 4000+ 4000+ 4500+
psi
Maximum Load
1032
a
Copper-lead Copper-lead High-lead tin bronze Semiplastic bronze Leaded red brass Bronze bearings Phosphor bronze Gun metal Navy G Leaded gun metal Aluminum bronze
Material
Nominal Composition (%)
Typical Copper Alloy Cast Bearing Materials
SAE 490 SAE 48 AMS 4840 SAE 67 SAE 40 SAE 660 SAE 64 SAE 62 SAE 620 SAE 63 ASTM B148-59-9c
Alloy Number
TABLE 27.7
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TABLE 27.8
Composition of Aluminum Bearing Alloys Nominal Composition (%) Bearing Type
Al
Sn
Cu
Ni
Si
Cd
Cast, solid Rolled, bimetal, or trimetal Wrought, trimetal Trimetal
91.5 90.5 95 79
6.5 6.5 — 20
1 1 — 1
1 0.5 — —
— 1.5 4 —
— — 1 —
Material SAE 770 SAE 780 SAE 781 Reticular tin-aluminum
From Booser, E.R. (1970), Machine Design, 42(15), 14–20. With permission.
TABLE 27.9
Material Test Results From Large Bearing Evaluations Material Combination
Pad Chromium oxide coating Nickel-bonded tungsten carbide coating Resin-bonded MoS2 film
Sintered-bronze facing impregnated with PTFE and lead Cobalt-bonded tungsten carbide coating
Shaft
Behavior in Start-Stop Tests
Behavior in High-Speed Rub Tests
Chromium oxide coating
Excellent; negligible wear
Excellent; material transfer
Aluminum oxide coating
Excellent; negligible wear
Hardened 416 stainless steel
Good; MoS2 coating almost worn away after 1000 startstops Fair; would not lift off if stress was greater than 14 kPa (2 psi) Poor; metal transfer and scoring after about 350 start-stops Fair; wear debris formed streaks on shaft and friction increased substantially Poor; tendency for pickup and scoring Excellent; for best results
Poor; material transfer and scoring Fair; coating beginning to wear through and scoring commencing Excellent; smooth, polished surfaces
Molybdenum coating
Hardened AISI M-50 steel
Nickel-bonded tungsten carbide coating
Nickel-bonded tungsten carbide coating
Nitrided nitralloy
Nitrided nitralloy
Carbon graphite
Hard, lapped chromium plate
Poor; material transfer and scoring Not run, but probably poor
Not run, but probably poor Not run, but carbon-graphite can score chromium plate
Air
–65–300
250–350
250–450
–65–500
–65–500
–65–900
–54–149
121–177
121–232
–54–260
–54–260
–54–482
Plasma-sprayed metalbonded carbide coatinga
Resin-bonded solid lubricants bonded to metallic substrate
Silver-impregnated carbon graphite Phosphor bronze (solid or sprayed coating) DU bonded to metallic substrate
Carbon graphites
Fused PTFE film on metal substrates
Bearing Materials
State of the Art
Wear life of PTFE film under Basic friction and wear tests start-stop conditions not indicate feasibility of known; durability of film obtaining at least 100 starts during high-speed rubs not and stops at low stresses (14 known to 21 kPa; 2 to 3 psi) Temperature limitation due to Proven to be capable of more design considerations, such as than 1000 start-stops at designing for differential stresses to 28 kPa (4 psi) thermal expansion; bearing may score shaft due to highspeed rub Same as above Excellent start-stop capability
Problem Areas
Used successfully in externally pressurized bearings Hard chromium plate; Relatively poor resistance to Excellent resistance to damage nitrided surfaces; hardened start-stops at stress levels >14 during high-speed rubs steel (40+ Rockwell C) and kPa (2 psi) electrolyzed steel Same as above Requires careful preparation Capable of 1000 start-stops at and stress levels to 21 kPa (3 psi); run-in wears rapidly during highspeed rubs Plasma-sprayed Al2O3 Poor for high-speed rubs Excellent start-stop behavior; coatinga negligible wear after 1000 start-stops at 28 kPa (4 psi) stress
Hard chromium-plated stainless steel Stellite or stellite hard facing Sliding compatibility
Hard chromium plate; nitrided steels
Fused Teflon film on metal substrate
Journal Materials
1034
Air
Air, inert gases
Air, inert gases
Steam
Steam
Helium, nitrogen
(°F)
Cryogenic
(°C)
Typical Process Gas
Gas Bearing Material Combinations for Use at Various Temperatures
Temperature Range
TABLE 27.10
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–65–900
900
–54–482
>482
Air, inert or reactive gases
Inert or reactive gases, air
Typical Process Gas
Hot-pressed Al2O3 Cemented Al2O3 Nickel-bonded titanium carbideb
Plasma-sprayed chromium oxidea
Bearing Materials
Same as bearing Same as bearing Al2O3
Plasma-sprayed chromium oxidea
Journal Materials
Gas Bearing Material Combinations for Use at Various Temperatures
b
Must be used on corrosion-resistant substrate for operation in corrosive environment. Oxidizes in air above 538°C (1000°F).
a
(°F)
(°C)
Temperature Range
TABLE 27.10 (continued)
Brittle materials Difficult to fabricate Thermal shock
Nonconductive nature of coating makes grooving difficult
Problem Areas
Excellent start-stop behavior at 28 kPa (4 psi); very promising for resistance to damage during high-speed rubs Very limited experience
State of the Art
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References Allaire, P.E. (1979), Design of journal bearings for high-speed rotating machinery, in Fundamentals of the Design of Fluid Film Bearings, Rhode, S.M., Maday, C.J., and Allaire, P.E. (Eds.), American Society of Mechanical Engineers, New York, 45–83. Allaire, P.E. and Flack, R.D. (1980), Journal bearing design for high-speed machinery, in Bearing DesignHistorical Aspects, Present Technology and Future Problems; Proceedings of the International Conference, Anderson, W.J. (Ed.), American Society of Mechanical Engineers, New York, 111–159. Anderson, W.J. (1964), Hydrostatic lubrication, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, National Aeronautics and Space Administration, Washington, D.C. Anon. (1965), General Guide to the Choice of Journal Bearing Type, Engineering Sciences Data Unit, Item 65007, Institution of Mechanical Engineers, London, England. Anon. (1967), General Guide to the Choice of Thrust Bearing Type, Engineering Sciences Data Unit, Item 67033, Institution of Mechanical Engineers, London, England. Anon. (1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England. Anon. (1983), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded, Off-Set Pivot, TiltingPad Thrust Bearings, Engineering Sciences Data Unit, Item 83004, Institution of Mechanical Engineers, London, England. Anon. (1984), Journal Bearing Calculations, Engineering Sciences Data Unit, Item 84031, Institution of Mechanical Engineers, London, England. Archibald, F.R. (1950), A simple hydrodynamic thrust bearing, Trans. ASME, J. Lubr. Technol., 72(4), 393–400. Ausman, J.S. (1961), An approximate analytical solution for self-acting gas lubrication of stepped sector thrust bearings, ASLE Transactions, 4, 2, 304–313. Ausman, J.S. (1964), Gas-lubricated bearings, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, 109–138. Bagci, C. and Singh, A.P. (1983), Hydrodynamic lubrication of finite slider bearings: effect of one dimensional film shape and their computer aided optimum designs, Trans. Am. Soc. Mech. Engrs., J. Lubr. Tech., 105, 48–66. Baildon, E. (1937), The performance of oil-rings, Gen. Dis. Lubrication, Inst. Mech. Engrs., Group I, pp. 1–7. Bao, G. and Li, S.F.Y. (1998), Lubricant effect on noncontact-mode atomic force microscopy images of hard-disk surfaces, Langmuir, 14, 1263–1271. Blok, H. and van Rossum, J.J. (1953), The foil bearing — A new departure in hydrodynamic lubrication, Lubrication Engineering, 9(6), 316–320. Boeker, G.F. and Sternlicht, B. (1956), Investigation of transitory fluid whirl in vertical machines, Trans. ASME, 78, 13–19. Booker, J.F. (1971), Dynamically loaded journal bearings, numerical application of the mobility method, J. Lubr. Technol., 168, 168–176. Booser, E.R. (1970), Plain bearing materials, Machine Design, 42(15), 14–20. Boyd, J. and Robertson, B.P. (1948), Oil flow and temperature relations in lightly loaded journal bearings, Trans. ASME, 70, 257–262. Braun, M.J., Choy, F.K., Dzodzo, M., and Hsu, J. (1994), Transient and steady state dynamic analysis of a foil bearing, Paper No. ISROMAC-4, presented at 4th Int. Symp. Transport Phenomena and Dynamics of Rotating Machinery. Brewe, D.E. (1986), Theoretical modeling of the vapor cavitation in dynamically loaded journal bearings, J. Tribol., 108(41), 628–638. (Also NASA TM-87076.) Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594.
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Brockwell, K., Dmochowski, W., and DeCamillo, S. (1994), Analysis and testing of the LEG tilting pad journal bearing — A new design for increasing load capacity, reducing operating temperatures and conserving energy, in Proc. 23rd Turbomachinery Symp., Texas A&M University, College Station, TX. Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York. Campbell, J., Love, P.P., Martin, F.A., and Rafique, S.O. (1967), Bearings for reciprocating machinery. A review of the present state of theoretical experimental and service knowledge, in Proc. Inst. Mechanical Engineers, 182(3A), 51–74. Chadbourne, L.E., Dobler, F.X., and Rottler, A.D. (1966), SNAP 50/SPUR Nuclear Mechanical Power Unit, Experimental Research and Development Program. 2. Bearing, Report APS-5249-R, AFAPLTR-67-34, PT. 2, AiResearch, Phoenix, AZ. Christopherson, D.C. and Naylor, H. (1955), The promotion of fluid lubrication in wire drawing, in Proc. Inst. Mechanical Engineers, (London), 169, 643–653. Coyne, J.C. and Elrod, H.G. (1971), Conditions for the rupture of a lubricating film. II. New boundary conditions for Reynolds equation, Trans. ASME, J. Lubr. Technol., 93, 156–167. Davis, J.E. (1972), Design and Fabrication of the Brayton Rotating Unit, NASA CR-1 870. DuBois, G.B. and Ocvirk, F. (1953), Analytical Derivation and Experimental Evaluation of Short Bearing Approximation for Full Journal Bearings, NACA Report 1157. Eshel, A. and Elrod, H.G., Jr. (1965), The theory of the infinitely wide, perfectly flexible, self-acting foil bearing, J. Basic Eng., 87(3), 831–836. Fleming, D.P., Cunningham, R.E., and Anderson, W.J. (1968), Stability Analysis for Unloaded Externally Pressurized Gas-Lubricated Bearings with Journal Rotation, NASA TN D-4934, Washington, D.C. Fleming, D.P. (1970), Steady-State and Stability Analysis of Externally Pressurized Gas-Lubricated Journal Bearings with Herringbone Grooves, NASA TN D-5870, Washington, D.C. Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: Bearings and Thrust Bearings, Tribology Series 33, Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. Fuller, D.D. (1956), Theory and Practice of Lubrication for Engineers, 1st ed., John Wiley & Sons, New York. Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. Fuller, D.D. (1992), Friction and Wear of Gas-Lubricated Bearings, in ASME Handbook Friction, Lubrication, and Wear Technology, Blau, P.J. (ed.), Vol. 18, 522–534. Garner, D.R., James, R.D., and Warriner, J.F. (1980), Cavitation erosion damage in engine bearing: theory and practice, J. Eng. Power, 102, 847–857. Gilbrech, R.J., Gu, A., Rigney, T., Saville, M., and Rossoni, I. (1993), Liquid Hydrogen-Foil-Bearing Turbopump, AIAA Paper 93-2537. Gross, W.A. (1962), Gas Film Lubrication, John Wiley & Sons, New York. Gunther, R.C. (1971), Lubrication, Chilton Book Company, Philadelphia. Hagg, A.C. (1947), The influence of Oil-Film Journal Bearings on the Stability of Rotating Machines, Trans. ASME, J. Applied Mech., 68, A211–A220, discussion 69, A77–A78. Hall, L.F. and de Guerin, D. (1957), An experimental comparison between three types of heavy duty thrust bearings, Inst. Mech. Eng. Lubr. Conf., Paper 79, 128-134. Hamrock, B.J. (1972), Optimization of self-acting step thrust bearings for load capacity and stiffness, ASLE Transactions, 15, 159–170. Hamrock, B.J. (1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. Hamrock, B.J. and Anderson, W.J. (1968a), Incompressibly Lubricated Rayleigh Step Journal Bearing. I. Zero-Order Perturbation Solution, NASA TN D-4839. Hamrock, B.J. and Anderson, W.J. (1968b), Incompressibly Lubricated Rayleigh Step Journal Bearing. II. Infinite-Length Solution, NASA TN D-4873. Harrison, W.J. (1913), The hydrodynamic theory of lubrication with special reference to air as a lubricant, Proc. Cambridge Philosophical Society, 22(3), 39–54. Heshmat, H., Walowit, J.A., and Pinkus, O. (1983), Analysis of gas-lubricated foil journal bearings, J. Lubr. Technol., 105(4), 647–655.
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Heshmat, H. (1991a), A feasibility study on the use of foil bearings in cryogenic turbopumps, Paper No. AIAA-91-2103, presented at the AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, June 24–26, Sacramento, CA. Heshmat, H. (1991b), Analysis of compliant foil bearings with spatially variable stiffness, Paper No. AIAA-91-2102, presented at the AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, June 24–26, Sacramento, CA. Heshmat, H. and Hermel, P. (1992), Compliant foil bearing technology and their application to high speed turbomachinery, Proc. 19th Leeds-Lyon Symp. Thin Films in Tribology — From Micro Meters to Nano Meters, Leeds, United Kingdom Heshmat, H. (1994), Advancements in the performance of aerodynamic foil journal bearings: high speed and load capability, J. Tribol., 116, 287–295. Holmes, R. and Craven, A.H. (1971), The influence of crankshaft and flywheel mass on the performance of engine main bearings, Proc. Inst. Mechanical Engineers Tribology Conference, Paper C63nI. Johnston, R.C.R. and Kettleborough, C.F. (1956), An experimental investigation into stepped thrustbearings, Proc. Inst. Mech. Engrs., 17, 511–522, 525–525, and 532–533. Jones, G.J. (1983), Crankshaft bearings, oil film history, in Tribology of Reciprocating Engines, Proc. of 9th Leeds-Lyon Symp. Tribology, Dowson, D. (Ed.), Butterworth, Guilford, England. Kettleborough, C.F. (1961), An approximate analytical solution for the stepped thrust bearing, Trans. ASME, 83E, 507–510. Kingsbury, A. (1950), Development of the Kingsbury thrust bearing, Mechanical Engineering, 72, 957–962. Ku, C.-P.R. and Heshmat, H. (1992), Compliant foil bearing structural stiffness analysis. I. Theoretical model including strip and variable bump foil geometry, J. Tribol., 114(2), 394–400. Ku, C.-P.R. and Heshmat, H. (1993), Structural stiffness and Coulomb damping in compliant foil journal bearings: theoretical considerations, Tribol. Trans. STLE, presented at the STLE Annual Meeting, Calgary, Canada, May 17–20. Licht, L. and Branger, M. (1973), Design, Fabrication, and Performance of Foil Journal Bearings for the Brayton Rotating Unit, NASA CR-2243. Licht, L., Branger, M., and Anderson, W.J. (1973), Gas-Lubricated Foil Bearings for High Speed Turboalternator Construction and Performance, ASME Paper 73-Lub-5. Linn, C.F. and Shepard, R. (1938), The tapered land thrust bearing, Trans. ASME, 60, 245–252. Lord Rayleigh (1918), Notes on the theory of lubrication, Philosophical Magazine, 35, 1–12. Lund, J.W. (1968), Rotor-Bearing Dynamics Design Technology. 7. The Three-Lobe-Bearing and Floating Ring Bearing, Report MTI-67TR47, Mechanical Technology, Inc., Lathem, NY. Malanoski, S.B. (1967), Experiments on an ultrastable gas journal bearing, J. Lubr. Technol., 89(4), 433–438. Marsh, H. (1964), The Stability of Aerodynamic Gas Bearings. 11. Noncircular Bearing, Ph.D. thesis, St. John’s College, Cambridge, England. Martin, F.A. (1983), Developments in engine bearing design, Tribol. Int., 16(3), 147–164. Martin, F.A. (1990), Cavitation erosion damage in engine bearings, in Current Research in Cavitating Fluid Films, Brewe, D.E., Ball, J.H., and Khonsari, M.M. (Eds.), STLE SP-28, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 17-20; NASA TM 103184/AVSCOM TM 89-C-007, 1989. Michell, A.G.M. (1905), British Patent 875. Michell, A.G.M. (1950), Lubrication: Its Principles and Practice, Blackie and Son Limited, London. Muijderman, E.A. (1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands. Muskat, M. and Morgan, F. (1939a), The theory of thick film lubrication of a complete journal bearing, of finite length with arbitrary positions of the lubricant source, J. Appl. Phys., 10, 46–61. Muskat, M. and Morgan, F. (1939b), The theory of thick film lubrication of flooded journal bearings and bearings with circumferential grooves, J. Appl. Phys., 10, 398–407.
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Neale, M.J. (1993), High speed bearings and rotordynamics, Bearings: A Tribology Handbook, Neale, M.J. (Ed.), Butterworth-Heinemann, Oxford. Ping, J.P. and Carpino, M. (1993), Calculation of stiffness and damping coefficients for elastically supported gas foil bearings, J. Tribol., 115(1), 20–27. Pinkus, O. and Sternlicht, B. (1961), Theory of Hydrodynamic Lubrication, McGraw-Hill, New York. Purday, H.F.P. (1949), An Introduction to the Mechanics of Viscous Flow, Dover Publications, New York. Ritchie, G.S. (1975), The prediction of journal loci in dynamically loaded internal combustion engine bearings, Wear, 35, 291–297. Saville, M., Gu, A., and Capaldi, R. (1991), Liquid Hydrogen Turbopump Foil Bearing, AIAA Paper 91-2108. Schuller, F.T. (1971), Experiments on the Stability of Water-Lubricated Rayleigh Step Hydrodynamic Journal Bearings at Zero Load, NASA TN D-6514. Schuller, F.T. (1973), Design of Various Fixed-Geometry Water-Lubricated Hydrodynamic Journal Bearings for Maximum Stability, NASA SP-333. Shaw, M.C. and Macks, F.E. (1949), Analysis and Lubrication of Bearings, McGraw-Hill, New York. Sternlicht, B. and Winn, L.W. (1964), Geometry effects on the threshold of half-frequency whirl in selfacting, gas-lubricated journal bearings, J. Basic Eng., 86(2), 313–320. Sun, D.C. and Brewe, D.E. (1990), A High Speed Photography Study of Cavitation in a Dynamically Loaded Journal Bearing, NASA TM-103178. Sun, D.C., Brewe, D.E., and Abel, P. (1993), Simultaneous pressure measurement and high-speed photography study of cavitation in a dynamically loaded journal bearing, J. Tribol., 115(1), 88–95. Suriano, F.J., Dayton, R.D., and Woessner, F.G. (1983), Test Experience with Turbine-End Foil BearingEquipped Gas Turbine Engines, Paper 83-GT-73, American Society of Mechanical Engineers. Szeri, A. (2001), Hydrodynamic and elastohydrodynamic lubrication, in Modern Tribology Handbook, Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. Vijayaraghavan, D., Brewe, D.E., and Keith, T.G., Jr. (1992), Effect of Out-of-Roundness on the Performance of a Diesel Engine Connecting-Rod Bearing, NASA TM-105600. Vliestra, S. (1987), Gaslagers in de rotordynamics, Master’s thesis (in Dutch), University of Twente, Enschede, The Netherlands. Vohr, J.H. and Chow, C.Y. (1965), Characteristics of herringbone-grooved, gas-lubricated journal bearings, J. Basic Eng., 87(3), 568–578. Whitley, S. (1964), Instabilities in self-acting bearings, in Gas Lubricated Bearings, Grassam, N.S. and Powell, J.W. (Eds.), Butterworth, London, 85–109. Wilcock, D.F. (1955), The Hydrodynamic Pocket Thrust Bearing, Trans. ASME, 77, 311–319. Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGraw-Hill, New York. Wildmann, et al. (1965), Gas-lubricated stepped thrust bearing — A comprehensive study, Trans. ASME, Basic Eng., march, 213–230. Yonushonis, T.M., Wiczynski, P.D., Myers, M.R., Anderson, D.D., McDonald, A.C., Weber, H.G., Richardson, D.E., Stafford, R.J., and Naylor, M.G. (1999), Development of Advanced In-Cylinder Components and Tribological Systems for Low Heat Rejection Diesel Engines, NASA/CR-1999209163, DOE/NASA/0375-2, ARL-CR-442.
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28 Rolling Element Bearings 28.1 28.2
Introduction ................................................................. 1041 Rolling Element Bearing Types................................... 1042 Ball Bearings • Roller Bearings • Special Bearings
28.3 28.4
Bearing Materials ......................................................... 1046 Contact Mechanics ...................................................... 1048 Theory of Hertzian Contact • Bearing Internal Contact Geometry • Non-Hertzian Contact
28.5
Bearing Internal Load Distribution............................ 1057 Bearings under General Load Conditions • Bearings under Pure Eccentric Thrust Load
28.6
Bearing Lubrication ..................................................... 1063 Elastohydrodynamic Lubrication • Effect of Spin Motion • Effect of Lubricant Starvation • Lubrication Methods
28.7
Bearing Kinematics...................................................... 1067 Outer Raceway Control • Inner Raceway Control • Minimum Differential Spin
28.8
Bearing Load Ratings and Life Prediction ................. 1071 Basic Load Ratings • Bearing Life Prediction
28.9
Bearing Torque Calculation ........................................ 1074 Starting Torque • Running Torque
28.10
Bearing Temperature Analysis .................................... 1079 Heat Generation • Heat Transfer
28.11 The Timken Company
Charles A. Moyer The Timken Company (retired)
Bearing Endurance Testing ......................................... 1082 Testing Procedure and Data Analysis
Xiaolan Ai 28.12
Bearing Failure Analysis .............................................. 1083 Contact Fatigue • Surface Depression and Fracture • Mechanical Wear • Corrosion • Electric Arc Damage • Discoloring and Overheating
28.1 Introduction Rolling element bearings are typical tribological components. They utilize rolling contacts between the rolling elements and raceways to support load while permitting constrained motion of one body relative to another. The standard configuration of a rolling element bearing comprises inner and outer rings, a set of rolling elements arranged in a row between the inner and outer rings, and a retainer or cage to maintain a proper annular spacing between the rolling elements (Figure 28.1). Some bearings also have seals as integrated components. Due to their wide availability and versatility, rolling element bearings are, perhaps, the most widely used bearing type. Rolling element bearings are characterized by little or
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FIGURE 28.1
A single-row, deep-groove, radial ball bearing. (Courtesy of SKF Bearing Industries Co.)
no sliding motion. They usually generate less friction and have low starting torque compared to hydrodynamic bearings. Unlike hydrodynamic bearings, the performance of rolling element bearings is less susceptible to changes in load, speed, and temperature. Most rolling element bearings are capable of carrying both radial and thrust loads. Because of rolling contact, the dependency on lubricant is not as critical. This makes rolling element bearings easier to maintain. Well-designed and well-built rolling element bearings can operate over wide ranges of load and speed. Such features often put rolling element bearings on the top of the bearing selection list.
28.2 Rolling Element Bearing Types Various means have been used to categorize rolling element bearings such as by the geometry of the rolling elements, by the manner in which a bearing is used or by certain technical features that the bearing possesses. However, the most common classification is by the rolling element geometry. There are two major categories: ball bearings and roller bearings. Within each category, bearings can be further divided into sub-categories. Each type of bearing has characteristics or properties that make it particularly suitable for certain applications. The main factors to be considered when selecting the optimum bearing type are: • • • • • • • • •
Available space Load condition Speed Temperature Misalignment Mounting and dismounting procedures Dynamic stiffness Motion error Noise factor
This section outlines the most popular bearing types used in various automotive and industrial applications. For comprehensive listings on bearing types and usage, the reader is referred to various bearing catalogs provided by bearing manufacturers.
28.2.1 Ball Bearings 28.2.1.1 Deep-Groove Ball Bearings A deep-groove ball bearing consists of a set of balls rolling between an inner and outer raceway (Figure 28.1). Both inner and outer raceways have high shoulders on each side. A deep-groove bearing can carry significant radial load and, due to the high degree of conformity between the balls and raceways, moderate thrust loads. When the elastic deflection of bearing races is used to introduce the balls into bearing raceways, bearings can have uninterrupted raceway grooves and are capable of carrying substantial
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load in either direction, even at high speeds. This type of bearing is often referred to as Conrad type. To incorporate the greatest possible number and size of balls, a deep-groove ball bearing may rely on a filling slot to introduce balls into the bearing. This type of bearing is referred to as Max type or “filling slot type.” Max-type bearings are capable of carrying higher radial loads. 28.2.1.2 Angular-Contact Ball Bearings Angular-contact ball bearings can be regarded as a variation of deep-groove ball bearings. Unlike deepgroove bearings, an angular-contact bearing has at least one race ring that has only one side shoulder. Angular-contact ball bearings are capable of carrying an appreciable thrust load in one direction with or without a radial load. Because an angular-contact bearing must have a thrust load acting on it, no endplay (lateral movement) exists within the bearing. The line that connects the nominal contact between the inner raceway and a ball and the contact between the outer raceway and the ball lies at an angle with the radial plane of the bearing. This angle is called the contact angle. It ranges from 15 to 40° for commercially available angular-contact ball bearings. Angular-contact ball bearings are commonly used in pairs to accommodate heavier radial loads, twodirectional thrust loads, or various combinations of radial and thrust loads. Tandem mounting is used for heavy unidirectional thrust loads and duplex mounting of either face-to-face or back-to-back is used for two-directional thrust loads. 28.2.1.3 Double-Row Ball Bearings Double-row ball bearings are similar in design to single-row ball bearings. They are designed with onepiece inner and outer rings. Most double-row ball bearings are made with opposite contact angles in rows like two face-to-face or back-to-back angular-contact ball bearings in duplex mounting. They are also made as two deep-groove rows. Like two single-row ball bearings in paired mounting, a double-row ball bearing is often used to carry heavy radial loads. It is also capable of carrying thrust loads in either direction. There are advantages to using a double-row ball bearing over two single-row ball bearings in paired mounting. Double-row ball bearings take less axial space and the internal relationship between two rows is predetermined and is not, or less, affected by mounting practice. 28.2.1.4 Thrust Ball Bearings Thrust ball bearings generally have a 90° contact angle. However, ball bearings with contact angle greater than 45° are also classified as thrust ball bearings. A thrust ball bearing whose contact angle is 90° can only be used to support thrust loads.
28.2.2 Roller Bearings 28.2.2.1 Cylindrical Roller Bearings In cylindrical roller bearings, the rollers are axially guided between integral flanges on at least one of the bearing rings. The most popular type is the single-row design, which offers various flange arrangements. Figure 28.2 shows a typical single-row cylindrical bearing with two flanges on the outer ring. Cylindrical
FIGURE 28.2
A single-row, radial cylindrical roller bearing. (Courtesy of SKF Bearing Industries Co.)
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a
b
FIGURE 28.3 Tapered roller bearings. (a) A single-row, tapered roller bearing. (Courtesy of the Timken Company). (b) “On-apex” design results in true rolling motion.
roller bearings have exceptionally high radial load-carrying capacity. They are also capable of carrying a small amount of thrust load when two flanges are positioned on opposing rings at opposite sides. In theory, true rolling motion exists in cylindrical bearings under radial load. Therefore, cylindrical bearings have lower starting torque and lower operating temperature than other roller bearings. This makes them suitable for high-speed applications. To achieve greater load capacity without increasing the tendency of roller skewing on the raceways, cylindrical bearings are frequently constructed in two or more rows rather than with one row of longer rollers. 28.2.2.2 Tapered Roller Bearings Tapered roller bearings have tapered inner and outer raceways, with tapered rollers guided between them by a very accurately positioned flange known as the rib (Figure 28.3a). The inner and outer raceways have different contact angles. The extensions of the inner and outer raceways and the rollers are designed to converge at a common apex point on the axis of rotation (Figure 28.3b). The on-apex design results in true rolling motion of the rollers on the raceways along the line of contact. At the contacts between the rib and roller-ends, however, sliding and spinning exist. The tapered raceways allow a tapered roller bearing to carry combined radial and thrust loads or thrust loads only. The ratio of thrust to radial load capacity is determined by the contact angle between the
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outer raceway and the axis of rotation. The long roller-raceway contact gives the tapered roller bearing a high load-carrying capacity. Tapered roller bearings are used in pairs. One bearing is adjusted against the other to achieve the desired endplay or pre-load. To acquire greater radial load-carrying capacity and eliminate problems of axial adjustment or thermal growth, tapered roller bearings are designed in two rows. Most double-row, tapered roller bearings have a single inner race and double outer races; or a single outer race and double inner races. Tapered roller bearings are also available in four-row arrangements. 28.2.2.3 Spherical Roller Bearings Most spherical roller bearings have an outer raceway that is a portion of a sphere. The bearings are internally self-aligning and permit angular displacement of the shaft relative to the housing. The most popular design has two rows of rollers that lie at an angle relative to the axis of the bearing. The rollers are in either symmetrical or asymmetrical barrel shape. The curvature of rollers in the direction transverse to the rotation conforms closely to the inner and outer raceways. The high degree of conformity between the rollers and raceways makes spherical roller bearings suitable for heavy-duty applications. Because of the non-zero contact angle, spherical bearings are also capable of carrying a certain thrust load in either direction along with the radial load. Unlike cylindrical roller bearings or tapered roller bearings, true rolling motion at contact between the rollers and raceways cannot be achieved with spherical bearings. Therefore, spherical roller bearings have inherently higher frictional torque than cylindrical bearings and are not suitable for high-speed applications. 28.2.2.4 Roller Thrust Bearings Cylindrical roller thrust bearings are the simplest of this type. A typical cylindrical roller thrust bearing is comprised of a pair of parallel thrust plates (washers): a row of cylindrical rollers sits between the thrust plates and a cage retaining the rollers. Cylindrical roller thrust bearings inherently experience a large amount of sliding as a result of the spin motion between the rollers and raceways. For this reason, cylindrical roller thrust bearings are limited to slow-speed applications. To reduce the magnitude of roller spinning, several rollers can be used in each cage pocket rather than a single long roller. The spin motion of rollers on raceways can be eliminated by using tapered rollers with an “on-apex” design, as illustrated in Figure 28.3b. Bearings of such design are referred to as tapered roller thrust bearings. Because at least one bearing raceway is tapered, an outboard flange is required to confine rollers from being expelled in the radial direction. Sliding contact exists between the outboard flange and rollerends. Friction forces generated at the sliding contact limit the bearings to relatively slow-speed applications.
28.2.3 Special Bearings 28.2.3.1 Clutch Bearings A clutch bearing combines the functionality of a bearing and a clutch together. It transmits torque between the inner and outer rings in one direction and allows free overrun in the opposite direction. When transmitting torque, either the inner ring or the outer ring can be used as the input member. The transition from the overrun to locked operation normally occurs with small backlash. Clutch bearings are generally used in indexing, backstopping, or overrunning. 28.2.3.2 Smart Bearings The functionality of a bearing can be extended by integrating electronic systems. The speed-sensing bearing used in automotive wheel application is a typical example of smart bearings. A typical speedsensing bearing is a self-contained, double-row tapered roller bearing featuring an integral sensing system designed to provide speed information for anti-lock brake systems (ABS) and traction control systems (TCS). The sensing system contains a target wheel within the bearing and a microchip speed-sensing element that detects the rotational speed of the target wheel. The sensor’s speed information can also be used for the vehicle dynamics control system, navigation system, speed control, speedometer, odometer, trip computer, and other purposes.
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TABLE 28.1
Modern Tribology Handbook
Chemical Composition of High-Carbon Bearing Steels Chemical Composition (%)
Grade
C
Si
Mn
Cr
Mo
P
S
Application
ASTM-A295(50100) ASTM-A295 (51100) JIS-G4805 (SUJ1)
0.98–1.10 0.98–1.10 0.95–1.10
0.15–0.35 0.15–0.35 0.15–0.35
0.25–0.45 0.25–0.45 ≤0.50
0.40–0.60 0.90–1.15 0.90–1.20
≤0.10 ≤0.10 —
≤0.025 ≤0.025 ≤0.025
≤0.025 ≤0.025 ≤0.025
Not commonly used
ASTM-A295-94 (52100) ASTM-A535-85 (52100) BS-535A99 DIN-100Cr6 JIS-G4805 (SUJ2) NF-100C6
0.98–1.10 0.95–1.10 0.95–1.10 0.90–1.05 0.95–1.10 0.95–1.10
0.15–0.35 0.15–0.35 0.10–0.35 0.15–0.35 0.15–0.35 0.15–0.35
0.25–0.45 0.25–0.45 0.40–0.70 0.25–0.40 ≤0.50 0.20–0.40
1.30–1.60 1.30–1.60 1.20–1.60 1.40–1.65 1.30–1.60 1.35–1.60
≤0.10 ≤0.10 — 0.30 — ≤0.08
≤0.025 ≤0.015 ≤0.025 ≤0.025 ≤0.025 ≤0.030
≤0.025 ≤0.015 ≤0.025 ≤0.025 ≤0.025 ≤0.025
Typical steels for small and medium-size bearings
ASTM-A485-89 grade 1 ASTM-A485-89 grade 2 JIS-G4805 (SUJ3)
0.90–1.05 0.85–1.00 0.95–1.10
0.45–0.75 0.50–0.80 0.40–0.70
0.95–1.25 1.40–1.70 0.90–1.15
0.90–1.20 1.40–1.80 0.90–1.20
≤0.10 ≤0.10 —
≤0.025 ≤0.025 ≤0.025
≤0.025 ≤0.025 ≤0.025
Used for large-size bearings
ASTM-A485-89 grade 3 ASTM-A485-89 grade 4 JIS-G4805 (SUJ5)
0.95–1.10 0.95–1.10 0.95–1.10
0.15–0.35 0.15–0.35 0.40–0.70
0.65–0.90 1.05–1.35 0.90–1.15
1.10–1.50 1.10–1.50 0.90–1.20
0.20–0.30 0.45–0.60 0.10–0.25
≤0.025 ≤0.025 ≤0.025
≤0.025 ≤0.025 ≤0.025
Used for ultralarge-size bearings
Future smart bearings will feature sensing elements capable of detecting speed, temperature, load, vibration, and other operating parameters that can be used not only for system control, but also for bearing and bearing system health monitoring.
28.3 Bearing Materials A bearing’s endurance life is largely determined by the strength of bearing material in relation to the contact stresses the bearing experiences during operation. While a well-designed internal geometry and good surface finish effectively reduce the actual contact stress and thus prolong the bearing’s service life, high-quality bearing material is essential. Bearing materials are selected on the basis of strength, fatigue resistance, wear resistance, elevated temperature resistance, corrosion resistance, toughness, hardenability and dimensional stability. A great majority of rolling element bearings are fabricated from vacuum-refined, high-quality lowalloy or carbon steels. Bearing steels can be categorized as high-carbon steels, which contain 0.8% or more carbon by weight; and low-carbon steels, which contain less than approximately 0.2% carbon. High-carbon steels, with chromium-alloy additions, are usually through-hardened to ensure a surface Rockwell hardness of 58 to 64 HRc. For large bearings, particularly those with thick cross-sections, increased amounts of manganese, chromium, silicon, molybdenum, and/or nickel are introduced to enhance the hardenability. Through-hardened steels are used extensively in ball bearings while casehardened steels are predominately used in roller bearings. Table 28.1 lists common grade and respective chemical compositions for high-carbon steels. Low-carbon steels are alloyed with nickel, chromium, molybdenum, and manganese to increase hardenability. Carbon is diffused into the steel under controlled temperature and atmospheric composition to increase carbon content at surface and subsurface layers to approximately 0.56 to 1.10%. The carburized steel is heat-treated to provide a hardened surface case for high contact load-carrying capability and a tough, ductile core for heavy shock load absorption. The softer core also helps to retard surface crack propagation. Low-carbon steels are historically used in tapered roller bearings, although they are wellsuited for other types of bearings. Table 28.2 lists the most commonly used carburizing steels. The hardness of bearing steels drops sharply when the tempering temperature is exceeded. Because most bearing steels are tempered between 160 and 280°C, bearings should not be used at temperatures
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TABLE 28.2
Chemical Composition of Carburizing Bearing Steels Chemical Composition (%)
Grade
P
S
—
≤0.035
≤0.040
0.30–0.70
0.08–0.15
≤0.035
≤0.040
0.35–0.75
0.35–0.65
0.15–0.25
≤0.035
≤0.040
0.90 0.55–0.90
0.70 —
0.60 0.85–1.25
0.25 —
≤0.025 ≤0.030
≤0.025 ≤0.030
0.15–0.35
0.55–0.90
—
0.85–1.25
0.15–0.35
≤0.030
≤0.030
0.17–0.23
0.15–0.35
0.60–0.95
0.35–0.75
0.35–0.65
0.15–0.30
≤0.030
≤0.030
ASTM-A534-90 (4320H) JIS-G4052/4103 (SNCM420)
0.17–0.23
0.15–0.35
0.40–0.70
1.55–2.00
0.35–0.65
0.20–0.30
≤0.035
≤0.040
0.17–0.23
0.15–0.35
0.40–0.70
1.55–2.00
0.35–0.65
0.15–0.30
≤0.030
≤0.030
ASTM-A534-90 (9310H) JIS-G4052/4103 (SNCM815)
0.07–0.13
0.15–0.35
0.40–0.70
2.95–3.55
1.00–1.45
0.08–0.15
≤0.035
≤0.040
0.12–0.18
0.15–0.35
0.30–0.60
4.00–4.50
0.70–1.00
0.15–0.30
≤0.030
≤0.030
ASTM-A534-90 (5120H) ASTM-A534-90 (4118H) ASTM-A534-90 (8620H) DIN 20NiCrMo2 JIS-G4052/4103 (SCr420H) JIS-G4052/4103 (SCM420H) JIS-G4052/4103 (SNCM220H)
TABLE 28.3
C
Si
Mn
Ni
Cr
Mo
0.17–0.23
0.15–0.35
0.60–1.00
—
0.60–1.00
0.17–0.23
0.15–0.35
0.60–1.00
—
0.17–0.23
0.15–0.35
0.60–0.95
0.23 0.17–0.23
0.35 0.15–0.35
0.17–0.23
Used for small-size bearings
Used for mediumsize bearings Used for large-size bearings
Chemical Composition of Special Bearing Steels Chemical Composition (%)
Grade
Application
Temperature Limits (°C)
C
Si
Mn
Ni
Cr
Mo
W
V
Co
M-50 M-50-NiL CBS-1000 CBS-600 TBS-600 VASCO X-2 M-10 M-1 M-2 SKH4
0.82 0.15 0.15 0.19 1.03 0.22 0.87 0.83 0.83 0.78
≤0.25 0.18 0.50 1.10 1.03 0.90 0.25 0.30 0.30 ≤0.40
0.25 0.15 0.50 0.55 0.70 0.30 0.25 0.30 0.30 ≤0.40
≤0.10 3.50 3.00 — — — — — — —
4.12 4.00 1.05 1.45 1.45 5.00 4.00 3.75 4.15 4.15
4.25 4.00 4.50 1.00 0.30 1.40 8.00 8.50 5.00 —
≤0.25 — — — — 1.35 0.75 1.75 6.15 18.00
1.00 1.00 0.38 — — 0.45 1.90 1.15 1.85 1.25
≤0.25 ≤0.25 — — — — — — 10.00
420 315 314–425 230–315 315 380 430 480 380 450
440-C BG-42 ASM 5749
1.10 1.15 1.15
≤1.00 0.30 0.21
≤1.00 0.50 0.12
≤0.60 — 0.10
17.00 14.50 4.13
≤0.75 4.00 4.80
— — 1.40
— 1.20 1.08
— — 7.81
200 480 480
Applications Used for hightemperature bearings
Used for hightemperature and corrosion-resistant bearings
above 120°C, if tempered at 160°C; or above 200°C if tempered at 280°C. When bearings are used at elevated temperatures, steels with high-temperature hardness are required. Table 28.3 lists some of the widely used high-temperature bearing steels along with their chemical compositions. Corrosion-resistant alloys should be used for bearings in applications where they are exposed to corrosive environments. Steels with high chromium content possess good corrosion resistance. Of the alloys listed in Table 28.3, 440C, BG-42, and ASM 5749 are good candidates for corrosion-resistant bearings. Non-ferrous bearing materials such as ceramic also provide excellent corrosion resistance and can be considered.
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TABLE 28.4
Modern Tribology Handbook
Properties of Engineering Ceramics and Bearing Steels
Material Silicon nitride (Si3N4) Silicon carbonate (SiC) Alumina (AL2O3) Partly stabilized zirconia (ZrO2) Bearing steel
Density (g/cm3)
Hardness (HV)
Young’s Modulus (GPa)
Flexural Strength (MPa)
Linear Thermal Thermal Fracture Expansion Shock Thermal Electric Toughness Coefficient Resistance Conductivity Resistance (MPa-m1/2) ×10–6/°C (°C) (W/m-K) (Ω-cm)
3.1–3.3 1500–2000 250–330
700–1000
5.2–7.0
2.5–3.3
800–1000
12–50
1013–1014
3.1–3.2 1800–2500 310–450
500–900
3.0–5.0
3.8–5.0
400–700
46–75
100–200
3.6–3.9 1900–2700 300–390
300–500
3.8–4.5
6.8–8.1
190–210
17–33
1014–1016
5.8–6.1 1300–1500 150–210
900–1200
8.5–10.0
9.2–10.5
230–350
2–3
1010–1012
—
14–18
12.5
—
50
10–5
7.8
700
208
Ceramics are superior to ferrous alloys in corrosion, heat, and wear resistance, but are limited in application because they have lower toughness and fracture resistance and are not able to sustain shock loads. Furthermore, ceramic bearing materials are more expensive than ferrous alloys and very expensive to machine. New engineering ceramics, to a certain degree, have improved some of the material property limitations and have increased use in bearing applications. Today, a fair number of bearings are made totally, or partially, from a variety of ceramics, including alumina, silicon carbide, titanium carbide, and silicon nitride. With the advances in material science and manufacturing technology, the demands for ceramic bearings will continue to grow. Table 28.4 provides the properties of engineering ceramics for bearing applications.
28.4 Contact Mechanics Rolling element bearings are typical mechanical components that operate under concentrated-contact conditions. Loads carried by rolling element bearings are transmitted through the discrete contacts between the rolling elements and the two raceways. Even under moderate bearing load, the stresses at the contact are quite high, being on the order of 1 to 4 GPa. Well-designed bearings are, however, capable of carrying an appreciable amount of load. This is attributed to the fact that contact stress increases slowly with the applied load (to one third power for point contact and one half power for line contact) and that the material is in general compression. In rolling element bearings, point contact refers to the conjunction of two surfaces such that under no load, the initial contact is a single point. As load is applied, the contact develops into a finite area of a generally elliptical shape. Point contact exists between the rolling elements and raceways of ball bearings, and of roller bearings with high-crown on rollers and raceways. It also exists in roller bearings between the roller-ends and flanges. Line contact is the conjunction of two surfaces such that the initial contact under no load is a straight line. When loaded, the line spreads to form an elongated rectangle. A concept of “modified line contact” is frequently used (Lundberg et al., 1947). The modified line contact is the major form of contact between the rolling elements and raceways for roller bearings. This chapter section outlines the classical Hertzian theory of contact that allows quick calculations of contact stress and deformation to be made from the applied load, material properties, and the internal geometry. Issues of non-Hertzian contact are also discussed.
28.4.1 Theory of Hertzian Contact 28.4.1.1 Point Contact When two elastic solids contact under load W, a contact area develops. For a point contact, the area, in general, assumes an elliptical shape and has a semi-major, a, in one direction and a semi-minor, b, in the perpendicular direction. For purposes of discussion, assume a lies in the x-direction; b lies in the
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Rolling Element Bearings
y-direction; and Rx and Ry are principal relative radii (composite radii) of curvature at origin of the contact. The ratio of the semi-minor axis b to the semi-major axis a is defined as ellipticity k = b/a (0 ≤ k ≤ 1). The ellipticity is related to the ratio of surface curvature radii, kr = Ry /Rx , through a transcendental equation, which can be approximated as follows (Johnson, 1985):
k ≈ kr2
3
(28.1)
Denote Re = (RxRy)1/2 as the geometrical average radius of surface curvatures, the geometrical average contact size, denoted as c = (ab)1/2, can be obtained as:
()
13
3 WR e F e c= 2E ′
()
(28.2)
where E′ is referred to as the effective Young’s modulus and is determined from the Young’s moduli E1 and E2, and Poisson ratios ν1 and ν2 of the contacting bodies,
1− ν2 1− ν2 1 2 E ′ = 2 + E2 E1
−1
(28.3)
F(e) in Equation 28.2 is an auxiliary function, varying only with the eccentricity of the contact ellipse, e = (1 – k2)1/2. For e > 0 (kr < 1), F(e) can be approximated in terms of kr by the following equation:
1 − k − ln k r r F e ≈ 0.726 kr1 6 4 3 1 − kr
()
13
0 < kr < 1
(28.4)
For the circular contact where e = 0, F(e) is equal to unity, F(e) = F(0) = 1. Having defined the shape k and size c of the contact ellipse, the semi-major and semi-minor axes, a and b, maximum Hertzian pressure pk , and maximum deformation at center of the contact δ can be determined.
a = k −1 2c ∝ W 1 3
(28.5)
b = k1 2c ∝ W 1 3
(28.6)
ph =
3 W ∝W1 3 2 πc 2
() ()
k1 2 K e 9W 2 δ= F e 2E ′2 Re
(28.7)
13
∝W 2 3
(28.8)
where K(e) is the complete elliptical integral of the first kind. The value can be determined by the following approximation (Hamrock et al., 1983):
()
Ke ≈
π π − − 1 ln kr 2 2
0 < kr ≤ 1
(28.9)
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Modern Tribology Handbook
TABLE 28.5 k z/b τmax/ph
Maximum Shear Stress and Its Depth 0
0.2
0.4
0.6
0.8
1.0
0.785 0.300
0.745 0.322
0.665 0.325
0.590 0.323
0.530 0.317
0.480 0.310
The stresses in x- and y-directions at the center of the contact are:
k σ x = − ph 2ν + 1 − 2ν 1 + k
(28.10)
1 σ y = − ph 2ν + 1 − 2ν 1 + k
(28.11)
(
)
(
)
The maximum shear stress occurs at a certain depth along the z-axis below the surface. The maximum shear stress has been used as the critical stress for contact fatigue analysis. Table 28.5 gives the maximum shear stress along with its depth as functions of ellipticity. Detailed information regarding stress calculations at arbitrary points below the contact surface is given in Jones (1964) and Sackfield (1983a,b). 28.4.1.2 Line Contact In line contact, one of the principal radii, Rx, approaches infinity (Rx → ∞). Accordingly, the ratio of surface curvature radii kr reduces to zero (kr = Ry /Rx = 0), and Re is redefined as Re = Ry . The contact area becomes a long strip of width 2b. Assume Wl is the contact load per unit length. The half-contact width b and Hertzian pressure ph can be expressed as:
8W R b= l e πE ′ ph =
12
(28.12)
2Wl ∝W1 2 πb
(28.13)
Assume the deformation is zero at a certain preset depth (z = Re) for both contacting surfaces. The maximum composite deformation δ at the center of contact can be approximated by:
δ=
(
) (
)
Wl 2 π E ′ 1 + ν1 ν1 1 + ν2 ν2 Re − ln − E1 E2 π E ′ 2 Wl
(28.14)
Alternative empirical equations for calculating surface deformation have been developed for modified line contact (Lundberg, 1939; Kunert, 1961). Assume two cylinders with parallel axes are pressed together under load W. The effective contact length is leff . The total deformation of the contact surfaces can be approximated by a power-law function
δ =C⋅
Wt lefft′
(28.15)
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Rolling Element Bearings
It is suggested that for steel, C = 4.05 × 10-5, t = 0.925, and t′ = 0.85 when W is in Newtons and leff and δ are in millimeters. For simplicity concerns, t = 9/10 has been widely adopted. The stresses at a general point (y, z) within the contact solids are given by McEwen (1949)
σy = −
ph b
σz = −
z 2 + n2 m1 + 2 2 − 2z m + n
(28.16)
ph z 2 + n2 m 1 − 2 2 b m +n
(28.17)
ph m2 − z 2 n b m2 + n2
(28.18)
τ yz = where
12 2 1 2 2 2 2 2 2 2 2 m = sign z b − y + z + 4 y z + b − y + z 2
()
(
)
(
12 2 1 2 2 2 2 2 2 2 2 n = sign y b − y + z + 4 y z − b − y + z 2
()
(
)
(
) )
12
(28.19)
12
(28.20)
Various critical stresses (orthogonal shear stress, maximum shear stress, von Mises stress, etc.) for contact fatigue life calculations can be derived from the stress components.
28.4.2 Bearing Internal Contact Geometry The previous section provided useful equations for contact analysis. To use these equations, bearing internal geometry must be defined. As can be seen, the shape and dimension of the contact ellipse or strip, the maximum Hertzian pressure, and surface deformation all relate to two important parameters: (1) the principal effective curvature ratio, kr = Ry /Rx, of the contact surfaces and (2) the geometrical average radius, Re = (RxRy)1/2 (for line contact, kr = 0 and Re is defined as Re = Ry). As will be seen, these two parameters also play important roles in lubricant film thickness and bearing torque calculations. This section defines the two geometry parameters for commonly used bearing types. 28.4.2.1 Ball Bearings The internal geometry of a ball bearing is determined by the raceway-groove radii ri and ro in the bearing’s axial plane, ball diameter db , bearing pitch diameter Dp , and the inner- and outer-raceway contact angles βi and βo. The radii of inner- and outer-raceway grooves and the pitch diameter are expressed in terms of ball diameter db as ri = gi (db /2), ro = go(db /2) and Dp = Gdb , respectively (Figure 28.4). For the inner-raceway contact, it can be shown that:
cos βi 1 kr = 1 − 1− G gi
(28.21)
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FIGURE 28.4
Modern Tribology Handbook
Internal geometry of a ball bearing.
cosβi Re = 1 − G
12
1 1 − g i
−1 2
db 2
(28.22)
Similar equations are obtained for the outer-raceway contact:
cos βo 1 kr = 1 + 1− G go cos βo Re = 1 + G
12
1 1 − g o
−1 2
(28.23)
db 2
(28.24)
where
D d G = o − 1 = i + 1 db db
(28.25)
and di and Do are the inner- and outer-raceway diameters measured at the central radial plane. The theoretical radial clearance δ0 is negligibly small, and this is not included in the calculation. In the absence of centrifugal forces, βi and βo are identical. For bearings under pure radial loads, βi = βo = 0.
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Rolling Element Bearings
FIGURE 28.5
Internal geometry of a tapered roller bearing.
28.4.2.2 Roller Bearings A roller bearing’s internal geometry is defined by the roller central or mean diameter dr , effective pitch diameter Dp*, inner-raceway contact angle βi, and outer-raceway contact angle βο (Figure 28.5). The effective pitch diameter Dp* is related to the inner-raceway mean diameter dm and outer-raceway mean diameter Dm through the following equation:
D p* = D p +
β +β β −β 1 Dm − dm tan i o tan o i 2 2 2
(
)
(28.26)
where Dp = (Dm + dm)/2 is the bearing’s pitch diameter. For spherical roller bearings, Dm is defined by the diameter of the outer-raceway sphere Do and the contact angle of the outer raceway βo ; for example, Dm = Docosβo . For most roller bearings, including spherical roller bearings, line contact exists between the raceways and rollers. Therefore, kr = 0. At the inner-ring raceway and roller contact, the geometrical average radius is:
Re =
dm 1 2G * cos βo − βi 2
(
)
(28.27)
At the outer-ring raceway and roller contact, the geometric average radius is expressed as:
Re =
Dm 1 2G * cos βo − βi 2
(
)
where G* is the ratio of effective pitch diameter to roller mean diameter, G* = Dp*/d r .
(28.28)
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Modern Tribology Handbook
For spherical roller bearings with symmetric rollers, βi = βo. For cylindrical roller bearings, βi = βo = 0. For high-crowned rollers and raceways, rollers may not fully engage with raceways along the roller length when the applied load is low relative to the load under which the crowns were designed. In such cases, elliptical contact exists. Assume the crown curvature radius of the rollers is Rw , and the inner and outer raceways have crown curvature of radii of ri = giRw and ro = goRw , respectively. The following relationships exist when βo – βi is small. At the inner-ring raceway,
cos βi 1 d kr = 1 − 1+ r ∗ G g i 2Rw 12
cos βi 1 Re = 1 − 1+ G∗ gi
−1 2
Rw dr 2
(28.29)
12
(28.30)
At the outer-ring raceway,
cos βo 1 d kr = 1 + 1+ r G ∗ g o 2Rw cos βo Re = 1 + G∗
12
1 1 + g o
−1 2
Rw dr 2
(28.31)
12
(28.32)
Equations 28.29 through 28.32 are applicable to spherical bearings in elliptical contact. In this case, bearing raceways are considered as being concavely crowned. Accordingly, negative values are used for gi and go . 28.4.2.3 Roller-End and Flange Contact For tapered roller bearings, rollers are retained by flanges, also known as ribs, at both ends of the inner ring. The rib located at the large end of the inner ring sees a setting force from each roller. The large end of a roller is a portion of a sphere with the radius Rs being a fraction of the apex length La, Rs = ζLa (0 < ζ < 1). Elliptical contact exists between the rib and each roller-end. The rib and roller-end geometry are designed such that the center of the contact is located at a height H, roughly half the rib height, and the major axis of contact ellipse is oriented along the sliding and rolling direction of rollers. Assume the rib angle is θ. As seen from Figure 28.6, the following relationships exist:
H = h Rs cosθ h=
( ) cos( γ − θ)
g r − sin γ − θ
gr =
kr = 1 −
(28.33)
(28.34)
Dr 2Rs
( ) h cos (β + θ) + g
(28.35)
sin βi + θ i
(28.36) i
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Rolling Element Bearings
FIGURE 28.6
Roller-end and rib contact geometry.
Re = kr−1 2 Rs gi =
Ri Rs
(28.37)
(28.38)
γ = (βo – βi)/2 is the roller half-included angle. Ri is the base-radius of the inner raceway at the large end, and Dr is the base-diameter of rollers at the large end. The above equations also apply to cylindrical bearings where γ = βi = βo = 0.
28.4.3 Non-Hertzian Contact Hertzian contact exists only in the idealized situation. For practical applications, Hertzian assumptions may not always be satisfied. While this, in general, does not undermine the usefulness of the Hertzian theory, it gives rise to the necessity of non-Hertzian contact. For finite line contact as seen in roller bearings, plane strain assumption is not applicable at the end portions of the contact where edge loading occurs. Moreover, contact surfaces are far from perfectly smooth. Surface imperfections or damage, whether resulting from manufacturing processes or from mishandling during transportation and assembling or from operation, are practically inevitable. A surface imperfection serves as a stress-raiser. It can cause perceptible stress deviation from the Hertzian theory. Under thin-film lubrication conditions, surface roughness also plays an important role in altering contact stresses. Life reduction due to surface roughness becomes an important issue. In this section, issues regarding non-Hertzian contact are discussed. 28.4.3.1 Edge Stress and Roller Crowning When a finite roller contacts a raceway of greater length, the material in the raceway is in greater tension along the contact strip at roller ends than at the central portion of the roller. Correspondingly, the roller receives a high compressive stress at its ends. This condition of edge-loading is shown in Figure 28.7 where a spherical roller is in contact with the raceway under heavy load conditions. To prevent edgeloading, rollers and raceways are usually partially or fully crowned to relieve the edge stresses. Crowning the contact members of a bearing also gives the bearing protection against edge stress resulting from
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1.00 0.50
) co 0.00 or din ate (m m X
(mm)
-1 0.0 0
rdinate
-5 .00
Y coo
0.0 0
5.0 0
0.00
10 .00
Pressure, P = p/Ph
Modern Tribology Handbook
FIGURE 28.7
Contact pressure in a spherical roller and raceway contact under heavy load conditions.
FIGURE 28.8 Contact pressure and interior von Mises stress for a roller in contact with a scratched surface. (From Ai, X. and Sawamiphakdi, K. (1999), Solving elastic contact between rough surfaces as an unconstrained strain energy minimization by using CGM and FFT techniques, ASME J. Tribol., 121, 639-647. With permission.)
misalignment (Hartnett, 1984). The amount of crowning is determined by the maximum load the bearing was designed for and by the degree of misalignment anticipated in the application. Substantial studies have been conducted over the years to provide methods of designing profiles based on a uniform contact pressure or contact stresses along the length of contact. For more detailed discussion on roller profiling, the reader is referred to Lundberg (1939), Poon et al. (1978), Rahnejat et al. (1979), Hartnett (1984), and Reusner (1987). 28.4.3.2 Effect of Surface Scratch and Indentation Surface scratches or indentations are common surface defects. They result from mishandling during the transportation and assembly processes. Lubricant contamination is another major source of surface damage. The presence of a surface scratch or indentation can result in a noticeable stress concentration at the edges of the defect. It brings the maximum stress closer to the surface, causing surface-originated spall initiation and subsequent propagation. Figure 28.8 shows the contact pressure and interior von Mises stress distributions from the reference (Ai et al., 1999) for a scratched roller in contact with its raceway. The scratch has slightly raised shoulders on both edges. Pressure spikes and high stress concentrations at the edges of the scratch are clearly demonstrated. Studies have indicated that the magnitudes of the pressure spike and stress concentration are largely dependent on the ratio of depth to half-width of the scratch or indentation. The ratio represents the average slope of the indentation profile. A deep slope gives rise to high contact pressure and stresses.
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Rolling Element Bearings
28.4.3.3 Effect of Roughness With increasing demand on power density, bearings are often required to operate under thin-lubricantfilm conditions. When the lubricant film is penetrated by the surface roughness, surface asperity causes perceptible stress concentration on the surface or in the near-surface layer. Consequently, surface distressrelated contact failure, mostly in the form of surface pitting and spalling, becomes an important issue. The contact problem under this condition is known as rough contact. Unlike smooth Hertzian contact, the contact area is now a myriad of micro-contacts of highly irregular shapes within the macro-contact. The contact pressure at these micro-contacts can be high enough to cause localized property changes both in contact bodies and in lubricant. Because the contact surfaces in rolling element bearings are, in general, smoother than other machine components such as gears, the mutual dependency between asperities is dramatic. Micro-contact areas are often connected and the ratio of actual to nominal contact areas is close to unity. Figure 28.9 depicts a typical surface roughness profile produced by grinding processes. The center-line-average roughness is 0.11 µm and average asperity slope is about 1 degree. When the surface engages in contact, micro-contact areas develop. Accordingly, contact stresses of different magnitudes are generated. Figure 28.10 shows contact pressure and footprint in a boundary-lubricated contact. As demonstrated in Figure 28.10, surface roughness causes perceptible pressure fluctuation. While reducing surface roughness decreases pressure rippling, lowering the surface slope has a dominating impact on reducing pressure fluctuation and peak pressure. In life-sensitive applications, bearing raceways must be honed or properly machined to provide good surface qualities.
28.5 Bearing Internal Load Distribution Bearing load is distributed among rolling elements. The load each rolling element receives is dependent, in general, on the azimuth position of the rolling element. The load distribution is important for predicting bearing contact stress, torque, temperature, and fatigue life. A bearing’s internal load distribution can be obtained by analyzing contact deflections and bearing geometry constraints. As a load is applied to the bearing, deformations of various magnitudes occur at different azimuth locations. The deformation must comply with certain geometrical constraints so that the bearing’s geometrical integrity is not violated. Assume the outer ring of the bearing is firmly seated in a housing and the inner ring is well-fitted on a solid shaft or a thick wall hollow shaft. In the absence of centrifugal forces, the load each roller receives can be determined from the deformation/load relationship outlined in Section 28.4.1. In this section, bearing load distribution is derived.
28.5.1 Bearings under General Load Conditions When a bearing is subjected to a radial and an axial load Fr and Fa, respectively, the centers of the inner ring and outer ring are displaced relative to each other in both radial and axial directions. Assume the movement is δr in the radial direction and δa in the axial direction. The deformations at any rolling element position x is expressed by
( )
δ ψ = δ r cos β cos ψ + δ a sin β −
δe cos β 2
(28.39)
where β is the contact angle and δe is the diametrical effective clearance. The equation can be rearranged in terms of δmax = δ(0):
1 δ ψ = δ max 1 − 1 − cos ψ 2ε
( )
(
)
(28.40)
ate
oo rdi n
yc
0
1.2
)
(m m
0 0.8
Surface roughness profile: ground surface.
0
1.6
0
0.4 0 .00 0.0 0
5
0.2
x
0 0.5 in ord co
0
1.0 5 0.7 ) m (m ate
0.00
0.40
0.80
1.20
1.60
0.00
0.25
0.75 x coordinate (mm)
0.50
1.00
1058
Roughness height (mm)
FIGURE 28.9
2.0
0
-00 4
5.0 E
—
0.0 E+ 00 0
y coordinate (mm)
2.00
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Modern Tribology Handbook
0.0 0 0 1.2
1.0 0
0
2.0
0
FIGURE 28.10
Pressure, P= p/Ph
3.0
Yc oo rd
0 0.4
te, Y
ina /b
=y
00
-0. 40
-0. -0
.80
0 1.2 0 6 . 0 0 x/a 0.0 e, X t 0 a 6 n -0. rdi 20 .20 oo c -1. -1 X
Contact pressure distribution and footprint for contact with ground surfaces.
0 0.8
Y coordinate, Y = y/b
-1.20 -0.60 0.00 0.60 1.20 X coordinate, X = x/a
-1.20
-0.80
-040
-0.00
0.40
0.80
1.20
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where ε is the load zone parameter and is defined as:
δ 1 δ ε = 1 + a tan β − e 2 δr 2δ r
(28.41)
For pure thrust load, ε approaches infinity (ε = ∞). The deflection at azimuth position ψ is the sum of deformations between the rolling element and each raceway:
δ = δ(o) + δ(i )
(28.42)
From the load and deformation relationship defined in Section 28.4.1, the load can be expressed in terms of the total deformation as
W = kt δ t
(28.43)
where
kt = kt−o1 t + kt−1i t () ()
−t
(28.44)
kt(i) and kt(o) are defined by Equation 28.8 for point contact and by Equation 28.15 for line contact. Accordingly, t = 3/2 for point contact and t = 40/37 or 10/9 for line contact. Assume Wmax as the maximum roller load. It can be easily shown from Equation 28.43 that:
( ) = δ(ψ )
W ψ
Wmax
t
(28.45)
δ max
Thus, the load distribution can be written as:
1 W ψ = Wmax 1 − 1 − cos ψ 2ε
( )
(
)
t
(28.46)
To achieve the state of static equilibrium, the following conditions must be satisfied:
()
(28.47)
()
(28.48)
Fr = ZWmax J r ε cos β Fa = ZWmax J a ε sin β where Jr(ε) and Ja(ε) are Sjövall integrals (Sjövall 1933) and are defined as:
()
1 Jr ε = 2π
xl
t
1 1 − cos ψ cos ψdψ 1 − 2ε − xl
∫
(
)
(28.49)
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TABLE 28.6
Jr(ε) and Ja(ε) for Single-Row Bearings
Point Contact (t = 3/2) ε 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.25 1.67 2.5 5 ∞ a
Line Contact (t = 10/9)
Jr(ε)
Ja(ε)
JR(ε)
Jr(ε)
Ja(ε)
JR(ε)
Ja(0.31)(ε)
0/0a 0.1156 0.1590 0.1892 0.2117 0.2288 0.2416 0.2505 0.2559 0.2576 0.2546 0.2289 0.1871 0.1339 0.0711 0
0/0a 0.1196 0.1707 0.2110 0.2462 0.2782 0.3084 0.3374 0.3658 0.3945 0.4244 0.5044 0.6060 0.7240 0.8558 1
0 0.0051 0.0306 0.1229 0.5988 ∞ 1.2554 0.5799 0.3934 0.3074 0.2546 0.1741 0.1128 0.0662 0.0294 0
0/0a 0.1268 0.1737 0.2055 0.2286 0.2453 0.2568 0.2636 0.2658 0.2628 0.2523 0.2078 0.1589 0.1075 0.0544 0
0/0a 0.1319 0.1885 0.2334 0.2728 0.3090 0.3433 0.3766 0.4098 0.4439 0.4817 0.5775 0.6790 0.7837 0.8909 1
0 0.0126 0.0512 0.1493 0.4938 ∞ 0.8704 0.4909 0.3659 0.2995 0.2523 0.1697 0.1092 0.0638 0.0283 0
0/0a 0.1709 0.2454 0.3055 0.3591 0.4095 0.4567 0.5084 0.5607 0.6196 0.7072 0.8143 0.8750 0.9227 0.9637 1
0/0 denotes a special number that any product or division by this number is zero.
xl
()
1 Ja ε = 2π
1 1 − cos ψ 1 − 2ε − xl
(
∫
t
dψ
)
(28.50)
ψl is the half load-zone angle and is a function of the load-zone parameter ε.
(
cos −1 1 − 2ε ψl ε = π
()
)
ε ≤1 ε >1
(28.51)
The values of Sjövall integrals are listed in Table 28.6. For an angular-contact bearing, with a given contact angle β, under the combined radial and thrust load condition, ε can be found from the following equation with the aid of Table 28.6.
J ε ( ) J ((ε)) = FF tanβ
J ε =
r
r
a
a
(28.52)
The maximum load of a rolling element is given by: 2
1 Fr Fa Wmax = + Z J r J a
2
(28.53)
For a radial bearing, with zero contact angle β = 0, under pure radial load, ε can be found from the following equation with the aid of Table 28.6.
()
Fr = Zkt J R ε δ e
t
(28.54)
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When δe ≥ 0,
0 ≤ ε ≤ 1/2 and
ε J R ε = Jr ε 1 − 2ε
() ()
t
(28.55a)
When δe < 0,
/2 < ε < ∞
1
and
ε J R ε = Jr ε 2ε − 1
() ()
t
(28.55b)
The values of JR(ε) for various ε are listed in Table 28.6. For angular-contact ball bearings under pure thrust load, the contact angle β is usually greater than the initial contact angle β00 that exists under zero load. The actual contact angle can be determined from the following equation (Eschmann, 1964).
∆l sin β00 + δ(o)
sin β =
∆l cos β00 + ∆l sin β00 + δ(o) 2
2
(28.56)
2
where δ(o) is the deformation at the contact between the ball and outer race. It can be calculated from Equation 28.8. ∆l is the distance between the centers of curvatures of the inner- and outer-raceway grooves.
(
) d2
∆l = g i + g o − 2
b
(28.57)
where db is the ball diameter, gi and go are the ratios of the inner and outer raceway groove radii to ball diameter.
28.5.2 Bearings under Pure Eccentric Thrust Load When a pure thrust load Fa is applied on a thrust or angular-contact bearing, each rolling element shares an equal amount of load; that is,
( )
W ψ =
Fa Z sin β
(28.58)
However, if the load is applied eccentrically, the radial planes of the two raceways are no longer parallel and they tilt at an angle φ to each other. The load is distributed unevenly among the rolling elements. The equations for δ(ψ), W(ψ), and Fa derived in the previous section are applicable provided that the load-zone parameter ε is redefined as:
2δ 1 ε = 1 + a 2 φD p
(28.59)
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where Dp is the bearing pitch diameter. Because of eccentric loading, a tilting moment M develops, where
M = el Fa =
Dp 2
()
ZWmax J r ε sin β
(28.60)
The eccentricity el is determined from the following equation:
el =
() J (ε )
D p Jr ε 2
(28.61)
a
28.6 Bearing Lubrication 28.6.1 Elastohydrodynamic Lubrication Under healthy operating conditions, contact surfaces in a rolling element bearing are separated and, therefore, protected by a thin layer of self-pressurized lubricant film. The applied load is transmitted from one surface to the other surface through this pressurized lubricant film. The formation of the lubricant film is the subject of the Elastohydrodynamic Lubrication (EHL) theory and has been described elsewhere (Dowson et al., 1977; Gohar, 1988). The lubricant film between the contact surfaces has an almost uniform thickness hc at the central region. At the outlet, a distinct constriction occurs and the film reaches its minimum thickness hmin. The thickness of the lubricant film in relation to surface roughness plays important roles in the determination of frictional torque, heat generation, wear, and fatigue failure. Equations derived from the numerical regression of EHL simulations or experimental measurements are available for film-thickness calculations. Based on numerical simulation results, Dowson and Higginson (1961) established an empirical formula to determine the minimum film thickness at the outlet of the EHL conjunction for line contact problems under fully flooded, isothermal conditions. Dowson (1968) revised the equation to make it compatible with the law of dimensionless analysis. In dimensional form, the equation reads:
(
)(
)(
)
hmin = 2.65 α 0.54 η0.7 E ′ −0.03 Re0.43 L0.13 ue0.7 w −0.13 1442443 14243 14243 Lube & material properties
Geometry
(28.62)
Operation conditions
where η and α are viscosity and pressure-viscosity coefficient of the lubricant, respectively; E′ is the effective Young’s modulus; Re is the geometrical average radius given in Section 28.4.2; L is the contact length; ue is the entrainment speed and is given in the following section as a function of bearing geometry and rotational speed for various bearings; and w is the applied contact load. The central film thickness is approximately 4/3 of the minimum film thickness for most of the EHL regime. However, the ratio of central film thickness to minimum film thickness reduces asymptotically to unity as load increases and speed decreases. The ratio also reduces under conditions of lubricant starvation. For point contact problems, Hamrock and Dowson (1977a) presented a minimum-film-thickness equation. The equation was restricted to circular contact or transverse elliptical contact where the major axis of the ellipse lies perpendicular to the direction of entraining motion. The restriction on the direction of entraining motion was lifted and generalized solutions for entrainment along either axis, or along any direction inclined to the principal axes, were presented by Chittenden et al. (1985a,b). A revised minimum film thickness equation was expressed in terms of the directional surface curvature ratio k *r (0 < k *r < ∞); that is:
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(
)(
1 − e k ) 1R4444 4244444 3
hmin = 3.68 α 0.49 η0.68 E ′ −0.117 ue0.68 w −0.073 144 42444 3 14 4244 3
Lube & material properties Operating conditions
0.466 * 0.233 e r
−0.67 kr* − 2 3
(28.63)
Geometry configurations
When the entraining motion is in the direction of the major axis of ellipse, k *r >1 and k *r = 1/kr . When the entrainment is along the direction of the minor axis of ellipse, k *r <1 and k *r = kr . The ratio of film thickness to the composite rms value of surface roughness, σ = (σ12 + σ22)1/2, is called the lambda (λ) ratio. It is the most used parameter among other quantities associated with EHL. It indicates the condition of lubricant film formation and somewhat reflects the severity of asperity contact between contact surfaces. Three lubrication regimes — from full-film lubrication to mixed lubrication and to boundary lubrication — can be distinguished based on the value of the lambda ratio. When the lubricant film thickness exceeds three times the composite rms roughness, a full separation of the contact surfaces is achieved. The contact load is carried almost entirely by the lubricant film. In full film regime, contact stresses are less affected by surface roughness. The overall performance can be predicted by the classical EHL theory considering smooth surfaces. When the lambda value becomes less than three but greater than one, a perceptible amount of asperity contact occurs. Local lubricant film can be interrupted at the tip of tall asperities. This regime is called partial EHL or mixed lubrication regime. The contact load is shared between lubricant film and contacting asperities. The load sharing ratio and contact friction forces are strongly dependent on the lambda value (Tallian, 1972). A majority of rolling element bearings operate in this regime. As the lambda ratio becomes less than one, the contact falls in the boundary lubrication regime where asperity contact predominates. Severe surface distress is expected. The overall performance can be well-predicted by the dry contact analysis.
28.6.2 Effect of Spin Motion In addition to rolling motion, spinning — a rotation of a rolling element about an axis normal to the contacting surfaces — often exists at the contacts between the rolling elements and raceways. A study on point EHL contact (Taniguchi et al., 1996) shows that spin motion reduces the minimum film thickness. The effect on center film thickness is, however, insignificant. The reduction in the minimum film thickness depends on load and speed parameters. An adjustment factor for the minimum film thickness was given by Taniguchi et al. (1996) as:
ϕ spin =
hmin = 1 − 3.47W 0.47 Ω hmin 0
(28.64)
where Ω is the spin-to-roll ratio defined as:
Ω=
2ω s Re
(28.65)
ue kr
—
and W is the non-dimensional load defined by:
W=
kr w E ′Re2
(28.66)
where ωs is spin angular velocity.
28.6.3 Effect of Lubricant Starvation When lubricant supply to the inlet of the contact is insufficient, reduction in film thickness occurs. This phenomenon is referred to as lubricant starvation. Under such conditions, the thickness of the lubricant
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film is largely determined by the availability of lubricant supplied at the inlet to the contact. The usage of lubricant becomes more efficient. Lubricant at the inlet zone is entrained into the contact with little or no side flows. The reduction in film thickness has been studied by many researchers, including Wolveridge et al. (1971), Wedeven et al. (1971), Kingsbury (1973), Chiu et al. (1974), and Elrod et al. (1974). A concept of inlet lubricant-air-meniscus distance to the center of contact was adopted to quantify the severity of lubricant starvation. Empirical equations were subsequently developed to correlate the reduction in lubricant film thickness to inlet meniscus distance (Castle et al., 1972; Hamrock et al., 1977b). The primary limitation of these meniscus-distance-based equations is that they only apply to the starvation regime where the meniscus is clearly observed outside the Hertzian contact. As the inlet meniscus distance approaches the half Hertzian contact width, the approach breaks down. In a recent work, inspired by the work of Kingsbury (1973), Chevalier et al. (1998) used the available lubricant film thickness at inlet to define lubricant supply conditions. An equation based on the inlet available film thickness was developed to estimate the reduction in central film thickness for circular contact problems:
ϕ strv =
hc γ = hcf q 1 + γ q
(28.67)
where hc is the central film thickness; hcf is the central film thickness under fully flooded conditions; and – γ represents the ratio of available film thickness at the inlet to the modified fully flooded film thickness at the contact center by considering lubricant compressibility.
γ=
hspl
(28.68)
ρ hcf
– ρ = ρ/ρ0 is the non-dimensional lubricant density; ρ is the lubricant density; ρ0 is the density under ambient pressure; hspl is the thickness of the supplied lubricant at the inlet; and q is an exponent and it increases as load increases or the entrainment speed decreases. For most of EHL regime, q varies from 2 to 5. As q → ∞, Equation 28.67 reduces to
ϕ strv =
γ ∞
1+ γ ∞
( )
= min γ ,1
(28.69)
Equation 28.69 underlines the physics. When lubricant supply at the inlet is abundant, the thickness of lubricant film is governed solely by load, speed, and contact geometry. Increasing lubricant supply at the inlet has no effect on film thickness. However, when the lubricant supply at the inlet is insufficient, the formation of lubricant film relies heavily on the availability of lubricant at the inlet. The film thickness at the contact center cannot exceed what can be generated at the inlet from the limited lubricant supply. – As γ decreases, the central film thickness hc decreases faster than the minimum film thickness hmin. – The ratio of hc to hmin approaches unity. When γ < 0.5, Equation 28.67 can be used quite accurately for calculating reductions in minimum film thickness. The concept of inlet lubricant availability also applies to elliptical contact as well as line contact. For transverse elliptic contact (kr* < 1) and line contact problems, side flows at the inlet to the contact encounter greater resistance. Consequently, q assumes a greater value when Equation 28.67 is used for a transverse elliptic contact or line contact problem.
28.6.4 Lubrication Methods In the proceeding equations and text, oil lubrication is considered and the EHL film between contacting surfaces is implied. Thus, for fluid lubrication, the determination of films and operating expectations
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are straightforward. In selecting a lubricant and method of lubrication, it is recommended that the first choice be as simple a selection as possible. For a simple system, straight mineral oil usually is the first choice. With reasonable temperature generated (temperature ranging from –50°C to 300°C), this system could be a simple sump. 28.6.4.1 Oil Bath The oil bath or closed sump is a popular means to lubricate bearings. A proper oil level should be about at the middle to almost the top of the bottom rolling element. For many systems, this provides for film formation and removes sufficient heat from the bearings. If load, temperature, or system speed leads to problems, then the lubricant viscosity or type of lubricant may need to be changed. When a wide range of temperature in the system is anticipated, a lubricant with higher viscosity index may be used. For bearings used at elevated temperature, a higher viscosity oil, additives or, in special cases, a synthetic lubricant such as polyalphaolefin should be considered. 28.6.4.2 Circulating Oil Systems If the above suggestions do not solve the problems, then a system may require circulating the lubricant through the bearings with an oil circulation system. The oil circulation system usually includes an external reservoir and pump and, in some cases, a heat exchanger that will maintain lubricant and bearing at a required temperature range. Very often, the appearance of too much wear debris or contamination may also indicate the need for filtration to be added to the system. Considering the environmental pressures to maximize lubricant life and reduce fluid contamination, the addition of a filtration system including a monitoring procedure may be required so that the quality of the oil going through the bearings and perhaps gears of the overall system can be continually assessed. 28.6.4.3 Oil Mist and Oil Jet Oil mist lubrication can be used for large bearing systems or high speed. For this type of lubrication, small amounts of oil droplets are carried by air onto bearings with an atomizer. This provides enough lubricant for fluid film formation and some cooling. It uses very little oil but can be limited in use, depending how well the mist can be contained within the system. An oil jet may be required for ultrahigh speed bearings because at such speeds, the lubricant would be driven off the bearing components. Thus, a jet velocity on the order of 10 to 20 m/s allows the lubricant spray to reach the internal bearing surfaces and provides the necessary fluid contact. 28.6.4.4 Greases Grease is a lubricant made up of about 10% soap thickener and 80% base oil, with the addition of rust and oxidation inhibitors and specific additives to provide anticorrosion, viscosity index improvement, or high film strength, depending on the need for extended life under required temperature, load, speed, and specific dry to wet conditions. It is recognized that more rolling bearings are lubricated with grease rather than oil because grease lubrication is simpler, more economical, and can provide sealing to bearings and thus keep out contaminants and resist water ingress more than oils. Conventional greases are usually limited to lower speeds ranging up to 3500 rpm (Boehringer, 1992). Lithium-based greases are commonly used because they can be pumped, have resistance to small particle ingress, and can be stored. For a rolling element bearing, grease that fills about 30 to 50% of the bearing inside cavity is recommended. Greater fill can cause higher temperatures or the grease may be forced out from the bearings. As to its shortcomings, grease does not flush out wear particles generated within a bearing as well and maintaining the proper amount of lubricant within a bearing is not as easily controlled as is possible with an oil. Finally, grease will not be the choice of lubricant when heat generated in a system must be dissipated quickly. Considering the EHL film formation with grease, tests on six lithium greases (Dalmaz and Nantuo, 1987) indicated that bearing fatigue life related to the viscosity of the base oil in the grease and therefore to the EHL film thickness. It has been recommended (Chetta et al., 1992) that an EHL film reduction factor of 0.5 to 0.7 be used with grease in a rolling element bearing. This was also suggested by Aihara
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and Dowson (1978), especially under longer operation when base oil moves from the grease and results in bearing starvation. 28.6.4.5 Solid Lubrication Other lubrication methods are solid lubrication and gas lubrication. Gas lubrication is usually not considered for rolling element bearings, but solid lubrication is used when severe conditions must be addressed. When temperatures are extreme or specific contaminants must be avoided, solid lubrication can be used although actual usage is much less than oil or grease, considering the costs and that most solid lubricants are not off-the-shelf products. Solid lubricant advantages include: there may be little or no movement of the lubricant, low volatility, and functionality at very low or high temperatures. The disadvantages are poor thermal conductivity, thermal expansion different than metals, and wear without means to replace the solid material worn away. Because solid lubricants are very special, their selection is more complex than the selection of oils and greases. The first solid lubricant was probably graphite, although molybdenum disulfide has been recognized and used for quite some time. Above 350°C, graphite provides low friction and may adhere firmly to metal surfaces but the purity and specific form of graphite must be known to provide worthwhile properties as a solid lubricant. Unfortunately, the same may be true for other solid lubricants, both natural and those developed in the laboratory. Because solid lubricants have different characteristics, relevant information must be reviewed when considering the use of solid lubricants. Information on solid lubricants is available (see, e.g., Landsdown (1998) and Sliney (1992)). Whatever the lubricant used in rolling element bearings, it should be selected based on the understanding of the overall system the bearings operate in and the ranges of speed, load (two most important), and temperature, along with the materials of the bearings and other components such as cage material or seals so that expected bearing life can be achieved.
28.7 Bearing Kinematics Kinematic analysis is very important for evaluating a bearing’s performance. It determines the entrainment speed ue as well as the sliding and spinning velocities required for lubricant film thickness calculation and subsequent bearing torque and temperature analyses. In this section, rolling speed (entrainment speed), sliding speed, and spin angular velocity at both inner- and outer-raceway contacts are discussed. Consider a reference coordinate system in a bearing’s axial plane as shown in Figure 28.11. To facilitate the discussion, assume for the moment that the rotating axes of rolling elements are fixed in space and no orbital movement exists. Denote ωr , ωi , and ωo as the angular velocities of the rolling elements, the inner raceway, and the outer raceway, respectively, in relation to the reference coordinate system. To simplify the analysis, further assume that ωr lies in the same plane as ωi and ωo. The assumption is valid for roller bearings with minimum or no roller skewing. The assumption is also valid for ball bearings under low and moderate speed applications where the gyroscopic moment of balls is negligible. In addition, this assumption may hold true for ball bearings under heavy loads where the gyroscopic moment is resisted by the frictional moment at the inner- and outer-raceway contacts. In general cases, a rolling element contacts the inner raceway at a contact angle βi and the outer raceway at a contact angle βo. As the rolling element revolves about the bearing’s axis (in general cases), the rolling element also rotates about its own axis that lies at an angle βr with respect to the bearing axis. At the inner-raceway contact, as shown in Figure 28.11, the angular velocity of the rolling element ωr resolves into two components, one parallel with the contact surface, ωrcos(βr – βi), one perpendicular to the contact surface, ωrsin(βr – βi). Similarly, the angular velocity ωi also resolves into two components, ωicosβi and ωisinβi in relation to the contact surface. The rolling speed, also known as the entrainment speed, at contact is:
uei =
1 ωr cos βi − βr − γ d cos βi + 1 D pω i γ d 4 ω i
(
)
(28.70)
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FIGURE 28.11
Modern Tribology Handbook
Rolling element and raceway contact.
where γd = De /Dp . De is the diameter of rolling elements measured at the central radial plane of each rolling element, and Dp is the bearing pitch diameter. Should gross slip occur at the inner-raceway contact, the sliding speed is:
1 ω vi = r γ d cos βi − βr + γ d cos βi − 1 D pω i 2 ω i
(
)
(28.71)
The spin angular velocity of a rolling element normal to the contacting surfaces at the inner-raceway contact can be expressed as:
ω ω si = r sin βi − βr + sin βi ω i ω i
(
)
(28.72)
Similarly, at the outer-raceway contact, the rolling speed, sliding speed, and spin angular velocity can be obtained as:
1 ωr γ d cos βo − βr + γ d cos βo + 1 D pω o 4 ω o
(28.73)
1 ω vo = r γ d cos βo − βr − γ d cos βo − 1 D pω o 2 ω o
(28.74)
ω ω so = r sin βo − βr − sin βo ω o ω o
(28.75)
ueo =
(
)
(
)
(
)
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In applications, bearing rotational speeds are usually prescribed by the absolute angular velocities of – – the inner and outer rings, ωi and ωo . The following relationships exist between the relative and absolute angular velocities:
ωi = ωi − ωc
(28.76)
ωo = ωo − ωc
(28.77)
where ωc is the angular velocity of the cage or the rolling element set. Now one has eight equations (Equations 28.70 to 28.77) and eleven unknown variables. Eight of the eleven unknown variables are placed on the left-hand side of the above equations. These unknown variables are not attainable unless the three remainder unknowns, ωr , βr , and ωc , are solved. Obviously, the three unknowns are governed by a bearing’s internal geometry design and surface frictional conditions at the inner- and outer-raceway contacts. Rather sophisticated numerical analysis of forces and moments is required to determine these unknown quantities (Harris, 1966, 1971a,b; Gupta, 1975, 1979a,b,c,d). Several computer programs are publicly available. The reader is referred to COSMIC, University of Georgia (Athens), for detailed program listings. As a practical matter, approximations can be made to simplify the analysis. For roller bearings, the orientation angle βr of the rotation axis for each roller is constrained by bearing geometry. Only two unknown variables ωr and ωc need to be determined. The two unknowns are usually obtained by assuming non-gross slip conditions at both the inner- and outer-raceway contacts (vi = vo = 0). From the non-gross slip conditions, it can be shown that
ωr =
γ d cos βo + 1 ω o − ω i γ d cos βo − βr 1 − mc
(28.78)
mc ω o − ω i mc −1
(28.79)
(
ωc =
)
where
( (
cos β − β i r mc = cos βo − βr
) 1 + γ cosβ ) 1 − γ cosβ d
o
d
i
(28.80)
The entrainment speed and spin angular velocity at the roller and inner raceway contact are determined as:
uei =
(
mc 1 − γ d cos βi 1 − mc
) ω − ω D
o
i
p
2
m 1 c ω si = − cos βi tan βi − βr + sin βi ωo − ωi 1 − mc γ d
(
)
(28.81)
(28.82)
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The entrainment speed and spin angular velocity at the roller and outer raceway contact are:
ueo =
1 + γ d cos βo Dp ω − ω o i 2 1 − mc
1 1 ω − ω ω so = + cos βo tan βo − βr − sin βo i o 1 − γ m d c
(
)
(28.83)
(28.84)
For ball bearings, the motion of balls is more complex. Each ball has an additional degree of freedom. The orientation angle βr of the rotation axis for each ball is unknown. Three spin control hypotheses, known as outer raceway control, inner raceway control, and minimum differential spin, are available.
28.7.1 Outer Raceway Control Experiments have revealed that balls of an angular-contact ball bearing normally operate with minimal spinning motion at one raceway, with nearly all the spinning motion occurring at the other raceway (Shevchenko and Bolan, 1957; Jones, 1959). Where spinning motion prevails is mainly dictated by friction and contact conditions and by contact conformability or between the ball and raceway. Outer raceway control theory assumes, in addition to non-gross slip at both inner- and outer raceway contacts, that no spin exists at the outer raceway contact, ωso = 0, and all spinning motion occurs at the inner raceway. The rotating axis of each ball intersects the extended tangent of the contact between the ball and outer raceway at bearing axis. For relatively high-speed, lightly loaded and oil-film-lubricated bearings, the outer raceway control theory is a rational approximation. The load and the spin-resisting frictional moment are greater at the outer raceway contact than at the inner raceway contact due to centrifugal effects. With the additional constraint ωso = 0, given by the outer raceway control theory, the orientation angle βr of the rotation axis for each ball can be determined.
tan βr =
sin βo γ d + cos βo
(28.85)
The entrainment speed at both the inner- and outer-raceway contacts and the spin angular velocity at the inner-raceway contact are given in Equations 28.81, 28.83, and 28.82, respectively.
28.7.2 Inner Raceway Control The inner raceway control theory assumes, in addition to the non-gross slip conditions at both inner and outer contacts, that there is no spin at the inner contact, ωsi = 0. The rotating axis of each ball intersects the contact tangent of ball and inner raceway at bearing axis. Under this constraint, it can be shown that:
tan βr =
sin βi − γ d sin 2 βi cos βi − γ d cos 2 βi
(28.86)
Equations for uei and ueo have the same forms as those for outer raceway control. The spin angular velocity at the outer-raceway contact is given in Equation 28.84. Inner raceway control probably occurs only in marginal lubricated bearings operated at low speeds. The formability of lubricant film is lower at the inner raceway than at the outer raceway. Consequently, the spin-resisting moment is higher at the inner raceway than at the outer raceway. Inner raceway control
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may prevail when the inner-raceway groove is designed to give a greater contact conformability with balls in the bearing’s axial plane than the outer-raceway groove. Thus, the inner-raceway contact has greater ellipticity and consequently a higher spin-resisting moment than the outer-raceway contact if the centrifugal forces are negligible.
28.7.3 Minimum Differential Spin For oil-lubricated bearings, in which elastohydrodynamic films exist at both inner- and outer-raceway contacts, spin occurs at both contacts. It has been shown that even under less favorable lubrication conditions, spinning and rolling occur simultaneously at both inner- and outer-raceway contacts. The spin moment at the inner raceway counteracts the spin moment at the outer raceway to achieve equilibrium. The minimum differential spin hypothesis assumes that no gross sliding exists at inner- and outer-raceway contacts, and that spin angular velocities at the inner and outer raceways have the same magnitude. The arithmetical summation of spin angular speed is zero, ωsi + ωso = 0. The minimum differential spin theory tends to approximate the minimum friction energy principle. Should the spinresisting moments at both the inner and outer raceways be the same, minimum differential spin theory reflects exactly the minimization of frictional energy. The minimum differential spin theory results in the following approximation:
tan βr ≈
sin βo + sin βi cos βo + cos βi
(28.87)
Rolling speeds and spin angular velocities for the inner- and outer-raceway contacts can be obtained from Equations 28.81 and 28.83 and from Equations 28.82 and 28.84, respectively. Because of the “on-apex” design of tapered roller bearings, no spin exists at either the inner- or outerraceway contacts if rollers are not skewed. However, the same cannot be said of spherical bearings. Perceptible spin occurs at both inner- and outer-raceway contacts.
28.8 Bearing Load Ratings and Life Prediction 28.8.1 Basic Load Ratings Bearing load rating is an important basis for bearing selections. Bearing manufacturers provide two basic load ratings: the basic static load rating and the basic dynamic load rating. The concept of dynamic load rating is introduced to reflect the fatigue nature of bearing failure. Rolling contact fatigue is a unique form of material failure that occurs at the surface or sub-surface layer due to repeated stresses. Because of the micro-scale inhomogeneities of bearing material, the strength or resistance to fatigue of bearing material varies from point-to-point. Even under identical stress conditions, there will be a wide dispersion in bearing lives. For this reason, bearing life is associated with a failure probability or a survival probability. The concept of percentage life is used. For example, L10 life refers to the number of hours at a certain speed or the number of revolutions that 10% of a group of supposedly identical bearings are expected to fail, or 90% of the bearings are expected to survive under a specific load. L10 life can also be interpreted as the number of hours at a certain speed or the number of revolutions that an individual bearing will survive with 90% reliability under the specified load conditions. Research over the years has shown that for a given failure probability, bearing life decreases as load increases. ISO adopts L10 = 106 revolutions as the standard rating life to establish the basic dynamic load rating. The basic dynamic load rating is defined as a constant load applied to a bearing with a stationary outer ring that will endure the standard rating life of 1 million revolutions, L10 = 106. The basic dynamic load rating for radial bearings is a central radial load of constant direction, denoted as C1, while the basic dynamic load rating for thrust bearings is an axial load in the same direction as the central axial and is
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TABLE 28.7
Basic Dynamic Load Rating Ball Bearinga
Radial bearing Angular contact bearing Thrust bearing β = 90°
Roller Bearing
bmfc (i cos β) Z D bmfc (cos β)7/10 tanβZ D bmfc Z 2/3 Dw9/5 7/10
2/3
9/5 w 2/3 9/5 w
29/27 bmfc (iLwe cos β)7/9 Z3/4 Dwe 29/27 bmfc (Lwe cos β)7/9 tanβZ 3/4 Dwe 7/9 Z 3/4 D 29/27 bmfc Lwe we
a When D > 25.4 mm, use 3.645D 7/5 for D 9/5. w w w Note: bm: Rating factor for contemporary bearing material and manufacturing quality, the value of which varies from 1.0 to 1.3, depending on bearing type and design. fc : Factor that depends on the geometry of the bearing components, the accuracy to which the bearing components are made, and the material. The values of fc for various bearings are given in ISO 281-1990. i: Number of rows of rolling elements in a bearing. β: Normal contact angle of a bearing. Ζ: Number of elements per row. Dw , Dwe: Diameter at the central plane of a rolling element (mm). Lwe: Effective contact length of rollers (mm).
TABLE 28.8
Maximum Permissible Contact Stress
Bearing Type
Maximum Stress (MPa)
Self-aligning ball bearings Non-self-aligning ball bearings Roller bearings
4600 4200 4000
denoted as C1a. The basic dynamic load ratings for various bearings are calculated by the equations shown in Table 28.7. The basic static load rating is used to determine the maximum permissible load that can be applied to a non-rotating bearing. The static radial load rating C0, and the static thrust load rating C0a, are based on a maximum contact stress between rolling element and bearing raceway at the center of the contact in a non-rotating bearing with a 180° and 360° load zone, respectively. The maximum stress varies slightly for different bearing types. Table 28.8 lists the maximum contact stresses. The maximum stress level listed in Table 28.8 may cause visible light Brinell marks on bearing raceways. These marks will not have a measurable effect on fatigue life when the bearing is subsequently rotating under lower application loads.
28.8.2 Bearing Life Prediction 28.8.2.1 Bearing Life Theory In studying the failure of brittle engineering materials, Weibull (1939) concluded that the strength of a material was a statistical variable, and assumed that the first initial crack led to the break of the entire structure under stress. By applying the calculus of probability, Weibull stated that the survival probability S could be expressed by:
∫()
1 ln = Γ σ dv S
(28.88)
V
where Γ(σ) is a material characteristic and is a function of stress conditions σ. Lundberg et al. (1947) extended Weibull’s weakest link theory to ductile bearing materials by arguing that a bearing’s life consists of crack initiation life and crack propagation life, and that initiation life predominates the bearing’s life. Based on extensive bearing tests, Lundberg and Palmgren proposed an empirical relationship:
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∫()
τc Ne 1 ln = Γ σ dv ∝ 0 h V S z0
(28.89)
V
where τ0 is the maximum orthogonal shear stress, z0 is the depth below the load-carrying surface at which the maximum shear stress occurs, V is the volume of stressed material, and N is the number of stress cycles before failure with survival probability of S. c, e, and h are exponents. Assume Hertzian contact exists between the rolling elements and raceways. For an assembly of one or more contacts, Equation 28.89 can be expressed in terms of bearing load P by substituting bearing geometry and by applying Hertzian contact theory: n
C L10 = × Lc10 P
(28.90)
where n is an exponent (n = 3 for ball bearings and n = 10/3 for roller bearings). Lc10 is the reference rating life under which the dynamic load rating C is established. In ISO standards, Lc10 = 106 revolutions and, accordingly, C = C1. As shown in Table 28.7, the influences of bearing geometry and material quality are lumped into the dynamic load rating C1. P is the equivalent load and can be calculated from the following equation.
P = XFr + YFa
(28.91)
Fr and Fa are bearing loads in radial and axial directions, respectively. Factors X and Y are determined based on the ratio of Fa /Fr . The values of X and Y are given in ISO 281-1990 and bearing catalogs for specific bearings. 28.8.2.2 Bearing Life Adjustment Factors Actual bearing operating conditions may vary perceptibly from the reference conditions under which the basic dynamic load ratings are established. To permit the quantitative evaluation of environment differences, such as reliability requirement, bearing material quality and processing, operation conditions, and failure criteria, various life adjustment factors have been introduced to the basic life Equation 28.90 by bearing manufacturers. ISO 281-1990 combines three factors into the following life equation to give the adjusted life:
Lna = a1a2a 3L10
(28.92)
Lna is the adjusted bearing life, in revolutions, and a1, a2, and a3 are life adjustment factors. The definition of life adjustment factors and the variables that have been incorporated in each factor are discussed as follows. Life adjustment factor for reliability (a1): For applications that require bearings to have reliability other than 90% (S = 0.9), the life adjustment factor can be obtained from:
ln 1 S a1 = ln 1 0.9
1e
where e is the Weibull slope; e = 1.5 is often recommended.
(28.93)
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Life adjustment factor for special bearing properties (a2): This factor allows improvements in bearing material and process to be incorporated in the bearing life estimate. For bearings made from standard bearing quality alloy and carbon steels, a value of a2 = 1 is recommended. Bearings are also made from higher grade steels with better controlled refining processes. These premium steels contain fewer and smaller inclusion impurities than standard steels and provide the benefit of extending bearing fatigue life where fatigue life is limited by nonmetallic inclusions. When bearings made from premium steels are used, a value of a2 greater than 1 can be adopted, provided that the maximum contact stress is less than 3 GPa and that favorable lubrication conditions are maintained. However, if a reduction in life is expected as the result of a special heat treatment, a reduced a2 value may be considered. Values of a2 range from 0.6 to 6.0 for different chemistries, melting practices, clearness levels and metal working, heat treatment, and surface modification practices. Information on a2 can be found in Zaretsky (1992). Life adjustment factor for operating conditions (a3): Variables considered in the life adjustment factor for operating conditions are load distribution, temperature, and lubrication. The inclusion of load distribution and temperature requires extensive analytical and experimental work. There is no general consent among bearing manufacturers regarding these effects on bearing life. ANSI/ABMA and ISO decided not to give general recommendations. Adequacy of lubrication is central to a3. The ANSI/ABMA and ISO standards are based on nominal lubrication conditions where the lambda ratio λ is equal to or slightly greater than 1. A value of a3 = 1 is recommended for such conditions. a3 increases as λ increases and reduces as λ decreases. Life adjustment factors were introduced to account for variances not included in the basic life model (Equation 28.90). However, choosing appropriate values of life adjustment factors is not as easy as it might appear. Environmental and design factors are often mutually dependent. Changing one factor can affect others. Some factors may not even be multiplicative. Not to restrict various means of combining the appropriate life factors, the ISO bearing life rating technical committee is currently working on a proposal in which a2 and a3 will be replaced by a single factor axyz. This factor is derived from a stressbased life calculation model that incorporates all possible factors affecting the generalized stress field. There are still effects on bearing life that cannot be properly accounted for by life adjustment factors. To incorporate these effects, extensive analytical work and bearing life tests are required. The ISO and ANSI/ABMA may further revise their life adjustment factors and/or life calculation method to reflect the advance of modern bearing technology. It is worth noticing that alternative bearing-life models are also available for bearing fatigue life prediction. These models can generally be classified into two categories: the engineering model and the research model. Tallian (1992) provided a comprehensive review of some of the published models. Discussions of various fatigue-life prediction models are beyond the scope of this handbook and thus are not presented here. The ISO and various bearing manufacturer associations may have their own practice for the selection of life calculation methods and life adjustment factors. For a specific application, seek a bearing manufacturer for advice.
28.9 Bearing Torque Calculation When efficiency and energy consumption of a mechanical system are of concern, a bearing’s frictional torque is often analyzed to determine its acceptance. Bearing torque calculations are also performed to assess bearing heat generation. When a bearing’s torque is obtained under normal running conditions, it is referred to as running torque. For angular-contact ball bearings and tapered roller bearings, torque is often used to determine the appropriate amount of pre-load. Bearing torque obtained under slow speed conditions or setup conditions is referred to as starting torque or setup torque. This section
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addresses bearings’ starting torque as well as running torque and provides empirical and analytical equations for torque predictions of angular-contact ball bearings and tapered roller bearings. The major source of bearing torque derives from the rolling resistance and, if applicable, the sliding resistance at the contacts between the rolling elements and raceways. Bearing torque also results from the sliding resistance at the contacts between the rolling elements and cage, and between the rolling elements and flange, if a flange exists. In moderate and high-speed applications, lubricant churning is an additional source of frictional resistance. The rolling resistance is caused by internal friction in the lubricant and bearing material and by the micro-slip. Sliding resistance results primarily from surface asperity interactions introduced by the sliding and/or spinning motion. Under high-speed and light-load conditions, gross sliding occurs at raceway contacts, which further complicates the torque analysis. A complete analytical approach for bearing torque predictions is very difficult, if not impossible. Torque models used by bearing manufacturers are mostly established through experimentation. However, there are cases where bearing torque models can be derived analytically or semi-analytically.
28.9.1 Starting Torque 28.9.1.1 Starting Torque for Angular-Contact Ball Bearings For angular-contact ball bearings, the starting torque results primarily from the slippage associated with spin motion between the balls and outer raceway. At slow speed, as suggested by inner-raceway control theory, the spin-resisting moment at the inner raceway prevails. Thus, the starting torque M is sought by only considering the spin moment at contacts between the balls and outer raceway. Z
M=
∑M
sj
sin β j
(28.94)
j =1
where Msj is the torque caused by Coulomb friction forces for the contact at the j th azimuth location. Poritsky et al. (1947) integrated the friction force over a contact ellipse and showed that:
()
3 M sj = µ a Wj a j E e j 8
(28.95)
where Wj , aj , and βj are the element load, the half major axis of contact ellipse, and the contact angle at the j th azimuth location, respectively (see Section 28.4). µa is sliding friction coefficient for the dry or boundary lubricated contact. E(ej) is the elliptic integral of the second kind, the value of which can be obtained from mathematical handbooks or from the following empirical equation (Hamrock et al.,1983):
π E e ≈ 1 + − 1 kr 2
()
0 ≤ kr ≤ 1
(28.96)
where kr is defined in Section 28.4. If the bearing is under pure thrust load, as in the bearing setup situation, bearing torque can be expressed in terms of the axial load Fa as:
M = 0.429
µa 1 3 E′ 123 Lubricationand Material
() ()
13 F e E e Re Fa4 3 { k Z sin β Axial Load 1444424444 3
(28.97)
Internal Geometry
where k is the ellipticity ratio at the outer-raceway contact, Re is the geometric average radius at the outer raceway contact, and F(e) can be calculated from equations given in Section 28.4.
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28.9.1.2 Starting Torque of Tapered Roller Bearings Although the “on-apex” design of tapered roller bearings enables rollers to achieve primarily true rolling motions on the raceways at every point along the line of contact, sliding and spinning inherently occur at the rib and roller-end contact for every roller. Under slow-speed or starved lubrication conditions, and when the load on a tapered roller bearing exceeds a certain level, usually about the level of pre-load, the sliding friction at the rib and roller-end contact becomes a decisive factor. Bearing torque caused by rolling resistance at roller and raceway contacts is comparatively negligible. This is due, in large part, to the inability of forming a full lubricant film at the rib and roller-end contact to separate the mating surfaces under these conditions. Severe asperity-to-asperity contact occurs. The friction torque from the rib and roller-end contact is perceptibly high. Therefore, the starting torque of a tapered roller bearing is sought by considering only the sliding and spinning motion at the rib and roller-end contact. The frictional torque at the rib and roller-end contact Mrib consists of two components: a sliding torque Msld and a spinning torque Mspn :
M rib = M sld + M spn
(28.98)
M sld = µ a HFa cos γ
(28.99)
M spn = χµ a HFa cos γ
(28.100)
where γ is the half included angle of rollers; H is the rib contact height and is determined by the bearing internal geometry from Equation 28.33; and χ is a factor depending primarily on rib and roller-end geometry and load distribution. For most applications, χ ≈ 0.5 is a good approximation. The starting torque can be calculated from the following approximation:
( )
M = µ a 1 + χ HFa cos γ ≈ 1.5µ a HFa cos γ
(28.101)
28.9.2 Running Torque 28.9.2.1 Running Torque of Ball Bearings The prediction of running torque for ball bearings is largely dependent on empirical equations. Based on experimental studies, Palmgren (1959) resolved the total torque into a load-related moment Ml and a lubricant viscous moment Mv . The load-related moment reflects elastic rolling resistance, including micro-slip and hysteresis loss, while the viscous-related moment accounts mostly for the losses of lubricant film shearing and bulk lubricant churning.
M = Ml + M v
(28.102)
This general approach has been adopted by various bearing manufacturers. However, the empirical equations established by various bearing manufacturers for Ml and Mv calculations may vary to reflect the differences in internal geometry design. Catalogs of manufacturers must be consulted for appropriate torque calculation equations. NSK uses the following equations for load- and viscous-related moments calculations for ball bearings under high-speed applications:
M l = 0.672 × 10−3 D p0.7 Fa1.2 M v = 3.47 × 10−10 D p3 n1i .4 ηa Qb
( N ⋅mm) ( N ⋅mm)
(28.103) (28.104)
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where Dp Fa ni η Q
= Bearing pitch diameter (mm) = Axial load (N) = Inner ring speed (rpm) = Lubricant viscosity at outer ring temperature (MPa.s) = Lubricant flow rate (kg/min)
The exponents a and b are functions of bearing angular speed only and are given, respectively, by:
a = 24 ni−0.37
(28.105)
b = 4 × 10−9 n1i .6 + 0.03
(28.106)
28.9.2.2 Running Torque of Tapered Roller Bearings Running torque of tapered roller bearings results primarily from the hysteresis and viscous-related rolling resistance at the contacts between the rollers and raceways, and from the slide-and-spin-related sliding resistance at the contacts between the roller-ends and rib face. As the speed of the bearing increases, and when ample lubricant is available at the inlet to the contact, contact surfaces between the roller-ends and rib may be fully separated by a layer of lubricant film. The thickness of the lubricant film at the rollerend and rib contact is approximately twice the film thickness at the roller and raceway contact. Consequently, the friction loss from the roller-end and rib contact reduces substantially. Figure 28.12 shows schematically the variation of frictional torque as a function of bearing speed for tapered roller bearings. For a tapered roller bearing, the running torque is composed of three components: the inner raceway torque Mrace(i), the outer raceway torque Mrace(o), and the rib torque Mrib .
M = M race(i ) + M race(o) + M rib
(28.107)
The raceway torque for a combined radial and axial load is obtained by advancing the work of Aihara (1987). 2 (0.31) Re Ro Fa cos 2γ M race(i ) = φTH φ SP ρD ζ DS α Re l E ′ sin βo
FIGURE 28.12
Bearing torque as a function of speed.
0.31
(28.108)
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2 Fa (0.31) Re Ri M race(o) = φTH φ SP ρD ζ DS α Re l E ′ sin βo
0.31
(28.109)
where
1.76 × 102
φTH =
(28.110)
1 + 0.29 L0.78
is a thermal factor that is introduced to consider the inlet shear heating. φTH is dependent only on
L=
βη0ue2 kcd
(28.111)
– where β is the temperature coefficient of viscosity, ηo is lubricant viscosity, and kcd is the thermal conductivity of lubricant.
αη u φ SP = 0 e Re
0.658
(28.112)
is a speed factor, and ρD = ---1- is the aspect ratio of rollers. D
( ζ DS
(0.31) ) = ZJ a
0.31
(28.113)
(ZJ )
0.31
a
is a load distribution factor. Ja(0.31) is called the extended Sjövall integral and is defined as:
a
xl
1 1 − cos ψ 1 − 2π 2ε − xl
1 0.31 J( ) =
(
∫
)
0.31t
dψ
(28.114)
The values of Ja(0.31) are listed in Table 28.6 for line contact (t = 10/9). Other parameters used in the above equations are defined as follows: α β0 l D Z Re Ri , Ro
= Pressure-viscosity coefficient of lubricant = Contact angle at the outer raceway contact = Roller length = Roller mean diameter = Number of rollers = Effective contact radius = Mean radii of the inner and outer raceways
The rib torque is expressed in a similar form as Equation 28.101:
( )
M rib = 1 + χ µHFa cos γ
(28.115)
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TABLE 28.9 at 20°C
Operating Temperature of Bearings in Different Machines Operating Approximate Operating Temperature (°C)
Bearing Application Cutter shaft of planing machine Bench drill spindle Horizontal boring spindle Circular saw shaft Double-shaft circular saw Blooming and slabbing mill Lathe spindle Vertical turret lathe Wood cutter spindle Calender roll of a paper machine Backup rolls of hot strip mills Face grinding machine Jaw crusher Axle box bearing/locomotive or passenger coach Hammer mill Wire mill roll Vibratory motor Rope stranding machine Vibrating screen Impact mill Ship’s propeller thrust block Vibrating road roller
40 40 40 40 40 45 50 50 50 55 55 55 60 60 60 65 70 70 80 80 80 90
Under normal running conditions, contacts between the roller-ends and rib face are partially or fully separated by a lubricant film. Friction coefficient µ at these contacts is reduced by virtue of the low shearing resistance of lubricant film. The reduction in µ is determined by the load sharing ratio ϑ, which in turn is a function of the lambda ratio (λ):
( )
µ = ϑµ a + 1 − ϑ µ f 1.2
ϑ = e −1.8 λ
(28.116) (28.117)
µa and µf are friction coefficients for dry contact (asperity contact) and lubricated contact, respectively. The empirical approach as outlined for running torque calculations of ball bearings is also applicable for various other bearing types, including tapered roller bearings, when a quick and simple torque estimate under normal operating conditions is desired. The reader is referred to Brandlein et al. (1999) or Harris (1991) for details.
28.10 Bearing Temperature Analysis The expected bearing operating temperature is important for designing the bearing arrangement, lubrication and sealing, and for determining the proper bearing setting and fitting practice. Excluding extraneous heat, the operating temperature of a rolling element bearing under medium speed and load conditions is relatively low. Table 28.9 provides reference values for the average operating temperature in various applications (Brandlein et al., 1999). When exposed to extraneous heat, the temperature that a bearing assumes can be very high. Table 28.10 lists the typical operating temperature for bearings exposed to extraneous heat (Brandlein et al., 1999). The operating temperature of bearings in a mechanical system is determined by the amount of heat generated within the bearing and the amount of heat that is transferred to or away from the bearing.
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Modern Tribology Handbook
Operating Temperature of Bearings Exposed to Extraneous Heat
Bearing Application Electric traction motor Hot gas fans Water pump in a vehicle engine Turbo-compressor Internal combustion engine crankshaft Dryer rolls of paper machine Calender for plastic substances Wheel bearings of kiln truck
Extraneous Heat Electric heat from armature, housing cooled by air Heat transmission to the bearing via the shaft from the impeller exposed to hot gas Heat from cooling water and engine Dissipation of compression heat through shaft Dissipation of combustion heat through crankshaft; cooled housing Heating steam of 140–150°C through bearing journal Supply of heat carrier at 200–240°C through bearing journal Heat radiation and transmission from kiln space
Approximate Operating Temperature (°C) 80–90 90 120 120 120 120–130 180 200–300
The actual system in which bearings are operated can be very complex. However, the principle of temperature analysis remains the same. The principle is based on the law of energy conservation, known as the first law of thermodynamics, and on the rate equations of heat transfer. Consider a control volume, a region of space bounded by control surfaces through which energy and mass can pass. The control volume can be a finite region or a differential (infinitesimal) region. For bearing temperature analysis, it is customary to use finite-control volumes. These control volumes are bounded by surfaces that define a bearing’s boundary dimensions. The law of energy conservation states that the net rate at which thermal and mechanical energy enters a control volume, plus the rate at which thermal energy is generated within the control volume, must equal the rate of increase in energy stored within the control volume. Under steady-state conditions, the amount of heat generated in the bearing is carried away by the net dissipated heat flow.
E˙ gen = E˙ out − E˙ in
(28.118)
To assess the temperature level at which a rolling element bearing operates, the heat generated and the heat transferred through various modes must be determined. This section intends to provide the basic elements being used by the bearing industry in temperature analysis.
28.10.1 Heat Generation The power loss in a rolling element bearing primarily comes from the frictional loss during operation that manifests itself mainly in a form of heat generation. Thus, the rate of heat generation in the bearing can be estimated from the bearing’s frictional torque through the following equation:
H f = ωM
(28.119)
where ω is the rotational speed and M is the bearing torque. For ball bearings and roller bearings, the frictional torque can be obtained by equations given in the previous section. The frictional torque equations for ball bearings are based on empirical formulae. The effect of sliding between the balls and cage pockets is included and so is lubricant churning effect. Thus,
E˙ gen = H f
(28.120)
For roller bearings, however, the friction between the rollers and cage pockets is not considered. In addition, lubricant churning loss is not included in the torque calculation. Lubricant churning effects
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must be accounted for when a bearing operates at a relatively high speed and churns a fair amount of lubricant. The rate of heat generation due to viscous drag can be approximated by:
H l = φVC c v where Z ξ l Drm Dp ωc g cv φVC
(
ZξlDrm Dp ω c
)
2.95
32 g
(28.121)
= Number of rollers = Density of oil-air mist; weight of lubricant in bearing cavity divided by the free volume within the bearing boundary dimension = Effective roller length = Roller mean diameter = Bearing pitch diameter = Orbital angular speed of rollers = Gravitational acceleration = Drag coefficient = Effective volume correction factor, 0 < φ VC < 1
Therefore, for roller bearings, the rate of heat generation is calculated as:
E˙ gen = H f + H l
(28.122)
28.10.2 Heat Transfer Heat generated in bearings is dissipated into the system via three basic modes: conduction, convection, and radiation. It is possible to quantify the heat transfer processes using rate equations. Because heat conduction within a solid and heat convection between the solid and fluid are the primary forms of heat transfer in a bearing system, the rate equations for these two modes are addressed below. The rate equation for radiation, if needed, can be found elsewhere (Pinkus, 1990). 28.10.2.1 Conduction Heat conduction is caused by the diffusion of energy from the more energetic to the less energetic molecules or particles through random motion. The rate of heat transfer via conduction is given by Fourier law:
qcd = kcd A
∂T ∂l
(28.123)
where kcd is the thermal conductivity; A is the area normal to the heat flux; and ∂T/∂l is the temperature gradient along the direction of heat flux. 28.10.2.2 Convection Heat convection is the result of energy diffusion due to random molecular motion and energy transfer due to bulk motion. The actual physical events associated with heat conduction may be quite complex when latent heat exchange is involved. Regardless of the particular nature of the convection heat transfer process, the appropriate rate equation is, in simple form, known as Newton’s cooling law:
(
qcv = hcv A Ts − Tr
)
(28.124)
where Ts is the surface temperature and Tr is the reference temperature of the fluid. For external flow, the free stream temperature Tr = T∝ is used; for internal flow, the reference temperature Tr refers to the mean temperature Tr = Tm. The proportionality constant hcv is the heat convection coefficient or film conductance. It encompasses all the parameters that influence convection heat transfer. In particular, it
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depends on conditions of the boundary layer, which is affected by surface geometry, the nature of fluid motion, and the thermodynamic and transport properties of the fluid. Any study of convection ultimately reduces to a study of determining hcv . The equation provided by Eckert (1950) can be used as an approximation for hcv when considering the convection heat transfer from bearing to oil that contacts the bearing assuming a laminar flow field (Harris, 1991):
u hcv = 0.0332 kcd P c νD p 13 r
12
(28.125)
where kcd and ν are the thermal conductivity and kinematic viscosity of the oil; Pr is the Prandtl number of the oil; and uc is the cage speed. The equation is also suitable for calculating the convection heat transfer from the housing insidesurface to oil, taking uc equal to 1/3 of the cage speed and Dp equal to the housing diameter. The temperature obtained through heat flow analysis using a finite-control volume outlined above gives the average bearing bulk temperature. The actual temperature at the contact between the rolling elements and raceways, or between the roller-ends and flange, can be perceptibly higher than the bulk temperature. For flash temperature analysis at bearing contact, the reader is referred to Gao et al. (2000). There are cases where comprehensive numerical programs must be used to accomplish bearing temperature analysis. When such need arises, seek a bearing manufacturer for advice.
28.11 Bearing Endurance Testing Bearing endurance testing is performed to establish life ratings, conduct quality auditing, and evaluate material, heat treatment, internal geometry, and surface finish improvements. Great variation can be expected despite the fact that bearings are run under “identical” conditions. Thus, statistical methods in planning and interpretation of bearing endurance tests have become a necessity. Accordingly, testing procedures have been developed to optimize the tests based on statistics.
28.11.1 Testing Procedure and Data Analysis Extensive testing results over the years have indicated that bearing life is approximately a power law function of load under a given failure probability. On a log-log plot, the life and load relation falls on a straight line. A family of such straight lines can be obtained, with each corresponding to a certain failure probability. For a given load, the cumulative percentage of failure assumes the Weibull distribution. On Weibull probability paper, the graphical presentation of the relationship between the failure probability and bearing life also assumes a straight line under constant load conditions. Bearing endurance testing is a time-consuming and costly process. To reduce testing time and cost, bearings are usually tested under accelerated conditions. Increasing applied bearing load is perhaps the most commonly adopted means for test acceleration. Care must taken to ensure that the load increase does not alter the bearings’ failure mode. As a general guideline, the maximum applicable load should not cause any plastic deformation. For this consideration, the applied load should not produce a maximum Hertzian stress in excess of 3.3 GPa. Even with accelerated tests, it is neither economical nor possible to test the entire bearing population. Instead, only a finite collection of bearings is tested. Statistical analysis is therefore used to derive the underlying life distribution for the general population from the finite bearing samples. Several methods exist to design testing procedures that reduce testing time. Sudden death testing, sequential testing, and parallel testing are exemplary test strategies. Among the various test methods, sudden death tests are the most recommended test procedures in the bearing industry. In sudden death tests, bearing samples of size m are divided into l groups with n bearings in each group (m = nl). When the first failure occurs in a group, the test is suspended for that group. After all groups are tested, l failures are obtained. Each failure represents an estimate of Lq life that is associated
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with a definite percentage q of the bearing population failing as if the entire population were tested. This percentage is called rank. Because the true rank is not known, estimations are made such that in a long run, the positive and negative errors of the estimate cancel each other. A rank with such property is called median rank and is denoted as q = r0.5. For a detailed discussion on the determination of median ranks, the reader is referred to Johnson (1951). The l estimates of Lq are tabulated in ascending order. The median rank for the j th estimate in l can be obtained approximately from the following equation (Johnson 1974):
r0(.5) = l
j − 0.3 l + 0.4
(28.126)
(l) Plotting Lq as abscissa in logarithm scale and 1/(1 – r 0.5 ) as ordinate in log-log scale, the Weibull distribution of Lq is established. The best estimate of Lq is the median life corresponding to the 50% level. An α% confidence band can be constructed by seeking the (50 ± α/2)% rank values of the life estimate Lq . The reader is referred to Johnson (1974) for detailed discussion. To ensure meaningful results, test controls are required. Caution must be exercised to make sure that the test bearings are free from material and manufacturing defects, and that all parts conform to established dimensional and form tolerances. Moreover, test conditions must be adequate for the variable that is under evaluation. The failure mode is of fatigue nature and no other variables or artifacts alter the outcome of test results. Finally, each failed bearing should be carefully examined to exclude nonfatigue-related failures in the life estimate and to determine if the endurance test series was adequately controlled before and during the test.
28.12 Bearing Failure Analysis Present-day bearings seldom fail when properly installed and maintained. Premature failures result primarily from damage to bearings while handling before and during installation, and damage caused by improper installation, setting, and operation. When premature failure occurs, post-mortem investigations are often conducted to determine the causes of failure so that similar failures can be prevented. In many cases, failures are easily identified visually on bearings, but the root cause of these failures is difficult, if not impossible, to determine. This section intends to provide some possible cause-and-effect relationships to help the reader determine the causes of the most common types of bearing failure so that preventive actions can be taken. A variety of means have been proposed to classify the types of bearing failure, some based on the mechanisms or causes of failure, and others based on failure appearances or failure locations, or a combination of all of the above. In this section, bearing failures are categorized into a number of major types according to the mechanisms. Each type may further be distinguished by specific modes based on the nature of the failure.
28.12.1 Contact Fatigue Contact fatigue can have different appearances, depending on the initial causes. It ranges from surface pitting, peeling, to spalling or flaking, and to section cracking in rare cases. Whatever the initial causes, cyclic stress is the common factor. Pitting. Pitting is indicated by the development of small cavities in the contact path. It is a surface-origin fatigue failure associated primarily with asperity contact and small debris dents that act as stress raisers. Pitting can also result from water corrosion. In such cases, pits usually have rough irregular bottoms (Figure 28.13). Peeling. Peeling is characterized by the formation of cracks that originate at a very shallow angle to the surface and propagate parallel to the surface at depths much smaller than the maximum nominal stress.
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(a)
(b)
FIGURE 28.13 Pitting (a) proceeded with spalling, and (b) caused by acid corrosion. (From Walp, H.O. (1971), Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL. With permission.)
ROLLING
(a)
(b)
FIGURE 28.14 (a) Spall initiated at surface damage. (From Harris, T.A. (1991), Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, New York. With permission.) (b) Spall nucleated at subsurface on cylindrical bearing inner-ring raceway. (From Derner, W.J. and Pfaffenberger, E.E. (1984), CRC Handbook of Lubrication, Vol. II, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Peeling may appear as a frosted area. Thus, it is sometimes called frosting. Peeling occurs when a relatively large percentage of the surface asperities are in direct contact with the mating surface. Asperity-scale plastic deformation is inevitable. The fact that depth of peeling often correlates with surface roughness supports the roughness asperity theory. Progressive superficial pitting can also lead to peeling. Spalling. Spalling is identified by the formation of large and deep cavities in the loaded area (Figure 28.14). In severe cases, a spall can extend along or across the bearing raceway, resulting in the removal of a large volume of material from the surface. The progressive state of spalling is sometimes called flaking. Spalling is considered the most common form of fatigue failure. It can be either surface or subsurface initiated. A surface-originated spall is usually associated with surface defects that act as stress raisers. Debris dents, nicks, and grinding grooves are common sites for surface-originated spalling. Surface-originated spalls often show an arrowhead growth pattern (Figure 28.14a). A multitude of small surface defects results in micro-spalling or pitting, which could potentially culminate in micro-peeling or frosting. Large surface defects tend to
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FIGURE 28.15 (a) Flaking with conchoidal pattern extending across the loaded part of the race. (From Neale, M.J. (1973), Tribology Handbook, John Wiley & Sons, New York. With permission.) (b) A greatly advanced flaking on inner raceway of a cylindrical roller bearing. (From Walp, H.O. (1971), Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL. With permission.)
cause deep and large spalls that penetrate to the depth of the maximum Hertzian shear stress. Subsurfaceoriginated spalling is associated with stress concentrations caused by constituents in the matrix, particularly oxide-type inclusions (Figure 28.14b). When the Hertzian stresses are dominant, cracks propagate transgranularly to the maximum Hertzian stress depth, causing material to break off from the surface. Flaking. Flaking is identified by material break-off with conchoidal and ripple patterns extending evenly across or along the loaded part of the race (Figure 28.15). Although there is no clear distinction between flaking and spalling, some consider flaking as a severe state of spalling. Flaking can be surface or subsurface originated. Surface-originated flaking is usually caused by a multitude of debris dents. Subsurfaceoriginated flaking most likely results from an inclusion inside the material. Edge loading tends to result in flaking more severe on one side of the raceway. Transverse cracking. Transverse cracking seldom occurs for case-carburized bearing components. It mainly affects bearings made from through-hardened steels. Transverse cracking is the result of crack propagation under cyclic tensile stress due to press fit or flexing of the section. This type of failure is usually preceded by another mode of fatigue.
28.12.2 Surface Depression and Fracture Unlike contact fatigue, surface depressions and fractures of bearing components are usually inflicted by static load or impact load. The load for inflicting such damage is greater than those that cause fatigue failure. Under some circumstances, surface depressions themselves may not cause significant concern. However, the consequences are usually detrimental. Whenever possible, this type of damage should be avoided. Brinelling. Brinelling is characterized by the plastic deformation of bearing surfaces due to extreme static or repeated shock loads. Brinelling is identified as dents or grooves on bearing raceways conforming to
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FIGURE 28.16 Brinelling marks on the inner raceway of a tapered roller bearing. (Courtesy of the Timken Company.)
the shape of rolling elements (Figure 28.16). Indentations by foreign objects do not fall into this category. Brinelling may not immediately terminate bearing operation if vibrations caused by brinelling marks do not arouse significant concern. However, the post over-rolling of brinelling marks will lead to crack initiation and subsequent propagation. Bearings with brinelling marks are eventually failed by spalling. Gouges or nicks. Improper handling and installation often inflict bearings with gouges or nicks. Gross grinding operation can also leave nicks on bearing raceways. These surface defects serve as stress raisers and are more likely to cause surface-originated pitting or spalling under cyclic loads. Debris bruises. Debris bruises are surface indentations caused by foreign particles that are entrained into the contacts between the rolling elements and bearing raceways during operation. Unless the surfaces are severely indented, the proceeding failure modes, mostly pitting or spalling, are the ultimate modes of failure. Fracture. On rare occasions, bearings suffer from component fracture, a sudden failure caused primarily by high stresses that exceed the material’s ultimate strength limits. Fracture occurs in bearings with improper tight fit and bearings with high internal tensile stresses that resulted from improper heat treatment. Cage damage or breakage. Cage damage and cage breakage are occasionally seen in bearing applications. Cage damage is usually a result of mishandling or improper installation. Cage breakage is primarily associated with torsional vibration or excessive acceleration and deceleration. Cage breakage can also result from excessive roller skewing due to misalignment or loss of internal geometry.
28.12.3 Mechanical Wear Mechanical wear is a gradual surface deterioration by relative motion. Compared to sliding bearings, mechanical wear in rolling element bearings is far less severe. This is particularly true for cylindrical and tapered roller bearings whose surfaces are subjected primarily to pure rolling contact. There are fundamentally three mechanical wear mechanisms existing in rolling element bearings: adhesive wear, abrasive wear, and fretting wear.
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FIGURE 28.17 (a) Scuffing at a roller end; surface showing spiral scuffing marks; (b) scuffing streaks in raceway of ball thrust bearing caused by light load and high speed. (From Walp, H.O. (1971), Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL. With permission.)
Adhesive wear. Adhesive wear is characterized by material transfer from one surface to the mating surface. It is often found on roller-ends and the corresponding guide face of the flanges, as well as at the interfaces between shafts and inner rings and between housings and outer rings. Adhesive wear can also occur at contacts between the rolling elements and raceways when substantial sliding exists. Adhesive wear appears in various forms, depending on its severity. 1. Scoring. Scoring occurs when lubricant film thickness is inadequate to separate the contact surfaces. Asperity-to-asperity contact occurs. Under high normal and tangential stresses, heat generation at the asperity becomes excessive. It gives rise to strong adhesive or welded junctions at isolated spots. With relative motion between the contacting asperities, junctions are torn apart, resulting in noticeable material transfer from surface to surface. 2. Scuffing. Scuffing is progressive scoring that occurs on a greater scale when the more welded junctions appear and the isolated scoring spots are joined together (Figure 28.17). Scuffing is identified by severe surface roughening, and is accompanied by perceptibly high friction and temperature. 3. Smearing. Smearing is sometimes called galling. It is considered scoring on a grand scale. It involves severe plastic deformation and massive material transfer from surface to surface. Although the final smearing mode may represent the gross breakdown of various surface films and near surface region, it may be triggered by the deterioration in surface topography as a result of progressive scoring or scuffing. 4. Seizing. Seizing is the final stage of adhesive wear. Welding between contacting asperities is so severe that it seizes the bearing, resulting in catastrophic failure. Seizing is, however, rarely seen in rolling element bearings. Abrasive wear. Abrasive wear occurs when asperity-scale plastic deformation leads to material removal and wear debris. It involves abrasive foreign particles harder than bearing materials, often nonmetallic. Abrasive wear is identified by microscopic furrows and the dulling of contact surfaces (Figure 28.18). Excessive wear results in a loss of bearing dimension or internal geometry, which in turn affects bearing performance. Fretting. Fretting results from micro-movement between mating surfaces. Fretting mostly occurs during transportation or machine idling. It is recognizable by the grooves worn into the raceway by vibrational movement between the rolling elements and raceways (Figure 28.19a). Fretting also occurs between bearing rings and the surfaces that they contact (Figure 28.19b). It usually indicates an inadequate fit. Fretting fatigue is now recognized as one of the outcomes of continuous fretting.
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FIGURE 28.18 Advanced stage of abrasive wear and corrosion in inner raceway and rollers of a spherical roller bearing. (From Walp, H.O. (1971), Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL. With permission.)
FIGURE 28.19 (a) Fretting grooves worn into the raceways by axial movement of the rollers during transportation. (Courtesy of the Timken Company.) (b) Fretting on the outer diameter of an outer race ring caused by nonuniform seat in housing. (From Walp, H.O. (1971), Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL. With permission.)
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FIGURE 28.20 Electric arc damage on bearing raceways showing fluted patterns. (From Harris, T.A. (1991), Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, New York. With permission; Widner, R.L. and Littmann, W.E. (1976), Bearing Damage Analysis, NBS 423, National Bureau of Standards, Washington, D.C.)
28.12.4 Corrosion Corrosion is a chemical wear. The common forms of corrosive wear seen in bearing applications are etching and hydrolysis. Acid etching. Acid etching occurs when a bearing operates in an acid environment. Acid substances react with and dissolve steel surfaces to form salts. As a result, numerous irregular and dark-bottomed pits are created on bearing surfaces, a condition that subsequently leads to surface-originated spalling. Hydrolysis. Bearings exposed to mist conditions are susceptible to hydrolysis, a corrosion by oxidation. Hydrolysis is identified by localized irregular pits. The affected area may appear red to dark brown, depending on the state of oxidation.
28.12.5 Electric Arc Damage Improperly grounded electrical equipment can cause bearings to suffer from electric arcing damage by localized material melting and metallurgical property alteration. Apparent visual effects range from random isolated pits to fluted patterns composed of numerous pits (Figure 28.20).
28.12.6 Discoloring and Overheating Discoloring is associated with heat generation at the contact where gross sliding occurs. The heat oxidizes contact surfaces, producing oxidation colors from dark brown to blue. Excessive heat can cause all parts of a bearing to show tempering colors. Overheating causes the lubricant to decompose, diminishing its ability to lubricate. The major impact is, however, the loss of material strength to contact fatigue. Table 28.11 lists the most common failure modes and the possible causes.
Appearance
⊗
Pitting
⊗
⊗
⊗ ⊗
⊗
⊗
Peeling
⊗ ⊗
⊗
⊗ ⊗
⊗
⊗
⊗ ⊗
Brinelling
⊗ ⊗
⊗
Nicks
⊗ ⊗
Debris bruises
⊗
⊗ ⊗
Fracture
⊗
⊗
⊗
⊗
⊗ ⊗ ⊗
Cage break/damage
⊗
⊗
⊗
⊗ ⊗
⊗ ⊗ ⊗
⊗
⊗
Wear
Fretting
⊗ ⊗
⊗
⊗
⊗
Corrosion
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
Electric Arcing
Overheating
⊗ ⊗
⊗ ⊗
Material/Surface Condition Improper heat treatment Inclusion Poor surface finish Inadequate surface profile Mounting Improper storage Improper handling Incorrect assembling Incorrect setting Misalignment Deflection Improper fit Environment Water in lubricant Ductile foreign particles Brittle foreign particles Defective seals Housing cleanness Chemical contamination Electric current Operating Conditions Impact or shock load High static overload Heavy load Vibration or oscillations Lubrication Quality of lubricant Quantity of lubricant
Possible Causes
1090
⊗
⊗
⊗ ⊗
⊗
Spalling
⊗ ⊗
Flaking
⊗
Cracking
Failure Mode
Adhesion
Surface Depression and Fracture
Abrasion
Contact Fatigue
Acid etching
Mechanism
Hydrolysis
Failure Modes and the Possible Causes
Discoloring
TABLE 28.11
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References Ai, Xiaolan and Sawamiphakdi, K. (1999), Solving elastic contact between rough surfaces as an unconstrained strain energy minimization by using CGM and FFT techniques, ASME J. Tribol., 121, 639-647. Aihara, S. and Dowson, D. (1978), A study of film thickness in grease lubricated elastohydrodynamic contacts, in Proc. 5th Leeds-Lyon Symp. Tribology, Dowson, D. et al. (Eds.), Mech. Eng. Pub., London, 104-115. Aihara, S. (1987), A new running torque formula for tapered roller bearings under axial load, ASME J. Tribol., 109, 471-478. Boehringer, R.H. (1992), Grease, in ASM Handbook, Vol. 18 Friction, Lubrication and Wear Technology, Henry, S. (Ed.), ASM International, 123-131. Brandlein, J., Eschmann, P., Hasbargen, L., and Weigand, K. (1999), Ball and Roller Bearings — Theory, Design and Application, 3rd ed., John Wiley & Sons, New York. Castle, P. and Dowson, D. (1972), A theoretical analysis of the starved elastohydrodynamic lubrication problem for cylinders in line contacts, in Elastohydrodynamic Lubrication Symposium, Proc. Inst. Mech. Eng., 131, 131-137. Chetta, G.E., Hosang, G.W., Needelman, W.M., Kannel, J.W., and Zaretsky, E.V., Chapter 5, Lubrication, in STLE Life Factors for Rolling Bearings, Zaretsky, E.V., (Ed.), STLE Pub. SP-34, 183-231. Chevalier, F., Lubrecht, A.A., Cann, P.M.E., Colin, F., and Dalmaz, G. (1998), Film thickness in starved EHL point contacts, ASME J. Tribol., 120, 126-133. Chittenden, R.J., Dowson, D., Dunn, J.F., and Taylor, C.M. (1985a), A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts, Part I, Proc. R. Soc. London, Ser. A, 397, 245-269. Chittenden, R.J., Dowson, D., Dunn, J.F., and Taylor, C.M. (1985b), A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts, Part II, Proc. R. Soc. London, Ser. A, 397, 271-294. Chiu, Y.P. (1974), An analysis and prediction of lubricant film starvation in rolling contact systems, ASLE Trans., 17, 22-35. Dalmaz, G. and Nantuo, R. (1987), An evaluation of grease behavior in rolling bearing contacts, Lubric. Eng., 43(12), 905-915. Derner, W.J. and Pfaffenberger, E.E. (1984), Rolling element bearings, CRC Handbook of Lubrication, Vol. II, Booser, E.R. (Ed.), CRC Press, Boca, Raton, FL. Dowson, D. (1968), Elastohydrodynamics, Proc. Institution of Mechan. Eng., 182, Part 3A, 151-167. Dowson, D. and Higginson, G.R. (1961), New roller-bearing lubrication formula, Engineering (London), 192, 158-159. Dowson, D. and Higginson, G.R. (1977), Elasto-Hydrodynamic Lubrication, SI ed., Pergamon Press. Eckert, E. (1950), Introduction to the Transfer of Heat and Mass, McGraw-Hill, New York. Elrod, H.G. and Adams, M.L. (1974), A computer program for cavitation and starvation problems, in Proc. 1st Leeds-Lyon Symp. Tribology, 37-41. Eschmann, P. (1964), Das Leistungsvermogen der Walzlager, Springer, Berlin. Gao, J., Lee, S.C., Ai, Xiaolan, and Nixon, H. (2000), An FFT-based transient flash temperature model for 3-D rough surface contacts, ASME J. Tribology, 122, 519-523. Gohar, R. (1988), Elastohydrodynamics, Ellis Horwood, Chichester, England. Gupta, P.K. (1975), Transient ball motion and skid in ball bearings, ASME J. Lubr. Technol., 97, 261-269. Gupta, P.K. (1979a), Dynamics of rolling element bearings. I. Cylindrical roller bearing analysis, ASME J. Lubr. Technol., 101, 293-304. Gupta, P.K. (1979b), Dynamics of rolling element bearings. II. Cylindrical roller bearing results, ASME J. Lubr. Technol., 101, 305-311. Gupta, P.K. (1979c), Dynamics of rolling element bearings. III. Ball bearing analysis, ASME J. Lubr. Technol., 101, 312-318.
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Gupta, P.K. (1979d), Dynamics of rolling element bearings. IV. Ball bearing results, ASME J. Lubr. Technol., 101, 319-326. Hamrock, B.J. and Brewe, D. (1983), Simplified solution for stresses and deformations, ASME J. Lubr. Technol., 105,171-177. Hamrock, B.J. and Dowson, D. (1977a), Isothermal elastohydrodynamic lubrication of point contacts. III. Fully flooded results, ASME J. Lubr. Technol., 99, 264-276. Hamrock, B.J. and Dowson, D. (1977b), Isothermal elastohydrodynamic lubrication of point contacts. IV. Starvation results, ASME J. Lubr. Technol., 99, 15-23. Harris, T.A. (1966), An analytical method to predict skidding in high speed roller bearings, ASLE Trans., 9, 229-241. Harris, T.A. (1971a), Analytical method to predict skidding in thrust-loaded, angular-contact ball bearings, ASME J. Lubr. Technol., 93, 17-24. Harris, T.A. (1971b), Ball motion in thrust-loaded, angular contact bearings with Coulomb fraction, ASME J. Lubr. Technol., 93, 32-38. Harris, T.A. (1991), Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, New York. Hartnett, M.J. (1984), “Roller Bearing with Specially Constructed Rollers,” U.S. patent 4,456,313. Johnson, L.G. (1974), The Statistical Treatment of Fatigue Experiments, Elsevier, The Netherlands. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press, Cambridge, Great Britain. Johnson, L.G. (1951), The median ranks of sample values in their population with an application to certain fatigue studies, Indust. Math., 2, 1-9. Jones, A. (1959), Ball motion and sliding friction in ball bearings, Transactions of the ASE, Ser. D., J. Basic Eng., 81, 1-12. Jones, A.B. (1946), Analysis of Stresses and Deflections, New Departure Engineering Data, General Motors Corp., Bristol, CT. Jones, A. (1964), The mathematical theory of rolling-element bearings, Mechanical Design and Systems Handbook, Rothbart (Ed.), McGraw-Hill, New York. Kingsbury, E. (1973), Cross flow in a starved EHD contact, ASLE Trans., 16, 276-280. Kunert, K. (1961), Spannugsverteilung im Halbraum bei elliptischer Flachenpressungsverteilung uber einer rechteckigen Druckflache, Forschung anf d. Gebiet d. Ingenieur-Wesens, 27, 6. Lansdown, A.R. (1996), Lubrication and Lubricant Selection; A Practical Guide, MEP Publications, London and Bury St. Esmunds. Lundberg, G. (1939), Elastische Beruhrung Zweier Halbraume, Forsch Gebiete Ingenieurw, 10, 201-211. Lundberg, G. and Palmgren A. (1947), Dynamic capacity of rolling bearings, Acta Polytech. Mech. Eng. Ser. 1, R.S.A.E.E. No. 3, 5-50. McEwen, E. (1949), Stresses in elastic cylinders in contact along a generatrix, Philosophical Mag., 40, 454-459. Neale, M.J. (1973), Tribology Handbook, John Wiley & Sons, New York. NSK (1994), Technical Report, Catalog No. E728 1994C-11. Palmgren, A. (1959), Ball and Roller Bearing Engineering, 3rd ed., S.H. Burbank & Co. Inc., Philadelphia. Pinkus, O. (1990), Thermal Aspects of Fluid Film Tribology, ASME Press, New York. Poon, S.Y. and Glanfield, G.A. (1978), Roller profile optimization, Proc. Int. Conf. Power Transmission, 5, 34-45. Poritsky, H., Hewlett, C.W., Jr., and Coleman, R.E., Jr. (1947), Sliding friction at ball bearings of the pivot type, J. Appl. Mech., 14(4), 261-268. Rahnejat, H. and Gohar, R. (1979), Design of profiled taper roller bearings, Tribol. Int., Dec., 269-275. Reusner, H. (1987), The logarithmic roller profile - the key to superior performance of cylindrical and tapered roller bearings, SKF, Ball Bearing J., No. 230. Sackfield, A. and Hills, D.A. (1983a), Some useful results in the classical Hertz contact problem, J. Strain Anal., 18(2), 101-105. Sackfield, A. and Hills, D.A. (1983b), Some useful results in the tangential loaded Hertz contact problem, J. Strain Anal., 18(2), 107-110.
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Shevchenko, R. and Bolan, P. (1957), A Visual Study of Ball Motion in a High-Speed Thrust Bearing, SAE preprint No. 37, SAE Annual Meeting. Sjövall, H. (1933), The load distribution within ball and roller bearings under given external radial and axial load, Teknisk Tidskrift, Mek., h. 9. Sliney, H.E. (1992), Solid Lubricants, in ASM Handbook, Vol. 18, Friction, Lubrication and Wear Technology, Henry, S. (Ed.), ASM International, 113-122. Tallian, T.E. (1972), The theory of partial elastohydrodynamic contacts, Wear, 21, 49-101. Tallian, T.E. (1992), Simplified Contact Fatigue Life Prediction Model. I. Review of published models, ASME J. Tribol., 114, 207-213. Taniguchi, M., Dowson, D., and Taylor, M.C. (1996), The effect of spin motion upon elastohydrodynamic elliptical contacts, in Proc. 23rd Leeds-Lyon Symp. Tribology, Dowson, D. et al. (Eds.), 599-610. Walp, H.O. (1971), Recognition of the causes of bearing damage as an aid in prevention, Interpreting Service Damage in Rolling Type Bearings — A Manual on Ball & Roller Bearing Damage, ASLE, Park Ridge, IL, 8-27. Wedeven, L.D., Evans, D., and Cameron, A. (1971), Optical analysis of ball bearings starvation, Trans. ASME, Series F, 93, 349-363. Weibull, W. (1939), A statistical theory of the strength of materials, Proc. R. Swedish Inst. Eng. Res., No. 151, Stockholm. Widner, R.L. and Littmann, W.E. (1976), Bearing Damage Analysis, NBS 423, National Bureau of Standards, Washington, D.C. Wolveridge, P.E., Baglin, K.P., and Archard, J.F. (1971), The starved lubrication of cylinders in line contact, Proc. Inst. Mech. Eng., 185, 1159-1169. Zaretsky, E.V., STLE Life Factors for Rolling Bearings, STLE Pub. SP-34, 1992.
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29 Gears 29.1 29.2
Introduction ................................................................... 1095 Gear Types ...................................................................... 1096 Spur Gears • Helical Gears • Bevel and Hypoid Gears • Worm Gears
29.3
Tribological Failure Modes............................................ 1097 Macro-pitting (Spalling) • Micro-pitting (Gray Staining) • Scuffing • Mild Wear
29.4
Full-Film Lubrication Performance.............................. 1101 Spur Gears • Helical Gears • Spiral Bevel and Hypoid Gears • Worm Gears
29.5
Mixed Lubrication Characteristics................................ 1110 Asperity Contact Pressure • Full Simulation of Asperity Contact and Fluid Film Pressure • A Macro–Micro Approach to Mixed Lubrication • Asperity Contact Temperature
29.6
Modeling of Tribological Failures in Gears ................. 1115 Conventional Pitting Life Model • Prospective Pitting Life Model • Conventional Scuffing Model • Prospective Scuffing Model • Wear Modeling in Spur Gears
Herbert S. Cheng Northwestern University
29.7 29.8
Failure Tests .................................................................... 1122 Conclusions .................................................................... 1124
29.1 Introduction Gear teeth contacts have been recognized as one of the most complicated applications of tribology. In an earlier review (Radovich, 1984) on gear lubrication, it was pointed out that despite the extensive research in gear lubrication, it has not been possible to reduce the “art” of gear lubrication to a science. There is no good substitute for practical experience in gear design. This situation is gradually changing, mainly due to rapid developments in elastohydrodynamic lubrication (EHL) and the effects on gear tribological failures. Dudley (1980) provided extensive coverage on how the relation between the pitting initiation life and contact stresses improves as the regime of lubrication or the EHL film changes from boundary to mixed and finally to full film lubrication. In each regime, Dudley proposed a different empirical exponent to relate the contact stress and fatigue life. This relation was also suggested by Kubo et al. (1991) in their review of gear lubrication. They also contributed a chart for determining the regime of lubrication when the EHL film thickness and the gear teeth surface roughness are known. It is widely recognized that gear scuffing is most strongly related to the flash temperature in a sliding gear contact. When it exceeds the critical temperature of the lubricant, scuffing is initiated. Most present scuffing predictive models are based on this argument. Kubo et al. (1991) compiled an excellent list of the present major scuffing models, from the well-known Blok-Kelly’s flash temperature formula to the complicated ISO proposal for estimating the scuffing load. 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
1095
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The current models for predicting gear tribological failures have been reviewed quite thoroughly in recent literature. It is not the intent here to add merely another updated review. Rather, the objectives here are to review recent research on EHL and tribological failures related to gear lubrication, pitting, scuffing, and wear, and to delineate future prospects in developing more advanced predictive pitting and scuffing models for gears.
29.2 Gear Types Among the many gear types, the most commonly used ones are spur, helical, bevel, and worm gears. The lubrication process and lubrication-related failures in these gears have a great deal in common because the loads in these gears are all transmitted through Hertzian lubricated contacts known as elastohydrodynamic (EHL) contacts. A brief description is given as to the geometry and operation of these gears.
29.2.1 Spur Gears Geometrically, spur gears are the simplest of all gears. They are perhaps the most commonly used gears in general applications. The spur teeth are parallel to the shaft and transmit motion and power between two parallel shafts, as shown in Figure 29.1. Except for some very special cases where extremely accurate motion is required, the tooth shape of most spur gears is of the involute form because of its tolerance to any change of center distance and ease of manufacture. Figure 29.2 shows a pair of spur gear teeth beginning to contact at point K2 at the tip of the driven gear. The force is transmitted along the line of action AB, which is tangent to both base circles and is inclined at an angle φ, known as the pressure angle, from the common tangent of the two pitch circles. The contact force always acts along the path of action during FIGURE 29.1 Spur gears. the entire engagement. At the beginning of the contact between one pair of teeth, there is usually a preceding pair in contact, shown at K1, at a distance p cosφ away from K2, where p is the circular pitch of the gears. Just prior to contact at K2, the preceding pair takes the full load. As soon as the contact begins, the load is shared between the two pairs. Before the advent of EHL, the lubrication process in gear teeth contacts was only understood qualitatively. With the rapid development of EHL, the lubrication characteristics for spur gears can now be quantified either by line contact EHL analyses for straight spur gears or by point contact EHL analyses for gears with axially modified profiles. Further discussion is given later in the section on lubrication performance of spur gears.
29.2.2 Helical Gears Like spur gears, helical gears are usually employed to transmit motion between two parallel shafts. In helical gears, the teeth are cut at an angle to the shaft axis, known as the helix angle, ψ, as shown in Figure 29.3 for a double-row-helical or herringbone gear. This arrangement allows helical gears to have more pairs of teeth in contact during the engagement compared to spur gears. It usually runs more quietly and has less vibration. The disadvantage of single-row-helical gears is that the tooth load includes a thrust component, requiring larger supporting bearings for the shaft and complicating bearing selection in that thrust loads must be supported. The contact pattern on the tooth face is not a line or elliptical contact with the major axis parallel to the shaft axis as in the case of spur gears. Instead, the major axis of the contact is now inclined to the shaft axis. The length of the major axis also changes during the engagement as it traverses from the root to the tip of the facing. The lubrication characteristics of helical gears will be described later in this chapter.
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Gears
FIGURE 29.2
Load sharing between two spur-gear contacts.
29.2.3 Bevel and Hypoid Gears Bevel gears are used to transmit motion between two non-parallel, usually orthogonal, co-planar intersecting shafts. If the bevel gear teeth are cut straight, they are called straight bevel gears, as shown in Figure 29.4. If the teeth are cut curved with a zero spiral angle in the mid-section, as shown in Figure 29.5, they are called zerol bevel gears. For bevel teeth that are cut along a spiral path, they are known as spiral bevel gears. Spiral bevel gears can carry a higher load capacity and run more quietly than other types of bevel gears. Figure 29.6 shows a typical spiral bevel gear. Hypoid gears are used for transmitting motion between two non-intersecting orthogonal shafts. Their tooth form resembles that of the spiral bevel except the pinion shaft is offset either above or below the gear shaft, as shown in Figure 29.7.
FIGURE 29.3 bone) gears.
Double-helical (herring-
29.2.4 Worm Gears Worm gears are primarily intended for transmitting motion between two-intersecting orthogonal shafts similar to hypoid bevel gears. However, the geometries of these two systems are very different. The driving member is a cylindrical worm resembling a screw, and it meshes with basically a helical gear. The speed ratio of worm gear sets can be large and the sliding can be very high. For this reason, worm gears are used mostly for light loads. Figure 29.8 shows a typical worm gear set.
29.3 Tribological Failure Modes There are at least four major modes of gear tooth failure that are directly related to deterioration of lubrication or change of lubrication performance in gear tooth contact such as loss of lubricant film thickness, rapid increase in contact temperature, and excessive foreign particles in the lubricant. These
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FIGURE 29.4
Straight bevel gears.
FIGURE 29.5
Zerol bevel gears.
FIGURE 29.6
Spiral bevel gears.
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FIGURE 29.7
Hypoid gears.
FIGURE 29.8
Worm gears.
failure modes include macro-pitting or spalling; micro-pitting or gray staining; scuffing; and mild wear. Brief discussions are given as to the characteristics and some possible mechanisms of these failure modes.
29.3.1 Macro-pitting (Spalling) Macro-pits can appear almost anywhere on the tooth facing. However, they are primarily found near the pitch line of spur and helical gears. Some of these pits have shapes like a shell. Figure 29.9 depicts such a spall located slightly above the pitch line of a helical gear (Dudley, 1980). These pits can have dimensions comparable to Hertzian contact size. They can originate on the surface due to intensified stresses around large asperity contacts or surface defects such as nicks and furrows. Also, they can be subsurface initiated from a material inclusion, as in the classical case of subsurface fatigue in rolling bearings and lubricated rollers. For subsurface macro-pitting, lubrication does not have a strong effect. It is more strongly influenced by the size, density, and material characteristics of the inclusions. Surface initiated macro-pitting is strongly related to lubrication because it strongly affects the intensity of the near-surface stresses.
29.3.2 Micro-pitting (Gray Staining)
FIGURE 29.9 ened pinion.
Pitting of case-hard-
When lubrication deteriorates in gear teeth contacts, the load is borne mainly by the asperity contacts. Under this condition, the mode of failure often shifts from macro-pitting to micro-pitting, particularly for high-quality or nearly inclusion-free materials. Micro-pitting is caused by rapid propagation of groups of cracks induced by multiple asperity contacts. These shallow pits are small — in the micron range — but cover a wide area, resulting in grayish patches. For this reason, they have often been referred to as “gray staining” or sometimes as “frosting.” Dudley (1980) showed a typical frosting appearance of micro-pitting on a high speed case carburized gear; it is reproduced here in Figure 29.10. Micro-pitting can be a slow progressive degeneration and is often considered to be nondestructive unless it leads to larger sized macro-pits.
29.3.3 Scuffing When there is substantial sliding between a lubricated rolling contact, excessive temperature at the sliding asperity contacts can cause all protective lubricating films to break down. The softer asperities can deform
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FIGURE 29.10
Micro-pitting (frosting) on a high-speed carburized gear.
FIGURE 29.11
Typical scuffing failure in gears.
plastically and transfer to the mating surface. This is usually accompanied by a rapid increase in wear rate or even seizing of the sliding pair. This phenomenon is known as scuffing, which in severe cases can lead to seizure. In gear tooth contacts, scuffing can occur in the contacting areas wherever the slide-toroll ratio is the highest. For spur and helical gears, scuffing is usually found near the tip or root of the tooth facing where the slide-to-roll ratio is the highest. Scuffing can also be found in other gears, such as spiral bevel, hypoid, and worm gears, where high sliding occurs. In Figure 29.11, Shipley (1991) shows a typical scuffing failure on the tooth facings of a medium hardened spur gear. The scuffing marks are clearly shown both at the tip and root areas. Another example of moderate scuffing of a medium hardened spur gear can also be seen in Figure 29.12 (Shipley, 1991). In this case, the scuffing marks did not cover the entire length of the tooth facing, indicating that the scuffing was still in the progressive stage.
29.3.4 Mild Wear When the operating conditions are not severe enough to cause major failure modes such as pitting and scuffing described earlier, materials can still be removed slowly by mild wear among sliding asperities. Mild wear can be due to adhesion, abrasion, and corrosion, as well as fatigue. It is not considered a failure mode unless the change of teeth geometry due to mild wear introduces intolerable gear performance, such as excessive dynamic loads, noise, as well as pitting or scuffing. In mild adhesive wear, the softer materials at the unlubricated sites in the sliding asperity contact are adhered, sheared, and removed. The wear rate depends on the asperity contact temperatures, which determine the fraction of the unlubricated area. When the asperity contact temperature reaches some critical range, the rate of adhesive wear would increase very rapidly and scuffing failure would ensue. In abrasive wear, the softer material is usually abraded by the harder mating gear.
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FIGURE 29.12
Scuffing failure in misaligned gears.
FIGURE 29.13
Typical abrasive wear in gears.
Figure 29.13 (Shipley, 1991) shows an example of heavily worn spur gear teeth due to two-body abrasion from a hardened, rough mating gear. In this case, the deeply abraded longitudinal grooves in the direction of sliding are clearly visible. This clearly shows an extreme case of abrasive wear. Corrosive mild wear in gears is usually introduced by lubricant additives intended for preventing scuffing failure, such as extreme pressure (EP) additives. The rough asperities are slowly corroded and abraded away, leaving a smooth and polished surface. A typical example of corrosive wear of a spiral bevel gear is given by Shipley (1991), and reproduced here in Figure 29.14. When the wear rate of corrosive mild wear is controlled at a reasonable level, it is highly desirable because it yields a higher specific film thickness, the ratio of film thickness to roughness, improves the elastohydrodynamic lubrication, and reduces the hazard of pitting and scuffing failure.
29.4 Full-Film Lubrication Performance For most gears, the geometry of the tooth contact at any point along the contacting path during the entire engagement can be determined from the Hertzian theory for two cylinders or ellipsoids. From the kinematic relations of gears, the rolling and sliding velocities can also be determined. With these inputs, one can determine the lubrication performance of the gears using recent EHL theories. The two primary concerns are: 1. Where are the areas of very thin film thickness that can initiate surface distress and lead to contact fatigue, and what are the levels of these thin films? 2. Where are the areas of very high surface contact temperature that can initiate scuffing, and what are the levels of these contact temperatures?
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FIGURE 29.14
Modern Tribology Handbook
Polishing in spiral bevel gears.
Ideally, a most desirable gear lubrication analysis should include the following features: • Transient effects due to variable load, contact radius, and rolling and sliding velocities • A coupled temperature and film thickness analysis to determine the variable bulk surface temperature distribution of both gears • Surface roughness effects on lubrication • Accurate friction models for the fluid film and asperity contacts Such complete analyses are yet to be developed for all the gears discussed here. However, for spur gears, a comprehensive analysis and software were developed by Wang et al. (1981). This analysis includes most of the effects listed above. Similar analyses were also recently contributed by Hua et al. (1995) and Larssen (1997). For helical gears and worm gears, Simon (1985, 1988, 1997) employed a full thermal EHL analysis and developed a list of empirical relations to study the effects of gear tooth geometry, lubricant viscosity, minimum film thickness, and pitch line velocity on the tooth load-carrying capacity, friction factor, and the relative maximum lubricant temperature. These analyses are summarized in the following sections.
29.4.1 Spur Gears For involute spur gears, Wang et al. (1981) developed a computer analysis to predict the variation of dynamic load, surface temperature, as well as the lubricant film thickness along the contacting path during the engagement of a pair of gears. The dynamic load analysis is not coupled with the other analyses and is solved independently. The other unknowns, including the lubricant film thickness, bulk equilibrium surface temperature, and total flash temperature, are solved simultaneously by an iterative process. The lubricant film thickness is based on a transient EHL analysis developed by Vichard (1971). This analysis includes the squeezefilm effect. The bulk-equilibrium surface temperature distribution was solved by a finite-element analysis, and the total flash temperature was solved by a simplified energy equation using a limiting shear concept for the heat dissipation in the film. Results were obtained for a pair of high-speed gears used in a gear experiment by Townsend et al. (1973). Figures 29.15 through 29.18 show typical variations of the dynamic load, lubricant film thickness, bulk-equilibrium surface temperature, and the total flash temperature along the line of action. Townsend and colleagues also studied the effects of gear geometry, load, speed, and ambient temperature on the gear lubrication performance. Figures 29.19 to 29.22 show that among the operating variables, the lubrication performance is improved more strongly by increasing the inlet viscosity, decreasing the ambient temperature, or increasing the convective heat transfer coefficient on the gear surface. Increasing the pitch line velocity gives only a slight improvement in lubrication performance at high speeds.
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FIGURE 29.15
Dynamic load variation (gear ratio = 1, NT = 28, dia. pitch = 8).
FIGURE 29.16
Dynamic film thickness distribution.
FIGURE 29.17
Distribution of equilibrium surface temperature, n = 1637 rpm.
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FIGURE 29.18
Distribution of total flash temperature, n = 1637 rpm.
FIGURE 29.19
Effect of lubricant viscosity on lubrication performance.
FIGURE 29.20
Effect of ambient temperature on lubrication performance.
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FIGURE 29.21
Effect of surface heat transfer coefficient on lubrication performance.
Effect of Speed
FIGURE 29.22
Effect of surface speed on lubrication performance.
More recently, Hua et al. (1995) employed a full EHL analysis and obtained the transient lubricant film thickness and pressure in spur gears along the line of action. They investigated the effect of gear ratio and module on the film thickness and pressure. Figures 29.23 and 29.24 show that as the gear ratio increases, the central film thickness increases markedly at the recess end, but only has a very slight reduction at the approach end. If the module is doubled without changing the size of the gear pair, the film thickness would decrease slightly at the recess end of the gear with the larger module, as shown in Figure 29.24. More recently, Larson (1997) included the effects of a non-Newtonian fluid and extended the EHL analysis for a pair of gears with a small contact ratio. Some interesting features of film thickness variations were found at the load transition points, as shown in Figure 29.25.
29.4.2 Helical Gears Although helical gears are used extensively in automotive transmissions, marine transmissions, and other high-speed applications, there have been relatively fewer contributions on lubrication of helical gears
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FIGURE 29.23
Effect of gear ratio on the variation of the central film thickness along the line of action.
FIGURE 29.24
Variation of central film thickness along the line of action with constant center distance.
compared to the work on spur gears. The application of full EHL including thermal effects was accomplished by Simon (1988). A thermal EHL computer program was employed to calculate the pressure and temperature distribution in the oil film of a typical helical gear set consisting of two identical gears of 730.8-mm outside diameter running at 3000 rpm. The minimum film was prescribed. Figures 29.26 and 29.27 show, respectively, the film pressure and temperature distributions in the contact region. The pressure variations in the central contact area show features common to those found in other EHL analyses. However, the temperature variations seem to deviate somewhat from the previous EHL results for rollers. Simon (1988) also analyzed the effect of numerous other variables on the lubrication performance including load, friction, and maximum temperature. Figures 29.28 through 29.30 show, respectively, the effect of face width, pitch line velocity, and ambient oil viscosity on the lubrication performance.
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FIGURE 29.25
Minimum film thickness along the line of action.
FIGURE 29.26
Pressure distribution in oil film.
29.4.3 Spiral Bevel and Hypoid Gears Lubrication in spiral bevel and hypoid gears falls into the same category as spur and helical gears. They also can be analyzed by EHL theories. However, their contact geometry and the sliding velocity vector are considerably more complicated than for spur and helical gears. Perhaps for this very reason, few lubrication analyses are found on these gears.
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FIGURE 29.27
Temperature distribution in oil film.
FIGURE 29.28
Performance curves for face width variation.
Chao et al. (1981) developed a computer solution for the dynamic load, lubricant film thickness, and surface temperatures in spiral bevel gears. Similar to the approach used by Wang et al. (1981), the dynamic load analysis is uncoupled from the lubrication analysis for a typical spiral bevel pinion, gear, and supporting bearing system (shown in Figure 29.31). The stiffness of the contacting pinion and gear is solved by an existing finite-element code as a function of the contact position. A separate computer solution was developed to predict the bulk surface temperature, flash temperature, and film thickness along the contacting path.
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FIGURE 29.29
Performance curves for pitch velocity variation.
FIGURE 29.30
Performance curves for ambient oil viscosity variation.
Figures 29.32a and b show typical variations of the dynamic load factor with the pinion shaft speed for a set of spiral bevel pinion and gear systems investigated experimentally at NASA–Lewis Research Center. It is seen that the peaks of the dynamic load are considerably lower for the case of a higher damping coefficient. Figures 29.33 to 29.35 show typical variations of film thickness distributions, bulk temperature, and total flash temperatures along the contacting path. Finally, the effect of increase in viscosity on the lubrication performance is demonstrated in Figure 29.36. As expected, an increase in viscosity would improve the lubrication performance with a much thicker lubricant film, and a slight drop in both bulk and flash temperatures.
29.4.4 Worm Gears A series of lubrication performance analyses were contributed by Simon (1985, 1997) on worm gears by employing a thermal EHL analysis. They provide a considerable pool of knowledge on worm gear lubrication. In Figures 29.37 and 29.38, it is shown that a new type of worm geometry can improve considerably the load capacity and friction factor over the conventional configurations.
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FIGURE 29.31
Modern Tribology Handbook
Geometry and mathematical model of spiral bevel gears.
29.5 Mixed Lubrication Characteristics Most gear lubrication analyses described in the previous sections are based on two important assumptions: (1) the teeth contacting surfaces are perfectly smooth, and (2) the film thickness distribution in the contact region is not affected by the surface roughness, its texture, or its orientation with respect to the flow direction of the lubricant. These assumptions are valid for some of the very high-speed gears in which the specific film thickness, the ratio of the film thickness to roughness (sometimes known as the lambda ratio) is greater than 3, such as those used in aerospace applications. However, this is not true for most industrial and automotive applications. For these cases, the lambda ratio is usually much below 3, and one needs to include the effects of roughness on lubrication and to consider mixed-mode lubrication, including both the fluid pressure generated hydrodynamically as well as the solid contact pressure at the contacting asperities. In the past decade, there have been considerable advances made in mixed lubrication in elastohydrodynamic contacts. These advances seem ready to be incorporated in the gear lubrication performance analyses to make more accurate predictions of contact fatigue life, the scuffing threshold conditions, and perhaps also conditions for other tribological failure modes. In mixed lubrication, the variables are no longer well-behaved smooth functions. They contain local fluctuations caused by the asperity interactions. For this reason, they can be described on two scales: (1) the macroscopic average variables, such as the average film thickness, h, and (2) microscopic fluctuations, such as the asperity film thickness. Figure 29.39 illustrates the qualitative features of macrovariables and micro-variables in a mixed-lubricated region. A brief summary of some recent developments on mixed EHL is given in the following sections.
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1111
FIGURE 29.32 Dynamic load factor vs. gear speed: (a) damping coefficient = 2627 N s/m (15 lb. s/in.), contact ratio = 1.16; (b) damping coefficient = 4378 N s/m (25 lb. s/in.), contact ratio = 1.16.
29.5.1 Asperity Contact Pressure The problem of determining the asperity contact pressure between two rough surfaces in dry contact is a very basic one in mixed EHL because it can yield the important relation between the average asperity contact pressure and the average gap. There have been many contributions in this area, including the well-known earlier model by Greenwood et al. (1966), Ren et al. (1993), and most recently by Polonsky et al. (1999). Figure 29.40 depicts a typical curve relating the average asperity contact pressure and the average for a gear surface obtained recently by Jiang et al. (2000) using an FFT (fast Fourier transform) method.
29.5.2 Full Simulation of Asperity Contact and Fluid Film Pressure The most direct method of determining the asperity contact and fluid film pressure in a mixed EHL contact involves solving the interacting elasticity and Reynolds equations for the pressure and film
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FIGURE 29.33
Film thickness distributions.
FIGURE 29.34
Typical bulk temperature distribution of pinion and gear along the contact path; ϖg = 523 rad/sec.
thickness in two different regions — the contact and non-contact regions. Because there is practically no flow in the contact region, a no-flow condition in the direction normal to the boundary between the two regions is imposed. Using this method, Jiang et al. (1999) have obtained the asperity contact and fluid pressure distributions in a mixed-lubricated circular contact. Figure 29.41 illustrates the total pressure distribution and the film shape in this contact under a pure rolling mode. Figure 29.42 reveals the fluid as well as the contact pressure, respectively, for the same case. Most recently, Hu et al. (2000) have developed a full numerical solution to the mixed EHL in point contacts. They have developed an alternative and ingenious method to reduce the Reynolds equation to
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FIGURE 29.35 523 rad/sec.
Typical bulk total flash temperature distribution of pinion and gear along the contact path; ϖg =
an expression of a dry contact problem in the contact region. In this manner, they were able to obtain very stable solutions throughout the full range of λ ratio, from infinitely large down to nearly zero (less than 0.003). Figure 29.43 shows the progressive growth of the contact area and the corresponding contact pressure profiles along the center section as the speed decreases from 2500 to 0.001 mm/s for a slide-toroll ratio of 0.2. For most gear tooth contacts, the ellipticity ratio of the contact is very large, and the lubrication performance can be predicted closely by line contact theories. Patching et al. (1996) have analyzed the micro-EHL behavior using their EHL line contact analysis for roughness lays oriented along the major axis of the elliptical contact, commonly known as transversely oriented roughness.
29.5.3 A Macro–Micro Approach to Mixed Lubrication Full simulation of asperity contact and fluid film pressure is a direct and accurate approach to a mixed lubrication problem, but the computation time is very extensive if not prohibitive, particularly for sizable Hertzian contacts with a major axis larger than 500 µm. For these contacts, Jiang et al. (2000) have developed a new method to determine mixed lubrication performance. In this new macro–micro approach, the relation between the average contact pressure and the average gap for a typical rough contact patch is first determined numerically in micro-scale. Using this relation, the average gap, average oil-film pressure, and average contact pressure in a mixed-lubricated EHL contact are solved simultaneously in macro-scale by treating the contact as smooth. The new approach is simple, efficient, and robust, and can cover the entire range of load ratio, from dry contact to full film condition.
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FIGURE 29.36
Effect of lubricant viscosity on lubrication performance.
FIGURE 29.37
EHD load-carrying capacity for different types of worm gearings.
Figure 29.44 shows the effect of speed on load ratio, average gap, and lambda ratio (the average film thickness to roughness ratio) for a typical gear rough surface contact.
29.5.4 Asperity Contact Temperature Because it is widely recognized that scuffing failure in gears is controlled by the high flash temperatures in gear tooth contacts, it is desirable to understand how the flash temperatures are related to the asperity
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FIGURE 29.38
Power losses in the oil film for different types of worm gearings.
temperatures in a gear tooth contact. Recently, Qiu et al. (1998) extended an earlier work by Lai et al. (1985) and developed a numerical simulation of the asperity contact temperature rise in a mixedlubricated rough contact sliding against a smooth surface. Figure 29.45 shows respectively the contour plot of the temperature rise for a mixed-lubricated circular EHL contact with longitudinal roughness. Qiu et al. (1998) also calculated the flash temperature distribution in a dry sliding circular contact using real measured surface roughness topography from a typical bearing surface.
29.6 Modeling of Tribological Failures in Gears From the review and discussions in previous sections, it can be observed that with the recent advancements in EHL and the applications of EHL in gear tooth contacts, one can now make reasonably accurate predictions of two primary variables for modeling tribological failures in gears. These are the minimum oil film thickness at the most heavily loaded points for modeling pitting failure, and the maximum flash temperature at the locations where the highest slide-to-roll ratio occurs for scuffing failure. There can be two types of models for predicting tribological failures in gears. The models of the first type are largely empirical and deduced from correlation of past gear failure data with the calculated variables such as lubricant film thickness and flash temperature. The second type of model can be based on using results from mixed lubrication and applying them to advanced failure models on contact fatigue and lubricant film breakdown. These models are still in the development stage and should be viewed as prospective models in modern tribology. Details of both types of models are discussed in the following sections.
29.6.1 Conventional Pitting Life Model The conventional model to account for the effect of lubrication on pitting life was first suggested by Dudley (1980) and later incorporated by Kubo et al. (1991). In their formulation, the allowable load, Wa, for a gear tooth contact at 107 cycles is assumed to be given or known. The pitting life, Lb , at any other load Wb can be determined by the following relation:
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FIGURE 29.39 Qualitative features of macro-variables (h, p, pa, τ, Ts) and micro-variables (h*, ρ*, τ*, Ts*) in mixed lubrication as a function of asperity contacts, Ai .
W = a 7 10 Wb Lb
q
(29.1)
where the exponent q depends on in which lubrication regime the contact operates. The value q is given as:
q = 3.2 for regime I; q = 5.3 for regime II; and q = 8.4 for regime III The regime of lubrication is located from Figure 29.46 with a known surface roughness and an oil film thickness calculated from an appropriate EHL analysis.
29.6.2 Prospective Pitting Life Model Since recent advancements in mixed EHL have shown that the asperity-induced fluid and contact pressure fluctuations can now be readily determined, the entire subsurface stress field, which includes the nearsurface intensified stresses induced by the asperities and the far-field Hertzian-type subsurface stresses induced by the macro EHL pressure, can also be analyzed using a new fast FFT algorithm recently
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FIGURE 29.40
Relation of average contact pressure and average gap on a gear surface; hardness = 8 GPa.
introduced by Polonsky et al. (2000). Figure 29.47 shows a typical near-surface subsurface Mises stress distribution in the central plane of a rough contact. With the near-surface and far-field Mises stress distributions known, it has been demonstrated by Ioannides et al. (1985), and more recently by Ai (1998), that the pitting life can be determined by damage accumulation theory. This method appears to be very effective for predicting the pitting life for rolling bearings, and can be employed for determining the life for initiation of surface or subsurface cracks. For most gear contacts, life does terminate at crack initiation. There is still a significant portion of the life cycle remaining during the propagation of these cracks to form a spall. The propagation life of gear tooth contacts can be predicted using the three-dimensional crack propagation model developed by Hanson et al. (1992) and a method developed by Blake et al. (1991).
29.6.3 Conventional Scuffing Model The conventional scuffing model accepted by most gear manufacturers is Blok’s flash temperature equation, as formulated in AGMA 2001-B88. It has been documented in detail by Enrrichello (1992) and is highlighted here. For further details of the model, readers are referred to Enrrichello (1992). In Blok’s flash temperature theory, scuffing will occur in gear teeth when the maximum contact temperature of the gear teeth reaches a critical temperature Ts, which is a property of the lubricant and is known to be dependent on viscosity. The contact temperature Tc is the sum of the gear bulk temperature Tb and the flash temperature Tf . It varies along the contacting path of the gear tooth contact.
Tc = Tb + Tf For ultra-high-speed gears: Tb = 95°C (171°F) + Ti (oil inlet temperature) For lower speed gears: Tb = 11°C (20°F) + Ti at 3700 m/min (1.2 × 104 ft/min) Tb = 22°C (40°F) + Ti at 4900 m/min (1.6 × 104 ft/min) For aircraft gears: Tb = 22°C (40°F) + Ti at 4900 m/min (1.6 × 104 ft/min)
(29.2)
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FIGURE 29.41 Total pressure distribution (top) and film shape (bottom) for a three-dimensional rough surface on 421 × 421 grids with pure rolling mode, nondimensional load W* = 8.177 × 10–6, velocity U* = 4.985 × 10–13, material G* = 4595, load ratio = 17%, contact area ratio = 12%, average gap = 1.16, λ = 0.18.
where Ti is the oil inlet temperature. The flash temperature for spur and helical gears is:
Tf =
( ) − (V ) (b )
0.8 µ m X Γ w Nr Vr1 BM
0.5
0.5
0.5
r2
(29.3)
H
where
50 µ m = 0.06 50 − S S XΓ wNr
(29.4)
= Average of the two rms surface roughness, micro inches = Load sharing factor taken from Figure 5 in Enrichello (1992) = WNr /Lmin, where WNr is the normal operating load and Lmin is the minimum contacting length, lbf /in. Vr1, Vr2 = Rolling velocities of pinion and gear, in./sec
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FIGURE 29.42 Fluid pressure (top) and asperity contact pressure (bottom) for three-dimensional rough surface on 421 × 421 grids with pure rolling mode, nondimensional load W* = 8.177 × 10–6, velocity U* = 4.985 × 10–13, material G* = 4595, load ratio = 17%, contact area ratio = 12%, average gap = 1.16, λ = 0.18.
BM λM ρΜ cM BM bH
= Thermal contact coefficient = (λM ρΜ cM)0.5, lbf /(in. × s0.5 × °F) = Heat conductivity = Density = Specific heat per unit mass = 43 lbf /(in. × s0.5 × °F) = Semi-width of the Hertzian contact band
Based on Blok’s theory, scuffing will occur if Tc is greater than Ts. The recommended scuffing temperatures (in °F) are: Ts = 146 + 59 ln ν40 for mineral oils without anti-scuff additives Ts = 245 + 59 ln ν40 for mineral oils with anti-scuff additives where ν40 is the kinematic viscosity at 40°C in centistokes.
29.6.4 Prospective Scuffing Model Since recent advancements in mixed EHL have shown that not only can the asperity-induced fluid and contact pressure fluctuations now be readily determined, but the asperity contact temperature and the surface temperature in the fluid film region can also be determined using a reasonable estimate of the boundary
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FIGURE 29.43
Modern Tribology Handbook
Cases for transverse ground surface at slide-to-roll ratio S = 0.20.
coefficient of friction for the asperity contacts as discussed earlier in the section on asperity temperature analyses. The results of the asperity temperature distribution in mixed EHL contacts can be applied to the existing criteria on breakdown of the micro-EHL, boundary, and oxide protective films to develop a more advanced model for predicting the onset of scuffing.
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FIGURE 29.44
Influence of speed on load ratio, average gap, and lambda ratio.
FIGURE 29.45
Contour plot of temperature rise of rough surface (at 263.2°C).
29.6.5 Wear Modeling in Spur Gears As mentioned earlier, wear is usually not a direct concern in gears unless it becomes excessive and triggers other types of tribo-failures such as pitting and scuffing. Perhaps for this reason, wear modeling in gears has not received the same level of interest as scuffing and pitting. However, there have been some advances on wear predictions in spur gears. For example, Wu et al. (1993) developed a sliding wear model for spur gears run in mixed EHL regime. In their predictions, Rowe’s adhesive sliding wear model for lubricated contacts was used at lower temperatures and Quinn’s oxidation wear model was used at higher temperatures.
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EHO film hmin. µin 2
3
4 5 6
8 10
20
2.5
30 40 50 60 80 100 100 80 70 60 50 40
zo
Regime l
ion
1.0
ne
1.5
Tra n
Surface finish. µm (AA).
sil
e
n
n zo
30
tio
i ns
Regime ll
a Tr
0.5
20 15
Regime lll 0.25
10 8 7 6 5
0.15
Surface finish. µin (AA)
1
4
0.10
3 2
0.05
1
0.025 0.025
0.05
0.10
0.15
0.25
0.5
1.0
1.5
2.5
EHO film hmin. µm
FIGURE 29.46
Example of guidance to predict the regime of lubrication from EHD film thickness and surface finish.
FIGURE 29.47
Mises stress distribution in the plane x = 0 for a rough contact with h = 20 µm and E2 /E1 = 2.
A spur gear performance code developed earlier by Wang et al. (1980) was extended from full-film to mixed EHL to include the sliding friction due to asperity contacts. Typical results were obtained for a set of 6-in. diameter, 1 diametral pitch 52100 steel pinion and 12-in. diameter 52100 steel gear spur gears with the pinion running at 1000 rpm and transmitting 100 KW. Figures 29.48a–d show, respectively, the distributions of dynamic load, film thickness, maximum average asperity contact temperature, and wear depth along the contacting path. The fluctuations along the path are due to the dynamic load variations. The excessive wear depth is found to occur at the beginning of the engagement, which is in accord with the practice.
29.7 Failure Tests Most gear pitting and scuffing tests are performed on two pairs of back-to-back power circulating gears. This gear bench test system is commonly known as the four-square test rig originated in Munich, Germany. The standard design of this type of tester is the FZG spur gear tester.
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Gears
Max. Average-Asperity-Temperature (K)
Static and Dynamic Load (kN)
20 Static Load Dynamic Load
15
10
5
0 -0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
440 0.34 µm (RMS) 0.40 µm (RMS)
430
420
410
400
390 -0.6
-0.4
-0.2
0.0
(a)
0.4
0.6
(c) 4
1.0 0.34 µm (RMS) 0.40 µm (RMS)
0.8
Sliding Wear Depth (µm)
Film Thickness Parameter
0.2
Normalized Line of Action
Normalized Line of Action
0.6
0.4
0.34 µm RMS roughness 0.40 µm RMS roughness
3
2
1
0 -0.6
0.2
-0.4
-0.2
0.0
0.2
0.4
0.6
Normalized Line of Action Wear depth distribution or tooth wear profiles after one million
0.0 -0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
(d)
Normalized Line of Action
(b) FIGURE 29.48 (a) Comparison between dynamic and static load patterns. (b) Distributions of film thickness parameters, the ratio of minimum film thickness to composite rms roughness. (c) Distributions of maximum averageasperity-contact temperature. (d) Wear depth distributions of tooth wear profiles after 1 million cycles.
Hohn et al. (1999) have recently obtained the pitting and micro-pitting, scuffing, and wear performances of spur gears lubricated with biodegradable gear lubricants using the FZG back-to-back spur gear test rig shown in Figure 29.49. Typical results for wear rate, scuffing load capacity, and pitting and micro-pitting are shown in Figures 29.50a–d, respectively. Based on these results, they were able to conclude that the wear, scuffing, and micro-pitting performances of fast degradable gear lubricants are comparable to mineral oil-based gear lubricants in some applications. For pitting performance, the fast degradable gear lubricants are all higher than the performance of mineral oil-based gear lubricants. Haizuka et al. (1999) have recently obtained extensive data on the surface strength of spur gears with a back-to-back power circulating gear four-square FZG-type tester. They focused their attention on the effects of lubricant oil, lubricant additives, and material and tooth surface heat treatment on tooth surface strength and pitting life relation. Figures 29.51a and b show that the lubricant viscosity has very little influence on the surface strength of case-hardened gears, but it has a very pronounced effect on the surface strength of tempered gears. For a lubricant with (EP) additive, Figures 29.52a and b show that the tooth surface strength decreases slightly for both case-hardened gears and tempered gears.
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FIGURE 29.49 FZG back-to-back gear test rig: (1) test pinion, (2) test wheel, (3) drive gear, (4) load clutch, (5) locking pin, (6) load lever and weights, (7) torque measuring clutch, and (8) temperature sensor.
29.8 Conclusions 1. The efficiency and durability of most major types of power transmitting gears depend strongly on the lubrication performance in gear tooth contacts. The surface roughness height and texture, the physical and chemical properties of the lubricant, as well as the lubricant additives must be carefully selected to yield a higher ratio of the lubricant film thickness to roughness or lambda ratio, a lower contact friction, and a lower maximum surface temperature in order to maximize pitting life, minimize power loss, and avoid scuffing failure. 2. Elastohydrodynamic lubrication (EHL) theories are highly developed and have been applied successfully to predict the lubrication performance of major types of gears, including spur, helical, spiral bevel, and hypoid, as well as worm gears. However, most of these analyses are for perfectly smooth gear tooth contacts. Because many gears, particularly automotive and industrial gears, operate in the regime of mixed EHL, further extensions of gear EHL analyses to include the roughness effects are needed. 3. Present failure models for predicting pitting, micro-pitting, and scuffing in gears are mostly empirical or semi-empirical. With the availability of advanced computational algorithms to accurately predict the asperity contact and fluid pressure and asperity contact temperature, there are strong possibilities to develop more advanced and accurate failure models for surface pitting and scuffing in gears.
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Gears
400
400 M
Ja = 60 Ja = 90
300
wear rate in mg
wear rate in mg
300
200 B
100
K
S68
C
0
C
200
H 100
S
N
0
0
0 0
50
100
150
200
0
running time in hours
50
100
150
200
running time in hours
(a)
600 12 11 400
10
300
9 8 7 6 5 4
200 100 0 K
B
S
N
oil
(b) FIGURE 29.50
(a) Measured wear rate; (b) scuffing load capacity.
H
scuffing load stage
scuffing torque in Nm
500
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9. torque stage
10. torque stage
Pc 1651 N/mm2
Pc 1834 N/mm2
50 40 30
test-end due to scuffing
Cycles at pinion in mio
20 10 5
2 1 Oil:
M
K
B
N
S 68
S
H
K
H
(C) 300
9 8
150 2. test run
1. test run
2. test run
1. test run
2. test run
1. test run
2. test run
1. test run
50
2. test run
7 100
1. test run
torque in Nm
200
0 B
K
S
N
oil
(d) FIGURE 29.50 (continued)
(c) pitting results; (d) micro-pitting results.
H
6 5 3
micro pitting load stage
10
250
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Gears
x10 16
Oil I ZDQ2 60oC( ) Oil llI ZDQ2 60oC( ) Oil lVZDQ2 60oC( )
14 12 10
(a)
9 8 7
Oil I ZDQZ 60oC ( ) Oil I Case h-lV (G)
N/mm 2
6 5 2 3 4 5 6 8 106 x10 2.8
2 3 4 5 6 8107
2.0 Kclim
3
Oil lVZDQ2 60oC
2.4
(b)
2
Oil lll ZDQ2 60oC
1.6
Oil ll ZDQ260oC
1.4 1.2 1.0
Oil l ZDQ2 60oC
0.8 0.7
Temp (G)
0.6 0.5 2 3 4 5 6 8 106
2 3 4 5 6 8 107
Number of cycles
FIGURE 29.51
2 3 45
N1
Influence of viscosity on tooth surface strength: (a) case-hardened gears, and (b) tempered gears.
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x10 16
Oil llI ZDQ2 60oC Oil llI EP6.0 60oC
14 12
(a)
Kclim
N/mm 2
10 9 8 7
Case h-lV (G)
6 2 3 4 5 6 8106 2.8 x10
2
2 3 45
Oil lll ZDQ2 60oC Oil lll EP6.0 60oC
2.4 2.0
(b)
3 4 5 6 8 107
1.6 1.4 1.2 1.0
Temp (G)
0.8 2 3 4 5 6 8 106
2 3 4 5 6 8107
Number of cycles FIGURE 29.52
2 3 45 N1
Influence of EP additive on tooth surface strength: (a) case-hardened gears, and (b) tempered gears.
References Ai, X. (1998), Effect of three-dimensional random surface roughness on fatigue life of a lubricated contact, J. Tribol., 120(2), 159-164. Chao, H.C., Baxter, M., and Cheng, H.S. (1981), A computer solution for the dynamic load, film thickness, and surface temperatures in spiral-bevel gears, in Proc. Adv. Power Transmission Technology, Fischer, G.K. (Ed.), NASA Technical Report 82-C-16, NASA Lewis R.C., Cleveland, OH, 345-363. Dudley, D. W. (1980),Gear wear, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), The American Society of Mechanical Engineers, New York, 755-830. Enrrichello, R. (1992), Friction, lubrication, and wear of gears, in Friction, Lubrication, and wear Technology, Blau, P. (Ed.), ASM International, 535-545. Greenwood, J. and Williamson, J.B.P. (1966), Contact of nominally flat surfaces, Proc. Roy. Soc. London, A295, 300-319. Haizuka, S., Naruse, C., and Tamenaka, J. (1999), Study on tooth strength of spur gears. I. Experimental procedure and determination of tooth strength. II. Special attention on effects on lubricating oil, material and tooth surface treatment, STLE Tribol. Trans., 42(1), 76-84 and 152-161. Hohn, B.R., Michaelis, K., and Dobereiner, R. (1999), Load carrying capacity properties of fast biodegradable gear lubricants, STLE Lubr. Eng., 55(11), 15-38. Hu, Y.Z. and Zhu, D. (2000), A full numerical solution to the mixed lubrication in point contacts, ASME J. Tribol., 122(1), 1-9. Hua, D.Y. and Khonsari, M. (1995), Application of transient elastohydrodynamic lubrication analysis for gear transmissions, STLE Tribol. Trans., 38(4), 905-913. Ioannides, S. and Harris, T. (1985), A new fatigue life model for rolling bearings, ASME J. Tribol., 107(3), 367-378.
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1129
Jiang, X., Cheng, H.S., and Hua, D. (2000), A theoretical analysis of mixed lubrication by macro micro approach. I. Results on a gear rough surface contact, to appear in STLE Tribology Transaction. Jiang, X., Hua, D.Y., Cheng, H.S., Ai, X., and Lee, S.C. (1999), A mixed elastohydrodynamic lubrication model with asperity contact, ASME J. Tribol., 121(3), 481-491. Kubo, A and Townsend, D.P. (1991), Gear lubrication, in Dudley’s Gear Handbook, Townsend, D.P. (Ed.), McGraw-Hill, New York, 15.1-31. Lai, W.T. and Cheng, H.S. (1985), Temperature analysis in lubricated simple sliding rough contacts, ASLE Trans., 28(3), 303-312. Larssen, R. (1997), Transient non-Newtonian elastohydrodynamic lubrication analysis of an involute spur gear, Wear, 207, 67-73. Patching, M.J., Evans, H.P., and Snidle, R.W. (1996), Micro-EHL analysis of ground and super-finished steel discs used to simulate gear tooth contacts, STLE Tribol. Trans., 39(3), 595-602. Polonsky, I and Keer, L.M. (2000), A fast and accurate method for numerical analysis of elastic layered contacts, ASME J. Tribol., 122(1), 30-35. Qiu, L. and Cheng, H.S. (1998), Temperature rise simulation of three-dimensional rough surfaces in mixed lubricated contacts, ASME J. Tribol., 120(2), 310-318. Radovich, J.L. (1984), Gears, Handbook of Lubrication (Theory and Practice of Tribology), Vol. II, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL, 539-564. Ren, N. and Lee, S.I. (1993), Contact simulation of three-dimensional rough surfaces using moving grid method, ASME J. Tribol., 115(4), 597-601. Shipley, E.E. (1991), Loaded gear in action, Dudley’s Gear Handbook, Townsend, D.P. (Ed.), McGrawHill, New York, 12.1-71. Simon, V. (1985), Thermoelastohydrodynamic analysis of lubrication of worm gears, in Proc. JSLE Int. Tribol. Conf., Tokyo, Japan, Japan Society of Tribologists, Tokyo, Japan, 1107-1152. Simon, V. (1988), Thermo-EHD analysis of lubrication of helical gears, ASME J. Mechanisms, Transmissions, and Automation in Design, 110(3), 330-336. Simon, V. (1997), EHD lubrication characteristics of a new type of ground cylindrical worm gearing, ASME J. Mechan. Design, 119(2), 101-107. Vichard, J.P. (1971), Transient effects in the lubrication of hertzian contacts, J. Mechan. Eng. Sci., 13(3). Wang, K.L. and Cheng, H.S. (1981), A numerical solution to the dynamic load, film thickness, and surface temperatures in spur gears. I. Analysis; and II. Results, ASME J. Mechan. Design, 103(1): 177-194. Wu, S. and Cheng, H.S. (1993), Sliding wear calculation in spur gears, J. Tribol., 115(3), 493-500.
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30 Rotary Dynamic Seals 30.1 30.2
Introduction ................................................................... 1131 Mechanical Seals ............................................................ 1131 Basic Concept • Configurations • Seal Face Materials • Sealing Region • Floating Seal Face: Location and Forces • Hydrostatic Seals • Non-contacting Hydrostatic Seals • Contacting Hydrostatic Seals • Hydrodynamic Seals • Gas Seals • Two-Phase Effects • Seal Analysis
30.3
Rotary Lip Seal ............................................................... 1146 Basic Concept • Configurations • Lip Materials • Sealing Region • Reverse Pumping • Microgeometry of the Lip • Macrogeometry of the Lip • Shaft Surface Microgeometry • Bidirectionality • Converse Mounting • Conceptual Model • Seal Analysis
Richard F. Salant Georgia Institute of Technology
30.4 30.5
Nomenclature ................................................................. 1154 Defining Terms............................................................... 1155
30.1 Introduction Fluid machines containing moving parts require dynamic seals to prevent leakage of fluid out of the machine, transport of contaminants into the machine, and leakage of fluid between components. Such seals play important roles in ensuring the reliable operation of fluid machines and, most importantly, in protecting the environment from undesirable and harmful emissions. Dynamic seals generally contain one or more interfaces between a stationary and a moving surface. Thus, they are considered tribological components. Most commonly, the dynamic seal is used to seal the space between a rotating or reciprocating shaft and a machine housing. Many types of dynamic seals are in use today. These include: • fixed clearance seals, such as the bushing, labyrinth seal, visco (or windback) seal, floating ring seal, ferrofluid seal • variable clearance seals, such as the reciprocating lip seal, mechanical (or face) seal, and rotary lip seal The latter two are the most widely used types of dynamic seal, and are the subject of this chapter.
30.2 Mechanical Seals The mechanical seal is a precision-engineered product. Typical applications are centrifugal pumps, compressors, turbines, mixers, marine propeller shafts, and aircraft engines. Although mass-produced mechanical seals, such as those used in automotive water pumps and household appliances, cost in the range of $1 to $2, most mechanical seal designs range in price from a few hundred dollars to several hundred thousand dollars (for a nuclear reactor coolant pump seal system).
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
1131
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1132
FIGURE 30.1
Modern Tribology Handbook
Schematic of a mechanical seal.
30.2.1 Basic Concept The essential parts of a mechanical seal are shown in Figure 30.1. The two annular seal faces have flat mating surfaces. One of those faces, the rotor, is mounted on the rotating shaft, while the other, the stator, is mounted on the housing. Either the rotor or the stator is free to float in the axial direction, while the mating face is fixed, axially. Secondary seals, such as O-rings, prevent leakage between the rotor and the shaft, and between the stator and the housing. Therefore, the only possible leakage path is through the interface between the two seal faces. A spring (or bellows; see Section 30.2.2) forces the floating seal face toward the fixed face, thereby closing the seal under static unpressurized conditions to prevent static leakage. Under dynamic conditions, the interface between the two faces is lubricated by the sealed fluid. Not shown in Figure 30.1 are the drive (or anti-rotation) devices that prevent the rotor from rotating relative to the shaft and the stator from rotating relative to the housing. These usually consist of pins or keys. The defining characteristic of the mechanical seal is its ability to tolerate some degree of eccentricity, misalignment, and runout, while maintaining a relatively low leakage rate. Even if the two faces are not perfectly parallel and concentric, they will still track each other (if properly designed) because one of the faces is flexibly mounted and floats. Because the seal is self-adjusting, the leakage path through the interface between the seal faces cannot be explicitly controlled (although a controllable seal has been proposed and built [Salant and Wolff, 1994]), but can be minimized by proper design. The thickness of the lubricating film in the interface (with the sealed fluid acting as the lubricant) is typically on the order of microns, and much smaller than the clearance in fixed clearance seals (which is determined by the need to avoid interference in the presence of eccentricity, misalignment, and runout). Thus, the leakage rate of the mechanical seal is much smaller than that of the fixed clearance seal — an important advantage. The disadvantages of the mechanical seal, compared to the fixed clearance seal, are its greater complexity and higher susceptibility to wear and mechanical and thermal failure. At the present time, the operation of the mechanical seal is generally well-understood (although many details still remain uncertain). This has allowed the construction of mathematical models of seal operation that can be used for design, development, and troubleshooting. Virtually all major seal manufacturers use computer programs based on such models. While the quantitative accuracy of the model predictions are sometimes questionable, their qualitative predictions are very useful. Thus, computer programs are usually used in conjunction with a test program.
30.2.2 Configurations Many different seal configurations are possible. A comprehensive enumeration is given by SummersSmith (1992). Figure 30.1 shows the most common configuration. The rotor is the floating seal face, which is loaded by a spring (or several springs). The sealed pressure is at the OD of the faces. Figure 30.2 shows a seal with a metal bellows, which replaces the spring and sliding O-ring of Figure 30.1. Removal of the O-ring eliminates shaft wear, hanging up of the O-ring, and the resulting hysteresis. It also allows
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Rotary Dynamic Seals
FIGURE 30.2
Metal bellows mechanical seal.
FIGURE 30.3
Mechanical seal with floating stator.
FIGURE 30.4
Mechanical seal with sealed pressure at the inner diameter.
1133
higher-temperature operation. A disadvantage of the metal bellows is its vulnerability to fatigue failure. Figure 30.3 shows a seal in which the stator is the floating face. This configuration is capable of higher speeds than that of Figure 30.2, because it avoids instabilities in the flexible element (bellows or spring). However, its major disadvantage is a larger axial and radial envelope. Figure 30.4 depicts a seal in which the sealed pressure is at the ID. This type of seal is sometimes necessary, due to the geometric design of the application. However, it is usually avoided, if possible. There are two reasons for this. Both stem from the fact that thermal deformation, which is difficult to control, contributes to coning of the seal faces such that the film thickness is a maximum at the OD. First, if the seal is designed to operate with fullfilm lubrication, with inside pressurization and maximum film thickness at the OD, the seal will be unstable and either the faces will fly open or the lubricating film will collapse (see Section 30.2.7). Second, if the seal is designed to operate with mixed lubrication, with inside pressurization and maximum film thickness at the OD, it will be difficult for the lubricant (the sealed fluid) to enter the interface. For some applications, a multiple seal arrangement is used. In a double seal, two seals facing opposite directions are mounted on the same shaft, and the cavity between the two individual seals is kept at a higher pressure than the sealed pressure. This arrangement is used when no leakage to the environment can be tolerated, as in the case of sealing hazardous materials. A second type of multiple seal arrangement
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is the tandem seal, also consisting of two seals mounted on the same shaft but facing in the same direction. However, the cavity between the two individual seals is kept at a pressure intermediate between the sealed pressure and the ambient pressure. This arrangement is used for sealing very high pressures because the total pressure drop can be apportioned between the two seals. The tandem seal also offers a degree of enhanced safety because if one seal fails, the second seal can usually take over the entire load for at least a limited period of time.
30.2.3 Seal Face Materials In most mechanical seals, one face is made of a soft material while the other is made of a hard material. The soft face is usually carbon-graphite. This is usually impregnated with a resin or a metal (e.g., antimony) to reduce porosity. A wide variety of materials are used for the hard face. The most popular material, today, is silicon carbide, either sintered or reaction bonded. It has comparatively good wear resistance and frictional properties, high thermal conductivity, and low density. Its disadvantage is its comparatively low toughness; it can be easily damaged, mechanically. The second most popular hard face material is tungsten carbide. Other face materials in use are Ni-Resist cast iron, Stellite, and aluminum oxide. While most mechanical seals consist of a soft face running against a hard face, for abrasive applications both faces frequently are hard — typically, silicon carbide against silicon carbide or tungsten carbide. Regardless of the face material, the running surface of the faces are lapped very flat and smooth, to approximately 0.1 micron.
30.2.4 Sealing Region The interface between the seal faces (Figure 30.1) is termed the sealing region, and is the most important portion of the seal. This is where sealing is most difficult, because of the relative velocity between the faces. Also, due to the relative velocity, it is the location where face damage and wear are most likely to occur. It is the location where frictional forces and processes occur, and where heat generation takes place. Thus, it is the most interesting part of the seal, from a tribological viewpoint. The rest of the seal must be designed so as to achieve optimum conditions in this region. The lubrication regime in the sealing zone is either full-film lubrication, with non-contacting faces; or mixed lubrication, with asperity contact, depending on the seal design and operating conditions. As mentioned earlier, the sealed fluid acts as the lubricant. The choice of lubrication regime depends on the seal requirements. Full-film lubrication results in maximum seal life and minimum probability of failure, but also relatively high leakage rate. Conversely, mixed lubrication results in minimum leakage rate, but shorter seal life and higher probability of failure.
30.2.5 Floating Seal Face: Location and Forces The axial location of the floating seal face determines the average film thickness and the lubrication regime, as illustrated schematically in Figure 30.5. Thus, it plays a major role in determining the other sealing region characteristics, such as heat generation rate, temperatures, pressures, contact areas and forces, wear rate, seal life, and leakage rate. The axial location of the floating face is determined by the forces acting on the face because the face will assume an equilibrium location such that the net axial force on it is zero. The forces are shown schematically in Figure 30.6. Forces that urge the floating face toward the fixed face are termed “closing forces,” while those that urge the floating face away from the fixed face are termed “opening forces.” There are two closing forces: the pressure force produced by the sealed pressure acting on the back side of the floating face, and the spring force. The pressure force is usually dominant except at very low sealed pressures. The spring force is usually important only under static, unpressurized conditions; it keeps the seal closed when the sealed device is inoperative. For moderate to high pressures, the spring force can usually be ignored. In general, however, the total closing force is given by:
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Rotary Dynamic Seals
b. Mixed Lubrication
FIGURE 30.5 lubrication.
Determination of lubrication regime by floating face location: (a) full-film lubrication, and (b) mixed
FIGURE 30.6
Forces on floating seal face.
Fclosing = Fspring + ps A′
(30.1)
where A′ is the effective area of the backside of the seal face. The total closing force can be expressed in terms of the effective face area, Af , by introducing the balance ratio:
N B = A′ A f =
ro2 − rb2 ro2 − ri 2
(30.2)
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Modern Tribology Handbook
Equation 30.2 is valid for a spring-loaded seal pressurized at the OD. (Equivalent expressions for a seal pressurized at the ID and for a bellows seal are given in Summers-Smith (1992). The closing force is then given by:
Fclosing = Fspring + ps N B A f
(30.3)
The balance ratio is known once the seal geometry is specified, and is usually between 0.65 and 0.90. Therefore, it is quite easy to determine the closing forces for a prospective seal design. However, the same cannot be said for the opening forces. From Figure 30.6, it is seen there are two opening forces: the pressure force due to the pressure distribution in the sealing region, and the contact force due to asperity contact. (The latter vanishes in the case of full-film lubrication.) Therefore, the total opening force is given by:
Fopening =
∫
Af
p dA + Fcontact
(30.4)
This opening force cannot be computed, a priori, for a given seal design. In fact, a good deal of seal analysis is required to evaluate this force. Equating the closing and opening forces, one obtains the equilibrium equation that determines the axial location of the floating seal face:
Fclosing = Fopening
(30.5)
or
Fspring + ps N B A f =
∫
Af
p dA + Fcontact
(30.6)
Note that the pressure distribution in the sealing region and the contact force (on the RHS of Equation 30.6) implicitly depend on the axial location of the floating face. However, they also depend on the film thickness distribution, which is affected by both mechanical and thermal deformation. While the latter are quite small, on the order of microns, they are of the same order as the film thickness and therefore play an important role. This is what makes Equation 30.6 difficult to solve.
30.2.6 Hydrostatic Seals Most mechanical seals are nominally hydrostatic seals. The term “hydrostatic seal” refers to a seal in which the pressure distribution in the sealing region is induced by the sealed pressure, and is not directly induced by the rotation of the seal face. In this regard, the hydrostatic seal is analogous to the hydrostatic bearing. The faces of a hydrostatic seal are axisymmetric, so that there is no circumferential variation in the film thickness. Thus, the film thickness can only vary radially, a condition referred to as coning. Coning, δ, is defined as the difference in the film thicknesses at the two radial boundaries of the sealing zone, and is positive when the film converges in the direction of leakage (flow), and negative when the film diverges in the direction of leakage. Positive coning for an outside pressurized seal is depicted in Figure 30.7. The fluid pressure distribution in the sealing region of a hydrostatic seal with a specified coning and average film thickness can be determined from the solution of the Reynolds equation:
∂ rh 3 ∂p 1 ∂ h 3 ∂p U ∂h + = ∂r 12µ ∂r r ∂θ 12µ ∂θ 2 ∂θ
(30.7)
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Rotary Dynamic Seals
FIGURE 30.7
Coning of mechanical seal faces.
FIGURE 30.8
Pressure distribution in a non-contacting hydrostatic seal.
For the hydrostatic seal, the second term on the LHS and the term on the RHS are zero. The solution is shown, qualitatively, for a seal with a face width much smaller than the radius (as is usually the case) in Figure 30.8. It is seen that the shape of the pressure distribution depends on the ratio δ/have . For parallel faces (δ/have = 0), the distribution is linear; for positively coned faces, it is convex; and for negatively coned faces, it is concave. Because the opening force due to the fluid pressure is proportional to the area under the pressure distribution curve, it is seen that for a given film thickness, the larger the coning, the higher the opening force due to fluid pressure. Similarly, for a given coning, the smaller the average film thickness, the higher the opening force due to fluid pressure.
30.2.7 Non-contacting Hydrostatic Seals Consider a non-contacting hydrostatic seal in which full-film lubrication occurs between the faces. At moderate and high sealed pressures, the spring force can be neglected and the equilibrium Equation 30.4 becomes,
NB =
∫p
p s
d
A Af
(30.8)
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Modern Tribology Handbook
For a given value of δ/have, the integral on the RHS of Equation 30.8 is just the area under the corresponding curve in Figure 30.8. Therefore, each curve in Figure 30.8 corresponds to a seal with a given balance ratio. Curves for positive values of δ/have correspond to balance ratios larger than 0.5, while those for negative values correspond to balance ratios less than 0.5. Equation 30.8 can be written as:
(
N B = f δ have
)
(30.9)
Thus, for a seal with a given balance ratio, the average film thickness is proportional to the magnitude of the coning — the larger the coning, the thicker the film. In designing a hydrostatic seal, it is therefore necessary to control the coning (produced by mechanical and thermal deformation). Too much coning will result in excessive leakage, while too little will result in too thin a film and contact between the faces. The axial stability characteristics of a non-contacting hydrostatic seal can also be deduced from Figure 30.8. First, consider the case of a seal with positive coning. Consider such a seal operating in equilibrium with the pressure distribution of curve b. If a small disturbance reduces have, the value of δ/have increases and the pressure distribution in the sealing region changes to that of curve a. Thus, the opening force increases and exceeds the closing force, causing the floating face to move back to its original location. Conversely, if a small disturbance increases have, the value of δ/have decreases and the pressure distribution in the sealing region changes to that of curve c. Therefore, the opening force decreases and the floating face is again moved back to its original location. Thus, a seal with positive coning (Nb > 0.5) will be stable to axial disturbances; it has positive axial stiffness. Now consider the case of a seal with negative coning, operating with the pressure distribution of curve f. If a small disturbance reduces have, the magnitude of δ/have increases and the pressure distribution in the sealing region changes to that of curve g. The opening force decreases and is less than the closing force, causing the floating face to move closer to the fixed face, away from its original location. Conversely, if a small disturbance increases have, the magnitude of δ/have decreases and the pressure distribution in the sealing region changes to that of curve e. The opening force increases and the floating face is moved further from the fixed face, again away from its original location. Thus, a hydrostatic seal with negative coning (Nb < 0.5) will be unstable to axial disturbances; it has negative axial stiffness. The faces will either fly open or collapse. A seal with parallel faces (zero coning, Nb = 0.5) will be in neutral equilibrium, without any preferred average film thickness. This is why all practical hydrostatic seals have balance ratios larger than 0.5, usually in the range 0.65 to 0.90.
30.2.8 Contacting Hydrostatic Seals While the non-contacting hydrostatic seal, discussed above, has the advantages of relatively long life and high reliability, the need to reduce leakage rates in certain applications (e.g., to meet U.S. EPA emission requirements) has caused designers to reduce the film thicknesses in hydrostatic seals to such a degree that asperity contact between the faces occurs. In addition, in low pressure applications (e.g., automotive water pump seals), hydrostatic pressures produce insufficient opening forces to maintain a continuous fluid film. For such contacting seals, the contact force term on the RHS of Equation 30.6 is very important and cannot be neglected. Therefore, the conclusions regarding the relationship between average film thickness and coning, and between coning and stability, described above for non-contacting seals are not valid for contacting seals. The latter may run stably with negative or zero coning, as well as with positive coning. In fact, zero coning (parallel faces) may be preferable for some contacting seals, because such a configuration will minimize the contact stresses.
30.2.9 Hydrodynamic Seals In a hydrodynamic seal, the pressure distribution in the sealing region is induced by the rotation of one of the seal faces. The term “hydrodynamic seal” arose by analogy with the hydrodynamic bearing. To
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FIGURE 30.9 Mechanical seal with shallow hydropads: (a) configuration of hydropad seal, and (b) pressure distribution in a hydropad seal.
generate elevated pressures through rotation, the film thickness must vary in the circumferential direction. This is usually due to a circumferential variation in face geometry. An element of the pair of faces, with one face moving in the circumferential direction, then acts like a slider bearing generating the elevated pressure distribution. Such a pressure distribution can be computed from the Reynolds equation (Equation 30.7), where the RHS is the hydrodynamic driving term (which is zero for a hydrostatic seal). These seals are usually designed to operate with full-film lubrication. One of the simplest types of hydrodynamic seals has one seal face containing micro-hydropads (see, e.g., Walowit and Pincus, 1982). Such hydropads are recesses, with depths on the micron scale, that are etched into the seal face, as shown in Figure 30.9a. As the mating face drags fluid past each recess, one of the edges acts like a Rayleigh step bearing, and an elevated triangular pressure distribution is developed, as shown in Figure 30.9b. The opening force per unit depth for each hydropad can be computed by solving the Reynolds equation, and is given by:
Fopening =
[ ] ( )
6µUa a + b d 3 a 3 h+d +h b
(30.10)
From Equation 30.10 it is seen that the opening force always increases with decreasing film thickness. Such a seal always has positive axial stiffness and will be stable to axial disturbances. A more common type of dynamic seal is one containing macroscopic hydropads with depths on the order of a millimeter, which are machined into the face. The operation of such relatively deep hydropads is different from that of the microscopic hydropads discussed above. This is seen from Equation 30.10, which shows that the opening force due to the Rayleigh step bearing effect becomes very small at large values of hydropad depth (when the depth is much larger than the film thickness) and is therefore
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FIGURE 30.10
Modern Tribology Handbook
Pressure distribution in a mechanical seal with a wavy face.
ineffective with macroscopic hydropads. The mechanism by which the macroscopic hydropad seal operates involves two phenomena (Key et al., 1989). First, the presence of the hydropads destroys the symmetry of the face such that, when the seal is in operation, the face becomes wavy due to asymmetric mechanical and thermal deformation. The amplitude of the waviness is on the order of microns, the same order as the film thickness. Second, due to the circumferential variation in film thickness, a periodic pressure distribution is produced, as shown in Figure 30.10 for a liquid film. This pressure variation is significant because the waviness amplitude is on the same order as the film thickness (unlike the depth of the hydropads). And because cavitation occurs below the cavitation pressure, this pressure distribution is truncated at the cavitation pressure, resulting in a net opening force. The hydrodynamic generation of elevated pressures due to face waviness can also occur unintentionally in seals that are designed as hydrostatic seals. Such waviness can result from asymmetries of the face structure and is invariably present to some degree. The consequence of such waviness can be a thicker film and higher leakage rate than the designer intended. It has also been suggested that a similar hydrodynamic effect is produced by surface roughness in the presence of inter-asperity cavitation (Lebeck, 1999). A hydrodynamic seal that is currently quite popular, is the spiral groove seal (e.g., Salant and Homiller, 1993). A series of spiral grooves is etched into one of the faces. The groove pattern covers the entire face except for an annular section at the OD or the ID, which is termed the sealing dam, as shown in Figure 30.11a. The grooves are oriented such that when the mating face rotates, the seal acts like a viscous pump, and fluid is pumped toward the sealing dam, which acts as a restriction to the flow. The result is an elevated pressure distribution, as shown in Figure 30.11b. The sealing dam may be at the OD or at the ID. If it is at the OD (as in Figure 30.11a), and the sealed pressure is at the OD, the seal is termed an upstream pumping seal. In such a seal, the hydrodynamic effect not only generates the opening force that keeps the lubricating film intact, but also reduces the leakage rate because the pumping by the grooves is in the direction opposite to the leakage.
30.2.10 Gas Seals Most mechanical seals in use today are liquid seals. Even such gas handling machines as gas compressors often use a liquid seal with a liquid lubricating system. However, this situation has been changing, as described below. Much of what has been discussed in this chapter thus far is equally applicable to gas and liquid seals. Thus, in principle, one could construct a hydrostatic gas seal. Although such seals have been discussed in the literature, they generally are not in use because of their comparatively low stiffness. The situation
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GROOVE
SEALING DAM
ID OD
ROTATION OF MATING FACE
1
P 2
3
4
a. Configuration of a spiral groove seal.
0
1.2 1.1 5
0.25
0 1.1 r 1.0
0.15
0.20
5
0 .1 0
0
1.0
0.0 5 0.00
b. Pressure distribution in a spiral groove seal.
FIGURE 30.11 Spiral groove mechanical seal: (a) configuration, and (b) pressure distribution. (From Salant, R.F. and Homiller, S.J. (1993), Tribol. Trans., 36, 55-60. With permission.)
is different for hydrodynamic seals, which can be designed to provide the required stiffness. While seals with microscopic hydropads have been used for some applications, the most popular gas seals today are spiral groove seals (and variations on the spiral groove design). These are usually referred to as dry gas seals. They are very attractive for such gas sealing applications as compressors because they eliminate the need for an elaborate lubrication system, which would be required for a liquid seal in such an application.
30.2.11 Two-Phase Effects When a mechanical seal is used to seal a liquid close to the vapor temperature, it is possible for the liquid to vaporize as it leaks across the seal face. This happens most frequently when sealing light hydrocarbons. If a stable interface between the liquid and vapor portions of the film is formed, the seal effectiveness is actually increased because the leakage rate is reduced from its single-phase value (Müller and Nau, 1998). However, when two-phase conditions exist, the lubricating film frequently becomes unstable. Puffs of vapor are emitted, the torque and leakage fluctuate erratically, and transient face contact occurs. Transient face contact can be quite violent, and will eventually destroy the seal. To prevent the phase transition and resulting instability, the sealed fluid temperature must be maintained below a certain maximum temperature. That maximum temperature is equal to the vapor temperature at the sealed pressure minus a temperature margin, which accounts for the fact that the fluid in the seal interface is at a higher temperature than that in the sealed cavity. The temperature margin is a function of sealed pressure, as illustrated in Figure 30.12, and also depends on the seal design, materials, and sealed fluid.
30.2.12 Seal Analysis As mentioned, virtually all major seal manufacturers use mathematical models in the design and development of mechanical seals. Because the physical processes governing seal behavior are all closely coupled, as shown in Figure 30.13, closed form analytical solutions are not possible. Therefore, numerical techniques utilizing iteration are used.
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Modern Tribology Handbook
FIGURE 30.12
Temperature margin in a mechanical seal.
FIGURE 30.13
Coupling of processes in a mechanical seal.
The principal components of a seal analysis are: a fluid mechanics analysis, a deformation analysis, a contact mechanics analysis (if mixed lubrication occurs), and a thermal analysis. The fluid mechanics and deformation analyses are coupled because the fluid pressures produce mechanical deformation and the deformations, in turn, affect the film thickness distribution, which determines the fluid pressure distribution. The deformation and contact mechanics analyses are coupled because the deformations affect the film thickness distribution, which determines the contact area and the degree of contact, while the contact pressures produce mechanical deformation. The contact mechanics and thermal analyses are coupled because the contact shear stresses generate frictional heat. The deformation and thermal analyses are coupled because the heat generation produces thermal deformation. Finally, the fluid mechanics and thermal analyses are coupled because the viscosity is affected by the temperature and the viscous heat generation rate is determined by the fluid mechanics. 30.2.12.1 Fluid Mechanics The fluid mechanics of the lubricating film is governed by the Reynolds equation. For a liquid it takes the form:
∂ ϕ r rh 3 ∂p 1 ∂ ϕ θh 3 ∂p U ∂h U σ ∂ϕ s − = + ∂r 12µ ∂r r ∂θ 12µ ∂θ 2 ∂θ 2 r ∂θ
(30.11)
This version of the Reynolds equation contains flow factors (Patir and Cheng, 1978), which are used to account for the effect of surface roughness. They are usually only important for mixed lubrication. If full-film lubrication occurs, the pressure flow factors (ϕr and ϕθ) can be set equal to 1 and the shear flow factor (ϕs) set equal to 0. The solution of Equation 30.11 yields the fluid pressure distribution. However, to solve Equation 30.11, it is necessary to know the film thickness distribution, h. Once Equation 30.11 is solved, the leakage rate can be computed from:
ml = −ϕ r
πrρh 3 ∂p 6µ ∂r
(30.12)
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As would be expected, the leakage rate is inversely proportional to the viscosity. However, note the strong (cubic) dependence of the leakage rate on film thickness. Very small changes in film thickness can result in large changes in leakage rate. This is why it is very difficult to accurately predict leakage rates. 30.2.12.2 Contact Mechanics For seals that operate with mixed lubrication, a contact mechanics analysis is necessary. The contact area and forces are determined by the location of the floating face, the film thickness distribution, and the roughness distribution. Significant contact occurs when the film thickness is less than or equal to approximately five times the equivalent standard deviation (roughness) of the two faces, σs, where:
σ s = σ12 + σ 22
(30.13)
The analysis could use either an elastic-plastic or a plastic model of asperity deformation. The plastic model is the easier to use, and is employed below. The probability that an asperity will have height z, f (z), is assumed to be given by the Gaussian distribution:
()
−
1
f z =
σ s 2π
e
z2 2 σs2
(30.14)
Using the plastic deformation model, at any location in the sealing region the contact force per unit nominal area (contact pressure) is given by:
Pcontact = H
∫
∞
h
1 σ s 2π
−
e
z2 2 σs2
dz
(30.15)
where H is the flow stress of the softer material. The total contact force contributing to the opening force on the seal is then:
Fcontact =
∫ H∫ A
h
∞
1 σ s 2π
−
e
z2 2 σs2
dz dA
(30.16)
Note that the contact force can only be computed after the film thickness distribution, h, is known. 30.2.12.3 Deformation Although the deformations of the seal faces are usually only on the order of microns, they play a very important role because they are of the same order as the film thickness. Thus, they strongly affect both the fluid and contact pressure distributions. The mechanical deformation is produced by the fluid and contact pressures, and is affected by boundary conditions. The thermal deformations are produced by the heat generation rate, and are also affected by boundary conditions. The latter (thermal) boundary conditions are usually the most difficult to specify. Two methods of performing the deformation analysis are used. In the first, a finite-element analysis (FEA), usually in the form of a commercial package, is employed. While such an approach produces accurate results (provided the boundary conditions are accurate), it is computationally intensive and can be extremely time-consuming if used within an iteration loop. Therefore, the second method, the influence coefficient method, is frequently used. In this method, it is assumed that the deformation is linearly related to the applied forces and heat generation rate, so that:
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n
∆i =
∑ (M
if
)
F j + TH ij q j + Si
j =1
(30.17)
where the influence coefficients Mij and THij represent the mechanical and thermal deformations at node i that are produced by a unit force or heat input at node j. Fj represents the force at node j due to the fluid and contact pressures, while qj represents the heat generation rate at node j. The influence coefficient Si represents the deformation at node i due to the combined effects of the sealed pressure, atmospheric pressure, and spring force. All the influence coefficients are computed with an off-line FEA. Thus, a finite element analysis need not be performed inside an iteration loop, only solution of Equation 30.17. Once the deformations are determined, the film thickness distribution can be found in terms of the minimum film thickness:
hi = hm + ∆ i
(30.18)
The minimum film thickness, hm , is found from a force balance on the floating face (Equation 30.6). 30.2.12.4 Thermal Thermal analysis encompasses computation of the heat generation rate and the film temperature. The latter is assumed to equal the interface temperature. Thermal analysis is important because the heat generation rate determines the thermal deformation, and the film or interface temperature determines the viscosity of the fluid. The interface temperature is also important because it controls some forms of face damage (e.g., blistering of carbon-graphite, coking) and determines if vapor is formed. The heat generation rate is due to viscous heat generation and frictional heat generation produced by asperity contact (in the case of mixed lubrication). These rates are given by:
∫
qviscous = µ A
U2 dA h
(30.19)
and
q frictional = f U pcontact A
(30.20)
where f is the coefficient of sliding friction for the asperities. The film or interface temperature is computed using the influence coefficient method: n
Ti = Tref +
∑T q ij
j
(30.21)
j =1
where Tij is the temperature influence coefficient representing the temperature change at node i due to a unit heat flux at node j, and TRef is the reference temperature, commonly chosen to be the fluid operating temperature in the seal chamber. Tij is computed with an off-line finite element analysis. Once the film temperature is determined, the viscosity can be computed from empirical viscosity-temperature data. 30.2.12.5 Computational Procedure A typical computational procedure (Ruan et. al, 1997) is shown in the flowchart of Figure 30.14. The computation starts with the initial input, including the influence coefficients, seal geometry, material properties, surface topography, and operating conditions. Then an estimation of minimum film thickness,
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Generate influence coefficients
Input operating conditions, material properties, surface topography and influence coefficients
Input initial guess for minimum film thickness hm, face temperature T, and assume uniform film distribution
Calculate contact force and frictional heat using elastic-plastic asperity contact model
Calculate pressure distribution using control volume solution of modified Reynolds equation, and compute viscous heat
Make guess for new face temperature and calculate viscosity based on the new temperature distribution
Make guess for new hm Calculate new film thickness using influence coefficients
Not converged
Check convergence of film thickness distribution and relax it
Converged
Opening force balance with closing force ?
No
Yes Calculate seal face temperature using temperature influence coeff.
No
Check convergence of face temperature Yes Equilibrium found Calculate leakage and output results
Full ANSYS run of seal assembly to get h and T, and to verify the influence coefficient method.
FIGURE 30.14 Flowchart of typical mechanical seal analysis. (From Ruan, B., Salant, R.F., and Green, I. (1997), Tribol. Trans., 40, 647-657. With permission.)
face profile, and face temperature is made. This is followed by the first iteration loop, where the contact force, pressure distribution, and viscous and frictional heat are calculated. Then the film thickness is computed by the influence coefficient method. The computed film thickness distribution is compared with the results from the last iteration. If the film thickness does not converge, then it is modified as:
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Modern Tribology Handbook
h(
( )
) = λh(i ) + 1 − λ h(i −1)
i +1
(30.22)
where h(i) and h(i–1) are the film thickness in the current and previous iteration, respectively, and λ is the relaxation factor. When the film thickness converges, the opening force is compared with the closing force. If the forces are not balanced, the minimum film thickness is revised. After the force equilibrium is found, the convergence of face temperature is checked. Only after the temperature has converged, can steady equilibrium seal operation be found. Otherwise, the face temperature is modified by the bisect method. With the updated temperature, viscosity is recalculated and the iteration process is repeated as described above. Once the temperature has converged, the leakage rate is calculated. Finally, a full finiteelement analysis is performed to verify the accuracy of the influence coefficient method.
30.3 Rotary Lip Seal The rotary lip seal is the most widely used type of dynamic seal. It is a relatively inexpensive, massproduced product, primarily used for low pressure applications. It is extensively used in the automotive industry to seal crankshafts, transmissions, wheel hubs, axle pinions, and power steering components. It is also extensively used in appliances and industrial equipment (e.g., gearboxes).
30.3.1 Basic Concept A schematic drawing of the rotary lip seal is shown in Figure 30.15. The most important part of the seal is the lip, constructed of an elastomeric material. Also important is the garter spring and the shaft. The seal is mounted on the shaft with an interference fit, so that the lip deforms near the contact region, and there is no static leakage. When the shaft rotates, the interface between the lip and the shaft is lubricated by the sealed fluid. As in the case of the mechanical seal, the thickness of the lubricating film is on the order of a micron. Also like the mechanical seal, the rotary lip seal can tolerate some degree of eccentricity, misalignment, and runout, due to the ability of the lip to track the shaft. In sharp contrast to the mechanical seal, however, a properly designed lip seal does not leak. Compared to the mechanical seal, the lip seal is much simpler, mechanically. However, its operation is much more complex and difficult to analyze. This is because some of the mechanisms that govern lip seal behavior are on a microscopic scale. In fact, it is only recently that significant progress has been made toward obtaining a comprehensive understanding of lip seal operation. Thus, very few analytical design tools are available for rotary lip seals. Commercial finite-element analysis packages are used for static structural analysis. However, there are currently no computer programs for performance prediction that can be used for design purposes. At present, the design and development of rotary lip seals is primarily an empirical process, involving a great deal of testing and the use of practical design guidelines.
FIGURE 30.15
Schematic of a lip seal.
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FIGURE 30.16
1147
Lip seal with exclusion lip.
30.3.2 Configurations Unlike the mechanical seal, there are few variations from the basic configuration of Figure 30.15. For some applications, the garter spring is omitted. For applications in which the exclusion of dust or other contaminants is important, a secondary exclusion lip is included, as shown in Figure 30.16. Another variation is the so-called hydrodynamic seal. (This name is a misnomer because all lip seals are hydrodynamic.) These seals have spiral grooves or ribs molded on the air side, generally external to the sealing zone. If there is an imperfection in the seal and a small amount of liquid leaks out, it is caught in the grooves and propelled back under the lip.
30.3.3 Lip Materials The most widely used lip material is nitrile rubber (NBR), due to its low cost and good oil and abrasion resistance. It is suitable for use at moderate temperatures (–40 to 110°C). For higher temperatures (up to 135°C), hydrogenated nitrile (HNBR) is frequently used, although it is significantly more expensive than NBR. Even more expensive, but increasingly popular, are fluoroelastomers (FKM), which are recommended for high-speed, high-temperature applications. Other elastomeric materials in use are polyacrylic (ACM) and ethylene acrylic (AEM). Another material that is increasingly used for rotary seals is polytetrafluoroethylene (PTFE), but this is a plastic, not an elastomer. PTFE seals are designed differently and behave differently from elastomeric seals, and are beyond the scope of this chapter.
30.3.4 Sealing Region The sealing region in a rotary lip seal is the interface between the lip and the shaft, as shown in Figure 30.15. The axial length of this region is initially approximately 0.1 mm, but is extended to approximately 0.2 to 0.3 mm during the break-in period. As in the case of the mechanical seal, this is the most important portion of the seal It is well-established that under normal steady-state operating conditions, full-film lubrication exists in the sealing region. This has been shown indirectly, through friction measurements, and directly, through film thickness measurements (Jagger, 1957). These studies have indicated that the thickness of the continuous fluid film is on the order of a micron. It is the presence of this film that prevents excessive wear, mechanical and thermal damage, and excessive frictional losses. The existence of a continuous fluid film between the lip and the shaft leads to two questions that have occupied researchers for the last 40 years: 1. What is the load support mechanism that produces elevated pressures in the film, which cause the lip to lift off of the shaft and which maintain the integrity of the film? 2. What is the sealing mechanism that prevents fluid from leaking through the interface?
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In efforts to answer these two questions, researchers have conducted a large number of experimental investigations, which revealed a number of important features of lip seal operation: reverse pumping, importance of the microgeometry of the lip, importance of the macrogeometry of the lip, importance of shaft surface microgeometry, bi-directionality characteristics, and the effect of converse mounting. These are described in the chapter sections below. While full-film lubrication occurs during steady-state operation, studies have shown that at very low speeds and during the break-in process, mixed lubrication occurs (Salant, 1999).
30.3.5 Reverse Pumping If the air-side of a successful seal is flooded with liquid, it is found that the liquid is pumped under the lip, toward the liquid-side of the seal. This phenomenon is called reverse pumping. The pumping rate is a measure of the effectiveness of the seal: if the pumping rate is too low, the seal will leak. (In addition, some researchers believe that if the pumping rate is too high, the seal could fail.) Therefore, some seal manufacturers measure the pumping rate of prospective seal designs during the development process. It is believed that the reverse pumping phenomenon is connected with the sealing mechanism. The reverse pumping (from the air-side to the liquid-side) is thought to counteract the natural leakage of the seal (from the liquid-side to the air-side) to give zero net leakage.
30.3.6 Microgeometry of the Lip The texture or roughness pattern of the lip surface in the sealing region plays a major role in determining whether or not a seal will be successful. If the lip surface is very smooth, with few asperities, the seal will not pump and will have a very short life (Horve, 1991). Figures 30.17 and 30.18 show the performance characteristics of two seals constructed with different rubber compounds such that one contains a large number of asperities, while the other contains few asperities. From these figures it is seen that a successful
Pump rate (ml/min)
0.4 Material............................. NBR Lubricant.......................... SAE 30 Engine Oil Sump temperature........... 93.3oC (200oF) Shaft size.......................... 76.2mm (3.000 inch) Shaft to-bore misalignment..0.0 Dynamic runout.................0.0 Shaft speed...................... 2100 rpm, CCW and CW
0.3
Large number of microasperities present
0.2
Little evidence of microasperities
0.1
0 0
1000
2000
3000
4000
5000
6000
Shaft Speed (rpm)
FIGURE 30.17
Effect of asperities on pumping rate. (From Horve, L. (1991), SAE Trans., 910530. With permission.)
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Rotary Dynamic Seals
Percent failure
99 95 90 80 70 60 50 40 30 20 Little evidence of microasperities
Large number of microasperities present
10
5
1 10
50
100
500
1000
5000
Hours to failure
FIGURE 30.18
Effect of asperities on sea life. (From Horve, L. (1991), SAE Trans., 910530. With permission.)
seal requires a large number of asperities (or other microscopic features, such as micro-undulations) in the sealing region. After the lip is molded, its surface is very smooth. It is during the break-in period that asperities are formed. Mixed lubrication occurs, and there is contact between the lip and the shaft. The resulting wear processes (preferential, due to heterogeneity of the lip material) develop the lip microgeometry. Thus, the primary function of the break-in period is to condition the lip. The final lip microgeometry is very much material dependent. The base material, fillers, additives, molding conditions, and mold geometry determine the microgeometry. Even the mold gate location can make the difference between a successful and an unsuccessful seal.
30.3.7 Macrogeometry of the Lip The macroscopic geometry of the lip also determines whether or not a seal is successful. As shown in Figure 30.19, the most important macroscopic geometric features of the seal are the lip angles and the spring location. The liquid-side angle must be larger than the air-side angle, and both must be within certain empirical limits: 40° to 70° for the liquid-side, and 20° to 35° for the air-side. The spring location, relative to the center of the sealing region, must be closer to the air-side than to the liquid-side.
FIGURE 30.19
Macroscopic geometric features of a lip seal.
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FIGURE 30.20
Modern Tribology Handbook
Contact pressure distribution in a new lip seal: (a) good seal, and (b) bad seal.
In the past it was thought that the importance of the macrogeometry was due to its influence on the contact pressure distribution in the sealing region. As schematically illustrated in Figure 30.20, experiments on new seals indicated that favorable macroscopic geometries produced a contact pressure distribution with a peak closer to the liquid-side of the seal than to the air-side, while unfavorable geometries produced a distribution with a peak closer to the air-side than to the liquid-side. However, subsequent experiments on a successful broken-in seal showed a rather flat contact pressure distribution, with no discernible peak (Gabelli et al., 1992). It is now believed that the effect of the macrogeometry is to produce a favorable distribution of circumferential displacement of the rubber surface in the sealing region. As schematically illustrated in Figure 30.21, favorable macroscopic geometries produce a circumferential displacement peak closer to the liquid-side, while unfavorable macroscopic geometries produce a circumferential displacement peak closer to the air-side, whether the seal is new or broken in (van Leeuwen and Wolfert, 1996). One can conclude that the same geometries that produce an asymmetric contact pressure distribution in a new lip produce an asymmetric circumferential displacement distribution in a lip, whether new or broken in.
30.3.8 Shaft Surface Microgeometry For a rotary lip seal to operate satisfactorily, the shaft surface finish must satisfy certain requirements (the shafts are typically finished by plunge grinding). The surface should not be too rough or too smooth, and must have minimal lead. If it is too rough, the lip will be damaged before a lubricating film can be established; and if it is too smooth, the lip surface will not be properly conditioned during the break-in period. The RMA (Rubber Manufacturers Association) and SAE (Society of Automotive Engineers) have set a standard of Ra = 0.25 to 0.50 microns (or 10 to 20 microinches). However, recent experiments have shown that Ra is not the only shaft surface characteristic that affects lip seal operation; Rsk (skewness), Rku (kurtosis), and Rv (maximum valley depth) are also important. The RMA is, therefore, in the process of developing a new standard. In addition to conditioning the lip during the break-in period, it is believed that the shaft surface influences lip seal operation in other ways, despite the fact that the shaft surface becomes polished and has a roughness typically less than 10% of the lip roughness. One possibility is that the shaft surface provides reservoirs to retain liquid during static
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FIGURE 30.21
1151
Circumferential displacement distribution in a lip seal: (a) good seal, and (b) bad seal.
periods, and thereby supply liquid to establish the lubricating film during the start-up process. Another possibility is that the shaft surface microgeometry can influence the load support mechanism. (Although the shaft roughness is small compared to the lip roughness, because the Reynolds equation is nonlinear in film thickness, small differences in the film thickness distribution could have large effects.)
30.3.9 Bidirectionality If the shaft rotation direction is reversed with a relatively new seal, the seal will continue to operate successfully. However, if a seal is run for an extended period of time (and the rubber lip material has aged), and then the rotation direction is reversed, the seal will leak. Experiments in which pumping rate was measured are related to this bidirectional behavior. It was found that if the rotation rate is suddenly reversed and the lip material is elastic, the pumping rate remains the same; but if the lip material is viscoelastic, the pumping rate is initially reduced due to a time delay in the response of the lip material.
30.3.10 Converse Mounting It is well-known that if a successful lip seal is conversely mounted (installed backward), it will leak profusely. This is connected with the asymmetric geometry of the seal. As described above, the macrogeometric features of lip angles and spring location make the seal asymmetric. Indeed, the phenomenon of reverse pumping is a consequence of the asymmetry. When the seal is installed conversely, the reverse pumping is in the same direction as the natural leakage of the seal, and therefore augments the natural leakage, rather than opposing it.
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30.3.11 Conceptual Model Based on the observations of seal behavior described above, a conceptual model of seal operation can be constructed. During the break-in period, there is mixed lubrication in the sealing zone, and asperities are formed on the lip surface due to preferential wear. These asperities, in combination with the shaft rotation, act as micro slider bearings and cause the lip to lift off the shaft. Eventually, the lip lifts completely off the shaft, and a continuous fluid film is established. Once the lip surface is conditioned, when the seal is run under normal steady-state conditions, the asperities again act as micro slider bearings, producing elevated pressures in the film that cause the lip to lift off the shaft and maintain the integrity of the film. This is the load support mechanism. Computations have shown that such elevated pressures are sufficient for producing the observed average film thicknesses (Salant, 1996). These computations have also shown that cavitation plays an important role in the sealing region, with more than 40% of the sealing region cavitated. Such cavitation has been observed experimentally. To understand the reverse pumping mechanism, consider a seal with a flooded air-side and a uniform distribution of asperities, as shown in Figure 30.22. Under static conditions the asperities are circular, as shown in Figure 30.22a (the vertical axis is compressed). However, under dynamic conditions, the rotating shaft produces shear stresses in the fluid film, which cause the rubber lip surface in the sealing region to deform in the circumferential direction. The circumferential displacement of the rubber varies in the axial direction, depending on the macrogeometry of the lip. In a successful seal, the point of maximum displacement is closer to the liquid-side of the seal than to the air-side. The asperities deform along with the bulk material, and assume shapes that act like vanes. The computed shapes for a successful seal are shown in Figure 30.22b. When the rotating shaft surface drags fluid over these deformed asperities, the asperities act like viscous pumps. Asperities below the point of maximum displacement pump liquid toward the liquid-side, while asperities above the point of maximum displacement pump liquid toward the air-side. Because there are more asperities below the point of maximum displacement than above it in a successful seal, there is net pumping toward the liquid-side. While a seal with a flooded air-side is useful for studying (and measuring) reverse pumping, it is not the normal configuration of a rotary lip seal. Under normal conditions, the air-side is not flooded, and a meniscus separates the air from the liquid film, as shown in Figure 30.23. Under equilibrium conditions, the meniscus will be located at some axial distance from the edge of the sealing region, lm, such that the net leakage through the film is zero. One can view the flow in the sealing region as the superposition of the leakage flow due to the sealed pressure and the reverse pumping flow. Under equilibrium conditions, these two flows balance each other, to give zero net flow rate. Note that the pressure on the liquid side of the meniscus, pa, is less than the ambient pressure, patm, due to the action of surface tension forces. The depression of pa below patm is inversely proportional to the radius of curvature of the meniscus. The latter will decrease as the separation between the bounding surfaces (shaft and lip) of the meniscus is decreased. Therefore, the closer the meniscus is to the sealing zone, the lower the pressure pa . Now consider the meniscus at some axial location to the left of the equilibrium location. Pressure pa is now higher than its equilibrium value. The leakage flow due to the sealed pressure is now reduced due to the smaller pressure gradient, and therefore the reverse pumping rate exceeds the leakage rate due to the sealed pressure, and negative leakage occurs. The fluid flows through the film from left to right, and the meniscus returns to its equilibrium location. Next consider the meniscus at a location to the right of the equilibrium location. Now, pa is lower than its equilibrium value, and the leakage flow due to the sealed pressure is increased above its equilibrium value and exceeds the reverse pumping rate. The fluid flows through the film from right to left, and the meniscus again returns to its equilibrium location. Thus, the equilibrium configuration is stable. As one might expect, because the reverse pumping rate increases with shaft speed, as the speed increases, the meniscus moves closer to the edge of the sealing region (Salant, 1996). At some critical speed, the meniscus is ingested into the sealing region.
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1.0 0.9 0.8 0.7
y*
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.8
0.9
1.0
x*
a. Static Asperity Pattern
1.0 0.9 0.8 0.7
y*
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5 x*
0.6
0.7
1.0
b. Dynamic Asperity Pattern FIGURE 30.22 Asperity patterns: (a) static asperity, and (b) dynamic asperity. (From Salant, R.F. (1997), Proc. 10th Int. Colloq. Tribology, Technische Akademie Esslingen, 131-140. With permission.)
Bearing seals with grease lubrication operate somewhat differently. Here, the primary concern is the exclusion of contaminants, rather than the retention of lubricant. Therefore, such seals are usually reversely mounted with the air-side facing the bearing interior and the oil-side facing the exterior and contaminants. The seals are lubricated by the small amount of oil bleeding from the grease, which is
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FIGURE 30.23
Non-leaking configuration of a lip seal.
much less than the pumping capability of the seal. The small amount of oil pumped out prevents wear and helps keep away liquid contaminants.
30.3.12 Seal Analysis As mentioned, at the present time there are no computer programs capable of predicting rotary lip seal performance suitable for design purposes, in contrast to the situation with mechanical seals. This is because the microgeometry of the lip surface plays a central role in the operation of the lip seal. Therefore, in analyzing the fluid mechanics, the microgeometry must be included when solving the Reynolds equation. For the mechanical seal (with mixed lubrication), this is done statistically through the use of flow factors. At the present time, such a statistical approach cannot be used with the lip seal because significant inter-asperity cavitation occurs, which cannot be handled by any existing statistical technique. Therefore, the Reynolds equation must be solved deterministically on a microscopic scale, but extending over macroscopic distances. This results in very large computation times, too large for design purposes. However, such deterministic analyses have been performed for research purposes, and have confirmed the conceptual model described above. Some typical analyses are described in Salant (1999).
30.4 Nomenclature A′ Af a b d Fclosing Fcontact Fj Fopening Fspring f f(z) H h have hm hi lm Mij ml NB p pa
Effective area of backside of seal face Face area Land width in hydropad seal Recess width in hydropad seal Recess depth in hydropad seal Closing force Contact force Force at node j Opening force Spring force Contact friction coefficient Probability that an asperity will have a height z Flow stress of the softer seal face Film thickness Average film thickness Minimum film thickness Film thickness at node i Distance of meniscus from the edge of the sealing region Mechanical deformation influence coefficient Leakage rate Balance ratio Pressure Pressure on liquid side of meniscus
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patm ps q frictional qj q viscous r rb ri ro Si Ti Tij Tref THij U ∆i δ θ λ µ ρ σ1 σ2 σs ϕr ϕs ϕθ
1155
Ambient pressure Sealed pressure Frictional heat generation rate Heat generation rate at node j Viscous heat generation rate Radial coordinate Balance radius Inner face radius Outer face radius Sealed pressure/spring/ambient pressure influence coefficient Temperature at node i Temperature influence coefficient Reference temperature Thermal deformation influence coefficient Surface speed Deformation at node i Coning, ho – hi for an outside pressurized seal Circumferential coordinate Relaxation factor Viscosity Density Standard deviation of seal face 1 Standard deviation of seal face 2 Equivalent standard deviation of two mating seal faces Pressure flow factor in radial direction Shear flow factor Pressure flow factor in circumferential direction
30.5 Defining Terms Closing forces: In a mechanical seal, the forces that push the floating face toward the fixed face. Coning: The difference in the film thicknesses at the two radial boundaries of the seal. It is positive when the film converges in the direction of leakage. For an outside pressurized seal, it is equal to ho – hi. Dry gas seal: A mechanical seal that operates with gas as the lubricant. Fixed clearance seal: A seal in which the clearance between the shaft (or rotating seal component) and the non-rotating seal component is geometrically fixed. Fixed face: In a mechanical seal, the face that cannot move in the axial direction. Floating face: In a mechanical seal, the face that is flexibly mounted and can move in the axial direction, within limits. Flow factor(s): Correction factors inserted into the Reynolds equation to account for the effects of surface roughness. Hydrodynamic seal: A mechanical seal in which the elevated pressures in the sealing region are induced by the rotation of one of the faces. Hydropad: A recess etched or machined into the face of a mechanical seal. Hydrostatic seal: A mechanical seal in which the elevated pressures in the sealing region are induced by the sealed pressure. Reverse pumping: The pumping of fluid from the air-side of a lip seal toward the liquid-side, when the air-side is flooded. Rotor: The rotating seal face in a mechanical seal. Seal face(s): The two components of a mechanical seal that have radially extended surfaces, one rotating relative to the other.
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Sealing dam: The portion of the face of a spiral groove mechanical seal that has no groove pattern and restricts the flow. Secondary seal: In a mechanical seal, the seals used to prevent leakage between components, such as an O-ring between the rotating face and the shaft. Sealing region: The interface between the rotating and non-rotating components of a seal. In a mechanical seal, the interface between the two faces. In a lip seal, the interface between the lip and the shaft. Stator: The non-rotating seal face in a mechanical seal. Temperature margin: The vapor temperature minus the maximum seal fluid temperature to avoid two-phase flow instability. Upstream pumping seal: A spiral groove mechanical seal in which the grooves are oriented such that they pump the fluid toward the high-pressure side of the seal. Variable clearance seal: A seal in which the clearance between the rotating and non-rotating seal components can vary.
References Gabelli, A., Ponson, F., and Poll, G. (1992), Computation and measurement of the sealing contact stress and its role in rotary lip seal design, Proc. 13th Int. Conf. on Fluid Sealing, BHR Group, Brugge, Belgium, 21-38. Horve, L. (1991), The correlation of rotary shaft radial lip seal service reliability and pumping ability to wear track roughness and microasperity formation, SAE Trans., 910530. Jagger, E.T. (1957), Rotary shaft seals: the sealing mechanism of synthetic rubber seals running at atmospheric pressure, Proc. Instn. Mech. Engrs., 171, 597-616. Key, W.E., Salant, R.F., Payvar, P., Gopalakrishnan, S., and Vaghasia, G. (1989), Analysis of a mechanical seal with deep hydropads, Tribol. Trans., 32, 481-489. Lebeck, A.O. (1999), Mixed lubrication in mechanical face seals with plain faces, J. Eng. Tribol., 213(J3), 163-175. Patir, N. and Cheng, H.S. (1978), An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, J. Lubric. Technol., 100, 12-17. Ruan, B., Salant, R.F., and Green, I. (1997), A mixed lubrication model of liquid/gas mechanical face seals, Tribol. Trans., 40, 647-657. Salant, R.F. (1996), Elastohydrodynamic model of the rotary lip seal, J. Tribol., 118, 292-296. Salant, R.F. (1999), Theory of lubrication of elastomeric rotary shaft seals, J. Eng. Tribol., 213(J3), 189-201. Salant, R.F. and Homiller, S.J. (1993), Stiffness and leakage in spiral groove upstream pumping mechanical seals, Tribol. Trans., 36, 55-60. Salant, R.F. and Wolff, P.J. (1994), Development of an electronically controlled mechanical seal for aerospace applications, SAE Trans., 941207. van Leeuwen, H. and Wolfert, M. (1996), The sealing and lubrication principles of plain radial lip seals: an experimental study of local tangential deformations and film thickness, Proc. 23rd Leeds-Lyon Symp. on Tribology, Leeds, Elsevier, 219-232. Walowit, J.A. and Pincus, O. (1982), Analysis of face seals with shrouded pockets, J. Lubr. Technol., 104, 262.
Further Information A good general text covering many types of seals (including some static seals) is Fluid Sealing Technology by Müller and Nau (Marcel Dekker, New York, 1998). For the theoretical aspects of mechanical seals, the most extensive discussion is in Principles and Design of Mechanical Face Seals by Lebeck (Wiley, New York, 1991). While this book is weighted toward the author’s own research, it contains the most detailed description of the mathematical modeling currently in use within the mechanical seal industry.
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Mechanical Seal Practice for Improved Performance, edited by Summers-Smith (Mechanical Engineering Publications Ltd., London, 1992), provides a good balance between the fundamental and practical aspects of mechanical seals. The latter include seal selection, installation and operation, and failure diagnosis. The most detailed description of rotary lip seals is in Shaft Seals for Dynamic Applications by Horve (Marcel Dekker, New York, 1996). This book covers both fundamental (from a descriptive rather than a mathematical point of view) and practical aspects, and is a must for anyone involved in rotary lip seal design or application. The RMA Handbook (Rubber Manufacturers Association, various dates) is a collection of about 20 booklets covering the practical aspects of rotary lip seals. Its section on “Sealing System Leakage Analysis Guide” (OS-17, 1990) is especially useful for failure diagnosis. A good summary of the current state of mechanical seal and lip seal research and design is in the Special Issue on Seals, Journal of Engineering Tribology (Proceedings of the Institution of Mechanical Engineers, Part J, 213(J3), 1999). Current research on mechanical seals and lip seals is reported in the following journals: ASME Journal of Tribology, STLE Tribology Transactions, IMechE Journal of Engineering Tribology, Tribology International, and Wear. An especially good source of material on all types of seals is the Proceedings of the International Conferences on Fluid Sealing sponsored by the British Hydromechanics Research Group, Ltd. (BHRG, formerly BHRA) every few years since 1961.
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31 Space Tribology 31.1 31.2 31.3 31.4
Introduction ................................................................... 1159 Lubrication Regimes ...................................................... 1159 Mechanism Components............................................... 1161 Liquid Lubricants and Solid Lubricants....................... 1162
31.5
Liquid Lubricant Properties .......................................... 1165
Liquid Lubricants
William R. Jones, Jr. NASA Glenn Research Center
Perfluoropolyethers and MACs
31.6
Accelerated Testing and Life Testing............................. 1175
31.7
Summary ........................................................................ 1181
Facilities for Accelerated Life Testing of Space Mechanisms
Mark J. Jansen AYT Corporation
31.1 Introduction Space tribology is a subset of the lubrication field dealing with the reliable performance of satellites and spacecraft (including the space station). It encompasses the entire gamut of tribological regimes, including elastohydrodynamic lubrication (EHL), parched EHL, transient EHL, boundary lubrication, and mixed lubrication. Historically, the lubricants for space mechanisms have been chosen on the basis of space heritage rather than on the latest technology or the best available materials. Early in the space program, this strategy almost always paid off because mission lifetimes and mechanism duty cycles were minimal. When mission lifetimes were extended, other spacecraft components, such as electronics, batteries, and computers, failed before the lubrication systems (Fleishauer and Hilton, 1991). However, in the last decade, these ancillary mechanism components have been greatly improved and the tribological systems have become the limiting factor in spacecraft reliability and performance. Although the tribological components represent only a small fraction of the spacecraft’s cost, they are often single-point failures that can render an expensive satellite totally useless. A classic example was the Galileo spacecraft. Galileo was launched from the Space Shuttle Atlantis in 1989. One of the most important components was a high gain, umbrella-like antenna that was closed during launch to conserve space. In 1991, this antenna only partially unfurled. It was concluded that 4 of the 18 ribs were stuck in place. In ground-based tests (Miyoshi and Pepper, 1992), it was determined that the Ti-6Al-4V alignment pins, which were lubricated with a bonded dry film lubricant, had galled and seized due to loss of lubricant. The mission was salvaged only by the use of the low-gain antenna and advances in data transmission technology.
31.2 Lubrication Regimes The purpose of lubrication is to separate surfaces in relative motion by interposing a third body that has a low resistance to shear so that the two surfaces do not sustain serious damage or wear. This third body can be a variety of different materials, including adsorbed gases, reaction films, and liquid or solid lubricants. 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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FIGURE 31.1 Coefficient of friction as a function of viscosity-velocity-load parameter. (From Stribeck, R. (1902), Characteristics of plain and roller bearings, Zeit. V.D.I., Vol. 46. With permission.)
Depending on the type of third body and its thickness, several different regimes of lubrication can be identified. One way of depicting these regimes is via the use of the Stribeck curve shown in Figure 31.1. Stribeck performed a series of journal bearing experiments in the early 1900s (Stribeck, 1902). He measured the coefficient of friction as a function of load, speed, and temperature. Later, Hersey performed similar experiments and devised a plotting format based on a dimensionless parameter, ZN/P (Hersey, 1914). This Stribeck/Hersey curve takes the form of the coefficient of friction as a function of viscosity (Z), velocity (N), and load (P). At high values of this parameter, which occur at high speeds, high viscosities, and low loads, the surfaces are completely separated by a thick (>0.25 µm) lubricant film. This is the area of hydrodynamic lubrication where friction is determined by the rheology of the lubricant. For nonconformal, concentrated contacts where loads are high enough to cause elastic deformation of the surfaces and pressure-viscosity effects on the lubricant, another regime — elastohydrodynamic lubrication (EHL) — occurs. Film thickness in this regime ranges from 0.025 to 1.250 µm. As this parameter decreases, film thickness decreases and surface interactions start taking place. This regime, in which both surface interactions and fluid film effects occur, is referred to as the mixed regime. Finally, at low values of ZN/P, the boundary lubrication regime is entered. The boundary lubrication regime is a highly complex arena involving metallurgy, surface topography, physical and chemical adsorption, corrosion, catalysis, and reaction kinetics (Godfrey, 1980; Jones, 1982). The most important aspect of this regime is the formation of protective surface films to minimize wear and surface damage. For space mechanisms, AISI 440C stainless steel is the most common bearing material. The formation of lubricating films is governed by the chemistry of both the film former as well as the bearing surface and other environmental factors. The effectiveness of these films in minimizing wear is
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determined by their physical properties. These include shear strength, thickness, surface adhesion, film cohesion, melting point or decomposition temperature, and solubility in the bulk lubricant. Typically, the EHL, mixed, and boundary lubrication regimes occur in lubricated space mechanisms, with the boundary lubrication regime being the most stringent. However, a subdivision of EHL — starvation theory — was described a number of years ago (Wedeven et al., 1971). It describes the situation occurring in ball bearings having a restricted oil supply, in which pressure buildup in the inlet region of the contact is inhibited, resulting in a film thickness thinner than calculated by classical EHL theory (Dowson and Higginson, 1959; Hamrock and Dowson, 1981). However, starvation theory fails to adequately describe instrument bearing behavior because there is no oil meniscus. Another subdivision of EHL — parched elastohydrodynamics — describes a behavior where there is no free bulk oil in the system (Kingsbury, 1985; Schritz et al., 1994). The lubricant films in this regime are so thin that they are immobile outside the Hertzian contact zone. This regime is of particular importance to space mechanisms because parched bearings require the least driving torque and have the most precisely defined spin axis. Finally, another area of EHL that is of importance to space mechanisms involves transient or nonsteady-state behavior. Unlike steady-state EHL behavior, non-steady-state behavior is not well-understood. However, many practical machine elements (e.g., rolling element bearings, gears, cams, and traction drives) operate under non-steady-state conditions. This is where load, speed, and contact geometry are not constant over time. In particular, stepper motors, which are commonly used in many space mechanisms, operate in this regime. This regime has been studied theoretically for line contacts (Wu and Yan, 1986; Ai and Yu, 1988; Hooke, 1994) and experimentally for point contacts (Sugimura et al., 1998).
31.3 Mechanism Components Spacecraft contain a variety of instruments and mechanisms that require lubrication. Devices include solar array drives; momentum, reaction, and filter wheels; tracking antennas; scanning devices; and sensors. Each of these devices has unique hardware, and therefore lubrication requirements. Gyroscopes, which are used to measure changes in orientation, operate at high speeds, typically between 8000 and 20,000 rpm, with high accuracy. This makes the bearings the most important element of a gyroscope. Fluctuations in the bearing reaction torque, noise, and excess heat generation can cause a loss of null position in the gyroscope. The ideal lubricant for a gyroscope provides a high level of wear protection, produces minimal friction, and has a low evaporation rate (Kalogeras et al., 1993). Also, a fixed, small (3 mg) amount of lubricant is used and must provide lubrication throughout the life of the gyroscope. Gyroscope gimbal supports are low-speed applications and the bearings operate in the boundary regime only. Momentum wheels, which typically operate between 3000 and 10,000 rpm, pose their own lubricant selection criteria. Currently, the majority of problems experienced by momentum wheels are related to the lubricant. Inadequate lubrication, loss of lubricant, and/or lubricant degradation are the reasons for the majority of wheel failures (Kalogeras et al., 1993). As higher speed wheels are designed, lubricants will be subjected to higher operating temperatures, which can increase creep or degradation rates. Current design practices to ease lubricant problems include use of improved synthetic lubricants, labyrinth seals and barrier coatings, lubricant-impregnated retainers, and a lubricant resupply system. Reaction wheels have similar design concepts as momentum wheels, but operate at lower speeds. The support bearings spend more time in the mixed lubrication regime. Therefore, lubricants chosen for reaction wheel use must also have good boundary lubrication characteristics. Control momentum gyroscopes (CMGs) combine the aspects of the gyroscope and the momentum wheel to provide attitude control of a spacecraft. Therefore, considerations of both groups must be weighed when selecting a lubricant for use in a CMG (Kalogeras et al., 1993). Devices that utilize scanning or rotating sensors represent another space mechanism that requires lubrication. An example would be a scanning horizon sensor. This device detects the Earth’s horizon,
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which allows spacecraft to orient themselves. Moderate operational speeds (400 to 1600 rpm) and low loads in the bearings make lubricant selection easy. On the other hand, sensors that use oscillatory motion place a high demand on the lubricant. Typically, the angle of oscillation is slight and the bearing operates in the boundary lubrication regime only. With the small oscillatory angle, no new lubricant is brought in the contact zones (Postma, 1999). Slip rings are another example of a common mechanism used in space applications that requires lubricants. Low-speed operation and electrical conductivity are two important factors that affect lubricant selection. Excessive electrical noise is the most common failure mechanism in slip rings (Kalogeras et al., 1993). This is usually due to surface contamination, which can be reduced by proper lubricant selection. Many other mechanisms that require lubrication are used in space applications. Some examples include solar array drives (SADs), which rotate a spacecraft’s solar arrays; ball, roller, and acme screws; and many types of gears and transmission assemblies (Sarafin and Larson, 1995).
31.4 Liquid Lubricants and Solid Lubricants Both liquid and solid lubricants are used for space applications. The choice is often left to the designer. However, each class has merits and deficiencies. The relative merits have been tabulated by Roberts and Todd (1990) and appear in Table 31.1.
31.4.1 Liquid Lubricants Many different chemical classes of liquid lubricants have been used for space applications in the last 3 decades. These include mineral oils, silicones, polyphenyl ethers, esters, and perfluoropolyethers. Recently, a synthetic hydrocarbon (Pennzane™) has replaced many of the older lubricant classes. Each of these types is discussed briefly herein. However, because the great majority of current spacecraft use either a formulated Pennzane or one of the PFPE materials, these two classes are discussed in much greater detail. 34.4.1.1 Mineral Oils This class of lubricants consists of a complex mixture of naturally occurring hydrocarbons with a fairly wide range of molecular weights. Examples include V-78, BP 110, Apiezon C, Andok C (Coray 100) (Bertrand, 1991), and the SRG series of super-refined mineral oils, which includes KG-80 (Dromgold and Klaus, 1968). These latter fluids have been highly refined, either by hydrogenation or percolation through bauxite to remove polar impurities. This makes them poorer neat lubricants, but greatly improves their response to additives. Apiezon C is still available commercially, but production of all others was discontinued many years ago. Nevertheless, the SRG oils have been stockpiled by some companies and are still used to lubricate bearings for momentum and reaction wheels. Their estimated shelf life is in excess of 20 years (Dromgold and Klaus, 1968). TABLE 31.1
Relative Merits of Solid and Liquid Space Lubricants
Dry Lubricants Negligible vapor pressure Wide operating temperature Negligible surface migration Valid accelerated testing Short life in moist air Debris causes frictional noise Friction speed independent Life determined by lubricant wear Poor thermal characteristics Electrically conductive
Wet Lubricants Finite vapor pressure Viscosity, creep, and vapor pressure all temperature dependent Sealing required Invalid accelerated testing Insensitive to air or vacuum Low frictional noise Friction speed dependent Life determined by lubricant degradation High thermal conductance Electrically insulating
From Roberts, E.W. and Todd, M.J. (1990), Wear, 136, 157-167. With permission.
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FIGURE 31.2 Screening test results (scanner and mechanism). (From Kalogeras, C., Hilton, M., Carré, D., Didziulis, S., and Fleischauer, P. (1993), The use of screening tests in spacecraft lubricant evaluation, Aerospace Corp. Report No. TR-93(3935)-6.)
31.4.1.2 Esters British Petroleum developed a triester-based lubricant in the 1970s designated BP 135. This material was laboratory tested but production was stopped and it never “flew.” Another ester used in the past is designated as NPT-4 (neopentylpolyol ester), but is no longer marketed. Nye Lubricants markets another series of low-volatility neopentylpolyol esters (UC4, UC7, and UC9). Esters are inherently good boundary lubricants and are available in a wide viscosity range. 31.4.1.3 Silicones This fluid class was used early in the space program. They are poor boundary lubricants for steel on steel systems. Versilube F-50, a chloroarylalkylsiloxane, was an early example. Comparisons of this fluid in boundary lubrication tests with a PFPE and a PAO have been reported (Kalogeras et al., 1993). Relative life is shown in Figure 31.2. The silicone performed poorly by degrading into an abrasive polymerized product. 31.4.1.4 Synthetic Hydrocarbons There are two groups of synthetic hydrocarbons available today: polyalphaolefins (PAO) and multiply alkylated cyclopentanes (MACs). The first class is made by the oligomerization of linear α-olefins having six or more carbon atoms (Shubkin, 1993). Nye Lubricants markets a number of PAOs for space applications. Properties for three commercial PAOs appear in Table 31.2. The other class of hydrocarbons is known as MACs. These materials are synthesized by reacting cyclopentadiene with various alcohols in the presence of a strong base (Venier and Casserly, 1993). The products are hydrogenated to produce the final product, which is a mixture of di-, tri-, tetra-, or pentaalkylated cyclopentanes. Varying reaction conditions controls the distribution. For the last several years, only one product has been available for space use — primarily the tri-2-octyldodecyl-substituted cyclopentane (Venier and Casserly, 1991). This product is known as Pennzane SHF-X2000, marketed as Nye Synthetic Oil 2001A. Various formulated versions are also available. A primarily disubstituted (lower viscosity, but higher volatility) version is also now available. Properties of the 2001A product appear in Table 31.3. Recent experience with this fluid appears in Carré et al. (1995). A 6-year life test of a CERES elevation bearing assembly using a Pennzane/lead naphthenate formulation yielded excellent results (Brown et al., 1999).
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TABLE 31.2 Typical Properties for Three Commercial Polyalphaolefins Property Viscosity at:
210°F, SUS 210°F, cs 100°F, SUS 100°F, cs 0°F, cs
Flash point Pour point Evaporation 61/2 hours at 350°F Specific gravity @ 25°C
Oil 132
Oil 182
Oil 186
39 3.9 92 18.7 350 440°F –85°F 2.2% 0.828
62.5 10.9 348 75.0 2700 465°F –60°F 2.0% 0.842
79.5 15.4 552 119 7600 480°F –55°F 1.9% 0.847
TABLE 31.3 Typical Properties of Nye Synthetic Oil 2001A (SHF X-2000) Viscosity at 100°C Viscosity at 40°C Viscosity at –40°C Viscosity index Flash point Fire point Pour point Specific gravity at 25°C Specific gravity at 100°C Coefficient of thermal expansion Evaporation, 24 hr at 100°C Refractive index at 25°C Vapor pressure at 25°C
TABLE 31.4
14.6 cSt 108 cSt 80,500 cSt 137 300°C 330°C –55°C 0.841 0.796 0.0008 cc/cc/°C None 1.4671 10–11–10–10 Torr
Physical Properties of Four Commercial PFPE Lubricants and Pennzane SHF X-2000
Lubricant
Average Molecular Weight
Fomblin™ Z-25 Krytox™ 143AB Krytox™ 143AC Demnum™ S-200 Pennzane SHF X-2000
9500 3700 6250 8400 1000
Viscosity at 200°C (cSt) 255 230 800 500 330
Viscosity Index 355 113 134 210 137
Pour Point (°C) –66 –40 –35 –53 –55
Vapor Pressure (Pa) At 20°C 3.9 2.0 2.7 1.3 2.2
× 10 × 10–4 × 10–6 × 10–8 × 10–11 –10
At 100°C 1.3 × 10–6 4.0 × 10–2 1.1 × 10–3 1.3 × 10–5 1.9 × 10–8
31.4.1.5 Perfluoropolyethers These fluids, designated as either PFPE or PFPAE, have been commercially available since the 1960s and 1970s in the form of a branched fluid (Krytox™) manufactured by DuPont (Gumprecht, 1966); a linear fluid (Fomblin™ Z) (Sianesi et al., 1973); and a branched fluid (Fomblin™ Y) (Sianesi et al., 1971), the latter two manufactured by Montefluous. Another linear fluid (Demnum™) was developed in Japan by Daikin (Ohsaka, 1985). The preparation and properties of these fluids appear in Synthetic Lubricants and High-Performance Functional Fluids, (Shubkin, 1993). Some typical properties of these fluids appear in Table 31.4. 31.4.1.6 Silahydrocarbons A new type of space lubricant has been developed by the Air Force Materials Laboratory (Snyder et al., 1992). These materials contain only silicon, carbon, and hydrogen, and therefore do not exhibit the poor
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FIGURE 31.3 Kinematic viscosity as a function of temperature for a series of silahydrocarbons. (From Jones, W., Shogrin, B., and Jansen, M. (1998a), Research on liquid lubricants for space mechanisms, in Proc. 32nd Aerospace Mechanisms Symp., Cocoa Beach, FL, NASA/CP-1998-207191, 299-310.)
boundary lubricating ability observed with silicones. In addition, these unimolecular materials have exceptionally low volatility and are available in a wide range of viscosities. There are three types, based on the number of silicon atoms present in the molecule (i.e., tri, tetra, or penta) (Paciorek et al., 1990, 1991). A series of silahydrocarbons have been synthesized and their kinematic viscosities as a function of temperature have been measured (Figure 31.3) (Jones et al., 1998). For comparison, a Pennzane plot has been included. As can be seen, the viscosity properties of the silahydrocarbons bracket the Pennzane data. EHL properties of two members of this class have been measured (Spikes, 1996). A trisilahydrocarbon had an α value of 16 GPa–1 (±0.3) at 21°C, while a pentasilahydrocarbon had an α value of 17 GPa–1 (±0.3). At 40°C, the trisilahydrocarbon had an α value of 11 GPa–1 (±1) and the penta, 13.5 GPa–1 (±1). For comparison, the α value for Pennzane at 30°C is 9.8 GPa–1 (±0.3), estimated by the same method. Therefore, these silahydrocarbons will generate thicker EHL films than Pennzane under the same conditions.
31.5 Liquid Lubricant Properties Numerous reviews of liquid lubricants for space applications have been published (Fusaro and Khonsari, 1991; Stone and Bessette, 1998; Zaretsky, 1990). Liquid lubricant data also appear in some handbooks (Fusaro et al., 1999; Roberts, 1999; McMurtrey, 1985). Because most applications today use either PFPEs or Pennzane (MAC) formulations, these two classes will be presented in more detail.
31.5.1 Perfluoropolyethers and MACs A liquid lubricant must possess certain physical and chemical properties to function properly in a lubricated contact. To be considered for space applications, these lubricants must have vacuum stability (i.e., low vapor pressure), low tendency to creep, high viscosity index (i.e., wide liquid range), good elastohydrodynamic and boundary lubrication properties, and resistance to radiation and atomic oxygen. Optical or infrared transparency is important in some applications.
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FIGURE 31.4 Relative evaporation rates of aerospace lubricants. (From Conley, P. and Bohner, J.J. (1990), Experience with synthetic fluorinated fluid lubricants, in Proc. 24th Aerospace Mech. Symp., NASA CP-3062, 213-230. With permission.)
31.5.1.1 Volatility Although labyrinth seals are extensively used in space mechanisms, lubricant loss can still be a problem for long-term applications (Hilton and Fleischauer, 1990). For a fixed temperature and outlet area, lubricant loss is directly proportional to vapor pressure. For a similar viscosity range, the PFPE fluids are particularly good candidates compared to conventional lubricants, as shown in Figure 31.4 (Conley and Bohner, 1990). Vapor pressure data for four commercial PFPE fluids and Pennzane appear in Table 31.4. 31.5.1.2 Creep The tendency of a liquid lubricant to creep or migrate over bearing surfaces is inversely related to its surface tension. Therefore, PFPE fluids, which have unusually low surface tensions (γLV , 17 to 25 dynes/cm at 20°C), are more prone to creep than conventional fluids such as hydrocarbons, esters, and silicones. However, these fluids may be contained in bearing raceways by using low surface energy fluorocarbon barrier films on bearing lands (Kinzig and Ravner, 1978). However, there is a tendency for PFPE fluids to dissolve these barrier films with prolonged contact (Hilton and Fleischauer, 1993). Therefore, they are not effective in preventing the migration of PFPEs. Pennzane-based lubricants have higher surface tensions and are thus less prone to creep. 31.5.1.3 Viscosity-Temperature Properties Although liquid lubricated space applications do not involve wide temperature ranges, low temperatures (i.e., –10 to –20°C) are sometimes encountered. Therefore, low pour point fluids that retain low vapor pressure and reasonable viscosities at temperatures to 75°C are desirable. The viscosity-temperature slope of PFPE unbranched fluids is directly related to the carbon-to-oxygen ratio (C:O) in the polymer repeating unit, as shown in Figure 31.5 (Jones, 1995). Here, the ASTM slope is used for the correlation. High values of the ASTM slope indicate large changes of viscosity with temperature. In addition, branching (e.g., the trifluoromethyl pendant group in the Krytox fluids) causes deterioration in viscometric properties. A comparison of ASTM slopes for three commercial fluids appears in Figure 31.6. Here, the low C:O ratio fluid Fomblin Z has the best viscometric properties. The Demnum fluid, with a C:O ratio of 3, has intermediate properties, while the branched Krytox fluid has the highest slope. 31.5.1.4 Elastohydrodynamic Properties The operation of continuously rotating, medium- to high-speed bearings relies on the formation of an elastohydrodynamic (EHL) film. This regime was briefly discussed in the introduction. A more detailed
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FIGURE 31.5 Viscosity-temperature slope as a function of carbon-to-oxygen ratio. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
FIGURE 31.6 Viscosity-temperature slope (ASTM D 341-43) as a function of kinematic viscosity at 20°C for Krytox™ (K), Demnum™ (D), and Fomblin™ (Z) fluids. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
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Modern Tribology Handbook TABLE 31.5 Pressure-Viscosity Coefficients α* at Three Temperatures for Several Lubricants Lubricant Ester Synthetic paraffin Z fluid (Z-25) Naphthenic mineral oil Traction fluid K fluid (143AB)
38°C
99°C
149°C
1.3 1.8 1.8 2.5 3.1 4.2
1.0 1.5 1.5 1.5 1.7 3.2
0.85 1.1 1.3 (extrapolated) 1.3 0.94 3.0
Note: α* given in units of Pa–1 × 108. From Jones, W.R., Jr., Johnson, R.L., Winer, W.O., and Sanborn, D.M. (1975), ASLE Trans., 18(4), 249-262. With permission.
discussion appears in Wedeven (1975). The two physical properties of the lubricant that influence EHL film formation are absolute viscosity (µ) and the pressure-viscosity coefficient (α) (Hamrock and Dowson, 1981). Both molecular weight and chemical structure influence viscosity. Except for low-molecular-weight fluids, α values are only related to structure (Spikes et al., 1984). Pressure-viscosity coefficients can be measured directly with conventional high-pressure viscometers (Jones et al., 1975; Vergne and Reynaud, 1992) or indirectly from optical EHL experiments (Cantow et al., 1987; Aderin et al., 1992). Conventional viscometry normally uses the Barus equation (Barus, 1893) for correlations.
µ p = µ oe αp
(31.1)
where µp = Absolute viscosity at pressure, p µo = Absolute viscosity at atmospheric pressure α = A temperature-dependent but pressure-independent constant This implies that a plot of log µp vs. p should yield a straight line of slope α. Unfortunately, this simple relationship is seldom obeyed. The pressure-viscosity properties that are important in determining EHL film thickness occur in the contact inlet where pressures are much lower than in the Hertzian region. Therefore, the slope of a secant drawn between atmospheric pressure and 0.07 GPa is typically used for film thickness calculations. Some researchers (Jones et al., 1975) favor the use of another pressure-viscosity parameter, the reciprocal asymptotic isoviscous pressure (α*) based on work by Roelands (1966). Pressure-viscosity coefficients (α*) for several lubricants at three temperatures (38°, 99°, and 149°C) are given in Table 31.5. Figure 31.7 contains α values for the branched PFPE, Krytox 143AB. Data obtained by conventional (low shear) pressure-viscosity measurements are denoted with open symbols. Indirect measurements from EHL experiments (effective α values) are shown with solid symbols. There is good agreement between the different sources as well as different measurement techniques. Figure 31.8 contains similar data for the unbranched PFPE Fomblin Z-25 as a function of temperature. Here, there is a definite grouping of the data, with effective α values being substantially lower than values from conventional measurements. Two possibilities exist for this discrepancy. First, inlet heating can occur during the EHL measurements, thus leading to lower viscosities, lower film thicknesses, and resulting in lower calculated α values. The second possibility is a non-Newtonian shear thinning effect, which can occur with polymeric fluids. Shear rates in EHL inlets can range from 105 to 107 sec–1 (Foord et al., 1968). However, the EHL measurements do represent actual film thicknesses that may be expected in practice. Effective α values for several nonPFPE space lubricants, including Pennzane base fluid and some Pennzane formulations, appear in Table 31.6 (Spikes, 1997).
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FIGURE 31.7 Pressure-viscosity coefficients for PFPE Krytox™ 143 AB as a function of temperature. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
FIGURE 31.8 Pressure-viscosity coefficients for PFPE Fomblin™ Z-25 as a function of temperature. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
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TABLE 31.6 Measured Viscosities and Calculated Pressure-Viscosity Coefficients (α Values) for Several Space Lubricants Temp (°C)
Pennzane 2001: Synth. Oil
PAO-186: Synth. Oil
40 80 100 120
88 19 12 8
90 21 13 8
NPE UC-7: Ester
Pennzane 2001+5% Pb Naphthenate
Pennzane 2001+3% Pb Naphthenate
98 21 12 8
96 21 12 8
12.0 9.0 6.5 6.0
10.0 9.0 7.0 7.0
Viscosity (cP) 37 10 6 4 α (GPa–1) 40 80 100 120
11.0 9.5 7.0 7.0
12.5 9.0 7.0 5.0
6.5 5.0 5.0 5.0
From Spikes, H.A. (1997), Film Formation and Friction Properties of Five Space Fluids, Imperial College (Tribology Section), London, U.K., Report TSO37/97.
FIGURE 31.9 Lubricant parameters for PFPE Y and Z fluids. (From Spikes, H.A., Cann, P., and Caporiccio, G. (1984), Elastohydrodynamic film thickness measurements of perfluoropolyether fluids, J. Syn. Lubr., 1(1), 73-86. With permission.)
From EHL theory, the greatest film thickness at room temperature should be obtained with a lubricant having the largest α value, assuming approximately equal inlet viscosities. However, for many applications, lubricants must perform over a wide temperature range. In this case, the EHL inlet viscosity can be the overriding factor if the temperature coefficient of viscosity is high. This can cause a crossover in film thickness as a function of temperature for some PFPE fluids, as shown by Spikes et al. (1984) in Figure 31.9. 31.5.1.5 Boundary Lubrication As described in the introduction, boundary lubrication is the regime where surfaces are not completely separated, which results in surface asperity interactions. The most important aspect of this regime is the formation of protective surface films to minimize wear and surface damage. The formation of these films
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is governed by the chemistry of both the film former as well as the contacting surfaces. Non-additive hydrocarbons, mineral oils, and esters will react in a boundary contact to produce “friction polymer” (Lauer and Jones, 1987). Except for electrical contacts, this material is usually beneficial, but does represent a lubricant loss mechanism. However, these conventional lubricants are never required to act alone and almost all are formulated with anti-wear, anti-corrosion, extreme pressure, or anti-oxidant additives to enhance their performance. Contrast this with a PFPE boundary lubricant, a relatively inert, very pure fluid, which in past years contained no additives. If these fluids were really inert, they would not provide any surface protection except for some local fluid film effects (micro-EHL) and some removal of wear debris. However, these fluids do react with bearing surfaces, producing a series of corrosive gases and friction polymer which, in turn, react with existing surface oxides to produce metallic fluorides (Mori and Morales, 1989; Carré, 1986; Herrera-Fierro et al., 1993). These fluorides are effective in situ solid lubricants that reduce friction and prevent catastrophic surface damage (Mori and Morales, 1989). Unfortunately, these fluorides are also strong Lewis acids (electron acceptors) that readily attack and decompose PFPE molecules (Herrera-Fierro et al., 1993; Carré and Markowitz, 1985; Kasai, 1992). This causes the production of additional reactive species, which, in turn, produce more surface fluoride, resulting in an autocatalytic reaction. This can cause a lubricated contact to fail abruptly, as shown in Figure 31.10a. In contrast, a non-PFPE space lubricant, such as Pennzane, has a greater lubricated lifetime and a much slower progression to failure. This is usually characterized by a gradually increasing friction
Friction Coefficient
0.3
0.2
0.1
0.0 0
1
2
3
4
5
6
7
Time (hrs) (a) KrytoxTM 143AC
Friction Coefficient
0.3
0.2
0.1
0.0 0
20
40
60
80
100
120
140
Time (hrs) (b) PennzaneTM
FIGURE 31.10 Coefficient of friction as a function of time for (a) Krytox™ 143AC and (b) Pennzane™ 2001A (spiral orbit rolling contact tribometer).
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FIGURE 31.11 Eccentric bearing screening test results for PFPE, PAO, and MAC oils. (From Carré, D.J., Kalogeras, C.G., Didziulis, S.V., Fleishauer, P.D., and Bauer, R. (1995), Recent Experience with Synthetic Hydrocarbon Lubricants for Spacecraft Applications, Aerospace Report TR-95(5935)-3.)
coefficient, as shown in Figure 31.10b. Therefore, the very reaction that allows the use of pure PFPE fluids in boundary contacts eventually leads to their early destruction and accompanying bearing failure. Of course, the progression of this mechanism is highly dependent on the local contact conditions (i.e., degree of surface passivation, type and thickness of surface oxides, amount of surface contamination, temperature, load, speed, etc.). Substantial improvements in bearing lifetimes can be obtained if ceramic or ceramic-coated balls are substituted for the standard bearing steels. TiC-coated balls (Boving et al., 1988) have shown considerable promise in alleviating some of these lubricant degradation problems. Gill et al. (1992) have observed a ninefold increase in bearing lifetime with a PFPE (Fomblin Z25 when TiC balls were used instead of 52100 steel balls. In accelerated life tests (Jones et al., 1999) using a spiral orbit tribometer, lubricant lifetimes with another PFPE (Krytox 143AC) were extended by factors of two to four, depending on the stress level. 31.5.1.5.1 Wear Characteristics and Relative Life Various Pennzane formulations have been compared to other hydrocarbons (PAOs) and PFPEs in eccentric bearing tests (Carré et al., 1995). The data shown in Figure 31.11 indicated that a Pennzane formulated with antimony dialkyldithiocarbamate yielded a lifetime of several times that of a PFPE (Krytox 143AB). Linear ball screw tests at ESTL (European Space Tribology Laboratory) (Gill, 1997) compared several lubricants. These included: Fomblin Z-25 oil, Braycote™ 601 grease, Pennzane SHF X-2000 oil, sputter coated MoS2, ion-plated lead, and Braycote 601 + ion-plated lead. The two PFPE lubricants failed rapidly, but the use of Braycote 601 and ion-plated lead reached the full test requirement of 2 million cycles. Ionplated lead alone failed at 400K cycles, while the MoS2 survived the full test, but some polishing of the contact zone was noted. The Pennzane oil completed the test but wear of the lead screw occurred and some dewetting was noted. Earlier work at ESTL (Gill, 1994) compared the performance of several solid and liquid lubricants in oscillating ball bearings. Three liquid/grease lubricants were tested with phenolic cages: Fomblin Z-25, Braycote 601, and Pennzane SHF X-2000. Torque levels were measured over 10 million oscillations. For a low angle of oscillation (±0.5°), Fomblin Z-25 yielded average torque levels 1.5 times that of Braycote and approximately 3 times that of Pennzane. At ±5°, mean torque measurements were similar for all three lubricants, but Pennzane did exhibit the lowest levels. Finally, at ±20°, the Z-25 yielded the highest torque, Braycote intermediate, and again Pennzane the lowest.
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FIGURE 31.12 Mean wear rates of various space lubricants using a vacuum four-ball tribometer. (From Jones, W., Shogrin, B., and Jansen, M. (1998a), Research on liquid lubricants for space mechanisms, in Proc. 32nd Aerospace Mechanisms Symp., Cocoa Beach, FL, NASA/CP-1998-207191, 299-310.)
Long-term, angular-contact bearing tests were also reported by Gill and Rowntree (1995). Pennzane SHF X-2000 was tested at 200 and 1400 rpm for 108 and 109 revolutions, respectively. The bearings did not fail, but they did suffer from oil starvation due to evaporation losses. It was not clear if this was due to insufficient sealing or related to a lubricant batch problem. However, it was stated that similar tests with PFPE oils have never failed due to starvation by oil evaporation. A vacuum four-ball tribometer (Jones et al., 1998) has been used to rank various space lubricants according to wear rates (Figure 31.12), including three PFPEs, Pennzane base fluid, a formulated Pennzane, and two other unformulated fluids (a silahydrocarbon and a PAO). In general, higher wear rates represent lower lifetimes in space. 31.5.1.6 PFPE Formulations Although no liquid PFPE additive formulations are currently being used for any space application, many additives, soluble in PFPEs, have been developed in the last few years. These include anti-wear, anticorrosion, and anti-rust additives (Gschwender et al., 1993; Helmick et al., 1997; Jones et al., 1996; Masuko et al., 1995; Nakayama et al., 1996; Sharma et al., 1990; Shogrin et al., 1997; Srinivasan et al., 1993; Williams et al., 1994). Several different additives exhibited anti-wear behavior in a Krytox basestock in vacuum four-ball tests (Figure 31.13) (Shogrin et al., 1997). 31.5.1.7 Greases Greases based on PFPEs with PTFE thickeners (Krytox 240 series and Braycote 600 series) have been used extensively in space mechanisms. In addition, hydrocarbon greases based on Pennzane and marketed by Nye Lubricants under the name Rheolube™ 2000 are also now available. The performance of various Pennzane-based greases appears in Rai et al. (1999). Recently, new PFPE formulations (commercially designated as Braycote 700 and 701) incorporating a boundary additive have yielded much improved wear characteristics (Figure 31.14) (Jones, D.G.V. et al., 1999). 31.5.1.8 Solid Lubricants A number of different solid lubricants have been used in space over the last 30 years. These include lamellar solids, soft metals, and polymers. Lamellar solids include transition-metal dichalcogenides like molybdenum disulfide and tungsten disulfide. Soft metals include lead, gold, silver, and indium. Polyimides and polytetrafluoroethylene are polymeric materials that possess lubricating properties. Unlike
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FIGURE 31.13
Modern Tribology Handbook
Anti-wear behavior of several additives in Krytox™ base stock using a vacuum four-ball tribometer.
FIGURE 31.14 Mean wear rates of various PFPE formulated greases using a vacuum four-ball tribometer. (From Jones, D.G.V., Fowzy, M., Landry, J.F., Jones, W.R., Jr., Shogrin, B., and Nguyen, Q. (1999a), An Additive to Improve the Wear Characteristics of Perfluoropolyether Based Greases, NASA TM-1999-209064.)
liquid lubricants, the metals and lamellar solids are applied as thin films (i.e., less than a micron). Ion plating (Roberts, 1990; Spalvins, 1987, 1998) and sputtering (Roberts, 1990; Spalvins, 1992; Fox et al., 1999) are preferred methods of applying these materials. Another method of applying lubricants to surfaces involves bonded films (Fusaro, 1981; Dugger et al., 1999). In this case, lubricants are mixed with an organic binder and applied to the surface via spraying or dipping. The films, which are typically greater than 10 microns, are then cured at high temperature. Self-lubricating polymers and polymer
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composites (Fusaro, 1990; Gardos, 1986) are sometimes utilized. The most common form of usage is as a cage or retainer in a rolling element bearing or as a bushing. By far the most common solid lubricants used in today’s space mechanisms are ion-plated lead and various forms of sputter-deposited MoS2. 31.5.1.8.1 Ion-plated Lead This is the lubricant of choice for precision spacecraft bearings in Europe. It is normally used in conjunction with a leaded bronze cage. Lead coatings and cages saw early success in cryogenic space applications (Brewe et al., 1974). Successful applications have been used on GIOTTO (Todd and Parker, 1987), OLYMPUS (Sheppard, 1983), and GERB (Fabbrizzi et al., 1999). Although not as common in the United States, this combination has recently been applied to encoder bearings for SABER. Extensive data have been published (Arnell, 1978) on the effects of speed, thickness, and substrate surface roughness. One disadvantage of this lubricant is its limited life in laboratory air. Much higher wear rates occur in air, producing copious amounts of lead oxide. This debris can also cause torque noise. 31.5.1.8.2 Molybdenum Disulfide MoS2 has been successfully used in space for many years (Lince and Fleishauer, 1997; Hilton and Fleischauer, 1994; Loewenthal et al., 1994; Hopple et al., 1993). These films display very low friction under vacuum conditions (i.e., 0.01 or less). Optimized thin films (1 micron or less) are deposited by sputtering. The tribological performance of these films is extremely dependent on the sputtering conditions. The sputtering conditions control the microstructure, which in turn determines crystallinity, morphology, and composition (Didziulis et al., 1992). For example, the presence of oxygen in the sputtering environment can affect both friction and wear life (Lince et al., 1990). For more details about the sputtering process, see Spalvins (1992). In addition, substrate surface roughness also has a pronounced effect on friction and wear. For steel bearing surfaces, optimum durability occurs at a nominal surface roughness of 0.2 µm (cla) (Roberts et al., 1992). The test environment also greatly affects the frictional behavior and life of MoS2 films. In ultra-high vacuum, these films display ultra-low friction (less than 0.01), as shown in Figure 31.15. Under normal vacuum conditions, the friction can range from 0.01 to 0.04, with exceptionally low wear and long endurance lives. When tested in humid air, these films have initial friction coefficients near 0.15 and very limited life (Roberts, 1987; Lince and Fleischauer, 1998). Because many space mechanisms must be ground-tested before launch, sometimes in room air, there has been much research to improve the performance of these films under atmospheric conditions. One method has been to modify MoS2 films by layering or co-depositing metals such as Au (Spalvins, 1984; Roberts and Price, 1995). In this work, inclusions of Au doubled the film durability in dry nitrogen and tripled or quadrupled it in air. Co-deposition with other metals (i.e., Cr, Co, Ni, and Ta) have also shown synergistic effects (Stupp, 1981). Ion implantation with Ag has also been reported to be beneficial (Liu et al., 1995) but not when co-deposited (Stupp, 1981). The properties of MoS2 films can also be improved by co-deposition with titanium (Renevier et al., 1999). These films were much less sensitive to atmospheric water vapor than pure MoS2 films. Studies have shown that the problems that occur in moist air are associated with adsorption of water molecules at edge sites on the MoS2 lattice (Fleishauer, 1984). Another method of enhancing MoS2 endurance in ball bearings is to use a PTFE composite as the retainer material (Suzuki and Prat, 1999). In gimbal bearing life tests (Hopple and Loewenthal, 1994), lives in excess of 45 million cycles were demonstrated with advanced MoS2 films combined with PTFEbased retainers.
31.6 Accelerated Testing and Life Testing Because of increasing demands of spacecraft mechanisms, new lubricants and additives are always under development. These materials must undergo ground-based testing to ensure they will meet the long duty cycle requirements and stringent conditions required by today’s space missions. In the past, two approaches to qualify lubricants for space were taken. The first approach was to perform system-level tests on actual flight hardware. The second was to attempt to duplicate the conditions
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0.20
Humid air
0.15
0.10
0.05
0.04
0.30
0.20
Ultra low friction
Vacuum
0.015
0.01 Super-ultra low friction
FIGURE 31.15 Frictional variation of sputtered MoS2 films. (From Spalvins, T. (1992), Lubrication with sputtered MoS2 films: principles, operation and limitations, J. Mater. Eng. and Perf., 1, 347-352. With permission.)
of flight system operation (Kalogeras et al., 1993). Although this type of testing produces results, they are costly, both in time and money. Therefore, only a few candidate lubricants are selected for testing. This has led to most lubricants being chosen through “heritage” or actual flight experience. Accelerated life testing is an approach that allows quick screening of several lubricants. Generally, test results cannot be extrapolated to predict lifetimes of components that are lubricated similarly but operate under different conditions (Conley, 1998). Instead, accelerated life testing allows for a better selection of candidate lubricants to undergo full-scale tests. Accelerated tests typically do not involve actual flight hardware, but rather utilize a setup that subjects the lubricant to an extreme condition. Test acceleration is achieved by varying various test parameters such as speed, load, temperature, contaminants, quantity of lubricant available, and surface roughness (Murray and Heshmat., 1995). When selecting which parameters to vary, it is important to have a thorough understanding of contact conditions and the lubricant used. In a liquid-lubricated environment, a significant change in speed or temperature could introduce a change of the lubrication regime. As speed increases or temperature decreases, film thickness also increases, taking the bearing from the boundary regime, through the mixed regime, and into the EHL regime. As described previously, each lubrication regime has specific and different wear characteristics. Also, time-dependent parameters such as creep, loss of lubricant through evaporation and centrifugal forces, and lubricant degradation are not modeled with accelerated life tests (Conley, 1998).
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TABLE 31.7
Strengths and Weaknesses of Accelerated Life Testing
Weakness Wetting condition with temperature Chemistry changes with temperature and pressure Oxidation changes with temperature and pressure Hydrodynamics region changes Wear/friction polymers change Coating fracture under high load (solid lube) Non-standardized Dynamic changes in cages and components Low confidence
Strength Easy to monitor Use to enhance design Use to validate model Rapid baseline data generation
From Murray, S. and Heshmat, H. (1995), Accelerated Testing of Space Mechanisms, NASA Contractor Report 198437.
Accelerated life testing with solid lubricants is somewhat easier. If a system uses solid lubricants exclusively and is a fairly low-speed application (<50 rpm), then testing at increased speeds can be done with confidence, provided that the specific wear rate is not a function of speed. Limitations with accelerated life tests of solid lubricants at higher speeds include additional loads from inertial effects and component stability (Conley, 1998). Advantages of accelerated life testing include: (1) quick relative ranking of lubricants, (2) tests that are easy to monitor, (3) data that can be used to enhance a lubricant or additive design or model, and (4) rapid generation of baseline data. Table 31.7 summarizes the strengths and weaknesses of accelerated testing.
31.6.1 Facilities for Accelerated Life Testing of Space Mechanisms 31.6.1.1
Eccentric Bearing Test Apparatus
Aerospace Corporation (Kalogeras et al., 1993) has developed an apparatus based on a 22.1-mm (0.900-in.) diameter bearing. In this test, the bottom (rotating) raceway is flipped over and the flat side polished to a 0.25-µm (10-µin.) finish. This allows the lower raceway to be mounted with eccentricity. The intentional misalignment accelerates the wear process and the flat surface operates at a higher stress level than the curved raceway. Both ensure that more severe tribological conditions are introduced. Also, post-test analysis can be more easily performed on a flat surface. Figure 31.16 shows the eccentric bearing tester. The lower raceway is mounted to a rotating shaft and rigidly supported. The upper raceway is placed inside an assembly containing a load cell. The load is induced into the bearing by compressing springs that push on the upper raceway fixture. The eccentricity of the setup can be altered from 0 to 3.06 mm (0 to 0.125 in.). The eccentricity introduces a skidding element into the motion of the ball that greatly accelerates lubricant degradation. It also provides a wide wear track for easy post-test surface analysis. The upper housing is connected to the lower housing through a set of aluminum flexures. This allows the upper housing to flex slightly during the test for torque calculations. Deflection is measured through a proximity sensor mounted in the lower housing. The entire assembly operates under vacuum of approximately 10–8 Torr. A similar test device exists at ESTL (Gill et al., 1993). 31.6.1.2 Spiral Orbit Rolling Contact Tribometer (SOT) NASA Glenn Research Center has developed a tribometer based on a simplified thrust bearing design. The rig consists of two flat plates with a single ball sandwiched between them (Figure 31.17). A load is applied through the bottom plate, which is held stationary as the top plate rotates. As the ball moves through the orbit, it travels in a spiral orbit. The orbit pitch has a direct relationship to the friction coefficient. The guide plate is used to return the ball to the original orbit diameter. The force required to do this is measured and the friction coefficient calculated. A small straight area develops on the lower
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Proximity probe
Vibration surface
Total bearing Eccentricity Elastic flexure
Reference surface
Proximity probe
Torque sensor
FIGURE 31.16 Aerospace Corp.’s eccentric bearing test mechanism. (From Kalogeras, C., Hilton, M., Carré, D., Didziulis, S., and Fleischauer, P. (1993), The use of screening tests in spacecraft lubricant evaluation, Aerospace Corp. Report No. TR-93(3935)-6.)
FIGURE 31.17 Spiral orbit rolling contact tribometer. (From Pepper, S.V., Kingsbury, E., and Ebihara, B.T. (1996), A Rolling Element Tribometer for the Study of Liquid Lubricants in Vacuum, NASA TP-3629.)
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FIGURE 31.18
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Detailed view of spiral orbit rolling contact tribometer.
plate where the ball is in contact with the guide plate and is termed the “scrub.” The rig operates at a vacuum level of 10–8 Torr or better. Figure 31.18 shows a detailed view of the setup. The most severe tribological conditions occur during the scrub. The scrub is easy to find on the surface of the plate and makes for simple post-test analysis. Also, all the contact surfaces being flat simplifies the analysis procedure. Lifetimes are controlled in two ways. First, the rig is capable of operating at a variety of stress levels, either by changing the applied load or varying the ball diameter. Hertzian stress is easily calculated for a sphere-on-flat geometry. The second way to control the lifetime is by varying the amount of lubricant used. For a typical test, 50 µg lubricant is used. With this limited amount of lubricant, almost all of it will be brought into the contacts thousands of times. Any tribologically induced changes can be more easily detected than with a large lubricant reservoir. The features of this rig are the following: 1. It is a rolling element tribometer operating in vacuum and at a contact stress level typically found in bearings. 2. It operates in the boundary lubrication regime. 3. It permits a simple and rigorous analysis of the contact stresses and the energy loss to the lubricant. 4. It enables an easy post-test examination of the tribological elements and the degraded lubricant with surface and thin-film analysis techniques. 5. It determines the coefficient of friction. 6. It determines the system pressure rise and allows a partial pressure analysis of the gas released by the lubricant as it degrades under tribological stress. 7. It operates with an extremely small and finite lubricant charge to provide maximum opportunity for lubricant molecules to be tribologically exercised and thus to undergo and exhibit tribological degradation (Pepper et al., 1996). 31.6.1.3 Vacuum Four-Ball Tribometer Figure 31.19 shows a tribometer developed at NASA Glenn Research Center based upon a four-ball configuration. It is designed to test liquid lubricants under pure sliding conditions at room temperature under a vacuum of at least 10–6 Torr. Figure 31.20 shows, in detail, the inside of the four-ball apparatus. The system consists of a rotating ball sliding against three stationary balls that are immersed in a lubricant. The system is loaded through a pneumatic cylinder, which pushes the lubricant cup and stationary balls against the rotating ball. The lubricant cup is held in position by a flex pivot. The flex pivot, which has a specific spring constant, allows for angular displacement in the direction of rotation. The amount of flex is measured to calculate torque and equivalent frictional force.
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FIGURE 31.19 Overview of four-ball vacuum tribometer. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
FIGURE 31.20 Detail of four-ball vacuum tribometer. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
Typical tests are run with 9.82-mm (3/8 in.) diameter balls, 100 rpm, room temperature, and an initial Hertzian stress of 3.5 GPa. This stress drops as a function of test time as a wear scar develops on the stationary balls. The test is stopped every hour and the wear scar diameters are measured. A special platform allows for the measurement of the wear scars without removing them from the cup (Masuko et al., 1994). This allows the test to resume exactly where it was stopped. A full test takes 4 hours. Upon completion, the wear volume is plotted as a function of sliding distance and the wear rate is calculated from the slope of the line. This rig provides quick information about the wear characteristics of lubricants and additive packages.
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Detail Load Friction force sensor 8
Ball or pin specimen Disk specimen
FIGURE 31.21 Ultra-high vacuum pin-on-disk tribometer. (From Miyoshi, K., Iwaki, M., Gotoh, K., Obara, S., and Imagawa, K. (1999), Friction and Wear Properties of Selected Solid Lubricating Films, NASA TM-209088.)
31.6.1.4 Vacuum Pin-on-Disk Tribometer Figure 31.21 shows an ultra-high vacuum pin-on-disk tribometer (Miyoshi et al., 1999) for testing of solid film coatings. The rig is a simple setup using a stationary pin with a known end diameter pressed against a rotating disk, which is coated with the desired lubricant. Displacement of the pin in the tangential direction is measured and a friction coefficient is obtained. The rotating mechanism is enclosed in a vacuum chamber and tests are typically run at a vacuum level of at least 10–9 Torr. The rig can also be back-filled with nitrogen or humid air to study the effects of the Earth’s atmosphere on space lubricant films.
31.7 Summary This chapter provides a current state-of-the-art review of the lubrication technology for space mechanisms. It is not intended to be an in-depth study. For more details, the readers are directed to the appropriate references.
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Bertrand, P.A. (1991), Absorption of Oil by Cotton-Phenolic Retainer Material, Aerospace Report No. TOR-0091(6404-10)-4. Boving, H.J., Haenni, W., and Hintermann, H.E. (1988), Titanium carbide coatings for aerospace ball bearings, in Proc. 22nd Aerospace Mechanisms Symp., Sunnyvale, CA, NASA CP 2506, 245-252. Brewe, D.E., Scibbe, H.W., and Wisander, D.W. (1974), Performance of high-speed ball bearings with lead and lead-alloy-plated retainers in liquid hydrogen at 1.2 million DN, J. Lubr. Tech., 437-442. Brown, P.L., Miller, J.B., Jones, W.R., Jr., Rasmussen, K., Wheeler, D.W., Rana, M., and Peri, F. (1999), The clouds and the Earth’s radiant energy system elevation bearing assembly life test, in 33rd Aerospace Mechanisms Symp., Pasadena, CA, NASA/CP-1999-209259, 197-212. Cantow, M.J.R., Barrall II, E.M., Wolf, B.A., and Geerissen, H. (1987), Temperature and pressure dependence of the viscosities of perfluoropolyether fluids, J. Poly. Sci. Part B: Poly. Phy., 25, 603-609. Carré, D.J. and Markovitz, J.A. (1985), The reaction of perfluoropolyalkylether oil with FeF3, AlF3, and AlCl3, STLE Trans., 28(1), 40-46. Carré, D.J. (1986), Perfluoropolyalkylether oil degradation: inference of FeF3 formation on steel surfaces under boundary conditions, ASLE Trans., 29(2), 121-125. Carré, D.J. (1990), The use of solid ceramic and ceramic hard-coated components to prolong the performance of perfluoropolyalkylether lubricants, Surf. Coat. Technol., 43/44, 609-617. Carré, D.J., Kalogeras, C.G., Didziulis, S.V., Fleishauer, P.D., and Bauer, R. (1995), Recent Experience with Synthetic Hydrocarbon Lubricants for Spacecraft Applications, Aerospace Report TR-95(5935)-3. Conley, P. (1998), Space Vehicle Mechanisms: Elements of Successful Design, John Wiley & Sons, New York. Conley, P. and Bohner, J.J. (1990), Experience with synthetic fluorinated fluid lubricants, in Proc. 24th Aerospace Mech. Symp., NASA CP-3062, 213-230. Corti, C. and Savelli, P. (1993), Synthetics profile: perfluoropolyether lubricants, J. Syn. Lub., 9(4), 311-330. Del Pesco, T.W. (1993), Perfluoroalkylpolyethers, in Synthetic Lubricants and High-Performance Functional Fluids, Shubkin, R.L. (Ed.), Marcel Dekker, New York, 145-172. Didziulis, S.V., Hilton, M.R., Bauer, R., and Fleishauer, P. (1992), Thrust Bearing Wear Life and Torque Tests of Sputter-Deposited MoS2 Films, The Aerospace Corp., El Segundo, CA, Report No. TOR92(2064)-1. Dowson, D. and Higginson, G.R. (1959), A numerical solution to the elastohydrodynamic problem, J. Mech. Eng. Sci., 1(1), 6-15. Dromgold, L.D. and Klaus, E.E. (1968), The Physical and Chemical Characteristics of an Homologous Series of Instrument Oils, Bearing Conference, Dartmouth College, Hanover, NH. Dugger, M.T., Peebles, D.E., Ohlhausen, J.A., Robinson, J.A., and Sorroche, E.H. (1999), Oxidation effects on the friction of lubricants and self-lubricating materials in the enduring stockpile, Proc. 22nd Aging, Compatibility and Stockpile Stewardship Conf., Oak Ridge, TN. Fabbrizzi, F., Sawyer, E., and Gill, S. (1999), Life test development and results for the Gerb mirror de-spinning mechanism, in 33rd Aerospace Mechanisms Symp., Pasadena, CA, NASA/CP-1999-209259, 221-235. Fleishauer, P. (1984), Effects of crystallite orientation on environmental stability and lubrication properties of sputtered MoS2 thin films, ASLE Trans., 27(1), 82-88. Fleishauer, P.D. and Hilton, M.R. (1991), Assessment of the Tribological Requirements of Advanced Spacecraft Mechanisms, Aerospace Corp., El Segundo, CA, Report No. TOF-0090 (5064)-1. Foord, C.A., Hamman, W.C., and Cameron, A. (1968), Evaluation of lubricants using optical elastohydrodynamics, ASLE Trans., 11(1), 31-43. Fox, V., Hampshire, J., and Teer, D. (1999), MoS2/metal composite coatings deposited by close-field unbalanced magnetron sputtering: tribological properties and industrial uses, Surf. Coat. Technol., 112, 118-122. Fusaro, R.L. (1981), Mechanisms of lubrication and wear of a bonded solid lubricant film, ASLE Trans., 24(2), 191-204. Fusaro, R.L. (1990), Self-lubricating polymer composites and polymer transfer film lubrication for space applications, Trib. Int., 23(2), 105-122. Fusaro, R.L. and Khonsari, M.M. (1991), Liquid Lubrication in Space, NASA TM-105198.
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Fusaro, R.L. (Ed.) (1999), NASA Space Mechanisms Handbook, NASA/TP-206988. Gardos, M.N. (1986), Self lubricating composites for extreme lubricating conditions, in Friction and Wear of Polymer Composites, Klaus, F. (Ed.), Elsevier Science, 397-447. Georges, J.M. and Melle, G. (1985), Microscopic behavior of the third body in dry friction or boundary lubrication, in Proc. JSLE Int. Tribol. Conf., Tokyo, Japan, 885-890. Gill, S., Price, W.B., Rowntree, R.A., Boving, H.J., and Hintermann, H.-E. (1992), In-vacuum performance of Fomblin Z25-lubricated, 52100 steel bearings with TiC-coated balls, in Proc. 5th Eur. Space Mechanisms and Tribology Symp., Noordwijk, The Netherlands, ESA SP-334, 165-170. Gill, S., Vine, M.K., and Rowntree, R.A. (1993), BLAST, A new lubricant screening tester for space oils and greases, in Proc. 5th Eur. Space Mechanisms and Tribology Symp., Noordwijk, The Netherlands, ESA SP-334, 365-371. Gill, S. (1994), A comparison of the performance of solid and liquid lubricants in oscillating spacecraft ball bearings, 28th Aerospace Mechanisms Symp., Cleveland, OH, 229-244. Gill, S. and Rowntree, R.A. (1995), Interim results from ESTL studies on static adhesion and the performance of Pennzane SHF X-2000 in ball bearings, 6th Eur. Space Mechanisms and Tribology Symp., Zurich, Switzerland, 279-284. Gill, S. (1997), A comparison of the performance of linear ballscrew devices when lubricated with dry and liquid lubricants in vacuum, in Eur. Space Mechanisms and Tribology Symp., Noordwijk, The Netherlands, 101-105. Godfrey, D. (1980), Review of usefulness of new surface analysis instruments in understanding boundary lubrication, in Fundamentals of Tribology, Suh, N.P. and Saka, N. (Eds.), MIT Press, Cambridge, 945-967. Gschwender, L.J., Snyder, C.E., Jr., and Fultz, G.W. (1993), Soluble additives for perfluoropolyalkylether liquid lubricants, Lubr. Eng., 49(9), 702-708. Gumprecht, W.H. (1966), PR-143 — A new class of high-temperature fluids, ASLE Trans., 9, 24-30. Hamrock, B.T. and Dowson, D. (1981), Ball Bearing Lubrication: The Lubrication of Elliptical Contacts, Wiley, New York. Helmick, L.S., Gschwender, L.J., Sharma, S.K., Liang, J.C., and Fultz, G.W. (1997), The effect of humidity on the wear behavior of bearing steels with RfO (n-C3F6O)xRf perfluoropolyalkylether fluids and formulations, Trib. Trans., 40(3), 393-402. Hersey, M.D. (1914), The laws of lubrication of horizontal journal bearings, J. Wash. Acad. Sci., 4, 542-552. Hilton, M.R. and Fleischauer, P.D. (1990), Lubricants for High Vacuum Applications, Aerospace Report TR-0091 (6945-03)-6. Hilton, M.R. and Fleischauer, P.D. (1994), Applications of Solid Lubricant Films in Spacecraft, Aerospace Report TR-92(2935)-6. Hooke, C.J. (1994), The minimum film thickness in lubricated line contacts during a reversal of entrainment — general solution and the development of a design chart, Proc. Instn. Mech. Engrs., J208, 53-64. Hopple, G.B. and Loewenthal, S.H. (1994), Development, testing and characterization of MoS2 thin film bearings, Surf. Coat. Technol., 68/69, 398-406. Hopple, G.B., Keem, J.E., and Loewenthal, S.H. (1993), Development of fracture resistant, multilayer films for precision ball bearings, Wear, 162/164, 919-924. Jones, D.G.V., Fowzy, M., Landry, J.F., Jones, W.R., Jr., Shogrin, B., and Nguyen, Q. (1999a), An Additive to Improve the Wear Characteristics of Perfluoropolyether Based Greases, NASA TM-1999-209064. Jones, W.R., Jr., Johnson, R.L., Winer, W.O., and Sanborn, D.M. (1975), Pressure-viscosity measurements for several lubricants to 5.5 × 108 Newtons per square meter (8 × 104 psi) and 149°C (300°F), ASLE Trans., 18(4), 249-262. Jones, W.R., Jr. (1982), Boundary Lubrication-Revisited, NASA TM 82858. Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. Jones, W.R., Jr., Ajayi, O.O., and Wedeven, L.D. (1996), Enhancement of Perfluoropolyether Boundary Lubrication Performance, NASA TM-107306.
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Jones, W., Shogrin, B., and Jansen, M. (1998a), Research on liquid lubricants for space mechanisms, in Proc. 32nd Aerospace Mechanisms Symp., Cocoa Beach, FL, NASA/CP-1998-207191, 299-310. Jones, W.R., Jr., Poslowski, A.K., Shogrin, B.A., Herrera-Fierro, P., and Jansen, M.J. (1998b), Evaluation of Several Space Lubricants Using a Vacuum Four-Ball Tribometer, NASA TM-208654. Jones, W.R., Jr., Jansen, M.J., Helmick, L.H, Nguyen, Q., Wheeler, D.W., and Boving, H.J. (1999b), The effect of stress and TiC coated balls on lubricant lifetimes using a vacuum ball-on-plate rolling contact tribometer, Proc. 33rd Aerospace Mechanisms Symp., Pasadena, CA, NASA/CP-1999-209259, 237-245. Kalogeras, C., Hilton, M., Carré, D., Didziulis, S., and Fleischauer, P. (1993), The use of screening tests in spacecraft lubricant evaluation, Aerospace Corp. Report No. TR-93(3935)-6. Kalogeras, C. and Tran, A., Rotating mechanisms, in NASA Space Mechanisms Handbook, Fusaro, R. (Ed.), NASA TP 1999-206988, chap. 8. Kannel, J.W., Lowry, J.A., and Dufrane, K.F. (1991), Lubricant Selection Manual, Phase III Report, contract NAS8-36655. Kasai, P.H. (1992), Perfluoropolyethers: intramolecular disproportionation, Macromolecules, 25, 6791-6799. Kingsbury, E. (1985), Parched elastohydrodynamic lubrication, ASME J. Trib., 107, 229-233. Kinzig, B.J. and Ravner, H. (1978), Factors contributing to the properties of fluoropolymer barrier films, ASLE Trans., 21, 291-298. Lauer, J.L. and Jones, W.R. (1987), Friction polymers, ASLE Spec. Publ. Sp-21, Tribology and Mechanics of Magnetic Storage Systems, III, 14-23. Lince, J.R., Hilton, M.R., and Bommannavar, A.S. (1990), Oxygen substitution in sputter-deposited mos2 films studied by extended x-ray absorption fine structure, X-ray photoelectron spectroscopy and X-ray diffraction, Surf. Coat. Technol., 43/44, 640-651. Lince, J.R. and Fleischauer, P.D. (1998), Solid lubricants, in Space Vehicle Mechanisms: Elements of Successful Design, Conley, P.L. (Ed.), John Wiley & Sons, New York, chap. 7, 153-183. Liu, H., Zhang, X., Yu, D., and Wang, X. (1994), The enhancement of wear life and moisture resistance of sputtered MoS2 films by metal ion implantation, Wear, 173, 145-149. Loewenthal, S.H., Chou, R.G., Hopple, G.B., and Wenger, W.L. (1994), Evaluation of ion-sputtered molybdenum disulfide bearings for spacecraft gimbals, Trib. Trans., 37(3), 505-515. Loewenthal, S.H., Jones, W.R., Jr., and Predmore, R. (1999), Life of Pennzane and 815Z-Lubricated Instrument Bearings Cleaned with Non-CFC Solvents, NASA/TM-209392. McMurtrey, E.L. (1985), Lubrication Handbook for the Space Industry, NASA TM-86556. Masuko, M., Jones, W.R., Jr., and Helmick, L.S. (1993), Tribological Characteristics of Perfluoropolyether Liquid Lubricants under Sliding Conditions in High Vacuum, NASA TM-106257. Masuko, M., Jones, W., Jansen, R., Ebihara, B., Pepper, S., and Helmick, L. (1994), A Vacuum Four-Ball Tribometer to Evaluate Liquid Lubricants for Space Applications, NASA TM-106264. Masuko, M., Takeshita, N., and Okabe, H. (1995), Evaluation of anti-wear performance of PFPE-soluble additives under sliding contact in high vacuum, Trib. Trans., 38(3), 679-685. Miyoshi, K. and Pepper, S.V. (1995), Properties Data for Opening the Galileo’s Partially Unfurled Main Antenna, NASA TM-105355. Miyoshi, K., Iwaki, M., Gotoh, K., Obara, S., and Imagawa, K. (1999), Friction and Wear Properties of Selected Solid Lubricating Films, NASA TM-209088. Murray, S. and Heshmat, H. (1995), Accelerated Testing of Space Mechanisms, NASA Contractor Report 198437. Nakayama, K., Dekura, T., and Kobayashi, T. (1996), Effect of additives on friction, wear and iron fluoride formation under perfluoropolyether fluid lubrication in vacuum and various atmospheres containing oxygen, Wear, 192, 1768-1785. Ohsaka, Y. (1985), Recent advances is synthetic lubricating oils (8). Perfluorinated polyethers, Petrotech, 8(9), 840-843. Paciorek, K.J.L., Shih, J.G., Kratzer, R.H., Randolph, B.B., and Snyder, C.E., Jr. (1990), Polysilahydrocarbon synthetic fluids. 1. Synthesis and characterization of trisilahydrocarbons, I & EC Res., 29, 1855-1858.
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Paciorek, K.J.L., Shih, J.G., Kratzer, R.H., Randolph, B.B., and Snyder, C.E., Jr. (1991), Polysilahydrocarbon synthesis fluids. 2. Synthesis and characterization of tetrasilahydrocarbons, I & EC Res., 30, 2191-2194. Pepper, S.V., Kingsbury, E., and Ebihara, B.T. (1996), A Rolling Element Tribometer for the Study of Liquid Lubricants in Vacuum, NASA TP-3629. Postma, R.W. (1999), Pointing mechanisms, in NASA Space Mechanisms Handbook, Fusaro, R. (Ed.), NASA TM-206988, chap. 9, 113-123. Rai, A.K., Massey, M.L., Gschwender, L.J., Snyder, C.E., Jr., Zabinski, J.S., and Sharma, S.K. (1999), Performance evaluation of some Pennzane-based greases for space applications, 33rd Aerospace Mechanisms Symp., Pasadena, CA, 213-220. Renevier, N.M., Fox, V.C., Teer, D.G., and Hampshire, J. (1999), Coating characteristics and tribological properties of sputter-deposited MoS2/metal composite coatings deposited by closed field unbalanced magnetron sputter ion plating, ICMCTF 99 Conference, San Diego, CA, paper E1-5. Roberts, E.W. (1987), The Lubricating Properties of Magnetron Sputtered MoS2, European Space Agency, ESA-5615/83-NL-PP. Roberts, E.W. (1990), Thin solid lubricant films in space, Trib. Int., 23(2), 95-104. Roberts, E.W. and Todd, M.J. (1990), Space and vacuum tribology, Wear, 136, 157-167. Roberts, E.W., Williams, B.J., and Ogilvy, J.A. (1992), The effect of substrate surface roughness on the friction and wear of sputtered MoS2 films, J. Phys. D: Appl. Phys., 25, A65-A70. Roberts, E.W. and Price, W.B. (1995), Advances in molybdenum disulfide film technology for space applications, in Proc. 6th Eur. Space Mechanisms and Tribology Symp., Zurich, Switzerland, 273-278. Roberts, E.W. (Ed.) (1999), The Space Tribology Handbook, 2nd ed., ESTL, AEA Technology. Roelands, C.H.A. (1966), Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils, O. P. Books Program, University Microfilm, Ann Arbor, MI. Sarafin, T. and Larson, W. (Eds.) (1995), Spacecraft Structures and Mechanisms — From Concept to Launch, Microcosm, Inc., Torrance, CA, 685-718. Schritz, B., Jones, W.R., Jr., Prahl, J., and Jansen, R. (1994), Parched elastohydrodynamic lubrication: instrumentation and procedure, Trib. Trans., 37(1), 13-22. Sharma, S.K., Gschwender, L.J., and Snyder, C.E., Jr. (1990), Development of a soluble lubricity additive for perfluoropolyalkylether fluids, J. Syn. Lubr., 7(1), 15-23. Sheppard, S. (1983), Design and development of an advanced solar array drive mechanism, Proc. 1st Eur. Space Mechanisms and Tribology Symp., ESA-SP 196, 19-26. Shogrin, B.A., Jones, W.R., Jr., Herrera-Fierro, P., Lin, T.Y., and Kawa, H. (1999), Evaluation of boundaryenhancement additives for perfluoropolyethers, Trib. Trans., 42, 747-754. Shubkin, R.L. (1993), Polyalphaolefins, in Synthetic Lubricants and High-Performance Functional Fluids, Shubkin, R. (Ed.), Marcel Dekker, New York, 1-40. Sianesi, D., Zamboni, V., Fontanelli, R., and Binaghi, M. (1971), Perfluoropolyethers. Their physical properties and behavior at high and low temperatures, Wear, 18, 85-100. Sianesi, D., Pasetti, A., Fontanelli, R., and Bernardi, G.C. (1973), Perfluoropolyethers by photooxidation of fluoroolefines, Chim. Ind., 55, 208-221. Snyder, C.E., Jr., Gschwender, L.J., Randolph, B.B., Paciorek, K.J.L., Shih, J.G., and Chen, G.J. (1992), Research and development of low-volatility long life silahydrocarbon-based liquid lubricants for space, Lubr. Eng., 48, 325-328. Spalvins, T. (1984), Frictional and morphological properties of Au-MoS2 films sputtered from a compact target, Thin Solid Films, 118, 375-384. Spalvins, T. (1987), A review of recent advances in solid film lubrication, J. Vac. Sci. Technol., A5(2), 212-219. Spalvins, T. (1992), Lubrication with sputtered MoS2 films: principles, operation and limitations, J. Mater. Eng. and Perf., 1, 347-352. Spalvins, T. (1998), The Improvement of Ion-Plated Ag and Au Film Adherence to Si3N4 and SiC Surfaces for Increased Tribological Performance, NASA TM-1998-207415.
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Spikes, H.A., Cann, P., and Caporiccio, G. (1984), Elastohydrodynamic film thickness measurements of perfluoropolyether fluids, J. Syn. Lubr., 1(1), 73-86. Spikes, H.A. (1996), Estimation of the Pressure-Viscosity Coefficients of Two Silahydrocarbon Fluids at Two Temperatures, Imperial College (Tribology Section), London, U.K., Report TS024b/96. Spikes, H.A. (1997), Film Formation and Friction Properties of Five Space Fluids, Imperial College (Tribology Section), London, U.K., Report TS037/97. Srinivasan, P., Corti, C., Montagna, L., and Savelli, P. (1993), Soluble additives for perfluorinated lubricants, J. Syn. Lub., 10, 143-164. Steinmann, P.A. and Spalvins, T. (1990), Influence of the Deposition Conditions on Radiofrequency Magnetron Sputtered MoS2 Films, NASA TP-2994. Stone, D. and Bessette, P. (1998), Liquid lubricants, in Space Vehicle Mechanisms: Elements of Successful Design, Conley, P.L. (Ed.), John Wiley & Sons, New York, chap. 8, 185-213. Stribeck, R. (1902), Characteristics of plain and roller bearings, Zeit. V.D.I., Vol. 46. Stupp, B.C. (1981), Synergistic effects of metals co-sputtered with MoS2, Thin Solid Films, 84, 257-266. Sugimura, J., Jones, W.R., Jr., and Spikes, H.A. (1998), EHD film thickness in non-steady state contacts, Trans. ASME, J. Trib., 120, 442-452. Suzuki, M. and Prat, P. (1999), Synergism of an MoS2 sputtered film and a transfer film of PTFE composite, Wear, 225/229, 995-1003. Suzuki, M. (1998), Comparison of tribological characteristics of sputtered MoS2 films coated with different apparatus, Wear, 218, 110-118. Tamborski, C., Chen, G.J., Anderson, D.R., and Snyder, C.E., Jr. (1983), Synthesis and properties of silahydrocarbons: a class of thermally stable, wide-liquid range fluids, Ind. Eng. Chem. Prod. Res. Dev., 22, 172. Tanaka, Y., Nojiri, N., Ohta, K., Kubota, H., and Makita, T. (1989), Density and viscosity of linear perfluoropolyethers under high pressure, Int. J. Thermophysics, 10(4), 857-870. Todd, M.J. and Parker, K. (1987), Giotto’s antenna de-spin mechanism: its lubrication and thermal vacuum performance, in Proc. 21st Aerospace Mechanisms Symp., NASA CP-2470. Vernier, C.G. and Casserly, E.W. (1991), Multiply-alkylated cyclopentanes (MACs): a new class of synthesized hydrocarbon fluids, Lubr. Eng., 47(7), 586-591. Venier, C.G. and Casserly, E.W. (1993), Cycloaliphatics, in Synthetic Lubricants and High Performance Functional Fluids, Shubkin, R. (Ed.), Marcel Dekker, New York, 241-269. Vergne, P. and Reynaud, P. (1992), High pressure behavior of space liquid lubricants, in Tribology 2000, Vol. 2, Bartz, W.J. (Ed.), Tech. Acad. Esslingen, Publ., Ostfildern, Germany. Westlake, F.J. and Cameron, A. (1972), Optical elastohydrodynamic fluid testing, ASLE Trans., 15(2), 81-95. Wedeven, L.D., Evans, W., and Cameron, A. (1971), Optical analysis of ball bearing starvation, ASME J. Lubr. Technol., 98, 349-363. Wedeven, L.D. (1975), What is EHD?, Lubr. Eng., 31(6), 291-296. Williams, J.R., Feuchter, D.K., and Jones, W.R., Jr. (1994), Development and Preliminary Evaluation of Aryl Ester Boundary Additives for Perfluoropolyethers, NASA TM-106603. Wu, Y. and Yan, S. (1986), A full numerical solution for the non-steady state elastohydrodynamic problem in nominal line contacts, in Proc. 12th Leeds-Lyon Symp. Tribology, 291-298. Zaretsky, E.V. (1990), Liquid Lubrication in Space, NASA Ref. Publ. 1240.
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32 Automotive Tribology 32.1 32.2
Introduction ................................................................... 1187 The Engine ..................................................................... 1188 Importance of Engine Tribology • Lubrication Regimes in the Engine • Engine Bearings • Piston Assembly • Valvetrain • Future Developments
32.3
Transmission and Drive Line ........................................ 1197 Transmission • Traction Drive • Universal and ConstantVelocity Joints • Wheel Bearings • Drive Chains
32.4
Introduction • Construction of a Tire • Mechanics of Load Transfer • Contact Area and Normal Pressure Distribution • Slip and Generation of Shear Traction • Hydroplaning • Wear Characteristics
Ajay Kapoor The University of Sheffield
Simon C. Tung
32.5
General Motors Powertrain
Martin Priest The University of Leeds
Rob S. Dwyer-Joyce The University of Sheffield
The Brakes ...................................................................... 1209 Introduction • Contact Pressure and Shear Traction • Materials • Friction • Wear
General Motors Research and Development Center
Shirley E. Schwartz
The Tire .......................................................................... 1203
32.6 32.7
Windshield Wipers......................................................... 1212 Automotive Lubricants .................................................. 1213 Lubricant Function • Lubricant Types • Engine Oil • Automatic Transmission Fluid • Air-Conditioning Lubricant • Gear and Axle Lubricants • Grease • Power Steering Fluid • Brake Fluid • Shock Absorber Fluid • Fuel Functional Fluids: Engine Coolant, Windshield Washer Fluid • Summary and Future Directions
32.1 Introduction The motor car is one of the most common machines in use today, and it is no exaggeration to state that it is crucial to the economic success of all the developing and developed nations of the world and to the quality of life of their citizens. The motor car itself consists of thousands of component parts, many of which rely on the interaction of their surfaces to function. There are many hundreds of tribological components, from bearings, pistons, transmissions, clutches, gears, to wiper blades, tires, and electrical contacts. The application of tribological principles is essential for the reliability of the motor vehicle, and mass production of the motor car has led to enormous advances in the field of tribology. For example, many of the developments in lubrication and bearing surface technology have been driven by requirements for increased capacity and durability in the motor industry. For the purpose of classifying the tribological components, one can divide the motor vehicle into engine, transmission, drive line, and ancillaries such as tires, brakes, and windshield wipers. In the following sections, each automotive component is discussed in detail. Lubricants used with these automotive tribological components are described in the last section of this chapter.
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Rockers Valve springs Piston rings Coolant Oil filter Journal bearings Oil pump Oil
FIGURE 32.1
Camshaft Valve Piston Cylinder block Connecting rod Dipstick Crankshaft Oil pickup tube Sump
Main engine components in a reciprocating internal combustion engine.
32.2 The Engine The reciprocating internal combustion engine as shown in Figure 32.1 is the prime mover in the motor vehicle, as well as in many other modes of ground and sea transport, including motorcycles, scooters, mopeds, vans, trucks, buses, agricultural vehicles, construction vehicles, trains, boats, and ships. Further applications can be found in the field of electrical power generation, where the internal combustion engine is used for primary and standby electricity generation and for combined heat and power plants. The popularity of the reciprocating internal combustion engine is testament to its performance, reliability, and versatility. However, there are also some major drawbacks. Thermal and mechanical efficiencies are relatively low, with much of the energy of the fuel dissipated as heat loss and friction. The internal combustion engine is also a significant contributor to atmospheric pollution through hydrocarbon, particulate, and NOx (nitrogen oxides) emissions and to the greenhouse effect via carbon dioxide (CO2) emissions. A viable alternative with the required portfolio of attributes including cost, however, has yet to be found and, hence, the reciprocating internal combustion engine is set to dominate the road vehicle market for the foreseeable future.
32.2.1 Importance of Engine Tribology To reduce friction and wear, the engine tribologist is required to achieve effective lubrication of all moving engine components, with minimum adverse impact on the environment. This task is particularly difficult given the wide range of operating conditions of load, speed, temperature, and chemical reactivity experienced in an engine. Improvements in the tribological performance of engines can yield: • • • • • •
Reduced fuel consumption Increased engine power output Reduced oil consumption A reduction in harmful exhaust emissions Improved durability, reliability, and engine life Reduced maintenance requirements and longer service intervals
With such large numbers of reciprocating internal combustion engines (Figure 32.1) in service, even the smallest improvements in engine efficiency, emission levels, and durability can have a major effect on the world economy and the environment in the medium to long term (Taylor, 1998). It is interesting to consider where the energy derived from combustion of the fuel is apportioned in an engine. In a published paper, Andersson (1991) showed the distribution of fuel energy for a mediumsize passenger car during an urban cycle. Only 12% of the available energy in the fuel is available to drive the wheels, with some 15% being dissipated as mechanical, mainly frictional, losses. Based on the fuel
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Drivetrain 7% • Differential gear 4% • Transmission 3%
Air drag 3% Rolling resistance 14% CRUISING RESISTANCE 17% Engine 41%
FRICTION LOSS 48%
Drivetrain 1% Vehicle weight 29%
Crankshaft system 2% Flywheel 3% ACCELERATION RESISTANCE 35%
FIGURE 32.2
Energy consumption developed in an engine.
consumption data in Andersson’s publication, a 10% reduction in mechanical losses would lead to a 1.5% reduction in fuel consumption. The worldwide economic implications of this are startling — in both resource and financial terms — and the prospect for significant improvement in efficiency by modest reductions in friction is clear (Taylor, 1998). Concerning energy consumption within the engine as shown in Figure 32.2, friction loss is the major portion (48%) of the energy consumption developed in an engine (Nakasa, 1995). The other portions are the acceleration resistance (35%) and the cruising resistance (17%). If one looks into the entire friction loss portion, engine friction loss is 41% and the transmission and gears are approximately 7%. Concerning engine friction loss only, sliding of the piston rings and piston skirt against the cylinder wall is undoubtedly the largest contribution to friction in the engine. Frictional losses arising from the rotating engine bearings (notably the crankshaft and camshaft journal bearings) are the next most significant, followed by the valvetrain (principally at the cam and follower interface), and the auxiliaries such as the oil pump, water pump, and alternator (Monaghan, 1987, 1989). The relative proportions of these losses, and their total, vary with engine type, component design, operating conditions, choice of engine lubricant, and the service history of the vehicle (i.e., worn condition of the components). Auxiliaries should not be overlooked, as they can account for 20% or more of the mechanical friction losses. For example, an oil pump in a modern 1600 cc gasoline engine can absorb 2 to 3 kW of power at full engine speed, while for a racing car this can rise to some 20 kW (Taylor, 1998).
32.2.2 Lubrication Regimes in the Engine As with any other system designed to operate with a liquid lubricant, the key operating tribological parameter in an engine is the lubricant film thickness separating the interacting component surfaces. More precisely, it is the relative magnitude of the lubricant film compared to the combined surface roughness of the two surfaces, the so-called film thickness ratio, or parameter, λ:
λ=
(
h 2 2 σ surface 1 + σ surface 2
)
12
(32.1)
where h is the film thickness calculated through the application of classical thin-film analysis taking the surfaces to be smooth, and σ is the root mean square (rms) surface roughness. A related version of this equation uses the center line average (cla) surface roughness values, (Rasurface 1 + Rasurface 2), in the denominator in place of the root mean square term. Figure 32.3 shows a plot of the relationship between the coefficient of friction and the oil-film thickness ratio. The diagrams at the top of the figure provide a visual example of the lubrication of two surfaces that are in relative motion to each other and that are separated by an oil film. At the box on the left side, there is surface contact; at the box on the right, a fluid film separates the surfaces; and between these
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FIGURE 32.3
Modern Tribology Handbook
Lubrication regimes for engine components and typical friction relationships.
two extremes partial, or intermittent, contact occurs. The various lubrication regimes are listed below the diagrams. The boundaries between these regimes are not sharply defined. The curved line below the lubrication regimes indicates the relationship between the friction coefficient and the oil-film thickness ratio. Examples of the lubrication regimes for several automotive components are shown at the bottom of Figure 32.3. Different automotive components rely on different modes of lubrication to achieve acceptable performance, and each may experience more than one regime of lubrication during a single cycle. Generally, journal and thrust bearings are designed to operate in the hydrodynamic lubrication regime in which bearing surfaces are separated by a lubricant film. Actual metal-to-metal contact is expected to take place only at low speeds and high loads and with low-viscosity lubricants. In contrast, valvetrain, piston ring assembly, and transmission clutch sliding generally take place under mixed or boundary lubrication conditions; surface contact occurs, and chemical films or reaction products may be an important means of surface protection. Furthermore, the importance of different lubrication regimes for each component may change with flattening of the surface roughness in the interface, wear of critical interacting surfaces, and degradation of the lubricant with time.
32.2.3 Engine Bearings Within the engine, rotating journal bearings are used to support the camshaft, the crankshaft, and the connecting rod. The basic construction is a split half-shell bearing fitted into a bore and incorporating some form of locating notch. The various forms the bearing shells may take are summarized in Heizler (1999). The shells are formed from a steel backing strip to give strength and tight dimensional tolerance and overlaid with a relatively soft bearing material such as tin-aluminum or lead-bronze. A further thin soft overlay is then put onto the bearing material to ensure a degree of initial conformability (Massey et al., 1991). Shafts designed for running against engine bearings are generally made of heat-treated steels or spheroidal graphite irons, with a hardness approximately 3 times that of the principal bearing material. Lubricant is directed to the bearings either by jet impingement or by passing through the bore of a hollow shaft. Provided the bearings are adequately lubricated, wear (after an initial running in period) is low. However, shaft misalignment or particulate contamination of the lubricant supply can lead to excessive wear. Bearing corrosion is an additional failure mechanism. As with most components in the engine, the tribology of journal bearings is complicated by issues such as lubricant supply, thermal effects, dynamic loading, and elasticity of the bounding solids. The Mobility technique for the analysis of dynamically loaded engine bearings was established some 30 years ago and remains the most common approach (Booker, 1965, 1969). The technique is robust and has proved amenable to simple computer analysis. It yields, among other results, the cyclic minimum film
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thickness between the journal and the bearing, which is an important design parameter. However, it is important to note that many simplifying assumptions are implicit in the use of the mobility method, which means that the predictions can only be used as a benchmark. Alternative approaches and research studies in which some of the assumptions have been relaxed are discussed in Martin (1983), Taylor (1998), and Xu (1999). The mobility method and many other alternative methods of solution assume that engine bearings operate entirely in the hydrodynamic lubrication regime. The benchmark prediction for a satisfactory minimum lubricant film thickness in an engine bearing used to be approximately 2.5 µm. Today, minimum film thickness predictions in the range 0.5 to 1.0 µm are being made for engine bearings in passenger cars, suggesting that asperity interaction may occur between the journal and bearing for at least part of the engine cycle. The implications of operation in the mixed lubrication regime for the analysis and design of engine bearings are significant and necessitate a fundamentally different approach (Priest et al., 1998; Xu, 1999).
32.2.4 Piston Assembly The piston is at the heart of the reciprocating internal combustion engine, forming a vital link in transforming the energy generated by combustion of the fuel and air mixture into useful kinetic energy. The piston carries the ring pack, which is essentially a series of metallic rings, the primary role of which is to maintain an effective gas seal between the combustion chamber and the crankcase. The rings of the piston ring pack, which in effect form a labyrinth seal, achieve this by closely conforming to their grooves in the piston and to the cylinder wall. Secondary roles of the piston ring pack are to transfer heat from the piston into the cylinder wall, and then into the coolant, and to limit the amount of oil that is transported from the crankcase to the combustion chamber. This flow path is probably the largest contributor to engine oil consumption and leads to an increase in harmful exhaust emissions as the oil mixes and reacts with the other contents of the combustion chamber. The desire to extend service intervals of engines and minimize harmful exhaust emissions to meet ever more stringent legislative requirements means that the permissible oil consumption levels of modern engines are very low compared to their predecessors of 10 or 20 years ago (Munro, 1990). The left side of Figure 32.4 is a schematic representation of a typical piston assembly from a modern automotive engine. From a tribological perspective, the main piston features of interest are the grooves,
FIGURE 32.4
Typical piston assembly and piston ring function from a modern automotive engine.
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Minimum Film Thickness (µm)
which carry the piston rings, and the region of the piston below the ring pack (the piston skirt), which transmits the transverse loads on the piston to the cylinder wall. The top two piston rings are referred to as the compression rings. Firing pressure pushes these rings out until the entire ring face engages the cylinder wall. Gas pressure is utilized to supplement the inherent elasticity of the ring to maintain an effective combustion chamber seal. The top compression ring is the primary gas seal and, as the ring nearest the combustion chamber, encounters the highest loads and temperatures. The top compression ring usually has a barrel-faced profile with a wear-resistant coating such as chromium or flame-sprayed molybdenum on the periphery and occasionally on the flanks. The second compression ring, which is sometimes referred to as the scraper ring, is designed to assist in limiting upward oil flow in addition to providing a secondary gas seal. The right side of Figure 32.4 illustrates how the second compression ring scrapes surplus oil from cylinder walls and how the ring rides on a film of oil and presents a lower edge to cylinder wall. As such, the second compression ring has a taper-faced, downward scraping profile that is not normally coated. The piston rings at the right of Figure 32.4 are notched. A more conventional design is a ring that is not notched, as in the drawing in the lower left portion of Figure 32.4. The bottom ring in the pack is the oil-control ring, which has two running faces (or lands), and a spring element to enhance radial load. As its name suggests, the role of this ring is to limit the amount of oil transported from the crankcase to the combustion chamber, and by design it has no gas sealing ability. The periphery of the lands and, occasionally, the flanks are often chromium plated. There are a large number of subtle variations to the basic ring design, a good summary of which can be found in Neale (1994). Notable examples are the keystone compression ring with tapered sides designed to prevent ring sticking due to deposit formation in the piston ring grooves of diesel engines; the internally stepped compression ring, which imposes a dishing on the ring when fitted to improve oil control; and the multipiece, steel rail, oil-control ring. In contrast to the one-piece oil-control ring, the multi-piece oil-control ring has smaller land heights, which increases conformability to the cylinder wall, and hence oil control, with reduced spring force and a ring of reduced overall axial height (Brauers, 1988). The piston ring is perhaps the most complicated tribological component in the internal combustion engine to analyze. It is subjected to large, rapid variations of load, speed, temperature, and lubricant availability. In one single stroke of the piston, the piston ring interface with the cylinder wall may experience boundary, mixed, and full fluid film lubrication (Ruddy et al., 1982). Elastohydrodynamic lubrication of piston rings is also possible in both gasoline and diesel engines on the highly loaded expansion stroke after firing (Rycroft et al., 1997). A typical prediction from a mathematical model such as Ruddy et al. (1982) for the cyclic variation of minimum film thickness between a piston ring and cylinder wall is shown in Figure 32.5, where zero degrees 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0
90
180 270
360
450
540 630
720
Crank Angle (degrees)
FIGURE 32.5 Typical predicted variation of film thickness between a top piston ring and cylinder wall of a gasoline engine with a plentiful supply of lubricant.
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of crank angle is top dead center firing. The prediction is for the top compression ring of a four-stroke gasoline engine assuming a plentiful supply of lubricant. The combined surface roughness of the piston ring and cylinder wall in this case was approximately 0.1 µm. The solution exhibits a characteristic shape of curve with small film thickness around the dead center positions where the sliding velocity, and hence lubricant entrainment velocity, is low and large film thickness at the mid-stroke positions where the sliding and entrainment velocities are large. Often piston rings are extremely starved of oil, leading to a reduction in the film thickness and a much more complex situation to analyze and interpret (Priest et al., 1999). During the engine cycle, the piston itself exhibits a complex secondary motion, transverse movement toward the cylinder wall, and tilting about the main piston pin axis (Li et al., 1982). This generally results in fluid film or mixed lubrication between the piston skirt and the cylinder wall. Modern, lightweight pistons have skirts that may deflect elastically during interaction with the cylinder wall, leading to the application of elastohydrodynamic lubrication theory to these components (Oh et al., 1987). Frictional losses between the skirt and the cylinder wall are significant, accounting typically for about 30% of total piston assembly friction, and the interaction with the cylinder wall can lead to noise generation, so-called piston slap. Gray cast iron, carbidic/malleable iron, and malleable/nodular iron are the most common base materials for all types of compression piston rings and single piece oil-control rings. However, steel is growing in importance as a piston ring material because of its high strength and fatigue properties and its manufacturing route, which enables rings of small axial height to be produced by, for example, forming steel wire. Steel is used for top compression rings and the rails of multi-piece oil-control rings. There are a multitude of piston ring running-in surface treatments and coatings, although many of these are subtle variations of similar processes. Chromium plating and flame-sprayed molybdenum are the most common wear-resistant coatings, although plasma-sprayed molybdenum, chromium, metal composites, cermets, and ceramics are growing in popularity as their technology progresses. Cylinder walls are generally manufactured from gray cast iron, either plain or with the addition of alloying elements, or an aluminum alloy. The surface treatment and coating of cylinder walls is less common than with piston rings, although proprietary wear-resistant coatings such as Nikasil plating are applied to aluminum bores. Aluminum-silicon alloy is the main material used for automotive pistons, occasionally with additions of other elements to enhance particular properties (e.g., copper to increase fatigue strength). Piston skirt coatings, based on materials such as polytetrafluoroethylene (PTFE) or graphite, are occasionally applied. In contrast to piston ring and cylinder liner coatings, piston skirt coatings are primarily intended to reduce friction rather than wear. Understanding and controlling the wear of the piston assembly is crucial to successful engine performance. Manufacturers through long experience have come to rely on early life wear of the piston rings and cylinder wall to modify the profile and roughness of the interacting surfaces to achieve acceptable performance as part of the running-in process. However, a clear understanding of the complex interactions between lubrication and wear of these components has only recently started to emerge (Priest et al., 1999). In addition to wear as a consequence of mechanical interactions, corrosive wear can occur in the upper cylinder region during short-trip service in a winter climate (Schwartz et al., 1994). The as-manufactured surface finish of piston rings and cylinders can have a major influence on wear behavior and thereby the success or failure of an engine. Although a wide range of surface finishing techniques has evolved for both piston rings and cylinder liners, the objectives of these processes appear to be the same: to improve oil retention at or within the surface, to minimize scuffing, and to promote ring profile formation during the running-in period. Plain cast iron piston rings are often used in a fineturned condition and electroplated; flame-sprayed and plasma-sprayed rings are generally ground to the desired finish. The poor wettability by oil of chromium-plated piston rings is overcome by etching a network of cracks and pores into the surface by reversing the plating current, chemical etching, grit blasting, lapping, or depositing the plate over a surface with fine-turned circumferential grooves. Cylinders are honed with ceramic stones, diamond hones, rubber tools, cork tools, or composite stones of cork or diamond. Piston skirts with a turned finish have been shown to give superior fuel economy and reduced risk of scuffing.
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FIGURE 32.6
Modern valvetrain system.
32.2.5 Valvetrain A modern valvetrain system as shown in Figure 32.6 should include valves, valve springs, valve spring retainers, valve keys, rocker arms, piston rods, lifter/tappets, and a camshaft. The primary function of the valvetrain system is to transform rotary camshaft motion into linear valve motion in order to control fluid flow into and out of the combustion chamber. The second function is to drive ancillary devices such as distributors, fuel pumps, water pumps, and power steering pumps. Many different styles of valvetrain mechanisms have been used on engines. Three basic valvetrain systems are (1) poppet valve, (2) sleeve valve, and (3) rotary valve. In a valvetrain system, the poppet valve configuration is the most popular and is used by virtually all the major automobile manufacturers for the inlet and exhaust valves of reciprocating internal combustion engines. The opening and closing of the valves is invariably controlled by a cam driven from the crankshaft to ensure synchronization of the valve motion with the combustion cycle and piston movement. Some of the typical mechanisms and some of the design variations have been executed on poppet valve systems. Common mechanisms are generally classified and referred to throughout the automotive industry as Type 1 through Type 5 (Nunney, 1998). The basic mechanisms for Type 1 through Type 5, as shown in Figure 32.7, include the following: 1. 2. 3. 4. 5.
Direct acting valvetrain End pivot valvetrain Center pivot Center pivot with cam follower Overhead (OHV) pushrod
camshaft located in cylinder head
Direct Acting
camshaft located in cylinder block
Pushrod
FIGURE 32.7
Valvetrain mechanisms.
End Pivot Rocker Arm
Center Pivot Rocker Arm
Center Pivot Rocker Arm with Lifter
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FIGURE 32.8 Comparison of friction, effective mass, engine speed, and overall engine package among these five types of valvetrain systems.
These types can be designed using either roller or sliding friction at each contact interface. There is, however, a large range of mechanisms in use to transmit the motion of the cam to the valve. These include push-rod operated, center-pivoted rocker, finger follower, direct acting bucket follower, and roller follower (Heizler, 1999). Other designs, such as rotary or sleeve valves, have proved difficult to lubricate, cause excessive oil consumption, have poor sealing properties, and generate excessive friction (Buuck, 1982). A comparison of friction, effective mass or valve weight, maximum engine speed, and overall engine package among the different types of valvetrain systems is shown in Figure 32.8. Friction also plays an important role in valvetrain type selection. The best configuration is roller follower, which can significantly reduce valvetrain friction. This is because the coefficient of friction at the camshaft/follower interface is less by an order of magnitude for rolling compared to sliding friction. The direct-acting system has poor frictional characteristics because it is not equipped with roller followers. The next most important characteristics — after rollers — for friction control are a function of the lowest mass, least number of components, and the lowest number of friction interfaces. The friction associated with the valvetrain is generally considered to be a small component of the mechanical losses, typically 10% compared to the 50% linked to the piston assemblies. However, at low engine speeds and for larger, slower running engines associated with the prestige car market, valvetrain friction is seen to rise significantly to 20 to 25%. This has been one of the main drivers behind introducing into the engine oil such friction modifier additives as molybdenum dithiocarbamate (MoDTC), which endeavor to reduce friction in the boundary lubrication regime (Korcek et al., 1999). The valvetrain presents a broad spectrum of problems to the tribologist in relation to the cam and follower, valve guides, valve stem seals, valve seats, hydraulic lash adjusters, lifter guides, pivots, camshaft bearings, belt drives, and chain drives. That said, the most critical interface in the valvetrain is that between the cam and follower, a contact that has proved difficult to lubricate effectively with all designs of valvetrain. Traditional design philosophy assumed that the cam and follower operated entirely in the boundary lubrication regime. Hence, attention tended to be limited to the materials and surface treatments of the components and the lubricant additives intended to produce wear-resistant surface films by chemical reaction (e.g., zinc dialkyldithiophosphates [ZDDP or ZDTP]). Scientific studies over the last 20 years or so, however, have shown that mixed and elastohydrodynamic lubrication have a significant role to play in the tribological performance of cams and followers (Taylor, 1994). These film thickness predictions can be usefully compared with typical surface roughness values for automotive metallic cams and followers of about 0.2 µm Ra. Although this analysis is relatively simple and neglects potentially important physical effects, it highlights the important message that the cam and follower may experience boundary, mixed, and elastohydrodynamic lubrication in a single cycle. Substantial film thickness tends to occur on the rising and falling flanks; whereas around the nose, the film thickness tends to be much smaller, with the potential for surface contact and wear.
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The most common materials for cams and followers are irons and steels with a variety of metallurgies and surface treatments to assist running-in and prevent early life failure. Ceramic followers are, however, becoming more common, especially in direct-acting valvetrains, in an attempt to reduce frictional losses (Gangopadhyay et al., 1999). Wear has been a persistent problem with cams and followers for many years, especially with finger follower configurations. Recent advances in our understanding of the link between kinematics, lubrication, and wear of valvetrains are now helping to overcome these difficulties (Bell, 1998), as is the trend toward direct acting and roller follower systems. The failure modes of cams and followers are pitting, polishing, and scuffing, all of which are influenced by materials, lubrication, design, and operating conditions. The durability and type of failure can vary considerably, depending on the combination of materials chosen, their surface treatment, and the lubricant and its additive package. Wear is also a problem at the valve/seat interface; the valve “recesses” into the seat and results in loss of engine timing. Loading is from a combination of the dynamic closing of the valve under cam action and the application of the firing pressure on the closed valve face, and therefore the seat is subjected to both high static and dynamic stresses. Temperatures in the region of the valve are high (typically 300°C to 500°C), and lubrication tends to be from small quantities of oil that flow past the valve guide. The valve may be allowed to rotate (usually slowly at about 1 to 2 revolutions per minute) under the action of the cam on the bucket. To reduce wear, an insert of hardened steel is shrunk-fit into the head. Valve and seat materials need to have high strength, wear resistance, temperature stability, and corrosion resistance (Narasimhan et al., 1985). Commonly, inlet valves are made from hardened, low-alloy martensitic steel for good wear resistance and strength. The exhaust valves are subjected to higher temperatures and are often made from precipitation-hardened, austenitic stainless steel for corrosion resistance and hot hardness. The valve seats are made from cast or sintered high-carbon steel. In some engines, the seat is formed by the induction hardening of the cylinder head material.
32.2.6 Future Developments The petroleum and automotive industries are facing tough international competition, government regulations, and rapid technological changes. Ever-increasing government regulations require improved fuel economy and lower emissions from the automotive fuel and lubricant systems. Higher energy-conserving engine oils and better fuel-efficient vehicles will become increasingly important in the face of both the saving of natural resources and the lowering of engine friction (Hsu, 1995). The United States Department of Energy conducted a workshop (Fessler, 1999) in which the focus was on industry research needs for reducing friction and wear in transportation. Reducing friction and wear in engine and drive trains could save the U.S. economy as much as $120 billion per year. Recommendations from that workshop (although each sector of the ground transportation industry has different needs and objectives) and desirable areas for future research (including current technical status, goals, and barriers related to fuel efficiency, emissions, durability, and profitability of powertrain systems) are as follows: 1. Develop a quantitative understanding of failure mechanisms such as wear, scuffing, and fatigue. This is important both for developing improved computational design codes and for developing bench tests to predict accurately and reliably the tribological behavior of full-scale automotive components. 2. Develop a variety of affordable surface modification technologies (Tung et al., 1995b) that are suitable for various vehicle components used with different fuels or lubricants under a variety of operating conditions. 3. Develop a better understanding of the chemistry of lubricants and how additives affect the interactions between lubricants and rubbing surfaces. This will provide a foundation for developing new lubricants that will be longer-lasting, environmentally friendly, capable of handling increased soot and acid loading from EGR (exhaust gas recirculation), compatible with catalysts, and compatible with new, lightweight nonferrous materials.
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Stringent federal legislation calling for better fuel economy and reduced emissions is the driving force for improved fuel efficiency and development of new engine technology. Among the various approaches for improving fuel efficiency, the use of energy-conserving engine oils is the most economical way in the automotive industry to acquire the necessary gains, compared to complicated hardware changes (Tung et al., 1995a). In addition, design and legislative pressures for cleaner, more efficient engines with higher specific power outputs is forcing tribological engine components to be operated with generally thinner oil films. One notable trend is the move toward lower viscosity engine oils (e.g., SAE [Society of Automotive Engineers] 5W-20 and 0W-20) in an effort to improve fuel economy. While this helps to reduce friction losses, it also leads to potential durability problems and a more critical role for the surface topography of engine components (Priest et al., 1998). In addition, there is a drive to extend engine service intervals. The engine has therefore to withstand an increasingly contaminated and degraded lubricant. The ability to incorporate more and more aspects of the physical behavior of lubricants into analytical modeling is an important and a fast-developing field (Coy, 1997). Uppermost in this regard are the reduction in viscosity at high shear rate, particularly with polymer-containing multigrade lubricants; the rise in viscosity at elevated pressure; and the boundary friction and wear behavior in the mixed and boundary lubrication regimes. Models of the rate of degradation of oil additives are also becoming available. One of the biggest challenges facing the engine tribology community is to make an effective link between the physical tribology of the components (Tung et al., 1996) and the complex chemical behavior and degradation of engine lubricants, both in the bulk fluid (Bush et al., 1991) and at the surface (Korcek et al., 1999). The engine oils are expected to last longer and simultaneously reduce engine losses.
32.3 Transmission and Drive Line 32.3.1 Transmission The tribological characteristics of the transmission clutch and band are highly important because they control transmission shift performance and clutch and band durability. From a friction standpoint, an automatic transmission clutch consists of two basic elements: the friction-lined clutch plates and the steel reaction plates. As shown in Figure 32.9, the clutch plate assembly consists of three major components: a steel core, an adhesive coating, and the friction facings. The steel core is a part onto which the friction facings are bonded. The core is blanked from medium carbon steel with a Rockwell C hardness of 24 minimum. The core hardness ensures maximum tooth contact area. The minimum compressive load requirement can reduce the potential for wear or fretting on both spline surfaces. The friction facing is bonded to one or both sides of the steel core with an adhesive. The adhesive, a thermosetting organic resin, is selected to withstand high shear forces and a wide range of operating temperatures. The friction material must have the required friction characteristics for effective engagement, a pleasing (to the customer) shifting of gears, and durability. It also must withstand a wide range of operating temperatures as well as high shear forces and compressive loads. Friction material is produced from a variety of fibers, particle fillers, and friction modifiers. These materials, with properly blended composition, can provide the necessary material strength and bulk uniformity for successful manufacturing, as well as providing a heat-resistant material with the required friction properties. The porosity of the friction material allows the transmission fluid to be stored near the friction interface as a lubricant reservoir, and the resilience of the friction material permits it to conform to transmission mating surfaces. In automatic transmissions, multiple plate clutches, band clutches, and the torque converter clutches are used either to transmit torque or to restrain a reaction member from rotating. The function of an automatic transmission clutch and band is to serve as a lubricated brake (e.g., for a planetary gear element) to transmit torque between transmission elements and the torque converter pump (input) and turbine (output). Dynamic and static band and clutch friction torque levels, and the difference between static
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FIGURE 32.9
FIGURE 32.10
Modern Tribology Handbook
Band and plate clutches used to shift gears in automatic transmission.
Automatic transmission clutch friction characteristics.
and dynamic friction torque, are important clutch performance criteria. They are closely dependent on transmission fluid characteristics. The transmission fluid can have a deep impact on shift-feel, chatter, static holding capacity, and the friction interaction between the transmission fluid and clutch material (Watts et al., 1990; Ward et al., 1993). All automatic transmission fluids recommended by vehicle manufacturers are formulated using a base stock plus a variety of additives, including friction-modifying additives to produce the desired transmission operation. Friction characteristics of the friction modifiers are described in Kemp et al. (1990) and Tung et al. (1989). Clutch friction characteristics for a base stock containing no friction-modifying additives are undesirable, as shown by the solid line in Figure 32.10. Although a high static coefficient of friction is desirable for good clutch-holding capacity, smooth engagement is difficult to achieve when static friction is greater than dynamic friction. As the clutch engagement approaches lock-up (decreasing sliding speed) with such friction characteristics, the increasing coefficient of friction tends to produce unstable stick-slip action between the rubbing surfaces and create abrupt and harsh clutch lock-ups. If these undesirable friction characteristics are too severe, shift-feel can be unsatisfactory to the vehicle’s passengers. Objectionable shift-feel is a major cause of customer complaints about vehicle/transmission performance. The most desirable friction characteristics (Tung et al., 1989) for smooth clutch engagement are those described by curve A in Figure 32.10 (Kemp et al., 1990; Tung et al., 1989). High dynamic friction promotes a rapid clutch engagement, and static friction that is lower than the dynamic provides
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FIGURE 32.11
1199
Automatic transmission clutch energy dissipation.
a smooth transition to clutch lock-up. However, the static friction coefficient must be high enough to provide good static clutch torque holding capacity. Friction-modified additives that produce properties described by curve B in Figure 32.10 are not entirely satisfactory. Although similar to curve A in shape, the low dynamic friction of curve B may demand increasing either the clutch area or the clutch applied pressure to complete a shift in a reasonable time. Under both dynamic and static conditions, clutch torque capacity is reduced. For curve C, friction characteristics are intermediate to those for curves A and B. However, due to unstable friction behavior for curve C, undesirable clutch lock-up and stick-slip action might occur for this case (Stebar et al., 1990). The amount of clutch energy dissipated during clutch engagement can affect both transmission fluid and clutch friction material life. In a transmission power shifting clutch or band, torque capacity must be great enough to produce a rapid clutch or band engagement. Otherwise, the energy dissipated as heat can produce clutch surface temperatures that contribute to the deterioration of both clutch materials and transmission fluids. Typical clutch surface temperatures have been measured and found to be on the order of 95°C above sump fluid temperatures for wide-open-throttle conditions (Stebar et al., 1990). Figure 32.11 illustrates clutch energy dissipation for different transmission operating conditions; the clutch horsepower (clutch friction torque × clutch sliding speed) vs. engagement time is shown for three simulated heavy-throttle shifts. Curve A can be considered a satisfactory shift for which the clutch surface area is designed to provide long clutch life. Curve B illustrates an unsatisfactory clutch engagement because of extended engagement time. This curve indicates excessive clutch slippage resulting from an inability of the clutch to transmit sufficient torque to lock up the clutch in a reasonable period of time. If the energy can produce dynamic torques higher than the clutch can transmit, the clutch will not lock up, and the resulting energy will be so high that cellulose clutch materials are likely to burn or char. Such deterioration can occur in only a few severe clutch engagements. A surface temperature as high as 230°C above sump temperature has been reported for automatic transmission power shifts (Stebar et al., 1990). Curve C illustrates a clutch engagement for which the energy level is much different than for curve A, but the capacity of the clutch is high enough to produce a short engagement. Although of short duration, high clutch surface temperatures will deteriorate clutch durability due to severe energy dissipation. In summary, clutch and band friction characteristics, transmission fluid viscosity, fluid oxidation, fluid shear stability, and wear properties of friction materials all play a vital role in the overall performance and durability of the transmission. Because of the important characteristics of automatic transmission fluids in controlling transmission shift performance and long-term durability, the transmission fluid is described in greater detail in Section 32.7.
32.3.2 Traction Drive The development of the continuously variable transmission (CVT) by vehicle manufacturers has increased dramatically to take advantage of the fuel economy and better drivability benefits that can be achieved
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FIGURE 32.12
Modern Tribology Handbook
Belt-pulley and traction drive units for continuously variable transmission.
with traction drive components. A unique advantage of the CVT is that it allows an engine to operate over a range of speeds and loads independent of the torque requirements that are placed on the wheels by the vehicle and the driver (Heilich, 1983). Traction drive CVT was applied to vehicles in the 1930s and was started by the Toric transmission (Hewko et al., 1962). Three basic types of commercial CVTs (Kluger et al., 1997) have been developed, as follows: (1) belt (steel, fabric, push, and pulley type); (2) half or full toroidal traction; (3) epicyclic. As indicated in Figure 32.12, two commercial CVTs (belt-pulley and traction drive) are the most common CVT drive units. Production vehicles equipped with steel beltpulley CVTs have been in the automotive market for more than 10 years. However, the full potential for reduction of fuel consumption could not be realized until the fully integrated electronic control system became available. The belt-pulley CVT relies on a metal link belt developed by Van Doorne’s transmission and is typically limited to use with engines of 2.0-liter displacement or smaller (Hendriks, 1993). Around 1990, a full toroidal traction drive device was developed to supplement the belt-pulley type because of the traction drive’s ability to handle larger engines. The toroidal traction drive provides better mechanical efficiency because of a very efficient rolling motion that operates in the elastohydrodynamic regime (Dowson et al., 1991). The current traction drive transmission transmits power through a rolling contact via forces that are varied with the radius at which the traction force is applied. Thus, power is transmitted in a continuous manner. This concept relies on two rolling elements that place a thin film of lubricant into an extreme shearing condition. The thin film between the two rolling bodies experiences high load and extreme shearing force, which produces complex elastohydrodynamic phenomena. The viscosity of the traction fluid increases significantly as a consequence of the high pressure, and the fluid becomes almost glasslike. The tangential force that is transmitted between the driving and driven elements is greatly enhanced by the traction fluid. The surface contact area between the two rolling elements is a finite area whose orthographic projection is an ellipse (Kluger et al., 1997). Within the ellipse, fluid is trapped between the rollers and is subjected to high compressive stresses of 0.7 to 3.5 GPa (100,000 to 500,000 psi). These stresses increase the instantaneous viscosity of the fluid by several orders of magnitude. This semi-solid lubricant can then transmit torque through the drive. Basic research was conducted with application to
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different traction drive units (Heilich, 1983). However, a traction drive CVT was not applied in practical use until 1990, due to three major barriers (Machida et al., 1990): 1. The traction drive rolling element materials were not sufficiently reliable due to high temperature and high pressure at the traction contact point. 2. There were no bearings that could support high speed and large axial load. 3. There were no traction fluids that could meet all traction component requirements. A traction drive requires not only higher traction coefficient to meet power transmission requirements, but also better lubrication and hydraulic lubricity requirements. Traction elements are generally made of materials similar to those used for ball or roller bearings for which the surface must withstand high loading and long duty cycles. This requirement also demands hardened steel or hardened materials for the contact surfaces. Because the traction drive operates at high speeds, it therefore provides high input and output ratios. Advanced tribological materials in the rolling element have made the life of the traction contact point long enough for use in high-power automotive transmissions. The efficiency of the traction drive relies heavily on the lubricant that is used. A high traction coefficient is required even at high contact temperatures. The temperature of a typical traction drive can rise to over 140°C. In addition to the traction requirements at high temperatures, traction fluids must not deteriorate when subjected to repeated shear or oxidation conditions. It has been indicated by traction fluid researchers (Tsubouchi et al., 1990; Hata et al., 1998) that naphthenic base compounds and several types of synthetic fluids have better traction characteristics than paraffinic or aromatic compounds. Research on traction fluids has also indicated that the traction coefficient of naphthenic compounds provides a higher rotational barrier and has a stronger molecular stiffness compared to paraffinic or aromatic compounds (Machida et al., 1990). Other variables affecting traction properties include rolling speeds, lubricant temperature range, quality of the roller surface finish, Hertzian contact pressure, degree of spinning, and the geometry of the rolling bodies. A substantial amount of CVT research is focused on traction fluid formulation and evaluation to determine whether the fluid can meet traction drive system performance requirements. Future research will concentrate on traction fluid formulation to optimize overall system performance and to adapt the traction fluids to the target automotive applications.
32.3.3 Universal and Constant-Velocity Joints Universal joints and constant-velocity joints are used to transmit power from the main driveshaft to the vehicle’s wheels, as shown in Figure 32.13 (Nunney, 1998). The top portion of the figure is a modern bipot universal joint, and the bottom figure portion is an application of constant-velocity universal joint for front-wheel drive. There are several different designs for joints. All have the ability to transmit power between two shafts with some degree of axial misalignment. The joints may be of the fixed or plunging type. The plunging type incorporates a spline coupling to allow axial approach of the shafts. Typically, the joints consist of an array of rolling elements held by a retaining cage between two raceways. The entire assembly is packed with grease and sealed inside a rubber boot. The contacts within the joint are between the rolling elements (balls, needles, or rollers), the raceway grooves, and the cage. The rolling elements are usually made from a high-carbon steel that is throughhardened. The raceways are made from a medium-carbon steel, and the load bearing areas are inductionhardened or carburized. When the shafts are aligned, the rolling elements are stationary. When the shafts are misaligned, the rolling elements undergo a low oscillation reciprocating motion. The load on the ball race contact is high, and the entrainment velocity is low. Because the surfaces tend to be relatively rough, boundary lubrication is the dominant lubrication regime. Possibly the most common form of failure in the field is by damage to the boot. This results in loss of lubricating grease and failure by gross damage to the joint components. However, contact fatigue is also observed. Cracks initiate at the surface and propagate to form spalls in the near-surface region. Extended use of the joint results in wear of the balls and raceways, leading to loss of dimensional accuracy.
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Trunnion shaft
Plunger housing
Spherical roller
Centering button Cover plate
Roller track
A modern bipot universal joint
CV joints
FIGURE 32.13 A modern bipot universal joint (top) and application of constant-velocity universal joint (bottom) for front-wheel drive. (From Nunney, M.J. (1998), Automotive Technology, SAE International, Butterworth-Heinemann. With permission.)
32.3.4 Wheel Bearings Conventional rolling element bearings are used in the road wheel hubs. These standard manufactured components are hardened high-carbon steel, machined and ground to a high tolerance and surface finish. Usually, deep groove bearings or a back-to-back angular contact bearing assembly is used. The bearings are packed with grease on assembly and sealed with elastomeric lip seals. The most common cause of wheel bearing failure is by damage to the surface caused during incorrect fitting or following impact during operation (the wheel striking a curb). The surface damage acts as an initiation site for rolling contact fatigue failure.
32.3.5 Drive Chains Some automotive engine designs use chain drives for timing and driving ancillary components. Chains have the advantage of a high capacity, increased durability, and being relatively cheap and simple. The basic components of a chain drive are the chain, sprockets, chain guides, and tensioners. There are two main types of drive chain: (1) roller chains consist of link plates with a pin, bush, and roller assembly; and (2) silent chains consist of an array of shaped link plates and pivot pins. The chain is lubricated by two means, firstly by splash as it dips into the sump during its travel and secondly through jets that impinge onto the sprocket/chain entry. The rollers in the case of roller chain, and the link plates in the case of silent chain, locate in the teeth of the sprockets. In the roller chain, the pin slides inside the bush during articulation, while the roller rolls across the sprocket tooth. The pin bush contact can therefore undergo excessive wear, causing chain elongation. For this reason, the pins and bushes are usually case-hardened and ground smooth, while the link plates are usually unhardened steel. With silent chain, the link plate slides across the sprocket tooth; this can result in wear of the link plate surface.
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The chain drive is subjected to dynamic loading. Chain guides and tensioners are incorporated to reduce the associated vibration. The guides are generally made of a polymer (typically Nylon 66) and either bolted in place or loaded against the chain by a spring or hydraulic tensioner. The chain tension and impact forces between the chain and guides can result in wear of the guide faces. Wear debris or dust in engine oil can become embedded in a polymeric tensioner and can act as an abrasive agent on the timing chain. Fuel components or fuel reaction products can enter engine oil and may soften a polymeric tensioner. Wear occurs on the guide face where it contacts the link plate edge, forming “tramlines.” In some cases, this continues until the grooves formed are deep enough that the rollers make contact with the guide; the load is then distributed to a greater extent and wear is reduced.
32.4 The Tire 32.4.1 Introduction The word “tire” is derived from “attire” — a protective cover to contain compressed air (or sometimes gas) in a toroidal chamber that is attached to a steel rim or wheel of an automobile. The North American spelling (tire) is closer to attire; the British spelling is tyre. Typically the tire has to perform the following functions. • The tire must transmit forces from the car to the road during driving. These forces include the weight of the automobile, passengers, and the cargo; the forces required to accelerate and decelerate the automobile; and the forces needed to steer the vehicle. These forces need to be transmitted in such a way that wear and fatigue failure of both the tire and the pavement are within acceptable levels. This is done effectively by providing a large contact area between the tire and the pavement, leading to a low contact pressure. • The tire must provide a firm grip on the road, which may be dry or wet, and sometimes even contaminated — intentionally (salt during winter) or accidentally (spillage). This is done by choosing an appropriately vulcanized rubber, to provide a large coefficient of sliding friction at the tire/pavement interface. The associated but rather conflicting demand on the tire is that the values of rolling friction and hysteresis loss should be as low as possible. Pneumatic tires are critical components of an automotive vehicle — about 14% of all fatal accidents occur when roads are wet (Pottinger et al., 1986) and the grip is lost, which is typically only about 3% of the driving time. • The tire is also used to absorb unevenness of the road and provide a comfortable journey. The texture or the roughness characteristics of the pavement and the tire become important in determining the quality of ride and the noise that is produced by micro-slip (described later) in the contact area. • Obviously, the tire has to do this at a low cost and must have a sufficiently long life with ample safety provisions against accidental deflation. It is not uncommon for truck tires to last about 160,000 kilometers (about 100,000 miles) and car tires about 80,000 kilometers (about 50,000 miles) (French, 1988). These lives can be increased by retreading.
32.4.2 Construction of a Tire In the early days, tires generally with toroidal tubes that were inflated with pressurized air, were cemented to the wheels and sometimes even fixed with rudimentary holding devices. This all changed with a patented design that incorporates rather inextensible steel wire hoops (tire beads) in the inside of the tire casing to fix and locate it on the wheel rim accurately, Figure 32.14a. The central depression in the rim facilitates tire fitting and its removal (Figure 32.14b). Subsequent tires were of cross-ply construction (Figure 32.15a), similar to the original produced by Dunlop in 1888. Michelin, in 1948, started producing tires with radial plies (Figure 32.15b). Both types carry patterned rubber treads and are used in different circumstances. The behavior of a particular tire
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FIGURE 32.14
Modern Tribology Handbook
(a) Normal operating positions of tire. (b) Tire position during fitting and removal.
FIGURE 32.15 Construction of a tire: (a) cross ply; (b) radial ply. (From Clark, S.E. (1971), The contact between tire and roadway, in Mechanics of Pneumatic Tires, Clark, S.E. (Ed.), National Bureau of Standards Monograph 122.)
in terms of load-carrying capacity, life, steering characteristics, resistance to damage, ride quality, and noise is dependent on the tire casing and is affected by the rubber/plies layout. In general, cross-ply is used in military applications, aeronautical, agricultural, cycle, and motorcycle tires; and radial ply is used for most passenger cars and trucks (French, 1988). Some of the common patterns for the rubber tread are shown in Figure 32.16. The purpose of these patterns is to squeeze water out of the contact in wet conditions and avoid skidding or hydroplaning. Feeder channels or smaller grooves flush water out of the contact. The grooves are generally 3 mm wide and 10 mm deep for a new tire (Moore, 1975). The tread between these grooves may be provided with cuts or sipes (small hook-shaped or bracket-shaped grooves in the tread of an automobile tire) to facilitate a wiping action to remove thin water films. Tread patterns, especially on the sides, help in cooling the tire by circulating the air.
32.4.3 Mechanics of Load Transfer Consider a cycle wheel: the hub is connected to the rim by wire spokes. An upward force at the bottom of the rim is transferred to the hub by the tension of the spokes. Load transfer from an automobile wheel
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(a)
(b) Sipes
(d) (c) FIGURE 32.16
Tire tread pattern: (a) zig-zag; (b) ribbed; (c) block; (d) sipes in tread.
FIGURE 32.17
Load transfer in a tire.
to the tire is analogous to that of the cycle wheel. The wheel behaves like the cycle hub, and the plies act like spokes. Pressurization of the tire produces tensile hoop stresses around the circumference and also along the direction of the plies. The tension in the plies is transmitted to the tire bead and then to the wheel rim. Application of a vertical force develops a contact area with the pavement, and the tire deforms near the contact. The angle at which plies are pulling the tire bead increases, and the component of tensile force in the radial direction decreases. The radial pull in other directions remains approximately the same, and the net result is a vertical force on the tire bead that gets transmitted to the wheel (French, 1988). Note that if the tire is rigid, a system of stresses will develop to transfer the load, as in the case of railroad wheels. Figure 32.17 shows a wheel rolling on the pavement and carrying a normal load W. The rolling resistance is shown by the resultant force Fr . In the case of free rolling, the wheel has no applied moment, and therefore the reaction of the contact forces passes through the wheel center (see Figure 32.17). In the case of a braking or a driving wheel, the presence of a turning moment implies that the resultant force does not pass through the center.
32.4.4 Contact Area and Normal Pressure Distribution The tire tread, which is fairly inextensible and loaded by the hoop tensile stresses, contacts the pavement and changes its curvature to drape over the surface. A fairly large contact patch is generated, the size and shape of which depend on tire pressure, tire construction, and applied load. Some typical contact patches are shown in Figure 32.18. A typical normal contact pressure distribution for a tire with no tread pattern is shown in Figure 32.19. A typical value for average contact pressure is about 1 MPa. By comparison,
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15
24
20
FIGURE 32.18 Tire contact area at increasing tire pressure (clockwise from top left corner). (From French, T. (1988), Tyre Technology, Adam Hilger. With permission.)
MO TIO
N
200 160
120 80 40m
m
40 80 0
0 2 4 6 8
(kp /cm2) PRESSURE
12 m 0m
20
FIGURE 32.19 A typical contact pressure distribution. (From Clark, S.E. (1971), The contact between tire and roadway, in Mechanics of Pneumatic Tires, Clark, S.E. (Ed.), National Bureau of Standards Monograph 122.)
steel wheels and steel rails in railroad applications produce an average contact pressure of about 1000 MPa. The presence of a tread pattern reduces the real contact area and increases the peak contact pressure.
32.4.5 Slip and Generation of Shear Traction The difference between the elasticities of the tire and the pavement material results in a difference in tangential displacement within the contact area, leading to a tendency to slip. Friction forces that are generated locally resist the slip. In some areas, known as stick regions, the local friction is sufficiently large to resist slip; but in other areas, known as slip regions, the friction force reaches its limiting value (equal to the load multiplied by the coefficient of sliding friction at that point) and local slipping occurs. Figure 32.20 shows stick and slip regions for a tire/pavement contact under normal pressure and stationary conditions. However, if the tire were to roll, whether braking or driving, the stick region shifts to the front of the contact (Figure 32.20b). In a braking situation, the slip direction is toward the stick region; whereas in a driving situation, the slip direction is away from the stick region. During cornering, the behavior is complicated by sideways slip (Moore, 1975; Clark, 1971); a typical contact patch is shown in Figure 32.20c. In the case of braking wheels, just before the tread enters the contact zone, it is under a tensile stress, and it elongates. In the stick zone, the tread and the pavement have no relative motion, and it is only in the slip zone that the tread slips toward the stick zone and starts to contract. In the case of driving wheels,
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(a)
FIGURE 32.20 (c) cornering.
(b)
(c)
Stick and slip (shaded) regions when the vehicle is (a) stationary; (b) braking or accelerating; and
Driving Contact length
Fx Longitudinal force,
Superimposed driving force
FD Driving Forward Backward
Free rolling Braking
Front of contact patch
Superimposed braking force FB
Braking
FIGURE 32.21 Distribution of shear traction within the contact area. (From Moore, D.F. (1975), Principles and Applications of Tribology, Pergamon Press. With permission.)
the tread is under a compressive stress and goes into the contact compressed. It recovers its compression in the slip region by slipping away from the stick region. The distribution of shear stresses in the contact area for free rolling, braking, and driving are shown in Figure 32.21. The shear stress distribution, as well as the normal pressure distribution, depends on the construction of the tire, inflation pressure, and several other factors. Because of the decreased (or increased) tread length in the stick region of the contact, the apparent wheel circumference is too short (or too long) for estimating the distance traveled. In one wheel rotation, the braked wheel travels a larger distance than its circumference, whereas the driving wheel covers a smaller distance. The brake slip ratio SB and the drive slip ratio SD are defined as (Moore, 1975):
(
)ω
(
)ω
S B = ω Ro − ω br
S D = ω dr − ω Ro
Ro
dr
(32.2) (32.3)
where ωRo is the angular velocity of a wheel in free rolling, and ωbr and ωdr are the angular velocities during braking and driving, respectively, for the same forward speed. Typical variations of braking force and driving force normalized with respect to the normal load are shown in Figure 32.22. Finally, being toroidal, the tire surface is non-developable; that is, it cannot be manufactured from an un-stretchable plane surface like a cylindrical surface can be (Clark, 1971). Contact with a flat pavement
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Braking force coefficients, fbr = FB W
Modern Tribology Handbook
A
(a) Braking
1.0
B 0.5
0
Lockedwheel skidding 0.2
0.4 0.5
Relative traction, fdr = FD W
Free rolling
1.0
1.0
Brake slip, SB (b) Driving
C
0.5 Very high spin values 0
0.5
Free rolling
1.0
Drive slip, SD
FIGURE 32.22 Variation of (a) braking force, (b) driving force, with slip. (From Moore, D.F. (1975), Principles and Applications of Tribology, Pergamon Press. With permission.)
Zone 1
FIGURE 32.23
Zone 2 Zone 3
Hydroplaning: the contact area is divided into three zones.
therefore requires the tread to undergo uneven local stretching, a phenomenon known as squirming. This movement is, however, very small in comparison to the slipping described above.
32.4.6 Hydroplaning In wet conditions, a fluid film can form between the tire and the pavement, as shown in Figure 32.23. In Zone 1, the fluid film is complete and there is no contact between the tread and the pavement. The tire experiences virtually no friction force in this zone. In Zone 2, the fluid film thickness gradually reduces to nearly zero. Here, there is partial contact between the tire and the pavement, but the contribution to friction is very small. In Zone 3, the fluid is completely squeezed out, and intimate contact occurs. It is only this zone that provides sufficient frictional traction for driving, braking, and steering. Under certain conditions of high speeds or thick water layers on the pavement, Zone 3 may be absent. The tire then rides on a film of water, and the condition is known as hydroplaning. Because the traction offered by a water layer is negligible and can provide only small braking or steering forces, this condition is dangerous, and the tire is provided with tread patterns so that water is squeezed out to the front and to the side of the contact.
32.4.7 Wear Characteristics When in service, the tire tread is subjected to many complex events. It deforms and un-deforms as it goes through the contact and drapes over pavement features. This produces a fatigue-type loading leading
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to failure. As shown in Figure 32.20, the tread slips over the pavement and endures abrasion by harder particles either buried in the pavement or present in the contact as third bodies. This manifests itself in the form of tears, cuts, and scratches. Sometimes, wear by roll formation may also be present, and the situation is complicated by chemical degradation and temperature effects (e.g., see Veith, 1986). Abrasion by slipping in the contact patch contributes most to the tire wear, and any maneuver that increases slipping increases wear. Cornering, swerving, and even excessive braking and accelerating increase the wear rate considerably. Some of the common terms used to define tire wear are: • Tread loss: The averaged value of the depth loss of tread through wear. It is measured for all the grooves and expressed in millimeters. Most countries have legal limits on the minimum tread depth for safety reasons. • Rate of wear: The loss of tread in millimeters per 10,000 km of travel. Typical values are a few millimeters per 10,000 km (Moore, 1975). • Tread wear index: The ratio of wear rate of a control or reference tire to that of the experimental tire, expressed in percent. As is usually true for wear of any component, the tire wear is also influenced by the two contacting bodies (i.e., the tire and the pavement), the interface, and the operating conditions. Various influencing parameters include the tire design and the pavement design, their construction, the composition of the tread, load on the tire, inflation pressure, speed, the manner in which the vehicle is being driven, and ambient temperature and other weather conditions. Because the variability in these is generally larger than that in other wear situations, a correlation between laboratory tests and field tests is very difficult. Even in field tests, differences exist in values obtained using fleet tests (driven cars) vs. trailer tests (towed cars) (Pillai, 1992).
32.5 The Brakes 32.5.1 Introduction Slowing down an automobile and/or permitting movement with a constant speed on gradients require dissipating kinetic and potential energy of the vehicle by a braking action. It is possible to convert this energy into rotational kinetic energy (spinning a flywheel) and reuse it later in accelerating the automobile, but the considerable weight and cost associated with regenerative braking systems limit their use to only a very few energy-conscious vehicles. Another method for slowing a vehicle involves dissipating this kinetic and potential energy by means of friction, which is the most common method of braking in passenger cars, light and heavy trucks, buses, and off-road vehicles. The generic systems used are shown in Figure 32.24. In a drum-type brake (Figure 32.24a), the shoe applies normal force on approximately 50 to 70% of the drum circumferential area. The drum and shoe are made of high-friction, low-wear materials, and the frictional loss at the
(a)
FIGURE 32.24
(a) Drum brake; (b) disc brake.
(b)
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Brake pads Contact pressure distribution: initial, final Fpad
Fpad
Brake disc (a) FIGURE 32.25
(b)
(c)
Variation of contact pressure in a disc brake.
interface provides dissipation of energy and the necessary braking action. In general, the brake shoe is the sacrificial component and wears faster than the drum, thus requiring comparatively frequent replacement. In a disc-type brake (Figure 32.24b), approximately 7 to 25% of the disc-rubbing surface is loaded by the brake shoe. Disc brakes provide relatively better heat dissipation because they have larger exposed surface areas and a better cooling geometry. However, the exposed surface area makes them vulnerable to unwanted contamination. Due to cooling characteristics, contamination, and other design issues, front brakes are of the disc type and rear brakes of the drum type (Anderson, 1992). Apart from the interface between the brake-lining and the brake-drum/disc, energy is also dissipated at the tire pavement interface, and it is the optimum combination of the two interfaces that produces effective braking. For example, if the road is icy, braking action will lock the wheel, and the tire will slip or skid on the road. The friction force will be very small, and braking will not be effective. A similar situation will arise if the brake-lining–brake-drum/disc interface becomes contaminated, and the friction generated at this interface becomes very small.
32.5.2 Contact Pressure and Shear Traction Figure 32.25a shows a brake shoe and disc in contact. The applied force generates a distribution of normal contact pressure at the interface. When the brake is new, the applied normal pressure is constant over the entire contacting area, as shown in Figure 32.25b. Sliding generates a distribution of frictional shear traction; the value of local shear stress equals the coefficient of sliding friction multiplied by the local normal pressure. The rate of energy dissipation is equal to the sliding velocity multiplied by the frictional shear stress. Because the sliding velocity increases linearly with the radial distance of the point from the center of the brake disc, more energy is dissipated at outer radii than inner. Wear at various points can be considered to be proportional to the rate of energy dissipation, and so it is larger away from the center. Under steady-state conditions, however, wear occurs uniformly over all the rubbing surface and requires that the energy dissipated at every point be constant. This means that the contact pressure multiplied by sliding velocity is constant, or that the contact pressure follows a 1/(radial distance) relationship (Figure 32.25c). As expected, the contact pressure at the ends gently drops to zero. Note that this mechanism is self-equilibrating; and, thus, if the local conditions change due to material inhomogeneity, contamination, or for any other reason, the contact pressure will change appropriately to produce a uniform wear rate. The reasoning given above assumes that the surfaces are smooth and ignores the fact that the surfaces are rough and contacts are made at asperity summits. The contact pressure is not smooth as depicted in Figure 32.25, but will have isolated peaks. However, the argument of uniform wear rate still applies.
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32.5.3 Materials Brake material must meet conflicting requirements: it must combine a high friction coefficient with a low wear rate. The large amount of kinetic and potential energy dissipated as frictional loss heats up the brake lining to a few hundred degrees Celsius (Moore, 1975). The asperities can reach a flash temperature of 1000 to 1100°C (Anderson, 1992). The demands on the brake materials are many and great, and the industry relies on highly proprietary formulations. Broadly, these can be classified as organic, metallic, and carbon (Anderson, 1992). Carbon-based brakes such as carbon-carbon composites are generally used for aircraft and racing car applications wherein weight is a critical design issue. Metallic brake linings, mostly of copper, iron, sintered bronze, and mullite, are used for very high power input density applications such as high-speed railways and racing cars. Cast iron is also used in some applications, but nowadays predominantly used as a counterface material in automotive drum and disc brakes.
32.5.4 Friction Figure 32.24 shows the most commonly used brake systems. Application of force on the brake shoe produces the required frictional torque. The frictional torque depends on the coefficient of friction between the brake shoe and the drum/disc and on many design parameters. In the case of drum brakes, the mechanism of self-actuation results in a nonlinear relationship between the frictional torque and the coefficient of friction. To overcome this, the frictional performance of a brake is characterized by Brake Effectiveness, which is the ratio of the brake frictional torque to the applied force. Figure 32.26 shows Brake Effectiveness for various drum and disc brakes. Surface irregularities and the cumulative effect of manufacturing tolerances in a new brake system mean that the contact is not made over the entire rubbing surface area. Only after some wear and burnishing (plastic flow of asperities) can the contact take place over most of the intended area. This results in the early Brake Effectiveness (Green Effectiveness) being lower than the steady-state value (Burnished Effectiveness). Brake Fading refers to dropping of the Brake Effectiveness to low values and results from excessively high temperature, migration of resin due to cooling, blistering of the brake material, and contamination. Brake Effectiveness is sensitive to speed and generally drops with increasing speed. Environment also has an effect. Contamination in the form of water, oil, dust, and/or corrosion products can change the effectiveness, and braking systems are designed so as not to be adversely affected by these factors. 15
20
a
a, Heel and toe
b
b, End biased
Brake effectiveness, N . m/N
Brake effectiveness, N . m/N
15
Duo-servo Leading-leading Leading-trailing Trailing-trailing Disk
10
10
c c, Uniform d
d, Center
Leading shoes
5
5
0
0 0
0.1
0.2
0.3
0.4
Brake lining friction coefficient
0.5
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
Brake lining friction coefficient
FIGURE 32.26 Brake effectiveness vs. brake lining friction coefficient. (From Anderson, A.E. (1992), Friction and wear of automotive brakes, in ASM Handbook, Vol. 18, Blau, P.J. (Ed.), 569-577. With permission.)
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32.5.5 Wear Brakes encounter the following wear mechanisms: thermal, abrasive, adhesion-tearing, fatigue, and macro-shear (Moore, 1975). As mentioned, very high flash temperatures (up to 1100°C) are reached at asperity junctions, and the brake material may melt or thermally decompose, leading to loss of material. Oxidative wear also occurs near the edges. Abrasive wear occurs due to plowing by wear debris and hard contaminants. Adhesion and tearing occur due to brake material sticking to the counterface and tearing off. Fatigue wear occurs due to repeated asperity encounters; and macro-shear is the sudden failure of friction material that has been weakened by heat. For practical purposes, brake wear is generally defined in terms of the distance traveled or the usage time. It can also be measured in mass worn per unit of frictional work. Typical values range from 40 to 100 mg/MJ (Anderson, 1992). During burnishing or break-in or running-in, wear of both the brake material and the counterface (drum or disc) is high. After burnishing, the wear stabilizes at a lower rate.
32.6 Windshield Wipers Windshield (or windscreen) wipers have a slender strip of a rubber compound, called the blade, supported by 4, 6, or 8 clips, as shown in Figure 32.27. The arm applies a load of 1 to 2 kg (10 to 20 N) to the clip hinge center, and this is distributed fairly uniformly along the length of the blade (Figure 32.28). The primary function of the wiper is to improve visibility by removing the dirt particles on the windshield by a wiping action. This is usually accomplished with the windshield washer on. The chemicals in the fluid help in loosening dirt particles, which are then scraped by the blade. If it is raining, the wiper removes excess water and leaves a thin and even film of water on the windshield. If there is only a little water on the windshield, the wiper spreads it evenly and improves visibility. Typical sliding speeds are 50 to 100 cm/s, and the coefficient of friction ranges between 0.15 and 0.2 for the wet case (rain water or with windshield washer fluid) and about 1.4 for the dry case. The friction coefficient in the wet case exceeds the value that would be expected if a hydrodynamic film was formed. It is generally believed that the wiper operates in the mixed lubrication regime, that is, some asperities touch the glass windshield. These asperities are formed by carbon filler material, which is incorporated in the blade to improve its wear performance. This intermittent contact leaves a thin stream of water behind, which then breaks into little droplets, reducing visibility. Sometimes, uneven wear of the blade can result in certain areas of the windshield not being wiped with sufficient contact pressure, leaving behind an unclean surface.
Construction of a typical wiper.
200
BLADE LENGTH
FIGURE 32.28
Contact pressure variation along the blade length.
450
400
350
300
250
200
150
100
50
100 0
PRESSURE (N/ cm)
300
FIGURE 32.27
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Various tribological tests for windshield wipers include running the wiper on a rotating flat glass disc, running it on a sample windshield, and also in field tests. During field tests or wind tunnel testing, air flow over the wiper generates a lift and reduces the contact pressure. This leads to a deterioration in wiping performance and produces a realistic test of the wiper performance.
32.7 Automotive Lubricants This section deals only with those substances that act as lubricants in cars and trucks.
32.7.1 Lubricant Function An automotive lubricant provides some or many of the following beneficial functions. It forms a fluid film that keeps one moving surface out of direct contact with the opposing surface. Additives in the lubricant are designed to lay down a chemical film that provides wear protection, particularly while operating under boundary lubrication conditions. Oil additives also help slow the rate of deposit, sludge, and varnish formation and slow the rate of corrosion, rust, and chemical attack on components. The circulation of the lubricant transfers heat away from hot surfaces, warms cold surfaces, and transports debris and contaminants to the filter. Oil additives that reduce friction contribute to the energy efficiency of the vehicle. Some automotive lubricants increase traction, control stick slip, and assist in sealing by providing a fluid barrier to reduce the escape of gases and by supplying chemical agents that provide a small amount of seal swell. In addition to performing these valuable functions, the lubricant must remain stable for an extended period of time and in some cases must act as a working fluid for such engine components as hydraulic lifters or chain tensioners.
32.7.2 Lubricant Types Engine oil and automatic transmission fluid are two of a vehicle’s lubricating fluids that provide many of these functions. Other substances in a vehicle that perform at least one lubrication function include air conditioner fluid and its associated lubricant, gear and axle lubricants, grease, brake fluid, power steering fluid, and shock absorber fluid. In addition to the above fluids that are commonly recognized as lubricants, several additional fluids also provide some lubrication functions. For example, fuel helps lubricate the fuel pump, injectors, valve guides, and valve seats. Engine coolant inhibits corrosion in the coolant system and lubricates the coolant pump. Windshield washer fluid carries away dirt. Several solid, composite, or polymeric components (e.g., spacers, tensioners, seals, or gasket materials) are also called upon to provide lubrication function. In the chapter sections that follow, for the substances in a car or light-duty truck that have lubricating properties, a variety of topics are addressed; for example: • • • • • •
Function of the lubricant Range of service conditions that the lubricant must withstand Properties and composition of the lubricant Changes in lubricant properties during service Test methods Current issues with regard to the lubricant
32.7.3 Engine Oil 32.7.3.1
Composition
Engine oil is composed primarily of base stock (70 to 90% of the total composition), with the remainder consisting of various protective additives. The base stock can be formed by distilling and collecting a fraction of a batch of crude oil such that the molecular weight of the fraction is within a desired range.
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This fraction can be purified by solvent extraction and solvent dewaxing so that the composition is appropriate for a lubricant base stock. Base stocks of this type are designated “Group I.” (Note: the American Petroleum Institute [API] has defined a series of base stock groups [currently I through V] according to base oil properties. Oils formulated with the same additive package and base stocks belonging to the same group are considered comparable for the purpose of base oil interchange, and thus may be eligible for a reduced amount of engine testing to certify them for licensing under the terms of the API Engine Oil Licensing and Certification System.) If further enhancement of the base stock properties is desired, various chemical reactions can be employed, such as reacting with hydrogen at high temperature and pressure in the presence of a catalyst. This process removes undesirable elements such as nitrogen, oxygen, and sulfur; removes double bonds in the carbon-containing compounds (which creates a structure that is less susceptible to chemical attack); and breaks larger hydrocarbon molecules into smaller, more fluid ones. Further treatment can remove any remaining fractions that are chemically reactive or are likely to solidify at low temperature. The resulting base stock is resistant to chemical attack, fluid at low temperature, and less volatile at higher engine operating temperatures. Fluids processed in some or all of the ways described here are classified as Group II or Group III base stocks. Alternatively, base stock can be formed by chemical reaction of low-molecular-weight building blocks to create a “synthetic” oil whose molecular-weight distribution range is small and whose chemical structure is resistant to degradation. Such oils can be classified as Group IV (for polyalphaolefin base stocks) or Group V base stocks (anything not covered in I through IV). Engine oil base stocks can consist of oils from any combination of these processes. Those base stocks that are derived primarily from the refining process are popularly termed “mineral” oil. Those that are derived primarily from the buildup of low-molecular-weight hydrocarbons are popularly termed “synthetic.” “Partial synthetic” and “semi-synthetic” are terms used to describe oils whose base stocks have been enhanced in some manner. In addition, synthetic esters can be added to semi-synthetic and synthetic base stocks to improve seal swell characteristics. Some additive suppliers also find that esters help solubilize additives in synthetic and semi-synthetic base stocks and help keep deposit-forming reaction products in suspension. Among the tribological fluids listed under Lubricant Types, engine oil is relatively complex. As a consequence of the harsh environment that engine oil must withstand, a number of additives are typically incorporated into engine oil to provide specific beneficial properties. One of the most important additives is the antioxidant, which is a sacrificial agent that reduces the tendency of the engine oil to oxidize, thicken, and form varnish, but that eventually becomes inactivated as a consequence of performing its protective function. Anti-wear agents are incorporated to provide a protective, wear-resistant chemical film, especially under high-load conditions. In particular, the zinc dialkyldithiophosphate antioxidant is also an anti-wear agent. Detergents neutralize acids that are formed from combustion or from overheating of engine oil, protect susceptible engine components against corrosion, inhibit deposit formation, and help keep surfaces clean. Dispersants suspend insoluble contaminants and inhibit varnish and sludge formation. Friction modifiers reduce friction, and therefore enhance the energy efficiency of a vehicle. The engine oil’s defoamer reduces the tendency of the engine oil to foam, thus ensuring that oil films in critical components will not be weakened by the presence of bubbles. A viscosity modifier or viscosity index improver helps the oil remain fluid when the oil is cold but allows the oil to be sufficiently thick when the oil is hot. Pour-point depressants help keep the oil from solidifying at very low temperature. 32.7.3.2 Functions of Engine Oil Engine oil has many functions. It must withstand the high heat of combustion and must not degrade excessively on exposure to contaminants such as fuel and combustion products. When an engine is newly manufactured, engine surfaces tend to be rougher than is the case after the engine has been in use for a while. During use, these rough surfaces are smoothed, and the metal debris from the smoothing process is transported by the flowing oil past a screen which can remove large particles and debris that is left in the engine from the manufacturing process. Next, the oil passes through a filter that removes smaller particles.
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The engine oil is then circulated to various engine locations that require specific kinds of protection, as follows. Bearings require sufficient oil pressure that the journal can be supported on an oil film to ensure that contact between journal and bearing is minimized. Engine oil provides a fluid film that lubricates moving valves and carries away heat. Engine oil splashes on the cylinder wall, is carried along the cylinder bore surface by the motion of the piston rings, helps provide a barrier to contain gases formed in the combustion process, and also provides a lubricated surface over which the piston rings can slip easily. Oil jets deliver oil to the undercrown of the piston to control temperature and prevent scuffing and ring sticking. Oil splashes or drips on cams and lifters, and causes the formation of a protective chemical film that reduces stress and wear between the cam and lifters. Hydraulic lifters contain oil within their interior to cushion the effect of the motion over the cams and to maintain proper clearance between the valve lifter and camshaft. Oil pressure is used in some applications to adjust the timing chain. Several additional protective capabilities are desirable for engine oil. For example, if oil volatility is low, there will be less tendency of the oil to evaporate on exposure to hot spots, and oil economy may be improved. If oil becomes contaminated with water during short-trip operation, rust-preventatives in the oil will reduce the tendency for the oil to corrode iron in the engine. An increasing concern with modern engine oil is the influence of the engine oil’s phosphorus on the deterioration of emission system components (Culley et al., 1995, 1996). Thus, oil formulators are faced with the dilemma of trying to provide adequate wear and antioxidant protection without damaging emissions control devices. 32.7.3.3 Oil Properties That Are Assessed in Standard Tests In many countries, engine oil must pass rigorous standard tests to be certified for use in vehicles. The tests vary from country to country, from one vehicle manufacturer to another, and from one fuel type to another. The standard tests were developed to simulate various types of service that were known to cause oil-related problems. As a consequence of a great amount of effort on the part of those individuals who developed the tests, the standard test methods are designed to ensure that the oil will protect the engine and its components against corrosion and wear; will not thicken excessively during high temperature service; and will withstand the effects of marginal quality fuel in city service in which there is a considerable amount of time spent at idle. There are tests to ensure that the engine oil, as it degrades, will not coat the insides of the engine with sludge or varnish and will continue to protect the engine against excessive rusting, even if water and acids (from the partial combustion of fuel) condense in the engine oil during short-trip service. Engine oil must keep particulates such as soot dispersed well enough that critical flow passages in the engine are not blocked and agglomeration is controlled, so that valvetrain, ring, and bore wear does not become excessive. The oil must not gel on long-standing, must remain fluid at low temperatures to allow proper engine cranking and oil pumpability, and must remain fuel-efficient during operation. 32.7.3.4 Effects of Service on Engine Oil Properties The tests described in the previous paragraph would not have been developed if the properties of engine oil had remained constant during use. However, engine oil properties change due to such factors as shear of the viscosity modifier or viscosity index improver and fuel entering the oil, which causes lower oil viscosity. Fuel reaction products can condense in the engine oil and inactivate some types of antioxidants (which therefore promotes oil oxidation, formation of acids, and oil thickening). Some fuel reaction products are acids that neutralize the detergent. Nitration of the oil can also occur, via nitrogen in the air or nitrogen reaction products. Such reaction products can cause the formation of a thick black sludge on engine surfaces. Heat from the combustion process lowers oil viscosity, but heat also evaporates the lighter ends of the oil, which eventually causes oil thickening and sluggish flow on cold starts. Causes of changes in oil properties are due to type of service, type of fuel, and characteristics and age of the engine. For example, high-temperature oil degradation is different from low-temperature degradation. In addition, gasoline, diesel oil, alcohol, natural gas, vegetable oil, hydrogen, etc., all cause their own unique type of damage to the oil and to the engine. Service-related changes to the engine oil can typically be categorized under one or more of the following driving styles:
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FIGURE 32.29
1. 2. 3. 4.
Change in engine oil viscosity with distance traveled, freeway service.
Freeway driving High-load or high-speed driving City driving in which the oil is fully warm, but where there are periods at idle Extreme short-trip, cold-start driving in which the engine oil never reaches the equilibrium operating temperature
32.7.3.4.1 Freeway Service In freeway service, the engine oil properties remain stable for a relatively long time. There may be a slight loss of viscosity during the first several thousand kilometers of operation after an oil change as a consequence of shear of the viscosity index improver. Eventually, the oil may thicken from oil oxidation, presence of insoluble contaminants, or evaporation of the lighter ends of the oil. An example of stability of engine oil viscosity during freeway service is shown in Figure 32.29 (Schwartz et al., 1994). At the end of the freeway service, the vehicle began a series of exceedingly short trips in winter. During the shorttrip service, fuel entered the engine oil and caused a significant drop in viscosity. 32.7.3.4.2 High Load Service In high load service, engine oil tends to thicken as a consequence of either evaporation of the lighter ends of the oil or oxidation of the base stock (or both of these effects simultaneously). Varnish and sludge form and the oil becomes acidic, which puts susceptible engine metals and polymeric materials at risk of corrosion or degradation. Nitration of the oil can cause formation of sludge. Additionally, in diesel engines, soot can enter the engine oil and cause the oil to thicken and to adsorb oil additives. For example, high soot levels can plug filters and cause a high pressure drop across the filter. Dispersants are used in engine oil to counteract some of these adverse soot effects. Soot can contribute to the inactivation of the engine oil’s antioxidant. In addition, soot can increase the wear rate by adsorption of antiwear additives and by agglomeration of soot into abrasive particles whose diameter may be greater than the clearances between critical engine components. Figure 32.30 shows an example of the loss of oxidative stability of engine oil in a gasoline-fueled vehicle being driven primarily in freeway service. One of the test vehicles was pulling a 900-kg trailer, and the other test vehicle was not pulling a trailer. Figure 32.30 indicates that even this relatively minor difference in load can be detected as an increased rate of degradation of the antioxidant. The differences in the rate of loss of oxidative stability illustrated in Figure 32.30 are predictable, based on engine measurements such as bulk oil temperature and fraction of the oil volume that is directly exposed to the high heat of the combustion process (Schwartz, 1992a,b). The Sequence IIIE test (ASTM D5533, for oxidation and wear control in oils for gasoline-fueled vehicles); the PSA TU3MH test (CEC L-55-T-95, for ring sticking, piston varnish, and viscosity increase);
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FIGURE 32.30 service.
Effect of pulling a 900-kg trailer on remaining antioxidant protection of engine oil, primarily freeway
the Nissan KA24E test (for wear); the L-38 test (ASTM D5119, for high-temperature bearing corrosion); the Toyota IG-FE test (for high-temperature oil oxidation and viscosity increase); and the Mack T-8 test (ASTM D 5967, for ensuring viscosity stability and measuring soot loading in diesel engines) are examples of standard tests that are designed to measure the extent to which an oil’s properties remain stable during high-temperature service. (Note: Sequence “III” is Roman numeral “three,” and “E” represents version “E” of the test method. The next upgrade of the test will be designated Sequence IIIF. Other Sequence tests also use Roman numeral designation: Sequence IID is Sequence 2 version E; Sequence VE is Sequence 5 version E; Sequence VIA is Sequence 6A.) 32.7.3.4.3 City Service In city service, fuel can accumulate in the engine oil if the engine is at idle for extended periods. Gasoline or diesel fuel in the engine oil can cause the viscosity of the oil to decrease. Incomplete combustion of the fuel can cause the formation of acidic combustion products which condense in the engine oil and begin to inactivate the protective alkaline detergents and dispersants. Acidification of engine oil can put bearings at risk of corrosion. Varnish and sludge can form on engine surfaces. Incomplete combustion can generate soot in diesel engines. An example of the effect of city service on engine oil properties is depicted in Figure 32.31, in which the oil degraded faster in city service than in freeway service. Both vehicles in this test experienced identical driving conditions on a chassis dynamometer. The nature of the fuel can also influence the 12 City, gasoline City, M85 11
3.1L V-6 engine API SG-quality SAE 10W-30 engine oil
Arrows indicate oil freshening as a consequence of adding makeup oil
Kinematic viscosity 10 at 40°C, cSt 9
8
7
6
Freeway, gasoline Freeway, M85 0
5000 10000 15000 Distance on oil, km
20000
FIGURE 32.31 Effect of service type and type of fuel on engine oil viscosity. (Note: M85 means fuel is 85% methanol and 15% gasoline.)
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0.2
0.2 Calcium engine percent
Transition from long trips to short trips 0.1
0.1
0.0
0.0 0
Transition from short-trips to a long trip 5.7L V-8 engine, gasoline fuel API SG-quality, SAE 5W-30 engine oil Short trips were 3-km long in cold weather. Engine oil became contaminated with fuel and water during short trips. 5000 10000 15000 Distance on oil, km
20000
FIGURE 32.32 Additive drop out during short-trip service and reversibility of the effect on commencement of long-trip service.
extent of oil degradation, as suggested by the fact that, in city service, the gasoline-fueled vehicle’s viscosity was starting to trend higher than that of the M85-fueled vehicle toward the end of the city-driving test shown in Figure 32.31. The Sequence VE test (ASTM D5302), which measures sludge, varnish, deposits, and valvetrain wear, is an example of a standard test method that monitors oil life in city service. 32.7.3.4.4 Extreme Short-Trip, Cold-Start Service In extreme short-trip, cold-start driving, the engine oil never warms completely. Fuel, combustion products, and water can accumulate in the engine oil and remain there for a long time (Schwartz, 1991). Engine oil additives can drop to the bottom of the oil pan, carried down by the water that has entered the oil (Schwartz, 1991). Once the engine oil’s corrosion inhibitors are inactivated by dropping to the bottom of the pan with the water, the engine is at risk of corrosion. An example of this reversible dropout effect is shown in Figure 32.32 (Younggren and Schwartz, 1993). In a gasoline-fueled vehicle, as a consequence of fuel entering the engine oil, the viscosity of the oil can become considerably lower than one would expect for a given temperature (Schwartz, 1992c). Because the oil temperature is always low in this type of driving, the thickening effect of the engine oil due to low oil temperatures is partially offset by the lower oil viscosity that is a consequence of fuel entering the engine oil during cold starts. Thus, during a cold start, fuel-contaminated engine oil is easier to pump than fresh oil. However, if the driver tows a trailer or takes a long trip after having taken many short trips in winter, the oil’s viscosity may be unacceptably low once the oil temperature reaches the normal operating range. Several opposite viscosity effects can also occur. A significant fraction of polar contaminants (derived from partial combustion products of the fuel or aging of the engine oil) in cold engine oil can cause the oil to gel on long standing. And, if the engine is running on an alcohol fuel such as methanol, when alcohol enters the engine oil, it forms an emulsion that can be more viscous than either the methanol or the oil alone. Some of these viscosity effects are shown in Figure 32.33 (Schwartz, 1992c). If an oil-water emulsion is formed, and if this emulsion contaminates a vehicle’s positive crankcase ventilation (PCV) emission control system, the PCV control function may not be as effective as it should be. Examples of standard tests that provide information about short-trip, gasoline-fuel service include the ASTM D5844 Sequence IID test and Ball Rust test, both of which assess the ability of the engine to protect engine components against corrosion. 32.7.3.5 Fuel Efficiency Fuel efficiency in a given engine can be influenced by surface properties of engine components, frictionmodifying additives in the engine oil, engine oil viscosity, and by changes in these properties with use.
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15
M85 fuel, short trips, emulsion formation
Viscosity of engine oil at 40°C, cSt
Evaporation of water and methanol during warm weather Long trip to remove fuel and water
10 M85 fuel, freeway
Gasoline fuel, freeway 5
Gasoline fuel, short trips, trips, fuel dilution
SAE 10W-30, API SG quality engine oil 0
FIGURE 32.33
0
2 0
400 600 Distance on oil, km
800
1000
Variability of engine oil viscosity with type of service and type of fuel.
Fuel efficiency provided by a given engine oil can be measured by monitoring the amount of fuel consumed in a standard test cycle and comparing the results to the fuel efficiency obtained in an identical test when using a standard engine oil of known fuel efficiency, as described in the Sequence VIA test. 32.7.3.6 Models of Engine Oil Performance and In Situ Devices to Monitor Oil Properties Over the many years since development of the first internal combustion engines, a vast amount of information has been gathered about the lubricant properties required for acceptable engine performance. For example, in recent years, computer models have provided answers to many questions related to engine design and oil performance. Models can predict the desired range for engine oil viscosity, extent of temperature rise in a working bearing, fluid film thickness, and the load that a given material can withstand. As a consequence, great strides have been made with regard to optimizing engine hardware based on computer models. As long as the engine operating conditions are within the range covered by the model, such predictions can usually be trusted. If some failure mode lies outside the domain addressed by the model, it becomes important to define the boundaries of validity of the model, identify the technical disciplines that are pertinent to the failure modes of the problem of interest, and create new classes of models that include all the technical disciplines involved in the problem of interest. As an example of a multidisciplinary approach, a variety of mathematical models are emerging to predict changes in oil properties as a function of engine operating conditions. One of the first of such models was created by Dyson, who considered that an engine could be treated mathematically as if it were a chemical reactor and who predicted the remaining alkalinity in diesel engines by monitoring fuel throughput and sulfur content of the fuel (Dyson et al., 1957). Schwartz found that the remaining useful life of the engine oil’s antioxidant in gasoline-fueled engines could be modeled by assuming that the antioxidant was completely inactivated in the small volume of oil that was directly exposed to the high heat of combustion at the top ring reversal point, top dead center (Schwartz, 1992a,b). Audette and Wong were able to estimate the oil film thickness, changes in the oil composition, and the amount of oil consumption that occurred as a consequence of evaporation of the lighter ends of the engine oil from the cylinder bore surface in a diesel engine as a function of the boiling point range of the engine oil, the temperature of the cylinder liner, the volume of oil that was carried to the upper cylinder area, and the characteristics of the piston rings (Audette et al., 1999). For fuels containing both methanol and gasoline, in short-trip service in which both fuel and water enter the engine oil, Schwartz found that emulsion-forming contaminants (methanol, water) in the engine
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oil caused a viscosity increase, solution-forming contaminants (gasoline) caused a viscosity decrease, and these combined effects on viscosity could be predicted based on the volume fraction of each type of contaminant in the engine oil (Schwartz, 1992c). An area of active investigation is the development of models to predict the end of useful life of engine oil. Because the nature of oil aging depends on engine design and type of service, incorporating these parameters into models of engine oil life will provide challenging opportunities for future model makers. An additional area that is sure to expand is the development of sensors that monitor one or more properties of engine oil during service. For example, oil viscosity sensors and conductance measurement devices are being developed, patented, and in some cases placed in production (Hellwig et al., 1998; Johnson et al., 1994; Kato et al., 1986; Kauffman, 1989; Kollmann et al., 1998; Wang et al., 1994). As witnessed by the diversity and success of the few examples described here, the process of developing sensors and models of oil performance that comprehend both changing oil properties and service conditions has already begun.
32.7.4 Automatic Transmission Fluid Automatic transmission fluids assist the transmission to shift gears. Under high load conditions, the automatic transmission fluid must be able to withstand the heat and forces that are generated. However, unlike engine oil, the transmission fluid is not exposed to contamination from the combustion process. Thus, transmission fluid does not experience the type of degradation modes that occur as a consequence of fuel and its combustion products entering the engine oil. Automatic transmission fluids must resist chemical changes (such as oil thickening and acidification) that are a consequence of oxidation and must minimize the adverse consequences of physical changes such as the low viscosity of hot oil and the high viscosity of cold oil. That is, transmission fluids must retain the ability to flow into critical areas when cold, but not flow out excessively when the oil is hot. The fluids need to maintain the appropriate amount of friction and reduce wear and corrosion, either by providing a fluid film between moving components or providing a protective chemical film on the surface. Transmission fluids need to maintain the appropriate amount of seal swell to reduce leakage, as well as retain stable shift properties, even after extended service. The fluids carry away heat and debris. They must also retain friction modifier durability in the harsh environment of constant slipping in electronically controlled slipping torque-converter clutches. 32.7.4.1 Composition All automatic transmission fluids recommended for use by car manufacturers are formulated using synthetic or mineral oil base stock plus a variety of additives. Synthetic fluids tend to provide properties that are more stable and last longer than mineral oil, but they also cost more. Additives in the oil include friction modifiers to produce the desired clutch operation, corrosion inhibitors, viscosity index improvers, dispersants, seal swell agents, antioxidants and antiwear agents, with a total additive treatment level typically in the range of 10 to 20% (Kemp et al., 1990). Among these additives, friction modifiers are of particular importance for proper transmission performance. The chemicals employed to produce good clutch friction characteristics are often long-chain hydrocarbon molecules with a polar group on one end. An example is dilauryl phosphate, which is composed of two chains, each containing 12 carbon atoms, with a phosphorus-containing acid polar group on one end of the dual chain. Another example is oleic acid, which is an 18-carbon chain with an organic acid polar group on the end. Both dilauryl phosphate and oleic acid are soluble in mineral oil, and their effectiveness in modifying clutch friction characteristics depends on the capability of the polar group to attach to the rubbing surfaces. Friction-modifier additives prevent surface adhesion and surface asperity contact that would generate high levels of friction and wear. The polar groups of friction modifiers either react chemically with the rubbing surfaces or physically adsorb onto the surfaces to form a tenacious film. Clutch friction characteristics using three friction-reducing additives (oleic acid, dilauryl phosphate, and glycol dioleate) formulated with mineral base stock have been compared in a laboratory clutch
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friction device (Tung et al., 1989; Stebar et al., 1990) as shown in Figure 32.10. Among these three additives, dilauryl phosphate (additive A in Figure 32.10) demonstrates the most desirable clutch friction characteristics. 32.7.4.2 Evaluating Automatic Transmission Fluids To ensure that the properties of automatic transmission fluids remain within an acceptable range, the fluids must meet various chemical and physical requirements. The fluids are also evaluated using performance tests that measure such characteristics as wear resistance, retention of appropriate friction properties, torque, time-to-lock-up, and shift-feel. References to North American test methods are provided in the 1999 SAE Handbook, Volume 1, “Fluid for Passenger Car Type Automatic Transmissions — SAE J311 Feb94 SAE Information Report,” pages 12.54 through 12.56, and in the requirements of the various automobile manufacturers. 32.7.4.2.1 Physical and Chemical Tests The following tests are used to assess the physical and chemical characteristics of automatic transmission fluids: 1. 2. 3. 4. 5. 6. 7. 8.
Flash point and pour point Fluid oxidation Kinematic viscosity at 40°C and 100°C Brookfield viscosity at various temperatures, including tests down to –40°C Copper corrosion Rust prevention Foaming tendency Elastomer compatibility
32.7.4.2.2 Transmission Fluid Oxidation Tests In the Transmission Fluid Oxidation test (a General Motors DEXRON®-III specification) formerly known as THOT (Turbo Hydramatic Oxidation Test), the transmission must provide satisfactory operation at an elevated temperature (163°C) for 300 hours in a full-scale transmission test. Air is passed through the transmission while the transmission is being motored. At the end of the test, the transmission fluid is evaluated for such oil properties as acidity, viscosity, and corrosion resistance. The transmission is also evaluated by comparing the parts to those obtained in a test using a reference oil. The Aluminum Beaker Oxidation Test (ABOT) is a bench oxidation test (used in the Ford Motor Company MERCON® specification) that also measures the ability of automatic transmission fluid to resist oxidization. 32.7.4.2.3 Transmission Cycling Test The Transmission Cycling Test (DEXRON-III specification) uses a V8 engine to drive a transmission. The transmission goes through 20,000 cycles of a test that includes acceleration from first through fourth gear. Each cycle lasts approximately 45 seconds, so that the test time is approximately 220 hours. Fluid temperature is maintained at an elevated temperature, and shift characteristics are monitored throughout the test. At the end of the test, the chemical properties of the fluid and the shift times must remain within specified limits, and the condition of the transmission parts must be equal to or better than those tested using a standard reference oil. 32.7.4.2.4 Plate Friction and Band Friction Tests An SAE No. 2 Machine (electrically driven inertial device) is used to evaluate the frictional characteristics of transmission fluids under both static and dynamic conditions. Dynamic friction levels are evaluated by engaging the clutch plates immediately after the electric motor is shut off, using the clutch plate friction to stop the rotating inertia of the electric motor and flywheel. The change of friction after thousands of lock-up cycles is evaluated as a measure of fluid durability. In a similar test, band friction is evaluated. Test requirements include no unusual wear or flaking on test parts and limits on changes in torque and stop time.
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Friction coefficient
Produces shudder
Higher sliding speed associated with less ability to grip the opposing surface
Not prone to shudder
Higher sliding speed associated with increased ability to grip the opposing surface
Sliding speed
FIGURE 32.34
Relationship between sliding speed and clutch frictional characteristics.
Rotating frictionmaterial plate Steel running surface plate Heater Cooling Applied pressure load cell Torque load cell
FIGURE 32.35
Test apparatus to measure friction characteristics at low sliding speed.
32.7.4.2.5 Shudder and Stick-Slip Test Shudder is low-frequency vibration that occurs mainly between 20 and 30 Hz. It is a resonance phenomenon that is influenced by both the stick-slip friction characteristics of the automatic transmission fluid and the materials in the transmission. The relationship between the coefficient of friction and the sliding speed is shown in Figure 32.34. The condition in which the friction coefficient decreases at decreasing sliding speed reduces the tendency for stick-slip, thus decreasing the probability of shudder. The condition of low friction at high speed, and high friction at low speed, fosters the generation of stick-slip or shudder (Ward et al., 1994). Mechanical design and transmission control can influence the susceptibility of a transmission to shudder. “Green shudder” can occur in a new transmission. Figure 32.35 is a diagram of a low-velocity friction apparatus for determination of the low-speed friction coefficient as a function of sliding speed. This type of testing is used to study the stick-slip durability of automatic transmission fluids with different friction materials. Variable-speed friction testers also provide valuable information. 32.7.4.2.6 Automatic Transmission Fluid Road Testing To determine shift-feel characteristics, test oils are evaluated in road tests and compared to various reference oils in specific transmission and vehicle combinations (Ashikawa et al., 1993). 32.7.4.3 Current Automatic Transmission Fluid Specifications Automatic transmission fluid specifications for commercially approved fluids have been significantly revised since approximately 1990. As a consequence of the development of continuous-slip torque converter clutches to improve fuel economy, automatic transmission fluid specifications have more stringent friction performance requirements than formerly. Two commercial specifications provide the primary transmission fluid performance requirements for North American cars and light-duty trucks: the DEXRON-III specification for General Motors automatic transmissions and the MERCON specification for Ford Motor Company automatic transmissions.
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Typical test requirements include most of the following: Vickers vane pump wear test, various bench tests, plate clutch friction test, band clutch friction test, oxidation test, cycling test, vehicle shift evaluation, electronic controlled converter clutch vehicle test, sprag clutch wear test, and the aluminum beaker oxidation test.
32.7.5 Air-Conditioning Lubricant Air-conditioning lubricants are fluids that lubricate the moving components of an automotive airconditioning system. The lubricant is transported through the air-conditioning system by the air-conditioning fluid, and therefore an air-conditioning lubricant must lubricate even when diluted with a significant amount of the air-conditioning medium. In addition, the lubricant must be sufficiently compatible with the air-conditioning fluid so that the fluid will carry the lubricant to all the critical parts of the air-conditioning system. Prior to 1995, R12 (which contains chlorine) was a major automotive air-conditioning fluid, and mineral oil was its associated lubricant. As a consequence of political and environmental concerns (e.g., the formation of the hole in the protective ozone layer in the upper atmosphere), the use of R12 was restricted by international agreement, and a search began for an alternative air-conditioning fluid. R134a (which contains fluorine rather than chlorine) was identified as a candidate replacement for R12. However, it soon became evident that mineral oil was not an optimum lubricant for use with R134a because mineral oil was not sufficiently transported through the air conditioner by R134a. Thus, it became necessary to identify a lubricant that could be transported by R134a and could protect the moving components of the air-conditioning system. After testing a variety of candidates, it was found that oxygen-containing lubricants such as polyglycols could be transported by R134a. This development process highlights the fact that if any component of a lubrication system (fluid, materials, design) is changed, tests must be conducted to determine whether any incompatibilities have arisen.
32.7.6 Gear and Axle Lubricants Gear lubricants are used to lubricate manual transmissions and axles. Gear lubricants must contain appropriate additives and must exhibit some or all of the following properties, depending on the application: thermal and oxidative stability, resistance to extreme pressure, and protection against corrosion, wear, and spalling. It has been shown that, through proper selection of gear lubricants, vehicle fuel economy can be improved. Gear lubricants must provide seal protection and appropriate frictional behavior. Gear and axle lubricants promote temperature reduction via friction reduction. In addition, they must maintain appropriate viscosity at both high and low temperatures, and must remain stable over long periods of time. Test methods for gear lubricants include such operating conditions as high torque at low speed and high speed with shock loading. Lubricant test measurements include oxidation resistance, protection against wear and material failure, corrosion protection, retention of desired friction characteristics, acceptable viscosity at both low and high temperatures, and seal compatibility. Gear lubricants used in manual transmissions must have appropriate friction characteristics to ensure proper functioning of the transmission synchronizers to prevent gear clashing and allow smooth shifting.
32.7.7 Grease Grease is a solid or semi-solid lubricant that is used whenever a lubricant must remain in the place in which it is needed. Grease is composed of oil or fluid, thickener, and additives. A typical composition would be petroleum oil thickened with soap, and additives as needed to impart the desired chemical and physical properties. Grease is used in more locations in a vehicle than any other lubricant, including such diverse places as door locks, remote-control mirror assembly, seat adjustment gears, window levers, windshield wiper
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gear, water-pump bearing, horn and other electrical contacts, brake system, heating and cooling system, wheel bearings, U-joint, and many other places in the vehicle’s powertrain. A good grease will resist oxidation and degradation, provide an anti-wear fluid film, and prevent metalto-metal contact. Greases must often provide various types of chemical protection such as extreme pressure agents, and corrosion and rust inhibition. Greases are often called upon to keep contaminants away, assist in the sealing process, and resist being washed or squeezed out of their desired location. The base stock in grease makes up 70 to 90+% of the grease composition and may be composed of either synthetic or mineral oil. Additives and thickeners represent the remainder of the composition. Tests for grease typically include measuring the hardness or consistency, and high and low temperature properties. Additional tests include corrosion resistance, stability in the presence of water, oxidative and shear stability, load-carrying capacity, wear resistance, and life performance properties.
32.7.8 Power Steering Fluid Some power steering systems may require a special power steering fluid; others may use one of the lubricants designed for some other application, such as transmission fluid or engine oil. Those fluids that are specialized for power steering applications must resist wear, rust, and oxidation, while maintaining the appropriate viscosity. Those fluids that are specialized for other applications typically do not need to meet any additional requirements when used as a power steering fluid.
32.7.9 Brake Fluid Brake fluids typically are either silicone based or glycol based. They must remain relatively stable during use, maintain appropriate alkalinity to resist becoming corrosive, remain fluid at low temperature, not cause elastomers to deteriorate, and be water tolerant. Because brake fluid can retain water, it needs to be changed once the water content becomes too high for proper braking performance.
32.7.10 Shock Absorber Fluid Shock absorber fluid is typically a hydraulic fluid that cushions the shock when the wheels of a vehicle travel over a rough surface. Shock absorber fluid needs to remain stable during use, not entrain an excessive amount of air, exhibit good sealing performance, and have the appropriate viscosity characteristics.
32.7.11 Fuel Various types of fuels are used in internal combustion engines. Gasoline, diesel oil, compressed natural gas, ethanol, and methanol are some that have been used in recent years. In a development program in which an existing engine is converted for use with a fuel that is different from the one for which the engine was originally designed, one must pay particular attention to material compatibility. The fuel must not cause unacceptable wear or deposits in injectors, fuel pump, or other components in the fuel system, and must not corrode the metals that it touches. In addition, the fuel should not generate so much soot that the engine oil becomes unacceptably contaminated. The fuel must be compatible with the materials in the fuel system, and must also be compatible with the materials in the lubrication system (because under some driving conditions, fuel condenses in the engine oil). If an alternative fuel is used, seals and polymeric or composite engine components must be tested for compatibility, because fuel that has accumulated in the engine oil can extract beneficial plasticizers from elastomeric materials, causing the elastomers to shrink, leak, or harden. If a fuel has a composition that is soluble in a given elastomer, the fuel may cause the elastomer to swell excessively. An example of the effects of an alternative fuel (M85: 85% methanol, 15% gasoline) on several engine elastomers is shown in Figure 32.36 (Schwartz, 1988). Alternative fuels that form emulsions in engine oil (rather than true solutions) can cause engine oil to thicken — as opposed to the effect of gasoline in
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12 Maximum swell Maximum loss of hardness
10 Maximum change in elastomer property, percent
8 6 4 2 0
FIGURE 32.36
Fluorocarbon
Acrylate Silicone Elastomer type
Nitrile
Effect of an alternative fuel (M85) on seal properties.
oil, which causes oil to become less viscous. Changes in viscosity due to fuel and water in engine oil were described in Section 32.7.3 and shown in Figure 32.33.
32.7.12 Functional Fluids: Engine Coolant, Windshield Washer Fluid Various fluids within a vehicle have some properties that are related to lubrication. For example, the engine coolant/antifreeze must carry away heat, must inhibit wear in the pump, and must not corrode materials or damage seals in the engine coolant system. Engine coolant is typically composed of water and glycol in such proportion that the freezing point is well below that of water and the boiling point is significantly above that of water. Corrosion inhibitors in the coolant must protect all the metals found in the coolant system. Windshield washer fluid should remain fluid at low temperatures, carry away dirt, and should not damage paint, windshield-wiper blades, or other materials.
32.7.13 Summary and Future Directions Fluids and components that provide a lubricating function in a vehicle differ widely. For example, engine oil must remain reasonably stable even if it becomes contaminated with fuel and combustion products. Transmission fluid must maintain anti-wear, oxidation, and friction modifier functionality under extremely harsh temperature conditions. Many different kinds of greases are required to satisfy a wide variety of conditions in automotive applications. To provide durable, problem-free vehicle performance, an awareness of lubricant properties and the ways in which they change during service will assist those who design components, assess component durability, choose materials, and model lubricant performance. The major issues on which automotive lubricants have a significant impact include energy conservation and reduction of pollution. Research is in progress on both of these issues. In addition, vehicle manufacturers are investigating all possible ways in which vehicle weight might be reduced and ways in which manufacturing might be made more efficient (via improved manufacturing procedures, recycling, scrap reduction, etc.). All these issues must be addressed without compromising the safety of those operating the vehicles and those working in the manufacturing plants.
Acknowledgments A. Kapoor thanks Drs. Francis Franklin and David Fletcher for reading the chapter and for help in drawing many of the figures. S.C. Tung and S.E. Schwartz thank the many individuals who supplied data, comments, and corrections, including: Stephen Hsu of the National Institute of Science and Technology; Raymond Fessler of
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the U.S. Department of Energy; Judith Donovan, Larry Smith and Carl Hendrickson of Infineum USA; Lewis Williams, Ewa Bardasz, and William Gergel of the Lubrizol Corporation; David Clark of PennzoilQuaker State; Pierre Willermet of Ford Motor Company; Michael McMillan, James Spearot, Russell Stebar, Susan Hartfield-Wünsch, Robert Olree, Robert Jacques, John Flaherty, Frank Caracciolo, Steve Kemp, James Linden, Russell Stebar (retired), and Tom Verdura (retired) of General Motors; Richard Kabel of Rich-Lo Consultant Corporation; Jon Root of Southwest Grease Products; Daniel Deneen, Jr. of Castrol Industrial North America, Inc.; Ian Shannon of Shell Europe Oil Products; Alan Steele of Shell Research, Ltd.; Tom McDonnell and Jerry Carlson of Ethyl Corporation; and Douglas Jahn of Delphi.
References Anderson, A.E. (1992), Friction and wear of automotive brakes, in ASM Handbook, Vol. 18, Blau, P.J. (Ed.), 569-577. Andersson, B.S. (1991), Company Perspectives in Vehicle Tribology — Volvo, in 17th Leeds-Lyon Symposium on Tribology — Vehicle Tribology, Tribology Series, Vol. 18, Elsevier Science, Oxford, U.K., 503-506. Ashikawa, R., Naruse, T., Kuroshima, H., Matsuoka, T., Adachi, T., and Nakayama, T. (1993), ATF Characteristics Required for the Latest Automatic Transmissions, SAE Paper No. 932849. Audette III, W.E. and Wong, V.W. (1999), A Model for Estimating Oil Vaporization from the Cylinder Liner as a Contributing Mechanism to Engine Oil Consumption, SAE Paper No. 1999-01-1520. Bell, J.C. (1998), Gasoline engine valve train design evolution and the antiwear requirements of motor oils, J. Engine Tribol., Proc. Inst. Mech. Engrs., 212(J4), 243-257. Booker, J.F. (1965), Dynamically loaded journal bearings: mobility method of solution, Trans. ASME, J. Basic Eng., D, 187, 537-546. Booker, J.F. (1969), Dynamically loaded journal bearings: maximum film pressure, Trans. ASME, J. Lubr. Tech., July, 534-543. Brauers, B. (1988), NF Steel Rail Oil Control Ring — Test Results and Further Development, Goetze AG, Technical Paper K42. Bush, G.P., Fox, M.F., Picken, D.J., and Butcher, L.F. (1991), Composition of lubricating oil in the upper ring zone of an internal combustion engine, in Tribol. Int., 24(4), 231-233. Buuck, B.A. (1982), Elementary Design Considerations for Valve Gears, SAE Paper No. 821574. Clark, S.E. (1971), The contact between tire and roadway, in Mechanics of Pneumatic Tires, Clark, S.E. (Ed.), National Bureau of Standards Monograph 122. Coy, R.C. (1997), Practical applications of lubrication models in engines, New Directions in Tribology, MEP, 197-209. Culley, S.A. and McDonnell, T.F. (1995), The Impact of Passenger Car Motor Oil Phosphorus Levels on Engine Durability, Oil Degradation, and Exhaust Emissions in a Field Trial, SAE Paper No. 952344. Culley, S.A., McDonnell, T.F., Ball, D.J., Kirby, C.W., and Hawes, S.W. (1996), The Impact of Passenger Car Motor Oil Phosphorus Levels on Automotive Emissions Control Systems, SAE Paper No. 961898. Dowson, D. and Higginson, E. (1991), Elasto-Hydrodynamic Lubrication, Pergamon Press. Dyson, A., Richards, L.J., and Williams, K.R. (1957), Diesel engine lubricants: their selection and utilization with particular reference to oil alkalinity, in Proc. Inst. Mech. Eng. 171, 717-740. Fessler, R. (1999), U.S. Department of Energy Workshop on Industrial Research Needs for Reducing Friction and Wear, Argonne National Laboratory. French, T. (1988), Tyre Technology, Adam Hilger. Gangopadhyay, A., McWatt, D., Willermet, P., Crosbie, G.M., and Allor, R.L. (1999), Effects of composition and surface finish of silicon nitride tappet inserts on valvetrain friction, in Lubrication at the Frontier, Leeds-Lyon Symposium on Tribology, Lyon, France, Tribology Series Vol. 36, Elsevier, p. 891. Hata, H. and Tsubouchi, T. (1998), Molecular structure of traction fluids in relation to traction properties, Tribol. Lett., 5, 69-74.
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Heilich, F. (1983), Traction Drives: Selection and Application, Marcel Dekker, 18-51. Heizler, H. (1999), Vehicle and Engine Technology, 2nd ed., Arnold, London, 783. Hellwig, G., Normann, N., and Uhl., G. (1988), Ein Sensor auf dielektrischer Basis zur On-Line-Charakterisierung von Motorenölen (Alkalinität, Viskosität), Mineralöl. Techn., 10, 1-26. Hendriks, E. (1993), Qualitative and Quantitative Influence of Fully Electronically Controlled CVT on Fuel Economy and Vehicle performance, SAE Paper No. 930668. Hendriks, E. (1995), Second generation technology repositions CVT, in VDI Berichte, 1175, 603-619. Hewko, L.O., Rounds, F.G., and Scott, R.L. (1962), Traction Capacity and Efficiency of Rolling Contacts, Elsevier Publishing Corp. Hsu, S. (1995), National Institute of Science and Technology (NIST) Engine Materials and Tribology Workshop, Gaithersburg, MD, 3-5. Johnson, M.D., Korcek, S., and Schriewer, D. (1994), In-Service Engine Oil Condition Monitoring — Opportunities and Challenges, SAE Paper No. 942028. Kato, T. and Kawamura, M. (1986), Oil maintenance tester: a new device to detect the degradation level of oils, Lubr. Eng., 42(11), 694-699. Kauffman, R.E. (1989), Development of a remaining useful life of lubricant evaluation technique. III. Cyclic voltammetric methods, Lubr. Eng., 45(11), 709-716. Kemp, S.P. and Linden, J.L. (1990), Physical and Chemical Properties of a Typical Automatic Transmission Fluid, SAE Paper No. 902148. Kluger, M. and Fussner, D.R. (1997), An Overview of Current CVT Mechanisms, Forces, and Efficiencies, SAE Paper No. 970688. Kollmann, K., Gürtler, T., Land, K., Warnecke, W., and Müller, H.D. (1998), Extended Oil Drain Intervals — Conservation of Resources or Reduction of Engine Life (Part. II), SAE Paper No. 981443. Korcek, S., Jensen, R.K., Johnson, M.D., and Sorab, J. (1999), Fuel efficient engine oils, additive interactions, boundary friction and wear, in Lubrication at the Frontier, Proc. Leeds-Lyon Symp. on Tribology, September 1998, Elsevier, Tribology Series 36, pp. 13-24. Li, D.F., Rohde, S.M., and Ezzat, H.A. (1982), An automotive piston lubrication model, ASLE Trans., 26(2), 151-160. Machida, H. and Kurachi, N. (1990), Prototype Design and Testing of a Half Toroidal CVT, SAE Paper No. 900552. Martin, F.A. (1983), Developments in Engine Bearings, in Tribology of Reciprocating Engines, Proc. 9th Leeds-Lyon Symp. Tribology, 1982, Leeds, Butterworth, 9-28. Massey, I.D., MacQuarrie, N.A., Coston, N.F., and Eastham, D.R. (1991), Development of crankshaft bearing materials for highly loaded applications, in Vehicle Tribology, Proc. 17th Leeds-Lyon Symp. Tribology, September 1990, Leeds, Tribology Series, Vol. 18, Elsevier, Amsterdam, 43-52. Monaghan, M.L. (1987), Engine Friction — A Change in Emphasis, Inst. Mech. Engrs., 2nd BP Tribology Lecture. Monaghan, M.L. (1989), Putting friction in its place, 2nd Int. Conf.: Combustion Engines — Reduction of Friction and Wear, in Inst. Mech. Eng. conf. pub. 1989-9, Paper C375/KN1, 1-5. Moore, D.F. (1975), Principles and Applications of Tribology, Pergamon Press. Munro, R. (1990), Emissions Impossible — The Piston and Ring Support System, SAE Paper No. 900590. Nakasa, M. (1995), Engine Friction Overview, in Proc. Int. Tribol. Conf., Yokohama, Japan. Narasimhan, S.L. and Larson, J.M. (1985), Valve Gear Wear and Materials, SAE Paper No. 851497. Neale, M.J. (1994), Drives and Seals, A Tribology Handbook, 1st ed., Butterworth-Heinemann, Oxford, U.K. Nunney, M.J. (1998), Automotive Technology, SAE International, Butterworth-Heinemann. Oh, K.P., Li, C.H., and Goenka, P.K. (1987), Elastohydrodynamic lubrication of piston skirts, J. Tribol. Trans. ASME, 109, 356-362. Pillai, P.S. (1992), Friction and wear of tires, in ASM Handbook, Vol. 18, Friction, Lubrication and Wear Technology, Blau, P.J. (Ed.), ASM International, 578-581.
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Pottinger, M.G. and Yager, T.J. (1986), The tyre pavement interface, in STP 929, American Society for Testing and Materials, IX-XV. Priest, M., Dowson, D., and Taylor, C.M. (1999), Predictive wear modelling of lubricated piston rings in a diesel engine, Wear, 231(1), 89-101. Priest, M. and Taylor, C.M. (1998), Automobile engine tribology — Approaching the surface, in AUSTRIB ‘98: Tribology at Work, The Institution of Engineers, Australia, 353-363. Ruddy, B.L., Dowson, D., and Economou, P.N. (1982), A review of studies of piston ring lubrication, in Proc. 9th Leeds-Lyon Symp. on Tribology: Tribology of Reciprocating Engines, Paper V(i), 109-121. Rycroft, J.E., Taylor, R.I., and Scales, L.E. (1997), Elastohydrodynamic effects in piston ring lubrication in modern gasoline and diesel engines, in Elastohydrodynamics — Fundamentals and Applications in Lubrication and Traction, Proc. 23rd Leeds-Lyon Symposium on Tribology, September 1996, Dowson, D. et al. (Eds.), Elsevier, pp. 49-54. Schwartz, S.E. (1988), Effects of methanol, water, and engine oil on engine lubrication-system elastomers, Lubr. Eng., 44(3), 201-205. Schwartz, S.E. (1991), Observations Through a Transparent Oil Pan During Cold-Start, Short-Trip Service, SAE Paper No. 912387. Schwartz, S.E. (1992a), A model for the loss of oxidative stability of engine oil during long-trip service. I. Theoretical considerations, STLE Tribol. Trans., 35(2), 235-244. Schwartz, S.E. (1992b), A model for the loss of oxidative stability of engine oil during long-trip service. II. Vehicle measurements, STLE Tribol. Trans., 35(2), 307-315. Schwartz, S.E. (1992c), A Comparison of Engine Oil Viscosity, Emulsion Formation, and Chemical Changes for M85 and Gasoline-Fueled Vehicles in Short-Trip Service, SAE Paper No. 922297. Schwartz, S.E. and Mettrick, C.J. (1994), Mechanisms of Engine Wear and Engine Oil Degradation in Vehicles Using M85 or Gasoline, SAE Paper No. 942027. Stebar, R.F., Davison, E.D., and Linden, J.L. (1990), Determining Frictional Performance of Automatic Transmission Fluids in a Band Clutch, SAE Paper No. 902146. Taylor, C.M. (Ed.) (1993), Engine tribology, in Tribology Series, Vol. 26, Elsevier, Amsterdam, 301. Taylor, C.M. (1994), Fluid film lubrication in automobile valve trains, J. Eng. Tribology, Proc. Inst, Mech. Engs., 208(J4), 221-234. Taylor, C.M. (1998), Automobile engine tribology — design considerations for efficiency and durability, Wear, 221(1), 1-8. Tsubouchi, T., Hata, H., Yamada, H., and Aoyama, S. (1990), Development study of new traction fluids for automotive use, in Proc. 17th Leeds-Lyon Symp., 433-443. Tung, S.C. and Hartfield-Wünsch, S. (1995a), Advanced engine materials: current development and future trends, in NIST (National Inst. of Science and Technology), Engine Materials and Tribology Workshop, Gaithersburg, MD, April 4-7, 1995. Tung, S.C. and Hartfield-Wünsch, S. (1995b), The effect of microstructure on the wear behavior of thermal spray coatings, in ASM Trans., 107. Tung, S.C., Hill, S., and Hartfield-Wünsch, S. (1996), Bench wear testing of common gasoline engine cylinder bore surface/piston ring combinations, STLE Tribol. Trans., 39(4), 929-935. Tung, S.C. and Wang, S. (1989), Using electrochemical and spectroscopic techniques as probes for investigating metal-lubricant interactions, STLE Tribol. Trans., 33(4), 563-572. Veith, A.G. (1986), The tyre pavement interface, in STP 929, American Society for Testing and Materials, 125-158. Wang, S.S., Lee, H.S., and Smolenski, D.J. (1994), The development of in situ electrochemical oilcondition sensors, Sensors and Actuators: B. Chemical, 17(3), 179-185. Ward, W.C. and Copes, R.G. (1993), The next ATF challenge — meeting fuel efficiency needs and providing driver satisfaction, in Proc. NPRA Annual Meeting, AM-93-06. Ward, W.C., Sumiejski, T.A., and Schiferi, E.L. (1994), Friction and Stick-Slip Durability Testing of ATF, SAE Paper No. 941883.
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Watts, R.F. et al. (1990), Prediction of low speed clutch shudder in automatic transmissions using the low velocity friction apparatus, in 7th Int. Colloq. on Automotive Lubrication, Technische Academie, Esslingen, Germany. Watts, R.F. and Richard, K.M. (1997), CVT lubrication: the effects of lubricants on the frictional characteristics of the belt-pulley interface, in 5th CEC Int. Symp. Performance Evaluation of Automotive Fuels and Lubricants, Sweden. Wills, G.J. (1980), in Lubrication Fundamentals, Marcel Dekker, Inc. Xu, H. (1999), Recent advances in engine bearing design analysis, J. Eng. Tribol., Proc. Instn. Mech. Engrs., 213(J4), 239-251. Younggren, P.J. and Schwartz, S.E. (1993), The Effects of Trip Length and Oil Type (Synthetic vs. Mineral Oil) on Engine Damage and Engine-Oil Degradation in a Driving Test of a Vehicle with a 5.7L Engine, SAE Paper No. 932838.
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33 Diesel Engine Tribology 33.1 33.2
Introduction ................................................................... 1231 Power Cylinder Components ........................................ 1233 Liners/Bores • Rings • Piston • Piston Pin and Connecting Rod • Friction in Power Cylinders • Tribological Systems • Ring/liner Interface Tribology • Fuels and Lubricants • Engine Deposits • Effect of Oil Film Thickness • Effect of Oil Cleanliness • Examples of Liner and Ring Wear Mechanisms
33.3
Overhead Components.................................................. 1246 Cam and Cam Followers • Push Rods, Rocker Levers, and Crossheads
33.4
Engine Valves.................................................................. 1249 Valve/Seat Wear Mechanisms • Valve Stem/Guide Wear Mechanisms • Materials Selection Criteria
Malcolm G. Naylor
33.5 33.6 33.7
Cummins Inc.
Padma Kodali
Fuel Injectors • Fuel Pumps
33.8
Fuels, Lubricants, and Filtration ................................... 1261 Diesel Fuel • Diesel Lubricants • Used Oil Analysis • Filtration: Air System • Filtration: Lubricating System • Filtration: Fuel System • Filtration: Cooling System
Cummins Inc.
Jerry C. Wang Cummins Inc.
Bearings and Bushings................................................... 1253 Turbomachinery............................................................. 1255 Fuel System..................................................................... 1258
33.9
Future Trends ................................................................. 1267
33.1 Introduction Diesel engines are based on the principle of compression ignition. Air is introduced alone into the combustion chamber with the opening of the intake valves. The air intake is facilitated by the downward movement of the piston that creates a pressure differential through volume expansion. Turbochargers are often used to force more air into the combustion chamber to increase air density to burn more fuel for the same displacement. The air, once in the system and the intake valve closed, is then compressed to reach high pressure and high temperature. Fuel is injected at this point to initiate combustion. The fuel is ignited by the high temperature induced by compressing air, hence the name compression ignition. The combustion of the air/fuel mixture creates the expansion that forces the piston to move downward again, producing power output. The whole diesel engine design is to support the power production through compression ignition. The key components include the power cylinders that house the combustion process, the cam and valve train system to control the timing of the combustion, the crankshaft and connecting rods to receive power and to provide mechanical movement of the compression/expansion process, the gear train to operate pumps and accessories essential to moving working fluids around, and, finally, all the working
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Valve pump
Valve and spring
Cylinder head
Piston & rings
Liner
Flywheel and housing
Oil cooler
Turbocharger Block
Connecting rod Oil filter
Crankcase
Rocker lever
Valve cover Push tube
Fuel pump
Oil pump
FIGURE 33.1
Electronic controller
Cam followers
Camshaft
Cutaway illustration of a diesel engine.
fluids that provide cooling, lubrication, and power to the engine (Heywood, 1998). All of these components are housed in an engine block with a cylinder head on the top. Figure 33.1 shows a cutaway view of a typical diesel engine. The engine block starts with the bore that houses the cylinder liners. Many larger diesel engines have removable liners for longer service life and easy rebuild. The skirt part of the block allows for the camshaft and crankshaft to be inserted. Gears and accessory pulleys are located in the front. A flywheel is attached to the rear that connects to the drive train that transmits power to the transmission. On top of the block is fitted the cylinder head that houses valves and fuel injectors. The oil pan is attached to the bottom of the block. The power cylinders include the liners, pistons, and piston rings. The liners are fitted inside the bore to guide the movement of the pistons. The movement of the piston inside the liner from the top to the bottom is called a stroke. The displacement of an engine is the volume defined as:
Displacement = π (Bore radius)2 × Stroke Piston rings are used to provide sealing of combustion gas and to control the oil film on the liner wall. Multiple rings are used for this purpose. The lowest ring is usually called the oil ring to limit the quantity of oil reaching the upper end of the liner to prevent excessive oil accumulation or deposits. The top ring is used to prevent compressed air or combustion gas from leaking past the rings so as to preserve the pressure in the cylinder. It does this by pressing the ring surface against the liner and allowing only an oil film between the liner and the ring. There are usually additional rings between the oil ring and the top ring to facilitate the process. Because the power cylinders are where the heat is generated, the liner is cooled by coolant flowing between the liner and the block. Further cooling is provided by crankcase oils squirted onto the bottoms of the pistons. Most heat, however, is rejected into the exhaust gas.
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Because air intake, fueling, and combustion occur in sequence in the power cylinders (i.e., only one cylinder fires at a time), each process must happen in exactly the right time to allow smooth and continuous operation. This is controlled by the design of the cam and the movement of the valve train. The cam has intake and exhaust lobes for each cylinder. Each lobe is designed with a profile that, when the cam rotates, will actuate the opening and closing of the valves at the right time. Most diesel engines rely on the fuel pump to control the amount and timing of the fuel injection. However, some unit injectors are actuated mechanically by the injector lobes on the cam. The actuation of valve and injector events are delivered by the overhead components, so named because most of them sit on top of the engine head. The cam lobe rises against a cam follower, which pushes against a push tube. The push tube will raise one end of the rocker lever, forcing the other end of the rocker lever to push down on either injector or valve tips, thus completing the action. The valve springs will force the overhead components to go in the other direction when the cam lobes have moved past their high points. Because the rotation of the cam is tied to the rotation of the crankshaft via gears, and the crankshaft is connected directly to the piston via a connecting rod, the movement of the cam, the crank, the valves, and the pistons are all synchronized. In addition to synchronizing the movement, the crankshaft also receives the power generated by the combustion. The power is either sent to the transmission for useful work, or used to power accessory pulleys and various pumps through the gear train. These components include the oil pump, the water pump that moves the coolant, the fuel pump, and accessories such as an air conditioner. Recent diesel engine designs are largely driven by emissions regulations (Figure 33.2). Major refinement in bowl design, air handling, and fuel injection have led to progressive reductions in NOx and particulate matter. Meanwhile, higher power density, better fuel economy, and extended service intervals are becoming an integral yet conflicting part of modern diesel engines. Currently, exhaust gas recirculation (EGR) and after-treatment devices are considered necessary to achieve the next level of emissions control. All of the above present different challenges to engine tribology. Tribological contacts in each part of the engine are discussed in this chapter.
33.2 Power Cylinder Components Simultaneous improvements in engine power density, reliability, and durability over the last five decades are due to advances in design, materials, fuel, and lubricants. The overall function of power cylinders is to convert the gas pressure resulting from the combustion of the air/fuel mixture inside the combustion chamber to the torque applied to the crankshaft. Power cylinder components include liners/bores, piston rings, pistons, piston pins, and connecting rods. In some engine designs, the bores are machined in the cylinder block and are referred to as parent bores and in some engines, liners are fitted into the cylinder block. A schematic of the ring pack arrangement in a piston is shown in Figure 33.3. To understand the tribology of power cylinders, it is important to understand the function of these components.
33.2.1 Liners/Bores The functions of liners/bores are to: 1. 2. 3. 4. 5. 6.
Confine the combustion gases Transfer the heat from pistons and rings to the coolant Seal the coolant Support piston-side loading Guide the pistons/rings Retain oil for start-ups
Liner/bore materials should have good break-in, wear, and scuff resistance; have a consistent surface finish to limit friction; retain oil in honing grooves for longer engine life; be free from embedded particles; and maintain good heat transfer.
FIGURE 33.2
1 9 8 6
0
1 9 8 8
1 9 9 0
1 9 9 2
Progression of diesel emissions regulations in the U.S.
g /b h p -h r
g / b h p -h r
1 9 9 4
1 9 9 6
1 9 9 8
2 0 0 0
1234
4
8
1 2
N O x
0
0 .2
0 .4
0 .6
P a rti c u la te
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FIGURE 33.3
TABLE 33.1
Schematic of ring arrangement in a piston.
Liner Materials Used in Diesel Engines
Low-alloyed gray cast iron Bainitic-cast gray iron Boron-alloyed cast iron
Pearlitic matrix with flake-type graphite; hardness 250 BHN Bainite and tempered martensite; hardness 300 BHN Lamellar pearlitic material with high percentage of boron carbides; hardness 240 BHN
Liners are typically manufactured from gray cast iron. To improve the wear resistance of liners, alloying elements such as chromium, nickel, molybdenum, copper, vanadium, and phosphorous are added. To improve the wear and scuff resistance of the cast iron liners, various surface modification techniques such as induction hardening or gas-nitriding are also used. Table 33.1 summarizes typical liner materials used in diesel engines.
33.2.2 Rings The main functions of both compression and oil rings are to: 1. Seal (to prevent gas and oil leakage between piston and cylinder) 2. Maintain lubricating oil film on the cylinder wall 3. Transfer the heat from the piston to the cylinder wall Cast iron, ductile iron, and steel are substrate materials used for both compression and oil rings. To improve the durability and performance of the rings, surface treatments that can provide strong adherence to the base material are used. Criteria such as compatibility with liner material, wear and scuff resistance, thermal conductivity, and the ability to survive in dry, partially lubricated, and lubricated sliding conditions, are the basis for choosing surface modification techniques for rings. Ring scuffing can lead to
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TABLE 33.2
Properties of Piston Ring Materials
Material Grey cast iron Carbidic/malleable iron Malleable/nodular iron Sintered irons
TABLE 33.3
Tensile Strength (MPa)
Hardness (BHN)
83–124 140–160 155–165 120
230–310 450–580 540–820 250–390
210–310 250–320 200–440 130–150
Substrate, Application, and Surface Engineering Methods of Steel Rings
Ring Type Top compression rings
Oil ring
Modulus of Elasticity (GPa)
Substrate
Surface Treatment
SAE 9254 13% Cr 18% Cr Low carbon steel 6% Cr 13% Cr
Cr-plated, plasma-sprayed Nitriding Nitriding, Cr-plated, plasma-sprayed Cr-plated Nitriding Nitriding
high blow-by and catastrophic failure of an engine. The coatings on piston ring faces can be applied on the entire face, or half of the face, or only in the middle. Currently, chrome-plating, gas-nitriding, and plasma-spraying are some techniques that are used for modification of piston ring faces. Also, engine manufacturers are evaluating the high-velocity oxygen fuel (HVOF) process for the application of chrome carbide/nickel chrome with Moly (Cr3C2-NiCr/Mo) coatings for compression rings (Shuster et al., 1999; Rastegar and Craft, 1993). The (Cr3C2-NiCr/Mo) coating has good wear and scuff resistance. Chrome nitride coatings with oxygen (CrNO) deposited by physical vapor deposition (PVD) also have good wear and scuff resistance. These coatings have not been widely used in diesels because of the high cost of the coatings (Rastegar et al., 1997). Shen (1987) explored multilayered PVD coatings for piston rings. Properties of the ferrous-substrate ring materials and low-carbon steels that are currently used in diesels are summarized in Tables 33.2 and 33.3 (Challen and Baranescu, 1999).
33.2.3 Piston The piston’s roles are to: 1. Transfer force originated from the combustion gas pressure inside the chamber to the piston pin 2. Provide support and guidance to piston rings and pin 3. Dissipate heat energy to the coolant Materials properties that are important for piston applications are low density, low thermal expansion, and good high-temperature fatigue strength. In addition, manufacturing considerations such as ease of casting, forging and machining, as well as low cost, factor into the materials selection. The original material used for pistons was grey cast iron. Cast iron with spheroidal graphite is commonly used as a piston material due to its good groove resistance, low thermal expansion, and high strength. Despite the difficulties in casting defect free thin sections of cast iron, cast iron pistons were successfully used in some production engines. Oxidation resistance of the piston crown at high temperatures and low wear of the ring grooves is also desirable. Aluminum-silicon alloys that are widely used for piston materials do not have adequate wear resistance from ring movement at higher operating temperatures and pressures. Therefore, inserts are cast into place to provide a harder and more-resistant surface. To prevent excessive ring or groove side wear, a Niresist ring groove insert (cast iron with high nickel content) is metallurgically bonded to the aluminum piston.
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Engine design trends toward high power density have driven the concept of composite pistons. In some engine designs, two-piece or articulated pistons are used, in which the crown is forged steel and the skirt is cast aluminum. In this case, cast-in ring carrier inserts are not necessary. Squeeze cast-aluminum has also been used for diesel pistons. The mechanical properties of the squeeze cast alloy can be improved by inserting ceramic fibers or metal inserts for reinforcements of grooves, pin bosses, and combustion-bowl rims. For the highest thermal loading, in order to reduce top ring and top ring groove temperatures, a cooling gallery is located in the heat path. Composite aluminum pistons with bolted steel crowns are used in large-bore and slow-speed diesel engines operating at high temperatures and with long durability. Changes in stress state at the piston combustion bowl can result in thermal fatigue cracks and erosion. In aluminum pistons, hard anodizing, a process in which the surface is modified to form aluminum oxide, is used to improve the piston crown resistance to thermal cracking. To help cylinder-kit run-in, soft coatings like graphite, tin, and moly-disulfide are used on piston skirts. Recently developed resin-bonded graphite/molybdenum coatings were reported to have longer life and better wear resistance than sprayed graphite (Challen and Baranescu, 1999).
33.2.4 Piston Pin and Connecting Rod The piston pin and connecting rod transform the combustion pressure delivered to the piston into torque at the crankshaft, resulting in shaft power. Connecting rods are made of high-quality medium-carbon steel. Piston pins are made of high-quality, high-carbon steels. The outer surface of the piston pin is surfacehardened, lapped, and polished to a mirror-like finish. Pin and pin bore designs are dictated by piston bore load-carrying capacity. The pin rides in a bushing, which is typically a layered bronze-bearing material.
33.2.5 Friction in Power Cylinders Figure 33.4a shows the distribution of the total energy in a typical fired diesel or spark ignition engine (Richardson, 1999). This figure indicates that 4 to 15% of total energy is lost by mechanical friction. Richardson cited that 40 to 55% of total mechanical losses are caused by pistons, rings, and piston rods. This is shown in the Figure 33.4b. Richardson indicated that 18 to 33% of friction is caused by rods, 28 to 45% by piston rings, and 25 to 47% by pistons. Design for low friction is often compromised by durability and oil consumption requirements.
33.2.6 Tribological Systems Based on the function of components, power cylinder components can be divided into eight systems with tribological interfaces: liner/ring; ring and ring groove, liner/piston skirt, piston pin and piston bore, piston pin and connecting rod, piston skirt/piston pin (articulated piston), piston crown/liner (articulated piston), and oil ring/expander. Wear can occur in any one of these eight systems. For all practical purposes, engines are rebuilt when oil consumption and blow-by become excessive. In the perspective of power cylinders, oil consumption is most often associated with excessive radial wear of the top compression ring and cylinder liner wear at the top ring reversal. A properly designed piston skirt has an adequate lubricating film between the skirt and the liner. Lowfriction coatings on the skirt are helpful when the piston skirt breaks through the lubricating film. Under some severe operating conditions, such as when extreme engine thermal transients can alter the clearances, changes in the friction between skirt and the liner can result. The wear caused by a mechanical contact in a well-designed pin and bore under normal operating conditions is minimal. Embedded particles in the piston pin from the lapping or polishing process can lead to excessive wear in the bore. One abnormal bore failure occurs when an engine experiences hot shutdown. The piston cooling oil ceases to flow, and the piston crown area is hotter than the piston bosses and piston pin. As a result, heat is transferred from the hot crown to the piston bore, which
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Mechanical Friction (4-15%)
(a)
Work Output (38-41%)
Other Losses (47-58%)
Pistons, Rings, Rod (40-55%)
(b)
Other (40-60%)
FIGURE 33.4 Distribution of (a) total energy in a fired engine; and (b) total engine mechanical friction. (From Richardson, E.E. (1999), Review of Power Cylinder Friction for Diesel Engines, ASME, ICE-Vol. 32-3, Paper No. 99ICE-196. With permission.)
experiences higher temperatures than normal operating conditions. These high temperatures at the piston bore bushing can lead to degradation of bearing material. Another abnormal failure may be caused by pin bending, which results in nonuniform load distribution, with high stresses biased to the inner edge of the bore. In this situation, cracking caused by fatigue is observed on the piston pin boss bushing. Piston pins and the piston skirts are designed to be the critical load path for the piston thrust load. In some articulated piston designs, the second land guides the piston movement on the liner. Typically, the contact between piston crown and liner is lubricated. A well-designed system under normal operating conditions shows minimum wear. Potential causes of high piston-liner wear include excessive oil deposits and external contaminants. Oil consumption is primarily controlled by the tension of the oil ring. Oil consumption is high at low unit pressure, decreases with an increase in unit pressure, and remains constant above a certain unit pressure. Normally, oil rings are designed in the unit pressure region where oil consumption is constant. In engines that employ oil rings with expanders, the unit pressure of the oil ring may drop either when the expander wears with time or when the spring embeds in the inner diameter of the ring. This results in increased oil consumption. Cr-plating and gas-nitriding are typical surface modification techniques used to extend the life of an oil ring. The primary factors in determining engine life before major overhauls are ring/liner interface and ring/ring groove wear. Thus, the remainder of the discussion focuses on ring/liner wear. Ring/ring groove wear is covered in Section 33.2.9.
33.2.7 Ring/liner Interface Tribology Kodali et al. (1999) reviewed the major factors influencing cylinder liner wear. Most of these factors are also valid for ring wear. The following sections discuss the major variables that influence ring/liner wear, including the aspect of the design, choice of materials, engine operating parameters, fuel sulfur, engine deposits, soot, and lubricant additives.
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33.2.7.1 In-cylinder Mechanical Design The design of power cylinder components can have a significant effect on system wear. The fundamental principles in designing for low-wear power cylinders are: • Design the system for hydrodynamic lubrication, which prevents direct contact between sliding surfaces. • Choose compatible materials for the sliding surfaces, which results in low wear when contact occurs between sliding surfaces. Engine design parameters that modify power cylinder dimensions can influence liner wear. Understanding the effect of parameters such as distribution of gas pressure, contact force at the ring/liner interface, the ring pack design and location, and piston type is critical. 33.2.7.2 Bore and Stroke Bore size has very little effect on ring/liner wear because the net pressures that act on the ring remain the same. The stroke and connecting-rod length affect the piston velocity. This may have some effect on the hydrodynamic oil films that are developed under the ring face. Excessive bore distortions result in increased ring/liner wear. 33.2.7.3 Load and Speed Engine load is governed by cylinder pressure. The higher or longer the cylinder pressure acts on the rings, the greater the potential for increased wear. Higher loads also tend to increase piston temperatures. Higher temperatures decrease oil viscosity, reduce oil film thickness, and increase wear; they can also cause distortions that may lead to high wear. Engine speed is an indication of the number of times that the ring and liner contact near the top dead center (TDC). Higher speed results in increased wear caused by an increased number of contacts of ring and liner at TDC. Higher rpm also increases the piston speed, which can reduce wear rates by increasing the oil film thickness. 33.2.7.4 Liner, Ring, and Piston Design Liner design is critical in minimizing the bore distortion that can lead to excessive wear. In boundary lubrication conditions, liner surface finish influences liner wear. For example, discontinuous hone marks, and torn or folded metal on the liner surface can cause high liner wear. During high cylinder pressure, ring width affects the net radial gas force acting on the ring. Reduced widths can decrease this force and potentially reduce wear. The ring face profile influences both the net gas pressure force and the hydrodynamic lubrication of the ring face, and should be optimized for low wear. Liner wear is also a function of the piston land design. If the top land clearance is not designed properly, carbon can build up. These carbon deposits, when trapped between the piston and liner, result in borepolishing at the top ring reversal area of the liner. Bore polishing results in significant amount of material loss and loss of oil control. Land clearances and groove widths affect the flow of gases through the ring pack. This affects the forces that are acting on the rings and ultimately the wear. Small clearances may result in excessive wear, sticking, and possible scuffing. Large clearances between ring and ring groove may lead to ring breakage. 33.2.7.5 In-cylinder Physical Environment The most significant factor that influences abrasive wear in an engine is the contact between two surfaces in relative motion. Environmental conditions that affect the contact pressure between two surfaces are discussed below. 33.2.7.6 Cylinder Pressure High cylinder pressures force the ring and liner together. If they move relative to each other, then wear occurs. With proper design, the effects of pressure can be minimized. For example, the net radial force acting on a
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Force (N) 12000 10000
Gas Pressure
8000
Asperity Contact
6000 4000 2000 0 0
20
40
60
80
100
120
140
160
-2000 -4000 -6000
Position (mm)
FIGURE 33.5
Variation of contact force and gas pressure with distance below the top dead center.
ring can be decreased by proper ring design and can help compensate for increased cylinder pressure. Highest cylinder pressures occur during the compression and expansion strokes. The peak pressure typically occurs after the TDC. Figure 33.5 illustrates the distribution of the gas pressure and the contact force as a function of distance from the TDC. Both gas pressure and contact load are at maximum just below the TDC. 33.2.7.7 Temperature The temperature at which the ring/liner or liner/piston skirts slide together influences liner wear. Improper liner cooling may result in higher ring/liner interfacial temperatures. For example, differential expansion, which may be caused by nonuniform cooling around the circumference and the length of the liner, may lead to bore distortion. The ring/liner wall temperature affects the abrasive wear term indirectly through the kinematic viscosity of the lubricant. The liner/ring wear may increase with decrease in the oil viscosity as a result of increasing temperature. Higher sliding temperatures may also aggravate liner wear because of local degradation of the lubricant. 33.2.7.8 Piston Velocity Lubrication conditions of the ring/liner interface are governed by piston velocity. In the middle of the stroke, the piston is moving the fastest, resulting in hydrodynamic lubrication. However, at the dead centers, the piston velocity goes to zero and the hydrodynamic lubrication breaks down. This can result in ring/liner surface contact that leads to loss of material from both the ring and liner surfaces.
33.2.8 Fuels and Lubricants 33.2.8.1 Effect of Fuel Sulfur Correlation between the sulfur content in the diesel fuel and the wear of liners/rings in diesel engines has been established (McGeehan and Kulkarni, 1987; Dennis et al., 1999; Weiss et al., 1987). Because of emissions requirements, the trends have been toward decreasing the sulfur content in fuel. Off-highway applications are still permitted to use high-sulfur fuels. The SOx products formed as a result of combustion can combine with water moisture to form sulfuric and sulfurous acid, leading to chemical attack. Concentration of the acid and the length of the time that the acid stays on the liner surface determine the severity of the chemical attack. Material loss as a result of this localized chemical attack is usually insignificant. However, at lower coolant temperatures, acid condensation is promoted, and thus can activate corrosive wear. Liner wear with 400 ppm sulfur in heavy-duty diesel engines indicated embedded corrosion by-products, corrosion pits, and severe abrasion as contributing factors for loss of liner material. A liner from an engine that ran with 1 ppm sulfur indicated much less abrasion and corrosion (Wang et al., 1999).
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33.2.8.2 Effect of Base Stocks and Additives One of the most important functions of the lubricant is to control the friction and wear of highly loaded components during operation. The many functions of a modern diesel lubricant are the result of careful blending of chemical additives and carefully refined base stocks. These additive packages have undergone tremendous improvement over the last 20 years and have played a major role in the improvement in engine life over that period of time. In a ring/liner interface, the lubricant helps in sealing against the leakage of combustion gases. Degradation of that lubricant or formation of deposits in the ring belt area can affect liner wear. For example, increased friction and wear of ring/liner interface are expected if the viscosity is too low. Similarly, if the viscosity is too high, oil flow may be poor, resulting in poor lubrication conditions that eventually lead to high wear and friction. Buildup of carbonaceous deposits on a piston can increase liner wear and decrease the ability of the rings to seal the combustion gases. The alkaline detergent additives perform a critical, dual role; they neutralize corrosive combustion acids and they help clean deposits that may form on hot metal surfaces. The buildup of combustion-derived soot in the lubricant promotes wear. Soot-induced wear mechanisms are not well-understood. There are several proposed mechanisms (Kim et al., 1992), such as adsorption of zinc dithiophosphate (ZDTP) by soot, competition between ZDTP and soot for adsorption sites on contacting surfaces, and the abrasive action of soot. Currently, there is no evidence to illustrate the role of soot on liner wear. The typical size of primary soot particles is reported to range between 0.01 to 0.1 µm (Kuo et al., 1998). These particle sizes might only result in polishing wear. When engines run for longer periods of time, bore/liner polishing may contribute to significant loss of liner material. Soot particles greater than 1 µm can result from some engine operating conditions, and the abrasive wear by soot may result in significant contribution of liner material loss. Similarly, if the soot absorbs the additives in the oil and thus inhibits formation of the anti-wear film on the contacting surfaces, liner wear may be accelerated. Formation of acids caused by condensation of some combustion products can degrade the oil in localized regions, resulting in chemical attack of the liner.
33.2.9 Engine Deposits Deposits are known to have an effect on the durability and emissions of an engine. The primary cause of engine deposits is a relatively complex reaction that occurs among the components, fuel, blow-by gases, and the engine lubricant. Most of these deposits derive from the fuel, with some contribution from the lubricant. These deposits are accepted to be a mixture of inorganic material (ash) and carbonaceous combustion products (soot), and resinous organic material that serves to bind the mixture together (Shurvell et al., 1997). Typically, deposits are seen on the crown, top land, and second land; in the ring groove; and on the under-crown. The deposits formed at different locations of the combustion chamber are chemically different, and probably vary in the mechanical aspect of being soft or hard. Top land deposits are known to be very hard and abrasive, whereas under-crown deposits, which occur mainly because of severe operating conditions, do not have serious effects. Carbon deposits trapped in the piston/liner interface result in bore-polishing at the top ring reversal area of the liner. When these carbon deposits are trapped between the ring and ring groove, side clearances may change. Reduced clearances caused by carbon deposits may result in excessive wear, sticking, and possible scuffing.
33.2.10 Effect of Oil Film Thickness The predicted oil film thickness (OFT) under the face of the top compression ring as a function of crank angle for various cases of liner roughness is shown in Figure 33.6a. The OFT is defined as the distance between the mean height of the asperities on the surface (Figure 33.6b). As the liner roughness increases, asperities are held apart, resulting in a thicker oil film. However, during the high-pressure portions of the cycle, the asperities are forced together and the film thickness decreases. In cases of lower surface roughness, there are more variations in the predicted OFT. At the mid-stroke, the asperities are small
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(a)
6 TDC Firing 2.0* Roughness
Film Thickness (microns)
5
4
3 1.0* Roughness 2
1 0.5* Roughness 0 -360
-270
-180
-90
0
90
180
270
360
Crank Angle (degrees)
(b)
FIGURE 33.6 (a) Oil film thickness as a function of roughness. (b) Interaction of ring/liner asperities: (i) smooth liner surface, and (ii) rough liner surface.
enough so that it is possible to form a fully hydrodynamic oil film. Near the dead center, part of the predicted OFT is once again affected by asperity contact between surfaces. The minimum OFT, below which metal-to-metal contact occurs, is known as a lower-limit for fluid film lubrication (LFFL). This boundary limit depends on the surface finish, elastic modulus, thermal distortion of sliding surface, and size of trapped contaminants found in their clearance space. Typically, the arithmetic surface roughness of the liner surfaces is no more than 0.8 to 0.9 µm and, thus, the minimum OFT for lubrication can be considered to be the same order of magnitude. The OFT falls below the LFFL value at and near regions of the extreme ends of the stroke. At the mid-stroke position, the piston speed is highest and thus one can expect a higher OFT than at the top and bottom ring reversal area. The OFT for the oil ring is typically smaller than the top compression ring. Oil film thickness can affect the size of the trapped contaminants under the ring face, whereas the contact pressure at the ring/liner interface influences the damage caused by these trapped particles. Damage on the liner can be understood by a simple assumption that the oil film thickness on the liner is affected by what is deposited by the previous ring. For example, during the down-stroke, the top ring
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sees the oil left behind by the second ring. The second ring sees the oil film left by the oil ring. The size of the particles that can be trapped under the ring face depends on its film thickness and the debris that is left behind from the previous ring. The bigger particles may get crushed or agglomerate on a ring. The top ring sees the particles from the combustion chamber first and is more susceptible to agglomeration of particles. Near the dead centers and during high pressure, film thickness tends to be smaller. This results in smaller particles passing under the ring face. Especially under high pressure, larger particles may get crushed under the forces acting on the ring. This, combined with the asperity contact, results in high wear and polishing of the ring and liner surfaces. During times of low pressure in the cycle, and when the piston is moving fast, the oil film thickness is larger. Larger particles may pass by the ring face. Because the forces are lower, the abrasive wear by debris is less.
33.2.11 Effect of Oil Cleanliness As a lubricated surface, liner wear occurs primarily through adhesion and abrasion. Adhesive wear is controlled by the formation of the oil film around the top ring reversal (TRR) area and by the anti-wear film in the vicinity of the TRR, where the film thins to boundary lubrication. Abrasion occurs as thirdbody wear from particulate contamination in the oil that becomes entrained in the oil film. These particles can come from both external and internal sources. Externally, they can come from dust-laden air that passes by the air filter or from the introduction of replacement oil that has not been handled or transferred in clean conditions. Any time the engine is opened for either scheduled maintenance or unscheduled repair, there is a possibility of adding external contamination. Internally, particulate contamination can come from debris left behind by the manufacturing process, such as core sand or machining chips, wear debris, surface fatigue, oil additive precipitation caused by acid neutralization, or massive additive precipitation caused by the accidental leakage of the coolant into the oil. The use of air and oil filters is designed to keep the particulate contamination under control to minimize wear. However, it is not clear to what extent a higher level of filter efficiency, by itself, would extend engine life as measured by oil consumption. Figure 33.7 shows a schematic of a particle-laden oil near the TRR as the oil film thins. While this figure shows particles at the ring/liner interface, one should not ignore the particle flow by means of lubricant from the back of the ring to the front of the ring. By hydrodynamic exclusion, larger particles do not pass under the ring face. This should result in finer and finer particles being captured by the film as it thins. For these smaller particles, the efficiency of standard oil filters, as measured by industry standard tests, drops off dramatically. As an example, for a current high-efficiency, single-stage filter, 99% of 30-micron particles and greater can be removed, but the efficiency drops to 85% for particles smaller than 10 microns. Because oil film thickness is roughly on the order of magnitude as roughness, trapped particles are no larger than 1 to 2 microns as TRR is approached, and standard filtration becomes much less effective in that regime. Using surface layer activation, the sensitivity of critical parts to cleanliness for several different engines has been established (Truhan et al., 1995). Newer engines and lubricants show much more tolerance to dirt in the oil than 15 to 20 years ago. This is reflected in the almost doubling of effective engine life during that period. It is much more effective to keep the external contamination out of the
FIGURE 33.7
Schematic and the observed regions above, at, and below the TRR area.
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Contact force (N)
Liner wear (microns) 0
5
10
-6000
-4000
-2000
0
0
0
10
15
20
25
5
10
15
20
Distance from top of liner (mm)
5
TRR
Distance from top of liner (mm)
TDO
25
30
40
FIGURE 33.8
Contact force at TRR and measured wear profile.
system in the first place, because any contamination passed by the air filter does damage going past the ring pack, regardless of the efficiency of the oil filter. The wear that occurs on the liner near the TRR is the wear that determines engine life and is only affected to a small extent by the bulk oil cleanliness. Ring wear is affected to some degree by cleanliness.
33.2.12 Examples of Liner and Ring Wear Mechanisms The major factors that influence ring/liner wear have been identified in previous sections. This section provides an example of liner and top compression ring wear mechanisms that have been identified using scanning electron microscopy (SEM). A typical contact load and the measured wear profile are shown in the Figure 33.8. At TRR, the oil film thickness is small (Figure 33.7) and the contact load is a maximum. Thus, liner wear at this location is a maximum. The liner surface outside the ring travel zone is shown in Figure 33.9a. This is equivalent to a machined liner surface. The scanning electron micrograph of the TRR interface of the liner after an engine test is shown in Figure 33.7. This micrograph reveals: • Typical polished area in the region below the TRR • Transition from the highly polished area to the region with the parallel grooves along the sliding direction. The region below the TRR, taken at higher magnification to look for finer details in the wear mechanisms, is shown in Figure 33.9b. This micrograph indicates parallel grooves in the sliding direction, surface cracks along the cell-boundaries, some regions with pits at microscopic level, and delamination of the graphite flakes. The carbon deposits that form on the piston lands and behind the rings, oil degradation products, soot, and wear debris generated because of the relative motion of the liner and ring can act as third-body particles. Some of these deposits can be hard and produce a polished surface on the liner even under poorly lubricated conditions. This loose wear debris can sometimes adhere to the ring face or mechanically scrape different regions, and can be transported from one region to another. Adhesive wear is also a mechanism between ring/liner interface. The difficulty associated with differentiating between adhesive wear and abrasive wear makes the quantification of the amount of wear caused by adhesive wear impossible. Combustion products from sulfur-containing fuel include NOx and SOx compounds. These oxides can react with water vapor to form acids. The condensed acids are rich in sulfurous and sulfuric acids, which
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(a)
(b)
(c)
FIGURE 33.9 (a) Liner surface outside ring travel zone. (b) Region below top ring reversal area. (c) Region showing corrosive wear.
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FIGURE 33.10
Modern Tribology Handbook
Worn face of a Cr-plated top compression ring after an engine test.
are aggressive to the liner surfaces chemically. Figure 33.9c indicates selective attack of the ferrite phase. This suggests that a chemical etch has taken place on the liner surface. Loss of material because of this chemical etch may not be significant. Figure 33.10 shows the worn face of a Cr-plated top-compression ring after an engine test. This figure reveals a highly polished region and parallel grooves along the sliding direction, the latter an indication of abrasive wear. In summary, the chief mechanism for the loss of material wear in ring/liner systems is abrasive wear. Factors that govern ring/liner interface tribology include oil film properties and thickness, contact pressure, material compatibility, external dust particles from the air system, the carbon deposits that form on the piston lands and behind the rings, oil degradation products, and wear debris generated because of the relative motion of the liner and ring. The contributions to loss of material in the liner by each one of these factors depend on engine operating conditions. These factors also contribute to the second ring and oil ring wear. Among all the tribological systems in the power cylinder system, the ring/liner interface plays a significant role in determining the effective engine life. One of the ways to meet more stringent emissions requirements is to design an engine with cooled exhaust gas recirculation (EGR). If next-generation engines are designed using this approach, wear due to corrosion might be significant during cold cycles of operation. To retain experience-based knowledge, the choice of materials is currently limited to conventional materials in use. Designing cleaner engines with greater durability remains a challenge to engine manufacturers.
33.3 Overhead Components Overhead components (Figure 33.11) are parts that link the camshaft and the intake/exhaust valves in the cylinder head in order to actuate the opening and closing of the valves in accordance with the contour of the cam lobes. This linkage is also used to actuate fuel injection events in engines equipped with electronically controlled but mechanically actuated fuel systems, although some modern electronic fuel systems now actuate injectors with hydraulic pressure from engine oil (Glassy et al., 1993). There are many varieties of designs. Overhead components in a typical diesel engine normally consist of cam followers, push rods, rocker levers, and crossheads. The key tribological contact is between the cam lobes and the cam followers. Additional tribological contacts include the joint between the push rods and the cam followers, the rods and the rocker levers, the rocker levers and the crossheads, and ultimately the contacts with valve and injector tips. Recent emissions controlled engines encounter high
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Valve Stem Tip
Rocker Lever
Adjusting Screw
Push Rod
Follower Lever
Flat Follower/Tappet Roller Follower Pin
Roller Follower
Camshaft
FIGURE 33.11
Overhead components and their arrangements in a diesel engine.
levels of soot in the oil, therefore exposing overhead components to the risks of high wear — not only due to mechanical stress, but also the interference of soot (Kuo et al., 1998).
33.3.1 Cam and Cam Followers Small- to medium-sized diesel engines usually use flat cam followers, or tappets, similar to small gasoline engines. When the cam rotates, the cam lobes slide across the flat tappet surface, and the contour of the lobe lifts the tappet upward. Once the contact slides past the peak of the lobe, the tappet will come down due to the spring pressure of the valves (or injectors) to remain in contact with the lobe surface. Tappets are usually positioned to be off-centered from the contact point. This allows the tappet to rotate when it is dragged by the friction of the sliding contact. This rotating motion introduces limited rolling to reduce friction, and helps distribute the wear across the tappet surface to prolong component life. To provide optimal performance at this contact, consideration must be given to the selection of materials, the contact stress, surface finish, and the mode of lubrication. Diesel cams are normally made of steel
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or chilled ductile iron. Tappets are usually made of various cast or alloyed irons, or steel, depending on the stress level (Korte et al., 1997). Ceramic tappets using materials such as silicon nitride have also been tested successfully to improve durability at high stress levels (Kitamura et al., 1997). Ceramics have been particularly effective in reducing wear when a poor-quality lubricant is used. Superfinishing on cam or tappet surfaces has been used successfully on many occasions, but overly smooth surfaces sometimes lead to early seizure and scuffing. Lubricant is provided by crankcase oil splashed onto the parts due to the mechanical movement of crankshaft and connecting rods inside the block. Lubrication in this contact is usually in the elasto-hydrodynamic to boundary lubrication regime with a λ ratio below 1. Friction modifier and antiwear additives are more important for wear protection than the rheological properties of the lubricant. Medium- to large-sized diesel engines usually use roller followers to accommodate the much higher stress involved. When the cam lobe rotates, it lifts a roller mounted on a roller shaft assembly, which in turn raises the push rod. The cam and roller follower contact now has turned into a rolling contact to reduce friction and improve durability. However, depending on the friction and lubrication characteristics of the several interfaces involved, the contact often has some sliding motion, or slippage, in addition to pure rolling. Many cam and tappet failures are associated with the transition from rolling to sliding. With limited slippage, fatigue life is reduced because the high friction of sliding introduces a shear stress that raises the maximum stress level closer to the surface, causing early spalling or pitting. With more slippage, immediate seizure or scuffing may result due to localized welding. Sometimes, the slippage is not caused directly by the lubrication of the cam/follower contact. Many roller followers are mounted on a bronze pin with the soft bronze material acting as a bearing material to better accommodate the steel roller. Lubricant is usually fed through oil drillings to this interface. Wear or corrosion of the steel roller/bronze pin interface will cause the roller to “stick” to the pin, then quit rolling (Cusano and Wang, 1993). It is important to look at all linkages when troubleshooting a tribology problem.
33.3.2 Push Rods, Rocker Levers, and Crossheads Push rods are used to transfer the lifting motion initiated by the cam and the cam followers to the rocker levers. The rocker levers engage on the valve tip or injector link to initiate the valve opening or fuel injection event. Ideally, the push rod will have only normal loading on both ends as it merely functions as a link between the follower and the rocker lever. However, both ends of the push rods are usually shaped like a ball joint and engage in sockets in the mating parts. This design allows limited sliding and sideward movement of the rod relative to the other two components it connects. As modern engine designs call for reduced emissions and higher power density, accurate actuation of valve and injector events become critical. Push rods represent a linkage among the overhead components that introduce additional inaccuracy due to tolerance stack-ups and wear. This linkage is eliminated in overhead cam designs where the cam and cam followers actuate the valve and injectors either directly or via the rocker levers. Many modern diesel engines have more than two valves per cylinder to improve air handling. Rocker levers sometimes push down on crossheads to actuate two valves simultaneously. This is in contrast to double overhead cam designs, in which each valve is actuated by individual cam lobes. This lever/crosshead contact has limited sliding in addition to normal loading. Of all the interfaces between overhead components, sliding is always directly or indirectly involved, and is primarily responsible for wear problems. Oil drillings are usually present to feed oil to the interfaces between components to provide boundary lubrication under all these sliding contact conditions. However, rheological properties like cold flow performance are still relevant in terms of pumping oil to the drilling without delay. The presence of contaminants, especially diesel soot, can greatly influence the effectiveness of lubrication to cause wear. Wear modes range from scuffing at the rod tip/bowl interface, to abrasion and scuffing on the crossheads. Another cause of wear is oil delay due to oil thickening or poor cold flow properties, and loss of wear protection due to oil soot contamination. Hardware improvements can also reduce or prevent wear. These may include ceramic inserts, coatings, or enlarged contact areas.
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Tip Spring retainer
Keeper Stem
Guide
Spring
Cylinder head Insert Fillet Seat
Margin
Combustion face FIGURE 33.12 Engine valve schematic. (From Schaefer, S.K., Larson, J.M., Jenkins, L.F., and Wang, Y. (1997) Evaluation of heavy duty engine valves — material and design, Proc. Int. Symp. Valvetrain Sys. Des. Mater., Dearborn MI, April 14-15.)
33.4 Engine Valves The engine valve system (comprising the valve, seat insert, and valve guide) is shown schematically in Figure 33.12.
33.4.1 Valve/Seat Wear Mechanisms Wear between the valve and seat is thought to occur primarily due to relative motion when the valve is seated, due to cylinder pressure that forces the valve into the seat, causing slight deflections of both valve and seat. Thus, cylinder pressure and rigidity of the valve face and seat are primary variables in determining valve/seat wear. Also, the valve/seat angle controls the contact stress normal to the seat and hence the tangential stress (friction coefficient times normal stress). Flatter seats (i.e., reduced seat angle θ) reduce the contact stress (which varies as 1/cosθ), but the effect is small, especially when there is substantial friction between the valve and seat. However, the most important effect of reducing the seat angle is to reduce lateral valve/seat displacements, which in turn reduce wear. The primary mechanism of valve/seat wear is adhesive wear, often combined with oxidative wear or corrosion due to sulfur compounds or other fuel-derived compounds. Sometimes, the wear surface shows surface waves (“sand dunes,” see Figure 33.13), which occur due to the surface shear stress that causes material to flow down the seating surfaces in addition to being removed as wear debris. Material can also transfer from the valve to the seat insert, or vice versa. In diesel engines, especially in constant-speed applications (typically industrial or power generation), intake valve recession is usually more severe than exhaust valve recession, although the intake seat temperatures are lower (e.g., 600°C for exhaust valve seat and 370°C for exhaust seat insert; 370°C for intake valve seat and 270°C for intake seat insert). This is thought to occur because of lack of lubrication on the intake side (especially when a dry stem seal is used), high boost pressure blowing off any oil films, and the lack of oil/fuel deposits or beneficial oxide layers leading to clean metal-to-metal contact, which favors adhesive wear. This is also consistent with the observed temperature sensitivity of wear in Figure 33.19 (Section 33.6): some materials show decreasing wear as the temperature is raised from 270 to 500°C. Factors affecting valve/seat wear are listed in Table 33.4.
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FIGURE 33.13 Wear of (a) intake valve seat insert, and (b) intake valve showing dark imaging oxide/transfer layers (left hand image) on the peaks of the “sand dunes.”
The end result of valve/seat wear is that the valve recesses into the head (measured as a change in valve protrusion). Valve recession tends to offset the increase in valve train lash due to wear of the cam follower, pushtubes, adjusting screws, rocker levers, crossheads, and valve tips. If excessive valve recession occurs, the valve-train lash can become zero, leading to higher contact stresses on the cam nose. Loss of seating load caused by valve/seat wear can also lead to poor heat transfer from the valve to the seat, leading to valve overheating, which may cause valve torching, excessive valve/seat wear, fatigue failures, or stemguide galling. Also, in cases of extreme valve wear, chordal fatigue failures of the valve can occur due to the loss in section.
33.4.2 Valve Stem/Guide Wear Mechanisms Wear between the valve stem and guide occurs due to the sliding motion of the stem in the guide (twobody abrasion and also adhesive wear under more severe conditions) and also due to three-body abrasion from oil deposits. Corrosive wear is also common for exhaust valves (and potentially for intake valves for engines equipped with exhaust gas recirculation). Stem/guide wear is sensitive to the rate of lubricant supply to the interface, which is usually controlled by means of a stem seal, which limits the ingress of
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TABLE 33.4 1. 2. 3.
4. 5. 6.
7.
8.
9.
10.
11.
1251
Factors Affecting Valve/Seat Wear
Valve/seat deflections during firing. The magnitude of the deflection depends on cylinder pressure and valve, seat, and head design (particularly seat angle). Valve and seat temperature (see text). Thermal and mechanical distortion of the seat insert (and possibly the valve) due to the temperature gradient from exhaust to intake and due to the effects of cylinder pressure and clamping stresses (e.g., head bolts, injector clamping). Swirl increases temperature gradients across intake valve head, which increases head distortion. This effect leads to deviations from circularity and nonuniform loading. In extreme cases, this may lead to loss of sealing, which can lead to valve “torching” or “guttering,” in which the high thermal flux around a leak results in gross local overheating of the valve and seat, resulting in oxidation/thermal fatigue and the complete loss of a piece of valve material. Impact wear caused by high seating velocities. Abrasion by oil/fuel deposits or by protruding carbides in the counterface. Surface deposits may also reduce the heat flow from the valve, causing high valve temperatures. Insufficient lubrication due to high boost pressure (intake) blowing off the oil film or use of a non-optimum valve stem seal which does not allow sufficient oil to flow into the guide. (Too much oil, on the other hand, can lead to torching due to buildup of oil deposits on the seat.) Excessive valve rotation, especially if a non-optimum valve rotator is used. Valve rotators normally reduce valve wear by evening out circumferential temperature variations and thermal distortions and removing oil deposits that reduce heat transfer from the valve. However, excessive rotational speeds may cause increased wear, partly by the increased sliding action and partly by removing beneficial surface deposits and oxides. Corrosive wear from fuel-derived species. Corrosion may occur due to condensation of exhaust gas constituents such as SO2, SO3, NO, and NO2 at low temperatures (e.g., <150°C) and by hot corrosion at high temperatures (e.g., >730°C, 1350°F). Excessive temperatures, leading to structural or dimensional changes in the valve and seat, softening of the seating surfaces, and increased oxidation. High temperatures may be caused by engine operating conditions (e.g., overfueling, retarded timing) and may also be due to weak contact between the valve and seat or too narrow seat contact or improper seating of the seat insert in the cylinder head, reducing the heat flux from the valve to the seat. Seat deposits may also contribute to poor heat flow and overheating. Valve/seat misalignment, leading to uneven contact stresses and poor sealing. Guide/seat concentricity is important and is influenced by the machining processes. Ideally, the guide bores and seating surfaces are machined in place in the cylinder head at the same time. Permanent elongation of the valve due to “cupping” of the valve head by creep. This leads to a decrease in lash, which can lead to torching of the valves due to insufficient seating force.
oil and also the amount blown out by port pressure. Modern engines normally run oil-starved in order to reduce valve guide oil consumption, which in turn reduces the lubricant contribution to particulate emissions. Factors that affect valve stem/guide wear are listed in Table 33.5.
33.4.3 Materials Selection Criteria As shown in Table 33.6, materials selection criteria include more than tribological properties. The evolution of valve materials to meet these demands has been reviewed by Schaefer et al. (1997). For most heavy-duty diesel applications, exhaust valves are two-piece with a high-strength, iron-based austenitic stainless steel head welded to a hardenable martensitic steel stem. The valve seat area can be coated with a variety of hardfacing alloys, including Stellites, Tribaloys, and various nickel-based overlays. Intake valves are typically made from one-piece martensitic steels such as Silchrome 1, which may be hardfaced at the seat area. Valve stems are often chrome plated or nitrided to improve wear and scuff-resistant for both exhaust and intake valves. Valve guides are typically made from either pearlitic grey cast iron or iron-based powder metal (PM) materials, which often include machinability aids and solid lubricants, as well as porosity which aids in oil retention. PM guide materials provide superior scuffing and wear resistance (Figure 33.14). A wide variety of valve/seat inserts is available (Rodrigues, 1997), including cast irons, steels, nickel and cobalt alloys, and powder metal steels incorporating solid lubricants for improved adhesive wear resistance. PM materials may be copper infiltrated to improve thermal conductivity. Materials selection
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TABLE 33.5 1.
2.
3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16.
17.
Factors Affecting Stem/Guide Wear
Oil supply, which is primarily controlled by the valve stem seal design or (if no seal is used) the stem/guide clearance. Other factors include boost pressure (intake valves), duty cycle (constant-speed applications tend to blow oil out of the guides, while varying speeds and loads can periodically bring in a fresh oil supply). Inadequate oil retention on the guide bore. Often, the guide bore is knurled for improved oil retention. Powder metal guides have inherent oil retention capabilities due to the porosity of the material. Some powder metal guides incorporate a solid lubricant for improved wear and reduced friction. Cocking and side loading of the valve stem due to actuation forces from the rocker lever or crosshead. This effect is increased by the use of non-guided crossheads. Excessive temperatures if the guide protrudes into the port. Displacements caused by inadequate mechanical support of the guide in the head. Valve lift, since the wear rate should be proportional to the sliding distance. Stem/guide clearance. Too tight a clearance can cause scuffing as the stem expands thermally relative to the guide (because the stem is normally hotter than the guide and also because the stem material may have a higher CTE than the guide). Too open a clearance can allow cocking of the stem in the guide, leading to excessive wear at the guide top and bottom ends (180° apart). Stem/guide wear should increase with cylinder pressure because the side loading/misalignment forces scale with cylinder pressure. Errors in as-machined roundness, straightness, and taper of the guide and/or stem will lead to heavy contact between the stem and guide in local areas. Thermal distortion of the stem and guide due to temperature gradients in the head. Mechanical distortion of the guide due to improper press fit in the head. Side loading and cocking caused by poor concentricity of the valve seat and the guide. Uneven seat wear, leading to side loading and cocking of the valve in the guide. Excessive stem and guide temperature, leading to reduced stem/guide clearance, corrosive wear, excessive oil deposits, loss of oil film, etc. Excessive valve rotation, especially if a non-optimum valve rotator is used. Abrasive wear of intake stems and guides caused by corrosion of the intake system, for example due to a leaking charge air cooler, use of EGR, inadequate air filtration, or improper installation of the air inlet where it can ingest excessive road dust or water. Corrosive wear of exhaust stems and guides caused by high fuel sulfur, other fuel impurities, or unstable oil additives. This may be linked with excessive temperatures or may be caused by condensation of acidic gases at low temperatures (e.g., during engine idling).
TABLE 33.6
Materials Selection Criteria for Valve System Components
Requirement Ability to forge and machine Fatigue strength at elevated temperature High temperature yield strength (hot hardness) Temperature resistance (phase stability and dimensional stability) Elevated temperature compressive yield strength Thermal fatigue resistance Corrosion resistance: sulfidation, oxidation, chlorides Creep resistance Indentation resistance (hot hardness) Resistance to adhesive wear (marginal lubrication, high contact stress, low temperature) Resistance to adhesive wear (marginal lubrication, high contact stress, high temperature) Resistance to sliding wear (marginal lubrication, low temperature) Resistance to sliding wear (marginal lubrication, high temperature) Weldability to steel Thermal expansion mismatch Resistance to sliding wear (well-lubricated, low temperature, potentially high-soot oil)
Component Exhaust and intake valves Exhaust valve Exhaust valve Exhaust valve and seat insert Exhaust seat Exhaust valve and seat insert Exhaust valve and guide Exhaust valve and seat insert Exhaust valve and seat insert Intake valve and seat insert Exhaust valve and seat insert Intake valve stem and guide Exhaust valve steam and guide Two-piece valves Exhaust valve stem to guide Stem tip/rocker lever or crosshead
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Cast iron
Stuck
Gall
Gall
Powder metal
FIGURE 33.14 Results of a split test run with cast iron and powder metal exhaust valve guides. The engine was run at rated for 5 minutes with the coolant level below the head gasket and the water pump disconnected (the steam temperature from the head was measured at 180°C). This procedure was repeated three times. One exhaust valve was stuck at the end of the third cycle. Three of the cast iron guides had galled, with no galling of the powder metal guides.
tends to be very application specific. The tribological compatibility of the valve/seat insert system is important because some materials couples do not match well.
33.5 Bearings and Bushings Table 33.7 characterizes some of the journal bearing systems found in diesel engines. Bearings and bushings are required to support the load applied to rotating or oscillating shaft/components with minimum friction and wear. Bearing materials selection is complicated by a number of requirements, which are often contradictory (Table 33.8). For example, bearings need to be compliant enough to conform to imperfect shaft alignment or distortion and to embed debris, but they also need to be hard enough to resist wear and fatigue. To overcome these conflicting requirements, a steel-backed “tri-metal” design is often used for connecting rod, crankshaft, and other bearings (Figure 33.15). Bearing design involves trade-offs between friction reduction (for best fuel economy) and durability. Durability is addressed by calculating the minimum oil film thickness (MOFT) and peak oil film pressure (POFP) at various design points. Low MOFT indicates the potential for wear and seizure, and high POFP indicates the potential for overlay or lining fatigue. Durability estimates are often made by comparing TABLE 33.7
Characterization of Bearing Systems for Heavy-Duty Diesel Engines
Location Piston pin bushing Connecting rod (small end) bushing Connecting rod (large end) bearing Crankshaft bearing Camshaft bushing Cam roller pin Rocker lever bushing Turbocharger bushing Fuel pump bushings (several locations)
Motion
Unit Load
Speed
Oscillating Oscillating Rotating Rotating Rotating Rotating Oscillating Rotating Rotating
High High High High Low Medium Medium Low Low
Low Low Medium Medium Medium Medium Low High High
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Bearing Material Properties
Property Fatigue strength Conformability Embeddability Corrosion resistance Friction reduction Wear resistance Seizure resistance Heat resistance
FIGURE 33.15
Steel Back
Leaded Bronze Lining
Aluminum/Tin Lining
Lead-Tin or Lead-Indium Overlay
Sputtered Aluminum-Tin Overlay
High Low Low High Low High Low High
High Medium Medium Medium Medium Medium Medium Medium
Medium Medium Medium High Medium Medium Medium High
Low High High Medium High Low High Low
High Medium Medium High Medium High Medium High
Steel-backed “trimetal” bearing design.
calculated MOFT and POFP values for new designs with those for established engines with known durability (“comparative engineering”). Bearing materials selection depends on many design- and application-specific factors. For most highly loaded bearings used in heavy-duty diesel engines, fatigue requirements dictate the use of steel-backed designs and high-strength leaded bronze lining materials. Steel-backed aluminum bearings are used where fatigue requirements are less stringent. These aluminum bimetal materials are used without overlays because of the difficulty of electroplating onto aluminum. In practice, this, along with fatigue requirements, tends to further limit the use of aluminum bearings in heavy-duty engines, although they find widespread use in light-duty applications. Overlay selection depends on the level of conformability/embeddability required for the application. In engines with good shaft tolerances, clean manufacturing processes, and good filtration systems, harder overlays may be selected for improved wear and fatigue resistance. Sputtered aluminum-tin overlays provide the ultimate in wear and fatigue resistance and can be applied to both bronze and aluminum linings, but at relatively high cost. Electroplated lead-tin-copper and lead-indium overlays are more commonly used. For the Pb-Sn-Cu system, the higher the copper level, the greater the hardness/wear resistance/fatigue resistance. Recently, electroplated overlays incorporating ceramic hard-phase particles have been introduced, providing performance and cost levels intermediate between conventional electroplating and sputtering. An alternative bearing design (termed “Rillenlager”) is to form inlaid bands of overlay material in the lining surface. This design provides improved wear resistance (provided by the exposed lining material), while still maintaining some degree of conformability and embeddability. Figure 33.16 shows wear comparisons between standard electroplated, “Rillenlager,” and sputtered Al-Sn overlays.
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0
200
100
running period (%) 300 400
sputter bearing
8 Rillenlager
overlay
wear [µm]
4
12 trimetal bearing
Ni
16
20
FIGURE 33.16 Wear of sputtered Al-Sn, “Rillenlager,” and electroplated overlays. (From Miba Gleitlager AG, Technical Information, Laakirche, Austria.)
A variety of proprietary bench tests is available for materials development and selection. Typically, such tests are used for comparing materials rather than to establish design limits.
33.6 Turbomachinery Although the majority of engine components are oil-lubricated, many turbocharger components are required to function at high temperatures with no (intentional) lubrication. Although loading is generally light for such components, durability expectations are the same as for the rest of the engine (e.g., a million miles for a heavy-duty diesel engine). An important example of this type of unlubricated, high-temperature system is the turbocharger wastegate mechanism (Figure 33.17), which typically comprises a flap valve with a valve shaft rotating in a bushing. Maximum operating temperatures range up to approximately 550°C for diesels and 650°C for natural gas engines. Wear occurs due to both intended actuator motion and also that induced by exhaust pressure pulses acting on the valve. The vibration amplitude depends on many factors, including the stiffness of the actuator mechanism, but is often in excess of 100 microns in amplitude, which can give rise to substantial wear because the frequency of the excitation pulses is extremely high. The effect of vibration amplitude is often greater than the effect of high temperature. For example, Waterhouse (1992) shows that wear rates increase by several orders of magnitude once a critical amplitude (of the order of 10 to 50 microns) is exceeded (Figure 33.18). Temperature has at least three competing effects on wear and scuffing: (1) softening of the materials, (2) formation of protective oxide layers/reaction products, and (3) formation of undesirable (soft, nonprotective and/or loosely attached) oxides/reaction products. The overall effect depends on material and temperature range (and also other factors, such as contact pressure). The effect of temperature on wear rates for various materials is shown in Figure 33.19. Wear rates can increase or decrease with increasing temperature. In general, a flat temperature response is optimal because the mechanism is required to function at all temperatures from ambient (on engine start-up) to maximum full-throttle conditions. Typical failure modes are high wear, galling, and material transfer on the shaft and bushing (Figure 33.20), which can lead to sticking of the mechanism. Wear also occurs on the actuator rod and the crank pin (which are external to the turbocharger), leading to loss of control function and consequent deterioration of engine emissions performance. Corrosion can also be a problem for internal components (due to high-temperature oxidation/sulfidation and condensation of exhaust acids at low temperatures) and external components (due to road salt).
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Rod end Pin
Valve shaft
Wastegate bushing Wastegate valve
FIGURE 33.17
Turbocharger wastegate components.
FIGURE 33.18 Effect of sliding amplitude on wear coefficient. (From Waterhouse, R.B. (1992), ASM Handbook, 18, 242-256. With permission.)
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FIGURE 33.19
Effect of temperature on wear coefficient for various materials.
(a)
FIGURE 33.20
(b)
Galled wastegate: (a) shaft and (b) bushing.
Control of wear and scuffing for these components is achieved by: • • • •
Minimizing loads and vibration amplitudes by design of the actuator mechanism Minimizing contact pressures Optimizing clearances Materials selection
Wastegate components have typically been fabricated from austenitic stainless steels, despite the generally poor scuffing resistance of this class of materials. However, future designs will require more wearresistant materials because improvements in engine emissions favor the use of a fully proportional wastegate valve, which will see more motion than previous “on/off ” designs. The use of variable geometry turbochargers will also provide several potentially similar unlubricated, high-temperature scuffing and wear applications.
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33.7 Fuel System Fuel injectors and fuel pumps contain many sliding interfaces that are subject to wear and/or scuffing.
33.7.1 Fuel Injectors Fuel injectors (e.g., Figure 33.21) are required to deliver high injection pressures that must be developed and contained within the injector body without leakage into the engine oil. This necessitates extremely tight running clearances between the various plungers and their bores (typically 2 to 4 microns), which leads to potential scuffing issues (Figure 33.22). High injection pressures, high fuel temperatures, low lubricity fuels, and fuel contamination (e.g., water or abrasives) can all contribute to scuffing problems. Figure 33.23 lists the variables that are either known or suspected to influence injector scuffing, illustrating the complex nature of the problem. Injector scuffing is addressed using a broad range of design, manufacturing, and materials technologies, including: • • • • •
Tight control of dimensions and tolerances Elimination of internal machining burrs and debris Minimizing distortions (e.g., dilation due to fuel pressure, injector clamp loads, etc.) Optimizing clearances Selection of scuff-resistant materials, surface treatments, and coatings
Timing Plunger
Metering Plunger Check Ball
Needle valve Cup
FIGURE 33.21
Schematic of Cummins Celect unit injector.
FIGURE 33.22
Scuffed injector plunger showing transferred and smeared material.
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FIGURE 33.23
1259
Factors affecting injector scuffing.
FIGURE 33.24 Examples of (a) zirconia ceramic injector metering plungers, and (b) PVD-coated WC/C injection pump plungers. (Courtesy of Balzers.)
A recent trend in modern fuel injectors is the use of ceramic plungers and plunger coatings to resist scuffing and wear (Figure 33.24). Ceramics such as zirconia are found to have extremely high scuff resistance in fuel-lubricated environments and are ideal candidates for components that see mainly compressive stresses (e.g., plungers). Materials selection for injectors is generally problematical because many components (e.g., nozzles and injector bodies) require fatigue and corrosion resistance in addition to scuffing/wear resistance. In addition, the combined wear of the plunger and bore surfaces must be minimized to avoid long-term fuel leakage issues. Thus, wear compatibility of the sliding materials needs to be considered, and materials or coatings that are abrasive to the sliding counterface must be avoided. Another wear mode that can be encountered is hard particle erosion around spill ports where machining debris or contaminated fuel has passed through the injector (Figure 33.25). This issue is addressed by manufacturing cleanliness, fuel filtration, and materials selection. Tribological testing can be used to assist in materials selection. For example, pin-on-disk tests have been used to compare the scuffing and wear properties of various materials combinations (Figures 33.26 and 33.27). Test severity can be increased using low-lubricity fluids or fuel-alcohol-water mixtures.
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FIGURE 33.25
Hard particle erosion around injector spill ports.
FIGURE 33.26
Pin-on-disk scuffing data for three plunger materials.
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FIGURE 33.27
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Pin-on-disk wear data for three plunger materials.
33.7.2 Fuel Pumps Several sliding wear interfaces in fuel pumps are sensitive to low-lubricity fuel, including shafts/bushings, plungers/bores, gears, and governor flyweight/thrust washer contacts. Wear of fuel pumps due to lowlubricity fuel has been well-documented (see Section 33.8.1) and can be addressed by either specifying a minimum fuel lubricity (which requires careful definition of test methods) or by using more robust materials for pump components. Materials selection is, of course, component specific, but wear-resistant options include case-hardened steels, high alloy tool steels, monolithic ceramics, and hard coatings.
33.8 Fuels, Lubricants, and Filtration Air, coolant, fuels, and lubricants are essential working fluids in a diesel engine. The combination of air and fuel provides the power output. The coolant maintains the working temperature, and the lubricant prolongs the life of engine components. Actually, the entire diesel engine design is usually broken down into just four basic functions: air handling, combustion/fuel, lubricating, and cooling. Filtration technology is used in all four working fluids. Specifically in tribology applications, fuels and lubricants, and their respective filters, are the most relevant.
33.8.1 Diesel Fuel Diesel fuel performance depends on several key properties, such as cetane number, viscosity, boiling point distribution, etc. (Owen and Coley, 1995). One key property relevant to tribology is fuel lubricity. Diesel fuel is used as a lubricant for many fuel system components (e.g., fuel pump and the unit injectors). In the past, diesel fuel lubricity problems were associated with very low viscosity fuel used under arctic conditions in exchange for engine startability. These arctic fuels often fall in the lighter category of jet
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fuel or kerosene. While it appears that hydrodynamic film thickness is the dominant factor considering the viscosity effect, low concentrations of polar compounds have been used in jet fuel to improve lubricity, which also indicates the influence of boundary lubrication (Wei and Spikes, 1986). In those cases, hardened diesel fuel system components are required to survive the reduced lubrication capability of the fuel. More recently, low lubricity is observed to be caused by the dramatic reduction of fuel sulfur as a result of emissions regulations. The earliest problems due to low fuel lubricity were reported in Sweden when fuel sulfur as low as 50 ppm or less was mandated by legislation, although viscosity in general did not change. The problem was relieved by the development of new fuel additive technology (Bovington and Caprotti, 1993). Later introduction of low sulfur fuel in the range of 300 to 500 ppm caused spotted problems but not widespread failures. This is likely because the refining processes producing 500 ppm sulfur fuel are not as aggressively removing polar and aromatic fuel components as those producing 50 ppm sulfur fuel (Wang and Cusano, 1995). Lubricity is primarily measured by two methods. One is the high frequency reciprocating rig (HFRR) using a steel ball oscillating on a steel plate immersed in the test fuel. The lubricity is evaluated based on the size of the wear scar generated during the test (Bovington and Caprotti, 1993). The other is the scuffing load ball on cylinder lubricity evaluator (SLBOCLE), which presses a steel ball down onto a rotating steel ring with increasing load (Lacey, 1994). The lubricity is evaluated by the maximum load the fuel can sustain without scuffing, as indicated by the sudden increase of friction. Both methods have been considered by the International Standardization Organization (ISO) and American Society of Testing and Materials (ASTM D975) for adoption as part of the fuel specification. However, no definite number has been agreed upon by the industry. In general, 460 microns or less at 60°C in HFRR, and 3100 to 3300 grams or higher at 25°C in SLBOCLE, have been proposed by various equipment producers to be the minimum acceptable performance. Diesel fuel contamination is another source of fuel system wear. Contaminated fuel, as often measured by the number and size of particles, can lead to abrasion of plunger and barrel surfaces and erosion of spill ports of unit injectors. Fine filtration at 10 microns or less is often installed on diesel engines that have tight clearances between moving parts in their fuel systems. Another common source of contamination is water. Excessive water can lead to injector scuffing and fuel pump wear. Water can also lead to filter plugging and fuel line rusting. Water separators attached to fuel filters are often used to remove water.
33.8.2 Diesel Lubricants There are two primary functions of a crankcase lubricant. First, a lubricant must lubricate. This includes cooling, cleaning, contaminants containment, and reduction of friction and wear. Second, a lubricant must continue lubricating. That is, a lubricant must keep all its functions for a prolonged period of time, even as the lubricant itself goes through continuous degradation, additive depletion, and contaminant accumulation. The former is usually referred to as the performance aspect of the lubricant, and is the subject of lubricant specification. The latter concerns the useful life of a lubricant, and is only sometimes covered by lubricant specifications. It should be noted that lubricant performance does not decrease linearly with time of use. A used oil before scheduled oil change should perform similar to when it is fresh. On the other hand, a poor performing oil cannot be helped by frequent oil changes. Details of lubricant properties and formulations can be found in Booser (1992). This chapter covers only those aspects that are directly related to diesel engine lubrication. 33.8.2.1 Lubricant Performance A lubricant is used to cool the power cylinder components. While some engines rely on natural splashing of oil to engine parts, modern heavy-duty diesel engines usually have oil injection nozzles aimed at the under-crown of the pistons to provide active cooling. This process, combined with coolant flowing around the cylinder liner, maintain the power cylinder components within their operating temperature limits.
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Overheated pistons and rings will seize on the liner, which leads to disastrous failures. The ability of oil to cool depends largely on the heat transfer properties of the oil, the amount of oil flow, and the thermostat setting that determines the maximum oil temperature allowed. Most engine oils today are mineral oil based and have properties well matched to engine cooling needs. However, the heat transfer properties of synthetic base oils can be very different from mineral oils. Synthetic oils can also sustain higher oil temperatures. Both will allow for more flexibility in oil temperature settings. Table 33.9 provides the lubrication mode and related oil properties for particular engine components. The oil sprayed onto the piston and that brought to the upper ring/liner contacts also serve as a cleaning agent to prevent deposit formation or to remove deposits once formed. Because the precursors of deposits are products of thermal or oxidative degradation of the oil, the prevention of deposit relies on the continuous presence of antioxidants and the combined stability of the oil/additive package. The detergency provided by additives, such as metal sulfonates or phenates, cleans deposits off the surface and keeps the deposits in suspension. Debris and particles that cannot be contained by additives are removed by oil filters. Modern oil filters normally include multiple stages to remove progressively smaller particles. The full flow section, so named because all oils are filtered through this part of the filter in each pumping cycle, normally removes particles larger than 20 to 25 µm. A bypass section, through which only a fraction of the oil flows during each cycle, removes the smaller particles. The most detrimental contaminant in today’s diesels is a lubricant soot. Soot is generated during the combustion process, and brought to the bulk of the oil primarily by the scraping of the sooted oil from the ring/liner area. A secondary source of oil soot is blow-by. While soot is generally described as a carbonaceous core covered with adsorbed fuel/oil fractions, soot is actually defined by the method used to measure it. The industry currently uses thermal gravimetric analysis (TGA) as the standardized procedure to measure the amount of soot in the oil (ASTM D5967, 1997). The process heats the sample gradually under nitrogen to evaporate the oil while the sample weight is recorded continuously. Once the weight has stabilized, indicating no more volatile fraction is present, oxygen is introduced to burn away whatever is combustible. What remains is ash. The weight loss during the burning process is defined as soot. That is, the measurement of soot is not devised to detect any characteristics of a particular class of material, but simply measure whatever responds to a defined measurement process. This is sometimes misleading because, for example, oxidized molecules may form nonvolatile polymers — but which are combustible during the burning process — making the soot concentration deceivingly higher. Modern engines meeting the latest emissions regulations can reach over 5% soot before an oil change. This number is expected to rise as long drain and emissions strategies such as exhaust gas recirculation (EGR) become more common. The accumulation of soot has two significant effects on oil: the thickening of the oil through agglomeration of soot particles, and the increase of wear, particularly those parts under boundary lubrication. Oil thickening can lead to loss of oil pressure, which leads to loss of oil flow to critical components. The effect of soot on wear remains controversial (Kim et al., 1992). Typical soot particles range in size from below 0.1 micron to over 1 micron. These particles cannot be removed by oil filters. The solution is to apply dispersants or multifunctional viscosity index improvers to keep soot particles from agglomerating. At the same time, anti-wear additives need to be rebalanced to maintain wear performance. When soot is properly contained, not only the oil viscosity will stay within limits, but wear increase is also minimized. TABLE 33.9
Engine Components and Their Respective Mode of Lubrication
Components Bearings, bushings Gears, piston rings, and liners Cam, valve train
Lubrication Mode
Oil Properties Related to Lubrication Mode
Hydrodynamic Hydrodynamic to boundary Mixed to boundary
Oil viscosity Oil viscosity, additives Oil additives
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TABLE 33.10
Tolerance of Soot by Oils as Defined by APIa Category
Oil Specification
CC/CD
CE/CF-4
CG-4
CH-4
1%
1.5%
3.8%
4.8%
Up to this much soot in wt% a
American Petroleum Institute
A diesel engine involves all lubrication regimes, from thick-film hydrodynamic lubrication, to elastohydrodynamic/mixed-film lubrication, to parts relying solely on boundary lubrication. For hydrodynamic lubrication, the rheological properties of an oil are primarily defined by kinematic viscosity measured at 40°C and 100°C (SAE J300). With the help of the Walther equation (ASTM D341), the viscosity at various temperatures can be derived. In addition, cold flow performance (ASTM D5293; ASTM D4684) and high-temperature, high shear viscosity (ASTM D4683) define oil performance at very high and very low temperatures. For mixed-film and boundary lubrication, anti-wear additives and their response in a base oil determine the performance of the lubricant. 33.8.2.2 Lubricant Life Acids are generated during the operation of a diesel engine. The primary types are sulfuric acid from the sulfur in diesel fuel, and nitric acids from NOx, both as combustion by-products. Organic acids are also generated as a result of oil degradation. Total base number (TBN) is an indication of the alkalinity reserve of a lubricant and the ability to neutralize acids. The depletion of TBN always coincides with the onset of bearing corrosion, as indicated by lead (Pb) increase in the oil. The acids can also attack other ferrous or non-ferrous metallic components, as well as elastomers and seals. Acids also serve as catalysts to accelerate oil degradation. Until soot becomes an issue in emissions controlled engines, TBN depletion remains the predominant reason for oil change. The combination of emissions regulation and extended oil drain interval have escalated soot concentration in oil to unprecedented levels. Table 33.10 shows that recent commercial oils are required to maintain performance with up to 5% soot. This number is expected to go higher, so improvement in oil formulation technology is of critical importance. Oil oxidation is primarily dominated by bulk oil temperature. Oil temperature is rising due to increased power density of modern engines, as well as reduced cooling by ever smaller frontal areas available for the radiator. When the oil temperature is raised over 250oF, oil oxidation is accelerated dramatically. This results in increased viscosity, bearing corrosion, and a general loss of lubricant functionality. Oil oxidation has not been a life-limiting factor, except for certain off-road applications and for areas using low-quality oils.
33.8.3 Used Oil Analysis Used oil analysis (Table 33.11) is very instrumental in revealing the health of the lubricant if it is done in a timely manner, and interpreted properly. Always bear in mind that used oil data are reported in concentrations; therefore, it is very important to know the oil capacity and oil consumption. Corrections to oil consumption and oil volatility loss are desirable. Used oil data are also time dependent, so the engine usage record is critical. Finally, most diagnostics are performed by correlating multiple criteria in the same sample. For example, TBN depletion is always accompanied by Pb increase in the oil (bearing corrosion). Otherwise, simply because TBN is below a certain number does not mean there is pending danger. Condemning limits by themselves, as often published by oil laboratories, are insufficient to point to problems, except for the most severe cases.
33.8.4 Filtration: Air System The intake air filter is the first line of defense in preventing external particulate contamination from entering the engine. The air system is an open one; that is, the quality of the intake air depends on the operating environment. Vehicles traveling on paved roads generally experience much cleaner air than off-highway construction and mining equipment; therefore, the latter applications place heavier demands
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TABLE 33.11
Oil Analysis Items and Their Usage
Category
Measured Property
Additive elements Wear elements
Ca, Mg, P, Zn, Mo Fe Cr Pb, Cu Al, Si Na, K Soot Total base number Kinematic viscosity
Contamination elements
Alkalinity Flow property
Unit ppm ppm
ppm % mg KOH per g oil cSt
Usage Identify oil source or type for misapplications Gear/valve train and liner wear Ring wear Bearing/bushing wear, cooler corrosion Dirt injection Coolant leak Soot accumulation Indicate ability to neutralize acid Detect shear thinning and fuel dilution (decrease), or oxidation (increase)
on the air filter. These applications most commonly use a primary air filter and a secondary or “safety” filter in case of failure of the first. The need for this level of protection is necessary because engine wear tests in the past have shown that only several grams of dust can destroy a heavy-duty engine. The principal contaminant removed by the air filter is silica dust, which can be very abrasive if circulating in the lubricating oil. Other possible contaminants encountered include moisture and road salt. Most common air filters are pleated elements constructed with a cellulose-based filter medium. There are several mechanisms for capturing the contaminant (Jaroszczyk et al., 1993). While it might be commonly thought that the filter medium merely acts as a screen to capture the dust, there is considerable evidence that powerful electrostatic charges, due to the air flow through the filter medium, attract and capture dust particles to individual fibers. The degree of electrostatic attraction depends on the humidity of the intake air. The drier the air, the greater the charge buildup, and the greater the filter efficiency. This important capture mechanism accounts for the very high levels of efficiency for typical air filters (>99%), at the same time maintaining a low restriction to air flow. In the initial stages, the dust particles coat the fibers, building up a layer. As the amount of contaminant captured increases with time, a continuous cake forms on the surface of the filter medium and the restriction to flow increases to the point that the filter needs to be replaced. Some filters contain a mechanical valve that activates a “flag” when the restriction reaches a predetermined limit and before serious loss of engine performance is experienced.
33.8.5 Filtration: Lubricating System In contrast to the air system, the lubricating system is relatively closed; that is, the fluid is controlled and the system is not frequently open to the outside environment. There are two common approaches to filtration in the lubricating system: single or two-stage filtration. For a single-stage or full-flow filter, all of the lubricating oil is continuously pumped through the filter. The disadvantage of this approach is that if a high level of efficiency is desired, the filter can reach a high flow restriction very rapidly, leading to short filter life. There are a variety of two-stage filter systems in current use, but the general approach is to use a relatively open, full-flow section while a portion of the flow (usually about 5 to 10%) is shunted or bypassed into a very high-efficiency second stage. This system produces high efficiency with longer life. Most full-flow filter elements are of pleated construction and the filter media include cellulose, glass, and polymeric materials. In some cases, blends and layers of different materials are used to produce a gradient density medium. The design of a lubricating filtration system is a trade-off between efficiency and capacity or life, and the use of different filtration materials can help control that balance. The second stage, or bypass section, can be a surface-type medium such as a higher efficiency fullflow type material in a pleated configuration or a depth medium constructed of stacked disks or packed fibers. Cellulose is the most common and effective second-stage material due to its affinity for the organic contaminants. Centrifuges are sometimes used as permanent, cleanable second-stage filters because of their high capacity.
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The most commonly encountered contaminants in the lubricating system are much more complex than in the air system. Analysis of contaminants extracted from used filters shows that at least 90% of the total contaminants are organic in nature. These are soot, sludge, tars, resins, and oxidation products. The inorganic portion includes spent additives, wear metals, neutralization products, and external dust. The organic material, if not removed, would increase the oil viscosity to the point where lubricity would be degraded. This material tends to coat the fibers of the filter, increasing the apparent fiber diameter and gradually reducing the pore size and increasing the restriction to flow (Stehouwer, 1996; Truhan and Stehouwer, 1998). When two-stage filtration is employed, the second stage collects the bulk of the contaminant, allowing the full-flow section to continue filtering. When longer service intervals are desired, such as for on-highway applications, extended filter life can be achieved by increasing the capacity of the second stage. Filter performance is closely related to oil quality, with better quality oils reducing wear for a given filter efficiency and longer filter life by keeping the organic contaminants dispersed.
33.8.6 Filtration: Fuel System The fuel system, like air, is an open system but with better control over the fluid quality. The fuel system, however, is still vulnerable to loads of fuel with biocontamination and water, which can foul injectors and create corrosive by-products. Because diesel fuel has poorer inherent lubricity compared to lubricating oil and tolerances in the fuel hardware are very close, fuel cleanliness is proportionately more important. Fuel filter elements are constructed similar to oil filters in that they are of a pleated configuration. They can be housed in a spin-on can or in a permanent housing that includes other features such as clear bowls and fuel heaters. Both spin-on and permanent housings may have drain valves to allow the removal of water separated by the filter medium. The filters can be mounted on either side of the fuel pump, depending on the engine design; and, in some cases, a lower efficiency primary filter is used to protect the pump and a higher efficiency secondary filter is used to protect the fuel injectors. As with lubricating oil filters, filter media include cellulose, glass, and polymeric fibers. The types of contaminants that fuel filters remove are similar to lubricating oil filters; that is, they are primarily organic, with a small inorganic component of wear metals, precipitates, and external dust (Martin, 1998). Because only a portion of the fuel is burned at a time, the remainder of the fuel flow is recirculated in the system to provide cooling. This recirculated fuel increases in temperature and can, with an unstable fuel, produce partial oxidation products called asphaltenes. This organic material will plug a fuel filter just as a lubricating oil filter, limiting its life. As mentioned previously, organisms growing in poorly stored fuel can cause occasional problems by prematurely plugging a filter. Because most injector systems operate at high pressure, most engine manufacturers require the use of a fuel/water separator, particularly for electronically controlled engines. Fuel/water separation is accomplished using a filter medium to which the fuel will wet and water will not. The water falls to the bottom of the filter by virtue of its higher density, where it can be collected and drained. Cellulose requires a coating to achieve this separation; however, this coating will degrade with use and the buildup of organic material. Polymeric fibers have the inherent ability to reject water and do not require additional surface treatments. Consequently, they are more durable for longer service operations.
33.8.7 Filtration: Cooling System Although not universally employed on diesel engines, coolant filtration is beneficial nonetheless (Hudgens and Hercamp, 1988). The cooling system is a partially closed system because the additional external plumbing, hoses, and clamps make it prone to leakage. Consequently, the system must be opened periodically for inspection and refilling if necessary, making it vulnerable to outside contamination. Internally, particulates can result from corrosion, scaling, or precipitation if the coolant is of poor quality. These particulates can cause erosion in pumps and internal passages. Lubricating oil can contaminate the coolant if internal seals fail and this oil can coat heat-rejecting surfaces, impeding heat transfer. Although cellulose is the most commonly used filter material, polypropylene has an affinity for oil, and
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filter fibers made from it will effectively remove oil if the quantities are not large. Coolant filters often have the additional job of adding supplemental additives to the coolant, which help prevent corrosion and scaling, keeping internal particulate formation under control.
33.9 Future Trends Future advanced diesel engine designs will require substantial improvements in the areas of emissions control, performance, and fuel economy. One effect of these requirements will be to place much greater stress on tribological systems in the engine through higher loads and temperatures with more marginal lubrication. Also, the use of exhaust gas recirculation will require improved wear and corrosion resistance, particularly for power cylinder components. These requirements, plus customer expectations of improved durability and reliability, dictate improvements in wear and friction performance of several key engine components and subsystems. Several future trends in engine design will impact valve system durability: 1. Higher cylinder pressures will lead to increased valve/seat contact pressures and tangential stresses and greater valve/seat deflection, resulting in increased wear. 2. Increasing power density will cause higher temperatures and pressures, resulting in increased thermal and mechanical distortion of the seats. 3. Reduced particulate emissions will require the use of tighter valve stem seals, which will reduce lubrication to the stem/guide and valve/seat interfaces. 4. The use of exhaust gas recirculation will potentially result in intake stem/guide corrosion due to condensation of sulfuric/nitric acids. The outcome of these changes will probably include: a. Reduction in seat angles for improved valve/seat wear b. Development of exhaust valve materials with improved high-temperature fatigue properties 5. Increased use of powder metal guide materials for wear and scuff resistance. 6. The use of improved seat insert materials for wear resistance and temperature capability. Future trends affecting bearing requirements include: 1. Increased unit loads (peak oil film pressure, POFP) due to higher cylinder pressure, packaging constraints, and lower oil viscosity, which will increase fatigue and wear 2. Greater flexibility of housings 3. Greater precision/reduced tolerancing for maximum bearing area 4. Greater emphasis on longevity and life prediction 5. Modeling capabilities for analysis of bearing features/structures 6. Increased bearing back temperatures due to higher unit loads and higher oil temperature, which will increase fatigue, wear, and corrosion 7. Reduced oil viscosity for improved fuel economy, which will reduce film thicknesses and increase wear 8. Environmental concerns over lead (Pb) in used oil and in manufacturing processes These trends will require further advances in bearing materials/processing technologies and will probably occur at the expense of conformability/embeddability, which will entail further improvements in dimensional tolerances and manufacturing cleanliness for bearing systems.
Acknowledgments The authors would like to thank Dr. J.J. Truhan, Dr. D.M. Stehouwer, Dr. D.E. Richardson, and Mr. M.A. Luehrmann for their contributions of materials and constructive comments; and Cummins Inc. for permission to write this chapter.
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References ASTM D5967-97 (1997), Standard Test Method for Evaluation of Diesel Engine Oils in T-8 Diesel Engine, ASTM Standards. Booser, E.R. (1992), CRC Handbook of Lubrication, 8th ed., CRC Press, Boca Raton, FL. Bovington, C. and Caprotti, R. (1993), Latest diesel fuel additive technology development, 4th Int. Symp. Perf. Eval. Auto. Fuels and Lubr., CEC/93/EF13, Birmingham, U.K., May. Cusano, C.M. and Wang, J.C. (1995), Corrosion of copper and lead containing materials by diesel lubricants, Lubr. Engr., 51(1), 89-95. Challen, B. and Baranescu, R. (1999), Diesel Engine Reference Book, 2nd ed., Society of Automotive Engineers, Warrendale, PA. Dennis, A.J., Garner, C.P., and Taylor, D.H.C. (1999), The Effect of EGR on Diesel Engine Wear, SP-1427, 45-57, Society of Automotive Engineers, Warrendale, PA. Glassey, S.F., Stockner, A.R., and Flinn, M.A. (1993), HEUI — A New Direction for Diesel Engine Fuel Systems, SAE Tech. Paper No. 930270. Hudgens, R.D. and Hercamp, R.D. (1988), Filtration of Coolants for Heavy Duty Engines, SAE Tech. Paper No. 881270. Jaroszczyk, T., Wake, J., and Conner, M. (1993), Factors affecting the performance of engine air filters, J. Eng. Gas Turbines and Power, 115, 693-699. Kim, C., Passut, C., and Zang, D.M. (1992), Relationships among Oil Composition Combustion-Generated Soot, and Diesel Engine Valve Train Wear, SAE Tech. Paper No. 922199. Kitamura, K., Takebayashi, H., Ikeda, M., and Percoulis, H.M. (1997), Development of Ceramic Cam Roller Followers for Engine Application, SAE Tech. Paper No. 972774. Kodali, P., Truhan, J. J., Richardson, D. E. (1999), 3rd Int. Conf. Filtration, Southwest Research Institute. Korte, V., Barth., R., Kirschner, R., and Schulze, J. (1997), Camshaft/Follower-Design for Different Stress Behavior in Heavy Duty Diesel Engines, SAE Tech. Paper No. 972776. Kuo, C.C., Passut, C.A., and Jao, T.C. (1998), Wear Mechanism in Cummins M-11 High Soot Diesel Test Engines, SAE Tech. Paper No. 981372, Sp. Pub. No. 1368. Lacey, P.I. (1994), Development of a lubricity test based on the transition from boundary lubrication to severe adhesive wear in fuel, Lubr. Eng., 50(10), 749-757. Martin, H. (1998), A comparison of the chemical and physical characteristics of field returned fuel filter plugging contaminants vs. a laboratory generated fuel filter plugging contaminant, Proc. 2nd Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 203-211. McGeehan, J.A., and Kulkarni, A.V. (1987), Mechanism of Wear Control by the Lubricant in Diesel Engines, SAE 872029, Society of Automotive Engineers, Warrendale, PA. Miba Gleitlager AG, Technical Information, Laakirchen, Austria. Owen, K. and Coley, T. (1995), Automotive Fuels Reference Book, 2nd ed., Society of Automotive Engineers, Warrendale, PA. Rastegar, F. and Craft, A.E. (1993), Piston ring coatings for high-horse power diesel engines, Surf. Coat. Technol., 61, 36-42. Rastegar, F., Graham, M., and Chang, P. (1997), Scuff Resistance Rig test for Piston Ring Face Coatings, SAE 970819, Society of Automotive Engineers, Warrendale, PA. Richardson, D.E. (1999), Review of Power Cylinder Friction for Diesel Engines, ASME, ICE-Vol. 32-3, Paper No.99-ICE-196. Rodriques, H. (1997), Sintered valve seat inserts and valve guides: features affecting design, performance and machinability, Proc. Int. Symp. Valvetrain Sys. Des. Mater., Dearborn MI, April 14-15, 129-139. Schaefer, S.K., Larson, J.M., Jenkins, L.F., and Wang, Y. (1997) Evaluation of heavy duty engine valvesmaterial and design, Proc. Int. Symp. Valvetrain Sys. Des. Mater., Dearborn MI, April 14-15. Shen, Q. (1987), Development of Material Surface Engineering to Reduce the Friction and Wear of the Piston Ring, SAE 970821, Society of Automotive Engineers, Warrendale, PA.
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Shurvell, H.F., Clague, A.D.H., and Southby, M.C. (1997), Method for determination of the combustion of diesel engine deposits by infrared spectroscopy, Appl. Spectrosc., 61(6), 827-835. Shuster, M., Mahler, F., Crysler, D. (1999), Metallurgical and metrological examination of the cylinder liner-piston ring surfaces after heavy duty diesel engine testing, Tribol. Trans., 42(1), 116-125. Stehouwer, D.M. (1996), The effects of extended service intervals on filters in diesel engines, Proc. 1st Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 211-214. Truhan, J.J., Covington, C.B., and Wood, L.M. (1995), The Classification of Lubricating Oil Contaminants and their Effect on Wear in Diesel Engines as Measured by Surface Layer Activation, SAE 952558, Society of Automotive Engineers, Warrendale, PA. Truhan, J.J. and Stehouwer, D.M. (1998), Engine measured filter performance, Proc. 2nd Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 152-157. Wang, J.C. and Cusano, C.M. (1995), Predicting Lubricity of Low Sulfur Diesel Fuel, SAE Tech. Paper No. 952564. Waterhouse, R.B. (1992), Fretting wear, ASM Handbook, 18, 242-256, ASM. Wei, D. and Spikes, H.A. (1986), The lubricity of diesel fuels, Wear, 111, 217-235. Weiss, E.K., Busenthuer, B.B., Hardenberg, H.O. (1987), Diesel Fuel Sulfur and Cylinder Liner Wear of a Heavy-duty Diesel Engine,” SAE 872148, Society of Automotive Engineers, Warrendale, PA.
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34 Tribology of Rail Transport 34.1
Introduction ................................................................... 1271 Historical Background • Wheel/Rail Interface and Axle Loads • Axle Load Increases
34.2
Wheel/Rail Contact........................................................ 1275 Wheel/Rail Materials • Forces at the Contact Patch • Adhesion • Repeated Contact — Plasticity, Shakedown, and Ratcheting • Consequences of Rail/Wheel Contact: Wear • Consequences of Rail/Wheel Contact: Rolling Contact Fatigue • Interaction of Wear and RCF • Grinding • Rail Corrugation
34.3
Generation of Mechanical Power • Tribological Issues in the Design of Diesel Engines • Supply of Combustion Air • Transmissions and Drives • Gas Turbines
Ajay Kapoor The University of Sheffield
34.4
The University of Sheffield
34.5
Axle Bearings, Dampers, and Traction Motor Bearings .......................................................................... 1321
34.6
New Developments and Recent Advances in the Study of Rolling Contact Fatigue.................................. 1324
The University of Sheffield
K.J. Sawley
Axle Bearings • Dampers for Suspension Systems
Transportation Technology Centre
Friction Modifiers • Wheelset Steering and Individually Driven and Controlled Wheels • Integrated Study of Rolling Contact Fatigue
M. Ishida Railway Technical Research Institute
Current Collection Interfaces of Trains........................ 1314 Earth Brushes • Current Collection Shoe and Gear • Pantographs • Registration Arms
David I. Fletcher F. Schmid
Diesel Power for Traction Purposes ............................. 1308
34.7
Conclusion...................................................................... 1325
34.1 Introduction For effective and economical railway operation, important tribological issues must be addressed at the wheel/rail interface, within the engines of locomotives and, for electric trains, at the current collection point (Figure 34.1). In this chapter, the authors present the background to these issues and follow this with a brief discussion of some recent developments in wheel/rail tribology and related research. Important tribological issues also affect other systems involved in rail transport, and some of these aspects are discussed toward the end of this chapter.
34.1.1 Historical Background Long before railway transport developed into the effective and complex system as generally understood today, rails were used to guide horse-drawn vehicles (Wickens, 1998) and by 1767 iron rails had been 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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FIGURE 34.1
Modern Tribology Handbook
Tuen Mun light rapid transit system (Courtesy of Tuen Mun, Hong Kong New Territories).
introduced (Snell, 1973). At the start of the 19th century, mechanically powered rail transport had started to develop, initially by modification and transfer onto wheels of stationary steam engines, which had by that time become commonplace. Engine design was initially derived from that of stationary steam engines, with the driving cylinders placed inside the boiler (Figure 34.2). However, over time, the designs evolved to satisfy more completely the requirements of a railway engine (Russell, 1998). Over a similar time period, passenger vehicle design also evolved, having initially been based almost entirely on stagecoach design (Russell, 1998). By the mid-1800s, the general form of rail and wheel had developed into something very similar to those in use today (Figure 34.3) but it was late in the 19th century when Hertz (1896) developed the first scientific description of the wheel/rail contact. Hertz developed an analysis method to describe the elastic contact of glass lenses but, following its publication, it was found that it could also be used to describe contacts within rolling element bearings, between gear teeth, and between rails and wheels (Johnson, 1985). Hertzian contacts between three-dimensionally curved bodies have an elliptical form, and pressure within this contact region varies with an elliptical distribution (Figure 34.4). The distribution is described by Equation 34.1, in which p0 is the maximum pressure within the contact, a and b are the semi-axes of the contact patch, and x and y are coordinates with their origin in the plane of the contact and at its center.
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Trevithick(1804-1805) Hackworth (1827)
Blenkinsop (1812) Stephenson (1815-1825)
Hedley (1813)
Stephenson (1828)
Stephenson (1830 on)
FIGURE 34.2 Evolution of boiler position on early steam trains. (From Russell, C.A. (1998), The developing relations between science, technology and the railways, Proc. Instn. Mech. Engs., 212(F), 201-208. With permission.)
FIGURE 34.3
The steel wheel rolling on a steel rail is the basis of almost all railway systems.
x 2 y2 p = p0 1 − 2 − 2 b a
12
(34.1)
With some additions, the theory is still in use today, and it forms the basis of much current work on the contact mechanics of rail and wheel.
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FIGURE 34.4
Modern Tribology Handbook
Elliptical, Hertzian contact patch.
34.1.2 Wheel/Rail Interface and Axle Loads Since the adoption of steel rather than iron as the material of choice for rails, the wheel/rail system has remained virtually unchanged. However, this does not imply that the system is ideal. The wheel/rail contact area is typically the size of a small coin and, commonly, eight such contacts (i.e., eight wheels) support a vehicle weighing from 30 t (lightweight passenger coach) to 140 t and more (heavy freight). The material in and around the contact area is therefore highly stressed. High rates of wear might be expected for such a contact but, in addition, because the load is applied and removed many times during the passage of each train, there is the possibility of fatigue of the rail surface. Further details of these loads and their effects on steel rails and wheels are discussed below. The ideal material, which does not wear or suffer fatigue and yet is economically viable as a rail or wheel material, has not yet been found. The axle-load examples given refer to the static loads applied in the contact patch area when a train is stationary. Dynamic loads (e.g., at rail-joints or in turnouts [points]) are much higher, with vertical accelerations reaching values of 100 g (1000 m/s2). This is a consequence of the high stiffness of the wheel/rail interface. Well-designed primary suspensions are essential to minimize the impact of these loads on track life and wheel life. Heavy freight trains are generally limited to 60 to 90 km/hr, the top speed being determined by gradients, aerodynamic considerations, and the capability of rolling stock. On high-speed passenger routes such as the French LGV (ligne grande vitesse or high-speed line), axle loads are limited to 15 t, a constraint necessary because of the much higher dynamic forces at 300 km/hr.
34.1.3 Axle Load Increases The requirement for efficiency dictates the use of ever-greater axle loads. In Europe, axle loads of freight vehicles were limited for many years to 18 t, but have now been standardized to 22.5 t by UIC.* In America, 30 t has been common for many years and moves are afoot in Sweden to increase the axleloads on the iron ore railway from Kiruna to Narvik from 25 t to 30 t. Also, on standard gauge, BHP Iron Ore (formerly Mount Newman Mining) in the Pilbara region of Australia, operates ore trains of 36,000 t, formed of 240 wagons with an axle load of 37.5 t. These are powered by two diesel locomotives *Union Internationale des Chemins de Fer, the international standard-setting body for the railways based in Paris, France.
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at the front and two at the rear, with a combined rating of 13,000 kW. Queensland Railways in Australia operates trains of similar size over hundreds of kilometers in their coal corridors, albeit on 1067-mm gauge track.
34.2 Wheel/Rail Contact Steel wheels rolling on steel rails is the principal characteristic that distinguishes railways from other forms of transport (Figure 34.3). Wheel and rail meet at a contact patch that is small (typically about 100 mm2) and carries the full wheel load through which all steering, traction, and braking forces are transmitted. This contact patch sees a severe working environment. Stresses normal to the plane of contact can reach values several times the wheel or rail tensile strength, and sometimes shear stresses in the plane of contact can exceed the shear yield stress. Rapid temperature rises, caused by relative slip between the wheel and rail, can reach several hundred degrees Celsius in routine operation, and over 1000°C in extreme circumstances. These stress and temperature conditions inevitably lead to wear, deformation, and damage to the wheels and rails; and a major goal of railroads is to arrange service conditions and maintenance procedures to minimize deterioration and hence extend component life. This is important because rails — and to a lesser extent wheels — constitute a large part of a railroad’s asset base. For example, there are about 1.4 million freight vehicles and some 25,000 locomotives in service in North America, which give a total population of about 13 million wheels. North American railroads also own over 170,000 miles of track, which equates to about 35 million tons of steel rail. Railways have more money invested in rail than in any other asset, excepting land and perhaps bridges. Extending the life of these components, and especially that of the rail, has a major impact on railroad profitability. An understanding of the tribology of the wheel/rail system is essential if wheel/rail life is to be extended. This system is complex, and its behavior depends on interactions between the materials (wheel, rail, and any third body introduced, such as lubricant/debris mixtures) and the stress-temperature environment (among other things, a function of vehicle weight, vehicle/track interaction, wheel/rail profiles, wheel/rail adhesion, and speed).
34.2.1 Wheel/Rail Materials The resistance of a train to rolling has several components, including grade and acceleration resistance, aerodynamic and wind drag, bearing resistance, and wheel/rail contact resistance. Only this last resistance is influenced by the choice of wheel and rail materials. Several factors contribute to wheel/rail contact resistance (Castelli, 1996). First, during rolling, the wheel and rail surfaces are elastically deflected such that relative motion can occur. Second, energy can be dissipated by plastic deformation. Third, surface adhesion phenomena can dissipate energy. To a first approximation, contact resistance is proportional to the length of the contact patch and, hence, resistance is minimized if, for a given geometry, the contact area is kept small by choosing materials with a high elastic modulus. Of the common and inexpensive metals, steel has one of the highest values of elastic modulus. For this reason — and because steel is relatively inexpensive and offers a very attractive combination of strength, ductility, and wear resistance — almost all wheels and rails worldwide are made from plain carbon-manganese pearlitic steel, which has a lamellar structure of iron and iron carbide. Table 34.1 illustrates typical wheel and rail chemistries and hardness values. In general, passenger vehicle wheels tend to have lower carbon content and hardness than heavy axle load freight vehicles. Steel of about 300 Brinell hardness is typically used for rail in straight track, while rail in the hardness range 340 to 390 Brinell tends to be used for curved track where the stress environment is more severe. Although numerous studies have examined the use of higher hardness materials, such as bainitic and martensitic steels, for wheel and rail materials (Clayton and Devanathan, 1992; De Boer et al., 1995; Hårkonen, 1985), few materials can compete on wear resistance with pearlitic steel, first used for wheels and rails last century.
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TABLE 34.1 and Rails
Typical Chemistries and Hardnesses of Freight and Passenger Wheels
Rails Passenger wheels Freight wheels
Standard Hardened Standard Hardened Standard Hardened
C (wt%)
Mn (wt%)
S (wt%)
P (wt%)
Hardness (Brinell)
0.75 0.75 0.50 0.55 0.62 0.72
0.90 0.90 0.80 0.80 0.72 0.72
0.02 0.02 0.04 max 0.04 max 0.05 max 0.05 max
0.02 0.02 0.04 max 0.04 max 0.05 max 0.05 max
290 370 260 270 300 340
34.2.2 Forces at the Contact Patch Within the wheel/rail contact patch, a force exists normal to the plane of the contact, mainly due to the load (weight) of the wheel on the rail. In addition, tractions are produced in the plane of contact by the vehicle steering forces (see below). This force system produces complex hydrostatic and shear stresses in the rail and wheel (Johnson, 1985). Of most interest is the compressive contact stress normal to the plane of contact, which has a generally elliptical distribution and affects both wheel/rail wear and rolling contact fatigue (see Section 34.2.6). The maximum value of the contact stress p0, occurs at the center of the ellipse, and is given by (Johnson, 1985):
6 PE *2 p0 = 3 2 π Re
13
[F (R′ R′′)]
−2 3
(34.2)
where P is the normal load, E * depends on the wheel and rail elastic moduli, F(R′/R″) is a function of the wheel and rail radii of curvature, and Re is the equivalent relative curvature of the wheel/rail system, defined as Re = (R′R″)1/2. Although studies of vehicles with independently rotating wheels have been made (Elkins, 1988), the solid axle with fixed coned (or nearly coned) wheels operating on inclined rails is used almost exclusively on main line railway vehicles worldwide (Figure 34.5). With this arrangement, each wheelset (axle plus two wheels) is effectively self-steering through the action of forces produced in the contact patches.
Left
R RL
Right
R RR
FIGURE 34.5 Self-steering is provided by the use of fixed coned wheels on solid axles. In this example, when the wheelset is offset to the left, the left wheel effective rolling radius increases (to RL), and the right wheel radius decreases (to RR), enabling the wheelset to steer back to a central position. The angles of the rails and the wheel shapes are exaggerated for clarity.
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Computer models are available to predict the steering forces, which depend on vehicle and track characteristics as well as the detailed wheel and rail profile shapes (Wilson et al., 1995). However, the theory behind the models is complex and cannot be described here. An understanding of how these contact patch forces arise can be gained by considering the difference in rolling radius between the left and right wheels of Figure 34.5. With the wheelset centered on straight track, if the left and right wheel rolling radii are equal (R), the wheelset can roll normally. However, if the wheelset is shifted laterally to the left, the left wheel rolling radius increases to RL while the right wheel radius decreases to RR . Because the two wheels must rotate at the same angular velocity, this difference in rolling radius produces longitudinal micro-slip (termed creep) between the wheels and rails which, in turn, leads to a longitudinal force on each wheel to steer the wheelset back to the center of the track. In a similar manner, lateral forces are produced on each wheel if the wheelset runs at an angle to the track. Equal and opposite forces are produced on the rails. Creep is a natural consequence of having fixed wheels on a solid axle, and is defined with respect to the forward and lateral wheel and rail velocities:
V F − VWF Longitudinal creep s x = 2 RF F VR + VW
(34.3)
V L −V L W Lateral creep s y = 2 RF F VR + VW
(34.4)
( )
( )
where V refers to velocity; subscripts R and W refer to the wheel and rail, respectively; and superscripts F and L refer to the forward and lateral directions. There is a further type of creep, known as spin creep, that is caused by a relative rotation of the wheel and rail around an axis normal to the plane of contact. This type of creep (Equation 34.5) is also implicated in wheel and rail damage.
Ω − ΩW Spin creep ω z = 2 RF F VR + VW
( )
(34.5)
In general, a wheelset will always be moving laterally with respect to the rail (producing lateral creep at each contact patch), and each wheel will not be moving at the forward speed of the vehicle (thereby producing longitudinal creep at each contact patch). All three types of creep will usually be present, although one may dominate. While total creep can increase continually, the steering forces are limited by the available adhesion between the wheels and rails, and this is discussed in detail in Section 34.2.3. Thus, the steering force on a wheel saturates at a value equal to the wheel load times the adhesion coefficient. This saturation occurs at a resultant creep of about 0.01. Relationships between these three types of creep and the resultant forces and moments have been derived by Kalker (1979). The steering forces caused by creep lead to surface and near-surface shear stresses that produce deformation in the contact patch. This deformation increases rolling resistance, and, more importantly, contributes to increased wear and rolling contact fatigue.
34.2.3 Adhesion In railway systems, the force acting at the wheel/rail contact, in the direction of the vehicle’s velocity, is called traction force or brake force. Variation of the traction coefficient, defined as traction force divided by vertical (normal) load, with slip (creep) ratio is shown in Figure 34.6 (Tevaarwerk, 1982). The results shown in this figure are based on work of Johnson and co-workers (Johnson and Roberts, 1974; Johnson and Tevaarwerk, 1977; Johnson and Cameron, 1967) and Tevaarwerk (1982), who have summarized the
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TRACTION COEFFICIENT FX/FZ
Modern Tribology Handbook
REGION-C REGION-B REGION-A
THERMAL
NONLINEAR
LINEAR
SLIDE ROLL RATIO DU/U
FIGURE 34.6 Typical traction/slip curve. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
general characteristics of the traction curve. There are three regions identified on the curve and the behavior in each of these regions can best be described by the Deborah (De) number. This number is the ratio of the relaxation time, for a simple Maxwell viscoelastic model, to the mean transit time. 1. The linear low slip region, thought to be isothermal in nature, is caused by the shearing of a linear viscous fluid (low De) or linear elastic solid (high De); see Johnson and Cameron (1967). 2. The nonlinear region is still isothermal in nature but now the viscous element responds nonlinearly. For low De, this portion of the traction curve can be described by a suitable nonlinear viscous function alone. For high De, a linear elastic element interacts with the nonlinear viscous element, as reported by Johnson and Tevaarwerk (1977). 3. At yet higher values of slip, the traction decreases with increasing slip and it is no longer possible to ignore the dissipative shearing and the heat that it generates in the film. Johnson and Cameron (1967) showed that the shear plane hypothesis advanced by Smith (1965) accounted for most of their experimental observations in this region. More recently, Conry et al. (1979) have shown that a nonlinear viscous element, together with a simple thermal correction, can also describe this region. In railways, the maximum traction coefficient is commonly called the adhesion coefficient. The adhesion coefficient is primarily used to estimate the brake performance of a vehicle and, accordingly, the phenomenon of adhesion between steel wheels and steel rails is a very important tribological issue for improving the performance of the railway as a transportation system. 34.2.3.1 Characteristics of Adhesion and Traction Coefficients under Dry Conditions Ohyama (1987) has shown the relationship between Hertzian pressure and adhesion coefficient to be a function of surface roughness (Figure 34.7). The data vary widely but the tendency of the adhesion coefficient to decrease with increasing Hertzian pressure can be estimated. Generally, under dry conditions, the friction coefficient does not depend on loading force (this is Amontons-Coulomb’s law). However, from results of experiments with carbon steels, Shaw (1960) concluded that, while AmontonsCoulomb’s law covers the case of light loading, at high loading the friction coefficient decreases. Also, a report of the Office for Research and Experiments (ORE, now known as the European Railway Research Institute, ERRI, 1978) described how adhesion coefficients decreased when axle loads increased; however, the influence of surface roughness on the adhesion coefficient, under dry conditions, was not so significant. Krause and Poll (1982) demonstrated a relationship between the initial gradients of dsx /dfx (where sx is the longitudinal creepage and fx is the longitudinal traction coefficient), the mean roughness Rz , and a parameter Rp /Rz (the ratio of the maximum smoothing depth to the mean roughness, Figure 34.8).
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0.4
f max
0.3
0.2 320- #320 240- #240 #320- #180 #
V= 200 km/h
#
0.1
0 0
100
200
300
400
500
600
700
Pmax
MPa
800
900
FIGURE 34.7 Relationship between adhesion and maximum Hertzian pressure. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
0.48
6.10-3
0.27
0.39
0.20
0.23
0.18 4.10-3
Rp Rz
dsx
= 0.33
0.12
dfx 2.10-3
0
6
12
18 R
z
24
30
36
[µm]
FIGURE 34.8 Dependency of the initial gradients of dsx/dfx on the mean roughness Rz, parameter Rp/Rz, test rig I (type Bugarcic). (From Krause, H. and Poll, G. (1982), The influence of real material and system properties on the traction/creep relationships in rolling contact, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 353-372. With permission.)
With greater values of Rz , there is a tendency for a particular value of friction force at higher creepage. This is in agreement with Ohyama (1987). 34.2.3.2 Adhesion and/or Traction Coefficients with Water Lubrication Experimental measurements of the adhesion coefficient for the Shinkansen lines (the Japanese bullet train) with water lubrication are shown in Figure 34.9 (Ohyama, 1991). The measured values are very scattered, some of them smaller than the values used for vehicle component design. Because the railway system is open to the atmosphere, there are a variety of factors that might account for this scatter. These include temperature variation and the source of the water (i.e., rain, snow, and ice). Variation in the quantity of water falling on the rail during rain may also affect the results because experience shows that
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0.14 Net condition
Adhesion coefficient
f
max
Series - 200
0.12 0.10 0.08 Planned Value f
max =
13.6
V +85
0.06 0.04 0.02 0
0
20
40
60
80 100 120 140 160 180 200 220 240 260 280 Speed V (km/h)
FIGURE 34.9 Adhesion coefficient measured on Shinkansen under wet conditions. (From Ohyama, T. (1991), Tribological studies on adhesion phenomena between wheel and rail at high speeds, Wear, 144, 263-275. With permission.)
light rain is an excellent lubricant, whereas heavy rain can clean the rails sufficiently for steel-to-steel contact to develop, leading to high levels of adhesion. However, the general trend of the data indicates that the adhesion coefficient decreases as the train speed increases (up to 270 km/hr). The wide spread of these field-test measurements agrees with the laboratory-based experimental results of Ohyama and Maruyama (1982) and Krause and Poll (1982). The relationship between adhesion coefficient and rolling speed, including the effect of differing surface roughnesses and Hertzian contact pressures, was investigated by Ohyama and Maruyama (1982) (Figure 34.10). As for the field measurements discussed above, the adhesion coefficient was found to decrease appreciably with an increase in rolling speed. Surface roughness has a significant influence on the adhesion coefficient, with smoother surfaces giving lower adhesion coefficients at a given Hertzian pressure. In addition: the higher the Hertzian pressure, the larger the adhesion coefficient, based on a given surface roughness (except for the case of #80; Figure 34.10). This suggests that relatively rough surfaces do not have a large influence on the adhesion coefficient for cases of large Hertzian pressure, perhaps because asperities at the surface are heavily deformed. Ohyama (1987) examined the relationship between the mean surface roughness and the adhesion coefficient for a rolling speed of 200 km/hr and Hertzian pressures of 588 MPa and 784 MPa (Figure 34.11). The data show some variation but, by rough estimation, the adhesion coefficient increases with an increase in Rz . This means that the heights of asperities and the number of asperities may have a significant effect on the traction and/or adhesion coefficients. More recently, Ohyama has focused on EHL (elastohydrodynamic lubrication) theory, investigating Johnson’s EHL regime (Johnson, 1970) and studying the application of EHL theory to water lubrication between wheel and rail. Using EHL theory, Chen et al. (1998) have examined the effects of rolling speed and pressure on water film thickness as a function of water temperature (Figures 34.12 and 34.13). For a Hertzian pressure of 800 MPa, water film thickness increases with an increase in rolling speed and with a decrease in water temperature. For a rolling speed of 300 km/hr, water film thickness increases with a decrease in Hertzian pressure as well as with a decrease in water temperature. Indeed, the water temperature has a significant effect on the water film thickness. A comparison of adhesion coefficients obtained from field tests on revenue railway lines with the results of numerical calculation is shown in Figure 34.14. The numerical calculation, using basic EHL theory, can predict (approximately) the adhesion coefficients
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0.20
f max Maximum traction coefficient
A B C D E F
G
0.15
# 600 # 600 # 320 # 320 # 80 # 80
G DIA.
490 MPa 785 MPa 490 MPa 785 MPa 490 MPa 785 MPa 490MPa
E F
0.10
D A
B C
0.05
0
0
50
0
100 20
30
150 40
200 50
300 (km/h)
250
60
70
80 (m/s)
Rolling speed FIGURE 34.10 Relationship between maximum traction coefficient and rolling speed with varied surface roughness and Hertzian pressure under water lubrication. (From Ohyama, T. and Maruyama, H. (1982), Traction and slip at higher rolling speeds: some experiments under dry friction and water lubrication, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 395-418. With permission.) V= 200km/h
f max
0.2
0.1
: 588MPa : 784MPa
0
0
1.0
2.0
3.0
4.0
Rz
(µm)
FIGURE 34.11 Relationship between Rz and adhesion coefficient. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
for water lubrication. The mechanism by which the adhesion coefficient decreases with an increase in rolling speed can be explained as an increase of water film thickness leading to a decrease in real contact area (i.e., the number of asperities making contact and supporting load decreases). 34.2.3.3 Influence of Contaminants on the Traction and Adhesion Coefficients In practice, the wheel/rail contact is exposed to significant contamination, not just the wet conditions described above. Tevaarwerk (1982) calculated example theoretical traction curves based on the method of Johnson and co-workers. Figure 34.15 shows typical theoretical curves for a low-viscosity mineral oil.
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FIGURE 34.12 Effects of rolling speed and temperature on water film thickness. (From Chen, H., Yoshimura, A., and Ohyama, T. (1998), Numerical analysis for the influence of water film on adhesion between rail and wheel, Proc. Inst. Mech. Engs., 212 (Part J), 359-368. With permission.)
FIGURE 34.13 Effects of pressure and temperature on water film thickness. (From Chen, H., Yoshimura, A., and Ohyama, T. (1998), Numerical analysis for the influence of water film on adhesion between rail and wheel, Proc. Inst. Mech. Engs., 212 (Part J), 359-368. With permission.)
Figure 34.16 shows theoretical traction curves for the same data and oil as used in Figure 34.15, but with the addition of 3% spin. By comparison of the two figures, the effects of rolling speed and spin on the adhesion coefficient and the initial gradient of the traction curve can be seen to be significant. Through rolling experiments with various materials, Bugarcic and Lipinsky (1982) focused on the influence of the complex reaction in the physicochemical boundary layer and obtained the variation of the adhesion coefficient with respect to relative humidity. Figure 34.17 shows the variation of the adhesion coefficient in clean air with 200 ppm SO2. At higher humidity levels, titanium alloy resulted in an improved adhesion coefficient in rolling experiments with various materials. This interesting effect was a result of reactions between the metallic surface, H2O, and SO2, accompanied by hydrogen embrittlement and hardening. Ohyama (1987) examined the effect of Hertzian pressure on the adhesion coefficient, for varying creepage, using paraffin lubrication (Figure 34.18). For a rolling speed of 200 km/hr, the initial gradient of the traction curve increases with an increase of Hertzian pressure, up to 0.15% creepage. Also, Krause and Poll (1982) examined the relationship between traction coefficient and creepage for various
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FIGURE 34.14 Adhesion coefficients obtained by the field tests and numerical calculation, where the calculating conditions are: load per unit length = 4.5 MN/m, temperature of water = 15 Fi, friction coefficient of asperity contact = 0.14. (From Bugarcic, H. and Lipinsky, K. (1982), Mechanical and tribological research on two newly developed rolling friction test rigs at the Technical University of Berlin, Germany, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 445-462. With permission.)
FIGURE 34.15 Typical theoretical traction curve. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
contaminants on the running surface (Figure 34.19). The gradient dsx /dfx increases with increasing solid content of the contaminant. The solid interface media have the primary effect of a reduction in the real contact area (compared to the Hertzian area) but, depending on the rheological properties of the powders or solid contaminants, the decrease in the initial gradient of the traction curve can be significant. Ohyama (1987) summarized the effects of Hertzian pressure under dry conditions; and the effects of surface roughness, rolling speed, and contamination of the running surface, with water lubrication. The decrease in traction and/or adhesion coefficients could be explained as an effect of contact rigidity in each case. 34.2.3.4 Locomotive Adhesion Control For non-powered passenger vehicles and freight cars, traction forces between wheel and rail need be no higher than those required to ensure that the vehicles steer adequately on straight and curved track. Indeed, to reduce wear, it is generally arranged, either through lubrication or the use of improved suspension bogies, to minimize wheel/rail adhesion to a level that provides satisfactory vehicle steering.
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FIGURE 34.16 Slip ratio as a function of aspect ratio and slip/spin ratio. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
FIGURE 34.17
The variation of adhesion coefficient.
However, good adhesion performance is still required for braking purposes and compromises between low friction running and good braking performance are therefore unavoidable. The situation is different for locomotives, in that high adhesion is required for the high tractive effort, either to pull the train away from a standstill or to maintain high speeds. The maximum tractive effort a locomotive can supply is limited by the product of locomotive weight and wheel/rail adhesion. High levels of locomotive adhesion are essential on heavy-haul railroads, where locomotives are often used that consist of up to five units to haul total train weights in excess of 10,000 t. A more detailed description of modern diesel electric traction arrangements can be found in Section 34.3.3.3, which also includes a comparison between DC and AC traction.
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ρmax : 784 MPa
0.04
0.03
637 MPa 0.02 490 MPa
0.01
P 350 V : 200 km/h (55.6 m/s) 0
0
0.05
0.10
ξ
0.15 %
FIGURE 34.18 Relationship between slip ratio and traction coefficient in micro-slip region. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
60 F
R
x [N] 40
20
x
x x - 0.08
- 0.04
0.04
x
0.08
0.12
0.16
sx [%]
0.2
x
-20
FIGURE 34.19 Relationship between longitudinal friction force FRx and longitudinal creep sx for various contaminants on the running surfaces, test rig I (type Bugarcic). (From Krause, H. and Poll, G. (1982), The influence of real material and system properties on the traction/creep relationships in rolling contact, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 353-372. With permission.)
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FIGURE 34.20 The increase in maximum locomotive adhesion demand with time, and the increased adhesion produced by AC traction technology. (From Iden, M.E. (1998), The AC traction revolution: putting rail-wheel adhesion to work, presented to ARM Rail/Wheel Interface Seminar: Crosstalk 1998, Session 13, Chicago. With permission.)
34.2.3.4.1 Increased Adhesion Through Creep Control The enhanced wheel slip control offered by modern DC and AC drive locomotives can be used to increase tractive effort through better control of wheel/rail adhesion. Figure 34.20 illustrates how maximum locomotive adhesion demand (locomotive tractive effort divided by weight) has risen over the past 50 years in North America, and how it is estimated to increase in the near future. Throughout most of the 1950s and 1960s, locomotives were designed to operate at a maximum adhesion of less than 0.2, an easily satisfied demand. During the 1970s and 1980s, the required adhesion levels rose to approximately 0.3, achieved with conventional DC traction systems. A step change in the exploitation of available adhesion arrived in North America with the general introduction of high-horsepower AC traction locomotives, which are currently using adhesion in the range 0.35 to 0.40 and are likely to reach 0.45. These high values of adhesion are achieved predominantly at low speed (substantially less than 15 km/hr), by the use of what is termed “creep control.” That is, the motors are used to run the wheels at a peripheral speed up to 25% greater than the forward speed of the vehicle. This high degree of rolling/sliding motion of the wheel scrubs the wheel/rail interface, promoting steel-on-steel contact and thus high adhesion. The long-term effect of high adhesion locomotives on wheel and rail performance is not yet known, but it is likely that wear and rolling contact fatigue damage will increase. As already noted, wheel and rail wear are both related to the energy dissipated in the contact patch, which is the product of traction force and creepage. High adhesion locomotives increase both force and creepage, and hence can be expected to increase wear. A greater problem may be increased rolling contact fatigue, manifested as cracks, spalls, and shells on the rail surface (see Section 34.2.6). An increase in adhesion leads to an increase in the shear forces that produce ratcheting of the surface layers of the rail, leading to an increase in surface cracks. An additional factor is that, as shown in Figure 34.21, shakedown limits decrease with increased traction coefficient. Thus, a given level of contact stress is more damaging at high traction coefficients than at low coefficients. 34.2.3.4.2 Thermal Damage with High Adhesion Locomotives A final problem is that of thermal damage to the wheel and rail surface layers. Although wear is related to the energy dissipated in the contact patch, most of the energy is dissipated as frictional heating. Tanvir (1980), for example, has produced explicit equations describing the temperature rise in a rail as a function of, among other things, contact stress and creep, as have Knothe and Liebelt (1995). Equation 34.6 (Tanvir, 1980) predicts rail temperature rise (∆T) for the case when the wheel is moving faster than the rail:
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Ratchetting Load
Plastic shakedown limit
(a )
FIGURE 34.21
(b)
stici ty
aked Elas tic sh
Elast ic
Elastic limit
Cyc lic p la
own
Elastic shakedown limit
Deflexion
Ratchetting threshold (c)
( d)
Response of material to repeated (cyclic) loading.
2.203 p0µ aαV ∆T = ⋅ π K
12
v 1 2 ⋅ 1 + s − 1 V
(34.6)
(p0 is the maximum contact stress, µ is the maximum adhesion demanded, a is the contact semi-length, V is the forward speed of the vehicle, vS is the slip speed, K is thermal conductivity, and α is thermal diffusivity.) Assuming typical values for the thermal constants, a contact stress of 2000 MPa, a creep of 0.2 (20%), a contact semi-length of 8 mm, an adhesion of 0.4, and a forward vehicle speed of 10 mph, the maximum predicted rail temperature rise is approximately 1500°C. This is a flash temperature, and heating and cooling are very rapid, leading to non-equilibrium transformation kinetics (Archard and Rowntree, 1988). The kinetics are also affected by the high hydrostatic pressures in the contact patch. However, such high temperatures may increase the production of the hard and brittle “white phase” that is seen to form on the surface of rails and has been seen to contribute to spalls in rails. It is clear that combinations of high contact stress and high creep lead to potentially high levels of frictional heating, possibly sufficient to cause thermal transformations of the wheel and rail surfaces. It is likely, therefore, that high adhesion AC (and some DC) locomotives will cause increased wear and fatigue damage to the wheel and rail, although, in mitigation, increased rail wear and damage will occur primarily in areas where high tractive effort is applied, for example, where trains pull away from standing and on steep grades. AC locomotives also generate higher dynamic braking effort, and wear and damage will thus also increase in areas where dynamic braking is continuously employed. However, this is also mostly a low-speed phenomenon because the available levels of dynamic braking are relatively low at higher speeds. The operational advantages of high adhesion AC locomotives are such that there is likely to be continuous business demand to increase adhesion, at least for the heavy-haul freight environment. Much work needs to be done in this area, and it is the job of the tribologist to understand and quantify the likely scale of damage, and to seek ways to mitigate the damage. 34.2.3.5 Improving Adhesion for Traction and Braking Rain, snow, ice, and leaf mulch on the rails often reduce adhesion levels below acceptable limits for safe braking and reliable acceleration. Sliding during braking leads to longer brake distances and wheel-flats, while high levels of wheel-slip during acceleration can lead to localized abrasion of the rail surface with increased risk of rail breaks. Rail surfaces are therefore cleaned with mechanical scrubbers, water jets, and high-pressure air, and some railway administrations routinely apply adhesion-enhancing substances
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such as Sandite in the U.K., during the leaf-fall season. Other railroad operators rely on substantial sanding for braking and small applications of sand to enhance adhesion during acceleration. The composition of the sand must be monitored closely if it is not to cause damage to the wheel and rail surfaces. Light rail operations frequently rely on magnetic track brakes to guarantee stopping under adverse rail surface conditions. These devices are pressed against the rail surface using a permanent magnet or an electromagnet, and rely on cast iron rubbing blocks to achieve high levels of friction.
34.2.4 Repeated Contact — Plasticity, Shakedown, and Ratcheting Wheels and rails are subjected to large numbers of repeated contacts. For example, a wheel on a passenger coach can travel 200,000 miles per year, equivalent to about 100 million revolutions. Although these contacts are scattered across the width of the wheel tread, a small area on the wheel is still likely to see more than 10 million contacts per year. This repeated rolling or sliding contact stresses the material cyclically, and it responds in one of the following four ways, as illustrated in Figure 34.21: 1. Perfectly elastic behavior if the contact pressure does not exceed the elastic limit during any load cycle (Figure 34.21a). 2. Elastic shakedown, in which plastic deformation takes place during the early cycles, but, due to the development of residual stresses and sometimes strain hardening, the steady-state behavior is perfectly elastic (Figure 34.21b). This process is known as shakedown, and the contact pressure below which this is possible is referred to as the elastic shakedown limit. 3. Plastic shakedown, in which the steady state is a closed elastic-plastic loop, but with no net accumulation of plastic deformation. This behavior is sometimes referred to as cyclic plasticity (Figure 34.21c), and the corresponding limit is called the plastic shakedown limit or the ratcheting threshold. 4. Above the ratcheting threshold, the steady state consists of open elastic-plastic loops, and the material accumulates a net unidirectional strain during each cycle, a process known as ratcheting (Figure 34.21d). The rational design criterion for heavily loaded tribological contacts is the avoidance of repeated plasticity and thus, by implication, of accelerating rates of wear and surface degradation. For frictionless sliding of a two-dimensional line contact, the elastic limit is 3.14 k, k being the shear yield stress, and the shakedown limit is 4 k, as shown in Figure 34.22. The load supported is proportional to the square of the maximum contact pressure (Johnson, 1985) and, thus, the use of the shakedown limit as the operation limit would lead to a 60% improvement in allowable loading, or corresponding savings in material and cost. 34.2.4.1 Surface Engineering and Shakedown Shakedown limits are well-established for solids whose properties do not alter with depth. In both wheels and rails, however, work-hardening due to rolling contact produces hardened surface layers which, with increasing depth, soften back to the base hardness. In head-hardened rails, such hardened layers are also produced directly during manufacture to reduce wear. For wheel/rail contact, therefore, it is important to understand the shakedown behavior of layers with varying strength. Most work on the shakedown of layers with variable strength has been done on surface-engineered components, but this work is directly applicable to wheel/rail tribology. Surface engineering, now part of established industrial practice, improves tribological performance, principally by enhancing the hardness (and thus the shear yield strength k) of material at or near the load-bearing surfaces. In some cases (e.g., ion-nitrided BD2 steel), the hardness drops almost linearly from a high value at the surface to a lower value in the core, while in others (e.g., nitrided and tempered En40B), this variation is rather gentler (Child, 1980). Variations in hardness imply corresponding changes in the value of the shear yield stress k. However, diffusion treatments of this sort will not change the elastic constants E and ν. Kapoor and Williams (1994a,b) have investigated the way in which the shakedown limit depends on such variations in the shear yield strength. The model is shown in Figure 34.23,
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5 sub-surface flow
surface and sub-surface flow
load intensity po/k
4
repeated plastic flow elastic shakedown
3
surface flow elastic
2 elastic limit elastic-perfectly plastic shakedown limit
1
kinematic hardening shakedown limit
0 FIGURE 34.22
0.1
0.2
0.3
0.4
0.5
Shakedown limits for line contact.
2a Po P
q
x
shear yield stress
h
1
k1 k2
2 z
z
(a) FIGURE 34.23
(b)
Heat-treated half-space. The case depth is h. The shear yield strength varies linearly with depth.
where the shear yield strength drops linearly from a higher value at the surface to a lower value in the core, over a case depth of h. Figure 34.24 shows the results of the analysis in terms of the shakedown limit ps /k2; that is, the maximum contact pressure normalized by the shear yield stress of the core. These are plotted against the case depth, which has been non-dimensionalized by the contact semi-width (i.e., h/a), for a range of surface to core shear yield stress ratios (i.e., values of k1/k2). Data are shown for two values of the coefficient of sliding friction µ, 0.1 and 0.5, typical of boundary lubricated and dry contact conditions, respectively. When µ = 0.1, increasing the case depth from a value of zero gives no immediate increase in the shakedown limit from its value of 3.65 k2, which is appropriate for a uniform half-space carrying this surface traction. Only if the case depth h is greater than about 0.5a does the shakedown limit start to grow. Increasing
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Modern Tribology Handbook
16
µ = 0.1 µ = 0.5
12
2
4 3 4 2 3 2 1 1
8 4
0
FIGURE 34.24
( kk1 )
0
1
2
3 Case depth (h/a)
4
5
Shakedown limits for line contact on a hardened half-space.
the case depth further results in an almost linear increase in the shakedown limit: this has a maximum value set by the factor k1/k2. For example, if this is equal to 3, then the maximum value of ps /k2 is just under 10, and is achieved when the case thickness h is just over three times the semi-contact width a. Increasing the case depth beyond this critical value will result in no further improvement in the shakedown limit. The initial behavior of the data for µ = 0.1 is readily explicable if it is appreciated that at this value of traction coefficient, the maximum shear stress occurs below the surface: specifically, when µ = 0.1, the maximum occurs at a depth of 0.45a. Increasing the shear yield stress of a surface layer of thickness of less than 0.45a cannot strengthen the critically stressed material, so that there is no increase in the shakedown limit. This is true for all values of the ratio k1/k2. When µ is greater than about 0.3, however, a value where the maximum shear stress occurs at the surface, hardening even a thin layer strengthens the critically stressed material and this increases the shakedown limit. The dotted curve for µ = 0.5 in Figure 34.24 shows an improvement even when the case depth is very small. As with a uniform halfspace, the shakedown limit drops with an increase in the coefficient of sliding friction. This is clear from Figure 34.24, in which the dotted curves for µ = 0.5 are significantly below those corresponding to µ = 0.1. The shakedown limits for a material that undergoes strain hardening have also been estimated for line and elliptical contacts (Jones et al., 1996; Dyson et al., 1999, respectively) (Figure 34.25). An important finding is that the friction coefficient beyond which plastic flow occurs at the surface (where it is most damaging), rather than in the body of the steel, moves from a value of about 1/3 to about 1/2. This happens because strain hardening of the material near the surface raises the shear yield strength of the steel in this region, making it more resistant to plastic flow. The surface friction coefficient, and therefore near-surface stresses within the steel, can therefore rise to a higher level than for a non-strain hardened steel, without yield taking place. Kapoor and co-workers have also analyzed the effect of coatings (Wong and Kapoor, 1996) and coating adhesion (Kapoor and Williams, 1997) on the shakedown limit by incorporating the variations of Young’s modulus and Poisson’s ratio with depth in the analysis. This remains a current area of research. 34.2.4.2 Roughness and Shakedown Limit As well as developing surface layers whose hardness varies with depth, both wheels and rails have surfaces that are not perfectly smooth. Roughness, even at the micro-level, affects the near-surface stresses and strains that affect performance. Kapoor and Johnson (1992) analyzed the effect of repeated sliding on roughness. A soft (elastic-plastic) surface was repeatedly loaded by a sliding harder (elastic) counterface. During the initial contact, some asperities (roughness bumps) experience a contact pressure greater than the shakedown limit. They undergo plastic deformation and their height and shape change; wear also assists in this process. Based on the hypothesis that the shape and height change such that the load is supported elastically (Johnson and Shercliffe, 1992), the new asperity heights were related to the original roughness and load. The changes in a Gaussian roughness distribution are displayed in Figure 34.26.
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FIGURE 34.25 (solid line).
Shakedown limits for a line contact: perfectly plastic material (dashed line) strain hardening material
(R1C/σ) <0.1 = 1
<0.1
=1
<0.1 =1
99.9
Cumulative Probability Density
99
90
50
10
1 0.1 -2
0 (z/σ) or (y/σ)
2
Modification of asperity heights Original distribution (Gaussian) Modified distribution for R1/R2 = 2 Modified distribution for R1/R2 = 1 Modified distribution for R1/R2 = 0.5 FIGURE 34.26
Modification of Gaussian distribution of asperity heights.
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Here, σ is the rms roughness and R1 and R2 refer to the radius of curvature of asperities of the hard and soft surfaces, respectively. The value of C is given as:
p C = s E *
2
E * 2 ln 4 − 1 ps
(34.7)
where E*, the equivalent elastic modulus of the two surfaces, is given as:
(
) (
1 − υ2 1 − υ22 1 E* = + E E2 1
)
−1
(34.8)
E is the Young’s modulus, υ is the Poisson’s ratio, and subscripts 1 and 2 refer to the hard and soft surfaces, respectively. In this diagram, the un-deformed Gaussian distribution appears as a straight line. As expected, the variance in height of the deformed asperities is much reduced and the distribution is bounded. As the nominal pressure increases, the deformed distributions move to the left, showing that more asperities get plastically deformed. For a particular nominal pressure, the smaller the value of (R1C/σ), the steeper the distribution, showing formation of plateaux. This can occur because of a low value of hardness or a high value of E* or σ. Kapoor et al. (1994) estimated the load carried in the shakedown state of a hard and a soft surface in repeated sliding by conjecturing that the maximum load is carried when the softer surface has been completely flattened. The peak height distribution of the hard surface was assumed Gaussian, but limited by a critical cut-off height. The maximum load for an elastic steady state was worked out by setting the contact pressure at the tallest asperity to the shakedown limit, and summing the loads for all asperities. The shakedown limits for a surface having longish (two-dimensional) asperities are plotted in Figure 34.27, for many values of the cut-off limit h. The non-dimensional nominal pressure at shakedown is given as:
Ps =
(P p ) ( NR σ ) s
s
(34.9)
1 1
Here, Ps is the nominal pressure, ps the shakedown limit for the softer surface, N the asperity density, R1 the radius of curvature of hard asperities, and σ1 the rms roughness for the hard surface. It is a function of the plasticity index in repeated sliding, given by:
E * σ1 ψs = ps R1
(34.10)
Note that it is similar in form to the Greenwood and Williamson (1966) plasticity index, which is a measure of the fraction of contacting asperities that are plastically deformed in static first loading. The plasticity index in repeated sliding is different in two major ways. First, in the expression for ψs , the shakedown pressure replaces the indentation hardness H to account for sliding. Second, the values of radius and rms roughness are those for the hard surface and not the combined values for both the surfaces. This shows that it is the hardness of the softer surface and the roughness of the harder surface that govern the shakedown limit. An increase in the value of ψs from 1 to 10 leads to a decrease in the safe nominal pressure by many orders of magnitude. The importance of the cut-off limit (i.e., the height of the tallest hard asperity) for high values of ψs , is visible in the plots.
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Curve
A 10
(h/σ) 4.0 3.5 3.0 2.5
B
0
C REPEATED PLASTIC FLOW
P'
SHAKEDOWN (ELASTIC STEADY STATE) -5
10
10-1
100 Smooth
FIGURE 34.27
101 ψs
102 Rough
Shakedown limits for a nominally flat rough surface.
It is important to point out that this section applies to a nominally flat surface where asperities do not interact with each other. In concentrated contacts of the type obtained in rail/wheel contact and gear teeth, the asperities would interact with each other and the above results would not be expected to be quantitatively accurate. Work on shakedown of concentrated contacts, taking into account roughness and elastohydrodynamic (EHD) action, is currently under way (Morales-Espejel et al., 1999). 34.2.4.3 Rupture of Material This section is devoted to exploring how material fails if loaded repeatedly. Within the elastic limit (see Figure 34.21), the material deforms elastically and the only possibility of failure is that by high cycle fatigue. For loading above the elastic limit, but within the shakedown limit, the material encounters plastic flow in early cycles but responds purely elastically in the steady state. Plastic deformation is required only to induce residual stresses — it is generally small (equal to the elastic strain at the point of yield) and the material would again be expected to fail by high cycle fatigue. For the plastic shakedown response, a closed elastic-plastic loop, failure will be by low cycle fatigue (LCF) and the number of cycles to failure Nf is given by the Coffin-Manson law:
∆ε p n 2 Nf =C
(34.11)
where ∆εp is the plastic strain range, the exponent n is approximately 0.5, and C is a strain related to the failure strain for monotonic loading. Kapoor (1994) studied the mechanism of rupture when a metal is ratcheting (accumulating unidirectional strain). He suggests that if the cycles of plastic strain are closed (i.e., there is no net accumulation
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Normalized strain per cycle
100
LCF :
Copper ; Room temp. ; C = 0.45 ; Present experiments.
RF :
Copper ; Room temp. ; εc x 0.45 ; Present experiments. Annealed Copper ; Room temp. ; εc = 0.36 ; Benham [9] OFHC Copper ; Room temp. ; εc = 1.86 : Coffin [11] OFHC Copper ; Swaged ; Room temp., εc = 1.27 : Coffin [11] Mild Steel ; Room temp. ; εc = 0.15 ; Benham & Ford [10] SAE 1018 Steel ; Room temp. ; εc = 0.73 ; Coffin [11] AISI - 347 Stainless Steel ; Room temp. : εc= 1.25 ; Coffin [11] 2S - Aluminium ; Room temp. ; εc = 1.95 ; Coffin [11] Nickel - A ; Room temp. ; εc = 1.2 ; Coffin [11] 0 Titanium Alloy ; -268.3 C ; εc = 0.25 ; Pisarenko [13] Titanium Alloy ; -1960C ; εc = 0.26 ; Pisarenko [13] Titanium Alloy ; Room temp. ; εc = 0.35 ; Pisarenko [13]
Curve II : LCF
10-2
10-4
Curve I : RF
10-6
0
10
2
10
104
106
Number of cycles to failure
FIGURE 34.28
Rupture of materials in cyclic loading. For key to the references, see Kapoor (1994).
of strain), the material will fail by conventional low cycle fatigue. However, if the cycles of plastic strain are open, such that the material accumulates plastic deformation with each cycle, then a different type of failure, termed “ratcheting failure,” is possible. It occurs when the accumulated strain reaches a critical value, εc , which is comparable to the failure strain for monotonic loading. For a ratcheting strain per cycle of ∆εr , the number of cycles to failure, Nr , is given by:
N r = ε c ∆ε r
(34.12)
Kapoor also suggests that LCF and RF (ratcheting failure) are competitive such that whichever corresponds to earlier failure governs the life of the specimen*; that is,
(
N = Min N f , N r
)
(34.13)
where N is the actual number of cycles to failure, and Nf and Nr are given by Equations 34.11 and 34.12. respectively. A wide range of tests in the literature is revealed to follow the above hypothesis, including some of Coffin’s early experiments (Figure 34.28).
34.2.5 Consequences of Rail/Wheel Contact: Wear Wear is the principal cause of rail replacement on almost all railroads. Wear tends to be concentrated on the high rail gauge face (i.e., the inner edge of the outer rail in curved track) where contact is made with the wheel flange (Figure 34.29). In straight track and large radius curves, vertical wear of the head is seen. If the rail wears severely, the stress in the rail rises, particularly in the head and, eventually, the rail needs to be replaced. All railroads have different criteria for removing worn rail, but often these criteria imply replacement when about 30 to 50% of the head area has been lost. The situation with wheels is different, in that they can be re-profiled by machining (turning) when worn. This is undertaken either when the flange is too thin, or when tread wear has left the flange too high. Wheels are also often machined when the profile has worn to a shape that causes the wheelset to have reduced steering ability. As with rails, wheels are removed from service when metal has been lost to such an extent that stresses in the wheel are unacceptably high. *The value of N can also be estimated by letting both the LCF and ratcheting to contribute to the damage. A linear damage summation leads to Miner’s rule (i.e. (1/N) = (1/Nf ) + (1/Nr)). If either Nf or Nr is very large (infinite), then both the Miner’s rule and Equation 34.6 produce identical values of N. The maximum possible difference in N arises when Nf and Nr are equal; then, N predicted by using Miner’s equation is half that by using Equation 34.6. In view of the scatter in fatigue lives, this difference of 50% is too small to be meaningfully verified experimentally.
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FIGURE 34.29 This figure illustrates wear on the outer (high) rail in curved track. The top of the rail is worn by the wheel tread, while the gage face is worn by the wheel flange. Measurement of the cross-sectional area lost with time gives the rail wear rate.
34.2.5.1. Mechanisms Wear is a complex phenomenon, to which a number of different damage mechanisms can contribute. Four classical mechanisms that act to produce wear between two bodies can be summarized as follows (Halling, 1989): 1. Adhesion. This can occur when, either in the absence of a lubricant or contaminant film, or when such a film has been disrupted, clean metal surfaces adhere strongly to each other at contacting asperities. Relative tangential motion between the two bodies then shears these junctions, and further motion generates wear particles. 2. Abrasion. This occurs when a relatively soft surface is ploughed, either by a harder surface (as in grinding), or when loose hard particles are introduced between the two bodies. 3. Fatigue. Both adhesion and abrasion require direct contact between the surfaces of bodies in relative sliding motion. In contrast, fatigue wear can occur even when a lubricant layer separates the bodies. In this mechanism, the action of normal and shear stresses produced by a rolling/sliding contact causes cracks to initiate and propagate, leading the surface layers of the material to delaminate. 4. Fretting. This occurs when wear particles are produced as a consequence of low-amplitude vibratory motion between the two bodies. Adhesion, abrasion, and fatigue can all contribute to wear in wheels and rails but, as described earlier, ratcheting is also important (Kapoor, 1997). In this mechanism, as indicated in Section 34.2.4.2, surface stresses cause a gradual cumulative plastic deformation, producing a highly sheared surface layer (Figure 34.30). With sufficient deformation, the material can deform no longer, its ductility is exhausted, and thin wear particles are formed (Tyfour et al., 1995). 34.2.5.2 Small-Scale Wear Tests The relative extent to which these different wear mechanisms contribute to wheel and rail wear is not known. However, examination of wear results from small-scale rolling/sliding dry wear tests can be useful in the investigation of the wear process. These tests typically use a twin-disc (cylinder-on-cylinder) approach, with the discs running with different peripheral speeds to introduce longitudinal creep. The first machines for this type of test were developed in the early part of the 20th century (Amsler, 1922), but more sophisticated machines are now available (Fletcher and Beynon, 2000). Using the twin-disc approach, Bolton and Clayton (1984) found that three types of wear can occur on the head of rails: 1. Type I wear: occurs at low contact stress and creep, and is characterized by large thin wear flakes containing metallic and oxidized wear debris. There is evidence that rolled-out manganese sulfide inclusions contribute to wear, but that rail steel type does not. Wear appears independent of creep once the limiting coefficient of friction is achieved, and is proportional to distance rolled multiplied by the contact stress.
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FIGURE 34.30 Section of rail (section taken parallel to the direction of travel) revealing the plastic deformation of the steel near to the rail surface. (From Tyfour, W.R., Beynon, J.H., and Kapoor, A. (1995), The steady state wear behavior of pearlitic rail steel under dry rolling-sliding contact conditions, Wear, 180, 79-89. With permission.)
2. Type II wear: occurs at medium contact stress and creep. Wear flakes are metallic, much smaller, and less regular than those found in Type I wear, and are often compacted. Wear depends both on contact stress and creep. 3. Type III wear: occurs at high contact stress and creep above 0.1. In Type III wear, the surface is much rougher than in Types I and II, with evidence of significant plowing and tearing away of surface particles. Wear particles are very irregular in size, and larger particles can have visible score marks. Wear rates are at least an order of magnitude higher than Types I and II. These laboratory results indicate that wear progresses from Type I to Type II to Type III as contact stress and creep increase. Observations of worn rails from curved track in service indicate that Type II wear occurs predominantly from the rail top to the gauge corner, while Type III wear occurs mainly on the gauge face. The work of Bolton and Clayton (1984) also demonstrated that, for Type II wear, the wear rate (WR, in terms of metal lost per unit contact area per unit distance rolled) depends on the tangential force in the contact (T), the creep, and the area of contact (A):
WR =
Ts x A
(34.14)
Tsx is equal to the energy expended by creep, and therefore Equation 34.14 links the wear rate to the energy expended per unit contact area. More generally, for the real wheel-on-rail situation, wear is related to the energy expended in all three types of creep (longitudinal, lateral, and spin).
WR = T1s x + T2s y + M 3ω z
(34.15)
where M3 is the spin moment. This relationship between energy expended and wear under dry conditions has been corroborated by full-scale laboratory experiments. It appears to hold also for lubricated conditions (McEwen and Harvey, 1986), although the effect of different types of lubricant is complex. Use is made of the relationship by vehicle dynamics models, which use calculated values of creep, tangential force, and spin moment to
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determine the energy expended in wheel/rail contact and thus to estimate wheel and rail wear during vehicle-track simulation studies (Wilson et al., 1995). However, an exception to the relationship between energy input to the contact and the wear rate is when wear is caused by a ratcheting mechanism (Kapoor, 1997). Tyfour and Beynon (1994) found that reversing the rolling direction of the rail disc during a twindisc contact simulation significantly reduced the wear rate of the rail steel, although the rate of energy input to the disc was unaffected by the rolling direction reversal.* Principal implications for the wheel/rail system found from small-scale laboratory wear tests are: 1. In dry wear, for a given hardness value, pearlitic steels offer much better wear resistance than bainitic or martensitic steels. The reason for this is not known, but it may be related to the carbideenriched, highly sheared hard surface layer formed on pearlitic steels during wear (refer to Figure 34.30). This layer can reach twice the hardness of the bulk material (Laufer, 1986). Bainitic and martensitic steels usually have much lower carbon contents. Although they form a highly sheared surface, they do not provide the same level of carbide enrichment nor the same hardness increase as pearlitic steels. 2. For pearlitic steel, increasing the carbon content, and hence increasing the hardness and the volume fraction of lamellar carbide, reduces the wear rate. 3. Refining the lamellar spacing of pearlite, either by alloying or by the more usual head-hardening process (Bramfitt et al., 1994), increases hardness and reduces wear. This is possibly due to the relationship between carbide lamella thickness and brittleness (Langford, 1977). Above a thickness of about 0.1 micron, lamellar carbides are more likely to fracture than deform, while the reverse is true at less than about 0.01 micron thickness. Thus, pearlite refinement may inhibit carbide fracture at the wear surface and hence reduce wear. 4. For all steels, liquid or dry lubrication dramatically reduces wear. 5. Small-scale dry wear tests rank materials in order of their performance in service. Thus, small-scale (generally cylinder-on-cylinder) laboratory wear tests are useful in characterizing service wear performance. A problem, however, is that such tests rarely replicate the contact conditions found in service. For example, to duplicate the type of severe wear seen on a rail gauge face, small-scale tests are usually performed at relatively low contact stress (of the order of 1000 to 1500 MPa) and high creep (above 0.1). In contrast, calculated rail contact stresses can easily reach 3000 MPa on the gauge face, with associated creepage of about 0.01. It may be that the requirement to use such large creep values in small-scale tests is related to surface roughness of the specimens. Small-scale specimens tested at high creep rapidly develop highly deformed and rough surfaces, which will give local contact stresses significantly higher than the nominal contact stress. Thus, use of high values of creep may produce local stresses approaching those seen in rail/wheel contacts in service, which would otherwise be difficult to generate on small-scale wear testing machines. 34.2.5.3 Service Wear Tests Factors that affect the wear of wheels and rails include rail and wheel metallurgy, the fastenings used to connect the rail to the sleepers or concrete slab, the curvature of the track, the wheel and rail profiles, the type and quantity of lubricant used, and the climate. The characteristics of the vehicles passing over the rails are also important. Curving ability is improved when the wheelsets in the bogie are able to take up a radial alignment in curves. Low-speed freight bogies tend to have suspensions with low axle yaw stiffness. This allows the wheelsets to take up a radial position more easily, thereby reducing wheel and rail wear. In contrast, to give better high-speed performance, passenger bogies have high yaw stiffness, which leads to poorer curving performance and higher wear. Because of the difficulty in controlling all these parameters in service experiments, in most cases measurements of wear in service are undertaken to quantify performance and the effect of lubrication rather than to identify wear processes or mechanisms. *It has not yet been possible to confirm whether rails on bi-directionally used railway track (e.g., on single track railways) last longer than rails on uni-directionally used tracks.
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FIGURE 34.31 The effect of accumulated traffic (million gross tons) on the rail cross-section caused by wear (refer to Figure 34.29).
The usual method of characterizing wear is by measuring the amount of metal lost from the wheel or rail as a function of mileage or tonnage increases respectively (tonnage is expressed in units of million gross tonnes, MGT, an accumulated total of the loads which have passed over the rail). For wheels, measurements are focused on the flange, which wears in sharp curves (less than about 500 m radius for heavy-haul traffic), and the tread (which tends to wear more in less-curved track). For rails, measurements are made of total height loss, and loss of metal at the gauge face which, as with the wheel flange, tends to be more pronounced at track radii less than about 500 to 1000 m radius. Wear can also be measured as the total loss of cross-section, using proprietary profile measuring equipment. An example of wear measurements on a rail is given in Figure 34.29, which illustrates the change in cross-section of a rail on the high side of a curve (the high side of a curve is the outer, or longer side). The wear on the gauge face is caused by contact with the wheel flange. Figure 34.31 gives an example of how the type of measurement shown in Figure 34.29 can be used to determine the effect of accumulated tonnage and lubrication on rail wear. The two head-hardened pearlitic rails were installed on the high side of a 350 m radius curve in the Facility for Accelerated Service Testing at the Transportation Technology Center, Colorado, U.S. The rails had seen 205 MGT of heavy axle load (36 tonnes) traffic. Light grease lubrication was applied for the first 167 MGT to give a measured friction of 0.35 to 0.4, while the rail was run dry for the final 38 MGT at a friction level of 0.5 to 0.55. The complex effect of lubrication on wear can be seen. Moving from a friction of 0.35/0.4 to 0.5/0.55 gives a rapid increase in wear rate, but the dry wear rate decreases as wear progresses, possibly as a consequence of the altered vehicle steering forces produced by the increase in friction. Service measurements broadly confirm the results of small-scale tests; however, additional factors affect service tests that are difficult to replicate in a small-scale test. The effects of the climate on wheel wear were investigated by Kalousek et al. (1996), and a strong correlation was found between the number of wheels removed from service due to excessive wear and the time of year. It was found that there was interaction between the performance and life of the brake shoes used on the train, wheel wear, and contact fatigue of the wheel surface, and that these were linked to the variation with the seasons of the time for which the rails were dry or wet. The underlying mechanism controlling these processes was found to be controlled by friction levels at the wheel/rail contact, which is partially dependent on the presence of water on the rail and wheel surfaces. This effect of lubrication on wheel and rail wear has been known for many years. Under dry conditions, wear is reduced by increased hardness; but when lubrication is applied, wheel and rail metallurgy have much less of an effect. Thus, Steele and Devine (1982) observed that while a 320 Brinell rail steel wore
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FIGURE 34.32 Train-based wheel flange lubrication system. Lubricant is transferred to the wheel flange (right) by a roller (center) when the train-based lubrication system is triggered.
a factor of six times as fast as a 399 Brinell rail under dry conditions, when grease lubrication was applied the factor was only 2. In service tests, good grease lubrication has been shown to have the potential to reduce wheel and rail wear by at least a factor of 20. Attention is usually focused on lubricating the high rail gauge face in curves, because the rail gauge face is a major wear area. Lubrication applied to the gauge face also protects the wheel flange. The low rail in curves tends only to be lubricated after rail grinding, to reduce lateral forces in curves rather than to reduce wear. While systems are available to lubricate the wheel flange directly from nozzles attached to the vehicle (Figure 34.32), most railroads concentrate on lubricating the track. Methods include hand application (in unusual or difficult circumstances), vehicle-mounted lubricators, and trackside lubricators where each wheel that passes pumps grease to a spreader bar mounted at the gauge face of the high rail (Figure 34.33). This latter method is preferred, typically using grease containing mineral or synthetic oil, soap, and boundary lubricants such as graphite and molybdenum disulfide. Lubrication effectiveness, however, depends critically on the positioning and maintenance of the lubricators. Reiff and Cregger (1999) summarize the North American systems approach to wheel/rail friction control, and illustrate the fuel savings also achievable by good lubrication of the wheel/rail interface. Other methods of lubrication have been put forward recently, and these are discussed later.
34.2.6 Consequences of Rail/Wheel Contact: Rolling Contact Fatigue Rolling contact fatigue (RCF) describes the phenomenon of crack growth in rails as result of repeated contact loading. Normal loads, longitudinal and lateral shear tractions all contribute to RCF damage. Figure 34.34 shows typical RCF cracks, including shells and spalls on the gauge face of the outer rail and the top surface of the inner rail in curved track carrying heavy-haul traffic. For rails, traditional terminology is that spall refers to loss of metal from cracks initiated at the surface, while shell refers to loss of metal from cracks initiated below the surface. RCF cracks are known to
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FIGURE 34.33
Track-based wheel flange/rail gage face lubrication system.
FIGURE 34.34
Illustration of damage caused by rolling contact fatigue at the rail surface.
propagate in and below the wheel surface but, in most cases, the cracks initiate by thermal mechanisms — either by thermal fatigue caused by the heat input from tread braking, or from sudden cracks formed in martensite produced when the wheel slides on the rail during braking. For wheels, the terminology is different, and spall refers to loss of metal from defects initiated by a thermal mechanism. Shell refers to metal lost by a pure RCF process. RCF shells have been observed on coal trains in western Canada, but these are not typical of most cracks in wheels. Although wear attacks both the wheel and the rail, the evidence is that RCF is much more likely to initiate cracks in rails than wheels.
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FIGURE 34.35 Schematic of a wheel moving across a rail containing a rolling contact fatigue (RCF) crack (see text for details). (After Bower, A.F. (1988), Trans. ASME, J. Tribol., 110, 704-711.)
34.2.6.1 Small-Scale Tests RCF is studied in the laboratory with the same type of test apparatus used to study wear: namely, twin cylinders loaded in contact with creep generated by arranging different peripheral speeds. For comparisons to be made between tests, either the fatigue life of the specimens is defined using crack detection equipment, or tests may run for a predetermined period after which the specimens are examined to determine the extent of crack growth. The main difference between RCF and wear tests is that RCF tests are run with a lubricant (often water) introduced into the contact zone. This is a key point. While crack initiation may take place by ratcheting even in dry conditions (Tyfour et al., 1996), laboratory tests have shown that RCF cracks rarely propagate in the absence of a liquid lubricant. When they do develop, cracks tend only to form in the slower-moving specimen, that is, in the specimen where the surface tractions act to shear the metal in the direction of rotation. Contact fatigue crack growth was first described by Way (1935) but, more recently, theoretical explanations of the observations have been proposed, and these are discussed below. Figure 34.35 illustrates a wheel passing over an angled RCF crack in the surface of a rail. The surface traction applied by the wheel is assumed to be in the direction shown. As the wheel approaches, the traction opens the crack mouth, allowing fluid to penetrate into the crack (Figure 34.35a). As the wheel meets the crack mouth, the fluid inside the crack is trapped (Figure 34.35b). Because the fluid is assumed to be incompressible, pressure inside the crack keeps part of the crack open. As the load moves further, the fluid is pushed toward the crack tip while its pressure rises to balance the pressure applied by the load and, eventually, the pressure in the crack leads to Mode I stress intensity at the crack tip (Figure 34.35c). As the load leaves the crack mouth, the crack opens to release fluid, and the crack is thus held apart to allow Mode II crack growth (Figure 34.35d). Thus, surface traction on the rail acting against the direction of the wheel is needed to allow water, or other low-viscosity lubricants, to enter the crack, causing low crack face friction and hydraulic loading at the crack tip. The model predicts that crack growth will not occur if the load approaches the crack from the other direction. In this situation, fluid will tend to be expelled from the mouth of the crack as the load passes over. Recent work has shown, however, that cracks can propagate when the rolling direction is reversed, but that the cracks tend to reverse direction to give a longer life before they reach some critical depth (Tyfour and Beynon, 1994). The crack growth model discussed above qualitatively explains the growth of RCF cracks in rails, while initiation is assumed to occur by the same mechanism of ratcheting that is most likely responsible for
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wear. Work on quantifying crack growth taking place by the mechanisms described above has been carried out by Hearle and Johnson (1985) and Bower (1988) at Cambridge University in the U.K., Fletcher and Beynon (1999a,b) at the University of Sheffield, U.K., Sheppard et al. (1987) and Keer and Bryant (1983) in the U.S., and Murakami et al. (1994) and Makita et al. (1991) in Japan. The most important advances still to be made in the work lie in accounting for the effect on crack growth of the extensive plastic deformation of the steel near the surface of rail and wheel components, which is where the early stages of crack propagation take place. Work is in progress to develop further quantitative descriptions of the propagation of RCF cracks in rails and, in particular, to predict the point at which the shallow-angle crack turns down into the rail to threaten fracture (Cannon, 1999). However, rolling contact fatigue is an intricate phenomenon, and many theoretical and practical problems need to be overcome before the growth of cracks and spalls such as those shown in Figure 34.34 can be understood quantitatively. These problems include: 1. A highly complex rolling contact stress field, whose components depend critically on the detailed wheel and rail profile shapes and on the presence or absence of lubricants and contaminants 2. The presence of other stresses, such as those developed in manufacture (residual), and those caused by bending and thermal expansion/contraction 3. Rail material properties that vary with depth, due to the surface hardening, and which are highly anisotropic, due to the high levels of surface shear 4. Crack morphologies that are much more complex than the idealized crack shown in Figure 34.35 34.2.6.2 Service Experience Many railroads suffer from RCF defects. In Britain, a particularly prevalent defect is the “squat,” which initiates on the surface of the outer rail in high-speed curved track. A similar type of defect occurs on Japanese track, where it is termed a “black spot.” Perhaps most RCF damage occurs on heavy-haul railroads, where axle loads are much higher than those operated by passenger railroads. Spalls and cracks like those shown in Figure 34.34 are relatively common and are traditionally dealt with by rail grinding (see below). The “shell” type of defect, mentioned earlier, is mostly seen on heavy-haul railroads. These defects initiate about 10 to 15 mm below the gauge corner of the outer rail and can eventually turn down to cause rail fracture. They almost certainly initiate at alumina inclusions introduced during rail manufacture (Steele, 1989), and there is evidence that their occurrence will reduce with the advent of modern clean steel-making practices for rails. For reasons given earlier, unlike wear, it is difficult to predict in-service behavior from the results of small-scale experiments. Limited service experience, however, tends to corroborate the idea that water accelerates RCF crack growth. First, in an analysis of RCF defects on the rail running surface of Japanese Shinkansen train tracks, the incidence of defects was noticeably lower in dry tunnel sections than in open sections where rain is present about 50 days per year (Ishida, 1990). The second example concerns wheel shells found on coal trains in western Canada (Blevins, 1998). Compelling evidence suggests that embryonic cracks on the wheel tread are driven by water supplied constantly through the winter by powder snow disturbed by the train. The first melt-freeze of spring reduces the number of wheels needing treatment, until fresh snow restarts shelling. Clayton (1996) and Grassie and Kalousek (1997) have summarized railroad-based research and experience with rolling contact fatigue. Clayton concludes that the development of new materials for the rail and wheel is the key to future improvement in the performance of these components. However, further significant component performance improvement may be attainable by the better use of current lubrication technologies, the development of improved lubrication methods, and more extensive use of grinding of rails and wheels.
34.2.7 Interaction of Wear and RCF Intuition suggests that there should be an interaction between wear and surface-initiated rolling contact fatigue. If wear of the wheel or rail is more rapid than the growth rate of RCF cracks, then cracks should
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not grow to a length where they cause spalls in rails or surface shells in wheels. One way of achieving this is to increase wheel or rail wear rate by reducing hardness. The corresponding increase in ductility decreases the incidences of RCF, and small RCF cracks are worn away before they can grow to compromise the integrity of the rail. However, the rail life is inevitably reduced by the high wear rate. The idea of removing small cracks to protect against RCF has led to the widespread use of rail grinding to control cracks, flakes, and spalls on the rail surface. (Grinding has other uses as described in Section 34.2.8.) This has been adopted on many railroads, using in-track machines to grind the rail in situ, but is especially used on heavy-haul railroads where it is a commonly used rail maintenance technique. Available machines are capable of grinding both rails simultaneously, and applying desired profiles (to reduce contact stress or improve vehicle steering) at speeds in excess of 10 km/hr. Attempts have been made to define metal removal rates and grinding intervals to give the best rail surface condition at minimum cost, with some success (Kalousek, 1989). Recent work on North American railroads (Sawley, 1999), however, indicates that the balance between wear and RCF is highly site-specific and rail-type-specific. That is, the propensity for RCF cracks depends critically on parameters such as the track radius and structure, the type of rail installed, the speed of traffic, and operating practices (such as the presence of signaling systems that may require trains to brake and accelerate always on the same pieces of track). There seems no doubt that, properly applied, rail grinding can reduce RCF and prolong rail life. Until recently, the academic study of wear/RCF interaction has been limited. Observations from smallscale tests (Kalousek et al., 1989; Beynon et al., 1996) have indicated that a period of dry rolling prior to the application of water lubrication accelerates RCF cracking. This is thought to occur because surface tractions rise with friction, giving an increased rate of ratcheting strain accumulation at the surface of the steel, which leads to the initiation of cracks. Recent work has examined the effect of preventive grinding on rail surface damage using rail/wheel test discs (Ishida and Abe, 1997), with the conclusion that a metal removal rate of 0.1mm for every 50 MGT has a significant effect on the reduction of RCF cracks. The complex interactions between wear and RCF are of great commercial and safety significance to railroads and merit further study.
34.2.8 Grinding Rolling contact fatigue (RCF) defects, such as those described in Section 34.2.4.2, are sites at which transverse cracks are relatively likely to initiate and thence to propagate, leading to broken rails. The decarburized surface material of new rails is relatively easily damaged and may be subject to rapid wear. Plastic flow can give rise to undesirable interaction between wheel and rail, decreasing the running stability of the vehicle, and can, in addition, be a direct cause of defects. Short- and long-pitch corrugations can cause track irregularity and deterioration of track components, and give rise to such environmental issues as noise and ground vibration. Removal of these rail defects contributes considerably to the cost of railway maintenance. Failure to remove these defects is even more costly to railroad and mass transit operators. Regular rail grinding is one of the most effective and widely accepted measures for coping with such rail defects, with the purpose of reducing maintenance cost, and has been for the past two decades. There are three broad categories of rail grinding: preparative, preventive, and curative (or corrective). These, and the subsequent surface roughness, are discussed below. 34.2.8.1 Preparative Grinding Preparative grinding is performed for the purpose of removing the decarburized layer, the mill scale, and any construction damage to the rail materials. It is especially used to ensure the flatness of the longitudinal profile of rails either newly installed (or in an early stage of service) as track or before installation. The efficacy of such grinding is gauged through field tests, but cannot so far be estimated quantitatively. On some Japanese lines, including heavy-haul and passenger transit, the rail profile proposed by Kalousek et al. (1989) is achieved through grinding of new rails. This profile is designed to permit steering by
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rolling radii differential at a contact point, which reduces the contact stresses and alleviates early deterioration of the rail surface. The profile is intended to maximize the total number of wheels that can pass over the rail before fatigue occurs. 34.2.8.2 Preventive Grinding The purpose of preventive grinding is to reduce maintenance work (and costs) and to ensure the safety of vehicles through removal of potentially hazardous rail defects. In particular, the transverse cracks that propagate from RCF defects can lead to broken rails. The preventive grinding approach is based on crack initiation studies (Nishida et al., 1985; Ghonem and Kalousek, 1988; Inoue et al., 1991), which show that cracks initiate by fatigue failure. The number of loading cycles before fatigue failure depends on the contact stresses, and the contact stresses are functions of the contact geometry and interacting forces, such as traction at the wheel/rail interface. Preventive grinding removes “micro” cracks (10 microns long, or less). Generally, these cannot be inspected by ultrasonic (or other) detectors, let alone visually. The basic questions of concern for optimizing the efficiency of maintenance are: when and how often to grind; what amount (i.e., depth) to grind off; and just how grinding should be carried out. Preventive grinding should maintain the desired rail profile as far as possible, but should not remove more metal than is required to free the rail of fatigue cracks. Kalousek et al. (1989) and Linn et al. (1993) reported on the preventive grinding of sharp curves of heavy-haul railroads. This early work indicated that, in sharp curves, the high rail (the outer rail) generally has a greater likelihood of RCF defects than the low rail (the inner rail). It was therefore recommended that lubrication of high rails be carried out in order to decrease the friction coefficient between the rail gauge face and the wheel flange, thus decreasing the tangential contact stresses. However, recently, with the advent of clean, head-hardened rails made by continuous casting processes, it has been found that the situation is more complex, at least on heavy-haul railroads, and it is the low rail that is suffering more from rolling contact fatigue. The main difference between corrective and preventive grinding is that the former requires deep cuts, while the latter requires only shallow but more frequent cuts. The relative benefits of each method are very site and rail specific, and it has been up to now impossible to generalize about their relative merits. Experience on high-speed Japanese lines shows that the benefits of the preventive grinding method over the corrective method are longer rail life and reduced grinding costs. Although with preventive grinding the rail is ground more frequently, less total volume of steel is removed compared with corrective grinding. However, on heavy-haul freight lines in North America, it has recently been found that preventive grinding gives greater metal loss than corrective grinding and, in fact, some high rails that have never been ground are still in good condition after more than 400 MGT traffic. This is a much higher traffic volume than traditionally thought possible without the use of grinding, and may be due to the use of modern, clean, continuously cast rail. On some Japanese lines, including heavy-haul and passenger transit, the following metal removal rates and grinding periods are recommended. To remove all the initiated cracks on the head of the rail, approximately 0.05 mm to 0.075 mm should be ground off. Preventive grinding requires higher metal removal rates at the gauge corners of the high rail and the field side of the low rail to prevent cumulative distortion of the rail profile through plastic flow. Depth of cut in these areas should be 0.1 mm to 0.15 mm. The recommended preventive grinding periods are: 5 to 8 MGT for curves* extending over more than 3°; 10 to 16 MGT for curves equal to or less than 3°; and 15 to 24 MGT for tangent (straight) track. Again, however, the site-specific nature of grinding requirements is illustrated by practice on North American and Australian heavy-haul lines, where there has been a move away from gauge corner grinding and toward much longer grinding intervals. This was because excessive gauge corner grinding led to twopoint contact conditions on the high rail, which was found to impair the steering ability of freight trucks, leading to an increase in rolling resistance and hence greater rail wear and fuel use.
*Curve radii on high-speed railway lines are generally between 3000 and 5000 m.
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0.12 analysis experiment
0.1 0.08 0.04
y = 0.0622 x0.155 — 0.083
0.06 0.02 0 0
200
400
600
800
1000
Accumulated passing tonnage to RCF defects (MGT)
FIGURE 34.36
The effect of preventive grinding on RCF defects.
Transverse profile grinding also has the two aspects of preventive and corrective grinding. Kalousek et al. (1989) proposed preventive grinding to maintain the desired geometry of the rail profile, but did not refer to the tolerance of transverse profile grinding. On preventive grinding of transverse profiles, Grassie (1997) reported that, in European countries, ±0.3 mm is commonly adopted as a tolerance. Some early theoretical and experimental studies have been carried out, but the relationship between the tolerance of the transverse profile and the damage to the rail is not yet clear. The experimental study of Grassie (1997) suggested that a tolerance for the transverse profile of ±0.5 mm should result in wheel/rail contact conditions which were no worse than those existing at present. From the findings obtained thus far, the effectiveness of grinding the transverse profile is recognized, but there is little quantitative understanding. Further study of the grinding process is a current research topic. With regard to squat-type defects on high-speed railroads, in particular the Shinkansen, Ishida et al. (1998a) carried out laboratory experiments to estimate the quantitative effect of grinding. Figure 34.36 shows the relationship between average grinding thickness for a grinding period of 50 MGT, and the number of loading cycles to defects. In the laboratory experiments, the ground profiles conformed to the original head profile of rail: 600 mm radius of curvature; the maximum Hertzian pressure was set as 1081 MPa, assuming initial profiles of wheel and rail discs. 34.2.8.3 Curative or Corrective Grinding Kalousek et al. (1989) also reported on the practice of corrective grinding on North American heavyhaul railroads. Here, contact fatigue corrugations (see Section 34.2.9) can grow to a depth of 2 to 3 mm but are usually ground off when they reach an average rail surface depth of 0.5 mm. In the case reported, this was carried out every 25 to 30 MGT. However, the interval required is very site specific and, more recently, as discussed above, with modern rail steels, these intervals have been increased. Because some corrugations are deeper than average, multiple pass cuts as deep as 1.5 to 2 mm may be required at some locations on the railhead. However, even at this thickness of cut, some of the cracks are not removed and will continue to propagate during the next phase of service. In sharp curves on Japanese railroads, (mainly low rail) corrugations are ground off in order to reduce noise and ground vibration. Also, rail welds have a longitudinal profile irregularity arising from the difference in hardness between rail matrix and weld metal or heat-affected zone and elsewhere. Ishida et al. (1998b) estimated the effect of corrective grinding on the fatigue life of rail welds with the purpose of reducing dynamic effects or improving the flatness of the longitudinal profile. Figure 34.37 shows the effect of corrective grinding on the fatigue life of rail welds. 34.2.8.4 Surface Roughness of Ground Rail There is some variation in the general level of the rail’s surface roughness caused by metrological and mechanical conditions. In Japan, the surface roughness of the rail is estimated to be approximately 0.2 to 0.8 microns (Ra) within the running band. Basically, rail surface roughness that is formed by grinding
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FIGURE 34.37 The effect of corrective grinding on extending fatigue life of rail welds: (a) effect of grinding thickness (grinding frequency = 100 MGT); (b) effect of grinding frequency (grinding thickness = 0.05 mm).
After grinding
50 µm
Location of measuring surface roughness
m
50 µm
0µ 50
In-service
0 50 µm
FIGURE 34.38
m 500 µ
500 µ
m
An example of three-dimensional surface roughness.
depends on the grit size of grinding stones and on how the rail is ground (i.e., on the number of passes, etc.). Figure 34.38 shows a surface profile of rail roughness after grinding with stones whose grit sizes are 20 to 24. In Table 34.2, Kalousek et al. (1989) give the surface roughness just after grinding with stones whose grit sizes are 16 and 20 — commonly used in North America. From this table, the roughness in North America is clearly much larger than that in Japan (because of the difference in the grit size of grinding stones, the number of passes, etc.).
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TABLE 34.2 The Relationship Between Grit Size and Roughness Grit #16
Grit #20
Parameter
2 mph
7 mph
2 mph
7 mph
Ra
10.7 430 61.8 2470 53.3 2130
11.0 440 73.5 2940 54.5 2180
8.3 330 60.7 2430 46.8 1870
8.4 340 70.0 2800 47.3 1890
(µm) (µin.) Rmax (µm) (µin.) Rtm (µm) (µin.)
Note: mph, miles per hour; Ra, centerline average, arithmetic mean of departure of the profile from a mean line through the profile; Rmax, maximum measured peak-to-valley height for the area sampled; and Rtm, mean peak-to-valley height between the adjacent peaks and valleys. From Kalousek, J., Sroba, P., and Hegelund, C. (1989), Proc. 4th Int. Heavy Haul Conf., Brisbane, 193-204.)
Grassie (1997) reported on the rapid roughness change with grinding. There is a considerable difference in the surface roughnesses inside and outside the running band. In the worst conditions outside the running band, where measurements were taken over the deepest grinding scratches, the small-scale surface roughness measured after the track had carried 43,500 tonnes, which corresponds to one day’s traffic at the test site, varies in the range 7 to 20 microns (Ra). Although there is some evidence that the maximum value may reduce over time, perhaps as a result of oxidation, the range of roughness outside the running band remains similar, regardless of the volume of traffic carried by the track. Within the running band, the surface roughness after the rails had carried 43,500 tonnes of traffic was in the range 0.4 to 3.5 microns (Ra). There is some indication in the data of a steady reduction in surface roughness with time, which would certainly be consistent with the mechanisms of wear and plastic deformation. Further work is required on the relationships between different measures of roughness, on possible undesirable effects of small-scale surface roughness (e.g., noise and track damage), and on the effects of such on the longevity of rails.
34.2.9 Rail Corrugation Following installation or re-grinding, the surface of railway rails is nominally flat, but will actually include minor random vertical irregularities. During the passage of trains, these irregularities lead to variations in the wheel/rail contact force, and the variation in contact force can in turn exacerbate the existing vertical irregularities in the rail. It was found (Igeland, 1996) that the amplitudes of some wavelengths of irregularity tended to increase with the passage of trains, while others decreased. Over time (several thousand wheel passes), a regular pattern develops on the railhead, and this is referred to as rail corrugation. It typically consists of repeated shiny ridges and dark hollows on the railhead (spaced approximately 30 to 80 mm apart along the rail in high-speed track, but at longer wavelengths in heavy-haul track). Although corrugations are too small to compromise the safety of the train (around 0.5 mm or less peak-to-peak on passenger lines), they cause vibration that can damage the train and track (Vadillo et al., 1998). They also make the passage of the train very noisy. Grassie and Kalousek (1993) identified possible mechanisms of corrugation formation and split these into those that fix the wavelength of the damage, and those that actually produce the damage. The wavelength-fixing mechanisms include resonance of the train mass on the track, which acts as a spring, and resonance due to sleeper positioning. The damage mechanisms include wear, plastic flow, and rolling contact fatigue, which were discussed above. Others who have modeled the corrugation process include Kalker (1994) and Frederick (1986).
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Although the mechanisms by which corrugations are produced have been identified, there are considerable problems in preventing rail corrugation from occurring. It is found that tracks over which similar types of train pass with great regularity can quickly suffer rail corrugation, especially if these trains repeatedly brake or accelerate in the same places.
34.3 Diesel Power for Traction Purposes Railroad engine tribology is similar in many respects to the corresponding components in an automotive context, but some areas require special consideration. For information specific to locomotive engines, the reader is referred to specialty papers that focus on engine design, reliability, and emission control for large diesel engines (e.g., Kotlin et al., 1980; Grinstein, 1993; Uzkan and Lenz, 1999). The present discussion focuses on areas that are specific to railroad traction applications. Diesel traction on railroads has been used since the mid-1930s when experimental locomotives were built in several countries. Named after its inventor, Rudolph Diesel, the compression ignition engine has become the prime mover of choice for today’s railroads. Its good efficiency over a wide power range makes it ideal for traction applications where the demand is relatively constant over long periods, punctuated by short bursts at full power for starting and periodic idling when trains are coasting. Although electric power for railway traction is dominant in Europe and on most high-capacity urban systems, diesel power accounts for the largest proportion of train services in the world. The U.S. was the first country to fully convert its railroads to diesel traction, with steam power eliminated by the late 1950s. The fuel used accounts for the differences between diesel engines and spark ignition (SI) engines. Diesel engines use cetane (C16H34) and α-methyl-naphthalene (C11H10), while petrol is n-heptane (C7H16) and iso-octane (C8H18). In the diesel engine, high compression ratios (15:1 to 20:1) raise the temperature of the combustion air sufficiently to ignite the fuel without the need for a spark. However, it must be injected into the cylinder at the time combustion is required. The engine must be more robust, and hence heavier, to withstand the higher pressures that are a consequence of the high compression ratio. Railway traction diesel engines are subdivided into: • High-speed engines: 1200 to 1800 rpm (20 to 30 rps) • Medium-speed engines: 600 to 1200 rpm (10 to 20 rps) • Low-speed engines: 60 to 600 rpm (1 to 10 rps) Most locomotive engines belong to the medium-speed range, which offers a good compromise between power density and wear performance. Essentially, the diesel engine consumes fuel and air, and produces mechanical torque from the chemical energy stored in the fuel. This mechanical torque is transferred to the wheels using a variety of drive arrangements, including direct mechanical transmission, hydraulic systems and, most commonly, electric transmission of power.
34.3.1 Generation of Mechanical Power To convert the energy stored within the fuel into mechanical torque, the engine uses a reciprocating piston inside a cylinder that is closed at one end. Air is taken into the cylinder, compressed, and fuel is injected into the cylinder. The combustion of the mixture causes a temperature rise, which increases the pressure in the cylinder and thus drives the piston, and hence, the load. This can be accomplished in either a two-stroke or a four-stroke process, both of which are used for diesel traction. For more information on diesel engines, refer to a standard thermodynamics text (e.g., Rogers and Mayhew, 1992). 34.3.1.1 Two-Stroke Engine The two-stroke engine completes a cycle of induction, compression, power, and exhaust in only two piston strokes. It accomplishes this using ports in the cylinder wall to control the flow of gases. Twostroke engines have better power-to-weight ratios than four-stroke units because power is produced
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during every down-stroke of the piston. The absence of valve gear makes the engine mechanically simpler than its four-stroke counterpart. However, the need for free-flowing exhaust makes the engines noisier, and they are better suited to medium- and high-speed operation. A typical two-stroke diesel engine for traction purposes, such as model 645 of General Motors’ Electromotive Division (GM-EMD), has 8, 12, 16, or 20 cylinders with a bore of 91/16 in. (230.2 mm) and a stroke of 10 in. (254 mm). At its maximum rated full load speed of 900 rpm (15 rps), the sliding piston seals experience a top speed of 12 m/s. With a compression ratio of 16:1 for the Roots blown version, these engines produce approximately 150 kW per cylinder. 34.3.1.2 Four-Stroke Engine The four-stroke engine uses a separate stroke for each of the four phases: exhaust and compression on the up-stroke, and induction and power on the down-stroke. Cam-driven valves are used to open the intake and exhaust ports at the appropriate time. Removing the exhaust gases by forcing them out with the piston means that better silencers can be used, and the engines produce greater low speed torque. The inherently complex camshaft and valve arrangements are more expensive and require more maintenance. However, four-stroke engines are common on multiple units where quiet and smooth operation with good low speed performance is important.
34.3.2 Tribological Issues in the Design of Diesel Engines While there are no generic differences between the tribological problems arising in the diesel engines of locomotives and those occurring in the engines of trucks, ships, and cars, there are clear differences in the operating environments, which lead to more exacting requirements for the design of diesel engines for railway traction. A typical railroad diesel engine is shown in Figure 34.39. Mechanical shock loading due to poor track (see Chapter 34.1.2) is a factor in locomotive applications, but resilient mounting of engines can overcome some of the problems. Most of the tribological problems stem from the mode of operation of the two-stroke diesel engine and the fact that the piston is always pushed down, leading to unidirectional wear patterns. The reason for this is that on two-stroke engines, there is no force reversal for aspiration. A more challenging issue concerns the rapid temperature changes that locomotive engines undergo when entering and exiting tunnels. In the U.S., this problem is compounded by multiple traction, with up to five locomotives a relatively common occurrence. Inside a tunnel, trailing locomotives ingest waste heat and exhaust of the leading locomotives. The temperature of the intake air in the winter can range from –30°C to +120°C in less than a minute, a severe thermal shock loading of the system. Differential expansion of individual parts due to temperature differences during the temperature transients creates complex problems. Operation at altitudes from sea level to 3000 m, a necessity on a number of railways in Latin America, also presents challenging problems due to changes in inlet air pressure, humidity, etc. The major manufacturers, such as GM-EMD that developed its solutions for the original 567 engine, eliminated many of the resulting problems in the 1970s. Many improvements were implemented on the model 645, which was introduced in 1965. The top compression rings of the pistons were originally manufactured from ductile iron and chrome plated. In later designs (post-1973), these were replaced by chrome-faced stainless steel rings that reduced side wear of the rings by 50%, thus increasing resistance to breaking (Ephraim et al., 1976, p. 3). Oil rings were improved to enhance cooling performance under extreme load conditions and a new method of honing cylinder liners was developed (see Section 34.2.4.2 for a discussion of surface roughness). This results in 2/3 plateaux and 1/3 valleys on the surface (Ephraim et al., 1976, p. 4) and offers reduced oil consumption at light load and better performance at peak load. A comparison of the two surfaces is shown in Figure 34.40. Further improvements to the cylinder liners were achieved thanks to laser hardening of the surface areas around the inlet ports (Kotlin et al., 1980, pp. 6–8). One of the last tribological problems encountered by GM engineers was the wrist pin bearing on high power rated engines for which the “rocking pin” solution was developed in the late ‘70s and first used
Cut-away view of a large diesel locomotive engine: overview of a General Motors Series 710 16-cylinder turbocharged diesel engine.
1310
FIGURE 34.39a
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FIGURE 34.39b Detailed view of the 710 Series engine. (Courtesy of Bozidar Simonovic, General Motors ElectroMotive Division, La Grange, IL.)
FIGURE 34.40 Comparison of standard linear bore finish and plateau finish. (From Ephraim, M., Jr., Kotlin, J.J., and Williams, H.A., Jr. (1976), A versatile two-cycle diesel engine, the EMD model 645 series, in Proc. Diesel and Gas Engine Power Conf. Exhibit., Chicago, IL, April 4-8, 1976, 1-15. With permission.)
on the 645E3B engine (Kotlin et al., 1980, pp. 5–6). Due to the length of the connecting rod, the unidirectionally loaded piston pin with a standard bearing has only a small angle oscillatory motion, which limits the penetration of lubricant between the bearing surfaces. The design developed by GM-EMD allows higher pressures during the working stroke and better lubrication of the bearing surface. Two parallel bearing surfaces are provided with an eccentricity of about 1 mm. During the working or downstroke, a slight gap opens between the steel piston pin and one of the bronze bearing surfaces. This fills with lubricant and then becomes the interface for the up-stroke. During this part of the cycle, a gap for the lubricating oil opens in the other half of the bearing. Each crankshaft revolution thus results in a complete renewal of the oil film in the bearings.
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34.3.3 Supply of Combustion Air Three common methods are used to supply the engine with combustion air: natural aspiration, turbochargers, and superchargers. Although all of these are also used in automotive applications, they have to satisfy more demanding criteria in railway traction. Particular attention must be paid to tribological issues. Natural aspiration allows the engine to take in air of its own accord, at atmospheric pressure. Good compression performance requires very accurate piston seals and thus close control of the wear of rubbing surfaces. Natural aspiration is the lowest cost method, but a given engine will not be as powerful as with forced induction because increasing the mass of air in the cylinder permits a greater quantity of fuel to be injected and burned, which in turn yields more power from the engine. Effectively, forced induction results in a higher overall compression ratio and thus greater efficiency. Turbochargers function by using the exhaust gases to turn a turbine at very high speed. This is connected to a compressor that increases the induction pressure by a factor of 2 or more. Turbochargers do not require direct engine power to operate but, when the engine speed rises quickly, the turbocharger is not able to keep up because there is a delay in the increase of the volume of exhaust gases. This is known as turbo-lag and results in clouds of black smoke being expelled from the exhaust until the engine reaches a constant speed. Turbines operate in a very hostile environment with high temperature differences between turbine components and compressor, rapid temperature changes and highly stressed turbine and compressor bearings, operating at 30,000 to 40,000 rpm. It is only recently that the complex tribological problems have been understood. The third method is to use a supercharger, which also compresses the incoming air. However, the compressor is driven directly from the engine crankshaft. Supercharged engines suffer no lag, but they require mechanical engine power for their operation. This power must be supplied through gears to increase the rotational speed available from the main crankshaft. These bearings operate in a hostile tribological environment at high speeds and are potentially subject to excessive wear. All forms of forced induction raise the temperature of the incoming air, and this higher temperature potentially reduces the efficiency of the engine. Intercoolers are sometimes fitted between the compressor and the engine intake to reduce the temperature of the air.
34.3.4 Transmissions and Drives As mentioned, there are three methods of transforming the output of the engine to torque and speed levels that can be used to drive the train. Both electric and hydraulic transmissions offer good controllability and high torque at low speeds. 34.3.4.1 Mechanical and Hydraulic Drives The mechanical gearbox uses various gear ratios to provide the wheel/rail interface with the necessary torque to either start the train from standstill or to keep it moving at a set speed. Clutches must be provided to disengage the engine to allow selection of the various gears. A freewheel device is provided to protect the engine on the overrun. The reversing mechanism is usually part of the final drive to give bidirectional operation. Mechanical drives are limited by the size and torque transfer capabilities of the gears. Wear is a major problem on traction drives because the distances run per day are high, with high peak loads. Today, mechanical gearboxes are primarily used for distributed power applications in lowcost multiple units. Monitoring of the quality of lubricants and of the consistency of lubrication is difficult and currently relies on the use of periodic analysis for contaminants. Remote condition monitoring is not yet cost-effective. Hydraulic drives consist of a hydraulic pump that is connected to a hydraulic motor where the circulation of the hydraulic fluid transfers energy to the wheels. Hydraulic drives are little used on mainline traction outside of Germany due to the high stresses of the mechanical components of the system. Contamination of hydraulic fluids leads to rapid deterioration of the pumps and hydraulic motors
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TABLE 34.3
Design Details for Newer AC Traction System Locomotives
Feature Tractive horsepower Maximum speed Weight Starting tractive effort Continuous tractive effort Continuous adhesion rating
General Motors EMD SD90MAC
General Electric GE AC6000 WC
6000 hp 75 mph 420,000 lb. 200,000 lb. 170,000 lb. 38%
6000 hp 75 mph 425,000 lb. 180,000 lb. 166,000 lb. —
due to third-body wear. Today, hydraulic transmissions are mainly used in low-speed track maintenance equipment where a hydraulic pump is installed as part of the machine’s function. 34.3.4.2 Electric Drives In an electric drive application, the diesel engine is mechanically connected to a generator or alternator, and the combination essentially serves as a dedicated, portable power station that supplies the electric traction drives with power. Locomotives using this type of technology represent complex electromechanical systems where tribological issues significantly affect the performance and reliability. The main bearings of the power unit, slip rings of the alternator, and commutators of the traction motors are all areas where the severe railroad environment increases the wear and tear of components. The development of out of roundness commutators is one of the important reasons for the move to AC traction motors. Until relatively recently, both freight and passenger diesel locomotives employed DC control and DC traction motors. A high-power diesel engine is used to turn an alternator whose output is rectified to produce a variable DC voltage.* This power is supplied to the DC traction motors that drive the wheelsets. Increasingly, locomotive design is moving to AC traction systems. These use a similar principle of operation, in that a diesel engine drives an alternator with the output again rectified to DC. However, the DC voltage is then supplied to inverters that convert the power back to a variable frequency AC form, which can be used by AC squirrel cage traction motors. There are many advantages to AC traction systems. They are “self-correcting,” thanks to a rapid reduction in the torque once the motor speed rises to between 95 and 100% of inverter frequency. The speeds of different axles are thus closely related and wheel or rail damage caused by wheel spin under high traction is reduced. Traction using AC motors also results in higher torque at low speeds, needed as the train starts moving. Finally, AC motors are smaller in size, allowing higher traction power to be achieved with reasonably sized motors. Table 34.3 gives design details for two of the newer generation, high tractive effort AC locomotives produced by General Motors and General Electric.
34.3.5 Gas Turbines Gas turbine engines also have a place in railway traction. Jet engines were adapted for railroad use by SNECMA in France in the 1960s. Their advantage is a high operating speed — between 20,000 and 30,000 rpm — and constant torque output. Their disadvantage is that they are noisy, and have tended to be unreliable in railroad applications. High bearing speeds, large shock loads, and contaminated combustion air all contribute to early failures, however, gas turbines can be used with both mechanical and electrical transmissions. Specific railway-related failure modes are bearing collapse at high speed because of track-related shock loading and abrasive wear of compressor and fan blades. The Federal
*The use of DC generators was abandoned due to problems with commutator wear once high-power semiconductors became available to build static rectifiers.
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Railroad Administration of the United States, in conjunction with Bombardier, is sponsoring the development of a new, high-power gas turbine locomotive.
34.4 Current Collection Interfaces of Trains Modern electric railways are supplied either via conductor rails or overhead lines. The former system is only suited for low-voltage applications because of the inherent safety risks. Typical conductor rail applications for light rail and metro type applications are limited to direct current (DC) voltages of 600 and 750 V. The extensive system of London Underground is supplied at 660 V. Railways with overhead power supply operate at DC voltages of between 600 V (tramways) to 3000 V (main line railways in Italy and Belgium) and at alternating current (AC) voltages of 11 kV, 16.7 Hz to 50 kV, 50 Hz (Sishen-Saldanha, South Africa). Light railways powered at 750 V DC will normally draw currents up to 800 A from the supply, while Eurostar trains on the classical routes between the English Channel and London require 5000 A and more at 750 V DC. Such extreme currents are required to supply both power units at less than half the rating available during AC operation. Typical AC applications involve currents of 400 A at 15 kV (Swiss locomotive of class 460) and 300 A at 25 kV (Eurostar half-train). With a few exceptions, the rails provide the return path for the traction current, while a conductor rail or the overhead line is used as the feeder. A typical third rail installation is shown in Figure 34.41a, while Figure 34.41b illustrates an overhead line. London Underground and the Skytrain system pioneered in Vancouver use separate conductors for both the feed and return paths; they are thus also known as fourth rail systems (Figure 34.41c). Because both the feed and return paths are supported on insulators and have a high and known impedance to ground, there is no need to make special arrangements to avoid stray currents, a major problem with third rail and overhead supplied railways, which use one or both rails as the return path. Trolleybuses with twin overhead lines are similarly free of stray current-induced problems but have clearly limited power ratings due to the small contact area of the collector shoes (Figure 34.42). Graphite inserts, acting as both conductor and solid lubricant, minimize wear of the overhead line but must be replaced frequently due to the sliding wear being confined to a very small area of the collector shoe. The high currents that must be transferred safely between the infrastructure (i.e., running rails, conductor rails, and overhead lines) on “low-voltage” DC systems (300 to 5000 A) require large currentcarrying sliding interfaces to avoid overheating in the contact point. The low currents at high voltage of most AC systems (100 to 500 A) can cause arcing if the contact force at the pantograph/overhead wire interface is insufficient. This chapter section takes a look at three essential contact interfaces: earth brushes, third rail shoe gear, and pantographs, and briefly touches on the problems associated with registration arms.
34.4.1 Earth Brushes Return currents on all third rail and overhead supplied electric railways must be conducted safely from the traction equipment to the wheel/rail interface. Any nonconducting components must be bridged using braids or flexible cable links. Normally, one finds links between the body and bogie to bridge air suspension, bellows, springs, and dampers, and between bogie and axle box to bridge the primary suspension. Both braids and cables pose interesting fatigue, corrosion, and internal wear problems because the copper strands rub against each other when there is relative motion between bogie and body, etc. Once more than 50% of the strands are no longer effective, there is a serious risk of fire occurring when starting a train with high current demand. The axles on all modern rolling stock rotate in cartridge roller bearings, generally lubricated for life. Such bearings offer minimal resistance when starting from stationary and allow heavy trains to be hauled with lower rated power systems. To achieve this, the contact area between bearing rollers and races must be very small and the bearings must therefore be protected from electrical current. Electrical currents above 1 or 2 A will quickly lead to heating within the cassette, evaporation of the lubricant, and rapid catastrophic failure of the bearing, with the associated risk of derailment.
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(a)
(b)
FIGURE 34.41 (a) Third rail current collection on the Chicago elevated metro 600 V DC system. (b) Overhead current collection on a Queensland Railways heavy haul locomotive (Australia).
Earth brush assemblies are fitted to axle box housings, generally on opposite wheels in bogies. A special traction link can be used to prevent the assembly from rotating. Figure 34.43 shows an earthing arrangement suitable for high-speed operation (180 km/hr). Contact is made by a carbon insert “C” that slides on a copper surface. For lower speed operations, a rotating steel disc is joined to the stub end of the axle, while a solid copper block with a slot is pressed against the disc with a relatively small force. These material combinations optimize wear performance of the earth brush. On Supertram in Sheffield, U.K., the “brush” has a diameter of approximately 40 mm and is approximately 20 mm long. The contact force is about 3 N. The brush has a central groove to allow the abraded material to settle, away from the contact surface. The blocks must be checked every 60 days, that is, after about 7000 km. On main-line locomotives, the units tend to be larger and therefore require less frequent maintenance. The rating of the earth brushes and associated cabling is safety and performance critical,
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(c)
FIGURE 34.41 (c) Third and fourth rail system (power rails and cover boards are visible beside the track) at Subang Depot (Kuala Lumpur).
A 1
A-B
C 2
C-D 2
1 3
3
4 5
5
5
4
B
FIGURE 34.42
D
Head of a trolley bus current collector with two individually sprung carbon collector shoes.
particularly in situations where one or several wheels have poor contact with the rail due to surface contamination of track or rail. On Supertram, each brush must be capable of carrying about 200 A, that is, about half the rated current of the unit.
34.4.2 Current Collection Shoe and Gear Both third rail and fourth rail systems require highly reliable “shoe gear” to pick up and return the traction current. The current collector shoes are normally made of graphite-doped cast iron, the graphite serving as a solid lubricant. Modern conductor rails for railroad applications are of the composite type: most of the conductor is made from aluminum while the top is made from stainless steel to minimize wear and friction (Figure 34.44). Because there are under-running, side-running, and top-running contact arrangements, there are also three types of shoe gear satisfying different constraints. From a vehicle safety viewpoint, the side running systems are the most critical because a failure could derail the vehicle. However, collector shoes for all systems have built-in shear necks to protect both third rail and vehicle from the consequence of shoe failures. The typical impact energy required to break such a link is 400 J (or ten impacts of 50 J). Figure 34.45a shows a typical under-running collector shoe and associated suspension gear, while Figure 34.45b provides a view of the overall arrangement. Key design constraints are related to the smooth
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(a)
C
FIGURE 34.43 Earthing arrangements for axle box housings: (a) schematic showing the carbon insert “C” used with an inclined roller bearing (SNCF); (b) photograph showing the earthing strap on the outside of the bearing housing.
pick-up face, a relatively low contact force of 150 to 300 N to minimize wear, and the substantial travel required to cope with conductor rail irregularities. Third/fourth rail operation is not suited to speeds substantially above 150 km/hr or voltages above 1200 V. The most severe loads occur when entering and leaving the contact rail because transitions tend to be steep and short, and thus apply very high shock loads to the pick-up system (8 g rms, 30 g peak acceleration; Hartland, 1999). The contact part of shoe gear is generally made from cast iron or steel, and wear rates of 0.2 mm/1000 km of sliding on the
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FIGURE 34.44
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Modern composite (stainless steel capped) third rail by Brecknell Willis.
(a)
(b)
FIGURE 34.45 Running-under current collection shoe from Amsterdam Sneltram: (a) photograph, and (b) schematic.
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FIGURE 34.46
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Lightweight pantograph mechanisms.
conductor rail with a contact force of 180 N have been reported. When ice is present on the third rail surface, wear can rise to 0.8 mm/1000 km (Sachs, 1973) and it may therefore be necessary to heat the third and, where present, fourth rail.
34.4.3 Pantographs Current collection by pantograph is the normal choice for street tramways, non-segregated light railways, and all high-voltage AC supplies. Pantographs are very lightweight and highly stressed devices, both mechanically and electrically. As shown in Figure 34.46, a pantograph requires a mechanism to maintain its head more or less parallel to the overhead line to ensure good current collection. The complex fourbar linkage in the main member of the pantograph frame visible in the figure not only ensures the correct alignment of the head, but also transfers the force provided by the lifting cylinder, or spring, to the current collection interface between the head and the copper wire of the overhead line. The design of the levers ensures that a constant force is applied over much of the vertical travel. For low-speed applications (up to 120 km/hr), it is possible to rely on the main lifting spring (either a steel spring or an air spring) to ensure reasonably accurate control of the contact force (e.g., between 60 and 120 N [for a nominal 80 N of force required to ensure good contact]). For higher speeds and overhead lines with poorly designed geometry, it is necessary to design heads with a primary suspension that absorbs minor line height variations. An example of a high-speed pantograph with primary suspension is shown in Figure 34.47. Copper, steel, and aluminum have all been used to produce the contact strips on the pantograph head where current densities of 1 to 2000 A/cm2 are not uncommon. However, these materials resulted in very severe wear of the overhead line (Figure 34.48a). Most modern pantograph heads are therefore equipped with carbon/graphite contact strips bonded to aluminum carriers. Carbon strips cause virtually no wear of the overhead line and have a very long life under normal circumstances. In winter, however, freezing rain can cause severe wear: on the East Coast Main Line
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FIGURE 34.47
Brecknell Willis high-speed pantograph with torsion spring primary suspension.
3.5
Specific wear of contact wire (mm2/year)
3 4 2.5
2
1.5
3
1 1
2
0.5
0 0
20
40
60
80
100
120
140
160
180
200
Number of trains/24h
FIGURE 34.48a Wear of the contact wire as a function of frequency of trains: Curve (1) 2 pantograph operation with single carbon contact strips (15 kV AC); (2) 1 pantograph operation with twin carbon contact strips (15 kV AC); (3) 1 pantograph operation with twin aluminium contact strips (15 kV AC); (4) 1 pantograph operation with four compound copper-steel contact strips (15 kV AC).
in the U.K., it has been reported that carbon/graphite strips fail after 2000 km in such conditions (Figure 34.48b). Carbon strips can also be monitored for failure simply by pressurizing a duct in the center of the strip. If an obstacle severely damages the carbon strip, the air is vented to atmosphere and a pilot valve then drops the pantograph. Because the overhead line has a lateral stagger, there is no risk of local overheating and it is therefore possible to carry very large currents, for example, on 1500 V DC routes. However, it is possible to overheat the contact area if a train is stalled. Figure 34.48c gives an indication of the relationship between traction current and wear of the contact strips for various materials. Figures 34.48a–c are based on Sachs (1973).
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4
3.5
3 Specific contact strip wear (cm3/h)
3
2 2.5
2
1 1.5
1
0.5
0 0
20
40
60
80
100
120
140
Mean traction current (A)
FIGURE 34.48b The influence of the season on wear of carbon strips: Curve (1) operation in summer; (2) mean wear values; (3) operation in winter.
34.4.4 Registration Arms Wherever the overhead line passes a mast or a fixing point in a tunnel, there is a need for a registration arm (Figure 34.49), which maintains the correct stagger. The registration arm must not interfere with the vertical movements of the overhead line. The quality and long-term performance of the plain bearing of the registration arm are therefore critical. Movements are generally small (around 2 to 3°) but occur frequently and may involve substantial vibrations at 10 to 15 Hz. Registration arm bearings fail regularly and can cause immediate overhead failures with extreme consequences, in terms of downtime cost.
34.5 Axle Bearings, Dampers, and Traction Motor Bearings As mentioned elsewhere, the stiffness of the wheel/rail interface imposes high mechanical shock loads on all components that are below the primary suspension.* Accelerations of up to 130 g at the wheel have been measured in service, often at high frequencies; for example, corrugations with a peak-to-peak distance of 0.1 m cause vertical oscillations of 300 Hz at a speed of 110 km/hr. Wheels, brake discs, bearings, axles, and axle boxes, as well as one end of the primary suspension, are all subject to these loadings. *Primary suspensions generally have a relatively high stiffness and absorb rail unevenness, while secondary suspensions are comparatively soft and designed to provide ride comfort. Most passenger railway vehicles have both a primary and secondary suspension, while freight vehicles very often have a combined suspension or only a primary suspension with relatively long travel.
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8
7 1
Specific contact strip wear (cm3/h)
6
5 2 4
3
3
2
4 5
1
0 0
20
40
60
80
100
120
140
160
180
Mean traction current (A)
FIGURE 34.48c The influence of the traction current on the wear of carbon strips: Curve (1) aluminum; (2) carbon with aluminum cladding; (3) carbon alone; (4) carbon with copper cladding; (5) compound copper and steel.
FIGURE 34.49
Registration arm.
34.5.1 Axle Bearings Many administrations and light rail operators still use wheels with tires that can be replaced when worn. In some cases, rubber inserts are provided to ensure a limited amount of shock absorption. Most modern railway wheels, however, are of solid forged or cast steel. They are pressed onto the axles which, in turn,
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run in bearings that are fitted into axle boxes. Until the 1950s, axle bearings of railway rolling stock were of the bushed type with white metal or graphite-doped bronze sliding surfaces. Such bearings were wellsuited to the shock loads transmitted by the axles to the axle boxes because the forces could be distributed over a third of the bearing surface, but required a relatively high tractive effort when starting a train from a standstill. Although these types of bearings were very reliable, they required a great deal of maintenance and had a tendency to overheat if they were not adequately greased and otherwise maintained. Many railroad administrations therefore introduced hot axle box detectors (HABDs), which stopped trains at the next signal if a hot spot was detected. Heavy-duty roller bearings were first introduced on passenger rolling stock, but have now replaced plain bearings on both locomotives and freight vehicles where they have allowed substantial increases in trailing loads. The sizing of roller bearings is a complex process because axle bearings must absorb both vertical and axial loads. Cylindrical roller bearings are able to accommodate both types of forces on separate running surfaces. Sachs (1973, p. 219) provides detailed information on the calculations required, and includes the example of a freight vehicle with cylindrical roller bearings where the axle load is 20 t and the mean speed is 75 km/hr. The two axle bearings together must be able to support a dynamic load of 190 t in this situation. Bearings must be replaced when wear exceeds preset limits or when the fatigue life is reached. Most railroad operators today expect bearings to last as long as the wheelsets, that is, in excess of 30,000 hr or 2 × 106 km, to minimize maintenance costs. The service behavior of roller bearings is very different from that of plain bearings. A roller bearing can fracture and seize over a distance of a few hundred meters and HABDs spaced 20 or 30 km apart can no longer protect trains. Some manufacturers have therefore started to install fusible plugs in bearings that vent the train’s brake pipe should a bearing be at risk of overheating. DC traction motors on metros, light rail vehicles, and locomotives operating at speeds of up to 120 km/hr were traditionally of a nose suspended type where approximately half the mass of the motor rests on axle-mounted bearings and the other half on plain bearings fitted to a bogie bolster or similar support point. Both the axle bearings and the motors are thus exposed to the high dynamic forces caused by the stiffness of the wheel/rail interface. As mentioned in Section 34.3.4.2, this imposes particularly high stresses on the commutator/brush interface where carbon brushes run on a slotted copper surface. The high unsprung mass of the nose suspended design in turn produces high dynamic loads, resulting in increased contact forces and consequently affecting rail/wheel tribology. A wheelset typically weighs 1000 kg, while a DC traction motor weighs up to 3000 kg. The mass to be accelerated at any track discontinuity is therefore 2500 kg instead of 1000. Modern drive designs no longer involve nose suspended traction motors but employ bogie-frame or body-mounted motors. In this type of arrangement, the unsprung mass of the wheelset is augmented by part of a cardan shaft and right-angle gearbox or a hollow shaft with a flexible coupling.
34.5.2 Dampers for Suspension Systems Some primary suspensions use leaf springs or rubber chevrons to provide inherent damping, while others use separate energy absorption devices using frictional or oil hydraulic damping. Secondary suspensions, normally between bogie and vehicle body, are usually of the coil-spring or air-bag type and require lateral, vertical, and yaw dampers, generally in the shape of oil hydraulic dampers. Shock-loading of primary dampers is extreme and can cause failure early in a damper’s life. The tribological environment of these dampers is also very severe, with operating temperatures ranging from –50°C to +50°C. Seal failure is relatively frequent but not readily discernible. Damper failure, both at the primary and secondary levels, creates a high risk of derailment as a consequence of excessive movement of wheelsets and bogies. Most railroads therefore require regular refurbishment or replacement of dampers, a process that reduces availability and reliability. KONI of Germany has developed a monitoring system for yaw dampers. As with all monitoring systems, reliability is a key consideration: sensors and all associated equipment must offer a reliability that is an order of magnitude better than that of the components or subsystems to be monitored. Failure
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of the sensor does not affect the performance of the damper. Sensing the behavior of the yaw dampers is an appropriate use of such a system because they are subject to wear and have a limited life. Traditionally, dampers had to be replaced before they were worn out, causing increased cost and downtime. Equipping such dampers with sensors allows a condition-based maintenance regime and, at the same time, the detection of excessive yaw motions (Kars and Wyes, 1998).
34.6 New Developments and Recent Advances in the Study of Rolling Contact Fatigue Railroads continually strive to extend the life of wheels, rails, and bearings through an improved understanding and application of wheel/rail tribology. In addition, changes in operating conditions designed to improve efficiency (i.e., increased train loads and higher traction locomotives) can negatively affect the wheel/rail interface, and ways must be found to counter their potentially damaging effects. Some of the more recent developments are outlined here.
34.6.1 Friction Modifiers A recent innovation has been the introduction of friction modifiers to control wheel/rail friction to desired levels. These can replace the flange lubricators and gauge face lubricators mentioned in Section 34.2.5.3. and are usually produced in solid “stick” form using a thermosetting polymer with additives, and applied directly to the wheel flange or tread. There are three basic types. The first is designed to reduce wear by giving a low coefficient of wheel/rail friction, potentially less than 0.1, and is applied to the wheel flange where it migrates to the rail gauge corner. The second type (also available in liquid form) is intended to control friction between the wheel tread and rail top to higher levels in the approximate range of 0.2 to 0.35, to reduce noise by reducing periodic defects on the rail top known as corrugation. This is achieved by designing the friction modifier to give increased friction when significant wheel creep occurs, thereby avoiding the wheel stick-slip conditions that can lead to corrugation. A third type of modifier aims to provide friction in the range 0.4 to 0.55 (in wet or dry conditions) to improve locomotive traction. Friction modifiers offer the engineer the ability to control wheel/rail friction in a more controlled way than by the use of traditional grease and sand. As mentioned in Section 34.2.3.5, a locomotive-mounted dispenser just ahead of the driving wheels has traditionally applied sand to the track and this is found to increase adhesion, although in a rather uncontrolled way. To date, these modifiers have been applied mainly to light rail and transit systems where maintenance of the application is more straightforward. Friction modifiers appear to have inhibited corrugation formation on the Vancouver Skytrain system by reducing wheel stick-slip. However, the Skytrain is unusual in that propulsion and braking are largely achieved by means independent of the wheel/rail interface — namely, the linear motor arranged in the center of the track.
34.6.2 Wheelset Steering and Individually Driven and Controlled Wheels A number of systems for wheelset steering using passive and active approaches have been developed since the 1930s. Cross-braced freight vehicle bogies on the Scheffel principle and similar designs are now commonplace and reduce flange wear and noise in narrow curves to a substantial extent. Similarly, good results have been achieved by reducing the yaw stiffness of wheelsets and bogies, although compromises are necessary to maintain good ride characteristics at high speeds. The latest systems therefore employ two-level, switched, secondary yaw-dampers that provide a higher equivalent yaw stiffness at high speeds. Better bogie designs allow the use of smaller wheels, limited however by the higher contact stresses and thermal loadings associated with any reduction in the wheel radius. New designs of traction and braking links prevent wheelset unloading during acceleration and deceleration, thus maintaining better adhesion performance and reduced wear. Better electronic wheel-slip and wheel-slide systems also improve the extent to which the available adhesion can be exploited. Both
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the move to three-phase AC traction and microprocessor control systems with accurate speed measurement have improved the performance of locomotives and multiple-unit rolling stock, as mentioned in Sections 34.2.3.4 and 34.3.3.3. Light rail vehicles are increasingly being equipped with individually driven wheels using “virtual axles” implemented in electronic form or by exploiting the steep torque gradient of the AC traction motor. The main reason for this development has been the demand for 100% low floor vehicles where large wheels and axles present insurmountable obstacles. Thus far, control is only being applied to the speed of rotation of the wheel, but not to its lateral and angular position on the rail. However, researchers at the University of Loughborough have embarked on a project to control both the speed of rotation and the yaw of wheelmotor driven wheels for tramway applications. In effect, they will create a self-steering behavior of the type normally provided by an axle but with the ability to adapt rapidly to changing circumstances. The approach has the potential for eliminating hunting (speed-dependent lateral oscillations of wheelsets and bogies). The control systems used to achieve such behaviors must be inherently and provably safe because the wheel/rail interface is safety critical.
34.6.3 Integrated Study of Rolling Contact Fatigue Some of the areas currently of greatest importance in the reduction of rail maintenance costs due to rail deterioration as a result of rolling contact fatigue were identified in the Brite/EuRam project ICON (integrated study of rolling contact fatigue) (Cannon, 1999). This project has combined both academic and industrial research taking place across Europe to investigate the operating conditions of railroads such as vehicle load and speed, track curving radius, and rail and wheel cross-sectional profiles, all of which determine the actual load at the wheel/rail interface. Once determined, this contact load can be converted into a contact stress, and various models have been used to determine the life of the rail before the initiation of cracks at its surface. Rolling contact fatigue crack propagation criteria are being established, both for the initial stages of crack growth and for the later stages of growth during which a crack may branch to cause a broken rail. It is anticipated that the increased understanding of rolling contact fatigue produced by this work will lead to: 1. The development of improved rail steels 2. Definition of new rolling stock criteria that will minimize rail damage through rolling contact fatigue 3. Determination of the optimum rail/wheel contact geometry for both supplied and re-ground rails 4. Determination of the influence of rail surface contaminants in rail rolling contact fatigue, including both unavoidable contamination and deliberately applied contaminants such as lubricants As demand for higher loads and faster trains continues to grow, research, such as that conducted within the ICON project and elsewhere, will lead to a better understanding of the problems of the wheel/rail interface and then to suggested solutions.
34.7 Conclusion Although rail transport in one form or another has been used for well over 200 years, there remain many unanswered questions about rail deterioration, performance of bearings and current collection equipment, and the maintenance of these systems. Fundamental materials and tribological research is leading to a better understanding of the mechanical and chemical interfaces involved in all areas. The major focus must be on increasing the allowable axle loads and wheel loads, while reducing both wheel wear and rail wear and without increasing the likelihood of rail breaks or severe damage to wheels. Improved methods of nondestructive testing of wheels and rails, including more advanced approaches to the processing of ultrasound information, are expected to lead to earlier detection of potential problems. Better control of the track condition through the application of automated “measured shovel” packing of ballast will reduce both the amount of bending of the rail and
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the dynamic loading caused by level differences. This method, now known by the term “stone-blowing,” is still under development — but is promising. Expert systems are currently being developed to better manage rail life and to extend the intervals between maintenance activities. Modern methods of track monitoring and inspection are essential if such expert systems are to be successful. Track recording vehicles using accelerometers and including video recording of the rail surface are powerful tools that can be used to achieve true condition-based maintenance. Similar tools are being applied to the management of rolling stock maintenance and will allow much better control of wheelsets and brake systems. Acoustic methods to detect the very early stages of bearing failure are under trial in the U.S. Such systems could displace HABDs and would be situated along the track at regular intervals in areas where tonnages are high or where high-risk cargoes are transported. On the current collection side, much progress has been made in providing good performance under normal operating conditions. However, current collection is still a major problem in adverse weather conditions and in areas where the physical characteristics of the overhead or third rail change rapidly. Active pantographs and shoe-gear, ideally coupled with online monitoring, will improve the situation, but much research still remains to be done. The provision of more and more processing power on-board trains is probably the most significant development of the 1990s. Intelligent trains can monitor both their own performance and that of the infrastructure. Technology is already available to monitor braking forces, bearing temperatures, damper effectiveness, and adhesion levels. With a limited amount of further development, it will be possible to use standard passenger or freight-carrying vehicles to carry out routine track quality monitoring. The generalized introduction of global positioning by satellite (GPS) and global system for mobile communications for railways (GSM-R) will allow rapid pinpointing of problem areas and much faster and more accurate responses by maintenance staff.
Acknowledgments The authors would like to thank Mr. Bozidar Simonovic of the General Motors Electromotive Division, La Grange, Illinois, USA, for supplying parts (a) and (b) of Figure 34.39.
References Amsler, A.J. (1992), Abnützungsmaschine für Metalle (Wear machine for metals), Z. VDI, 66(15), 377-378. Archard, J.F. and Rowntree, R.A. (1988), Metallurgical phase transformations in the rubbing of steels, Proc. R. Soc. Lond. A, 418, 405-424. Beynon, J.H., Kapoor, A., and Tyfour, W.R. (1996), Deterioration of rolling contact fatigue life of pearlitic rail steel due to dry-wet rolling-sliding line contact, Wear 197, 255-265. Blevins, W.G. (1998), CN wheel spalling and shelling, presented at the 90th Annu. Meet. Air Brake Assoc., Chicago. Bolton, P.J. and Clayton, P. (1984), Rolling-sliding wear damage in rail and tyre steels, Wear, 93, 145-165. Bower, A.F. (1988), The influence of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks, Trans. ASME, J. Tribology, 110, 704-711. Bramfitt, B.L., Cross, R.L., and Wirick, D.P. (1994), Advanced in-line head hardening of rail, ISS Symp. Rail Steels for the 21st Century, Baltimore, 23-29. Bugarcic, H. and Lipinsky, K. (1982), Mechanical and tribological research on two newly developed rolling friction test rigs at the Technical University of Berlin, Germany, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 445-462. Cannon, D.F. (1999), ICON — A European Research Project to Combat Rail Rolling Contact Fatigue, in preparation. Castelli, V.R. (1996), Friction, in Marks Standard Handbook for Mechanical Engineers, Avallone, E.A. and Baumeister, T., (Eds.), McGraw-Hill, New York, 3.20-3.29.
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Chen, H., Yoshimura, A., and Ohyama, T. (1998), Numerical analysis for the influence of water film on adhesion between rail and wheel, Proc. Inst. Mech. Engs., 212 (Part J), 359-368. Child, H.C. (1980), Surface Hardening of Steels, Oxford University Press, Oxford, U.K. Clayton, P. (1996), Tribological aspects of wheel-rail contact: a review of recent experimental research, Wear, 191, 170-183. Clayton, P. and Devanathan, R. (1992), Rolling/sliding wear behavior of a chromium-molybdenum rail steel in pearlitic and bainitic conditions, Wear, 156, 121-130. Conry, T.F., Johnson, K.L., and Owen, S. (1979), Viscosity in the thermal regime of traction, Proc. Leeds/Lyon Conference, Lyon, Paper VIII (i). De Boer, H., Datta, S.R., Kaiser, H.-J., Lundgreen, S.O., Msgen, B., Schmedders, H., and Wick, K. (1995), Naturally hard bainitic rails with high tensile strength, Stahl und Eisen, 115, 93-98. Dyson, I.N., Williams, J.A., and Kapoor, A. (1999), The effect of surface hardening on the elastic shakedown of elliptical contacts, Proc. Inst. Mech. Engs., 213(J), 287-298. Elkins, J. (1988), Independently rotating wheels: a simple modification to improve the performance of the conventional three-piece truck, in 8th Int. Wheelset Congr., Montreal, 7.5.1-7.5.8. Elkins, J.A. and Gostling, R.J. (1978), A general quasi-static curving theory for railway vehicles, in Proc. of 5th IAVSD Symp. Dynamics of Vehicles on Roads and Railway Tracks, Swets Publishing Service, Lisse, 388-406. Ephraim, M., Jr., Kotlin, J.J., and Williams, H.A., Jr. (1976), A versatile two-cycle diesel engine, the EMD model 645 series, in Proc. Diesel and Gas Engine Power Conf. Exhibit., Chicago, IL, April 4-8, 1976, 1-15. Fletcher, D.I. and Beynon, J.H. (1999a), A simple method of stress intensity factor calculation for inclined fluid-filled surface-breaking cracks under contact loading, Proc. Instn. Mech. Eng., J. Eng. Tribol., 213(J), 299-304. Fletcher, D.I. and Beynon, J.H. (1999b), A simple method of stress intensity factor calculation for inclined surface breaking cracks with crack face friction under contact loading, Proc. Instn. Mech. Eng., J. Eng. Tribol., 213(J), 481-486. Fletcher, D.I. and Beynon, J.H. (2000), Development of a machine for closely controlled rolling contact fatigue and wear testing, ASTM Journal of Testing and Evaluation, 28, 4, 267-275. Frederick, C.O. (1986), A rail corrugation theory, Proc. 2nd Int. Symp. Contact Mechanics and Wear of Rail/Wheel Systems, Kingston, Rhode Island, 181-211. Ghonem, H. and Kalousek, J. (1988), Study of surface crack initiation due to biaxial compression/shear loading, Eng. Frac. Mech., 30(5), 667-683. Grassie, S.L. and Kalousek, J. (1997), Rolling contact fatigue of rails: characteristics, causes and treatments, in Proc. 6th Int. Heavy Haul Conf., Cape Town, 381-404. Grassie, S.L. (1997), Requirements for transverse railhead profile and railhead roughness following grinding, Proc. 6th Int. Heavy Haul Conf., Cape Town, South Africa, April, 1997, 549-564. Grassie, S.L. and Kalousek, J. (1993), Rail corrugation: characteristics, causes and treatments, Proc. Instn. Mech. Engs., 207(F), 57-68. Greenwood J.A. and Williamson, J.B.P. (1966), Contact of nominally flat surfaces, Proc. Roy. Soc. Lon., A295, 300-319. Grinstein, G. (1993), Setting the pace in the North American freight rail market, Siemens Rev., 60(5), 24-29. Halling, J. (1989), The Principles of Tribology, Macmillan Education Limited. Härkonen, S. (1985), A new low carbon steel for railway wheels, in 8th Int. Wheelset Congr., Madrid, 1.4-1.6. Hartland, D.J. (1998), Developments toward an active pantograph, presented at the Institution of Electrical Engineers, London, October, 2. Hartland, D.J. (1999), New shoegear for London Underground, 2nd Annu. Railway Electrification and Power Supply Conf., London, 10-11 March. Hearle, A.D. and Johnson, K.L. (1985), Mode II stress intensities for a crack parallel to the surface of an elastic half-space subjected to a moving point load, J. Mech. Phys. Solids, 33, 61-81.
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Hertz, H. (1896), On the contact of elastic solids, in Miscellaneous Papers by H. Hertz, Jones and Schott (Eds.), Macmillan, London. Iden, M.E. (1998), The AC traction revolution: putting rail-wheel adhesion to work, presented to ARM Rail/Wheel Interface Seminar: Crosstalk 1998, Session 13, Chicago. Igeland, A. (1998), Railhead corrugation growth explained by dynamic interaction between track and bogie wheelsets, Proc. Instn. Mech. Engs., 210(F), 11-20. Inoue, Y., Satoh, Y., and Kashiwaya, K. (1991), Estimation of growth in rolling contact fatigue damage to rail steel with development of texture, 32(1), 35-41, Quarterly Report of the Railway Technical Research Institute. Ishida, M. (1990), Relationship between rail shellings and track surroundings, Quart. Rep. RTRI, 31(1), 22-28. Ishida, M. and Abe, N. (1997), Experimental Study on the Effect of Preventive Grinding for Shinkansen Rails, in Proc. 6th Int. Heavy Haul Conf., Cape Town, 565-575. Ishida, M., Abe, N., and Moto, T. (1998a), Experimental study on the effect of preventive grinding on RCF defects of Shinkansen rails, Quart. Rep. RTRI, 39(3), 136-141. Ishida, M., Kono, A., and Moto, T. (1998b), The influence of track stiffness on the bending fatigue of rail welds in Shinkousen track, Railway Technical Research Report, Vol. 12, No. 3, 47-52 (in Japanese). Johnson, K.L. and Cameron, R. (1967), Shear behavior of elastohydrodynamic oil films at high rolling contact pressures, Proc. Instn. Mech. Eng., (London), 182(I,14), 307. Johnson, K.L. and Roberts, A.D. (1974), Observations of viscoelastic behavior of an elastohydrodynamic oil film, Proc. Roy. Soc. (London), A337(160.9), 217. Johnson, K.L. and Tevaarwerk, J.L. (1977), Shear behavior of elasto-hydrodynamic oil film, Proc. Roy. Soc. (London), A356(1685), 215. Johnson, K.L. (1970), Regimes of elastohydrodynamic lubrication, J. Mech. Eng. Sci., 12(1), 9-16. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press. Johnson, K.L. and Shercliffe, H.R. (1992), Shakedown of 2-dimensional asperities in sliding contact, Int. J. Mech. Sci., 34(5), 375-394. Jones, C.P., Tyfour, W.R., Beynon, J.H., and Kapoor, A., (1996), The effect of strain hardening on shakedown limits of pearlitic rail steels’, submitted to Proc. of the Instn. Mech. Engs., Part F in 1996. Kalker, J.J. (1979), Survey of wheel-rail rolling contact theory, Vehicle Syst. Dynam., 5, 317-358. Kalker, J.J. (1994), Considerations on rail corrugation, Vehicle Syst. Dynam., 23, 3-28. Kalousek, J., Magel, E., Strasser, J., Caldwell, W.N., Kanevsky, G., and Blevins, B. (1996), Tribological interrelationship of seasonal fluctuations of freight car wheel wear, contact fatigue shelling and composite brakeshoe consumption, Wear, 191, 210-218. Kalousek, J., Sroba, P., and Hegelund, C. (1989), Analysis of rail grinding tests and implication for corrective and preventive grinding, in Proc. 4th Int. Heavy Haul Conf., Brisbane, 193-204. Kapoor, A., 1994, A re-evaluation of the life to rupture of ductile metals by cyclic plastic strain, Fatigue Fract. Eng. Mater. Struct., 17(2), 201-219. Kapoor, A. (1997), Wear by plastic ratcheting, Wear, 212, 119-130. Kapoor, A. and Johnson, K.L. (1992), Steady state topography of surfaces in repeated boundary lubricated sliding, in Thin Films in Tribology — Proc. 19th Leeds-Lyon Symp., Dowson, D., Taylor, C.M., Childs, T.H.C., Godet, M., and Dalmaz, G. (Eds.), held at the Inst. of Tribology, Leeds, 8-11 Sept. 1992, Elsevier, Amsterdam, 81-90. Kapoor, A. and Williams, J.A. (1994a), Shakedown limits in sliding contacts on a surface hardened halfspace, Wear, 172, 197-206. Kapoor, A. and Williams, J.A. (1994b) Shakedown limits in rolling/sliding point contacts on a anisotropic half-space, Wear, 191, 256-260. Kapoor, A., Williams, J.A., and Johnson, K.L. (1994c), The steady state sliding of rough surfaces, Wear, 175, 81-92. Kapoor, A. and Williams, J.A. (1997), The effect of interfacial shear strength on the performance of coated surfaces in repeated sliding, Trans. ASME, J. Tribol., 119(3), 541-548.
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Kars, J.W. and Wyes, H. (1998), Elektronische Überwachung der Dämpferkraft bei modernen Hochgeschwindigkeitszügen, ZEV+DET Glaser’s Annalen, 211(9/10), 556-562. Keer, L.M. and Bryant, M.D. (1983), A pitting model for rolling contact fatigue, ASME J. Lubr. Tech., 105, 198-205. Knothe, K. and Liebelt, S. (1995), Determination of temperatures for sliding contact with applications for wheel/rail systems, Wear, 189, 91-99. Kotlin, J.J., Williams, H.A., and Malina, J.A. (1980), A new medium speed two stroke cycle diesel engine — the General Motors EMD 645EB series, presented at the Energy Technol. Conf. Exhib., New Orleans, LA, February 3-7. Krause, H. and Poll, G. (1982), The influence of real material and system properties on the traction/creep relationships in rolling contact, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 353-372. Langford, G. (1977), Deformation of pearlite, Met. Trans., 8A, 861-875. Laufer, E.E., Fegredo, D.M., and Kalousek, J. (1986), The effect of microstructure on wear in standard and head-hardened rails in heavy-haul service, in Proc. 3rd Int. Heavy Haul Conf., Vancouver, Canada, 176-192. Linn, S., Abell, D., Kalousek, J., and Sroba, P. (1993), Planning of production rail grinding on the Burlington Northern Railway, Proc. 5th Int. Heavy Haul Conf., Beijing, China, June, 1993. Makita, T., Kitakoga, S., Nakamura, K., Jono, M., and Tsukizoe, T. (1991), A continuous observation on rolling-sliding contact fatigue crack initiation and propagation — effect of viscosity and contamination of lubricant, Trans. JSME, 57, 539C, 2400-2405. McEwen, I.J. and Harvey, R.F. (1986), Wheel/rail wear and lubrication — laboratory studies and their relevance to field situations, in Proc. Int. Symp. Contact Mechanics and Wear of Rail/Wheel Systems II, Univ. of Waterloo Press, Canada, 269-287. Morales-Espejel, G.E., Kapoor, A., and Rodríguez-Sánchez, S. (1999), Shakedown in dry and lubricated surfaces, Lubrication at the Frontier, Dowson, D. et al. (Eds.,), Proc. of the 25th Leeds-Lyon Symposium on Tribology, Lyon, 8-11 September 1998. Murakami, Y., Sakae, C., and Ichimaru, K. (1994), Three-dimensional fracture mechanics analysis of pit formation mechanism under lubricated rolling-sliding contact loading, STLE Trib. Trans., 37, 445-454. Nishida, S., Sugino, I.K., Urashima, C., and Masumoto, H. (1985), Study on contact rolling fatigue of rails, Bull. JSME, 28(243), 1819-1824. Ohyama, T. and Maruyama, H. (1982), Traction and slip at higher rolling speeds: some experiments under dry friction and water lubrication, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 395-418. Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). Ohyama, T. (1991), Tribological studies on adhesion phenomena between wheel and rail at high speeds, Wear, 144, 263-275. Office for Research and Experiments (ORE), B44 Report No. 14, 31, published 1978. Reiff, R. and Cregger, D. (1999), Systems approach to best practices for wheel/rail friction control, Int. Heavy Haul Assn. Special Tech. Conf. on Wheel/Rail Interface, Moscow. Rogers, G.F.C. and Mayhew, Y.R. (1992), Engineering Thermodynamics, Work and Heat Transfer, 4th ed., Longman Scientific. Russell, C.A. (1998), The developing relations between science, technology and the railways, Proc. Instn. Mech. Engs., 212(F), 201-208. Sachs, K. (1973), Elektrische Triebfahzeuge, Erster Band, Allgemeine Grundlagen und Mechanischer Teil, Schweizerischer Elektrotechnischer Verein (Hsg.), Springer-Verlag, Vienna. Sachs, K. (1973), Elektrische Triebfahzeuge, Zweiter Band, Elektrischer Teil und Spezialfahrzeuge, Schweizerischer Elektrotechnischer Verein (Hsg.), Springer-Verlag, Vienna. Sawley, K.J. (1999), North American Rail grinding: Practices and Effectiveness, Association of American Railroads Report R-928, September.
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Shaw, M.C., Bel, A., and Mamin, P.A. (1960), Friction characteristics of sliding surfaces undergoing subsurface plastic flow, Trans. ASME, J. Basic Eng., No. 82, 342. Sheppard, S., Barber, J.R., and Comninou, M. (1987), Sub-surface cracks under conditions of slip stick and separation caused by a moving compressive load, ASME J. App. Mech., 54(2). Smith, F.W. (1965), Rolling contact lubrication — the application of elasto-hydrodynamic theory, Trans. ASME, 87(D), 170. Snell, J.B. (1973), Railways: Mechanical Engineering, Arrow Books, London, 2. Steele, R.K. (1989), Recent North American experience with shelling in railroad rails, AREA Bulletin, 90, 311-345. Steele, R.K. and Devine, T.J. (1982), Wear of rail/wheel systems, in Proc. Int. Symp. Contact Mechanics and Wear of Rail/Wheel Systems, Univ. of Waterloo Press, Canada, 293-315. Tanvir, M.A. (1980), Temperature rise due to slip between wheel and rail — an analytical solution for hertzian contact, Wear, 61, 295-308. Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. Tyfour W.R. and Beynon, J.H. (1994a), The effect of rolling direction reversal on the wear rate and wear mechanism of pearlitic rail steel, Tribol. Int., 27(6), 401-412. Tyfour, W.R. and Beynon, J.H. (1994b), The effect of rolling direction reversal on fatigue crack morphology and propagation, Tribol. Int., 27(4), 273-282. Tyfour, W.R., Beynon, J.H., and Kapoor, A. (1995), The steady state wear behavior of pearlitic rail steel under dry rolling-sliding contact conditions, Wear, 180, 79-89. Tyfour, W.R., Beynon, J.H., and Kapoor, A. (1996), Deterioration of the rolling contact fatigue life of pearlitic rail steel due to dry-wet rolling-sliding line contact, Wear, 197, 255-265. Uzkan, T. and Lenz, M.A. (1999), On the concept of separate aftercooling for locomotive diesel engines, ASME Trans., J. Eng. Gas Turbines and Power, 121(2), 205-210. Vadillo, E.G., Tárrago, J.A., Zubiaurre, G.G., and Duque, C.A. (1998), Effect of sleeper distance in rail corrugation, Wear, 217, 140-146. Vaughan, A. (1992), Isambard Kingdom Brunel — Engineering Knight Errant, John Murray, London, 102. Way, S. (1935), Pitting due to rolling contact, ASME J. Appl. Mech., 2, A49-A58. Wickens, A.H. (1998), The dynamics of railway vehicles — from Stephenson to Carter, Proc. Instn. Mech. Engs., 212(F), 209-217. Wilson, N.G. et al. (1995), NUCARS Users Manual, Version 2.1, Association of American Railroads, Transportation Technology Centre, Pueblo, CO, September 1995, AAR Report SD-043 (Rev/9/95). Wong, S.K. and Kapoor, A. (1996), The effect of hard and stiff overlay coatings on the strength of surfaces in repeated sliding, Tribol. Int., 29(8), 695-702.
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35 Tribology of Earthmoving, Mining, and Minerals Processing 35.1 35.2
Introduction ................................................................... 1331 Wear Processes in Mining and Minerals Processing ..... 1333 Digging and Loading • Haulage • Crushing • Conveying/ Handling/Storage • Screening • Grinding • Size Classification • Minerals Separation and Concentration
35.3
Equipment Used in Earthmoving Operations............. 1339
35.4
Equipment Used in Mining and Minerals Processing .... 1344
Small-scale Earthmoving • Large-Scale Earthmoving Crushers • Grinding Equipment • Sand Pumps • Classifiers • Flotation Machines • Magnetic Separators
35.5
General Classification of Abrasive Wear ...................... 1347 Abrasive Wear
35.6
Surface Mining • Shaft Mining and Drilling • Ore Processing and Related Activities
Jeffrey A. Hawk U.S. Department of Energy
35.7
R.D. Wilson U.S. Department of Energy
Tribological Losses in the Mining of Metallic Ores, Coal, and Non-metallic Minerals ................................. 1359
35.8
Financial Cost of Wear in Earthmoving, Mining, and Minerals Processing................................................ 1366 Concluding Remarks ..................................................... 1368
35.1 Introduction Earthmoving, mining, and minerals processing each involve frequent, and often severe, mechanical interactions between metals, and between metals and abrasive nonmetallic and metallic materials (i.e., mineral bearing ores). The abrasive nature of ores causes significant wear to extracting, handling, and processing equipment. Consequently, wear in earthmoving, mining, and minerals processing operations results in the removal of large amounts of material from the wear surfaces of scraping, digging, and ore processing equipment. From an energy point of view, material wear of this nature is classified as an indirect tribological loss (Imhoff et al., 1985). Additionally, a significant amount of energy is expended to overcome frictional forces in the operation of all earthmoving, mining, and minerals processing machinery (i.e., a direct tribological loss). However, in these particular processes, wear losses are more than five times those of frictional losses (Imhoff et al., 1985). In general, the amount of material lost from a particular component in these operations, before it becomes unserviceable, is far greater than that which can be tolerated in typical metal-to-metal wear situations (e.g., lubricated bearing-shaft wear couples in machinery). Consequently, much of the equipment
1331
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used in earthmoving, mining, and ore processing makes use of easily replaceable or repairable, and preferably low-cost, wear components. The mechanisms by which metal-to-metal and abrasive wear occurs, and the relationships between material properties and wear behavior, are reasonably well-understood in general terms (Haworth, 1949; Khruschov, 1957; Richardson, 1967; Moore, 1974, 1981). However, the specific wear mechanisms/wear material interactions that occur during earthmoving, digging, and the processing of ore are more complex, and depend on the wear material, and on the nature of abrasive, the type of loading, and the environment (Avery, 1958, 1961, 1974; Norman and Hall, 1968; Norman, 1980; Mutton, 1988). For example, the direct impact of metallic components with the earth requires alloys that have excellent ductility and work-hardening properties. The transport of material across a surface, such as chutes, conveyors, and screens, or the scraping of earth and gravel with a blade, requires a material with high surface hardness. The crushing and fragmentation of ore requires materials with even higher surface hardnesses. Mining and mineral processing operations in corrosive environments, such as slurry transport pumps, require materials that are both wear and corrosion resistant. As a result of this general knowledge, reliable predictions can be made regarding the performance of particular materials under a range of in-service operating conditions. This knowledge has allowed the rational selection of wear-resistant materials for use as earthmoving, mining, and minerals processing components, and new wear-resistant materials can be designed using our knowledge of the impact and abrasion mechanisms encountered in the day-to-day operation of components used in these operations. However, developing new abrasion- and impact-resistant materials used in these industries has not been particularly easy. During the last 30 years, the earthmoving and mining industries have gravitated toward the use of larger and more capital-intensive equipment (Norman, 1980; Gill, 1991). In the mining industry particularly, this has been due in part to the lower-grade ores being mined in some segments of the industry, thereby requiring a larger throughput of raw material with concomitant lower operating costs in order to allow the industry and individual operations to remain economically viable. Hand-in-hand with the mining industry, companies that provide earthmoving equipment have also seen the size of their equipment increase. The increase in the material tonnage handled per unit operation has made material and component design more difficult. As a result, the severity of conditions to which abrasion-resistant materials are subjected has increased dramatically. For example, higher impact levels are required in semi-autogenous grinding mills. In addition, the need to avoid — or at least minimize — unscheduled maintenance requires that the service life of wear consumables be predictable to some reasonable degree of reliability. The replacement of wear consumables represents a minor, but nonetheless significant cost to the mining and minerals processing industries. These costs arise from the need to purchase replacement parts and equipment; from scheduled and unscheduled equipment downtime with attendant loss of production; and from the labor and equipment costs expended during the replacement of worn equipment and component parts. Of all the capital and operating expenses associated with these industries, the cost of downtime and lost production outweigh the cost of component replacement (Norman, 1980; Imhoff et al., 1985; Mutton, 1988; Gill, 1991). Although wear represents a minor portion of the operating expenses in earthmoving, mining, and minerals processing, it is uppermost in the minds of maintenance personnel, due to its recurring nature. Because of this, those responsible for the purchase and replacement of wear consumables are always watchful for new materials and/or component designs that will last longer, be easier to install, and are more cost-effective than those currently in use. Other factors involved in wear material selection include availability, potential risk of catastrophic failure, and environmental considerations such as the potential for noise reduction (Mutton, 1988). The experience gained through maintenance operations has allowed particular mines and mineral processors to develop extensive in-house information on wear materials for their unit operations. Businesses that sell or lease earthmoving equipment also have in-house repair facilities, and draw heavily on the experience of the equipment manufacturer in doing routine repair and maintenance. Those involved in the design and construction of new equipment are sometimes able to draw upon this extensive database when specifying wear materials and equipment. However, two major constraints
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exist to restrict the specification and use of higher-cost wear consumables in new facility construction and component fabrication (Mutton, 1988): 1. Wear materials that offer improved performance will, in general, cost more. Although such materials may be cost-effective in terms of the improved life obtained, their higher purchase price serves to increase capital requirements. 2. In some cases, the original design for particular pieces of equipment may not be optimal in terms of process performance. Such factors are usually addressed either during, or immediately following, the commissioning of new equipment. This may involve alterations to the design of particular components, and under these circumstances the use of higher-cost and more durable wear materials in original equipment may not prove to be cost-effective in the longer term. The nature of the wear problems addressed in this chapter is quite large. In fact, wear from metal-tometal contact, abrasion, impact, and erosion in earthmoving, mining, and minerals processing is greater than that of almost any other major industry (Imhoff et al., 1985). Much research over the last 50 years has been devoted to this subject. This chapter cannot hope to cite all the literature that exists on the tribology of earthmoving, mining, and minerals processing. As such, much of the material contained herein was culled from some excellent review articles (Norman, 1980; Mutton, 1988; Olson and Cross, 1992); books on wear (Zum Gahr, 1987; Rigney, 1981) and materials beneficiation (Gill, 1991); compilations of wear literature on mining and minerals processing (Barr, 1974); an Energy Conversion and Utilization Technologies (ECUT) Division review on tribological sinks in industry (Imhoff et al., 1985); a National Materials Advisory Board (NMAB) report on “Comminution and Energy Consumption” (NMAB, 1981); and individual research papers (as listed in the Reference section).
35.2 Wear Processes in Mining and Minerals Processing This section presents an overview of the wear mechanisms and wear processes that occur in earthmoving, mining, and minerals processing. In general, the wear behavior of materials used in these operations is determined by a number of factors, which can be grouped into three main categories: (1) the properties of the wear material; (2) the properties of the abrasive material; and (3) the nature and severity of the interaction between the metal-to-metal wear surfaces and between the abrasive and the wear materials. These categories are interdependent because the nature of the metal-to-metal contact and the abrasive/wear material interaction are influenced by the properties of the wear material, and to a great extent, by the properties of the abrasive. Increasing the size, density, or hardness of the abrasive particles, for example, influences the contact stress between the abrasive and wear materials, possibly leading to increases in the wear rate of the wear material. Similarly, if the abrasive particle is sharp, and upon fracture remains sharp, then the cutting or gouging action of the abrasive particle will continue to be effective in removing material from the machine component (Moore, 1981). Alternatively, in the case of metal-tometal wear, increasing loads place increased stress on contacting parts, which can change the normal mode of adhesive wear to some other damage mechanism (e.g., contact stress fatigue or even plastic yielding). Also influencing the wear of earthmoving, mining, and mineral processing components is their function and design. In earthmoving operations, the abrasive wear from scraping operations will be less severe than operations requiring earth penetration and removal (e.g., the wear of digger teeth on bucket excavators). Wear rates in crushing and grinding units will be much higher than the wear exhibited in chute linings, screens, and classifiers. Indeed, crushing and grinding operations account for approximately 95% of the material wear in ore processing (Norman, 1980). These high wear rates arise because crushing and grinding are more energy intensive, and result in more severe impact and abrasive wear. Consequently, the severe impact and abrasive conditions found in crushing and grinding equipment necessitate compromises in material selection criteria in order to minimize the risk of catastrophic failure of these units (Norman, 1980; Moore, 1981; Mutton, 1988).
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The dominant wear mechanism in earthmoving, mining, and minerals processing is abrasion. Secondary to abrasion — but no less important — is metal-to-metal wear, which in many instances is complicated by abrasion as a result of the environmental conditions in which the machinery operates. Abrasion is arbitrarily subdivided into broad classifications corresponding to the nature of the wear material/abrasive particle interaction. The abrasive wear classifications usually cited include: • Gouging abrasion (the removal of large volumes of material per event from the wear surface) • High-stress grinding abrasion (i.e., the abrasive particle is crushed during the wear interaction) • Low-stress scratching abrasion (i.e., the abrasive particle remains intact as it moves freely across wear surface) • Erosion (low-stress scratching) • Erosion-corrosion (low-stress scratching abrasion in a corrosive environment) The mechanisms of material removal during abrasion are complex and vary with the type of service conditions. The wearing surfaces of equipment are continually subjected to high rates of wear, such that repair and replacement of worn components is a regular maintenance activity. To facilitate easy replacement of worn components, most earthmoving, mining, and mineral processing equipment makes use of components that are designed for easy and rapid replacement and/or repair (Austin, 1974; Dawson et al., 1982). A typical example is the design of the digging teeth used on dragline buckets and power shovels, a design where the use of quick release pins on the digger teeth facilitates their easy repair or replacement in the field (Stoody, 1998). Table 35.1 highlights the generic tribological loss mechanisms that occur in earthmoving, mining, and minerals processing. All generic wear mechanisms occur in ore processing operations. In mining and drilling operations, three-body abrasion (i.e., high-stress conditions) is common to each, and results in substantial wear to equipment. At this point, mention of metal-to-metal wear is relevant. In earthmoving, mining, and mineral processing equipment, metal-to-metal interactions are prevalent in the engines, drive trains, connectors, bearings, and gearing. In engines and drive trains, much of the system is closed to the environment and the wear surfaces are lubricated. It is beyond the scope of this chapter to discuss engine and drive train lubricated wear (other chapters in this volume discuss these issues). However, metal-to-metal wear in connectors, bearings, and gearing, sometimes complicated by abrasion, does pose severe wear problems TABLE 35.1
General Tribological Loss Mechanisms in Mining Active Tribological Mechanism
Operational Activity Surface Mining Exposing and digging Loading Transporting Shaft Mining Digging Transporting Ore Processing Drilling Mud pumps Drill pipe Drill bits
Three-Body Abrasion
High-Stress Gouging
Impact Wear
High Friction
Erosion
Lubricated Wear
X X X
X — —
X X —
X — X
— — —
X — —
X X X
— — X
X — X
— X X
— — X
X — X
X X X
— X X
— — X
— X —
X X X
— — —
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
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in this type of equipment. The types of metal-to-metal wear and damage typically encountered include: contact stress fatigue or spalling, plastic yielding, and adhesive wear. Additionally, metal-to-metal contacting parts are also susceptible to corrosion, fretting corrosion and creep, fracture (i.e., fatigue failures and ductile/brittle fracture), and handling and installation damage. The severity of the wear and/or damage is a function of the design, lubrication, and stress on the part. The wear/damage that occurs in metal-to-metal contact can be greatly accelerated if abrasive particles enter the system. In earthmoving, mining, and minerals processing, relatively large amounts of material are removed by wear from a component before it becomes unserviceable, with a concomitant decrease in its operating efficiency as a result of changes in the dimensions of the wearing surface. This may not be a serious problem for digger teeth or chute liners, but in more complex equipment such as crushers and cyclones, operating efficiency may be seriously impaired with relatively minor dimensional changes. In some ore processing equipment, such as gyratory crushers, these changes can be accommodated through the adjustment of machine settings. In many cases, the operating efficiency of equipment is monitored by means of its power consumption, with adjustment or the replacement of components carried out when a predetermined operating level of performance falls below some critical value. Earthmoving, mining, and minerals processing operations can be subdivided into a number of separate unit operations, each of which can experience its own particular type of wear, depending on force levels, abrasive particle type and size, and other operating or environmental factors. Of particular importance are the characteristics of the abrasive, which have a significant effect, not only on the wear behavior, but also on the type of equipment selected to carry out a particular operation. For example, size reduction (comminution) of hard minerals is usually carried out in gyratory crushers that operate at relatively low speeds and subject the mineral to high compressive stresses (Gill, 1991). Softer, less abrasive minerals, such as limestone or coal, can be comminuted in impact-type crushers, where a large proportion of the energy required for size reduction is developed through the kinetic energy of the rotating crusher bars and impact hammers (Norman, 1980; Gill, 1991). The following list of generic unit operations (Norman, 1980; Mutton, 1988; Gill, 1991) summarizes the abrasive wear that can occur during earthmoving, mining, and ore processing. Figure 35.1 depicts generic ore processing operations in schematic form with the materials used for the particular wearing surfaces and some typical wear rates (Norman, 1980). Table 35.2 expands on the list of wear mechanisms and associated wear materials used in earthmoving, mining, and minerals processing shown in Figure 35.1.
35.2.1 Digging and Loading Digging and loading involve a wide range of abrasive sizes and high force levels with significant impact. The major wearing areas for the buckets used on draglines and power shovels are the digger teeth and lip region, the inner floors and walls of the bucket, and the heel of the bucket (i.e., the outside lower surface) (Kennedy, 1975; Mutton, 1988; Olson and Cross, 1992). The digger teeth are subjected to high impact-gouging forces and abrasion. Consequently, digger teeth have been designed for easy replacement and/or repair (Austin, 1974). Typically, digger teeth are made of cast martensitic steels (Mutton, 1988). To increase the abrasive wear resistance of the digger teeth and lip region, weld overlays of hardfacing alloys (such as CrC) are used (Kennedy, 1975; Olson and Mueller, 1977; Horsfield, 1980; Olson and Cross, 1992). To reduce abrasive wear in other areas of the bucket, wear plates are used extensively to line the inner walls, floor, and heel. The dragline and power shovel buckets have been designed so that the wear plates can be easily installed, repaired, and/or replaced, usually through weld overlays (Avery, 1947, 1968; Osborn, 1973; Kennedy, 1975; Chavanne, 1976; Hickl, 1980; Dawson et al., 1982). Wrought martensitic steels (in low- and high-stress grinding and sliding/scratching wear areas), laminated white irons (in the heel areas where high-stress grinding and sliding/scratching occurs), and CrC hardfaced plate (high impact and high-stress grinding and sliding/scratching areas) are the typical materials used for wear plates in dragline and power shovel buckets (Mutton, 1988).
700
Mart. W.I. Pearl steel Aust. low-Mn steel Mart-steel Elastomers
Liners
Mart. steel Mart. W.I.
5*
3*
Elastomers Mart. W.I. Ceramics
Lining & Orifice
Abbreviations: Aust. = Austenitic, Mart. * Martensitic, Pearl. * Pearlitic, W.I. = White Iron
* Metal wear is negligible when elastomers can be used
2*
Mart. steel Stainless steels Cr. plated steel
Fine
Agitator - Impeller
2*
Elastomers Mart. W.I. Ceramics
Cont.
Tailing 1- Low stress 2- Corrosion-erosion
Air
Minerals separation
FIGURE 35.1 Schematic representation of the major steps in ore processing. (From Norman, T.E. (1980), Wear in ore processing machinery, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, New York, 1009-1051. With permission.)
50
Elastomers Mart. W.I.
Mart. steel Pearl steel
Aust. Mn steel Mart. W.I. Elastomers Balls
Impeller & Case
Rods
Coarse Screens
Aust. Mn steel Mart. W.I. Fine Screens
Coarse
Classifying
1- Low stress 1- Low stress 2- Corrosion-erosion 2- Corrosion-erosion
Pumping
Liners
1- High stress 2- Gouging 3- Corrosion - erosion
Grinding
1- Low stress 2- Gouging 3- Corrosion-erosion
Fine
Water
1- Gouging 2- Low stress
Coarse
Screening
1336
Typical metal wear rates (Grams per tonne)
Recommended materials
Principal wear types
Crushing ore
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TABLE 35.2
Wear Materials Used in Mining and Minerals Processing Operations
Operation Mining Digging/loading
Haulage
Crushing
Screening
Abrasive Wear Classification 1. Gouging 2. Low-stress
1. Gouging 2. Low-stress
1. 2. 3. 1. 2. 3.
Gouging High-stress Low-stress Low-stress Gouging Erosion-corrosion
Conveying/handling/storage
1. Low-stress 2. Erosion-corrosion
Grinding
1. High-stress 2. Gouging 3. Erosion-corrosion
Pumping
1. Low-stress 2. Erosion-corrosion
Classification
1. Low-stress 2. Erosion-corrosion
Separation
1. Low-stress 2. Erosion-corrosion
Material Types Austenitic Mn steels Cast martensitic steels Alloy white irons/CrC hardfacing UHMW polyethylene Wrought martensitic steels CrC hardfacing Rubbers UHMW polyethylene Austenitic Mn steels Alloy white irons CrC hardfacing Alloy white irons/CrC hardfacing Austenitic Mn steels Stainless steels Wrought martensitic steels Elastomers, rubbers, polyurethanes Wrought martensitic steels Alloy white irons/CrC hardfacing Ceramics Elastomers, rubbers, polyurethanes UHMW polyethylene Wrought martensitic steels Forged/cast martensitic steels Alloy white irons Cast pearlitic steels Elastomers, rubbers Alloy white irons Ceramics Elastomers, polyurethanes, rubbers Alloy white irons Ceramics Elastomers, polyurethanes, rubbers Alloy white irons Elastomers, polyurethanes, rubbers Stainless steels Ceramics
From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.
35.2.2 Haulage The same type of abrasive wear conditions (gouging and low-stress abrasion) occur in haulage operations of coarse, hard ores as occur in digging and loading. However, impact energy levels can be quite high in the loading of skips and haul trucks, particularly for coarse-sized ore (up to 2 to 3 m in diameter) and dense materials (Mutton, 1988). During unloading, severe sliding abrasion, with high tangential forces, occurs. The same types of wear materials are used in haulage as in digging and loading: wrought martensitic steels for impact/sliding abrasion and CrC hardfaced plate for sliding abrasion areas. For moderately soft and/or fine abrasives like bauxite and coal, low-stress abrasion and corrosion are the predominant degradation mechanisms. In these instances, material selection is predicated on obtaining a degree of corrosion protection along with wear resistance. Materials used in wear-corrosion haulage environments include stainless and corrosion-resisting steels, aluminum alloys, wrought martensitic steels, and ultra-high-molecular-weight (UHMW) polyethylene (Bauman, 1974; Doennecke and Shelton, 1974; Mutton, 1988).
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35.2.3 Crushing Abrasive wear conditions in crushing operations range from heavy impact and gouging (primary crushing) to high-stress abrasion (tertiary crushing and impact crushing) (Norman, 1980; Mutton, 1988; Gill, 1991). Metallic materials are used exclusively for the crushing of ores. During crushing operations, the ore is reduced from a maximum of approximately 2 m in diameter to about 10 mm, maximum diameter. Three or four stages of crushing are usually involved (Gill, 1991). Crushing is accomplished by squeezing the ore between two metal surfaces with sufficient pressure to fracture the pieces. For softer and less abrasive minerals, such as limestone or coal, an impact-type crusher can be used, in which the ore pieces are struck with a rotating hammer with enough velocity to cause fracture (Norman, 1980). Typical materials used in crushers are austenitic manganese steels, laminated/reinforced alloy white irons, and CrC hardfacing, with final selection of the material made on the basis of abrasion resistance and toughness (Fabert, 1974; Hegmegee, 1974; Moore, 1981; Mutton, 1988).
35.2.4 Conveying/Handling/Storage Ore is moved between the various unit operations by conveyor belts, chutes, and launders. Slurries of ground ore in water are moved through pipes. Typically, low-stress abrasion, with moderate impact and erosion-corrosion, occur during these unit operations. For example, wear (low-stress abrasion) in chute liners is a minor, but significant factor in ore processing, especially for the feed chutes to grinding mills. However, the degradation in pipes carrying slurries can be quite serious, with wear (erosive-corrosive) severe at bends, reducers, and other locations where flow conditions are disturbed (Norman, 1980; Mutton, 1988; Madsen, 1992). High alumina ceramic tiles, austenitic manganese steels, wrought martensitic steels, and laminated alloy white irons are standard materials used in chutes and hoppers under sliding conditions with moderate to low impact. Only the metallic materials are used when impact conditions become more severe (Mutton, 1988). For pipelines handling coarse abrasive slurries (i.e., particle diameters greater than 50 mm), CrC hardfacing or alloy white irons are often used to line the pipes. For fine slurries, linings such as fused cast basalt and elastomers (rubber or polyurethane) are used (Mutton, 1988). Low-stress abrasion occurs in bins and hoppers. Corrosion can also be a problem if the moisture content of the material being handled is high. Wrought martensitic steels and corrosion resisting steels are frequently used in these applications (Mutton, 1988; Gill, 1991).
35.2.5 Screening Abrasive wear conditions in screening operations can range from severe impact, gouging abrasion on primary screens, to low-stress/corrosion in wet screening of fine product. Coarse crushed ore is screened on metal-bar, or in some cases, on rubber-deck screens (Gill, 1991). Finely crushed ore is normally screened on wire mesh or rod-deck screens (Mutton, 1988). Screens are closely coupled to crushing units, so it is important to minimize shutdown time for screen replacement (Norman, 1980; Gill, 1991). Various steels (austenitic manganese, wrought martensitic, and wrought pearlitic) are used as “grizzlies” in primary screening operations. For run-of-the-mill ores and the discharge from grinding mills, wrought martensitic steels and elastomeric coated screens are used. For wet screening and dewatering operations, the screens are either made from stainless steel or a mild steel coated with an elastomer, typically polyurethane (Mutton, 1988).
35.2.6 Grinding The dominant wear mechanisms in grinding are high-stress abrasion and erosion-corrosion. In autogenous and semi-autogenous mills, high impact and gouging abrasion also occur. During grinding (usually in water), the ore is ground from a maximum 20-mm diameter down to about 0.3 mm or less (Norman,
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1980; Gill, 1991). The wear of grinding media (balls or rods), plus the wear of grinding mill liners, accounts for a major portion of the wear in an ore processing plant (Nass, 1974; Farge and Barclay, 1974; Avery, 1974; Norman, 1980; Mutton, 1988; Gill, 1991). The wear in grinding mills, along with the energy consumed, is a major expense in ore processing plants (Norman, 1980; NMAB, 1981; Imhoff et al., 1985; Gill, 1991). Grinding media (balls, rods) are usually metallic (primary grinding), typically either forged or cast martensitic steels, or alloy white irons (Nass, 1974; Farge and Barclay, 1974). Mill liners can either be metallic (cast pearlitic or martensitic steels, or alloy cast irons), or rubber. Liners made of rubber provide increased life, reduced noise, and the possibility for higher cylinder rotational speeds (Dougall, 1974; Norman, 1974, 1980; Mutton, 1988; Gill, 1991). The performance of grinding mills, and the consumption of grinding media and wear liners, are influenced to a great degree by liner design.
35.2.7 Size Classification Abrasive wear conditions in classifiers consist of low-stress abrasion and erosion-corrosion (Norman, 1980; Mutton, 1988). Appreciable wear in these units occurs in the larger, heavy media classifiers, especially hydrocyclones. The ground ore, upon leaving the grinding mill, is normally divided into a sufficiently ground fraction that passes on to flotation or other methods of minerals separation, while the insufficiently ground fraction is returned to the mill for further grinding. The size classification is made in gravity, or centrifugal-type, classifiers. Cyclone classifiers, especially hydrocyclones, are finding increasing usage (Gill, 1991). Wear prevention or reduction in these classifiers is important because a shutdown to replace worn parts also requires a shutdown of the grinding mill that is in closed circuit with, and feeds, the classifier (Norman, 1980; Gill, 1991). Typically, three classes of materials are used in classifiers: ferrous alloys (alloy white irons, corrosion resisting steels), elastomers (rubber and polyurethane), and ceramics (alumina and partially stabilized zirconia) (Mutton, 1988).
35.2.8 Minerals Separation and Concentration Wear (abrasive and corrosive) primarily occurs in the agitator impellers of the flotation machines. These impellers are usually made from molded rubber, or in some cases, from martensitic white iron. Due to the fineness of the particles in the ore slurry and the moderate impingement velocities, wear of the impellers is quite slow. However, some types of rubber may deteriorate from additives (mineral oils) in the slurry (Norman, 1980). Where minerals separation is done in gravity or magnetic separators, the wear of moving parts is almost negligible (Norman, 1980; Mutton, 1988; Gill, 1991).
35.3 Equipment Used in Earthmoving Operations A wide variety of equipment is available for use in the scraping, digging, and large-scale removal of earth. It is not possible to discuss every piece of equipment available for these operations. However, much of the equipment is similar in its design and fundamental use, and as such, a discussion of the most common ones will provide an overview of their functionality and their associated problems with wear. The following discussion is divided into two sections; the first section looks at earthmoving equipment of modest size (i.e., typical equipment used in road construction and small-scale earthmoving operations, such as excavation for buildings), and the second section looks at equipment used in the removal of overburden in surface mining operations. At the end of each section, certain components associated with this equipment will be examined from a wear point of view.
35.3.1 Small-scale Earthmoving This chapter section focuses on earthmoving equipment used for non-mining applications, such as smallscale earthmoving in building, bridge, dam, road, and highway construction. When any structure of the sort mentioned above needs to be built, the first step is always the preparation of the site. This preparation
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GROUSER
SPROCKET
DOZER END BITS RIPPER TEETH AND SHANKS
IDLER
ROLLER
TOP CARRIER ROLLS TRACK RAILS
FIGURE 35.2 View of a bulldozer showing major components affected by abrasive wear. (From Stoody (1998), The Rebuilding and Hard-facing of Earth-Moving Equipment, Bulletin 8203, Industry, CA. With permission.)
almost always starts with the removal of earth and rock so that some sort of foundation can be constructed upon which the desired structure rests. To remove the earth and rock, the following types of equipment (of a size necessary to effectively complete the job) are typically used: bulldozers, scrapers, graders, excavators, and front-end loaders. Of course, for many applications, other specialty equipment is also used, such as asphalt compactors, pavers, wheeled compactors, etc. Only the most common earthmoving machines are described here. 35.3.1.1 Bulldozers A bulldozer is a large tracked vehicle, with a large curved blade (the dozer) in the front that is used to move earth and other debris out of the way. Behind the bulldozer can be a curved tool, called a ripper, that is used to engage and loosen the earth. Specialty blades allow the bulldozer to perform a variety of jobs, such as extinguishing fires, pushing rocks and other debris out of the way, sweeping agricultural fields of stumps, managing landfills, and building stockpiles. Bulldozers range in size from small (74.6 kW) to very large (Komatsu 575A-2 Superdozer at 857 kW). The majority of bulldozers owned in the U.S. are owned by construction companies. However, the mining industry probably uses bulldozers the most, operating them an average of 2700+ hours per year. Figure 35.2 shows a schematic of a bulldozer, with the various components common to all manufacturers. The Komatsu Superdozer has a blade that is 3.4 m high by 7.6 m wide, and is capable of moving 70 m3 of earth. The vehicle weighs an astounding 135,000 kg. Abrasive wear is the primary material degradation mechanism in bulldozers. Abrasion is most prevalent in the undercarriage (i.e., the grousers) and ground engaging equipment (ripper teeth and shanks, as well as the dozer end bits, side frame, and wear plates on the bottom of the blade). However, metal-tometal wear, complicated by abrasion, also occurs in the sprockets, idlers, rollers, track rails, and pins. 35.3.1.2 Scrapers A scraper is a mechanized wheeled shovel that cuts the earth, scoops it up, and moves it to another location where it is dumped. The front portion of the scraper consists of the tractor where the driver is located. The rear of the scraper consists of the bowl, or can, that holds the earth. The cutting edge of the bowl has metal pieces called slobber bits that are used to cut the earth when the bowl is lowered to the ground while the scraper is moving. Other types of scrapers may have a second engine in the rear and various dirt loading systems. Scrapers are more efficient than bulldozers when it is necessary to move the earth more than 150 m or so. Scraper bowls can typically hold 15 m3 of earth, but bowls up to 34 m3 are available (Caterpillar 657E 708 kW twin-engine scraper). One area of extreme wear on scrapers is the tires, which are worn and cut by the terrain they move over. Certainly, the slobber bits that engage the ground also wear heavily. The surface of the bowl is worn to a lesser degree by scratching abrasion.
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HOOK ROLLS (NOT SHOWN)
HOUSE RING
HOUSE ROLLS (NOT SHOWN)
GEAR TEETH SPROCKETS
TUMBLERS
TREAD ROLLERS
IDLERS
BOTTOM ROLLS
TRACK PAD
CHAIN DRIVE SPROCKETS
FIGURE 35.3 View of a tractor undercarriage showing the major components affected by abrasive and metal-tometal wear. (From Stoody (1998), The Rebuilding and Hard-facing of Earth-Moving Equipment, Bulletin 8203, Industry, CA. With permission.)
35.3.1.3 Graders Once a majority of the earth and other debris has been moved by a bulldozer or scraper, then a grader is used to sculpt the terrain. Graders are most commonly used in road or highway construction. The grader, like the scraper, is a wheeled vehicle. It has a single angled blade, or moldboard, near the center of the vehicle that is used to sculpt the ground below. The moldboard can be adjusted from side to side, up and down, and rotated 225° to give the ground below the shape desired. The largest graders are used for building and maintaining mining roads, for reclamation projects, and for other large-scale projects. The Caterpillar 24H motor grader weighs 58,960 kg, has a 373-kW engine, and carries a 6.1 to 7.3 m wide by 1 m high moldboard. Like scrapers, the tires on graders suffer wear and cutting from the surfaces they work on. Abrasion of the scraper blade occurs as a result of its interaction with the material being moved. Another area of wear is in the moldboard, where there is significant metal-to-metal wear, which is further complicated by abrasion from the dust and dirt. 35.3.1.4 Excavators Excavators were originally known as steamshovels. A modern excavator consists of a tracked vehicle with a digging shovel on the end of a hydraulic arm. Most modern excavators are used for heavy digging, although they are also used for trenching, knocking down small buildings, uprooting trees, etc. Figure 35.3 shows a schematic of the undercarriage, or crawler portion, of a typical excavator. The hydraulic arm consists of a boom and stick, and can stretch as long as 18 m. Excavators range in size from 22,680 kg up to 90,700 kg, with bucket sizes ranging from 0.4 to over 8.0 m3. The smaller machines primarily serve as utility machines in and around building construction sites, while the larger machines are used almost exclusively for loading and digging earth. In the undercarriage area, abrasion occurs primarily on the track pads. Metal-to-metal wear, once again complicated by abrasion, is a problem in the idlers, bottom rolls, chain drive sprockets, tread rollers, tumblers, and sprockets. Metal-to-metal wear also occurs in the gear teeth, house rolls, house ring, and hook rolls. Impact and abrasion are the major degradation mechanisms of the ground-engaging shovel teeth on the bucket. Scratching abrasion occurs on the side frame and wear plates on the bottom of the shovel.
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35.3.1.5 Front-end Loaders A front-end loader is a versatile machine that serves a dual role: as a fixed position excavator and a shortdistance transporter. Unlike the excavator, the front-end loader is usually a wheeled vehicle with a bucket (the width of the machine) in the front. This machine is primarily designed to excavate soil, rock, debris, and other materials; lift this load to the desired location (usually into a truck or to a stockpile); and then dump the material. Machine and bucket sizes vary, with the smaller machines having bucket sizes of 0.8 m3, and the larger machines (226,800 kg) having buckets approaching 25 m3. (Front-end loaders with a tracked crawler are available and used where traction and tight maneuverability are needed.) Like the grader and scraper, the front-end loader is typically a wheeled vehicle and, as such, tire wear and cutting is a problem. Like the hydraulic excavator, impact and abrasion are the major degradation mechanisms of the ground-engaging shovel teeth on the bucket. Scratching abrasion on the side frame and wear plates on the bottom of the shovel also occurs.
35.3.2 Large-scale Earthmoving This section examines the earthmoving equipment used for mining applications. Mining operations require the continuous removal of earth, that is, the overburden, in order to expose the valuable mineral component. As such, massive equipment is needed to dig up and haul away the overburden and ore. To remove the large quantities of earth and rock in surface mines, the following types of equipment are used: draglines, stripping shovels, giant hydraulic excavators, giant dump trucks, and bucket wheel excavators. 35.3.2.1 Dragline Draglines are huge machines constructed to sit above ground at the mine site and are used to remove overburden and mineral at a high rate of speed. These large machines operate continuously from the time they are built until they are decommissioned, and they are considered to be a “life-of-mine asset.” That is, the machine is designed for the specific mine site and mineral to be mined, and it is expected that the unit will work until all the mineral is removed from that site. (Properly maintained, a dragline is capable of operating for 30 to 40 years.) A typical machine may weigh in at 7.7 million kg, have as many as 40 motors operating, and generate up to 37,250 kW. The buckets range in size from 7.6 m3 to more than 115 m3, with the largest one built to date capable of holding 170 m3 of earth and rock. A separate electricity source is needed to supply energy to the units, and two men are needed to operate it. A typical mining dragline bucket can hold and move 115 m3 of earth and rock (180,000 kg) 100 m in 90 seconds. The dragline operates at a fixed location in the mine until all mineral is removed that is within reach of the bucket. It then “walks” to the next mining site and begins all over again. (Walking draglines move on large metal pontoons at a very slow rate of speed.) In draglines, most of the heavy abrasive wear occurs to the bucket teeth and on the wear plates on the bottom and sides of the bucket (Figure 35.4). Other areas of wear include the scratching abrasion of the dragline chains, and the severe metal-to-metal wear (again complicated by abrasion) on the dragline pins and clevises. Another area where a combination of metal-to- metal wear, scratching abrasion, fretting fatigue, and corrosion occurs is in the wire ropes used to maneuver the dragline bucket. 35.3.2.2 Stripping Shovel Stripping shovels are very large tracked machines with a boom/dipper assembly. However, these machines can weigh as much as 1.8 million kg, with dippers (i.e., buckets) capable of holding as much as 70 m3 of earth and rock. They are electrically powered, with the dipper/boom assembly mounted on two tracks, each of which is 13.7 m long and 3 m wide. Most stripping shovels are matched to current dump truck size, and with a 72,500-kg bucket, they can fill a 220,000-kg dump truck in three passes in less than 90 seconds. They are less expensive to use than draglines and will last almost as long with proper care and maintenance.
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FIGURE 35.4 View of a dragline bucket showing digger teeth, dragline chains, and wear plates on the sides and bottom of the bucket. (From Stoody (1998), The Rebuilding and Hard-facing of Earth-Moving Equipment, Bulletin 8203, Industry, CA. With permission.)
In the stripping shovel, heavy abrasive wear occurs to the teeth on the dipper and on the wear plates on the bottom and sides. Metal-to-metal wear, fretting fatigue, and corrosion also occur in the wire ropes that maneuver the dipper/boom assembly. 35.3.2.3 Giant Hydraulic Excavator Giant hydraulic excavators are much like their smaller counterparts. They are an attractive alternative to draglines and stripping shovels because of their relatively low cost, fast speed, and high productivity. They are usually used in mines for removing earth and minerals. The big advantage that the giant hydraulic excavators have over draglines and stripping shovels is their hydraulic system. Draglines and stripping shovels rely on gears to maneuver the dipper/boom or bucket, thereby creating friction with subsequent losses in efficiency. Hydraulics are a more efficient way of lifting heavy objects, although the giant hydraulic excavators are smaller and cannot lift as heavy a load as the draglines and stripping shovels. They are, however, very much faster and more maneuverable than their gear-driven counterparts, and are also less costly to operate. A drawback to the giant hydraulic excavator is that its lifetime is much shorter than that of either the dragline or stripping shovel, typically 40,000 hours of operation if cared for well. The Caterpillar 5230 weighs in at 300,000 kg, carries a 17-m3 bucket, and has a 15-m reach. Larger units exist, such as the Liebherr R996 Litronic, a 2235-kW, 545,000-kg unit with a 33.5-m3 bucket. Like the dragline bucket and the stripping shovel dipper, impact and abrasion are the major degradation mechanisms of the ground-engaging shovel teeth on the bucket. Scratching abrasion on the side frame and wear plates on the bottom of the shovel also occur. 35.3.2.4 Giant Dump Truck The typical dump truck for mining operations now has a 218,000-kg carrying capacity. It has six tires, each of which is 3.7 m in diameter and weighs 3600 kg. These trucks are assembled at the mining site (as they are not allowed on the public roads because of their size). The role of the giant dump truck is simple: carry the overburden and mined ore to the appropriate spot as quickly as possible. The size of these vehicles is governed by both mining efficiency (get as much material out of the pit as fast as possible; these trucks can reach speeds of 55 kph) and the need to conform to environmental regulations (i.e., leave the land in roughly the same condition as it existed prior to mining). Larger trucks are also available; for example, the 280,000-kg Komatsu 930E.
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The major cost associated with wear in the giant dump trucks involves the wear and tear to the tires. Being as large and heavy as they are, and given the environment they operate in, tires are a major cost item as far as wear is concerned. Impact damage from the loading of earth and rock from the various machines described above and scratching abrasion contribute to wear of the bed of the dump truck. 35.3.2.5 Bucket Wheel Excavator The concept of a bucket wheel excavator is simple: a large circular wheel studded with buckets spins around scooping piles of dirt, coal, or some other material and dumps it onto a conveyor system for transport to another site. Most often seen in mining operations (especially in Germany), these machines are also used in digging canals and for projects requiring the removal of massive quantities of dirt. They are not especially effective where the ground is hard or where there are large rocks or ledges. Basically, the bucket wheel excavator consists of the following components: (1) the undercarriage and crawlers that hold up and move the machine; (2) the superstructure that holds the booms, conveyor systems, and hoisting winch; (3) the booms that hold the bucket wheel, the counterweight to the working end of the machine, and the conveyor system that removes the debris; (4) the conveyor belts that remove the excavated material; and (5) the bucket wheel that does the actual digging. The largest bucket wheel excavators have buckets of between 6 and 8.5 m3 apiece, with anywhere from 10 to 24 buckets on the wheel. Usually, the harder the material being dug, the greater the number of buckets on the wheel. The giant Krupp Bucket Wheel Excavator 288 weighs 13.2 million kg, is over 185 m long, and can remove 190,000 m3 of soil per day with its 18-bucket wheel. If properly maintained, a bucket wheel excavator will be operational for 40 years. The buckets on the bucket wheel excavator will see the same type of scratching abrasive wear as the aforementioned machines, except that the severity will be much less, given the nature of the environment in which the equipment operates. Wear and fretting fatigue to the wire ropes that control the movement of the bucket wheel boom and associated structures will also occur.
35.4 Equipment Used in Mining and Minerals Processing To the mineral processing operations schematically illustrated in Figure 35.1 can be added other major mining operations that contribute to wear of components: namely, digging, drilling, loading, and hauling. Abrasion within these operations range from severe (high impact, large abrasive size) in digging and crushing operations, to relatively mild (low force levels, small abrasive sizes) in classification and separation processes. The presence of aqueous or other liquid environments of variable pH can cause significant corrosion in grinding and subsequent conveyance and processing operations. Table 35.3 summarizes the types of equipment used in these mining and mineral processing operations and identifies the major wear components of each. TABLE 35.3
Mining and Minerals Processing Equipment
Operation
Equipment
Wear Components
Screening Conveying/handling Grinding
Shovels, draglines, front-end loaders, trucks, scrapers Jaw, cone, and gyratory crushers Impact crushers Grizzlies, screens, trommels Conveyors, chutes, pipes, launders Semi-autogenous mills, rod mills, ball mills
Pumping Classification Separation
Slurry pumps Cyclones, spirals Flotation cells, magnetic separators
Buckets, teeth, adaptors Trays, blades Jaws, mantles, concaves, bowels, liners, hammers, blow bars Screen decks, underpans, discharge lips Liners, impact curtains, bends Balls, rods, liners, grates, feed chutes, discharge trommels Impellers, volute and frame plate liners Hood, vortex finders, bodies, spigots Agitators, drums
Mining Crushing
From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.
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TABLE 35.4
Properties of Typical Ores and Minerals
Ore/Mineral Type
Density (g/cm3)
Vickers Hardness (GPa)
Compressive Strength (MPa)
Abrasion Index
Bond Work Index
Bauxite Coal Limestone Heavy sulfides (lead/zinc) Copper ore (chalcopyrite) Hematite Granite Quartz
4.9–5.2 1.2–2.0 2.3 7.4–7.6 4.1–4.3 5.3 — 2.7
1.5–4.1 1.5–2.5 1.5–2.5 — 3.4–4.0 4.6–6.4 5.0–7.8 7.8
— 5–40 130–200 60–100 — 180–250 100–300 140–650
— — 0.03 0.13 0.15 0.17 0.39 0.78
— 12 12 11 12 9 17 17
From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.
An ore processing plant takes the mined ore and reduces it in size so that the valuable mineral component (metal sulfides and iron oxides, for example) can be separated from the gangue. In many instances, the size of the incoming ore can be as great as 2 m in diameter (Norman, 1980; Gill, 1991). Therefore, the primary ore must be crushed and ground into very fine particles. The gangue in many cases is either silica or silicates, which are relatively hard and abrasive compared to metallic alloys (Moore, 1981; Imhoff et al., 1985; Mutton, 1988). Separation of the valuable mineral from the gangue is usually done in a water slurry, by flotation, magnetic separation, or gravity (Gill, 1991). Each of the mining and minerals processing stages involves two or more wear modes. Selection of the most suitable wear material for the components used in each operation is made on the basis of the most severe one, minimizing the risk of catastrophic failure (Norman, 1980). The abrasive materials (ore, mineral, or waste material) to be mined and treated can be characterized to some extent by their abrasivity, and the energy required for comminution in crushing and grinding operations (Bond, 1952, 1964). These two parameters are in turn dependent on abrasive hardness and shape, and its compressive strength and fracture properties. Table 35.4 shows some of the characteristics for a range of typical ores and minerals. Some of the minerals handled in processing operations may be relatively benign in terms of their abrasivity, in which case they present no substantial wear problems. However, the untreated mineral may contain a small proportion of hard, abrasive material that is removed during processing. This is particularly true for coal, which sometimes contains coarse particles of harder minerals such as quartz (Norman, 1980). The presence of the quartz, or another hard mineral, gives rise to significant abrasive wear in the processing equipment, which may not have otherwise occurred. In other cases, the required product may constitute only a small volume fraction of the total material handled, in which case the abrasive characteristics of the waste mineral are of major importance in the selection of wear materials. An example of this is diamond mining, in which relatively large tonnages of rock are processed to yield very small volumes of the desired product. Under these conditions, the efficiency of the classification and separation equipment is very important (Imhoff et al., 1985). Unit operations in ore processing are described in the next sections. A short description of the equipment and its general operation are provided, with the major causes of wear highlighted.
35.4.1 Crushers The primary crusher in ore processing is usually a gyratory or jaw type, which in large operations is capable of accepting rocks up to 2 m in diameter. The crushing forces have to be intense so that the elastic limit of the material being crushed is exceeded. Crushers tend to be massive and rugged (although sometimes portable), requiring large drive motors. They are energy intensive and expensive, both to construct and to operate (Gill, 1991). The rock is crushed to a maximum size of about 0.20 to 0.25 m in diameter at this stage. From this point, the ore passes on to a second or a third stage of crushing in
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either gyratory, cone, or roll crushers. Intermediate screening occurs at each stage to separate out the larger rock chunks for further crushing. The final product of the ore crushing plant is usually all 10 to 20 mm in diameter (i.e., particles of this size will pass through a screen with these openings), with a high percentage of the product finer than this. This product then passes on to the ore grinding operation (Norman, 1980). The gyratory, jaw, cone, and roll crushers crush rock by applying high compressive forces to each rock. Another type of crusher accomplishes similar results using impact hammers or blow bars mounted on a rotor, thereby producing high kinetic energy impacts on each rock at velocities of around 30 m/s (Norman, 1980). These impact crushers are capable of producing a high ratio of size reduction in one stage of crushing. However, due to the high velocities of the hammer, the wear rate is very high. Impact hammers are, therefore, typically used to crush softer ores such as coal, limestone, and cement plant feed (Gill, 1991).
35.4.2 Grinding Equipment Grinding of the crushed ore is almost always performed in cylindrical rotating mills, which are filled about half full of steel or iron balls, steel rods, or some other form of grinding medium. The grinding medium might also take the form of ceramic balls, flint pebbles, or for autogenous grinding, the fraction of ore between about 50 and 200 mm in diameter (Gill, 1991). In semi-autogenous grinding, steel balls about 125 mm in diameter are charged into the mill to occupy approximately 8 to 10% of the mill volume and supplement the grinding produced by the large pieces of ore in the mill. The interior chambers of all these mills are lined with easily replaceable liners whose thicknesses range from 50 to about 250 mm when installed. Wear of these liners, as well as the wear of the grinding balls and rods, is a major item of expense in most ore processing operations (Dougall, 1974; Norman, 1974, 1980; Gill, 1991). The crushed ore fed into the grinding mills is almost always mixed with water so that the grinding is done in a slurry containing about 75% solids. The ore is ground to at least 0.3 to 0.7 mm in diameter, although some operations require the ore to be ground to finer particle sizes (e.g., 0.04 mm). The ground ore is then passed through the classifiers, from which incompletely ground ore is returned to the grinding mills, while the rest is passed on to the separators. Primary grinding can also be performed in two stages. The first stage might use a rod mill, with rods 75 to 100 mm in diameter, which reduces the ore from 15 to 25 mm down to about 1.5 mm (Gill, 1991). After this grinding operation, the ore goes to a ball mill where it is reduced to about 0.3 mm in diameter or finer. Autogenous or semi-autogenous grinding may in many instances be followed by a second stage of grinding in a ball or pebble mill (Norman, 1980).
35.4.3 Sand Pumps Sand pumps are used to move slurries from grinding mills to classifiers or concentrating equipment, and to dispose of tailings. Rapid wear occurs to the impellers and case linings of the pumps, so molded rubber impellers and linings are used wherever it is feasible to do so (Norman, 1980). However, when the slurries contain coarse sand or sharp-cornered stones, or when the impingement velocities of the sand particles are high, the rubber is cut and worn quickly. In these instances, a high chromium martensitic white iron can be selected (Mutton, 1988).
35.4.4 Classifiers Classification can be described as separating mixtures of fine particles into two or more products, depending on the variations of size, shape, and specific gravity, by allowing these particles to settle in a fluid. Water is the usual medium, although air is used as well (Gill, 1991). Original classifiers were gravity fed and, as a result, wear in this process is minimal. However, classification using gravity is also slow. To speed up the operation, cyclone (fluid medium is air) and hydrocyclone (fluid medium is water) classifiers have been developed. Abrasive forces in these cyclones are more severe, but in most cases rubber or
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elastomeric linings give satisfactory service. The most severe wear occurs to the lining of the coarse sand discharge orifice. Here, hard ceramics or martensitic white irons can be used in place of the elastomers (Norman, 1980; Mutton, 1988).
35.4.5 Flotation Machines The flotation process is used extensively to separate valuable minerals (e.g., metal sulfides) from siliceous gangue in the ground ore. These machines typically use an agitator-type impeller, plus induced air, plus chemical reagents, to produce a froth that selectively collects and “floats” the desired mineral. The agitator impellers are subject to wear, but it is usually relatively mild. Molded rubber or elastomers are used for these impellers and they usually last for years of continuous operation before they need to be replaced (Norman, 1980; Mutton, 1988).
35.4.6 Magnetic Separators In practically all high-tonnage operations, magnetic separators operate in a sand slurry. Separation depends on the attraction of the paramagnetic minerals, such as magnetite, to the surface of a rotating drum in a localized magnetic field (Gill, 1991). The drums are made from non-magnetic grades of sheet steel, such as austenitic stainless steel or austenitic manganese steel. They suffer from mild scratching abrasion during the process, but have a relatively long life. Much of the abrasion damage results from the removal of a continually reforming oxide film; in this case, use of a high chromium stainless steel reduces wear because it forms an adherent, relatively abrasion-resistant chromium oxide coating on the surface (Norman, 1980).
35.5 General Classification of Abrasive Wear The dominant abrasive wear conditions that exist in earthmoving, mining, and minerals processing equipment can be described using the following broad classifications (Avery, 1961; Norman, 1980; Mutton, 1988): • • • •
Gouging abrasion High-stress, or grinding, abrasion Low-stress, or scratching, abrasion Erosion-corrosion
Gouging abrasion occurs under conditions where abrasive particles indent and move over the wear surfaces under high stress levels. It involves both cutting and tearing types of wear, in which small chips of metal are removed from the wearing surface by the movement of the sharp points of rock, under considerable pressure, over the wearing surface. This type of action is very similar to machining by a cutting tool. In gouging abrasion, the wearing surface is plastically deformed and work-hardened by the abrasive forces, so that cutting and tearing of metal occurs on the work-hardened surface. Typical operations that involve gouging abrasion include crushing and primary grinding operations. The wear liners of crushing units are particularly susceptible to gouging abrasion. This type of wear also occurs to the liners of large grinding mills, particularly large autogenous and semi-autogenous mills where large chunks of ore (up to 250 mm in diameter) are to be broken up by the tumbling action. Gouging abrasion also occurs in impact crushers or almost anywhere where coarse rocks impact a metal surface under considerable pressure or force (e.g., digger teeth on power shovels and dragline buckets used to scoop up loose rock). Gouging abrasion normally occurs in the crushing and handling of large chunks of rock. It is accompanied by heavy impact and by high bending and compressive forces on the wearing parts, which are made as heavy section castings. As a result, the choice of ferrous alloys that can be used with confidence in these applications is limited. Traditionally, austenitic 12% manganese steels are used as crusher liners.
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They have fairly good resistance to gouging abrasion, combined with good toughness and the ability to be heat-treated in heavy sections (Norman, 1980). For other applications involving gouging abrasion, such as autogenous mill liners, impactor bars in impact crushers, and earthmoving tools, the manganese steels have been partially displaced by low-alloy quench and tempered steels and martensitic white irons (Mutton, 1988). High-stress, or grinding, abrasion occurs when abrasive particles are compressed between two solid surfaces, as for example, between grinding rods or balls. The high-stress abrasion that occurs in grinding mills takes place over a very small contact region, where the ore particles are caught between the grinding balls, or between grinding balls and the mill liner. The high contact pressure produces indentations and scratching of the wearing surfaces, and fractures and pulverizes the abrasive ore particles. Hard minerals such as quartz will indent and scratch martensitic steels having yield strengths of 2100 MPa (Norman, 1980). High-stress abrasion is sometimes referred to as three-body abrasion, although two-body, highstress conditions can sometimes exist. High-stress abrasion implies that the abrasive particle is fractured and broken apart during the wear process. How these small abrasive particles affect the actual removal of material in mineral processing is not well-understood. It has been speculated that high-stress grinding abrasion produces wear by a combination of cutting, plastic deformation, surface fracture on a microscopic scale, as well as by tearing and fatigue, or spalling (Norman, 1980). In ore processing plants, high-stress abrasion produces practically all of the wear on grinding balls and liners in ball mill grinding units. In rod mills that accept larger chunks of ore, during the first stage of grinding, the wear of the grinding rods and liners proceeds by both gouging abrasion and high-stress grinding abrasion. In autogenous grinding mills, charged with ore from 250 mm to 0.2 mm in diameter, both gouging abrasion and grinding abrasion occur. In high-stress grinding abrasion, the microstructure of the balls and liners influences the wear rate. In unalloyed or low-chromium white iron balls, an Fe3C-type carbide (Vickers hardness, Hv, of 7.8 to 9.8 GPa) structure coexists in a relatively soft ferrite or pearlite (Hv of about 1.0 to 2.9 GPa) matrix. This results in a composite Hv for the alloy of between 4.9 and 5.9 GPa. However, despite the relatively high hardness of the composite structure, the balls tend to wear at a rate equivalent to that of the ferrite or pearlite matrix. The abrasive forces that occur during grinding are sufficient to fracture and crumble the carbides, which are poorly supported by the ferrite or pearlite matrix. In a matrix that contains martensite, however, the carbides do not fracture as readily, and consequently, better abrasion resistance is obtained. Low-stress, or scratching, abrasion occurs when lightly loaded abrasive particles impinge upon, and move across, the wear surface, cutting and plowing it on a microscopic scale. In aqueous or other liquid environments, corrosion may also contribute to the overall wear rate, in which case erosion-corrosion is the operative wear mechanism. In both cases, low-stress abrasion is the primary mode of wear. The wear rates in terms of metal thickness removed per day are quite low in low-stress abrasion, so a significant portion of the total wear is probably due to the abrasion of a continually reforming oxide film. This may be especially true in the handling of particulates in a wet environment, such as slurries. Low-stress scratching abrasion in ore processing machinery occurs primarily in the pumping of sand slurries, in size classifying equipment such as cyclones and gravity classifiers, in chute liners, screens and flotation impellers, and in hydraulic and pneumatic conveying operations. Generally, the impingement angles and particle impact forces are so low that hard and brittle constituents of the microstructure are not fractured or micro-spalled by the abrasive forces. Under these circumstances, ferrous alloys containing hard carbides have good to excellent wear resistance. Ceramics and synthetic stone (e.g., fused silicates) are also used for these applications. Molded rubbers and polyurethanes can also work well in low-stress abrasive conditions, particularly in pump and flotation impellers, linings for cyclone classifiers, and in pipes and screen decks in some screening applications (Mutton, 1988). Table 35.5 summarizes each of these classifications in terms of the abrasive size, the nature of contact, and the environmental factors. Figure 35.5 shows in schematic form the four classifications. All of these mechanisms are similar in that a hard particle moves across the component surface in some manner. Particle type, shape, size, and hardness ultimately determine the type and severity of abrasive wear. The next section discusses in more detail the various factors that influence abrasive wear in materials.
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TABLE 35.5
General Classification of Abrasive Wear in Mining and Minerals Processing Equipment
Classification Abrasive size Contact Conditions Impact Force Velocity Impingement angle Environmental Principal mechanisms
Gouging Abrasion
High-stress Abrasion
Low-stress Abrasion
Erosion-Corrosion
Large
Medium
Small
Fine
High High Low Low Generally dry
Low High Low Low Generally as slurry, variable pH Cutting, some fragmentation corrosion
Low Low Variable Medium-low Variable
Low Moderate High Variable Generally as slurry, variable pH Cutting, plowing, fragmentation, and corrosion
Plowing, cutting
Cutting, some corrosion
From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.
GOUGING LARGE PARTICLES, EXTREMELY HIGH STRESS, IMPACT, ABRASIVE FRACTURES. EXAMPLES:
JAW AND GYRATORY CRUSHERS.
HIGH STRESS GRINDING SMALLER PARTICLES, HIGH STRESS, SLIDING RATHER THAN IMPACT, ABRASIVE FRACTURES. EXAMPLES: SMALLER BALL AND ROD MILLS.
LOW STRESS SMALL PARTICLES, LOW STRESS, ABRASIVE DOES NOT FRACTURE. EXAMPLES :
SCREENS, CHUTES, TRAYS.
EROSION - CORROSION FINE PARTICLES IN AIRBORNE OR SLURRY FORM: ABRASIVE DOES NOT FRACTURE. EXAMPLES : PUMPS, CYCLONES.
FIGURE 35.5 Schematic representation of the four abrasive wear classifications. (From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.)
35.5.1 Abrasive Wear The individual factors that influence wear behavior are shown in Table 35.6. For both the abrasive and wear material, the majority of factors that affect wear behavior are related to their respective mechanical properties. Also of importance is the mechanical aspect of the abrasive/wear material interaction. Chemical
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TABLE 35.6
Factors that Influence Abrasive Wear Behavior
Abrasive Properties
Contact Conditions
Wear Material Properties
Particle size Particle shape Hardness Yield strength Fracture properties Concentration
Force/impact level Velocity Impact/impingement angle Sliding/rolling Temperature Wet/dry pH
Hardness Yield strength Elastic modulus Ductility Toughness Work-hardening characteristics Fracture toughness Microstructure Corrosion resistance
From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.
processes, however, are also important (i.e., corrosion or oxidation) because they directly influence the rate of wear of a material in the environment of interest. The influence of the parameters listed in Table 35.6 can be explained by their effect on the mechanism by which material is removed from a worn surface. The simplest model of abrasive wear is one in which rigidly supported hard particles indent and are forced across the surface of the wear material. Depending on the properties of the abrasive and wear materials, one of several wear mechanisms (Figure 35.6) can occur (Zum Gahr, 1987; Mutton, 1988): 1. Plowing occurs when material is displaced to the side, away from the wear particles, resulting in the formation of grooves that do not involve direct material removal. The displaced material forms ridges adjacent to grooves, which can be removed by subsequent passage of abrasive particles. 2. Cutting occurs when material is separated from the surface in the form of primary debris, or microchips, with little or no material displaced to the sides of the grooves. This mechanism closely resembles conventional machining. 3. Fragmentation occurs when material is separated by a cutting process and the indenting abrasive causes localized fracture of the wear material. These cracks then freely propagate locally around the wear groove, resulting in additional material removal by spalling. The plowing and cutting mechanisms involve predominately plastic deformation of the wear material, while the third mechanism also involves fracture. Thus, the dominant mechanisms that occur for a particular operating condition are influenced to a great extent by the plastic deformation and fracture behavior of the wear material. Materials that exhibit high fracture resistance and ductility with relatively low yield strength are more likely to be abraded by plowing. Conversely, materials with high yield strength and low ductility and fracture resistance abrade through fragmentation (Moore, 1981; Zum Gahr, 1987; Mutton, 1988). Additional wear mechanisms can operate in materials that exhibit a duplex microstructure or that are composed of two or more component phases (e.g., a composite type material like a high-chromium white iron or a composite drill bit such as diamond or tungsten carbide inserts in a steel matrix), the individual components of which vary in their mechanical properties. Under some abrasive wear conditions, removal of the softer phase (usually the matrix) can occur by one or more of the above mechanisms. This process then leaves the harder phase unsupported, in which case it may either become detached from the wear surface by a pull-out mechanism, or be more susceptible to wear by fragmentation. In addition, the presence of an interface between the various components of the composite may promote cracking and fragmentation of the harder phase, particularly under impact-abrasion conditions. The rate of material wear for any of the above processes is influenced by the extent of indentation of the wear material surface by the abrasive particle. This depth of indentation, for a given load, will be a function of the hardness of the wear material and the shape of the abrasive particle. Angular particles
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Microploughing
Microcutting
Microcracking
FIGURE 35.6 Microscopic mechanisms of material removal between abrasive particles and the surfaces of materials. (From Zum Gahr, K.H. (1987), Microstructure and Wear of Materials, Elsevier Science, Amsterdam, The Netherlands. With permission.)
will indent the wear surface to a greater extent than rounded particles, leading to higher wear rates. In addition, angular particles are more efficient in cutting and machining (Moore, 1981). The hardness of the wear material, or more specifically the hardness of the worn surface, is an important parameter in determining a material’s resistance to abrasion. An increase in the surface hardness of the wear material reduces the depth of penetration by the abrasive particle, leading to lower wear rates. However, an increase in a material’s hardness is also accompanied by an attendant reduction in its ductility, resulting in a change in the abrasion mechanism, for example, from predominantly plowing and/or cutting to fragmentation (Murray et al., 1979). For mechanisms involving predominantly plastic deformation (i.e., plowing and cutting), the wear rate can be expressed through the following parameters (Moore, 1981; Mutton, 1988): the probability of wear debris formation; the proportion of plowing, and cutting processes; the abrasive particle shape and size; the applied stress; and the hardness of the wear surface. For brittle materials (e.g., ceramics), a transition from a purely cutting mechanism to one that also involves fragmentation occurs when the nature of contact changes from elastic-plastic indentation to Hertzian fracture (Moore, 1981). The conditions under which this transition occurs are dependent on the size and shape of the abrasive particles, the applied stress, and the hardness of the wear surface. In addition, the fracture resistance of the wear material, as measured by the fracture toughness, is also important. Decreasing the hardness of the wear material, and increasing the fracture toughness, increases
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the critical abrasive size at which the transition to fragmentation occurs. Thus, reducing the hardness of brittle materials, or alternatively increasing their fracture toughness, leads to lower wear rates (Zum Gahr, 1987; Mutton, 1988). Abrasive wear mechanisms involving plastic deformation, cutting, and fragmentation occur predominantly in materials with relatively high elastic modulus, that is, metals, ceramics, and rigid polymers. As the elastic modulus decreases, the nature of the abrasive/wear material contact changes, with localized elastic deformation becoming more significant. The probability of wear occurring by plastic deformation mechanisms decreases, such that for elastomers, cutting mechanisms can occur only with contact against sharp abrasive particles. For contact against blunt abrasive particles, the two main wear mechanisms are tensile tearing and fatigue. For the abrasive wear of polymeric materials, the following material parameters are important (Mutton, 1988): elastic modulus and resilience, friction coefficient, tensile strength and tear resistance, elongation at break, and hardness. The wear behavior of elastomers is particularly sensitive to abrasive impingement angle, as this influences the dominant modes of deformation, and hence, the wear mechanisms. At low impingement angles, tensile tearing occurs and the material’s tear resistance is important. At impingement angles close to 90°, the behavior of the elastomer is essentially elastic, and resilience is a major factor in determining wear resistance. For abrasive wear conditions in which significant energy levels are dissipated in the abrasive/wear material contact, elastomeric linings are usually designed such that impingement angles are as close to 90° as possible. 35.5.1.1 Abrasive Characteristics Abrasive particle size has a significant effect on material wear, with the greatest effect being for nonmetals (i.e., ceramics and polymers). In non-metals, the effect of particle size is associated with changes in the predominant mechanism of material removal. Ceramics undergo a transition to fragmentation above a critical abrasive particle size, whereas elastomers undergo a transition from elastic behavior to either tearing or fatigue. In metals, the effect of abrasive particle size is minimal for particle sizes greater than 100 µm. Below this size, the wear rate decreases rapidly with decreasing particle size (Moore, 1981). This particle size effect is usually attributed to the nature of the abrasive/wear material contact, with decreasing size favoring elastic rather than plastic contact. Abrasive hardness, or the ratio of the hardness (Vickers) of the wear material to the hardness (Vickers) of the abrasive (H/Ha), is a critical parameter in abrasive wear. It is well-known that the abrasive wear rate decreases as the hardness of the worn surface approaches that of the abrasive (Richardson, 1968). When the hardness of the worn material exceeds that of the abrasive, the wear rate decreases rapidly. Figure 35.7 shows this particular effect for metals and ceramics. This effect of H/Ha on abrasive wear results from a change in the nature of the contact mechanics. At H/Ha ratios ≈ 0.6 to 0.8, the contact conditions give rise to extensive plastic deformation. At higher H/Ha ratios, the nature of the contact becomes essentially elastic (Moore, 1981; Mutton, 1988; Hutchings, 1992). As a result, wear rates decrease unless material is removed by mechanisms other than cutting and plowing (e.g., fragmentation). As the hardness of the worn surface approaches that of the abrasive, plastic flow of the abrasive may occur, leading to a reduction in the abrasive particle’s cutting ability. In addition, it is possible to fracture the abrasive when the plastic zone in the abrasive particle reaches a critical size (Richardson, 1968). This effect for the abrasive particle is analogous to the transition from purely cutting to fragmentation in the abrasion of brittle materials. The effect of H/Ha on wear behavior is also influenced by the size and compressive strength of the abrasive particles. Coarse abrasives are more likely to fracture than fine abrasives, partly due to a decrease in tensile strength with increasing particle size. In addition, fracture of the abrasive can regenerate sharp facets and produce loose abrasive fragments, which in turn increase wear rates. Loading conditions also have an effect, because increasing the contact stress between abrasive and wear material increases the probability of fracture of the abrasive particles.
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VOLUME WEAR RATE (ARBITRARY UNITS)
103
102
101
100
10-1
10-2 10-2 10-1 100 101 HARDNESS OF WORN SURFACE / HARDNESS OF ABRASIVE
FIGURE 35.7 Effect of abrasive hardness on wear behavior of metals and ceramics. (From Moore, M.A. (1981), Abrasive wear, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, Metals Park, OH, 73-118. With permission.)
35.5.1.2 Contact Conditions It is difficult to assess the effects of individual contact conditions on the wear interactions between abrasive and wear material because their effect is synergistic in nature. Force, impact level, velocity, and impingement angle combine to influence the wear rate of the material. Increasing the contact stress between the abrasive and the wear surface results in greater indentation depths and an increased tendency for fracture and fragmentation in both brittle wear materials and abrasives (Richardson, 1968). This generally leads to increased wear rates, although exceptions can occur if the abrasivity of particular minerals decreases with failure of the abrasive particle. The effect of nominal contact stress on the relative abrasion rating of a range of metallic materials is shown in Figure 35.8. The general effect of increasing nominal contact stress levels is to increase wear rates. However, the occurrence of significant impact during the abrasive/wear material contact can also accelerate the rate 100
INCREASING ABRASION RESISTANCE RELATIVE ABRASION RATING
QT PLATE STEELS
0 ABRASION TYPE
QT PLATE STEELS
CAST MARTENSITIC STEELS AUSTENITIC MANGANESE STEELS
QT PLATE STEELS
CAST MARTENSITIC STEELS
CAST MARTENSITIC STEELS
QT PLATE STEELS
AUSTENITIC MANGANESE STEELS
ALLOY CAST IRONS
CAST MARTENSITIC STEELS
CrC HARDFACING
AUSTENITIC MANGANESE STEELS
AUSTENITIC MANGANESE STEELS
ALLOY CAST IRONS CrC HARDFACING
ALLOY CAST IRONS AND CrC HARDFACING
ALLOY CAST IRONS AND CrC HARDFACING
GOUGING
HIGH STRESS
HIGH STRESS
LOW STRESS
ABRASIVE HARDNESS
800-1000HV
1800-2000HV
800-1100HV
900-1300HV
ABRASIVE SHAPE
ANGULAR
ANGULAR
ANGULAR
ROUNDED
NOMINAL STRESS
250 MPa
2.1 MPa
2.1 MPa
0.6 MPa
FIGURE 35.8 Effect of nominal contact stress on relative abrasion rating of metallic wear materials. (From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.)
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INCREASING WEAR RESISTANCE EROSIVE WEAR
CERAMICS WHITE CAST IRONS
RUBBER
TOOL OR BEARING STEEL MILD STEEL
IMPACT VELOCITY
FIGURE 35.9 Effect of impact velocity on erosive wear. (From Lansdown, A.R. and Price, A.L. (1986), Materials to Resist Wear, A Guide to their Selection and Use, Pergamon Press, Sydney, Australia. With permission.)
of material removal. This acceleration results from the increased amount of kinetic energy dissipated during contact. This energy can arise either from the moving abrasive particles, or from the moving wear surfaces, as in the case of impact crushers. For brittle materials, increased fragmentation occurs under impact conditions, whereas elastomers may only suffer an increase in cutting and tearing modes, associated with insufficient elastic recovery. The nominal force level can also determine the level of constraint experienced by abrasive particles. Under low-stress abrasive conditions, the abrasive particles can be free to rotate as they move across the surface of the wear material, and are less likely to indent and scratch the surface. The tendency for the abrasive particle to rotate also depends on the abrasive particle shape, with angular particles being more likely to slide rather than roll. Increasing the nominal force acts to constrain the abrasive particle in its orientation to the wear surface, thereby increasing the wear rate. The effect of velocity on wear behavior is associated with the dissipation of kinetic energy during abrasive/wear material contact. For a large number of abrasive wear environments, the velocity of abrasive particles is relatively low (<10 m/s), and therefore of little importance. However, in slurry pumps (i.e., the transport of abrasive particles in slurry or pneumatic form), the effect of velocity is significant. Under these conditions, the wear rate is proportional to velocity (W ∝ Vn, where W is the wear rate, V is the velocity of the abrasive, and n is a constant for the abrasive/wear material synergism). The value of n falls in the range of 2 to 3, although the exact value for any particular condition is dependent on the properties of both the abrasive and wear material, and on the angle of impingement (Mutton, 1988; Hutchings, 1992; Kosel, 1992). For softer abrasives, n tends to increase with decreasing abrasive particle size. For brittle materials and high impingement angles, the value of n tends toward the higher extreme. In erosion, a change in abrasive impact velocity can lead to a change in the dominant wear mechanism (Lansdown and Price, 1986), resulting in a change in wear rate. Higher values of n are associated with increased cutting and fragmentation. Figure 35.9 depicts the effect of erosive particle velocity on the wear of a range of materials. The influence of impingement angle on wear depends on the properties of the wear material, and is associated with changes to the dominant wear mechanism. At high impingement angles (60 to 90°), brittle materials typically experience elevated wear rates, resulting from increased fragmentation and spalling. Conversely, elastomers are more effective under these conditions because much of the impact energy can be dissipated through elastic deformation. At low impingement angles (10 to 30°), elastomers cut and tear more readily, leading to increases in wear rates. Hard, brittle materials usually perform better under these conditions. For materials intermediate in their mechanical properties (e.g., some metals), the effect of impingement angle depends on the ductility of the material (Lansdown and Price, 1986). The effect of impingement angle on the erosive wear behavior of a number of materials is shown schematically in Figure 35.10.
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INCREASING WEAR RESISTANCE EROSIVE WEAR
CERAMICS
WHITE CAST IRON TOOL OR BEARING STEEL MILD STEEL RUBBER
00
300 600 IMPACT ANGLE
900
FIGURE 35.10 Effect of impingement angle on erosive wear. (From Lansdown, A.R. and Price, A.L. (1986), Materials to Resist Wear, A Guide to their Selection and Use, Pergamon Press, Sydney, Australia. With permission.)
35.5.1.3 Properties of the Wear Material The properties of the wearing material that influence wear behavior are grouped into the following categories: mechanical properties, microstructure effects, and other properties (corrosion resistance, friction, thermal effects). Because abrasive wear is primarily a mechanical process, particularly in the absence of corrosive environments, mechanical properties are of major importance, whereas the role of microstructure depends upon the severity of the wear environment. The following discussion is patterned after the approach of Moore (1981) and Mutton (1988). 35.5.1.3.1 Mechanical Properties The resistance to indentation (hardness) is an important variable in determining abrasion resistance. Laboratory wear tests indicate that the abrasive wear resistance for particular material types increases with increasing hardness (Figure 35.11). However, large differences in abrasion resistance can also occur at similar hardness levels. These differences arise from variations in the plastic flow characteristics of the various materials, which in turn influence the predominant wear mechanism (Zum Gahr, 1987). The general relationships between abrasion resistance and hardness for plowing and fragmentation are similar to those shown in Figure 35.12 for pure metals and ceramics. In the absence of fragmentation, plowing and cutting involves plastic flow of the wear material either in front of, or to the sides of, the indenting abrasive particles. The plastic flow behavior of the material can be characterized by the ratio E/σy , where E is the elastic modulus and σy is the flow stress of the non-work-hardened material.
ls bc c ee An
ne
ale d
St
Martensite + Retained Austenite
Austenit ic
High Cr-Mo
Ma r tens itic White Cast
Heat Treated Steels
Iron
e
M
et a
ls an d
Increasing Carbon Content
Cold Worked Metals
ing Precipitation Harden Polymers
Pu r fcc
ABRASIVE WEAR RESISTANCE
Pin Abrasion Test, Silicon Carbide
ics
Ceram
BULK HARDNESS
FIGURE 35.11 Abrasion resistance vs. hardness for various material types in high-stress abrasion tests. (From Zum Gahr, K.H. (1987), Microstructure and Wear of Materials, Elsevier Science, Amsterdam, The Netherlands. With permission.)
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CUTTING PLOUGHING
PROPORTION OF GROOVE VOL, REMOVED
0.8 0.7 0.6
E/σ
y
0.5 0.4
HARDNESS
0.3 0.2 0.1 0 0
200
400
600
HARDNESS AND E/σy
800
FIGURE 35.12 Influence of hardness and E/σy on dominant wear mechanism. (From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.)
Decreasing E/σy favors a cutting mechanism, in which a high proportion of material is removed as microchips. Increasing the hardness of the wear material will have a similar effect, as shown in Figure 35.12. Although Figure 35.12 indicates that changing E/σy can significantly affect the dominant wear mechanism, its impact on wear resistance is not as clearly established. For a constant value of E, a decrease in σy favors plowing, which should lead to lower material wear rates. However, decreasing σy also decreases hardness, which favors greater depths of indentation and a reduction in the wear resistance of the material. For materials of equivalent hardness, the general trend is for wear resistance to increase with higher E/σy values (Moore, 1981). The wear material properties discussed thus far (i.e., hardness, elastic modulus, and flow strength) relate to material behavior at relatively low strains. For example, the plastic strain produced by indentation hardness testing of metals is typically between 8 and 10%. During the abrasive wear process, the extent of plastic strain experienced by a worn surface may approach these values. For these cases, the behavior of the wear material at high plastic strains is important, and here high values of the work-hardening coefficient and ductility are favorable. Tensile strength and ductility are also important mechanical property parameters in a wear environment, especially for polymers, which undergo elongations-to-fracture approaching 500%. Laboratory wear studies indicate that the wear resistance of both rigid and ductile polymers is roughly proportional to the work of rupture, which is defined as the product of the rupture stress and elongation-to-fracture. The abrasion resistance of polymers also increases with increasing indentation resistance, although this relationship is not as well-defined for polymers as it is for metals and ceramics. This is due in part to the visco-elastic nature of polymer deformation behavior. In addition, the absolute hardness levels for polymers are much lower than those for metals and ceramics. For elastomeric materials such as natural rubbers and polyurethanes, the deformation behavior during abrasive wear may be entirely elastic, in which case resilience or hysteresis loss is important. High resilience favors increased abrasion resistance, while increasing hysteresis losses under high impact levels results in material breakdown, exacerbated by heat buildup. For materials that undergo wear by fragmentation, abrasion resistance varies with fracture toughness. However, the contribution from microcracking and fragmentation depends on the severity of the wear environment, in particular the applied load and abrasive particle size. For metals and ceramics, the general form of the relationship between wear resistance, hardness, and fracture toughness (Kc) is illustrated in Figure 35.13 (Zum Gahr, 1978). For low fracture toughness materials (Kc < 14 MPa m1/2), wear resistance increases with increasing fracture toughness, despite a
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FRAGMENT
CUTTING/ PLOUGHING INCREASING APPLIED LOAD, ABRASIVE SIZE, HARDNESS AND ANGULARITY WEAR RESISTANCE
HARDNESS
FRACTURE TOUGHNESS, Kc
FIGURE 35.13 Schematic relationship between wear resistance, hardness, and fracture toughness. (From Zum Gahr, K.H. (1987), Microstructure and Wear of Materials, Elsevier Science, Amsterdam, The Netherlands. With permission.)
marked decrease in hardness. This increase in wear resistance results from a reduction in the fragmentation contribution to the total wear rate. For materials with high fracture toughness, wear occurs by cutting and plowing only, and hence the wear rate is controlled by the indentation resistance. In this case, the wear resistance decreases with decreasing hardness. The transition from fracture (fragmentation) to plastic deformation (cutting and plowing) is dependent on the critical groove size (pcrit) and the contact stress. These parameters, in turn, also depend on the ratio of fracture toughness to hardness (Kc /H). From Figure 35.13, maximum abrasion resistance is obtained by optimizing the ratio Kc /H, while maintaining the indentation hardness or groove size slightly below that at which the transition to fragmentation occurs (Moore, 1981). Increasing the severity of the wear environment, by increasing either the applied load, or the size, hardness, or angularity of the abrasive particles, shifts the transition from fragmentation to cutting/plowing to higher values of fracture toughness (Figure 35.13). This results in a decrease in the maximum wear resistance.
3.0 BAINITIC STEELS (AUSTEMPERED)
AUSTENITIC ALLOYS
QUENCHED AND TEMPERED STEELS
2.0
T
N
TE
N
O
Y LO
G
C
AL
N
SI
EA
R
C
IN
COLD WORK
INCREASING CARBON CONTENT
RELATIVE WEAR RESISTANCE (PURE IRON = 1.0)
35.5.1.3.2 Microstructure Microstructural effects on abrasive wear depend on the overall magnitude or scale of the wear environment. For high impact loads, large abrasive particle size, etc., the size of the microstructural features is generally much smaller than that of the abrasive wear damage. In this case, the role of microstructure on wear resistance is limited to its effect on bulk mechanical properties. Abrasive wear rates, particularly for materials that exhibit homogeneous microstructures, may correlate with bulk hardness (Moore, 1981). Figure 35.14 shows the effect of microstructure and hardness on the high-stress abrasion resistance of
PEARLITIC STEELS 1.0 100 200 300 400 500 600 700 800 900 1000 VICKERS HARDNESS
FIGURE 35.14 Effect of microstructure and hardness on the abrasion resistance of steels: high-stress abrasion, alumina abrasive. (From Moore, M.A. (1981), Abrasive wear, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, Metals Park, OH, 73-118. With permission.)
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RELATIVE ABRASION RESISTANCE
PLOUGHING/ CUTTING
FRAGMENTATION
INCREASING CARBIDE HARDNESS
0
40 20 CARBIDE VOLUME FRACTION (%)
60
FIGURE 35.15 Influence of microstructure on abrasive wear behavior of alloy white irons and chromium carbide materials. (From Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia.)
steels. Over a limited hardness range (200 to 300 Vickers or 2.0 to 3.0 GPa), relative abrasion rate decreases in the order (Moore, 1981):
austenite > bainite > pearlite > martensite This effect can be attributed to the influence of microstructure on plastic deformation behavior. However, bainitic and martensitic microstructures offer greater abrasion resistance at higher hardness levels (>400 Vickers or 4.0 GPa). At lower loads, and with smaller abrasive particle sizes, microstructural features are more effective as discrete components, and the mechanical properties of individual phases assume increased importance. This occurs when the size of the microstructural features is approximately equal to, or larger than, that of the abrasive. Under these conditions, materials with duplex microstructures (e.g., alloy white irons and some ceramics) are more sensitive to microstructural effects. In such materials, size, spacing, and volume fraction of the harder phase, as well as the mechanical properties of both hard and soft (matrix) phases, can significantly affect wear behavior. Abrasion resistance can either increase, decrease, or remain the same by increasing the volume fraction of the harder phase. The net effect depends on the various contributions of the plowing, cutting, fragmentation, and pull-out mechanisms to the total wear rate. Figure 35.15 shows schematically this behavior for alloy white irons and alloy carbide materials. The transition from increasing to decreasing abrasion resistance with increasing carbide volume fraction is associated with the relative contributions of fragmentation of the carbides, and plowing/cutting of the matrix, to the total wear. Carbide hardness and size relative to that of the wear damage will also influence these trends (Zum Gahr and Doane, 1980; Moore, 1981). 35.5.1.3.3 Other Properties Wear processes that involve plastic deformation (i.e., cutting and plowing) also generate significant increases in temperature at the wearing surface. These increases occur as a result of frictional energy dissipation at the interface between the wearing surfaces. Under these circumstances, the wear behavior is influenced by characteristics such as the friction coefficient and thermal conductivity of the two wear bodies. In materials that exhibit low values of thermal conductivity, one of two additional effects can arise, depending on other material properties. Localized thermal expansion in ceramics can result in additional material loss by spalling; conversely, localized temperature increases in polymers can give rise to melting. Materials that exhibit low friction coefficients under dry sliding conditions (e.g., some polymers and finely ground ceramics) will suffer less degradation through frictional temperature rise effects.
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35.6 Tribological Losses in the Mining of Metallic Ores, Coal, and Non-metallic Minerals Mining operations can be broadly classified into the exploration, extraction, and beneficiation of minerals. Differences in the equipment and technology used in mining depend on the mineral’s proximity to the surface, the characteristics of mineral formation, and the intended downstream use of the product. For example, the proximity of the mineral to the surface will determine whether the mineral-bearing ore is extracted by surface mining, shaft mining, or drilling. Seam dimension and orientation will affect the selection of the “digging” equipment. Beneficiation operations will depend on the mineral concentration in the ore body, the surrounding gangue material, and the product form required in downstream operations. Mineral extraction includes those processes related to digging, loading, and transporting the ore. Digging machinery is needed to access and remove the mineral-bearing ore from its environment. Draglines, power shovels, and bucket-wheel excavators are used in surface mining operations. Removing especially hard ore bodies requires substantial drilling and blasting. The loose ore body is then transported to either intermediate storage facilities or beneficiation facilities by trucks, conveyors, or railcars, depending on the terrain and transportation distance. Shaft mining requires specialized compact equipment, which is usually operated continuously. In these operations, continuously rotating teethed surfaces cut away material from the ore-bearing deposit, with the loose ore then transported by conveyor to an intermediate storage facility. Beneficiation includes those activities that increase the concentration of the desired mineral or improve its form. Typical beneficiating activities include grinding, screening, washing, and flotation. Gravitational and magnetic separation are also used to separate materials. Some ores can be leached with acids to remove the desired mineral if physical separation techniques are impractical. The two major methods of extracting ores, minerals, and coal are surface mining and shaft mining. The equipment used in these two processes are quite different and distinct; however, five common process steps are utilized in both methods: exposing, digging, loading, transporting, and ore processing. The information on tribological losses in the following sections derives from the ECUT report by Imhoff et al. (1985) entitled “A Review of Tribological Sinks in Six Major Industries.”
35.6.1 Surface Mining Surface mining operations are typically in the form of open pit or strip mines, where the valuable mineral ores must first be exposed through the removal of the overburden. Substantial drilling and blasting are needed to loosen the ore from the surrounding rock strata. Power shovels and draglines are used to scoop up the loose ore for loading and transporting to the ore processing facility, which is typically in close proximity to the mining operations. Surface mining operations are huge, covering tens to hundreds of square kilometers. During the lifetime of an open pit mine, tens of thousands of tonnes of ore are extracted from the earth and processed for the valuable mineral component. The next few sections discuss the various operations used in surface mining. 35.6.1.1 Exposing and Digging The surface mining of most materials requires that the overburden be removed to reveal the ore body. The overburden may be as slight as a few feet of loose soil and rock, or as troublesome as solid veins of rock. In surface mining operations, overburden removal is typically accomplished using either draglines, power shovels, or bucket-wheel excavators. The operating principles of these three techniques are very different; however, their tribological losses are very similar. These tribological losses are also common to other forms of digging and excavation equipment. The components that cause the greatest tribological losses (i.e., wear, friction, and reduced work capacity) for draglines, power shovels, or bucket-wheel excavators are: use of digger lubricant; wear of digger/bucket teeth, bucket liners, and wear plates; carryback (i.e., material stuck in the buckets of the diggers after dumping); and wear and fatigue of wire rope.
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TABLE 35.7 Direct and Indirect Tribological Energy Losses for Digging and Exposing in Surface Mining Operations Wear Part Digger lubricant Bucket teeth and liners Carry-back Wire rope
Direct Losses (108 kW-h/year)
Indirect Losses (108 kW-h/year)
— 1.10 13.50 Small
0.85 0.75 — 20.50
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
TABLE 35.8
Yearly Lubrication Used in Draglines (103 liters) Bucket Capacity
Lubrication Type Multipurpose grease Open-gear grease Wire rope lubricant Gear case oil Walking cam lubricant (on machines > 35 m3)
23 m3
115 m3
7.6 3.4 1.1 2.5 —
11.4 6.6 2.3 13.2 12.3
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
Table 35.7 presents data on the direct (i.e., energy losses due to friction) and indirect (i.e., material loss due to wear processes) tribological losses in surface mining operations. Tribological losses due to friction (1.5 × 109 kW-h) during digging and exposing are approximately four times higher than material losses due to wear (0.4 × 109 kW-h). Lubricant losses arise from the need to keep the machinery in good operating condition. The common lubricants used in draglines are multipurpose grease, open-gear grease, wire rope lubricant, gear case oil, and walking cam lubricant. The amount of lubricant consumed in typical draglines is shown in Table 35.8. Loss of bucket teeth and wear liners from abrasion is routine in surface mining operations. The life of bucket teeth and wear liners is strongly dependent on the type of overburden and ore being excavated. Table 35.9 gives an estimate of typical blade life under various digging conditions. In general, blade life varies from a minimum of 15 minutes for moving blasted rock, hardpan, or other hard, blocky material, to a maximum of 6 to 9 months for moving loose, soft, free-running materials (i.e., soil and small gravel). It is estimated that 6350 kg of replacement steel for bucket teeth and liners are used per bucket every 6 months. Carry-back leads to the largest tribological energy losses during exposing operations, resulting from the combined effects of lifting useless weight and reduced bucket capacity. The extra useless weight consumes energy above that needed to move the empty bucket, while the reduced carrying capacity of the bucket means additional bucket passes will be needed to remove a fixed amount of material. The degree of carry-back is influenced by the type and moisture content of the material removed. Wire ropes used in diggers for hoisting typically fail from fatigue or fretting fatigue. The drag ropes used in draglines suffer from abrasive wear and corrosion. 35.6.1.2 Loading At some point in the mining operation, the material must be handled by some type of loader having a bucket capacity in the range of 7 to 15 m3. Loaders simply load material that has been piled or exposed by one of the large diggers, into a truck or onto a conveyor system. Tribological losses in loading
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TABLE 35.9
Blade Life Under Various Digging Conditions Ease of Digging
General material description
Specific material names
Blade life
Easy
Medium
Hard
Rock
Loose, soft, free-running materials Close lying, which will fill dipper of bucket to capacity and frequently provide heaped load Overload compensates for swell of materials Dry sand or small gravel Moist sand or small gravel Loam Loose earth Sandy clay Loose clay gravel Cinders or ashes Bituminous coal Very well-blasted material
Harder materials that do not require blasting, but break up with bulkiness, causing voids in dipper or bucket
Materials requiring some breaking up by light blasting or shaking. More bulky and somewhat hard to penetrate, causing voids in dipper or bucket
Blasted rock, hardpan, and other bulky materials, which cause considerable voids in dipper or bucket and are difficult to penetrate
Clay, wet or dry Coarse gravel Clay gravel, packed Packed earth Anthracite coal
Well-broken limestone, sand rock, and other blasted rocks Blasted shale Ore formation (not of rock character) requiring some blasting Heavy, wet, sticky clay Gravel with large boulders Heavy, wet gumbo cemented gravel
Hard tough shale Limestone Trap rock Granite Sandstone Taconite Conglomerate Caliche rock Any of these blasted to large pieces mixed with fines and dirt Tough, rubber clay that shaves from bank 15 minutes
6 to 9 months
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
equipment are a consequence of abrasion, and are directly related to the abrasive nature of the material being moved. This wear affects the carriages, tires or treads, and buckets and blades. The tribological losses are very similar to those previously discussed for digging operations. The same life expectancies and observations are applicable (see Table 35.9) to a loader’s teeth inserts, blade inserts for scrapers and dozers, ripper blades that break up the soil, and wear plates for buckets. 35.6.1.3 Transporting Transporting activities in mining and minerals processing can be divided into three main categories: trucks, conveyors, and railcars. Trucks are the predominant means of transporting large quantities of materials (70%) to intermediate storage facilities or mineral processing operations. They are a very flexible transportation system, capable of climbing the steep ramps found in surface mining operations. However, trucks require good roads to minimize tire wear and subsequent replacement, and are limited by economic considerations to an operating radius of approximately 5 km. Tire wear represents approximately 30% of the total operating costs of a truck. Tire life is influenced by such factors as tire inflation, speed, curves in the load and dump cycle, road surface, total load, wheel position on the truck, and road grade. In general, depending on the capacity of the truck and the road conditions, the lifetime of a tire is typically between 3000 and 6000 hr. Belt conveyors are economical for high-volume, long-distance hauling of medium-sized particulate matter, and are advantageous for haulage distances over 3 km. These conveyors can handle grades up to 40%. Unlike trucks, conveyors typically only handle small chunks of material. On the other hand, hydraulic systems can be used to move slurries of sand, gravel, kaolin (clay), and phosphates. Hydraulic conveying may involve the pumping of slurry mixtures cross-country in a pipeline. This method is the dominant mode of transfer of small particulates; however, the total volume conveyed is small when compared to the total amount of material conveyed by conventional methods. Tribological losses in conveyor systems are caused by many sources, such as friction in the pulleys, friction in the belt riding over the pulleys, and skirtboard friction from the conveyed material rubbing against the sides of the
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conveyor. The direct tribological frictional losses have been estimated to be 200 kW-h per 2000 tonnes per 1000 horizontal meters conveyed. This number is calculated based on the assumption that 20% of all surface mined material is transported an average distance of 5200 m. Railcars are similar to conveyors in that they handle large volumes of material over long distances. Unlike conveyors, they can handle coarse, blocky materials. However, railcars have a high capital cost and are limited to grades of 3% when fully loaded. The transportation of large quantities of material using railcars is declining today for several reasons. Primarily, the processing of the ore is done near the mining operation, negating the need for railcars to convey material long distances. Additionally, trucks and belt conveyors are more economically feasible and require less overall initial capital investment.
35.6.2 Shaft Mining and Drilling Shaft mining differs from surface mining in that there is no need to remove large amounts of overburden to reach the mineral ore body, and there is no need to load the material to convey it. In shaft mining operations, the deposit of coal, ore, or mineral is removed by a continuous mining system. Generally, the continuous miner has an assembly that rotates against the mine wall surface, removing chunks of material with its cutter teeth. The material is then simultaneously gathered, partially crushed, and fed onto an attached conveyor. The conveyor carries the material to either a dumping station or to the surface. The tribological losses for continuous mining systems are summarized in Table 35.10. Typically, about 360 million tonnes of ore are mined by this method each year (270 million tonnes of coal, 65 million tonnes of copper, 18 million tonnes of potash, and 4.5 million tonnes of iron ore). As seen in Table 35.10, primary material losses occur through lubricants and cutter teeth replacement. Direct tribological losses occur through frictional sinks in the conveyor system. Many types of hydraulic equipment are used in shaft mining. Roof bolters, roof support jacks, drills, loaders, and continuous miners all use hydraulics. Much of the lubricant loss occurs through the improper selection and maintenance of lubricants. Lubricant contamination by dust is a major cause of wear in hydraulic machinery, bearings, and gearing in the mining industry, because a contaminated fluid carries particles that accelerate wear through abrasion that the lubricant was originally intended to combat. In some mines, the lubricant is deliberately contaminated with water to reduce fire hazards, thereby increasing the wear in hydraulic systems. In addition to the wear caused by intentionally and unintentionally contaminated lubricants, the loss of lubricant through seal leakage is also great. In long-wall cutter operations, lubricant leakage may reach 19,000 L/day. Tribological losses from the cutter system occur in the cutter teeth, chassis bottom, propulsion treads, and conveyors. Of these, the cutter teeth and conveyor experience the most significant wear. For example, a cutter bit will have to be replaced for every 5 tonnes of ore processed, when rock is encountered. When cutting pure coal, potash, soda ash, or salt, one cutter bit will need to be replaced for every 20 tonnes of material processed. In making these types of calculations, the same conditions and assumptions discussed for surface mining also hold for shaft mining, except the average distance that the mineral is conveyed in shaft mining is 3650 m. Drilling is another route by which minerals are extracted from the earth. The major tribological losses from drilling operations occur with the mud pump and mud pump liners, mud lubricant/coolant, drill TABLE 35.10
Tribological Losses in Shaft Mining Operations
All types of lubricants Cutter drum parts (primarily teeth inserts) Conveyors
Direct Tribological Losses (kW-h/year)
Indirect Tribological Losses (kW-h/year)
— Small 7.0 × 107
1.1 × 109 2.1 × 109 —
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
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TABLE 35.11 Component Name Mud pump Liner Piston Mud Drill pipe Drill bits
Tribological Losses for Drilling Components
Embodied Materials 70 kg of chromium cast iron per liner 1.1 kg of rubber per piston Asphalt and diesel fuel (oil-based muds onlya) 250 kg of alloy steel or 150 kg of aluminum per drill pipe Inserts of diamond and/or tungsten carbide in 20 kg alloy steel baseb
Indirect Tribological Loss (106 kW-h/year)
Direct Tribological Loss (106 kW-h/year)
5.5 2.0 1376.5 76.0 18.0
— — — 126.0 41.0
a
Approximately 20% of wells drilled in U.S. use oil-based mud. From increased torque or time requirement due to worn bit. From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA. b
pipe, and cutting bits. The tribological losses for drilling components are shown in Table 35.11. Most material loss in drilling operations occurs with the drill string assembly and the cutter bits. The drill pipe that makes up the drill string is attacked by a variety of mechanisms, both tribological and otherwise, which result in indirect loss of drill pipe components and eventually the entire drill pipe. The major causes and sites of tribological attack of the drill pipe are the following: uniform abrasive wear of the outside surface as it rubs against hard formations during drilling, and localized (improperly sealed threads and damaged joints) and uniform (outside surface) erosion due to the high-pressure flow of drilling mud. Although filtered, the drilling mud retains fine particles of rock from the drilling operation, which increases the severity of the abrasive action. These tribological actions serve to reduce the load-carrying capacity of the pipe by reducing overall wall thickness and preferentially weakening threaded, joined sections. Causes of attack by nontribological mechanisms include localized galvanic corrosion and metal fatigue. Galvanic corrosion occurs in dents and scratches along the outside pipe surface, which is accelerated by the wear processes described above (and very similar to slurry erosion-corrosion observed in piping). Drilling lubricant (mud) often contains corrosion inhibitors, but the pipe may rust while standing in air. Metal fatigue of the drill string occurs as it is rotated and twisted within the narrow and crooked confines of the hole. Fatigue failures often occur at the stress risers caused by any of the aforementioned mechanisms. Drill bits are divided into two main categories: rolling cutter bits and drag, or shear, bits. The basic design difference is that the rolling cutter bits generally have three cones supported by bearings, whereas the shear bits are rigidly fixed to the drill string (Anderson, 1974; Coffman and Conners, 1974; Perrott, 1979). Currently, rolling cutter bits account for 90% of the market (Imhoff et al., 1985). Rolling cutter bits consist of three alloy steel cones, each having rows of cutting teeth. The teeth can be composed of a solid hard material or a diamond or carbide insert, or can be studded with wearresistant inserts. The rollers are supported with both radial and thrust bearings. Rolling cutter bits typically fail because of seal failures, which lead to bearing failures, wear of the inserts and supporting material, and occasionally, fracture of a cone or erosion of the steel that supports the insert. In as many as 80% of the cases, bits fail in the bearing seals, allowing the drilling mud to abrasively destroy the bearing. The bearing seals are weakened by extreme pressure, high temperatures from geothermal and frictional heating, chemical attack from corrosive deposits drilled, or simply abrasive attack by the drilling mud. Bits that do not fail from the above processes typically wear out from three-body abrasion. Shear bits in current use consist of polycrystalline (man-made) diamonds mounted in tungsten carbide inserts that rest in a ferrous alloy body. The main cause of failure of these bits derives from three-body wear. The ferrous alloy surrounding the cutting diamond-tungsten carbide insert is worn away, allowing the inserts to be lost. Under extreme mud pressure and velocities, the surrounding metal can also erode. However, the primary wear mechanism is the extreme abrasive conditions that exist at the bottom of the hole.
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The condition of the drill bit directly affects the direct energy (friction) losses in the drill string. If a bit is worn, the drilling rig operator can either allow reduced penetration rates or raise the drill string load and resulting torque to maintain a given drilling rate. In either case, energy is wasted due to the worn bit. In the first instance, if the bit penetration rate is reduced 50%, the drill string will have to turn twice as long, and all the energy consumed during the longer drilling time is the direct result of reduced bit performance. If the drilling load and torque are raised, the additional torque requirement represents a direct energy loss. Consequently, the rate of penetration and the drilling torque are two of the drilling parameters monitored and used to determine when the drill string should be pulled to change bits.
35.6.3 Ore Processing and Related Activities The processing of the ore through grinding (e.g., milling, pulverizing, etc.) materials results in significant direct and indirect tribological losses. Although the phrase “ore processing” can be used to describe the processing of a large range of materials, this discussion focuses on the processing of metal ores because of the large tonnages involved and the typically high abrasiveness of metal ores. Ore processing components that experience significant tribological losses include the following unit operations: crushers, grinding mills, slurry pumps, and cyclone separators. Of these processing components, grinding mills represent the largest tribological sink. Table 35.12 shows some typical wear rates for the unit operations listed above during the processing of high-silica, low-grade copper, molybdenum, and taconite iron ores. For other industries (e.g., cement or coal processing), where the abrasive mineral is much softer (except pyrite in coal), the wear rates will be much lower. Typically, impact hammers experience the highest wear rates, due in large part to the tremendous energy of the impacting blows. Impact hammers are not usually used on hard and abrasive minerals; this is the province of crushers. Operators of ore processing plants are concerned with wear in terms of the weight loss per tonne of ore processed, especially in crushing and grinding operations. In addition, the energy consumption per tonne of ore processed is also a major concern, especially in the design and construction of new processing plants. Over the years, it has become apparent that in any specific crushing and grinding operation, there
TABLE 35.12
Typical Wear Rates Normal to Wear Surface in Ore Processing
Ore Processing Application Austenitic manganese steel in gouging abrasion Impact pulverizer hammers Crusher liners for gyratory and coned crushers Lifter bars in semi-autogenous millsb Chute liners and screens for coarse ores Low-alloy, high-carbon steel in high-stress grinding abrasion Rod and ball mill liners (wet grinding) Grinding balls in ball mills (wet grinding) Large grinding balls in semi-autogenous millsc White iron in low-stress scratching abrasiond Sand pump impellers Agitator and flotation impellers Spiral classifier wear shoes a
Wear Ratea (µm/hr) 100–25,000 50–500 20–100 2–250 10–30 4–20 15–50 2–50 1–10 1–5
Wear rate is in terms of linear loss of material from the wear surface as a function of time. b Lifter bars mostly medium-carbon, low-alloy steel. c Rough estimate due to insufficient data. d Both pearlitic and martensitic white irons included. Norman, T.E. (1980), Wear in ore processing machinery, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, New York, 1009-1051. With permission.
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TABLE 35.13
Wear Rates per Tonne in Crushing and Grinding of Siliceous Ores Wear (grams per metric ton)
Ore Processing Application
Minimum
Maximum
Average
45 10 280 136 200 86 520 840 700 35 44 40 78
118 55 500 730 844 600 760 1070 1500 77 73 75 450
74 19 420 420 401 440 630 950 990 50 53 51 214
Liners in crushing taconite iron ores Liners in crushing Cu/Mo ores Rods in two-stage grinding of taconite iron ores Rods in two-stage grinding of Cu/Mo ores Balls in two-stage grinding of taconite iron ores Balls in two-stage grinding of Cu/Mo ores Balls in single-stage grinding of Cu/Mo ores Balls in crushing and grinding of taconite ores in semi-autogenous mills Balls in crushing and grinding of Cu/Mo ores in semi-autogenous mills Mill liners in two-stage grinding of taconite ores Mill liners in two-stage grinding of Cu/Mo ores Mill liners in single-stage grinding of Cu/Mo ores Mill liners in crushing and grinding; autogenous and semi-autogenous mills
Norman, T.E. (1980), Wear in ore processing machinery, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, New York, 1009-1051. With permission.
is a direct relationship between the amount of wear of the materials in that operation and the energy consumed by that operation. Therefore, by controlling the amount of wear in the various unit operations of an ore processing plant, the energy consumed can also be controlled. Table 35.13 provides some information on the wear that occurs per tonne of siliceous ore processed for some unit process operations. It can be seen from the wear losses in Table 35.13 that grinding media suffer the highest wear rates. The mill liners see much less wear per tonne of ore processed, unless the operation is performed in an autogenous or semi-autogenous mill. In this case, the mill liners experience higher wear than mill liners used in ball or rod mills. In the copper industry, one third of the total energy expended is used to concentrate the ores from typical values of 0.5% copper (as mined). Concentration is accomplished by crushing and grinding the mined ores into powder (85% passing –0.15 mm mesh) from which the gangue (rock and useless minerals) and metal are separated. This process requires about 6.4 × 103 kW-h per tonne of copper produced. Of this energy consumption, the following percentages are lost to friction in running the machinery: about 0.25% is lost in the mill support bearings; 1.5% is lost in the main gears; and up to 0.75% is lost in additional reducer gears when they are required. The total bearing friction losses in milling various metals were calculated assuming a total tribological loss of 1.75% (i.e., ignoring reducer gear losses). Table 35.14 lists the direct tribological energy losses during grinding that occurred in 1973 for the copper, aluminum, and iron industries. Approximately 4.4 × 108 kW-h were lost to friction. Table 35.15 shows the approximate wear rates for key ore processing steps. Wear of ore grinding equipment represents the largest indirect tribological loss in ore processing. This loss comprises an average TABLE 35.14
Direct Tribological Energy Losses in Grinding
Industry
Year
Grinding Energy (1010 kW-h)
Direct Tribological Portion of Grinding Energy (Bearing Lossesa – 107 kW-h)
Copper Aluminum Iron
1973 1973 1973
1.15 0.10 1.20
20.20 0.90 21.10
a Bearing losses in grinding equal 0.75% × grinding energy. From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
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TABLE 35.15
Wear Rates in Key Ore-Producing Steps
Process Step Crushing Screening Grinding Pumping Classifying Mineral separation
Wear Rate (gram metal/metric ton) 50 2 700 5 3 2
Data from Norman, T.E. (1980), Wear in ore processing machinery, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, New York, 1009-1051; Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
of 0.7 kg of iron alloy (grinding balls, rods, and liners) per tonne of ore or mineral processed. Alternatively, in milling coal for power plants, only about 2 g of steel is worn per tonne of coal produced. This difference in material consumption is a direct reflection on the abrasivity of the mineral being processed. Because this wear represents an embodied energy consumption of 9.3 × 103 kW-h per tonne of ore processed, the indirect tribological energy loss (i.e., wear) for ore grinding is estimated to be 7 kW-h per tonne of ore or minerals ground per year. Based on production figures for materials that are typically ground (iron ore, copper ore, clay, phosphate, and potash), the total tribological loss associated with wear from grinding is 6 × 109 kW-h per year. Crushing constitutes the second greatest source of wear in mineral processing, although the magnitude of loss is only about 7% as large as that for ore grinding per tonne. However, more minerals need to be crushed than ground. The total tribological loss associated with crushing is estimated to be 1.2 × 109 kW-h per year. The remaining areas where tribology influences ore processing are slurry pumps, screens, and cyclone separators. Slurry pump impellers and cases are subject to erosion and low-stress abrasion, and they require fairly frequent replacement. Generally, backup pumps are included to allow the system to continue operating during pump maintenance. Although wear of slurry pump components is significant to plant operations, it does not constitute nearly as much embodied energy as does wear of grinding mill media. Screens and cyclone separators are used to separate various size ranges of ores that are to be returned to the mill for further grinding. Although they do experience wear, the overall resultant material loss is not a major concern.
35.7 Financial Cost of Wear in Earthmoving, Mining, and Minerals Processing The overall cost of material degradation to the industrialized nations of the world has been the subject of a number of studies during the past three decades, and is included in reports to the Department of Education and Science, United Kingdom (DES, 1966); NMAB (1981) and ECUT (Imhoff et al., 1985), United States. The NMAB study (1981) estimated the overall annual costs of corrosion and fracture of materials to be equivalent to about 4% each the country’s gross national product (GNP). The cost of friction and wear is more difficult to assess, but it is generally thought to be roughly comparable to corrosion costs, making the total cost of materials degradation over 10% of a country’s GNP. It has been further suggested that 10% of all energy generated by man is dissipated by various friction processes (Rabinowicz, 1976). Maintenance, repair, and replacement of materials, including “downtime,” are responsible for a large portion of this cost. Design redundancies and excessive maintenance and inspection
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TABLE 35.16
Annual Direct Tribological Energy Losses in Mining
Operational Activity Surface mining Exposing and digging Loading Transporting Shaft Mining Digging Transporting Ore Processing Drilling Mud pumps Drill pipe Drill bits
Principal Energy Form Consumed
Energy Loss Rate
Total Energy Loss (108 kW-h)
Electricity Diesel Electricity
240 W-h/m3 4 W-h/m3 85 W-h/metric ton-km
— Electricity Electricity
— 85 W-h/metric ton-km 1.75% of grinding energy
— 0.70 4.20
— Diesel Diesel
— 1200 W-h/m drilled 400 W-h/m drilled
— 1.25 0.40
14.65 0.20 11.15
From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA.
TABLE 35.17
Annual Indirect Tribological Energy Losses in Mining
Operational Activity Surface mining Exposing and digging Loading Transporting Shaft mining Digging Transporting Ore processing Drilling Mud pumps
Material Wear Rate
Total Energy Loss (108 kW-h)
Steel Steel “Rubber”
30,140 metric ton/year 1950 metric ton/year 0.02 kg/m3
3.50a 0.20 35.15
Steel — Steel
0.41 kg/metric ton — 0.62 kg/metric ton
31.35a — 66.80
Cast iron, “rubber”
3.0 kg iron/1000 m 0.4 kg rubber/1000 m 10.9 kg steel/1000 m 6.4 kg alum/1000 m 102.7 kg steel/1000 m
13.80b
Material Type Worn
Drill pipe
Alloy steel, aluminum
Drill bits
Alloy steel
0.75 1.80
a
Total energy loss includes lubricant loss. Total energy loss includes drilling mud consumption. From Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL-5535, Pacific Northwest Laboratory, Richland, WA. b
to minimize accidents and product liabilities also contribute to the expense. It is estimated that 20 to 30% of materials degradation costs could be avoided by the use of known technologies and other preventive measures. Tribological energy losses — directly through friction (Table 35.16) and indirectly through wear (Table 35.17) — in the mining and minerals processing industries are a major cost factor (with an estimated equivalency to 15 × 109 kW-h of energy), accounting for about half of the nation’s wear losses in the industrial sector (Imhoff et al., 1985). Energy losses due to wear, resulting primarily from threebody abrasion, were five times greater than frictional losses. Wear losses are associated with the wearing out of equipment, as well as lubricant losses and drilling mud consumption. Table 35.17 highlights the generic tribological loss mechanisms in mining. The most significant material wear losses identified are iron and steel wear in ore processing, steel wear in shaft mining digging, and tire wear in surface mining.
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Carbon and low-alloy steels are the most common materials subjected to wear and also contribute the most to wear losses in the industry. Conversely, the energy needed to overcome friction between surfaces also contributes greatly to the tribological losses in these industries (approximately 3 × 109 kW-h). The most important direct energy losses are found in power shovels, draglines, and conveyors. Direct energy losses in mining are from the consumption of electricity and/or diesel fuel. Surface mining operations account for the two largest energy-consuming activities — exposing/digging of the ore and its transport. In this case, the largest direct loss is from electricity consumption. Each of these tribological sinks can be reduced through selection and utilization of the more wearresistant materials currently available, and through the design of more energy-efficient unit processing operations, especially grinding. Currently available materials, properly utilized for corrosion-wear applications, can also decrease material losses.
35.8 Concluding Remarks As long as there is a need to obtain minerals from the earth in order to further societal desires for valueadded goods, mining and minerals processing will continue unabated. As the quality of the mineral bearing ores decreases, there will be a driving force for larger scale mining operations, necessitating new and improved wear-resistant materials and more energy-efficient equipment to expose, extract, and process the ore. Therefore, applied research will continue in areas of equipment design, unit operating processes, wear-resistant materials, and repair and replacement techniques. Basic research will continue to be directed at understanding the wear mechanisms involved in abrasion, erosion, impaction, and wearcorrosion, particularly as they apply to the wear processes that occur in full-sized components. Only by understanding the relationship between wear mechanisms and operating equipment wear processes can small-scale laboratory wear tests be developed to simulate the requisite wear environment. Development of small-scale laboratory wear tests will enhance development of newer wear-resistant materials for these operations. Small-scale laboratory wear tests can be run in a shorter period of time and at a much reduced cost in terms of capital expenditure and labor. The effort that goes into understanding the relationships between wear mechanisms and wear processes in earthmoving, mining, and minerals processing also benefit other industries, because the basic tribological mechanisms are universal and are found in many different industrial processes (e.g., primary metals production, agriculture, pulp and paper processing, etc.). Understanding the nature of the wear mechanisms in the tribological environment will facilitate development of new wear-resistant materials, and hopefully lead to less expensive materials that are easy to install and repair in the field.
References Anderson, F.R. (1974), Modern materials for percussion drilling, in Materials for the Mining Industry, (R.Q. Barr, ed.), Climax Molybdenum Co., Greenwich, CT, 150-110. Austin, H.B. (1974), Technical developments of large wheel loaders affecting mining applications, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 133139. Avery, H.S. (1947), Hard surfacing by fusion welding, Monogram on Wear, American Brake Shoe Company, New York. Avery, H.S. (1958), Wear resistance, in Engineering Approach to Surface Damage, Lipson, C. and Colwell, L.V. (Eds.), University of Michigan Press, Ann Arbor, MI, 413-454. Avery, H.S. (1961), The measurement of wear resistance, Wear, 4, 427-449. Avery, H.S. (1968), Hardfacing Alloys, Technical Report C6-17.3, ASM, Metals Park, OH. Avery, H.S. (1974), Work-hardening in relation to abrasion resistance, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 43-77.
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Barr, R.Q. (Ed.) (1974), Materials for the Mining Industry, Climax Molybdenum Co., Greenwich, CT. Bauman, H.C. (1974), Engineering and material factors in increased availability for LHD’s, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 141-144. Bond, F.C. (1952), The third theory of comminution, Min. Eng., 4, 484-494. Bond, F.C. (1964), Lab equipment and test help predict metal consumption in crushing and grinding, Eng. Min. J., 165, 169-175. Chavanne, R.L. (1976), Thirty-five ways to improve hardfacing, Rock Products, 79, 76-77 and 100. Coffman, K.W. and Connors, J. (1974), Rolling cutter bit development and application in the mining industry, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 111-123. Dawson, R.J., Shewchuck, S., and Pritchard, J.E. (1982), Selection and Use of Hardfacing Alloys, in Intermountain Mineral Symposium, Barr, R.Q., Doane, D.V., and Miska, K.H. (Eds.), Climax Molybdenum Co., Greenwich, CT, 109-120. Department of Education and Science (1966), Lubrication (Tribology), Education and Research — A Report on the Present Position and Industry’s Needs, Her Majesty’s Stationary Office, London. Doennecke, H.C. and Shelton, J.A. (1974), Materials for the construction of haulage equipment for the mining industry, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 145-149. Dougall, J.R. (1974), An approach to mill liner materials for critical grinding service, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 169-172. Fabert, Jr., H.A. (1974), Manganese Steels in Crushing and Grinding Service, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 163-168. Farge, J.C. and Barclay, G.A. (1974), Properties and performance of cast iron grinding balls, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 189-199. Gill, C.B. (1991), Materials Beneficiation, Springer-Verlag, New York. Haworth, Jr., R.D. (1949), The abrasion resistance of metals, Trans. ASM, 41, 819-869. Hegmegee, Jr., P.E. (1974), Utilization and application of a superior abrasion resistant material for severe crushing application, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 201-205. Hickl, A.J. (1980), An alternate to cobalt-base hardfacing alloys, J. Metals, 32, 6-12. Horsfield, A.M. (1980), Weld surfacing processes, Weld Surf. Hardfacing, The Welding Institute, Cambridge, U.K., 32-39. Hutchings, I.M. (1992), Tribology: Friction and Wear of Engineering Materials, CRC Press, Boca Raton, FL. Imhoff, C.H., Brown, D.R., Hane, G.J., Hutchinson, R.A., Erickson, R., Merriman, T., Gruber, T., and Barber, S. (1985), A Review of Tribological Sinks in Six Major Industries, Technical Report PNL5535, Pacific Northwest Laboratory, Richland, WA. Kennedy, G.A. (1975), Welding Technology, Howard W. Sams and Co., Indianapolis, IN. Kosel, T.H. (1992), Solid Particle Erosion, in Friction, Lubrication, and Wear Technology, Blau, P.J. (Ed.), ASM International, Materials Park, OH, 199-213. Lansdown, A.R. and Price, A.L. (1986), Materials to Resist Wear, A Guide to their Selection and Use, Pergamon Press, Sydney, Australia. Moore, M.A. (1974), A review of two-body abrasive wear, Wear 27, 1-17. Moore, M.A. (1981), Abrasive wear, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, Metals Park, OH, 73-118. Murray, M.J., Mutton, P.J., and Watson, J.D. (1979), Abrasive Wear Mechanisms in Steels, in Wear of Materials, Glaeser, W.A., Ludema, K.C., and Rhee, S.K. (Eds.), ASME, New York, 257-265. Mutton, P.J. (1988), Abrasion Resistant Materials for the Australian Minerals Industry, Vol. 1, Australian Minerals Industries Research Association Limited, Melbourne, Australia. Nass, D.E. (1974), Steel grinding media used in the United States and Canada, in Materials for the Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 173-188.
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National Materials Advisory Board (1981), Comminution and Energy Consumption, NMAB-364, National Academy Press, Washington, D.C. Norman, T.E. (1974), A review of materials for grinding mill liners, in Conf. Mining Industry, Barr, R.Q. (Ed.), Climax Molybdenum Co., Greenwich, CT, 207-218. Norman, T.E. (1980), Wear in ore processing machinery, in Wear Control Handbook, Peterson, M.B. and Winer, W.O. (Eds.), ASME, New York, 1009-1051. Norman, T.E. and Hall, E.R. (1968), Abrasive Wear of Ferrous Materials in Climax Operations: Evaluation of Wear Testing, in ASTM-STP 446, ASTM, Philadelphia, PA, 91-114. Olson, D.L. and Mueller, W.M. (1977), Comprehensive Survey of Material Problems Associated with Welding in the Mining Industry, Final Report G0166160, Colorado School of Mines, Golden, CO. Olson, D.L. and Cross, C.E. (1992), Friction and Wear in the Mining and Minerals Industries, in Friction, Lubrication, and Wear Technology, Blau, P.J. (Ed.), ASM International, Materials Park, OH, 649-655. Osborn, A.J. (1973), Hardfacing in the mining industry, Australian Mining 65, 56-57 and 60-61. Perrott, C.M. (1979), Tool materials for drilling and mining, Ann. Rev. Mater. Sci., 9, 23-50. Rabinowicz, E. (1976), Gaps in Our Knowledge of Friction and Wear, in Materials Technology — 1976, Chynoweth, A.G. and Walsh, W.M. (Eds.), Amer. Inst. Physics, New York, 165-174. Richardson, R.C.D. (1967), The wear of metals by hard abrasives, Wear, 10, 291-309. Richardson, R.C.D. (1968), The wear of metals by relatively soft abrasives, Wear, 11, 245- 275. Rigney, D.A. (1981), Fundamentals of Friction and Wear of Materials, ASM, Metals Park, OH. Stoody (1998), The Rebuilding and Hard-facing of Earth-Moving Equipment, Bulletin 8203, Industry, CA. Zum Gahr, K.H. (1978), Relation between abrasive wear rate and the fracture toughness of metallic materials, Z. Metallkde., 69, 643-650. Zum Gahr, K.H. (1980), Optimizing fracture toughness and abrasion resistance in white cast irons, Metall. Trans., 11A, 613-620. Zum Gahr, K.H. (1987), Microstructure and Wear of Materials, Elsevier Science, Amsterdam, The Netherlands. Zum Gahr, K.H. (1998), Wear by hard particles, Tribol. Int., 31, 587-596.
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36 Marine Equipment Tribology 36.1 36.2
Introduction ................................................................... 1371 Marine Oil Properties and Chemistry.......................... 1371 Fuel and Oil Rheology and Chemistry • Environmental Concerns
36.3
Steven R. Schmid University of Notre Dame
Karl J. Schmid John Deere Corporation
Diesel Engine Lubrication ............................................. 1374 Slow-Speed Diesel Engines (<250 rpm) • Medium-Speed Diesel Engines (250 to 1000 rpm) • High-Speed Diesel Engines (>1000 rpm)
36.4 36.5
Steam and Gas Turbines................................................ 1380 Ancillary Equipment...................................................... 1381 Stern Tubes • Rigging Equipment • Pumps • Oil Maintenance Equipment
36.1 Introduction Marine equipment presents an extremely demanding environment to tribologists. While the machine elements and lubricants used are substantially the same as in other applications, some fundamental differences regarding the operating environment play a substantial role in their success. Chief among these are the chemical nature of the fuels used, the operating temperatures achieved, and the speed ranges commonly encountered. Also, a ship at sea may need to be totally self-sufficient for weeks at a time. One of the most demanding and exciting aspects of marine equipment design is the huge equipment scale. Small ships can use diesel motors of only a few horsepower compared to the largest aircraft carriers with nuclear reactors of sufficient capacity to power a medium-sized city. Very large thrust loads developed by propeller shafts must be efficiently transferred to the ship structure (and present perhaps the most common application of hydrodynamic thrust bearings). Cams, gears, chains, journal bearings, pistons, rolling element bearings, etc., are all found in marine applications. The basic theory for these machine elements is covered in other sections of this handbook and in a number of excellent reference texts, such as Hamrock et al. (1999), Shigley et al. (1989), and Juvinall et al. (1991). This chapter is intended as a broad overview of marine equipment tribology. It is not intended as a detailed investigation into individual machine elements or applications. Instead, this chapter focuses on the aspects of marine tribology that differentiate it from other applications.
36.2 Marine Oil Properties and Chemistry 36.2.1 Fuel and Oil Rheology and Chemistry In the past 15 years, diesel engines have exerted a dominance over other power sources in commercial ships and have displaced steam engines and steam and gas turbine engines to minor roles. Steam and 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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gas turbine engines are still very popular for warships, however. For economic reasons, ships are routinely powered by fuels with rather high viscosity in order to lower the fuel cost by reducing refining requirements. Pevzner (1998a) gives the general fuel oil types and their viscosities as follows: • • • •
Bunker (marine) fuel oils: viscosities between 380 and 700 cSt at 50°C Intermediate fuel oils: viscosities between 30 and 380 cSt at 50°C Marine diesel oils: viscosities between 11 and 14 cSt at 40°C Gas oil: viscosity less than 6 cSt at 40°C
The thicker fuels will not be easily pumped or atomized in the combustion chamber at ambient temperatures, and are therefore usually preheated to up to 130°C. The goal is to achieve a viscosity value near 20 cSt (Pevzner, 1998a). The drive toward high-viscosity fuels is an economic one because the thicker fluids undergo less refining and are therefore less expensive. There has been a considerable increase in the viscosity of fuels used in the past decade or so. As a comparison, Wilkison’s (1983) excellent overview of marine tribology restricted attention to fuel blends with viscosities up to 180 cSt at 50°C, while much more viscous fuels are routinely used today. The trend of ever-higher viscosity fuels has a serious shortcoming in that contaminants and increased acidity result. While sulfur is intentionally used in low concentrations as an extreme pressure additive for automotive lubricants, sulfur concentrations are sufficiently high in fuels to make sulfur corrosion an important concern. Sulfur content in some fuels can be over 4%,* leading to significant SO2 and SO3 combustion products, and a very acidic environment. Also, carbon particles can be suspended in the fuel, leading to fouling of cylinders and causing ring and piston sticking. In addition, abrasive particles are conveyed into the engine by the lubricant, so that abrasive wear rates are much higher than in other applications. Further, the thick fuels result in operating temperatures somewhat higher than normally encountered. The base stocks used in the lubricants have seen a drastic change in recent years. While naphthenic oils were dominant prior to the early 1980s, paraffinic base oils and synthetics are now totally dominant in the industry, mainly due to the need for higher viscosity indices (VI) associated with high operating temperatures. Oils with VIs in the 100 to 150 range are used, although specific values are manufacturer specific. A summary of selected available lubricants is given in Table 36.1. The chemical considerations of the fuel are overcome by formulating lubricants with specific additives, both to compensate for the acidic nature of the fuel and combustion products and to aid in lubrication. Alkalinity is reported in terms of a total base number (TBN) of milligrams KOH per gram and varies by application. While specific values depend on application, the TBN of low-speed diesels is roughly 70; that of medium-speed diesel engines is roughly 30; and that of high-speed engines is comparable to automotive oils (5 TBN or so). TBN plays a large role in a lubricant’s success. For example, Hellingman et al. (1982) showed that lubricants with TBNs of 100 reduce cylinder liner and top ring wear in low-speed diesel engines. Other additives include the typical blend of boundary additives, extreme pressure additives, defoamants, detergents, etc., but in higher concentrations than in automotive applications (Woodyard, 1990). Additive functions are discussed in the specific chapter sections for different classes of equipment.
36.2.2 Environmental Concerns Most of the harmful emissions from marine equipment arise from combustion products and contaminants, mostly sulfur in the fuels. While some lubricant is inevitably combusted,** the major concerns *Fuel sulfur content varies with the fuel source. Fuels with high sulfur content are known as “sour crudes,” while those with low sulfur content are “sweet crudes,” and fuels are sour or sweet depending on their source. This has led to quite a few detective quandaries, where cylinder liner wear will appear and disappear at apparently random times, when often they are attributable to the fuel used. Also, because the advantage of using high TBN oils vanishes with low sulfur content in the fuels, the lubricant TBN can be tailored to anticipated fuel quality. **Note that low-speed diesel engine cylinder lubricant is totally combusted, and contributes significantly to metal (Ca) emissions.
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TABLE 36.1
Properties of Selected Marine Application Low- and Medium-Speed Diesel Engine Lubricants Viscosity
Manufacturer
Designation
Low-speed diesel engines — crankcase Mobil Mobilgard 312 Mobilgard 412 Mobilgard 512 Texaco DORO AR 30 TARO 16 XD 30 TARO 16 XD 40 Low-speed diesel engines — cylinder Chevron Delo Cyloil Extra Delo Cyloil Special Delo Cyloil Heavy Mobil Mobilgard 570 Shell Alexia D Alexia Xb Texaco TARO 70 TARO 85 Medium-speed diesel engines Chevron Delo 1000 30 Delo 1000 40 Delo 1000 50 Delo 6170 CFOa Mobil Mobilgard 330 Mobilgard 430 Mobilgard 450a Shell Argina S 30 Argina S 40 Argina T 30 Caprinus HPD40a Texaco TARO 20 DP 30 TARO 20 DP 40 TARO 40 XL 40 a b
TBN (mg KOH/g)
Sulfated Ash (wt%)
SAE No.
cSt at 40°C
cSt at 100°C
Viscosity Index
30 40 50 30 30 40
103 141 199 111 98 139
11.4 14.4 18.4 11.9 11 14
100 100 100 96 97 97
15 15 15 6 16 16
2.1 2.1 2.1 0.75 1.95 1.95
60 50 50 50 50 50 50 60
320 214 244 247 260 211 225 320
14.8 18.0 18.1 21 19.0 19.5 19 25
95 101 100 100 80 95 95 95
85 70 50 70 70 100 70 85
2.0 2.0 9 11.00
30 40 50 40 30 40 40 30 40 30 40 30 40 40
110 145 227 144 106 143 145 104 139 104 160 95 135 139
11.9 14.4 19.4 14.8 11.0 13.5 14.5 11.39 14.13 11.8 14.5 11 14 14
97 98 97 101 99 100 98 102 102 102 98 100 100 97
12 12 12 17 30 30 13.5 20 20 30 13.0 20 20 40
1.67 1.67 1.67 2.0 4 4 1.65
1.5 2.5 2.5 4.9
Zinc-free formulation. For fuels with sulfur content greater than 3.5%.
about the lubricant itself involve disposal. Air pollution is mostly due to the chemical nature of the fuel oil used, but any changes in the fuel oil have far-reaching implications on lubricant formulation. Fuel quality is the most important variable in controlling emissions. For example, Thomas (1992) suggests that carbon (soot) emission can be correlated to the fuel quality by:
(HR) S P ∝ V (N ) 1.7
c
0.3
(36.1)
a
where Pc is the particulate carbon emissions (excluding ash) at 4% excess oxygen in percent of fuel weight; HR is a measure of the carbon-forming tendency of the fuel measured chromatographically; S is the weight percent of sulfur in the fuel; and V is the vanadium content and Na is the sodium content, both in parts per million. In 1992, the International Maritime Organization (IMO), a United Nations organization, identified two pollutants (NOx and SOx) for control by the year 2000 (Bastenhof, 1992). However, no specific requirements or procedures for achieving emissions reductions have been mandated. It is entirely possible that sulfur may in the future be removed from fuels through a costly refining process (dehydrosulfurization). Lanz (1995) has calculated SOx emission rates as a function of fuel sulfur content, along with the increased
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TABLE 36.2
Effect of Fuel Sulfur Content on SOx Emissions and Fuel Cost
Fuel Sulfur Content (%)
Reduction in SOx Emissions (%)
Increase in Fuel Cost per Tonne ($)
3.5 3.0 1.5
5 10 52
15–30 — 46–58
After Lanz, R. (1995), The Motor Ship, 5, 22-23.
cost of fuel. The results of his model are given in Table 36.2. Lanz also mentioned that an alternative approach is the treatment of exhaust gases, which will represent a fuel cost of about $25 per tonne with fuel consumption increased by 3%. A number of countries enforce emissions regulations in coastal waters, which can extend a few hundred miles from the shoreline. However, the economic reasons for using bunker oil as fuel are so compelling that a common practice is to use bunker oils in international waters and more refined fuels (i.e., reducedsulfur fuels) along coastlines. This has a dramatic influence on acid rain because the vast majority of sulfur emissions are not deposited on land, but at sea. The sulfur content of seawater is 1015 tonnes, while all fossil fuels combined would contribute only 1011 tonnes, which is accepted as producing no deleterious effect (Lanz, 1995). Lanz also noted that the total sulfur emissions from all ships (105 tonnes per year) is roughly the same as that produced by a single coal-fired power station. The implications of sulfur reductions are very far reaching. If fuels were refined enough to eliminate most of the sulfur content, then the need for increased alkalinity in the lubricant would be removed. In fact, lubricants would need to be reformulated, in that sulfur when present in small amounts is an extremely useful EP additive. Thus, as discussed by Golothan (1976), using fuels without sulfur can actually lead to an increase in engine wear. Also, important tertiary functions (oxidation inhibition, detergency, etc.) aided by high alkalinity would need to be achieved with different lubricant additives. Nitrous oxide emissions are also a concern, and a number of approaches can be used to reduce NOx emissions. For example, NOx emissions can be reduced by 50% from uncontrolled levels by retarding fuel injection timing, albeit at a loss in specific fuel consumption of about 10% (Hold, 1993). Retarding timing increases soot loading in the cylinder lubricant oil, requiring reformulation, higher cylinder oil flow rates, or reduced oil change intervals, all of which have their own environmental concerns. For larger emission reductions, some type of catalytic reduction is necessary. This will necessitate reformulation of lubricants because popular extreme pressure (EP) additives such as zinc dithiophosphate are incompatible with NOx-reducing catalysts. The sources of particulate emissions in the exhaust consist mostly of the sulfur and carbon particles in the fuel. However, some lubricant is always combusted and can contribute to the gas and particle emissions. High TBN oils contain up to 12% sulfated ash, which during combustion is converted into inorganic ash particles. In addition, some attention has been paid to reducing particulate emissions of diesel engines, although regulatory agencies have pursued the marine industry much less arduously than other industries to date. Particulates are also a concern. Fuel oil and lubricants contain metals such as calcium (provided as CaOH) to improve alkalinity. The metal ions form ashes with sulfur (e.g., CaS), which is then a potential particulate exhaust. Carbon particles (soot) are also exhausted. Gros (1990) reports that typical mediumspeed diesel engine exhaust pollutants are about 66% metals (oxides and sulfides), 25% carbon, and 10% hydrocarbons from fuel and lubricating oil.
36.3 Diesel Engine Lubrication Many of the concerns of diesel engine lubrication are identical to the issues discussed in Chapter 33 of this section. However, a few distinctions must be made. Many of the issues result from the acidity of combustion products as discussed above. However, there are other peculiarities of diesel engines in marine applications.
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Exhaust valve
Exhaust gas manifold
Cooling jacket
Piston Air cooler Scavenging ports (quills) Cylinder liner
Scavenge air collector Piston rod
Cam shaft
Crankshaft Connecting rod
Bed plate
FIGURE 36.1 Schematic illustration of cross-head diesel engine. (Adapted from Pevzner, L.A. (1998a), Aspects of marine low-speed, cross-head diesel engine lubrication, Lubr. Eng., 54, 16-21.)
36.3.1 Slow-Speed Diesel Engines (<250 rpm) Slow-speed diesel engines are large, two-stroke engines with crosshead construction (Figure 36.1), and usually run between 90 and 250 rpm. These engines use a diaphragm and stuffing boxes to separate the cylinder and crankcase, allowing each to be lubricated independently. Slow-speed diesels are the largest engines, with bore sizes around 1 m and strokes of over 3 m. Piston speeds are around 7 to 8 m/s, and power output for the largest engines is over 65,000 kW. These engines are primarily used in large tankers and passenger liners. The motor directly powers the propeller shaft without a reducing gear or clutch. These engines are very fuel efficient because of long combustion times and low break-specific friction, but as will be seen, this has its drawbacks as well. Slow-speed diesel engine tribology is itself a unique specialization with its own very characteristic concerns. Excellent summaries of the issues and concerns in low-speed diesel engine tribology include the papers by Pevzner (1998a), Lane et al. (1987), Langer et al. (1987), and Hold (1993). 36.3.1.1 Cylinder Lubrication The fact that the cylinder is separated from the crankcase is both a boon and a curse. It is a curse in that separate lubricant supplies and preventive maintenance schedules must be maintained. It is beneficial in that the special environment presented by the cylinder can be treated without adversely affecting other components. This design was conceived for this reason. Because the fuels and combustion products are acidic, isolating them from as much of the engine as possible is the best approach to preventing corrosion and corrosion-assisted fatigue and wear. For the
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cylinder itself, the unalterable presence of corrosive elements requires pursuit of unique tribological solutions. These are divided into lubricant chemistry and coatings efforts. The lubricant is applied by cam-actuated reciprocating pumps through a number of ports or quills (usually 4 to 8) positioned around the cylinder liner. The cylinder oil must be thin enough to spread quickly, but must also allow formation of a hydrodynamic film at operating temperatures. Cylinder lubricants are most commonly SAE 50 or SAE 60 to ensure the desired viscosity at the cylinder liner operating temperature of around 200°C, with TBN values of 50 to 70. In addition, EP additives and detergents are especially important for these lubricants. Many problems associated with lubrication arise from too low or too high an application rate. If the application rate is too high, overlubrication can cause fouling of the cylinder or can even cause postcylinder fires in the engine, especially the turbocharger. Further, overlubrication adds significantly to maintenance cost in a highly competitive industry. If the application rate is too low, then the alkaline nature of the lubricant is neutralized before it spreads over the entire cylinder. This usually means that the oil applied just below the quill will neutralize the sulfuric acid but will become increasingly ineffective as the distance from the quill increases. This leads to classic periodic wear patterns on cylinder liners, called “clover leafing,” where significant corrosion fatigue wear and corrosion-assisted abrasive wear occurs between quills, but almost none occurs near the quills. An example of clover leafing is shown in Figure 36.2. Pevzner (1998b) investigated the effect of oil feed rate into the cylinder and its effect on cylinder liner temperature and liner wear rate. His results are shown in Figure 36.3 for a number of different power levels for the low-speed diesel engine examined. Pevzner noted that wear and temperature do not continue
FIGURE 36.2 An example of severe clover leafing on a chrome-plated cylinder liner. Note the position of the wear patterns relative to the quills. (From Wilkison, J.L. (1983), Marine equipment, in CRC Handbook of Lubrication, Vol. I. Booser, E.R. (Ed.), CRC Press, Boca Raton, FL, 227-248. With permission.)
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350
Liner wear rate, mg/hr
300
100% 80% 64% 50%
250 200 150 100 50 0 0.4
0.8
1.2
1.6
2.0
Oil feed rate, g/kWhr (a)
Cylinder liner temperature, °C
150
100% 80% 64% 50%
140 130 120 110 100 90 0.4
0.8
1.2
1.6
2.0
Oil feed rate, g/kWhr (b)
FIGURE 36.3 Effect of oil feed rate on cylinder liner: (a) wear rate vs. oil feed rate; (b) liner temperature vs. oil feed rate. (Data from Pevzner, L.A. (1998a), Aspects of marine low-speed, cross-head diesel engine lubrication, Lubr. Eng., 54, 16-21.)
to decrease with lubricant feed rate above a certain threshold. Also, Pevzner noted that ash deposits formed on supercharger turbine blades and on the piston crown at high feed rates. Pevzner conducted sea trials of the result for verification. The optimal feed rate changed with power rate of the engine, but there really is no rationale for overlubricating an engine. The level of alkalinity required depends primarily on the fuel’s sulfur content. If the sulfur content is in the 2 to 3% range, then a TBN of 60 or so is sufficient. High-performance lubricants, which operate successfully for fuels with over 3% sulfur, can have TBN values of 70 or more. Obviously, the higher the sulfur content, the more rapidly the TBN is consumed in the engine. Coatings are commonly used in low-speed diesel engines, especially for cylinder liners and piston rings exposed to the highly acidic environment. Liners are commonly chrome electroplated, and rings are chrome plated or plasma sprayed to reduce wear rates. 36.3.1.2 Crankcase Lubrication The crankcase oil lubricates the gearing, bearings, and other engine components, including the turbocharger. A chief concern with low-speed diesel engines is the isolation of crankcase and cylinder oils, although some migration of oils through the piston rod diaphragm is inevitable. This can introduce cylinder liner wear debris as well as the acid combustion products mentioned above. Seawater contamination is also a concern. All of these contaminants can facilitate corrosion and rusting of journal bearings and white metals, and require special lubricant formulation to obtain good product life.
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Three crankcase oil types are used in marine service (Pevzner 1998a): • Rust and oxidation oil types (for older engine designs) • Low alkalinity (TBN = 4–6) for water-cooled piston engines • Medium alkalinity (TBN = 8–12) for oil-cooled piston engines or when a water-cooled piston engine uses the same oil for main and oil-cooled auxiliary engines Given the adverse affects of contaminants, lubricant additives are especially important. Wilkison (1983) gives the following requirements for crankcase lubricants, which are either base oil (B) or additive (A) determined properties: 1. Sufficient viscosity (B), especially at the operating temperatures. This is ensured by producing the oil from highly refined medium- or high-viscosity index base oils or from synthetic blends. 2. Oxidation and thermal stability (B, A). Piston temperatures can be very high, and these features of a lubricant are required to prevent a loss of viscosity (breakdown). 3. Demulsibility (A). It is advantageous if any seawater contamination can be quickly separated from the oil; hence, additives that limit the volume fraction of water which can be dispersed or emulsified in the oil. This is also referred to as a “water-shedding” capability. 4. Rust and corrosion prevention (A). Often in the form of alkaline additives to quickly suppress acidic contaminants, these are also additives that inhibit corrosive interactions with surfaces. 5. Antifoaming (A). Antifoaming additives are added to ensure proper flooding of contacts and pump operation. 6. Detergency (A). Because of the possibility of carbon- or ash-based soot, deposits can foul engine components and inhibit efficient operation. 7. Extreme pressure (EP) performance (A). Most contacts are highly loaded at operating temperature and will use extreme-pressure additives to reduce friction and wear. 8. Biocides (A). Biological attack of the base oil and additives can reduce lubricant effectiveness. Many of these properties are of inherent benefit or requirement to tribologists. A few special considerations should be addressed, however. White metal babbits (tin-based alloys) are commonly used as a bearing material in slow-speed engines. Saltwater contamination can allow galvanic corrosion of the tin, forming a black oxide layer. This layer can cause increased interference between bearing and journal, and can also flake off, resulting in a three-body wear condition. The obvious solution is to prevent seawater contamination, but when this is not practicable, effective demulsifiers are essential. In many low-speed diesel engines, up to 200 L of oil will flow through the engine per minute (a few hundred liters per day will be consumed), and the lubricant will collect contaminants and combustion by-products. Ideally, the oil would be discarded after one pass through the engine, but this is obviously a wasteful and expensive proposition. Instead, effective detergent additives are included in the lubricant formulation to prevent fouling of machine elements by these contaminants. Large ships typically have equipment to centrifugally water separate, filter, and condition lubricants. Biological attack of lubricant has been experienced. However, because biological organisms require water to survive, this problem can be eliminated by preventing seawater contamination and by removing water from the oil (greatly assisted by demulsifiers). Various biocides can be added to oils and fuels to prevent microbial growth; otherwise, the oil can be heated to a temperature sufficient to kill the microbes. Microbes are of special concern because of their tendency to plug filters. Turbochargers present special problems in that heat must be quickly removed. Traditionally, this has been done with separate low-viscosity oils that allowed for large volume flow rates and easy circulation; but more recently, SAE 30 oil has become the norm.
36.3.2 Medium-Speed Diesel Engines (250 to 1000 rpm) Medium-speed diesel engines are usually four-stroke engines and have a slightly higher power-to-weight ratio than slow-speed diesel engines. They are commonly used for ferries, container ships, and cruise
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Total base number - mg/KOH/g
30 25 Low sulfur fuel and high oil consumption 20 15 10 High sulfur fuel and low oil consumption 5 0
0
1000
2000 3000 Hours of operation
4000
FIGURE 36.4 Drop in total base number (TBN) as a function of time and operating conditions. (From Wilkison, J.L. (1983), Marine equipment, in CRC Handbook of Lubrication, Vol. I. Booser, E.R. (Ed.), CRC Press, Boca Raton, FL, 227-248. With permission.)
ships. Maximum power delivered is around 1500 kW per cylinder, or 27,000 kW from an 18-cylinder engine. Medium-speed diesel engines usually use the same fuels as slow-speed engines, although sometimes use lower viscosity fuel blends for improved performance. However, the same oil usually lubricates both cylinder and crankcase, so the lubricant must have the ability to deal with acidity, soot, and other combustion products. Some medium-speed diesels will have separate forced feed cylinder lubrication, which allows direct application of fresh, fully alkaline oil to the cylinders. The oil is usually taken from the crankcase, because there is inevitably some mixing, but this arrangement keeps most contaminants out of the crankcase. As can be seen from Table 36.1, the TBN level of medium-speed engine oils is not nearly as high as for slow-speed diesel engine cylinder oils, but these lubricants do have many of the same requirements. These include proper viscosity and alkalinity, oxidation and thermal stability, corrosion prevention, antifoaming capability, detergency ability, and extreme pressure (EP) additives for wear prevention. A difficult maintenance task is establishing intervals for lubricant maintenance. Oil must be periodically added to the crankcase because it is tapped to provide cylinder lubrication. However, as the alkalinity drops, the corrosion prevention capability of the oil is seriously compromised. Therefore, oil exchange is a fairly complicated function of the fuel sulfur content and the rate at which oil is consumed and replenished. Wilkison (1983) compared the change of TBN in crankcase oil, and typical results are shown in Figure 36.4. Most lubricant suppliers provide a chemical oil analysis service to assist operators in determining proper oil change intervals. Alkalinity has another beneficial effect: there is a latent detergency associated with high TBN. This is beneficial if there are insoluble contaminants present in the oil. A high TBN keeps the soot suspended and prevents deposit formation and sticking rings. Obviously, the rate at which particulate contaminants build up in the oil is a function of the fuel quality, and is inversely related to oil consumption. Also, large amounts of particulate matter can drastically increase the viscosity of the oil (see Wilson et al. (1993) for a summary of solid-phase concentration effects on viscosity). Regardless, continuous centrifuging of the crankcase oil is recommended by engine manufacturers to keep insolubles below a desired threshold; Wilkison (1983) suggests 3% concentration. Fuel quality plays an important role in the success or failure of a lubricant system. More highly refined fuels will have lower sulfur content, such as distillate fuel with a sulfur content of 0.2 to 1.3% by weight, but usually less than 0.5% for American fuels (Wilkison, 1983). Medium-speed diesel engines powered by distillate fuels are relatively rare, but these engines place a much lower burden on the lubricating oil and require oils with lower TBN.
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It should be mentioned that many manufacturers have specific requirements for their engines. For example, some General Motors two-stroke engines use a silver piston pin bushing, which then necessitates the use of zinc-free oils to prevent damage to the bushings.
36.3.3 High-Speed Diesel Engines (>1000 rpm) High-speed diesel engines are the engines of choice for pleasure craft as well as special applications on larger vessels such as power for winch operation, pumping engines, electric power generation, etc. Many of the design challenges with high-speed diesel engines are identical to those faced by automotive diesel engines discussed in Chapters 32 and 33. For these engines, only the highest quality distillate fuels are used, and heavy duty automotive type diesel oils are used as lubricants.
36.4 Steam and Gas Turbines Steam and gas turbine engines are used for very large ocean-going vessels and for many warships. Nuclearpowered craft use a steam turbine engine for propulsion. In general, turbine engines have the following advantages over comparably sized diesel engines: • • • • •
Higher efficiency at high-speed operation Relatively small and light, requiring smaller foundations and deck space than diesel engines Lubricant consumption is low and the exhaust is relatively free of oil Less vibration due to the absence of reciprocating parts For large sizes, initial and maintenance costs are lower than for diesel engines
Because turbine engines are efficient at high speeds (4000 rpm and higher), and propellers are limited to low speeds (100 rpm approx.), a large speed reduction is needed. This is usually accomplished with reduction gearing. Usually, a turbine-powered ship will have a high-pressure (HP) turbine with the exhaust fed into a second, low-pressure (LP) turbine. On some ships, an intermediate-pressure (IP) turbine will be used, with the HP exhaust heated before being fed into the IP turbine. Figure 36.5 depicts a typical arrangement of a twin turbine geared propulsion unit.
Nested double reduction gear Reduction gear radial bearings
Low pressure turbine Astern element
Line Shaft Packing Radial bearings Packing
Bearing Solid coupling Reduction gear radial bearings
FIGURE 36.5
Main thrust bearing
High pressure turbine
Typical arrangement of geared-turbine propulsion unit.
Turbine thrust bearings
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It should be noted that turbine engines are not easily reversible; geared systems as shown are arranged to provide most of the power in the forward direction. Astern (rearward) propulsion is achieved by arranging a few rows of blades in the LP turbine appropriately, giving low-power propulsion astern. The tribological issues with turbine engines are the journal and thrust bearings and the associated large hydrodynamic film which is desired, and the gears in the speed reduction units, which require effective EP additives for wear resistance.
36.5 Ancillary Equipment 36.5.1 Stern Tubes The stern tube supports the propeller shaft; it must also effectively isolate the ship, drive components, and engine from the water. The propeller shaft thrust is absorbed by the hydrodynamic thrust bearing, but stern tube bearings are needed to support the weight of the propeller shaft (Figure 36.6). Historically, stern tube bearings were constructed of water-lubricated lignum vitae (Latin for “the wood of life”), a tropical wood, but today are oil-lubricated rolling element bearings. For obvious reasons, effective sealing of the stern tube is of great concern, especially because the lubricating oil for the stern tube is often tapped from the main propulsion engine. Any contamination of this oil has extremely serious consequences. To promote effective sealing and to prevent water seepage into the stern tube, a static pressure is placed on the oil. This can result in excessive oil seepage through the stern tube seals in the case of seal wear or other unusual circumstances. Seal wear is of special concern with shallow-draft vessels and riverboats because of the abrasive particles (sand) in suspension in the water. Worn seals result in oil slicks around the sterns of vessels, which is obviously undesirable from an environmental standpoint. When a seal is worn and excessive oil leakage occurs, the only long-term solution is to replace the seal. In the meantime, a common practice is to use higher weight oils to reduce oil leakage. For example, one manufacturer recommends oil up to 275 cSt at 40°C in such circumstances (Wilkison, 1985). A separate issue is the support of a kort nozzle, commonly used in cargo vessels, which encloses the ship’s propeller and is slewable. A kort nozzle (sketched in Figure 36.7) improves propeller efficiency and allows pitching of ships for greater maneuverability. The rudder shaft bearing shown must carry the entire weight of the rudder, and also carries a large axial load during pitching of the ship. The stern lubrication system does not include the kort nozzle, which instead is isolated with seals, and water contamination of the bearings is a possibility. Oil head tank Oil level gage
Cooler Oil vent (stern tube)
Oil inlet (stern tube)
Grease connection (backup) Pump Filter Drain line Pressure gage Temperature gage
FIGURE 36.6
Schematic illustration of a typical stern tube lubrication system.
Oil drain tank
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Top rudder shaft bearing
Bottom rudder shaft bearing
Kort nozzle
Rudder Propeller
(a)
(b)
FIGURE 36.7 Schematic illustration of a kort nozzle: (a) general view of ship stern with kort nozzle; (b) detail of rudder shaft bearing.
36.5.2 Rigging Equipment Winches and capstans are devices used with wire rope under tension. Wire rope is commonly used for rigging and hoisting and is also run between two ships at sea. These are usually electric, diesel, or hydraulically powered and equipped with gear reducers. The enclosed gears require a good-quality gear oil, and hydraulic equipment of course needs high-quality working fluids. The wire rope is lubricated with thick greases to reduce friction between wires, thereby increasing the fatigue life of the wire (Hamrock et al., 1999).
36.5.3 Pumps Pumps are used to move ballast water, transport fuel, circulate engine coolant, and transfer liquid cargoes. Centrifugal pumps operate at high speed and usually do not use a gear reducer. These use light turbine oils as lubricants and grease-packed bearings. Positive displacement pumps operate at lower speeds and use a gear reducer, which requires a good-quality gear oil. Often, lubrication is performed by the fluid being pumped.
36.5.4 Oil Maintenance Equipment Given the large number of contaminants that can be present in a lubricant, there is a need for treatment of used lubricant before it is recirculated. One important device is a centrifuge, shown in Figure 36.8, run either as a separator/purifier or as a clarifier. The distinction between these two modes is that separator/purifiers are arranged to remove any entrained water, while the clarifier attempts to remove soot and sediment from the oil. To decrease the viscosity of the oil and the centrifuge efficiency, oils are commonly preheated before centrifuging. Filters are commonly used upstream of the oil pump to remove fine debris. For smaller vessels, where centrifuging is not economically viable, filters are used to remove entrained particulates.
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Oil outlet
Oil outlet
Water outlet
Sediment
Used oil inlet Used oil inlet
Separator
Clarifier
(a) Used oil inlet
Used oil inlet
Oil outlet
Oil outlet Water outlet
Separator
Clarifier (b)
FIGURE 36.8 type.
Schematic illustration of lubricant centrifuges in service in marine applications: (a) tube type; (b) disk
References Bastenhof, D. (1992), Maritime exhaust emissions: levels and consequences, First Int. Symp. Marine Engineering, Taipei. Golothan, D.W. (1976), The low sulfur problem — some notes on the incidence of high cylinder wear and scuffing when low sulfur fuels are used in marine diesel engines, IMAS. Gros, S. (1990), Exhaust Gas Emissions in Marine Installations, Wartsila Diesel News and Views, 28-32. Hamrock, B.J., Jacobson, B.O., and Schmid, S.R. (1999), Fundamentals of Machine Elements, McGrawHill, New York.
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Hellingman, G. J. and Barrow, S. (1982), Shipboard Investigations with Selected Fuels of Tomorrow, ASME Paper 82-BGP-9, American Society of Mechanical Engineers, New York. Hold, G.E. (1993), Large-Bore Diesel Engines Require Different Lubrication, Past, Present and Future, ASME Paper No. 93-ICE-25, American Society of Mechanical Engineers, New York. Juvinall, R.C. and Marshek, K.M. (1991), Fundamentals of Machine Component Design, John Wiley & Sons, New York. Lane, G., Casale, P.G., and Chadwick, R.E. (1987), Development of Marine Lubricants for the Future Slow and Medium Speed Engines, SAE Paper No. 871396, Society of Automotive Engineers, Warrendale, PA. Langer, A.J. and Lim, K.C. (1987), Marine Cylinder Lubricants Development — Today and Tomorrow, Lubr. Eng., 43, 858-870. Lanz, R. (1995), Sulfur sours emissions level agreement, The Motor Ship, 5, 22-23. Pevzner, L.A. (1998a), Aspects of marine low-speed, cross-head diesel engine lubrication, Lubr. Eng., 54, 16-21. Pevzner, L.A. (1998b), Cylinder lubrication and feed control in relation to low-speed, cross-head engine load and speed, Lubr. Eng., 54, 22-28. Shigley, J.E. and Mischke, C.R. (1989), Mechanical Engineering Design, McGraw-Hill, New York. Thomas, R. (1992), Lube oil dominates cylinder maintenance costs, The Motor Ship, 3, 65-69. Wilkison, J.L. (1983), Marine equipment, in CRC Handbook of Lubrication, Vol. I. Booser, E.R. (Ed.), CRC Press, Boca Raton, FL, 227-248. Wilson, W.R.D., Sakaguchi, Y., and Schmid, S.R. (1993), A dynamic concentration model for lubrication with oil-in-water emulsions, Wear, 161, 207-212. Woodyard, D. (199), Matching lubes to engine needs, Marine Log, 95, 33-37.
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37 Tribology in Manufacturing 37.1 37.2
Introduction ................................................................... 1385 Unique Aspects of Manufacturing Tribology .............. 1385
37.3
Metal Cutting ................................................................. 1394
Lubricants • Surface Flattening and Roughening Cutting Tool Materials • Cutting Tool Wear • Cutting Fluids
37.4 University of Notre Dame
William R.D. Wilson University of Washington
Finishing Operations ..................................................... 1398 Coated and Bonded Abrasives • Advanced Machining Operations
Steven R. Schmid 37.5
Bulk Forming Operations ............................................. 1399 Rolling • Forging • Extrusion and Drawing • Sheet Metal Forming Operations
37.1 Introduction Manufacturing operations present extremely demanding applications of tribology. Elevated temperatures, high processing speeds, demanding surface finish and reliability requirements, and environmental considerations all play a role in determining tooling life, product surface aesthetic quality (e.g., brightness) and surface functional properties, galling resistance, or lubricant retention. Tribological phenomena are important to the viability and optimization of most manufacturing processes, but relatively little attention has been paid to this subject compared to the efforts directed toward tribology in machine elements, for example. An engineer who wishes to become an expert in manufacturing tribology has a difficult task. A multidisciplinary background is required for any tribological research, and this is compounded by the need to develop an appreciation of the multi-disciplinary nature of manufacturing processes. This chapter is intended only as a broad overview and introduction to the complexities of tribology in manufacturing. For readers who require additional information, they are directed to the classic manufacturing texts by Kalpakjian (1996), Kalpakjian et al. (2000), and Schey (1999), as well as the monograph on tribology in metal working by Schey (1984), which although published over 15 years ago is still the most valuable reference text in the field. Manufacturing processes are extremely diverse, and no brief introduction can reasonably cover all operations. This chapter is restricted to the manufacturing operations depicted in Figure 37.1, although tribological issues exist in many other processes, such as spinning, powder metal compaction, friction welding, etc.
37.2 Unique Aspects of Manufacturing Tribology In cutting and forming operations, the pressure in the tool/workpiece contact often exceeds the yield stress of the workpiece material. This renders the traditional theories of contact and lubrication of limited 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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FIGURE 37.1 Schematic illustration of the manufacturing processes discussed in this chapter: (a) metal cutting; (b) grinding; (c) rolling; (d) extrusion; (e) drawing; (f) open die forging; (g) impression die forging; (h) deep drawing.
value. Special mechanisms of friction and wear may also be active and constraints on lubrication may apply. Thus, while the basic principles used in the tribology of machine elements are still valid, great caution must be used in applying them to the systems used in manufacturing. This section is intended to identify some of the major differences between manufacturing tribology and more traditional applications. Most differences are attributable to two causes: the very high temperatures and pressures that exist at tooling/workpiece interfaces, and the bulk straining of the workpiece surface. These fundamentally change the type of problems encountered by the tribologist.
37.2.1 Lubricants Lubricants are expensive and difficult to apply, remove, and dispose of. They also create problems in subsequent operations such as welding, adhesive bonding, and painting. However, in many operations, lubricants are critical to control surface quality, tool wear, and power consumption, and must be tolerated as a necessary evil. Metal forming operations are usually classified as cold or hot, based on metallurgical considerations. Classifications are usually based on temperature expressed as a fraction of the material’s melting temperature (Wilson, 1997). For example, hot working is an operation in which the billet temperature exceeds roughly one half the melting temperature, and usually takes place at 70 to 80% of the melting temperature.
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This classification is not as meaningful for tribology because the actual temperatures restrict the lubricants that can be used. Therefore, while deformation of lead at room temperature is hot working from a metallurgical standpoint, it can best be considered as cold working here because liquid organic lubricants are still viable options. In contrast, working steel at around 500°C is cold working from a metallurgical standpoint, but cannot use organic lubricating oils. Therefore, “cold working” and “hot working” operations will here refer to those that take place below or above 250°C, respectively. 37.2.1.1 Cold Working Lubricants Cold working lubricants are often based on organic compounds such as fatty and petroleum oils, although inorganic compounds such as molybdenum disulfide are used in severe applications. Cold working lubricants can be either liquid or solid. Liquids are preferred in high-speed, continuous forming operations and in machinery. Solid lubricants, including soaps and waxes, tend to be used in severe low-speed operations. Lubricant formulation requires considerable chemical engineering sophistication. For example, a liquid lubricant will typically contain roughly 90 to 95% by volume base oil and the remainder will consist of additives such as boundary lubricants, anti-foaming and anti-bacterial agents, brighteners, detergents, etc. As in the lubrication of machine elements, liquid lubricants in metal forming operate through a combination of hydrodynamic and boundary action to prevent metal-to-metal contact and galling or scoring. Both actions must be carefully controlled to provide good surface quality. One of the major differences between liquid lubricants used for manufacturing compared to those used for machine elements is the much wider application of aqueous lubricants, especially emulsions. Oil-in-water emulsions are common in metal forming, cutting, and grinding operations. It has long been known that oil, when mixed in water in the form of small droplets (typically 1 to 10 µm in diameter), provides an excellent metal working lubricant. A solution of 10% oil in 90% water can lubricate essentially as well as neat oil and cool as well as water. Thus, emulsions are an extremely valuable lubricant, and coolant, for metal forming at high speeds. Occasionally, solids will be used as cold working lubricants, although this is much more common for hot working. Solids such as molybdenum disulfide and graphite have a planar lattice structure; this allows layers to slide over one another at relatively low shear stresses, making them outstanding lubricants for demanding applications. Often, solid lubricants are delivered as suspensions in mineral oils. Waxes can be considered solid, although they become liquid at working temperatures. Waxes are used for some processes; for example, beeswax has been used as a lubricant in hydrostatic extrusion. Soaps are of great significance in metal working. They are highly viscous or solid, and possess very valuable rheological properties. They are usually compounded with thickeners, often lime (CaO), to obtain desired viscosity at process temperatures. Alkaline soaps are valuable because they are water soluble and therefore relatively easy to apply. Zinc and calcium stearates are the most important soaps because of their tribological properties. Because of the demanding environment encountered in cold forging, conversion coatings of phosphate crystals are often used. An outstanding summary of conversion coating behavior is given by Bay (1997). Conversion coatings do not lubricate in themselves, but they serve as excellent carriers of other lubricants, usually soaps or solid lubricants such as molybdenum disulfide or graphite. For light-duty applications, emulsions or oils can impregnate the conversion coating. SEM images of conversion coatings are shown in Figure 37.2. A typical conversion coating consists of platelets of phosphates that grow in the same direction as surface grains. The platelets are 10 to 100 µm in size and produce a porous coating 1 to 10 µm in thickness. The pores in the phosphate can serve as liquid lubricant reservoirs, but more normally, this coating serves as a carrier for solid lubricant layers deposited over it. Conversion coatings were first developed in metal forming for cold steel forging, although chemistry modifications allow application of phosphate coatings to aluminum, zinc, titanium, and stainless steel forging and extrusion. After phosphating, the lubricant layers are physically applied, resulting in a layered surface such as shown in Figure 37.3. Special care must be taken in developing soap layers of proper
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FIGURE 37.2
SEM images of phosphate coatings: (a) needle structure; (b) grainy structure. (Courtesy of N. Bay.)
FIGURE 37.3
Schematic illustration of phosphate coating with soap coatings.
thickness; insufficient film thickness results in rapid tool wear, while excess soap can build up on tooling and compromise part tolerances. Metal coatings are often used in combination with a liquid lubricant. For example, tin and zinc can be applied to sheet metal to reduce die pickup and improve formability. The liquid lubricant used is then formulated for the coating, not the base material, so the coating can be considered as the lubricant carrier. Copper is sometimes used because die pickup is minimal and copper has a low shear stress.
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In some cases, a polymer-coated workpiece will be used in cold metal forming. While relatively rare in practice, this is useful for circumstances where reasonable lubrication and a porous final surface are needed. The polymers can sometimes be applied as a separate film, but this is usually too awkward for industrial application, and the polymer coatings are applied through lamination or powder spray. Although their function is mainly cooling, metal cutting fluids should be briefly addressed. Because the fluid can penetrate into a metal cutting contact only through capillary action or in interrupted cutting, the main purpose of these fluids is to cool the workpiece and tool. Not surprisingly, emulsions have therefore been widely applied because of the superior cooling behavior of water. Other metal cutting fluids include typical low-viscosity mineral and vegetable oils. 37.2.1.2 Hot Working Lubricants Lubricants are usually employed in hot working to reduce tooling wear, which tends to be accelerated by softening of the tooling material and oxidation. Reduction of forces and power consumption is often a secondary benefit. Hot working lubricants are usually consumed during the operation. This makes their use inherently expensive. Thus, if fine tolerances or surface finish are not required, hot working operations are often performed without a lubricant. Tolerances and/or surface quality can often be achieved in a subsequent cold forming operation. Organic liquids burn or evaporate at the temperatures used in hot working. Thus, their main application in hot working lubricants is as a carrier for solid lubricants. Because of environmental considerations, they are largely being displaced by water. However, petroleum oils are used in the hot rolling of steel. Their effectiveness in this application may be due to the residue left from their decomposition. Glass is often characterized as a solid lubricant, although it behaves like a liquid at hot forming temperatures. Using glass as a lubricant is very common in hot forging and extrusion operations to prolong die life. By blending different chemical constituents, the viscosity of the glass can be tailored to the particular workpiece and operating temperature, as shown in Figure 37.4. Non-Newtonian effects can be induced in glass through introduction of suspensions or partial crystallization. Glass is applied at room temperature by dipping a workpiece into a slurry of glass particles, or the glass is coated with organic binders and applied directly, often in a spray operation. At elevated temperatures, workpieces exposed to glass powders or fibers will force melting and with proper surface wettability the molten glass forms a uniform film. Often, workpiece surface treatment is necessary to ensure good wettability. After
1014
Viscosity, Pa-s
1010 108
Si
ate ilic ros Bo d ea a-l od h-s d tas lea Po sh a Pot e Borat Lead
1012
li c
a
Bo ra te
106 104 102 100 400
600
800
1000
1200
1400
Temperature, °C
FIGURE 37.4 Glass viscosity as a function of temperature. (Data from Schey, J. (1984), Tribology in Metalworking, American Society for Metals, Metals Park, OH. With permission.)
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metal forming, the glass film can be easily removed by dipping the hot workpiece in a cooler medium, causing large thermal stresses that cause gross fracture in the solidified glass. Solid lubricants such as graphite and molybdenum disulfide were discussed above, and these are especially useful as hot working lubricants. These are usually applied as a spray, using suspended particles in a water-based or mineral oil-based suspension. Conversion coatings are often required to ensure proper performance of the solid lubricant.
37.2.2 Surface Flattening and Roughening Surface geometries and chemistries are extremely dynamic in manufacturing operations. An atomically smooth workpiece, rolled by atomically smooth rollers in the presence of a lubricant, will experience significant roughening. On the other hand, a very rough surface rolled by smooth tooling and a boundary lubricant film will become smoother. Because friction and wear phenomena depend greatly on real areas of contact, and because final surface workpiece roughness is usually of primary concern, this evolution of surface profile is critical. 37.2.2.1 Surface Flattening Mirror-quality finishes can be obtained in metal forming using highly polished tooling and thin lubricant films. This is mainly due to workpiece asperities being flattened. This phenomenon also has a large effect on the magnitude of friction stresses that will develop. Wilson et al. (1983), Sutcliffe (1988), and Korzekwa et al. (1992) have all shown that workpiece surface asperities flatten readily against smooth tooling when the bulk material is straining. Sheu et al. (1994) suggest that asperity hardness can be expressed by the relationship:
H=
(()
2
( ))
f1 α E + f2 α
(37.1)
where H is the effective hardness of the workpiece:
(
H = pa − pb
)k
(37.2)
E is the dimensionless strain rate given by:
E=
ε˙ l vf
(37.3)
a is the indentor area ratio, a = a/l and f1 and f2 are defined by:
()
f1 a = 0.515 + 0.345a − 0.860a 2
f2 =
1
(2.571 − α − α ln(1 − α))
(37.4)
(37.5)
The effective hardness given by Equation 37.1 is shown in Figure 37.5. An extremely important trend can be seen: the hardness of the workpiece asperities falls dramatically in the presence of substrate straining. This means that the rate at which asperities flatten will be much higher in metal working than in machine design applications.
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FIGURE 37.5 Plot of asperity hardness as a function of substrate strain rate. (From Wilson, W.R.D. and Sheu, S. (1983), Flattening of workpiece asperities in metal forming, Proc. NAMRC XI, Society of Manufacturing Engineers, 172-178.)
FIGURE 37.6 processes.
Friction force as a function of normal force and approximate range of application for manufacturing
Friction in metal forming depends greatly on the degree to which asperities have been flattened (Figure 37.6). If the asperities have not been flattened to a great extent, or if the surfaces have actually roughened (see below), then the real area of contact between workpiece and tooling will be low and the Coulomb friction model will be appropriate. On the other hand, if the asperities are essentially completely flattened and the real and apparent areas of contact are equal, the friction stress on the tooling is given by the Tresca model:
τ = mk
(37.6)
where k is the workpiece shear strength and m is the friction factor. This friction model works fairly well for bulk forming operations such as forging, extrusion, drawing, and ironing, which are typified by large interfacial pressures and bulk strains. Between these two extremes lies a challenging area of great importance, where the asperities have been flattened to a large extent but not completely. This situation is the most difficult to model, but is also
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FIGURE 37.7 ALCOA, Inc.)
Modern Tribology Handbook
Evolution of surface roughness in aluminum under tensile strain. (Courtesy of L.G. Hector, Jr.,
essential for modeling of sheet metal forming operations, where pressures are often insufficient to totally flatten surfaces. Unfortunately, it is difficult to estimate the friction factor between two materials from first principles, and empirical characterizations are necessary. 37.2.2.2 Surface Roughening Another important phenomenon is that of surface roughening. A workpiece undergoing a strain develops Lüders bands and relative motion between grains to effect an increase in surface roughness. As an example of this phenomenon, Figure 37.7 shows the evolution of surface roughness within grains of aluminum undergoing uniaxial stretching. In practice, surface roughening from slip lines is less important than grain-induced roughening or the “orange peel” effects. At small strains, the surface roughness in the absence of tooling varies almost linearly with total strain. Osakada et al. (1971) suggest that the roughening propensity may be related to the grain size and the lattice structure of a material. Roughening is greatest with large grain size and for structures with a limited number of slip systems. Thus, for a given grain size, HCP materials roughen the most, with much less roughening for FCC and BCC metals. Tokizawa et al. (1973) generally support these ideas but also include the influence of two material phases on the roughening process. Wilson et al. (1997) were able to model roughening of a surface with an upper bound model. In unlubricated bulk forming operations such as forging, rolling, and extrusion under large plastic deformation, a significant sliding distance between the tooling and workpiece surface can render long scratches on the workpiece surface. However, under small plastic deformation, the tooling surface finish can be effectively impressed or replicated into the workpiece for specific purposes. For lubricated conditions, the interaction of tooling and workpiece becomes somewhat more complicated. Wilson and Schmid (1992) showed that the final surface roughness is strongly dependent on the lubricant film thickness and the tooling surface. Examples of their results are shown in Figure 37.8. Sheet metal forming operations are more complicated, and surface evolution is also material dependent, regardless of lubricant film thickness.
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Ra =0 .05 +0 .15 4h
Surface Roughness (Ra), µm
0.8 0.7 0.6 0.5 0.4
Dry Light Paraffin
0.3
Cold Rolling Emulsion Base Oil Thick Petroleum Oil (slow)
0.2
Thick Petroleum Oil (fast) 0.1 0 0
2
4
6
8
10
Film Thickness, µm
FIGURE 37.8 Surface roughness vs. film thickness in rolling of 5052-O aluminum. (From Wilson, W.R.D. and Schmid, S.R. (1992), Surfaces in metal rolling, in PED, Vol. 62, Engineered Surfaces, Ehmann, K.F. and Wilson, W.R.D. (Eds.), ASME, New York, 91-100. With permission.)
The lubricant effectiveness has other implications with regard to surface quality. Material transfer from workpiece to tooling (pickup) can cause continual surface degradation, requiring periodic refinishing. Small workpiece particles can adhere to tooling or be generated through abrasive action of tooling asperities, and these can loosely adhere to the workpiece surface. These give the workpiece a black appearance and can be easily removed with a soft cloth, hence the reference to these particles as “smudge” or “smut.” One of the implications of roughening is the dynamic state of workpiece surface chemistry. New surface is generated from workpiece bulk during forming or cutting. This new surface will not have the characteristic oxide layers, entrained species, Bielby layers, etc., of conventional surfaces. Not surprisingly, these new surfaces are the critical locations with respect to adhesion, galling, and wear, and extreme demands are placed on the lubricants used to spread over newly created areas. 37.2.2.3 Miscellaneous Tooling and Workpiece Surface Effects In cold metalworking, tooling surfaces have a ground or polished finish. Less smooth surfaces are used for hot working tools. Recently, attempts have been made to investigate the added benefit of modified tool topography to increase the performance and reliability of metal working operations (Sheu et al., 1998). In the mixed lubrication regime, which is the most common regime for metalworking, the lubricant film thickness is affected by the size and orientation of the surface asperities in the manner investigated by Patir et al. (1978). This has important consequences in processes such as rolling. Some attempts have been made to tailor the tooling surface to optimize a process. For example, in impression die forging, the flashing regions will be made rougher to obtain higher friction, thereby improving die-filling. Special tool surface textures can be obtained through laser or EDM texturing. For example, Figure 37.9 shows an electron beam textured profile placed on a roll surface to produce a sheet that has an excellent lubricant retention capability for facilitating subsequent sheet forming. Workpiece asperities are a direct cause of adhesive and abrasive friction and wear, but the valleys of workpiece surfaces have a lubricating benefit that does not occur in machine design applications of tribology. The effects of subsurface straining and flattening of asperity peaks cause the lubricant trapped in valleys to become released and reduce friction and wear. This so-called micro-pool theory has been investigated by numerous researchers (Kudo et al., 1987; Lo, 1994; Lo et al., 1997; among others).
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734 µm
718 µm FIGURE 37.9 Photomicrograph of electron beam textured work roll surface for use in aluminum rolling. D3 is the diagonal length of the rectangle shown. (Courtesy of L.G. Hector, Jr., ALCOA, Inc.)
37.3 Metal Cutting Metal cutting places extreme demands on tool materials. In addition to the very high pressures and temperatures in metal cutting, the geometries of the process often preclude the introduction of lubricant. Process geometries tend to become extremely complicated, and it is difficult to obtain closed-form solutions for temperature distributions, film thicknesses, etc. An excellent summary of the mechanical and tribological concerns in cutting is given by Shaw (1984). A simple orthogonal cutting operation is shown in Figure 37.10. From the image, it can be seen that there is intense shear along a plane of the workpiece; this observation is the basis of the Ernst and Merchant shear plane theory and is the classic start of machining analysis. For the purposes of this chapter, it should be recognized as a heat source, as should the frictional interface between the chip and the tool. The main result is that the cutting tool temperatures can be very high, as shown in Figure 37.11.
Chip
Tool
Shear plane Workpiece
(a)
(b)
FIGURE 37.10 The Ernst and Merchant shear plane theory: (a) schematic illustration; (b) photograph with dashed lines for emphasis. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
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600
500
Chip
360
6 50
600 500
380
130 Workpiece
650
7
00
400
450
60
Temperature °C
Tool
80 30
FIGURE 37.11 Illustration of temperature distribution in metal cutting. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
Thus, although the wear mechanisms to be discussed in this chapter are also present in gears, bearings, and the like, the superposition of high temperatures makes them much more serious. Also, it should be recognized that the portion of the chip in contact with the tool has a freshly generated surface and therefore does not contain an oxide coating or entrained lubricant. This very reactive material, thrust against the tool under great pressure and high sliding speeds, can cause significant and rapid wear in the tool.
37.3.1 Cutting Tool Materials According to the Archard wear law, the tool life can be maximized using a tool material with high hardness. It is critical that the hardness be maintained at cutting temperatures, and also that it have a high fracture toughness in case of interrupted cutting conditions or chatter. In addition, the tool should have chemical inertness at high temperatures and, to reduce operating temperatures, should have high thermal conductivity. Very few materials display all of these properties. One of the common solutions to the material selection dilemma is to apply a coating of hard and chemically inert material to a ductile and thermally conductive substrate. Some of the more successful coatings and tool materials are summarized in Table 37.1. A relatively recent development is the production of multiphase coatings, such as shown in Figure 37.12, where each layer is on the order of a few micrometers. Because hardness is known to increase with decreasing grain size, each layer has very high hardness.
37.3.2 Cutting Tool Wear The wear of cutting tools is extremely complex, involving many competing phenomena, including: 1. Abrasion. This can arise from direct abrasion from chip/tooling or workpiece/tooling interactions, or it can be due to fragments of built-up edge against the tool face or occasional hard inclusions in the workpiece. 2. Adhesion. The hot, chemically reactive workpiece can bond to the tool material and gradually remove material. Adhesion can facilitate diffusion of workpiece material into the tool, further emphasizing the importance of tool material chemical inertness. 3. Delamination of a coating can occur, especially when temperatures become very high and bond strength is suspect. In addition, it is beneficial to have similar thermal expansion coefficients
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Selected Properties of Useful Cutting Tool Coatings
Tool Substrate Cemented-carbide cutting tool Cemented-carbide cutting tool
Coating Material/Treatment
Coating Thickness (µm)
TiC, TiN HfN, TiC/Al2O3, Al2O3, TiC/TiN (Ti, Al)N, TiN/TiC
8–10 —
CVD CVD
Several times
—
CVD IP
Three times better with (Ti, Al)N Three times better with (Ti, Al)N Fifty times Several times
Cemented-carbide (M15) cutting tool HSS drill
(Ti, Al)N, TiN
—
HSS (M-7) drill Cemented-carbide cutting tool Cemented-carbide cutting tool Cemented-carbide cutting tool HSS (M42) cutting tool HSS (M-10) drill
TiN TiN TiN, HfN, ZrN TiN, TiC TiC TiC, TiN
1–2 5 8–15 5 5–8 2
Deposition Methoda
MS MS CVD, IP, MS, ARE IP, CVD ARE ARE
Improvement in Wear Life
Three to eight times Twenty times
a
Key: CVD, chemical vapor deposition; MS, magnetron sputtering; IP, ion plating; ARE, activated reactive evaporation. From Bhushan (1991).
FIGURE 37.12 SEM image of multiphased coating for use in metal cutting. (From Kalpakjian, S. and Schmid, S.R. (2000), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
between coating and substrate, because the coating must maintain its integrity at process temperatures as well as at room temperature (when the tool is installed). 4. Thermal fatigue can be a concern, especially in interrupted high-speed machining. 5. Thermal shock can cause gross fracture of tooling material. 6. Corrosion is a concern. Rupture of material along the shear plane can lead to the production of charged species. An electrical current is then generated in the vicinity of the tool nose, and can lead to corrosion assisted wear. Opitz (1957) reports that a superimposed current forcing the tool to be the cathode can be very effective in reducing wear for this reason. The sites of cutting tool wear are shown in Figure 37.13. Crater wear occurs on the tool face a short distance from the tool nose. This can be readily understood by comparing the wear pattern to the temperature distribution shown in Figure 37.11. Crater wear is predominantly due to abrasion and adhesion phenomena. Flank wear occurs on the flank edge of the cutting tool due primarily to abrasive action against the workpiece surface. Flank wear causes increased friction with the workpiece, a loss in dimensional accuracy, and a compromised workpiece surface finish. Nose wear is important because it can result in higher cutting forces and in the generation of a built-up edge (BUE). BUE is inherently
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Thermal cracks in interrupted cutting Chamfer 5 2
6
2
5
2 4
3
1
4 1
4
Carbide
1
3
High-speed steel
1. Flank wear (wear land) 2. Crater wear 3. Primary groove or depth of cut line
Ceramic
4. Secondary groove (oxidation wear) 5. Outer metal chip notch 6. Inner chip notch
FIGURE 37.13 Illustration of the forms of cutting tool wear. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
unstable, causing dynamic changes in cutting conditions and therefore perturbing the tooling from its desired path. Cutting tool inserts are used for a number of reasons. First, inserts can be quickly changed, so that machine downtime is very low. Inserts are produced with a number of cutting edges to improve economy. Finally, inserts are small and hard coatings can be more easily deposited onto an insert than onto large tool shanks, for example. Tool life predictions are available for most machining operations. The basic theory was developed by F.W. Taylor (1907) and is simply expressed by the Taylor equation:
VT n = constant
(37.7)
where V is the cutting speed, T is the tool life, and n is a constant of the cutting tool material. Because n is usually around 0.2 or so, speed is seen to have a drastic effect on tool life. The Taylor tool life is often generalized as:
TV 1 nt 1 mb1 l = constant
(37.8)
where t is feed rate and b is depth of cut. Usually, n < m < l (Shaw, 1984). One of the problems with wear models is that they have different meanings for different process parameters and operations. For example, in lathe turning, it is common to perform one or more “roughing cuts” with high feed rates, cutting speed, and depth of cuts where the surface quality is not a concern and the tool does not need to be replaced until it fractures. On the other hand, “finishing cuts” occur at low feed rates and depth of cuts, and the surface quality is extremely important. Thus, the tool can be replaced when crater wear adversely affects surfaces, and is in general much earlier than in roughing cuts. Also, the exponents given in Equation 37.8 are fairly constant only over a range of temperatures. If a circumstance should arise that causes an increase in temperature (such as speed increase, cutting fluid supply interruption, etc.), then the constants inserted into the wear model expressions are immediately suspect.
37.3.3 Cutting Fluids Cutting fluids are very commonly applied to metal cutting operations. The benefits and mechanisms of cutting fluid action in cutting operations depend on the process kinematics.
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For uninterrupted cutting, the main benefit of a cutting fluid is to cool the workpiece and tool. Fluids are commonly emulsions made of mostly water to further emphasize the cooling function of these fluids, and the workpiece is flooded with a generous stream of liquid. A less obvious benefit is the potential of capillary action to allow fluid to seep into the tool/chip interface from the side. In interrupted cutting, such as in face milling, tapping, etc., the fluid serves as a coolant but also as a lubricant. These fluids are formulated to develop boundary films on hot tooling surfaces, thereby increasing tooling life. As such, EP additives, antioxidants, corrosion inhibitors, and brighteners will be incorporated into the fluid formulation.
37.4 Finishing Operations Finishing operations such as grinding, lapping, polishing, etc., use the abrasive action of small particles to remove material and refine surface finish. It is essential for the production of superior surfaces required for applications ranging from hard disk to bearing manufacture. For the interested reader, the books by Shaw (1996) and Malkin (1989) are excellent resources.
37.4.1 Coated and Bonded Abrasives Operations such as grinding, polishing, buffing, etc., utilize the high hardness and aggressive nature of small aluminum oxide or silicon carbide particles, either in coated or bonded form. In either case, the basic process mechanics are similar, but this chapter section emphasizes the application of bonded abrasives. Bonded abrasives consist of small abrasive particles suspended in a polymer or ceramic matrix, referred to as resinoid or vitrified, respectively. When mounted on a high-speed spindle and pushed against a surface, the particle can interact with the surface in a number of different ways: • With high attack angle, the particle can generate a chip in the workpiece. • At lower attack angle, a chip will not be generated, but the abrasive will plow a groove in the workpiece. • When the contact forces are relatively low, the abrasive will merely interact elastically. Compared to conventional machining processes, abrasive machining is much less efficient in terms of the energy required to remove a unit volume of material. The mathematical description of chip generation in abrasive machining is similar to that in cutting, but a major distinction is that material removal takes place at large negative rake angles, therefore requiring much higher specific energies. Thus, the chip and workpiece have the potential of reaching much higher temperatures than in cutting, and thermal damage of the workpiece is a serious concern. Plowing results in energy dissipation through plastic deformation of the workpiece surface layers, and is one of the reasons for the high energy requirements in grinding. However, there are benefits to plowing action; namely, that the plowed groove’s ridges are more easily removed by subsequent abrasive particles and plowing leads to a high degree of surface cold work. Wear results in the dulling of abrasive grains. Workpiece material can also adhere to an abrasive wheel, having the effect of shielding the more abrasive particles. In addition, abrasives are sometimes broken from the wheel surface, so that workpiece/tool interactions are substrate dominated. These effects require periodic treatment of the wheel to expose fresh, new abrasives. Grinding wheel wear will inevitably occur, but the wear rate depends on process parameters as well as geometry and material considerations of the wheel. The grinding ratio is defined as the ratio of workpiece volume removed to the volume of wheel wear, and can vary over a wide range; Kalpakjian (1998) gives the range as from 2 to 200. Malkin (1989) explains that the grinding ratio is a function of the equivalent chip thickness:
v a G = G1heq− g = G1 w vs
−g
(37.9)
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1399
where vw is the workpiece feed rate, a is the wheel depth of cut, vs is the grinding wheel surface velocity, and G1 and g are constants. Equation 37.9 was derived in a similar form by Snoeys et al. (1974). Grinding is often performed in the presence of a fluid. This fluid has two main requirements: it must (1) cool the workpiece and wheel, thereby reducing thermal stresses and the amount of material adhering to the wheel and reducing wear rates; and also (2) reduce friction during plowing and elastic contact.
37.4.2 Advanced Machining Operations Sometimes, a better surface is desired than can be attained through the abrasive machining processes described above, or else the workpiece material is difficult to machine. There are a number of specialized machining operations that should be briefly noted for their unique tribological nature. Lapping uses a slurry of abrasive particles forced between a large wheel and a workpiece. The abrasive particles in the slurry are extremely small, and allow machining of surfaces as smooth as 0.025 µm (Kalpakjian et al., 2000). Material removal is due to the three-body wear phenomenon, with the particles in the slurry being a purposefully introduced third body. Electrochemical machining uses a metal wheel embedded with diamond or aluminum oxide abrasives. An electrical power source is attached to the wheel and workpiece, and an electrolytic fluid (usually sodium nitrite) is provided. Material removal is predominantly through electrolytic action, and the abrasive particles serve to remove electrolytic products and to cold work the surface layers. Chemical mechanical polishing uses a chemically reactive environment in combination with abrasives to assist surface machining. Hydrodynamic machining, also referred to as water jet cutting, uses the abrasive action of a highly focused stream of fluid to remove material. Material removal is through erosion, or a combination of erosion and abrasion if particles are suspended in the fluid.
37.5 Bulk Forming Operations Bulk forming operations are characterized by their very high strains and large forming speeds. In bulk forming, friction is usually brought to as low a level as possible, given other constraints (such as on surface finish). The exception to this is metal rolling, in which a certain amount of friction is necessary to cause the strip to pass between the rolls. Wear of tooling is a cost concern, and hard materials and coatings are being sought for tool or insert construction. As is typical, surface finish is critical in many operations.
37.5.1 Rolling Rolling is an extremely demanding — and arguably the most important — metal forming process because most metal parts are, at one point or another, rolled. Rolling takes place hot or cold. In hot rolling, the demands on surface finish are not as stringent, and the operations are usually performed in larger thickness products and on reversing mills. Cold rolling has strict surface finish requirements and thinner gages and usually occurs on tandem mills. 37.5.1.1 General Theory of Metal Rolling Lubrication From a process mechanics standpoint, a very important concept is that of the neutral point. Because rolling can be taken as a plane strain operation, the workpiece velocity will increase during a rolling operation. The elastically deformed rolls move at constant velocity, which in the absence of front and back tension is faster than the workpiece initially, but eventually is slower than the workpiece velocity. The position where the roll and workpiece velocities are equal is the neutral plane or neutral point. Note that the friction forces acting on the workpiece change direction at the neutral point, a critical consideration for process modeling. With front and back tension, the location of the neutral point can be adjusted and can even occur outside of the roll bite. It is then useful to express the forward slip in an operation by:
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Sf =
v1 − vr yn − y1 = vr y1
(37.10)
where Sf is the forward slip, v1 is the final workpiece velocity, vr is the roll velocity, yn is the gap thickness at the neutral plane, and y1 is the final workpiece thickness. Forward slip is an extremely important process control parameter. It can be directly related to the neutral point location and can be readily measured. The mean friction coefficient and the neutral point location are related by:
1 2R′ S f = φ2 − 1 2 y1
(37.11)
where φ is the angular location of the neutral plane and R′ is the effective roll radius after compensating for roll flattening. One expression for φ is given by Ford et al. (1951) as:
y −y 1 φ = sin−1 0 1 2 R
12
−
(
)
σ h0 − h1 + h0t 0 − h1t1 2σR′µ
(37.12)
where σ is the workpiece material flow stress of the workpiece, and t0 and t1 are the back and front tensions, respectively. Therefore, the forward slip gives a direct and reliable method of obtaining the average friction coefficient. Rolling requires friction. In the absence of friction, no workpiece can be drawn into the gap and the roll will slide over the workpiece.* Therefore, pure hydrodynamic films are rarely encountered, although the mechanisms of hydrodynamic lubrication are still worthwhile for tribological understanding. The main benefit is the ability to predict the lubricant film thickness at the entry of the contact zone, such as with the Wilson-Walowit (1972) equation:
h=
6 ηγU
(
tan θ 1 − e − γσ
)
(37.13)
where h is the film thickness, η is the lubricant viscosity, γ is the viscosity pressure coefficient, U is the mean inlet rolling speed, and θ is the contact angle between roll and workpiece. It should be noted that the product γσ is usually a large number; the denominator term in parentheses is usually very close to unity for most lubricants. A common lubricant in metal rolling consists of oil droplets suspended in water. Oil-in-water emulsions are widely used but poorly understood. A recent summary by Schmid et al. (1996) identified a number of suggested modeling approaches, including plate out of oil, dynamic concentration of oil, mixture theory, and surface tension-driven replenishment. Apparently, each of these is dominant at a different speed range, further complicating the mathematical and experimental investigations of emulsions. Wilson et al. (1993, 1994), Schmid et al. (1996), and Kimura et al. (1987, 1989) have forwarded explanations for this paradox. This is best explained by the Dynamic Concentration theory, shown in Figure 37.14. Basically, as oil droplets become entrained between tooling and workpiece (rolling is depicted in the figure), they are preferentially entrained further into the contact because of their higher viscosity. Water is forced back through the inlet zone as it is displaced by the ever-flattening cylindrical oil droplets. An additional mechanism in hot working is the loss of stability of the emulsion when it is *Note that rolling with a front tension can still take place. Steckel rolling uses sufficient front tension to pull material through the idler work rolls.
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y x oil U
z x supply region
concentration U pressurization region region
water
contact region
FIGURE 37.14 Illustration of the dynamic concentration theory of emulsion lubrication. (From Schmid, S.R. and Wilson, W.R.D. (1996), Lubrication mechanisms for oil-in-water emulsions, Lubr. Eng., 52, 168-175. With permission.)
heated. Apparently, the oil will more readily separate from the solution at elevated temperatures and will provide thicker lubricant films. 37.5.1.2 Hot Rolling When metal is continuously cast into slab or into ingot, it is fairly thick. Usable plates, sheets, and foils require a large reduction in thickness, requiring large ductility of the workpiece, which can be obtained by hot rolling. Hot rolling reductions are as high as 50% per pass, although a 1- to 2-in. draft (thickness reduction) per pass is more usual. Hot rolling is done on reversing mills so that a slab can be rolled repeatedly by changing the roll rotation direction after each pass. The large draft requires high friction in order to draw the workpiece through the rolls. The high temperatures associated with hot rolling, and the fact that nascent surface generated from the workpiece will be extremely active implies that the propensity for material transfer to the rolls is very strong. This transferred material or pickup can adhere strongly and generate a stable coating on the rolls (roll coating), or it can become spalled due to high contact pressure at work/backup rolls’ interface and then be redeposited on the workpiece surface, compromising surface appearance. In addition, billets may have a very hard, thick, brittle, and abrasive oxide layer that can damage roll surface finish. Therefore, it should be realized that the surface roughness that can be obtained in hot rolling is usually higher than that which results from cold rolling. Often times, to develop the large friction forces necessary to roll material, a rough surface is machined into the work rolls. More commonly, the surface of rolls is made smooth and a natural roughness from roll coating eventually develops. When a lubricant is used, it is usually an oil-in-water emulsion with additives formulated for the workpiece material. Although speeds are high and the contact angles can be small in hot rolling, boundary lubrication is the usual regime when liquid lubrication is present. Schey (1985) mentions that glasses can develop full hydrodynamic films, but these lubricants are rare in practice. 37.5.1.3 Cold Rolling Cold rolling is usually conducted on metal that has already been hot rolled. The smaller material thicknesses require higher rolling speeds for economic considerations. Gage and surface control are more important in cold rolling, so lubrication is vital to reduce roll bending and material transfer and re-transfer. Although carbide rolls are used in foil rolling, most rolling is conducted with cast or forged steel rolls. Most rolls for steel rolling have a slightly rough surface produced by electro-discharge texturing, while those for aluminum have a ground finish. Chrome plating to reduce roll wear and material transfer is common. Figure 37.8 showed that the surface finish is strongly dependent on film thickness, so that the WilsonWalowit equation (Equation 37.13) can give a direct feel for the surface roughness that can develop. Clearly, a smooth surface can be produced at very low speed for any lubricant. For economic reasons,
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however, rolling is conducted at high speeds using low-viscosity lubricants. Traditionally, this meant short-chain-length paraffins and aromatics, but emulsions are used extensively in modern practice. Emulsions have the benefits of good lubricating and cooling properties, combined with economy and fire resistance. It should be recognized that a smooth surface can be generated by flattening mechanisms as described above. However, intimate asperity contact results in pickup and roughening of the work rolls; this forces periodic refinishing or in-line wire brushing to remove pickup, particularly with aluminum. Smudge is a common concern; Reich et al. (1994) suggest that effective lubricant additives reduce surface energy and make smudge a more severe problem with aluminum. Maintenance of the lubricant is a difficult proposition. Residual lubricant from hot rolling stages can contaminate cold rolling lubricants. Another contaminant is tramp oil, a term for greases and heavy oils whose sources are the bearings, gears, and hydraulic pipes of the rolling mill. If there are a number of hot and cold rolling operations, the residual oil on the workpiece surface is an increasingly complicated mixture of all upstream lubricants and becomes increasingly difficult to control. Often times, a final oil is applied to a roll to prevent welding of adjacent wraps of coiled sheet or foil. Obviously, this is sometimes compromised by residue lubricants.
37.5.2 Forging Forging is the controlled deformation of metal using compressive stresses. There is usually a distinction between open die forging (where flat or other simple tooling shapes are used) and closed or impression die forging (where quite intricate dies can be used). Open die forging is always performed hot, while closed die forging can occasionally be done on cold workpieces. Extrusion of small discrete parts is often done in dies and has similar lubrication issues as forgings, as discussed here. Extrusion of continuous cross-sections is discussed in Section 37.5.3. 37.5.2.1 Hot Forging Open die forging is commonly performed hot on cast billets to obtain a form more suitable for further processing. Open die forging operations can be upsetting, cogging, or any plane strain compression operation. Dies are usually constructed from a hardened tool steel and are of simple shapes. Surface finish is usually not a primary concern; indeed, hard oxide scale will often break off of the billet during the operation, making the production of smooth surfaces extremely difficult in hot forging. Friction is of major concern and has an effect on the strains experienced by the workpiece. Figure 37.15 shows a sequence of steps in the upsetting of a metal cylinder. Note that the originally cylindrical workpiece takes on a barreled profile due to restricted flow at the die interface caused by friction. The upsetting force and maximum die pressure is strongly affected by friction. It can be shown that the die pressure distribution in plane strain upsetting of a workpiece obtained from a slab method analysis is given by:
p=
( )
2µ x − a Y exp h 3
2
(37.14)
where p is the die pressure at location x; x is the distance from the edge of the workpiece; Y is the material uniaxial flow stress; µ is the friction coefficient; a is the workpiece semi-width; and h is the workpiece thickness. A similar expression can be obtained using a friction factor, but the importance of friction is clear. Lubricants, when used in hot open die forging, consist of solid lubricants such as graphite or glass. Closed die hot forging is performed in drop hammers, mechanical presses, and hydraulic presses. Dies are constructed from highly alloyed (tool) steels or carbide for inserts. Workpieces are usually phosphated prior to hot forging operations (see Section 37.2.1). Lubricants usually include graphite in a liquid carrier, either oils or emulsions of oils. The carrier is chosen for good spreadability on the tooling and workpiece.
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FIGURE 37.15 Upsetting of a solid cylinder. Note the increase in barreling as the thickness is reduced. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
Top die
1. Erosion 2. Pitting (lubricated dies only) 3. Thermal fatigue 4. Mechanical fatigue 5. Plastic deformation
2
5
1 5 3 4 2 1
5
1 5
3 4
1
Bottom die Ejector
CL
FIGURE 37.16 Wear patterns in a forging die. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., Prentice-Hall, Upper Saddle River, NJ. With permission.)
Impression die forging usually requires flashing in order to develop sufficient pressure to completely fill a die cavity. It would be desirable to obtain a high friction coefficient on the flashing to aid die filling, but lubricants are used to reduce friction over the entire die. Wear patterns can be quite complex, with multiple phenomena occurring within a single die (Figure 37.16). 37.5.2.2 Cold Forging When improved material properties or surface finishes are required, cold forging operations are often applied. Examples include impression die forging, heading, orbital forging, and extrusion. Because forging temperatures are fairly low, a much larger variety of lubricants is available and can be tailored through additives to a particular process and material. The main role of the lubricant is to reduce friction. As such, the chemical makeup of the lubricating oil will be fairly complex. An additional role of lubricant is to present a thermal barrier between the die
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and workpiece. This serves two purposes. First of all, because the tooling rarely achieves a steady-state temperature as high as the workpiece preheat, the lubricant can help slow loss of workpiece heat through the tooling. Because cooler workpieces have a higher flow strength, this thermal isolation effect is one mechanism by which friction is reduced. In addition, a good thermal barrier slows die wear. Lubricants used in cold forging include: 1. Metal coatings: examples include zinc or tin and occasionally copper. This is an especially viable option when parts will be coated with these metals after forging. The advantages to using these metallic coatings are reduced material transfer to the die and reduced friction. The main effect of using a soft metal is a reduction in shear strength, which from Equation 37.6 reduces the friction with fully flattened asperities. 2. Solid lubricants: mainly graphite and molybdenum disulfide. 3. Polymer coatings: usually as an intermediate film or deposited onto the workpiece. The main concern associated with polymer coatings is the propensity for tool pickup and chemical degradation. 4. Liquid lubricants formulated with proper additive packages: can be used for light-duty applications. 5. Phosphate conversion coating: the vast majority of forging operations are conducted with these coatings, as described in Section 37.2.1. The phosphate coating is used in combination with an oil, emulsion, soap, or solid lubricant. One of the main drawbacks to a thick lubricating film is the generation of a rough workpiece surface, a phenomenon known as orange peel. Wilson et al. (1997) have described the mechanisms associated with surface roughening. In addition, some lubricants — most notably powdered soaps — can adhere to and foul tooling, resulting in a loss of dimensional tolerance.
37.5.3 Extrusion and Drawing When simple sketches of extrusion and drawing operations are made, the only apparent difference is that the workpiece is pushed through dies in extrusion, while it is pulled through the dies in drawing. In actuality, the processes have very real differences, perhaps the most important being that extrusion is a batch process, while drawing can be a continuous process. More subtly, extrusion will use far greater reductions in area per pass than drawing, and therefore will generally be performed at a higher temperature to obtain greater workpiece ductility. Good general references on extrusion are Saha (2000), Schey (1985), and Laue et al. (1981). General drawing references are Schey (1985) and Tassi (1981). 37.5.3.1 Extrusion Extrusion can be used as a pressworking operation as a complement to forging, as discussed in Section 37.5.2. This section relates to the more specialized process wherein semifabricated products are produced. The starting material is a cast or previously rolled billet, placed in a container and pushed by a hydraulic press through a die. Three main processes — direct extrusion, indirect extrusion, and hydrostatic extrusion — are shown in Figure 37.17. In direct extrusion, the material moves in the same direction as the pressing stem, and significant friction can develop between workpiece and container. In indirect or reverse extrusion, the billet is at rest in the container, so that friction is generated only at the die/billet interface. Hydrostatic extrusion uses a pressurized liquid to effect extrusion, giving increased process flexibility and effectively increased workpiece ductility at the expense of reduced process simplicity. Surface finish is usually a concern with extrusion, and a number of surface defects are associated with friction and lubrication problems. Oil peel is a workpiece roughening that results from excessively large film thicknesses. Bambooing is associated with stick-slip, with the characteristic length of the bambooing defect having essentially the same value as the land in the extrusion die. With excessive land lengths, workpiece scoring and abrasion can result. Hot extrusion is commonly conducted with glass as the lubricant. The glass is applied as a pillow of glass powder placed in front of the billet. The glass is often mixed with binders such as sodium silicate
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Container
Container Liner Billet Die
Pressing Stem
Die Backer
Dummy Block
Extrusion
(a)
Seals
Billet Dummy Block
Die
Container Liner
Pressing Stem
Backing Disc
Tool Stem
Fluid Container
Container Die
Extrusion
Extrusion
(b)
Die Backer
(c)
FIGURE 37.17 Schematic illustration of the basic forms of extrusion: (a) direct; (b) indirect or reverse; (c) hydrostatic. (From Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., PrenticeHall, Upper Saddle River, NJ. With permission.)
or bentonite. Another approach is to expose the hot billet to glass powders before insertion into the cylinder. This causes particles to adhere to and melt on the billet surface, and has the added benefit of insulating the billet and retarding heat loss to the container. Glass films are generated by hydrodynamic means and are usually relatively thick, as evidenced by force measurements and the unavoidable presence of orange peel. Other melting solids such as waxes and polymers can be used, but are less popular than glass. Solid lubricants in the form of soft metals, polymers, or lattice-layer compounds can also be used in hot extrusion. Metallic coatings can reduce friction, as discussed above. Often, the extrusion process is used as a cladding operation to manufacture a coated workpiece, and in this case the coating has the additional beneficial effect of providing lubrication. Graphite and polymers are used in hot and cold extrusion, respectively. Liquid organic lubricants are commonly used for cold extrusion because product surface finish requirements are usually more stringent and the lower process temperatures allow their application. Extrusion does allow for thick lubricant films to be entrained once the process reaches steady state, but there is a difficulty with the start of a process. Wilson (1971) showed that the lubricant entrainment velocity is one half the billet velocity, resulting in lubricant breakdown unless the extrusion operation is initiated using displacement increments through the die.
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Hydrostatic extrusion presents unique difficulties because the hydrostatic pressure in the container promotes thick lubricant films. However, because all but the most inviscid oils would solidify in the container under process pressures, mixed lubrication is, by far, the more widely encountered condition. The working fluids are therefore formulated with EP additives to reduce die friction. Often, additional lubricants such as grease or a soap/phosphate coating are applied to the billet. The bambooing defect due to lubricant breakdown is especially a concern in hydrostatic extrusion. 37.5.3.2 Drawing Drawing should not be confused with deep drawing, which is a sheet metal forming operation discussed in Section 37.5.4. Continuous lengths of wire and tube can be obtained by drawing, as can finite lengths of finished products. As compared to extrusion, drawing has more stringent surface finish requirements and is more commonly performed cold. Tube drawing can be performed with an internal mandrel or plug mandrel. Using a plug mandrel is the only situation where friction is advantageous, and usually lubrication will be pursued to reduce drawing stresses. Liquid lubricants are commonly used, with the desire to obtain a mixed film regime. (Soap and wax are common for steel extrusion.) In theory, using a sufficiently viscous liquid will promote the formation of a hydrodynamic film, but in practice a number of die features are used to develop thicker inlet films or reduce friction. These include: 1. A bell and entrance section of the die encourages lubricant flow into the interface. 2. Contouring the die profile to promote lubricant entrapment or to promote more uniform strain distributions. An example is the streamlined die of Richmond et al. (1967). 3. Inlet tubes, shown in Figure 37.18a, can be used to develop a hydrostatic pressure in a viscous lubricant just before a drawing die, as shown by Christopherson et al. (1955). The drawback is that the tube must be relatively long (50 to 400 mm) and the clearance with the wire in the tube must be small (0.05 to 0.01 mm). Contaminant particles can also plug the tube. Note that the wire deforms somewhat due to hydrostatic pressure before it reaches the actual die. 4. Multiple dies can be used, as shown in Figure 37.18b. Here, the first die acts as a seal to allow lubricant, usually grease or soap, to pass through and become pressurized in the chamber between dies. Harper (1976) used a form of double die with a liquid lubricant, and found that this encouraged formation of films sufficiently thick to eliminate the bright surface finish desired in drawing. 5. Hydrostatic pressure is occasionally introduced in the chamber of a double die. Schey (1984) reports that real lubricating effects are only encountered when the pressures are sufficient to cause initial yielding in the chamber. Most research has been performed on isothermal drawing. As discussed by Schey (1984), there is a significant die temperature increase over the first meter or so of a drawing operation, so that a thermal analysis of drawing is needed.
Full-size wire
Leader wire
Direction of flow ~200mm (a)
(b)
FIGURE 37.18 Approaches for encouraging lubrication entrainment in wire drawing: (a) inlet tubes; (b) multiple dies. (From Schey, J. (1984), Tribology in Metalworking, American Society for Metals, Metals Park, OH. With permission.)
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37.5.4 Sheet Metal Forming Operations Sheet metal forming comprises an important group of processes with a wide range of applications. The most important are probably the stamping of automobile bodies from steel, and the drawing and ironing of beverage containers in steel and aluminum. Tribology has important implications in tooling design and formability in sheet metal forming operations. 37.5.4.1 Friction Modeling As discussed in Section 37.2, friction in sheet metal forming operations is a difficult phenomenon to incorporate into process models. However, with low friction, the sheet tends to slide over the tooling and distribute strains over a larger area, which has the effect of reducing the maximum strain and increasing formability. When designing tooling, it is desirable to predict sheet strains in order to design robust tooling. The use of a Coulomb friction model leads to highly inaccurate predictions, requiring a more sophisticated approach toward friction. The most important concept in the tribology of sheet metal forming is that any of the lubrication regimes (boundary, mixed, thin film, full film) can occur simultaneously at different locations in the tooling/workpiece interface. Friction tends to be lowest in the full film regime and to increase as the system passes through the mixed regime into the boundary film regime. Wear rates show similar trends. Figure 37.19 shows the friction data measured by Emmens (1988) for strips of different surface finish drawn between flat platens with different lubricants and sliding speeds. The results are quite similar to a Stribeck chart with the abscissa variable being the dimensionless speed defined by:
Ss* =
µUx pR2
(37.15)
where µ is the coefficient of friction, U is the sliding speed, x is the length of contact, p the interface pressure, and R the roughness (maximum peak height). Wilson et al. (1995) defined the local film thickness in a stretch forming operation using an internal variable approach. Their model included a lubrication analysis for the local film thickness and a friction stress calculation for different lubrication regimes, including the full film, mixed film, and boundary regimes. Figure 37.20 compares the predicted strains with the measurements performed by Hector et al. (1991) for forming a brass dome. The approach used is able to accurately predict strain distributions,
boundary
mixed
full film
Friction coefficient
0.20 0.15 0.10 0.05 0 0.01
EDT shotblast lasertex 0.1
103 Nondimensional speed, Ss* 1
10
100
104
FIGURE 37.19 Friction coefficient in deep drawing as a function of dimensionless speed. (From Wilson, W.R.D. (1997), Tribology in cold metal forming, J. Manufact. Sci. Eng., 119, 695-698; with data from Emmens, W.C. (1988), The influence of surface roughness on friction, in Controlling Sheet Metal Forming Processes. American Society for Metals, Metals Park, OH, 63-70. With permission.)
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0.3 experiment computer simulation n ai str l a di ra
0.3
radial strain
Engineering strain
Engineering strain
0.4
0.2
circum feren tial stra in
0.1
0
0
0.2
0.4
0.6
circu mfe ren t
0.2
ial st
rai n
0.1 experiment computer simulation
0.8
Dimensionless radial position
0 0
0.2
0.4
0.6
0.8
Dimensionless radial position
FIGURE 37.20 Predictions of strains in axisymmetric stretch forming of brass over a spherical punch: (a) low-speed conditions; (b) high-speed conditions. (From Wilson, W.R.D., Huang, X.B., and Tsu, T.C. (1995), A realistic friction model for computer simulation of sheet metal forming operations, J. Eng. Ind., 117, 202-209. With permission.)
regardless of speed without any arbitrary changes in friction characterization parameters, a result that is impossible using constant coefficient of friction models. 37.5.4.2 Lubricants Sheet metal forming operations, as opposed to bulk deformation operations and metal cutting, present an application for liquid lubricants. Single-phase lubricants consist of base oil with usual additives (boundary, EP, brighteners, corrosion inhibitors, etc.). In addition, oil-in-water emulsions are commonly used in stamping and can-making operations, two situations where part cleanliness and cooling capability are important reasons for their success. Soft solid coatings (waxes, soaps, polymers, etc.) are also important in forming difficult sheet metal parts. Coduti (1986) has shown that they often have lubricating properties superior to liquids. Unfortunately, relatively little research has been performed on solid coatings in sheet metal forming. Initial work was performed using polymer sheets placed as an intermediate layer between tooling and workpiece; for example, Schey (1984) reports work by Blaich (1981) using oiled polyethylene sheets successfully. A more common approach is to use polymer coatings. Franks and Plevy (1979) observed that Teflon® coating applied to ceramic substrate fired onto aluminum sheet reduced draw and peak forces and also increased the depth to which a container can be deep drawn without rupture. More recently, Jaworski et al. (1999a,b) presented mathematical and experimental results of ironing with polymer coatings on steel. Metal coatings are widely applied to sheet metal, especially steels. For example, tin-coated steels had the dual beneficial effects of lubrication and corrosion inhibition for food containers. Another approach is to modify the tool surface, either with a tribologically beneficial coating or through texturing. Dohda (1990) describes the tribological properties of thin hard coatings, while Sheu et al. (1998) give an excellent overview of tooling surface texture development. 37.5.4.3 Smudge, Orange Peel, and Galling Surface finish concerns are critical with sheet metal parts. Smooth surfaces result in a marketing advantage for containers and automotive sheet metal parts, as well as performance improvements. Major obstacles to generation of superior surfaces are smudge, orange peel, and galling. Smudge and galling are somewhat related. When tooling asperities interact with workpieces, wear fragments are occasionally generated. Sheu et al. (1988), as well as Hector et al. (1993), have suggested
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that microcutting is the dominant mechanism in obtaining this wear debris, similar to grinding operations discussed in Section 37.4. If these particles are removed from and loosely adhere to the workpiece, they are easily removed with a soft cloth and have the appearance of a dirty surface — hence, the term “smudge.” If the particles adhere to the tooling, they will result in gross machining marks or grooves in the product, known as galling. Lubricants are formulated to hinder galling through use of boundary additives and through cooling of tooling. Much of the propensity for galling is material based. For example, 3004 aluminum alloy was specifically developed for can-making to reduce material transfer to the tooling. One of the benefits is that hard inclusions of Al12(MnFe)3Si particles continuously scrape the tooling surface and remove transferred aluminum (see Hosford et al., 1994; Opalka et al., 1999). Orange peel is caused by roughening of surface due to plastic deformation, and has been described in Section 37.2.2.2. In sheet metal forming operations, a workpiece may roughen, regardless of film thickness. More accurately, the workpiece does not flatten because of the low interface pressures that can be present. Saha et al. (1994) encountered both behaviors with different aluminum alloys.
References Bay, N. (1997), Cold forging lubricants, Proc. 1st Int. Conf. On Tribology in Manufacturing Processes, Gifu, Japan, 9-21. Bhushan, B. and Gupta, B. K. (1991), Handbook of Tribology, McGraw-Hill, New York. Blaich, M. (1981), Report No. 61, Inst. fur Umformtechnik, University of Stuttgart, 1981, (in German). Christopherson, D.G. and Naylor, H., Proc. Inst. Mech. Eng., 169, 643-665. Coduti, P.L. (1986), Tribological Behavior of Solid Lubricant Films on Bare and Coated Sheet Steel Products, SAE Technical Paper 870648, Society of Automotive Engineers, Warrendale, PA. Dohda, K. (1990), Tribological properties of thin hard coatings used in metal forming, Proc. Japan Int. Trib. Conf., 1973-1980. Emmens, W.C. (1988), The influence of surface roughness on friction, in Controlling Sheet Metal Forming Processes. American Society for Metals, Metals Park, OH, 63-70. Ford, H., Ellis, F., and Bland, D.R. (1951), J. Iron Steel Inst., 168, 57-72. Franks, R. and Plevy, T.A.H. (1979), Sheet Metal Industries, 56, 500-511. Harper, S. (1976), Lubrication aspects for drawing non-ferrous wire, Wire Ind., 43, 623-626. Hector, L.G. and Sheu, S. (1993), Focused energy beam work roll surface texturing science and technology, J. Mat. Proc. Man. Sci., 2, 63-112. Hector, L.G. and Wilson, W.R.D. (1991), Hydrodynamic lubrication in axi-symmetric stretch forming. Experimental investigation, J. Tribol., 113, 667-674. Hosford, W.F. and Duncan, J.L. (1994), The aluminum beverage can, Sci. Am., 271, 48-53. Jaworski, J.A. and Schmid, S.R. (1999), Survivability of laminated polymer lubricant films in ironing, Tribol. Trans., 42, 32-38. Jaworski, J.A., Schmid, S.R., and Wang, J.E. (1999), An experimental investigation of the formability and friction characteristics of tin coated and polymer laminated steels, J. Manufact. Sci. Eng., 121, 232-237. Kalpakjian, S. (1998), Manufacturing Processes for Engineering Materials, 3rd ed., Addison-Wesley, Reading, MA. Kalpakjian, S. and Schmid, S.R. (2001), Manufacturing Engineering and Technology, 4th ed., PrenticeHall, Upper Saddle River, NJ. Kimura, Y. and Okada, K. (1985), Elastohydrodynamic lubrication with oil-in-water emulsions, Proc. JSLE Int. Trib. Conf., 937-942. Kimura, Y. and Okada, K. (1987), Film thickness at elastohydrodynamic conjunctions lubricated with oil-in-water emulsions, Proc. IMechE, C176, 85-90. Korzekwa, D.A., Dowson, P.R., and Wilson, W.R.D. (1992), Surface asperity deformation during sheet forming, Int. J. Mech. Sci., 34, 521-540.
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Kudo, H. and Azushima, A. (1987), Interaction of surface microstructure and lubricant in metal forming, Proc. 2nd Int. Conf. On AdTechnol. Plasticity, Stuttgart, 373. Laue, K. and Stenger, H. (1981), Extrusion, American Society for Metals, Metals Park, OH. Lo, S.-W. (1994), A study of flow phenomena in mixed lubrication regime by porous medium model, J. Tribol., 116, 640-647. Lo, S.-W. and Wilson, W.R.D. (1997), A theoretical model of micro-pool lubrication in metal forming, Proc. 1st Int. Conf. Tribology Manufacturing Processes, Gifu, Japan, 83-92. Malkin, S. (1989), Grinding Technology, Society of Manufacturing Engineers, Dearborn, MI. Opalka, S., Hector, L.G., Schmid, S.R., Reich, R.A., and Epp, J.M. (1999), Boundary lubricant effect on single asperity plowing, J. Tribol., 121, 384-393. Opitz, H. (1957), in Proc. Conf. Lubrication and Wear, Institution of Mechanical Engineers, London, 664-669. Osakada, K. and Oyane, M. (1971), On the roughening of free surface in deformation processes, Bull. JSME, 14, 171-177. Patir, N. and Cheng, H.S. (1978), An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, J. Lubr. Tech., 100, 12-17. Reich, R.A., Epp, J.M., and Gantzer, D.E. (1994), A mechanisms for generating aluminum debris in the roll bite and its partitioning between the surface of the roll and the surface of the sheet as smudge, Tribol. Trans., 39, 23-32. Richmond, O. and Davenpeck, M.L. (1967), A die profile for maximum efficiency in strip drawing, J. Mech. Phys. Solids, 15, 195. Saha, P.K. (2000), Aluminum Extrusion Technology, American Society for Metals, Metals, Park, OH. Saha, P.K. and Wilson, W.R.D. (1994), Influence of plastic strain on friction in sheet metal forming, Wear, 172, 167-173. Schey, J. (1984), Tribology in Metalworking, American Society for Metals, Metals Park, OH. Schey, J. (1999), Introduction to Manufacturing Processes, 3rd ed., McGraw-Hill, New York. Schmid, S.R. and Wilson, W.R.D. (1996), Lubrication mechanisms for oil-in-water emulsions, Lubr. Eng., 52, 168-175. Shaw, M.C. (1984), Metal Cutting Principles, Oxford, Clarendon Press. Shaw, M.C. (1996), Principles of Abrasive Processing, Oxford, Clarendon Press. Sheu, S., Hector, L.G., and Richmond, O. (1998), Tool surface topographies for controlling friction and wear in metal-forming processes, J. Tribol., 120, 517-527. Sheu, S. and Patula, R.T. (1994), Influence of reduction schedule on wear residue in cold rolling of aluminum, STLE Annual Meeting, May 9. Sheu, S. and Wilson, W.R.D. (1994), Mixed lubrication of strip rolling, Tribol. Trans., 37, 483-493. Snoeys, R., Peters, J., and Decneut, A. (1974), The significance of chip thickness in grinding, Ann. CIRP, 23, 227. Sutcliffe, M.P.F. (1988), Surface asperity deformation in metal forming processes, Int. J. Mech. Sci., 30, 847-868. Tassi, O.J. (Ed.), Nonferrous Wire Handbook, The Wire Association, Guilford, CT. Taylor, F.W. (1907), Trans. ASME, 28, 31. Tokizawa, M. and Yosikawa, Y. (1973), The mechanism of lubricant trapping under the cold compression of metals, J. Jpn. Inst. Met., 37, 19-25. Wilson, W.R.D. (1971), The temporary breakdown of hydrodynamic lubrication during the initiation of extrusion, Int. J. Mech. Sci., 13, 17-28. Wilson, W.R.D. (1997), Tribology in cold metal forming, J. Manufact. Sci. Eng., 119, 695-698. Wilson, W.R.D., Huang, X.B., and Tsu, T.C. (1995), A realistic friction model for computer simulation of sheet metal forming operations, J. Eng. Ind., 117, 202-209. Wilson, W.R.D. and Lee, W. (1997), Mechanics of surface roughening in metal forming processes, Proc. 1st Int. Conf. Tribol. Manufacturing Processes, Gifu, Japan, 71-76. Wilson, W.R.D., Sakaguchi, Y., and Schmid, S.R. (1993), A dynamic concentration model for lubrication with oil-in-water emulsions, Wear, 161, 207-212.
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Wilson, W.R.D., Sakaguchi, Y., and Schmid, S.R. (1994), A mixed flow model for lubrication with emulsions, Tribol. Trans., 37, 543-551. Wilson, W.R.D. and Schmid, S.R. (1992), Surfaces in metal rolling, in PED, Vol. 62, Engineered Surfaces, Ehmann, K.F. and Wilson, W.R.D. (Eds.), ASME, New York, 91-100. Wilson, W.R.D. and Sheu, S. (1983), Flattening of workpiece asperities in metal forming, Proc. NAMRC XI, Society of Manufacturing Engineers, 172-178. Wilson, W.R.D. and Walowit, J.A. (1972), An isothermal lubrication theory for strip rolling with front and back tension, Trib. Conv. 1971, Institution of Mechanical Engineers, London, 164-172.
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38 Macro- and Microtribology of Magnetic Storage Devices 38.1 38.2
Introduction ................................................................... 1413 Magnetic Storage Devices and Components ............... 1415
38.3
Friction and Adhesion ................................................... 1423
38.4 38.5
Interface Temperatures .................................................. 1447 Wear ................................................................................ 1448
38.6
Lubrication ..................................................................... 1482
Drives • Magnetic Media • Magnetic Heads Conventional Friction • Liquid-Mediated Adhesion (Stiction)
Head/Tape Interface • Head/(Thin-Film) Rigid Disk Interface Measurement of Viscosity at High Shear Rates • Measurement of Localized Lubricant Film Thickness in Rigid Disks • Lubrication Mechanisms in Particulate Magnetic Tapes • Lubrication Mechanisms in Thin-Film Rigid Disks
38.7
Bharat Bhushan The Ohio State University
Micro/Nanotribology and Micro/Nanomechanics...... 1491 Description of AFM/FFM • Friction • Scratching and Wear • Indentation • Lubrication
38.8
Closure ............................................................................ 1501
38.1 Introduction A magnetic recording process involves relative motion between a magnetic medium (tape or disk) against a stationary or rotating read/write magnetic head (Mee and Daniel, 1996). For ever-increasing, high areal recording density, the linear flux density (number of flux reversals per unit distance) and the track density (number of tracks per unit distance) should be as high as possible. The areal densities of commercial tape and rigid disk drives shipped in the year 2000 were up to 1/2 Gbits/in.2 and 10 Gbits/in.2, respectively; these are expected to increase by 2005 to 4 and 100 Gbits/in.2, respectively. Areal recording densities of 100 Gbits/in.2 for a disk drive correspond to track densities of 150K to 200K tracks per inch (6K to 8K tracks/mm) and linear densities of 500K to 600 Kbits/in (20K to 30Kbits/mm). Thus, the size of a single bit dimension for these densities is on the order of 160 nm × 40 nm. This dimension for these densities places stringent restrictions on the defect size present on the head and medium surfaces. Reproduced (read-back) magnetic signal amplitude decreases with a decrease in the recording wavelength and/or the track width. The signal loss results from the magnetic coating thickness, read gap length, and head-to-medium spacing (clearance or flying height). Based on a Wallace equation (Wallace, 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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FIGURE 38.1 A magnetic head slider flying over a disk surface compared with an aircraft flying over ground with a close physical spacing.
1951), it is known that the signal loss as a result of spacing can be reduced exponentially by reducing the separation between the head and the medium. However, tribological issues prevent the zero spacing (or intimate contact). To minimize damage to the interface, the head/medium interface is designed such that under steady operating conditions, a load-carrying air film is formed at the interface. However, because very low flying heights are comparable to the peak-to-valley distance of magnetic head and medium surfaces, there are intermittent contacts between these surfaces. A physical contact also occurs between the medium and the head during contact start-stops (CSS). The developed air film at the operating conditions is desired to be thick enough to mitigate much of the asperity contacts, yet it must be thin enough to give a large read-back magnetic signal. In modern tape and flexible and rigid disk drives, the head-to-medium separation ranges from about 20 to 50 nm, and RMS roughness of the head and medium surfaces ranges from 1.5 to 10 nm. The flying heights, on the order of 5 to 8 nm, must be realized in order to achieve areal densities of 100 Gbits/in.2 Incidentally, in some consumer tape drives and some floppy drives, negligible separation can occur (Bhushan, 1996a, 2000a). As an analogy, a magnetic head slider flying over a rigid disk surface with a flying height of 25 nm and a relative speed of 20 m/s is equivalent to an aircraft flying at a physical spacing of 0.2 µm at 900 km/h (Figure 38.1). This is what a disk drive experiences during its operation. Environment, usage time, and contamination (external and wear debris) play a significant role in the reliability and usable lifetime of the interface. Head load/unload (L/UL) technology is an alternative to CSS technology in rigid disk drives that eliminates stiction and wear failure mode associated with CSS (Albrecht and Sai, 1999). Other benefits of L/UL include increased areal density due to smooth disk surfaces, thinner protective overcoats for disk surfaces, and lower head flying height. In an L/UL drive, a lift tab extending from the suspension load beam engages a ramp or cam structure as the actuator moves beyond the outer radius of the disk. The ramp lifts (or unloads) the head stack from the disk surfaces as the actuator moves to the parking position. Starting and stopping the disk only occur with the head in the unloaded state. The major disadvantages are generation of wear debris during L/UL, requirements of extra space for this mechanism in drives with ever-decreasing size, and added cost. Since 1997, these mechanisms have been primarily used in 63.5-mm (2.5 in.) mobile disk drives requiring very high areal density and low flying heights. In a tape drive, the life expectancy of a head is about 3 to 5 years, which is equivalent to about 100,000 to 150,000 km of tape over the head. Some data tapes can be used for 100 to 10,000 file passes. The tape reel may be subjected to up to several thousand CSS cycles. For high reliability, the wear of the air bearing surface (ABS) of the head and pole-tip/gap recession (PTR) (recession of the pole tips with respect to the ABS surface) should be on the order of 50 and 10 nm, respectively, over the head life of 3000 to 5000 hours, and the tape wear should be on the order of 10 nm over 10,000 file passes! The disk drive is expected to last about 7 years with less than 1% failure rate, and can be used for 10 billion or more revolutions and 7500 or more CSS cycles during turning the drive on and off. During the life of the drive, wear of the head slider and disk surfaces should be on the order of a few nanometers, with acceptable static/kinetic friction after the required number of CSS cycles. As mentioned, the need for increasingly higher recording densities requires that surfaces be as smooth as possible and the flying height (physical separation or clearance between a head and a medium) be as
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low as possible. The ultimate objective is to run two surfaces in contact (with practically zero physical separation) if the tribological issues can be resolved. Smooth surfaces lead to an increase in adhesion, friction, and interface temperatures, and closer flying heights lead to occasional rubbing of high asperities and increased wear. Friction and wear issues are resolved by appropriate selection of interface materials and lubricants, by controlling the dynamics of the head and medium, and the environment (Bhushan et al., 1984–1990; Bhushan, 1990, 1991–1999, 1993a, 1994, 1996a,b, 1999a,b, 2000a,b). A fundamental understanding of the tribology (friction, wear, and lubrication) of the magnetic head/medium interface, both on macro- and micro/nanoscales, becomes crucial for the continued growth of this more than $80 billion a year magnetic storage industry. In this chapter, initially, the general operation of drives and the construction and materials used in magnetic head and medium components are described. Then, the status of understanding of friction and adhesion, interface temperatures, wear, and solid-liquid lubrication relevant to magnetic storage devices is presented. Macrotribological studies are followed by a brief overview of micro/nanotribological and micro/nanomechanics studies.
38.2 Magnetic Storage Devices and Components Magnetic storage devices used for information storage and retrieval are tape, flexible or floppy disk, and rigid disk drives. This section describes the general operation of tape and rigid disk drives and construction and materials used in magnetic media and heads in various drives (Bhushan, 1996a, 1999a, 2000a).
38.2.1 Drives Schematics of tape and rigid disk drives are shown in Figure 38.2. In the linear, data-processing IBM 3490/STK4490 type tape drive shown in Figure 38.2a, after loading the cartridge into the drive, the tape header is threaded into the drive over a read-write head to the take-up reel by a pentagon threading mechanism. A decoupler column placed near the cartridge entrance decouples any tape vibrations that may occur inside the cartridge. The tension is sensed and controlled by a tension transducer. In a rigid disk drive, shown in Figure 38.2b, a stack of disks is mounted on a sealed, grease-lubricated ball bearing spindle. Air bearing spindles are being developed for high track density disk drives for operation at very high rotational speeds. They have less run-out than ball bearing spindles, generate less noise, and can run at substantially higher rotational speeds than ball bearing spindles. The absence of rolling elements, which couple surface defects between inner and outer bearing surfaces, make air bearing spindles the preferred choice in high track density disk drives where non-repeatable run-out must be minimized. However, to obtain the desired high radial and vertical stiffness, the air gap in an air bearing spindle is on the order of a few micrometers, making manufacturability of air bearing spindles expensive and difficult. The disk stack mounted on a spindle is rotated by a DC motor at high speeds, ranging from a few thousand RPM to a maximum speed of about 15,000 RPM. A head slider is supplied for each disk surface. The slider-suspension assembly is actuated by a stepping motor or a voice-coil motor for read-write operation (Bhushan, 1996a, 1999a, 2000a).
38.2.2 Magnetic Media Flexible (tape and flexible disk) and rigid magnetic media fall into two categories: (1) particulate flexible media, where magnetic particles are dispersed in a polymeric matrix and coated onto the polymeric substrate (Bhushan, 2000a); and (2) thin-film media, where continuous films of magnetic materials are deposited by vacuum techniques onto the polymeric substrate for flexible media or onto a rigid substrate such as aluminum, glass, or glass ceramics (Bhushan, 1993b; Miller and Bhushan, 1996) for rigid disks. Currently, particulate tapes are more prevalent than thin-film tapes. However, requirements of higher recording densities with low error rates have resulted in increased use of thin-film tapes, which are smoother and have a magnetic coating that is considerably thinner than the particulate tapes. Thin-film rigid disks are exclusively used for rigid disk drive applications.
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FIGURE 38.2
Modern Tribology Handbook
Schematics of (a) a tape path in an IBM 3490 data-processing tape drive, and (b) a rigid disk drive.
38.2.2.1 Flexible Media Cross-sectional views of a particulate and a thin-film (evaporated) metal tape are shown in Figure 38.3. Flexible disks are similar to tapes in construction except that they have a magnetic coating on both sides and the substrate is generally about 76.2 µm thick. The most commonly used base film for flexible media is polyethylene terephthalate (PET) film. Recently, polyethylene naphthalate (PEN) and polyamide (ARAMID) films have been used for better dimensional stability of thinner tapes (Weick and Bhushan, 1995a,b,c, 1996a,b; Bhushan, 2000a). Typically, 4.3- to 14.4-µm thick PET substrate with RMS roughness of about 1.5 to 5 nm and peak-to-valley (P-V) distance of 50 to 100 nm for particulate media and 1.5 to 2 nm RMS for the recording side of the thin-film media is used for tapes, and 76.2-µm thick PET substrate is used for flexible disks. Many tapes use a substrate which has a dual roughness (the magnetic side is smoother). Particulates such as silica and titania with a bimodal distribution of sizes with mean diameters on the order of 0.5 µm and 2 µm, respectively, are added in the substrate as anti-slip agents to reduce interlayer friction and to control the air film (to provide air leakage for trapped air), respectively (Bhushan, 2000a). The base film is coated on one side of a tape and both sides of a flexible disk with a magnetic coating, typically 1 to 2 µm thick (0.3 to 0.5 µm thick for double-coated metal particle tapes, to be described
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FIGURE 38.3
1417
Sectional views of a typical particulate tape (bottom) and a metal-evaporated magnetic tape (top).
later) and containing 70 to 80% by weight (or 43 to 50% by volume) sub-micron and acicular magnetic particles. Magnetic particles include Co-modified γ-Fe2O3, CrO2 (only for tapes), metal particles (MP), and hexagonal platelets of barium ferrite (BaO·6Fe2O3). Metal particles are a pure iron core covered with a passivated iron oxide layer and coated with a ceramic layer of alumina and/or silica to prevent oxidation (corrosion) of the iron core. All particles, except barium ferrite particles, are acicular in shape. The size of the barium ferrite particles is 0.06 to 0.15 µm, with long dimensions to a thickness ratio of 3 to 30 with their easy axis (axis of magnetization) oriented perpendicular to the substrate. Their size is much smaller and their coercivity is higher than that of other particles. Among particulate tapes, MP tapes are most commonly used with a particulate length of about 0.1 to 0.2 µm and an aspect ratio of about 5 to 10. The magnetic particles are held in polymeric binders such as polyester-polyurethane, polyetherpolyurethane, nitrocellulose, poly(vinyl chloride), poly(vinyl alcohol-vinyl acetate), poly(vinylidene chloride), VAGH, phenoxy, and epoxy. To reduce friction, the coating consists of 1 to 7% by weight of lubricants (mostly fatty acid esters, e.g., tridecyl stearate, butyl stearate, butyl palmitate, butyl myristate, stearic acid, myristic acid). Finally, the coating contains a cross-linker or curing agent (such as functional isocyanates); a dispersant or wetting agent (such as lecithin); and solvents (such as tetrahydrofuran and methyl isobutylketone). In most media, carbon black (typically 20 to 30 nm in diameter spherical) is added for antistatic protection if the magnetic particles are highly insulating. Nonmagnetic abrasive particles (such as A12O3 and Cr2O3, typically 0.2 to 0.3 µm in diameter spherical) are added as a head cleaning agent. In addition, in most cases, carbon particles with an order of magnitude larger size and a bimodal distribution are used as load-bearing particles to improve friction and wear properties. The coating is calendered to a surface roughness of 5 to 10 nm RMS. For smooth tapes with ultra-thin magnetic coating for high density recording, some MP tapes use a double coat technology. These tapes are double coated with a top magnetic layer with a thickness of about 0.2 to 0.3 µm, and non-magnetic underlayer with a layer thickness of about 1.2 µm (Shibata et al., 1992; Saitoh et al., 1995). The nonmagnetic underlayer, which is used as a leveling device for thin magnetic layers, consists of ultra-fine TiO2 of about 35 nm in diameter and with the same conductive carbon and
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lubricant as in the magnetic layer dispersed in the same polymeric binder as that in the top magnetic layer. The small particle sizes of TiO2 are used to provide a smoother surface for the top magnetic layer. A backcoating is generally applied to maintain the roughness of the front coat in the wound reel (which is required for low friction), and to improve tracking and provide anti-static protection. It is 0.3- to 0.5-µm thick, and consists of polyester-polyurethane binder containing conductive carbon black and TiO2, typically 10% and 50% by weight, respectively. Flexible disks with a 90-mm form factor are packaged inside an acrylonitrile-butadiene-styrene hard jacket. Inside the jacket, a protective fabric liner is used to minimize wear or abrasion of the media. Wiping action of the liner on the medium coating removes and entraps particulate contaminants that may originate from diskette manufacturing, the jacket, head/disk contact (wear debris), or the external environment. The liner is made of nonwoven fibers of polyester (PET), rayon, polypropylene, or nylon that are thermally or fusion bonded to the plastic jacket at spots. In manufacturing of the fabric, the fibers are lubricated with lubricants such as 2 wt% oleic acid. The soft jacket near the data window is pressed against the disk with a spring-loaded lifter, to create slight friction and hence stabilize disk motion under the heads. The hard cartridge is provided with an internal plastic leaf spring for the same purpose. Thin-film (also called metal-film or ME) flexible media consist of polymer substrate (mostly PET) with an evaporated film of Co-Ni-O (with about 20% Ni) or Co-O, which is typically 100 to 130 nm thick. Electroplated Co and electroless plated Co-P, Co-Ni-P, and Co-Ni-Re-P have also been explored, but are not commercially used. Because the magnetic film is very thin, the surface of the thin-film medium is greatly influenced by the surface of the substrate film. Therefore, an ultra-smooth PET substrate film (RMS roughness ~1.5 to 2 nm) is used to obtain a smooth tape surface. A 10- to 25-nm thick precoat composed of polymer film with additives is generally applied to the ME-treated side of the PET substrate to provide controlled topography. The precoat generally contains inorganic particulates (typically SiO2 with a particle size of 100 to 200 nm in diameter and an areal density of ~10,000/mm2). The RMS and P-V distances of the ME-treated side and the backside are typically 1.5 to 2 nm and 15 to 20 nm, and 3 to 5 nm and 50 to 100 nm, respectively. The polymer precoat is applied to reduce the roughness (mostly P-V distance) in a controlled manner from that of the substrate surface, and to provide good adhesion with the ME film. Particles are added to the precoat to control the real area of contact and consequently the friction. A continuous magnetic coating is deposited on the polymer film. The polymer film is wrapped on a chill roll during deposition, which keeps the film at a temperature of 0 to –20°C. Co80Ni20 or pure Co material is deposited on the film by a reactive evaporation process in the presence of oxygen; oxygen increases the hardness and corrosion resistance of the ME film. The deposited Co-Ni film, with a mean composition of (C80Ni20)80O20 consists of very small Co and Co-Ni crystallites that are primarily intermixed with oxides of Co and Ni (Feurstein and Mayr, 1984; Harth et al., 1989). The mean composition of Co-O is Co80O20 (Kawana et al., 1995). The crystallites of the magnetic layers are oriented oblique to the coating surface. For advanced ME tapes (e.g., for digital video applications or DVC), pure Co is used to attain high coercivity and higher magnetization. Also, a double layer of ME film is used for improved squareness and higher output. Durability and corrosion resistance of ME tapes without an overcoat is poor and diamond-like carbon (DLC) overcoats of about 8 to 10 nm in thickness, deposited by plasmaenhanced chemical vapor deposition (PECVD), are used to protect against corrosion and wear. A topical liquid lubricant film (typically a mixture of polar perfluoropolyether and fatty acid/fatty acid esters for long durability in shuttle and pause modes, respectively) of 2 to 3 nm in thickness is then applied to the magnetic coating surface by rolling. The topical lubricant enhances the durability of the magnetic coating. A backcoating is also applied to balance stresses in the tape, and for anti-static protection. A topical liquid lubricant (same as that on the front coat) of thickness 8 to 10 nm is applied to the backcoat to allow replenishment of the lubricant on the magnetic coating during winding of the tape on the reel. 38.2.2.2 Rigid Disks Figure 38.4 shows a sectional view of a thin-film rigid disk. The substrate for rigid disks is generally nonheat-treatable aluminum-magnesium alloy AISI 5086 (95.4% Al, 4% Mg, 0.4% Mn, and 0.15% Cr) with a surface roughness of about 15 to 25 nm RMS and a Vickers hardness of about 90 kg/mm2. The substrate
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FIGURE 38.4
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Sectional view of a thin-film magnetic rigid disk.
is electroless plated with a nickel-phosphorous (90-10 wt%) layer to improve its surface hardness to 600 to 800 kg/mm2 (Knoop) and its smoothness. The coated surface is polished with an abrasive slurry to a surface roughness of about 0.5 to 2 nm RMS. During the turning on and off of the drive, the head slider lands in the landing (start-stop) zone, which is a band at the inner diameter of the disk surface. To minimize static friction at the head/disk interface, landing zones of thin-film disk substrates are either mechanically or laser textured in order to minimize static friction at the interface. Mechanical texturing is carried out using either free or fixed abrasives with the circumferential or random orientation to a typical RMS roughness of 4 to 8 nm (Bhushan, 1993b). Circumferential direction of texturing in the data zone (if textured) is preferred in order to keep the magnetic orientation ratio as high as possible (Bhushan, 1993b). Laser texturing processes allow production of patterned surfaces with precise and controllable topography. In the laser texturing of Ni-P plated substrates, a high repetition rate Q-switched, infrared neodymium-doped yttrium-lithium-fluoride (Nd-YLF) laser is used. The high-energy focused laser is used to rapidly melt a microscopic area of the disk substrate and the surface tension will cause the pool to deform. This molten pool will instantaneously solidify because of high rate of heat distribution into the surrounding areas when the incident beam is turned off. The focused laser beam creates discrete topographic features in either rounded, dome-like protrusions (sombrero shaped) (Baumgart et al., 1995), or craters (V or W type or donut shaped) usually known as bumps (Ranjan et al., 1991) over the disk surface. Typical sombrero, V and W type bumps have about 10 to 15 µm rim diameters and heights of about 15 to 25 nm with a 50 µm × 50 µm pitch. This gives on the order of 400,000 bumps in the landing zone of a 95-mm diameter disk. V or W type bumps are more commonly used because they can be manufactured reproducibly. For high volumetric density and for use in portable computers, thinner disk substrates are employed. As the substrates get thinner than about 0.635 mm, traditionally used Al-Mg substrates warp (curl on the edges) during disk manufacturing and assembly. Furthermore, in a drop test, sliders can dent the AlMg disk surfaces; this problem is known as “head slap.” Therefore, the substrate for these applications should have high yield strength with little plastic deformation. For contact and near-contact recording applications, one would like to have the substrate as flat and smooth as possible, and with as few asperities and defects as possible. Al-Mg alloy disks can only be used to flying heights greater than about 25 nm. Two materials — chemically strengthened glass and glass ceramics — are commonly used for ultra-low flying interfaces and for portable computer applications (Bhushan, 1993b; Bhushan and Gupta, 1995; Bhushan et al., 1996a; Miller and Bhushan, 1996). A thinner substrate of glass or glass ceramic can be processed without warpage during disk manufacturing, and these exhibit high dent (shock) resistance (because of their high yield strength, deformation occurs without much plastic deformation). Texture on the glass or glass-ceramic substrates is obtained by mechanical polishing or laser texturing. Entire glass-ceramic substrates are also textured by either controlling the grain size of a chromium underlayer deposited for film texturing purposes (selected crystallization) (Kawai et al., 1992), or by deposition of a low-melting-point metal as an underlayer to form isolated spherical features (Mirzamaani et al., 1992). Laser texturing is carried out using an IR laser (e.g., a sealed RF CO2 laser) to produce surface temperature rise beyond the glass reflow temperature and induce bump formation (Teng et al., 1996; Kuo et al., 1997). It should be noted that if head load/unload technology is used in the drive, the slider does not land on the disk surface and a textured zone is not required.
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The finished substrate is coated with a magnetic film of 25 to 75 nm thickness. Some metal films require a Cr undercoat (10 to 50 nm thick) as a nucleation layer to improve magnetic properties, such as coercivity. Magnetic films used are metal films of cobalt-based alloys (e.g., Co-Pt-Cr, Co-Pt-Ni). Magnetic films used to achieve the high recording density have weak durability and poor corrosion resistance. Protective overcoats with a liquid lubricant overlay are generally used to provide low friction, low wear, and corrosion resistance. One protective coating used almost exclusively is 8 to 10 nm thick hydrogenated DLC deposited by DC or RF (mostly DC) planar magnetron sputtering in the presence of an Ar/H2 mixture, and in isolated cases is sputtered SiO2. A 1 to 2 nm thick layer of perfluoropolyether lubricant with reactive polar ends is used. The trend is to use a partially bonded lubricant film consisting of an unbonded or mobile film over a bonded lubricant film. The unbonded top layer would heal any worn areas on the disk surface where the lubricant may have been removed, and the bonded underlayer provides lubricant persistence. Furthermore, the bonded layer does not contribute to the meniscus effects in stiction (Bhushan, 1996a; Bhushan and Zhao, 1999).
38.2.3 Magnetic Heads Magnetic heads consist either of conventional inductive or of thin-film inductive and magnetoresistive (MR) devices (Bhushan, 1993b, 1996a, 1999a, 2000a). If MR head design is used, it is only used for read purposes. Film-head design capitalizes on semiconductor-like processing technology to reduce fabrication costs, and thin-film technology allows production of high-track density heads with accurate track positioning control and high reading sensitivity. Inductive heads consist of a body forming the air bearing (referred to as air bearing surface or ABS), and a magnetic ring core carrying the wound coil with a readwrite gap. In the film heads, the core and coils or MR stripes are deposited by thin-film technology. The body of a thin-film head is made of magnetic ferrites or nonmagnetic Al2O3-TiC, and the head construction includes coatings of soft magnetic alloys, insulating oxides, and bonding adhesives. 38.2.3.1 Tape Heads Air-bearing surfaces of tape heads are generally cylindrical in shape. The tape is slightly underwrapped over the head surface to generate hydrodynamic lift during read-write operations. For inductive-coil tape heads, the core materials have typically been Permalloy and Sendust. However, because these alloys are good conductors, it is sometimes necessary to laminate the core structure to minimize losses due to eddy currents. The air-bearing surfaces of most inductive-coil type heads consist of plasma-sprayed coatings of hard materials such as A12O3-TiO2 and ZrO2. MR read and inductive write, thin-film heads in modern tape drives (such as in IBM 3490/STK 4490 type drives) are miniaturized using thin-film technology, Figure 38.5. Film heads are generally deposited on Ni-Zn ferrite (11 wt% NiO, 22 wt% ZnO, 67 wt% Fe2O3) substrates. Flexible-disk heads are inductive-coil type composite devices that are either spherically contoured or flat. Mn-Zn ferrite (30 wt% MnO, 17 wt% ZnO, 53 wt% Fe2O3) and A12O3-TiC (70-30 wt%) are generally used for head cores and barium titanate for the magnetically inert support structures. 38.2.3.2 Rigid-Disk Heads The head sliders used in rigid disk drives are supported by a nonmagnetic steel leaf spring (flexure) suspension to allow motion along the vertical, pitch, and roll axes, Figure 38.6a. The sliders are either the two- or three-rail, taper-flat design, or two-rail, step, negative pressure design. The front taper or step pressurizes the air lubricant, while some air leaking over the side boundaries of the rail results in a pitch angle. The width and shape of rails are optimized to control slider flying characteristics. Important requirements are that the flying height should change to a minimum from the inside to the outside of the disk, the flying height should be somewhat insensitive to changes in atmospheric pressure, the air bearing stiffness should be high to minimize impact damage, and the slider attitude should have high pitch angle and low roll. The inductive type or inductive/MR type thin-film read-write elements used are integrated in the Al2O3-TiC (70 to 30 wt%) slider at the trailing edge of one of the rails for the tworail, or at the pad at the trailing edge of a tail dragger slider or at the center rail in the three-rail design
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FIGURE 38.5 Schematic of inductive/MR thin-film head (with a radius of cylindrical contour of about 20 mm) in an IBM 3480/3490 data-processing tape drive.
where the lowest flying height occurs. Suspension supplies a vertical load dependent upon the size of the slider (see discussion later), which is balanced by the hydrodynamic load when the disk is spinning. Stiffness of the suspension (~25 mN mm–1) is several orders of magnitude lower than that of the air bearing (~0.5 kN mm–1) so that most dynamic variations are taken up by the suspension without degrading the air bearing. Some of the small disk drives of the late 1980s and early 1990s commonly used inductive-coil type heads of one or two types: minimonolithic (mini-Winchester) and minicomposite (Bhushan, 1993b; 1996a). The minimonolithic slider design was inherited from the so-called IBM 3340 or Winchester technology. The minimonolithic head slider consisted of a slider body and a core piece carrying the coil, both consisting of monolithic magnetic material (typically Mn-Zn ferrite). The taper-flat bearing area was provided by the outer rails of a tri-rail design. The center rail defined the width of the magnetic element in the trailing edge where a ferrite core was formed. A minicomposite head slider consisted of a Mn-Zn ferrite core and read-write gap, glass bonded into the air-bearing surface of a nonmagnetic, wear-resistant slider (typically calcium titanate). The IBM 3370/3380/3390-type suspensions normally used for heads in small drives applied a 95 mN (9.5 g) load onto the slider. The IBM 3390 type sliders were about 4.05 mm long by 3.20 mm wide by 0.850 mm high, with a weight of 0.45 mN (45 mg), as opposed to about 4.1 mm long by 3.1 mm wide by 1.4 mm high and 0.7 mN (70 mg) for the mini-Winchester. For 95-mm and 63.5-mm diameter drives, the size and weight of the sliders and their gram load have continued to decrease. Lower weight results in higher air-bearing frequency, which reduces dynamic impact. Smaller size and required lower gram load result in improvement in stiction and start-stop and flyability lives. Microsliders (2.80 × 2.24 × 0.595 mm), also known as 70% sliders, with a weight of 0.15 mN (15 mg) at a vertical load of 60 mN (6 g), were first used. Nanosliders (2.08 mm × 1.58 mm × 0.425 mm and weight of 0.56 mN or 5.6 mg) with a two-rail, three-rail, or negative pressure design (Xu and Bhushan, 1998b), or picosliders with a negative pressure design (1.25 × 1.00 × 0.300 mm and a weight of 0.167 mN or 1.67 mg (Yoon and Bhushan, 2000) using thin-film inductive and MR heads and Al2O3-TiC as a substrate material, are commonly used both in modern drives which are about 50% and 30% of the regular slider sizes, respectively; and vertical loads on the sliders are 35 mN (3.5 g) and 25 mN (2.5 g), respectively. The surface roughness of the air-bearing rails is typically 1.5 to 2 nm RMS.
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FIGURE 38.6 Schematic of (a) an IBM 3370/3380/3390 type suspension-slider assembly, (b) a taildragger thin-film nanoslider, and (c) a step, negative pressure thin-film picoslider.
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In the case of thin-film heads, pole tip/gap recession (relative wear of the pole tip and gap materials with respect to ABS) in the inductive head and scratching/smearing, electrical short, electrostatic charge buildup, and corrosion of MR stripe in the MR heads are important concerns. In the composite inductive heads with nonmagnetic core, the pole tips are wider and gap recession becomes an even bigger problem. Wear of head structure can be minimized by the application of a wear-resistant coating over the entire ABS, including the head structure. All MR heads with Al2O3-TiC substrate are coated with amorphous hydrogenated-carbon coatings deposited mostly by DC or RF planar magnetron sputtering with a thickness ranging from 3.5 to 5 nm (Chang et al., 1992; Grill et al., 1992) with an adhesion layer of about 5-nm thick amorphous sputtered silicon. More recently, other deposition techniques have been explored and ion beam deposition is used by some manufacturers (Bhushan, 1999d). Figures 38.6b and c show examples of a commonly used nanoslider and picoslider. The nanoslider consists of two side rails with a pad at the trailing edge with the thin-film structure. It is a “proximity slider” designed to fly at a low flying height of about 25 nm and the rear pad is in close proximity to the disk surface during flying; hence, it is known as a “tail-dragger.” The negative-pressure picoslider consists of two shaped rails, a leading edge bridge, and a cavity that is on the order of several microns below the surface level of the air-bearing surface. The air-bearing contour of the slider is manufactured by reactive ion etching or a similar method and has crown and camber (Bhushan, 1996a) in the range of 0 to 50 nm.
38.3 Friction and Adhesion When two normally flat surfaces are placed in contact, surface roughness causes contacts to occur at discrete contact spots. The sum of the areas of all the contact spots constitutes the real (true) area of contact or simply contact area, Ar . The load is supported by the deformation at the tips of the contacting asperities (Figure 38.7) (Bhushan, 1999c). The proximity of the asperities results in adhesive contacts caused by interatomic attractions. In a broad sense, adhesion is considered to be either physical or chemical in nature. Experimental data suggest that adhesion is primarily due to weak van der Waals
FIGURE 38.7
Schematic of two rough surfaces in contact and corresponding contact areas.
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FIGURE 38.8 Schematic illustration of (top) a body sliding on a horizontal surface, where W is the normal load (force) and F is the friction force experienced by the body; and (bottom) friction force vs. time or displacement. Fstatic is the force required to initiate sliding and Fkinetic is the force required to maintain sliding.
FIGURE 38.9 Schematic of a wet interface with meniscus formation, showing various forces being applied during sliding. FM is the meniscus force, W is the normal force, and FA and FS are the intrinsic friction force and stiction force, respectively.
forces (Bhushan et al., 1984b; Bhushan 1996a, 1999a,c). When two surfaces (in contact) move relative to each other, frictional force, commonly referred to as “intrinsic” or “conventional” frictional force, is contributed by adhesion and deformation of these asperities (Figure 38.8a). For most practical cases, adhesional friction is the primary contributor (Bhushan, 1996a). Figure 38.8b shows friction force vs. time or displacement. In some cases, static friction force required to initiate sliding is larger than the kinetic friction force required to sustain sliding. In addition, “stiction” (or high static friction) can occur due to meniscus/viscous effects, microcapillary evacuation, and changes in surface chemistry (Bhushan et al., 1984a; Bradshaw and Bhushan, 1984; Bradshaw et al., 1986; Miyoshi et al., 1988; Bhushan and Dugger, 1990a; Bhushan, 1996a). This section concentrates only on the meniscus/viscous effects (Figure 38.9). In general, any liquid that wets or has a small contact angle on surfaces will condense from vapor in the form of an annular-shaped capillary condensate in the contact zone. The pressure of the liquid films of the capillary condensates or preexisting film of lubricant can significantly increase the adhesion between solid bodies. Liquid-mediated adhesive forces can be divided into two components: meniscus force (FM) due to surface tension and a ratedependent viscous force (FV). The total tangential force F required to separate the surfaces by sliding or to maintain sliding is equal to an intrinsic friction force (FA) and stiction force FS (combination of friction force due to meniscus effect and the peak viscous force)
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(
)
F = FA + FS = µ r W + FM + FV
1425
(38.1a)
where µr is “true” coefficient of static or kinetic friction during initiation or maintenance of sliding, respectively, and W is the normal load. The coefficient of friction µ, including the effect of the meniscus and viscous forces, is given by:
µ=
F F F = µ r 1 + M + V W W W
(38.1b)
The normal force required to move two flat, well-polished surfaces (such as magnetic head and medium surfaces) in the presence of liquid medium and/or sticky substance can be large (up to 1 Newton in some cases). Stiction can be differentiated from conventional static and kinetic friction by noting that stiction requires a measurable normal force (normally several milliNewtons or higher) to pull the two surfaces apart from the static conditions.
38.3.1 Conventional Friction From Tabor’s classical theory of adhesion (Bowden and Tabor, 1950, 1964; Bhushan, 1999c), frictional force due to adhesion (FA) in dry contact is:
FA = A r τa ,
[
( )]
(38.2a)
FA = A r ατa + 1 − α τl
(38.2b)
τl = ηl V h
(38.2c)
and for lubricated contact,
where Ar is the real area of contact; α is the fraction of unlubricated area; τa and τl are the shear strengths of the dry contact and the lubricant film, respectively; ηl is the absolute viscosity of the lubricant; V is the relative sliding velocity; and h is the lubricant film thickness. In the following, discussion is limited to static contact models. 38.3.1.1 Statistical Contact Models The contacts can be either elastic or plastic, primarily depending on the surface topography and the mechanical properties of the mating surfaces. The classical model for a combination of elastic and plastic contacts between rough surfaces, that of Greenwood and Williamson (1966) (G&W), assumes that the surface is composed of hemispherically tipped asperities of uniform size with their heights following a Gaussian distribution about a mean plane. The radius of these asperities is assumed equal to the mean radius of curvature obtained from roughness measurements. Real area of contact for elastic (e) and plastic (p) contacts are (Bhushan, 1984):
(
A re pa A a ~ 3.2 E* σ p R p
)
12
(38.3a)
for ψ p < 1.8 or ψ < 0.6, elastic contact Arp pa Aa ~ 1 H for ψ p > 2.6 or ψ > 1, elastic contact
(38.3b)
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and
( )(
ψ p = E* Y σp R p
(
)(
ψ = E* H σp R p
)
12
)
12
, for polymers
(38.3c)
, for metals ceramics
(38.3d)
where Aa is the apparent area of contact; pa is the apparent pressure (W/Aa); E* is the composite modulus of elasticity; and H and Y are the hardness and yield strength of the softer material, σp and Rp are the composite standard deviation and radius of curvature of the surface summits, and ψ and ψp are the plasticity indices for metals/ceramics and polymers, respectively. For contact analysis of non-Gaussian surfaces with skewness and kurtosis, see Kotwal and Bhushan (1996). Equation 38.3 for elastic and plastic contacts in the case of metals/ceramics is plotted in Figure 38.10 for better visualization of the dependence of Ar on ψ. Note that the plastic contact results in minimum contact area. However, repeated plastic contact would lead to undesirable permanent deformation and smoothing to a higher real area of contact and elastic contacts. Because wear is more probable when asperities touch plastically than in elastic contacts, it is desirable to design components in the elastic regime with ψ close to the elastic contact limit (ψ ~ 0.6, or E*/(σp /Rp)1/2 as high as possible). In most cases with plastic contacts, and particularly in the case of ductile metals, there is a growth in contact area under the influence of combined normal and tangential stress by as much as an order of magnitude, and this affects friction (Bhushan, 1999c). The growth in contact area occurs because plastic yielding of the contact is controlled by the combined effect of the normal and tangential (shear) stresses. To use the G&W model, the modulus of elasticity and hardness of magnetic coatings of tapes were measured by dynamic mechanical analysis (DMA) (Bhushan, 1984, 1985a, 1996a) and those of rigid disks by nanoindentation hardness apparatus (Bhushan and Doerner, 1989; Bhushan, 1996a, 1999d). Surface roughness parameters of tapes and disks were measured using a non-contact optical profiler (NOP) with a lateral resolution in the 1 µm range and down to the atomic scale with an atomic force microscope (AFM) (Bhushan et al., 1988; Bhushan and Blackman, 1991; Oden et al., 1992; Bhushan 1996a; Poon and Bhushan, 1996a,b). AFM can measure topographic features that cannot be measured with conventional profilers. Table 38.1 presents the topography and contact statistics predictions, which are found to be a strong function of lateral resolution of the roughness measurement instrument (Bhushan and Blackman, 1991; Oden et al., 1992; Bhushan, 1999c). Here, σ is the standard deviation of surface
FIGURE 38.10 Influence of plasticity index on the real area of contact in metals/ceramics. (From Bhushan, B. (1984), Analysis of the real area of contact between a polymeric magnetic medium and a rigid surface, ASME J. Lubr. Tech., 106, 26-34. With permission.)
0.25 6.9 6.0 22.6
1.75 122
113 450
H (GPa)
7.33 1.63
19.5 2.15
NOP
6.33 1.55
36.3 3.61
AFM
7 2
19.0 2.51
NOP
6.7 1.4
45.4 5.47
AFM
σp (nm)
Note: NOP, noncontact optical profiler; AFM, atomic force microscope.
Head/tape interface Polymeric tape Nm-Zn ferrite head Head/disk interface Rigid disk Al2O3-TiC head slider
Component Designation
E (GPa)
σ (nm)
4.90 0.53
2.20 0.23
NOP 5.7 × 103 1.2 × 103 732 2.4 × 103
4.0 × 103 1.2 × 103
NOP
9.1 × 106 13.3 × 106
8.0 × 106 6.2 × 106
AFM
η (1/mm2)
1.4 × 105 7.8 × 103
AFM
1/Rp (1/mm)
0.12
0.05
NOP
ψ
3.4
50.17
AFM
4.3
241.6
Ar/Aapa (1/GPa) NOP
2.5
9.6
n/Aapa (1/mN) NOP
1.7
25.3
Ar/n (µm2) NOP
pr (GPa) NOP
0.24
4.23 × 10–3
TABLE 38.1 Real Area of Contact Statistics Calculations for a Magnetic Polymeric Tape Against a Ni-Zn Ferrite Head, and a Magnetic Thin-Film Rigid Disk Against Al2O3-TiC Head Slider
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FIGURE 38.11 Schematic of local asperity deformation during contact of a rough surface (upper profile measured by NOP and lower profile measured by AFM; typical dimensions shown for a thin-film rigid disk) against a flat surface. The vertical axis is magnified for clarity. Solid lines show the surfaces before contact, and dotted lines show surfaces after contact. (From Bhushan, B. and Blackman, G.S. (1991), Atomic force microscopy of magnetic rigid disks and sliders and its applications to tribology, ASME J. Tribol., 113, 452-457. With permission.)
heights, η is the density of summits per unit area, n is the number of contact spots, and pr is the real pressure. Surface topography statistics show that the average summit radius (Rp) for the AFM data is two to four orders of magnitude smaller than that for the NOP data, whereas the summit density for the AFM data is two to four orders of magnitude larger than that for the NOP data. The plasticity index (ψ) calculated using the AFM data suggest that all contacts made of nano-asperities are plastic, and NOP data suggests that all contacts made of microasperities are elastic. The question remains as to how large spots become elastic when they must have initially been small plastic spots. The possible explanation is graphically shown in Figure 38.11. As two surfaces touch, the nano-asperities (detected by AFM-type instruments) first coming into contact have smaller radii of curvature and are therefore plastically deformed instantly and the contact area increases. When load is increased, nano-asperities in the contact zone merge and the load is supported by elastic deformation of the larger-scale asperities or micro-asperities (detected by NOP-type instruments) (Bhushan and Blackman, 1991; Poon and Bhushan, 1996a,c). 38.3.1.2 Comments on the Multiscale Nature of Surfaces and Fractal Model of Elastic/Plastic Contact Surface roughness is generally characterized by the standard deviation of surface heights (σ), which is the square root of the arithmetic average of squares of the vertical deviation of a surface profile from its mean plane. A random and isotropic surface with a Gaussian height distribution and exponential autocorrelation function can be characterized by the standard deviation of surface heights (σ) and correlation distance (β*) (Bhushan, 1999c). Due to the multiscale nature of surfaces, it is found that the surface roughness parameters depend strongly on the resolution of the roughness measuring instrument or any other form of filter, and hence are not unique for a surface (Bhushan and Blackman, 1991; Poon and Bhushan, 1995a,b, 1996a,b; Koinkar and Bhushan, 1997). As an example, Figure 38.12 shows the surface profiles of a glass ceramic disk obtained using an AFM, a stylus profiler, and a non-contact optical profiler (Poon and Bhushan, 1995a). The vertical roughness parameter σ is seen to increase with the measuring instrument in the following order: NOP < SP < AFM, whereas the spatial parameter β* is seen to increase in the reverse order. The figure shows that roughness is found at scales ranging from millimeter to nanometer scales. The measured roughness profile is dependent on the lateral and normal resolutions of the measuring instrument. Instruments with different lateral resolutions measure features
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FIGURE 38.12 Comparison of surface plots of a glass-ceramic disk measured using an atomic force microscope (AFM, lateral resolution ~ 0.16 µm), a stylus profiler (SP, lateral resolution ~ 0.2 µm), and noncontact optical profiler (NOP, lateral resolution ~ 1 µm), drawn on the same scale. Note that σ roughness measured using AFM is the highest, followed by SP and NOP.
with different scale lengths. It can be concluded that a surface is composed of a large number of length scales of roughness that are superimposed on each other. Due to the multiscale nature of surfaces, it is found that the variances of surface height and its derivatives and other roughness parameters strongly depend on the lateral resolution of the roughness measuring instrument (Bhushan, 1999c), Figure 38.13 (Poon and Bhushan, 1995a). The scale dependence
FIGURE 38.13 Variation of standard deviation of surface height (σ) and correlation length (β*) with scan size for a glass-ceramic disk measured using AFM (scan length/256 data points), NOP (~1 µm), and SP (~2 µm).
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in Figure 38.13 suggests that instruments with different resolutions and scan lengths yield different values of these statistical parameters for the same surface. To use the roughness parameters for prediction of real area of contact, friction, and wear, it is first necessary to quantify the multiscale nature of surface roughness. The contact analyses developed over the last quarter century only consider an averaged surface with a single scale of roughness to be in contact with another surface. The multiscale nature of surface roughness can be characterized by fractal modeling. Fractal characterization on surface roughness is scale independent and provides information on the roughness structure at all length scales that exhibit the fractal behavior, called herein the M-B model (Majumdar and Bhushan, 1990, 1991); and the G-B model (Ganti and Bhushan, 1995). The fractal model of elastic/plastic contact was developed by Majumdar and Bhushan (1991), Majumdar et al. (1991), and Bhushan and Majumdar (1992). They reported relationships for the cumulative size distribution of the contact spots, the portion of the real area of contact in elastic and plastic deformation modes, and the load-area relationships (Bhushan, 1999a, 1999c). Ganti and Bhushan (1995) have reported that most engineering surfaces cannot be characterized by the commonly used fractal parameters, fractal dimension (D) and characteristic length scale of the surface. Therefore, the fractal approach is not practical for engineering surfaces. In using the conventional contact analysis, the question often asked is what instrument should one use for roughness measurement? For a given instrument, what scan size and sampling interval should one use? As mentioned earlier, nano-asperities deform by plastic deformation, which is undesirable. Therefore, an instrument that can measure high frequency, such as AFM, should be used, particularly in low-load condition. A sampling interval equal to 0.25 to 0.50 times the correlation distance at the selected scan size should be selected (Poon and Bhushan, 1995a,b, 1996a,b). A scan size equal to or greater than the value at which σ approaches a constant value (long wavelength limit; see Figure 38.13), or twice the nominal contact size of the physical problem, whichever is smaller, should be used. 38.3.1.3 Numerical Three-dimensional Contact Models and Computer Simulations A measured surface profile can be digitized and used for computer simulation. Over the last few years, numerical techniques have been developed and used to numerically solve contact problems of rough surfaces. Webster and Sayles (1986), Tian and Bhushan (1996a), Yu and Bhushan (1996), Peng and Bhushan (2001), and others have developed three-dimensional contact numerical models that allow analysis of a large number of contact spots which go through elastic and elastic/plastic deformations. (For reviews, see Bhushan, 1996c,d, 1998a). The numerical model does not require an asperity model and makes no probabilistic assumptions (e.g., the distribution of asperity heights, slopes, and curvatures). It provides useful information on the number of contact spots, their sizes and distributions, and the spacing between contacts. The model can be used to develop optimum surface roughness distributions for the head and medium surfaces. The numerical model has been used to study contact mechanics of both computer-generated and measured surfaces (Poon and Bhushan, 1996a,b,c; Tian and Bhushan, 1996a; Yu and Bhushan, 1996; Bhushan et al., 1997a; Chilamakuri and Bhushan, 1997, 1998a,b, 1999a,b; Peng and Bhushan, 2000). Figure 38.14 shows the computed results of the real area of contact of a computer-generated Gaussian surface in contact with a rigid smooth flat surface under various applied nominal pressures. As expected, the real area of contact and number of contact points increase with nominal pressure. Poon and Bhushan (1996a,b) reported that disk surfaces with finer frequency structure experience a higher level of plastic deformation. For better durability of the head/disk interface, it is not desirable to have high frequency structure. 38.3.1.4 Measurement of Contact Area The real area of contact of magnetic tapes and rigid disks has been measured using the optical-interference technique (Bhushan, 1985a; Bhushan and Dugger, 1990a). A loading-unloading experiment was conducted to determine if most contacts in the range above 0.7 µm in diameter were elastic (Bhushan, 1984). Photographs of tape contacts were taken at 28 kPa; then a higher pressure (1.38 MPa) was applied for short durations and the tape contact was brought back to 28 kPa and rephotographed, Figure 38.15. The
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σ = 1.0 nm, β∗ = 0.5 µm pn = 32.8 kPa
Ar/An = 6.05E–8 W/Ar = 0.24 GPa
pn = 328 kPa
Ar/An = 4.44E–7 W10/Ar = 0.32 GPa
pn = 32.8 MPa
Ar/An = 3.35E–5 W100/Ar = 0.43 GPa
FIGURE 38.14 Two-dimensional images of real area of contact between a computer-generated rough surface (σ = 1 nm, β* = 0.5 µm) on a rigid smooth flat surface (E* = 100 GPa) at three different nominal pressures (pn = 32.8 kPa, 328 kPa, and 32.8 MPa). (From Yu, M.H. and Bhushan, B. (1996), Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact, Wear, 200, 265-280. With permission.)
lack of changes in the real area of contact before loading to 1.38 MPa and after unloading to 28 kPa suggests that the contacts were elastic, an observation in agreement with contact model predictions. If the contacts are elastic, then the real area of contact and friction are governed by the E* and σp /Rp of the interface. Figure 38.16a shows that the friction of various magnetic tapes studied by Bhushan et al. (1984a) depend significantly on the complex modulus. Stable frictional behavior was exhibited only by those tapes that displayed a complex modulus of greater than 1.2 to 1.5 GPa. Figure 38.16b shows that the coefficient of friction also strongly depends on the surface roughness and doubles for CrO2 particulate tape for RMS surface roughness below about 50 nm for the given tape. Figure 38.17 shows an example of the coefficient of friction dependence on the surface roughness for a thin-film rigid disk (Bhushan, 1996a). Typical contact diameters for tapes and rigid disks were found to be about 6 µm and 1.5 µm, respectively (Bhushan, 1996a).
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100 µm 28 kPa
1.38 MPa
28 kPa after exposure at 1.38 MPa for 5 minutes
FIGURE 38.15 Optical interference photographs of tapes taken at 28 kPa; then subjected to higher pressure (1.38 MPa) for about 5 min, and brought back to 28 kPa and rephotographed. No change is seen in the real area of contact, implying an elastic contact. (From Bhushan, B. (1984), Analysis of the real area of contact between a polymeric magnetic medium and a rigid surface, ASME J. Lubr. Tech., 106, 26-34. With permission.)
Bhushan and Dugger (1990a) reported a significant increase in the contact diameter, number of contacts, and total real area of contact of the thin-film rigid disk as a function of loading time (Figure 38.18). Viscoelastic and viscoplastic deformations not only increase the size of existing asperities, but also bring the two surfaces closer to allow contact of additional asperities. To minimize the rate of increase in the real area of contact as a function of loading time, attempts should be made to select materials for disk coatings with low creep compliance, to reduce normal stress at the head/disk interface, and to use methods (such as load/unload mechanisms) to minimize or avoid the storage of the head in contact with the disk. In the case of magnetic tapes, creep compliance and hydrolytic degradation of the binder also need to be optimized for sustained low friction after storage at high pressure (e.g., near endof-tape on a reel) and high temperature/humidity (Bhushan, 1996a).
38.3.2 Liquid-Mediated Adhesion (Stiction) A smooth magnetic medium tends to adhere or stick to the smooth magnetic head. Liquid-mediated adhesion, commonly referred to as “stiction” in the computer industry, is especially pronounced when a partial film of liquid lubricant and/or adsorbed moisture is present at the interface. Liquid-mediated adhesion can be divided into two significant components: a meniscus term that depends on surface tension of the liquid and a viscous term. The viscous term does not depend on surface tension and can be observed even when the surfaces are completely immersed in the liquid. If the surfaces are covered with a liquid film, they may be separated easily, provided the separation is carried out very slowly. However, if the rate of separation is rapid, liquid must flow into the space between them and the viscosity of the liquid will be the determining factor in stiction.
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FIGURE 38.16 (a) Coefficient of friction during starting at 30°C/85% RH measured on a commercial tape drive vs. complex modulus at 50°C. The CrO2 tapes were stored at 50°C/60% RH for 14 days before the tests; (b) the effect of surface roughness on coefficient of friction for CrO2 particulate tapes. (From Bhushan, B., Bradshaw, R.L., and Sharma, B.S. (1984a), Friction in magnetic tapes. II: Role of physical properties, ASLE Trans., 27, 89-100. With permission.)
38.3.2.1 Stiction Modeling For analysis purposes, consider a model of contact region between two surfaces with different levels of “fills” of the interface and it depends on the mean interplanar separation and the liquid levels (Figure 38.19). Four distinct regimes are shown. In the first three regimes, menisci are formed that contribute to the meniscus forces. Two of the first three are extreme regimes in which either a small quantity of liquid bridges the surfaces around the tips of contacting asperities (the “toe-dipping” regime), or the liquid bridges the entire surface (the “flooded” regime). In the intermediate “pillbox” regime, the liquid bridges the surface around one or more asperities to a large fraction of the apparent area. The flooded regime has the potential of generating very high adhesive forces. In the fourth regime (the immersed regime), menisci do not exist and thus do not contribute meniscus forces; only viscous forces are present. The different regimes can be modeled and the expression for FM and FV can be obtained (Bhushan, 1996a, 1999c). In the toe-dipping regime, the liquid adhesion force between a single asperity and a surface can be modeled by a sphere of composite radius of curvature in contact with a flat surface, with a liquid bridge
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FIGURE 38.17 Coefficient of friction as a function of degree of disk texturing for a thin-film rigid disk with sputtered carbon overcoat against ferrite slider.
FIGURE 38.18 Contact statistics and log normal distribution of asperity contact diameters for a thin-film rigid disk loaded by 500 mN (9.27 MPa) at two loading durations: (a) initial and (b) after loaded for 60 hours. (From Bhushan, B. and Dugger, M.T. (1990a), Real contact area measurements on magnetic rigid disks, Wear, 137, 41-50. With permission.)
in between. Total meniscus and viscous forces of all wetted asperity contact can be calculated by multiplying the number of contacts by meniscus and viscous forces at a typical contact. The flooded regime can be modeled by a liquid bridge between two flat surfaces. The pillbox regime can be modeled by two flat surfaces. If one assumes that surface asperity radii are constant and their heights follow a Gaussian distribution, the true coefficient of friction µr can be obtained from the following expressions (Bhushan, 1996a):
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FIGURE 38.19
Regimes of different liquid levels at the interface with a smooth slider in contact with a rough surface.
For toe-dipping regime:
F~
µrW
(
1 − 16.6 γ l cos θ1 + cos θ2
)
(
E* σ p σ p R p
)
12
(38.4)
For flooded regime:
ηA A γ F = µ r W + a l cos θ1 + cos θ2 + l a Lα h h
(
)
( )
12
e −1 2
(38.5a)
where
h σ p ~ 1.4 log 0.57 ηR pσ pE * σ p R p
(
)
12
0.65
pa
(38.5b)
and F is the friction force, γl and ηl are the surface tension and viscosity of the liquid, θ1 and θ2 are the contact angles of the liquid on the two surfaces, h is the average thickness of the liquid bridge, L is the distance surfaces need to slide to become unstuck, α is the start-up linear acceleration, and Aa is the apparent area. In the toe-dipping regime, adhesion force is independent of the apparent area and proportional to the normal load (i.e., number of asperity contacts). However, the flooded regime shows the opposite tendencies.
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The pillbox regime is intermediate and can exhibit either behavior at the extremes. In all three regimes, adhesion force decreases with an increase in σp and a decrease in Rp, and is independent of η. The static friction or stiction increases with an increase in the time of stationary contact and this effect is commonly observed in storage devices, especially at high humidities. For the first time, Chilamakuri and Bhushan (1999c) developed a kinetic meniscus model to account for time and viscosity dependence of meniscus formation, which explains the experimental trends. Typical results of their study are shown in Figure 38.20. Note that the equilibrium meniscus force is independent of the film thickness and the
FIGURE 38.20 Effect of liquid film thickness (h), liquid viscosity (ηl), and radius (R) of the sphere on the timedependent meniscus force. (From Chilamakuri, S.K. and Bhushan, B. (1999c), A comprehensive kinetic meniscus model for prediction of long-term static friction, J. Appl. Phys., 86, 4649-4656. With permission.)
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viscosity of the liquid on the surface and is dependent on the surface tension, contact angle, and the interface geometry; whereas the rate of increase of meniscus force increases with decreasing viscosity of the liquid. The meniscus force, as well as the equilibrium time, are proportional to the asperity radius. The equilibrium time increases with a decrease in film thickness. Many of these observations have been verified experimentally. Statistical models for multi-asperity contacts in the presence of liquid film have been developed to quantify the effect of roughness and liquid film on stiction (Li and Talke, 1990; Tian and Matsudaira, 1993; Gao et al., 1995). In these models, contact statistics are predicted using the Greenwood and Williamson model. Bhushan and Tian (1995) carried out contact analysis of regular patterned rough surfaces to develop design criteria for size, shape, and number of asperities for minimum real area of contact, plastic deformation, and meniscus contribution. To control meniscus force, the number of asperities must be below a certain number. On the other hand, to prevent plastic deformation from occurring at the interface, the number of asperities must be greater than a certain number. For a given radius of asperity, there is a range of asperity numbers within which neither plastic deformation nor severe stiction problems will occur. The optimum number of asperities is the situation in which the contacting materials will be allowed to deform to their elastic limit within an upper limit on the meniscus force. Tian and Bhushan (1996b) developed a numerical meniscus model to predict the effect of multiple menisci of arbitrary geometry on the meniscus force. This model adequately predicts the effect of liquid film and the relative humidity on stiction. In this wet contact analysis, elastic/plastic dry contact of rough surfaces is first analyzed. In the next step, a liquid film of known mean thickness is introduced over the deformed rough surfaces. Wetted areas are determined by selecting the area in which asperities of both contacting surfaces touch the liquid. The total projected meniscus area is then used for the calculations of meniscus forces. The model can be used to develop optimum surface roughness distributions for the head and medium surfaces. Figure 38.21 shows representative contact area and meniscus area maps for a computer-generated random rough surface in contact with a smooth surface in the presence of water film. As expected, the meniscus area is larger than the contact area, and the meniscus force is three times that of the normal force. Tian and Bhushan (1996b) and Poon and Bhushan (1996b,c) used the model to predict the effects of relative humidity and liquid film thickness on the meniscus force. Effect of relative humidity on the meniscus force at an interface is shown in Figure 38.22a. Effect of liquid film thickness and interface roughness on computer-generated rough surfaces in contact with a smooth surface is shown in
pa = 32.8 kPa Contact area
Meniscus area
Ar/Aa = 1.23 E-4 W/Ar = 0.32 GPa Am/Aa = 1.5 E-3 Fm/Aa = 0.10 MPa
FIGURE 38.21 Contact area and meniscus area for the case of computer-generated rough surface (σ = 1 nm, β* = 0.5 µm) in contact with a smooth, flat surface with a composite elastic modulus of 100 GPa and a water film (γ = 73 dynes/cm, θ = 60°) with thickness of 1 nm and meniscus height of 1 nm. (From Poon, C.Y. and Bhushan, B. (1996c), Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slider/disk contact, Wear, 202, 68-82. With permission.)
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FIGURE 38.22 (a) The effect of relative humidity on the relative meniscus force for a glass-ceramic disk substrate in contact with a smooth surface. (From Tian, X. and Bhushan, B. (1996b), Micro-meniscus effect of ultra-thin liquid film on static friction of rough surface contact, J. Phys. D: Appl. Phys., 29, 163-178.) (b) The effect of water film thickness and surface roughness on the relative meniscus force for computer-generated Gaussian surfaces (correlation distance β* = 0.5 µm) in contact with a smooth surface. The dotted line defines the critical film thickness for different σ. (From Poon, C.Y. and Bhushan, B. (1996c), Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slider/disk contact, Wear, 202, 68-82. With permission.)
Figure 38.22b. An increase in either relative humidity or liquid film thickness increases the liquid present at the interface. The thicker a liquid film, the more asperities touch the liquid surface and the more menisci form on a larger number of asperities. In addition, with a thicker film, a larger volume of liquid is present around the asperities, resulting in a greater amount of meniscus volume accumulated at the contact interface and a greater meniscus height. These effects lead to larger meniscus forces. There is a critical film thickness for a surface with given roughness, above which the meniscus force increases rapidly. The critical film thickness is on the order of three quarters of the composite σ roughness of the mating surfaces. Bhushan and Chilamakuri (1996) and Chilamakuri and Bhushan (1998a) used the numerical model to study contact between flat rigid surfaces and non-Gaussian rough surfaces with known skewness (Sk) and kurtosis (K). Rough surfaces with different skewness and kurtosis were generated using a 2-D digital filter technique. Figure 38.23 shows the probability density functions of surfaces with various skewness and kurtosis values. Figure 38.24a shows the effect of skewness and kurtosis on the fractional real area of contact (Ar /Aa, where Ar is the contact area and Aa is the apparent area) and relative meniscus force (Fm /W) at different nominal pressures (p). A positive skewness between 0 and 0.2 at low pressure and about 0.2 at higher pressures, results in the lowest real area of contact and meniscus force. Contact area and meniscus force decrease with an increase in kurtosis. Fewer peaks present on a surface with range
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FIGURE 38.23 (K) values.
1439
Probability density functions for surfaces with (a) different skewness (Sk) and (b) different kurtosis
of positive skewness values or high kurtosis can explain the trends. Figure 38.24b shows the variation of relative meniscus force with the h/σ ratio for different skewness and kurtosis values. Note that the sensitivity of h/σ to the meniscus force decreases in the range of positive skewness of 0 to 0.2, and kurtosis of about 5 or larger is optimum. Experimental evidence of the significant effect of skewness and kurtosis on friction/stiction is presented by Poon and Bhushan (1996b) and Bhushan et al. (1997a). As mentioned earlier, laser textured disks are commonly used in the manufacture of rigid disks. In the laser texturing technique, discrete topographic features with either rounded, dome-like protrusions (sombrero shaped) or craters (V or W types or donut shaped) usually known as bumps are generated over the disk surface. The stiction phenomena at the head/disk interface can be controlled by controlling the size and shape of the laser bumps. Studies to identify an optimum bump shape and the relationship between the optimum number of bumps as a function of the bump geometry for a given bump shape have been conducted by Chilamakuri and Bhushan (1997, 1998b, 1999a,b). The following design methodology has been used to determine an optimum number of bumps. For a given size and shape, the meniscus force increases with an increase in the number of bumps. Thus, it is important to minimize the number of bumps to control the stiction phenomenon. On the other hand, too few bumps can result in the failure of disk surface due to plastic deformation and wear. To prevent the bumps from yielding, the number of bumps on the disk surface should be greater than a certain minimum, which would also give a lower bound for the stiction. Numerical analyses of computergenerated surfaces are used to predict an optimum number of bumps. Figure 38.25 shows typical computer-generated surfaces with various bump types and variable heights. The three-dimensional numerical contact model mentioned earlier was used to perform contact analysis of a computer-generated laser textured surface against a flat surface. Figure 38.26 shows an example of an optimum number of bumps, contact area, and meniscus force as a function of yield stress at different values of coefficient of friction.
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FIGURE 38.24 (a) Fractional real area of contact and relative meniscus force as a function of skewness and kurtosis at various nominal pressures; and (b) relative meniscus force as a function of h/σ for different skewness and kurtosis values, for an interface in the presence of perfluoropolyether film (γl = 25 dynes/cm; θ = 10°). (From Chilamakuri, S.K. and Bhushan, B. (1998a), Contact analysis of non-gaussian random surfaces, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 212, 19-32. With permission.)
As expected, the optimum number of bumps increases with an increase in the value of the coefficient of friction. The contact area and meniscus force follow similar trends. Measurements made on experimental disks verified numerical predictions (Chilamakuri et al., 2000). 38.3.2.2 Experimental Observations The relative humidity of the environment, rest period, ABS area, surface roughness, lubricant viscosity and its thickness, and relative velocity affect the liquid-mediated adhesion (Liu and Mee, 1983; Bhushan
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nm 100 240 50
180
Sombrero
0 0
120 60 60
120 180 240
0
nm 100 240 50
180
V-type
0 0
120 60 60
120 180
0
240 micron
nm 100
240
50
180
0
W-type
0
120
60 60
120 180
0 240 micron
Sombrero V-type 40 nm
W-type 60 micron
FIGURE 38.25 Three-dimensional surface plots (top) and two-dimensional line plots (bottom) of sombrero, V, and W type laser surfaces (Rrim = 7.5 µm, Hmean = 25 nm, σ = 5 nm) with a Gaussian height distribution.
et al., 1984a; Miyoshi et al., 1988; Bhushan and Dugger, 1990b; Bhushan, 1996a; Li and Talke, 1990; Streator et al., 1991a,b; Gitis and Sonnenfeld, 1993; Tian and Matsudaira, 1993; Gao and Bhushan, 1995; Gerber et al., 1996; Bhushan and Zhao, 1997, 1999; Zhao and Bhushan, 1996, 1997, 1998). Miyoshi et al. (1988) found that the adhesive force (normal pull-off force) of a Ni-Zn ferrite pin in contact with a flat of Ni-Zn ferrite or a particulate tape (Figure 38.27) remained low below 40% RH, but nearly doubled with increasing relative humidity to 80%. Changes in the adhesion of contacts were reversible on humidifying and dehumidifying. The adhesive forces for a liquid bridge between a spherical surface with radius
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FIGURE 38.26 Effect of coefficient of friction, µ, on number of bumps, contact area, and meniscus force for sombrero, V, and W type bumps at σ = 3 nm.
FIGURE 38.27 Effect of humidity on adhesion of CrO2 particulate tape in contact with a Ni-Zn ferrite pin. (From Miyoshi, K., Buckley, D.H., Kusaka, T., Maeda, C., and Bhushan, B. (1988), Effect of water vapor on adhesion of ceramic oxide in contact with polymeric magnetic medium and itself, Tribology and Mechanics of Magnetic Storage Systems, Vol. 5, Bhushan, B. and Eiss, N.S. (Eds.), SP-25, STLE, Park Ridge, IL, 12-16. With permission.)
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FIGURE 38.28 Normalized static (after a rest time of 100 s) (top) and kinetic (middle) friction forces and durability in revolutions (bottom) as a function of the lubricant film thickness of lubricant Z-DOL, untreated, applied on disks with two roughnesses against a smooth slider.
the same as the pin and a flat surface calculated using surface tension and contact angle values for water, compared well with measured values. It was concluded that ferrites adhere to ferrites or tapes in a saturated atmosphere primarily because of meniscus effects of a thin film of water adsorbed on the interface. For two surfaces in contact in the presence of liquid, coefficients of static and kinetic friction are a function of the amount of liquid present at the surface with respect to the interplanar separation. The liquid film thickness and composite roughness of the interface are known to have an opposite effect on static and kinetic friction and durability; that is, an increase in film thickness or a decrease in roughness results in an increase in the values of static friction, kinetic friction, and durability (Figure 38.28) (Zhao and Bhushan, 1996). For rough surfaces with a composite roughness σ and a uniform liquid film thickness h, to first order, the friction force and durability are a function of h/σ (Streator et al., 1991a,b; Gao and Bhushan, 1995; Bhushan, 1996a; Zhao and Bhushan, 1996, 1998; Bhushan and Zhao, 1999) (Figure 38.29). The coefficient of friction remains low below a certain value of h/σ and increases, in some cases rapidly, beyond this value. Larger values of h/σ correspond to a larger number of asperities wetted by the liquid film, resulting in a larger meniscus and viscous contributions. Below the critical value, much of the liquid remains in the valleys and does not readily form menisci. It appears that for low static and kinetic friction, h/σ should be less than or equal to about 0.7. Of course, if the contact is immersed in the liquid, menisci are not formed and shear occurs in the liquid film, leading to very low friction. The durability data in Figure 38.28 show that the durability increases with an increase in lubricant film thickness and with a decrease in the surface roughness. A rapid decrease in durability above a critical film thickness occurs because of a large meniscus being formed around slider edges and the presence of the stick-slip phenomenon (Zhao and Bhushan, 1996). In a humid environment, the amount of water present at the interface increases with an increase in relative humidity. The adsorbed water film thickness on a diamond-like carbon-coated magnetic disk, for example, can be approximated as follows (Bhushan and Zhao, 1997, 1999):
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FIGURE 38.29 Normalized static (top) and kinetic (middle) friction forces and durability in revolutions (bottom) as a function of the ratio of the lubricant film thickness to composite σ roughness (h/σ). Data on untreated, partially bonded, and fully bonded Z-DOL lubricants are presented. For static and kinetic friction data, h used is a mobile fraction; for durability, h used is a total film thickness.
( )
[(
)]
h = h1 RH + h 2 exp α RH − 1
(38.6)
where h1 = 0.3 nm, h2 = 0.5 nm, α = 20, and RH is the relative humidity fraction ranging from 0 to 1. In the data shown in Figure 38.30, the coefficient of static friction of the lubricated disk increases rapidly above a relative humidity (RH) of about 60%. This critical humidity is dependent on the interface roughness. Trends observed in Figures 38.28 to 38.30 are consistent with those predicted by contact modeling earlier. In Figure 38.30, the coefficient of friction of the unlubricated disk remains low at high humidities. It is the total liquid film thickness (including water and lubricant) that contributes to the meniscus effect; therefore, an unlubricated disk can sustain much more water condensation than a lubricated disk before friction increases significantly. For kinetic friction, little change is observed. The coefficient of kinetic friction of the unlubricated disk remains unchanged with humidity, whereas the kinetic friction of lubricated disk increases with increases slightly above 60% RH. The durability of both unlubricated and lubricated disks increases with an increase in humidity. Condensed water acts as a
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FIGURE 38.30 Coefficients of static friction (after a rest time of 100 s) (top) and kinetic friction (middle), and durability (bottom) as a function of relative humidity for unlubricated and lubricated (Z-DOL lubricant) head/disk interface.
lubricant and is responsible for an increase in the durability, whereas the drop in durability at high humidity of a lubricated disk occurs because of high static friction. Static friction starts to increase, in some cases rapidly, beyond a certain rest time and then levels off (Figure 38.31). The rest time required for increased static friction is again dependent on the total liquid present at the interface; a lubricated disk requires less rest time than an unlubricated disk (Zhao and Bhushan, 1997, 1998). Figure 38.32 shows the coefficient of static friction as a function of acceleration (Gao and Bhushan, 1995; Bhushan et al., 1995a; Bhushan, 1996a; Bhushan and Zhao, 1999). Static friction increases with the acceleration because of viscous effects, as earlier discussed. 38.3.2.4 Fly Stiction in Rigid Disk Drives Low flying heights (~25 nm or less) and high disk speed (7200 RPM or higher) have posed a new challenge in head/disk interface tribology. Flying over the disk surface becomes one of the leading sources in causing stiction during subsequent stops and, consequently, interface failure. Disk drives with low flying height experience severe stiction after extensive seeking/flying time (Zhao and Bhushan, 2000b). The observed
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FIGURE 38.31 Coefficient of static friction as a function of rest time for unlubricated and lubricated (Z-DOL lubricant) head/disk interface.
FIGURE 38.32 Coefficient of static friction (after rest time of 100 s) as a function of acceleration of the disk during start-up of the magnetic disk drive.
increase in stiction is caused by the collection of liquid on the head slider after flying. The source of the liquid is primarily lubricant film on the disk surface and the liquid contaminants present in the environment. Low flying height and high disk speed can significantly increase the probability of liquid pickup by the head slider from the disk surface. This fact, along with the existence of a smooth disk surface, results in high stiction during subsequent start-up. Because this type of stiction is primarily caused after a head slider flies over a disk surface, the name “fly stiction” is used to distinguish it from the stiction previously mentioned (i.e., conventional stiction). The main difference between fly stiction and conventional stiction is that the source causing the wet asperity contact in fly stiction is mostly liquid droplets formed during flying, whereas in conventional stiction, the source causing the wet asperity contact is during the contact at the interface. Zhao and Bhushan (2000b) have reported that, in the short sweep test, stiction is sensitive to humidity and increases with an increase in humidity. In the long sweep test, liquid droplets accumulated during flying were observed on the slider surface. The vortex around the slider was found to be responsible for the accumulation of liquid droplets. The droplets then migrated to the rail surface and led to fly stiction during subsequent start-up. Stiction was sensitive to the existence of these liquid droplets, in addition to the humidity. Both negative and positive pressure sliders could cause fly stiction. Lower flying height was found to be more susceptible to fly stiction. A disk with a fully bonded lubricant film lowered the stiction.
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38.4 Interface Temperatures During sliding, almost all frictional energy is converted to heat in the material close to the interface, and asperity interactions produce numerous high-temperature flashes. To predict the head/medium interface temperature, the contact can be modeled as a series of spherically topped asperities (Bhushan, 1987a,b, 1992). The interaction problem at an asperity contact reduces to a sphere against another sphere, assuming the distance to the center of the two spheres is fixed. When one sphere comes in contact with the other, the real area of contact starts to grow; when one sphere is directly above the other, the area is at maximum; as one sphere moves away, that area starts to get smaller. The real area of contact is a source of frictional heat and the heat intensity is proportional to the real area. The total flash temperature consists of the temperature rise of an individual asperity contact, supplemented by the related influence of other nearby asperity contacts (Cook and Bhushan, 1973). Relevant equations for the average and maximum asperity temperature rise of the interface are given as (Bhushan, 1987a):
(
)(
)
ρ1C p1 + µpa Vl κ1
(
)(
)
ρ1C p1 + 1.5 µpa Vl κ1
θ = r1 0.65 µpa A a A r Vd max κ1 θmax = r1 0.95 µpa A a A r Vd max κ1
12
12
(
(
)
ρ1C p1
12
)
12
ρ1C p1
(38.7a)
(38.7b)
and
(
r1 ~ 1 1 + k 2ρ2C p2 k1ρ1C p1
)
12
(38.7c)
where µ is coefficient of friction, pa is apparent pressure, ρCp is volumetric heat capacity, κ is thermal diffusivity, k is thermal conductivity, dmax is the maximum contact diameter, and l is half length of the slider. Average and maximum transient temperatures predicted for a typical particulate tape/head interface are 7˚C and 10˚C, respectively (Bhushan, 1987b). These predictions compared reasonably well with infrared measurements (Gulino et al., 1986). Asperity contact temperatures at a head/tape interface are relatively low because of its high area of contact, as compared to that of metal/metal or ceramic/ceramic contacts. The transient temperature rise of 7 to 10˚C rise can lead to high friction in some tapes because transition of some tape mechanical properties occurs within 5˚C above ambient temperature. In isolated cases of high-speed contact of magnetic particles with the head surface, the average and maximum transient temperature rise could be about 600˚C and 900˚C, respectively. These temperatures would cause breakdown of the medium lubricant and degradation of the medium binder to give excessive friction and even seizure. Average and maximum transient temperatures predicted for a typical thin-film disk/slider interface are 56˚C and 81˚C, respectively, for an A12O3-TiC slider, and 77˚C and 110˚C for a Mn-Zn ferrite slider. These match reasonably well with the infrared measurements by Bair et al. (1991) and Suzuki and Kennedy (1991). The size of an asperity contact is on the order of 1.5 µm. Because the duration of asperity contact at full operating speed is less than 1 µs, the thermal gradients perpendicular to the sliding surfaces are very large (a temperature drop of 90% in a depth typically less than 1 micron). Bhushan et al. (1994a) used the thermal analysis to predict temperature rise at the tape edge/guide interface. They reported that even at tape speeds as high as 8 m/s, the temperature rise at the tape edge/guide interface with guides made of metallic or ceramic materials is only a few degrees Centigrade. They noted, however, that at high tape speeds, edge guiding surfaces get coated with a hard-to-remove
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polymeric layer of about 1 µm in thickness. Thus, it becomes the case of PET polymer sliding against itself. The temperature rise in these situations can be on the order of a few hundred degrees Centigrade. In fact, these authors have reported the melting of the tape edge against alumina guides because of polymeric coatings on guiding surfaces at tape speeds of 8 m/s.
38.5 Wear 38.5.1 Head/Tape Interface Studies to understand failure mechanisms of the head/tape interface have been conducted by several authors (e.g., see Potgiesser and Koorneef, 1974; Hahn, 1984a; Bhushan, 1985b, 1996a; Bhushan et al., 1986; Calabrese et al., 1989; Bhushan and Patton, 1998). The first signs of ferrite head wear with a particulate tape are very fine scratches as small as 25 nm on the head surface. The ferrite surface is microscopically removed by abrasive wear mode in a brittle manner as strips or islands, depending on the tape smoothness. The worn ferrite head surface is work-hardened (resulting from plastic deformation) with a large compressive stress field which is detrimental to magnetic signal amplitude (Chandrasekar and Bhushan, 1988; Chandrasekar et al., 1987a, 1987b, 1990). During contact of a particulate tape with the head in CSS or during partial contact in streaming, tape debris is generated, primarily by adhesive wear. The debris can be either loose or adherent (Bhushan and Phelan, 1986). Tape debris, loose magnetic particles, worn head material or foreign contaminants that are introduced between the sliding surfaces, abrade material of each by a three-body abrasion. Debris that adheres to drive components leads to polymer/polymer contact whose friction is higher than that of rigid material/polymer contact and can lead to magnetic errors and sometimes catastrophic failures (Bhushan, 1996a). With ME tapes, the wear mode is primarily adhesive. Debris is initially generated from the DLC overcoat and ME film, and the topical lubricant acts as a cementing agent that holds the debris on the head surface. The debris then sometimes results in a three-body abrasion. Thin, adherent head deposits called “stains” are encountered intermittently when used with particulate tapes (Lemke, 1972; Ota et al., 1991; Stahle and Lee, 1992; Bhushan and Hahn, 1995; Gupta et al., 1995; Tsuchiya and Bhushan, 1995; Scott and Bhushan, 1999a, 2000b). These deposits are not the same as common, readily removable tape debris (loose debris). Stains are sometimes transparent but usually have an intrinsic blue or brown coloring. Coverage of the head surface varies from spotty to continuous, with thicknesses ranging from a couple of nanometers to tens of nanometers. Stains are generally insoluble in most common solvents and require abrasive cleaning tapes for removal. These stains can be organic or metallo-organic friction polymers; however, most stains consist of both organic and iron and oxygen (inorganic) constituents. Stains may be produced with any head structure and with all kinds of particulate tapes. Staining occurs more readily at relative humidities below 35 to 45%. The stain produced over metal-in-gap (MIG) head surfaces has an affinity to the Sendust and glass region, as compared to ferrite ABS. Scott and Bhushan (1999a) reported that loose wear debris and adherent debris were found at distinct locations on a thin-film tape head. ME tapes produce spotty deposits that cannot be characterized as stains but are much more prevalent because ME tape does not have abrasive particles to keep the head clean. A certain amount of stain is beneficial in reducing friction and wear of the head/tape interface (Bhushan and Hahn, 1995; Kattner and Bhushan, 2000a,b; Scott and Bhushan, 2000b). The poles on the head may fill with stain, which reduces growth of PTR. However, significant buildup may begin to separate the poles from the tape and increase contact area and, consequently, friction. This additional head-to-tape separation caused by staining is undesirable. Optimization of HCA particles added to the magnetic coating provides a balance between head wear and stain thickness. Sometimes, chelating agents are added to the magnetic coating to remove stain from the head surface by reacting with metal (Fe2+) in the stain to form a complex metal oxide, and removing them by chemical polishing. In some drives, cleaning the head provides a good way to prevent stain from becoming thick, provided a sufficient amount of stain is produced. However, cleaning the head too much can be catastrophic. Tape has only a finite amount
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of stain-producing material. If the head is cleaned after the tape has run out of this material, excessive head and tape wear will occur. However, if only one tape was to be used in the lifetime of a head, then only one cleaning cycle may be needed. Corrosion of tape heads, metal particle tapes, and metal evaporated tapes is also a concern (Scott and Bhushan, 2000a). Thin-film construction in thin-film heads consists of metal poles that are susceptible to corrosion. Metal particles (pure iron) in MP tapes are covered with a passivated iron oxide layer and coated with a ceramic layer of alumina and/or silica to prevent oxidation (corrosion) of the iron core. The ME coating is deposited in the presence of oxygen so as to form metal oxides to improve the corrosion resistance of the ME coating. Furthermore, a thin DLC coating is used as an overcoat for corrosion and wear protection. Scott and Bhushan (2000a) conducted elevated temperature and humidity (60°C/90% RH) tests and a multi-component flowing mixed gas test (known as the Battelle Class II test) for accelerated corrosion studies. They reported that Battelle II tests were much more severe than elevated temperature and humidity tests. They further reported that MP tapes do not corrode, whereas significant corrosion of ME tapes and thin-film heads can occur when exposed to the Battelle II test. ME tape specimens exposed inside the cartridge show much less evidence of corrosion than those exposed outside the cartridges. 38.5.1.1 Wear Mechanisms of MP and ME Tapes A number of studies have been conducted to study failure mechanisms of various particulate and metalevaporated tapes (e.g., Tsuchiya and Bhushan, 1994; Anderson and Bhushan, 1996, 1997; Patton and Bhushan, 1995, 1996a,b,c, 1997a,b, 1998, 1999; Osaki, 1996; Bhushan and Patton, 1998; Smith, 1998; Sullivan, 1998; Kattner and Bhushan, 2000a,b; Luk and Bhushan, 2001; Topoleski and Bhushan, 2001). Consumer recording devices are used in a streaming/shuttle mode (play/rewind cycling) and a pause mode (with tape stationary), whereas the data recording devices in most cases are only used in a streaming/shuttle mode. In a streaming mode test, the entire tape length in a cartridge is used; whereas in a shuttle test, a tape segment (typically 5 to 10 m) is cycled. If the wear mechanism is dominated by tape wear, then shuttle mode tests and pause mode tests can properly accelerate the wear process. Patton and Bhushan (1997a, 1998) and Luk and Bhushan (2001) have reported that the wear mechanisms and durability of ME and MP tapes in pause and streaming/shuttle modes are different. Therefore, for data recording applications, streaming/shuttle tests should be conducted as much as possible to study the failure mechanisms, although the duration of a streaming/shuttle test can be up to several tens of hours as compared to approximately 30 minutes for a pause mode test. We present some results of a failure mechanism study of new-generation MP and ME tapes (Luk and Bhushan, 2001). Osaki (1996), Patton and Bhushan (1998), Luk and Bhushan (2001), and others have reported that ME tapes without DLC exhibit poor durability, both in streaming mode and pause mode tests, and their tribological performance is unacceptable for data recording applications. Figure 38.33 shows surface height maps obtained using an AFM and NOP of an ME tape with DLC (a new generation for digital mini DV and data storage applications), ME tape without DLC (for Hi-8 VCR applications) and double-coated MP tape (for various data recording applications). Bumps (waviness) are observed on the surface maps obtained using the optical profiler for both ME tapes and the MP tape is much flatter. AFM maps for Hi-8 ME without DLC exhibit more sharp isolated peaks than digital ME tapes. The bumps on the tape surface in the ME tape are believed to be produced as a result of addition of particles in the polymeric undercoat, as well as thermal damage to the substrate during deposition of the magnetic coating (Patton and Bhushan, 1997a). The bumps reduce contact area at the head/tape interface, thus reducing friction. However, bumps on the surface induce localized wear and compromise recording performance at high linear recording densities due to spacing loss (Patton and Bhushan, 1996a, 1997a, 1998). The surface texture of the ME tape substrate (size and number of asperities) must be optimized for tribological and recording performance (Patton and Bhushan, 1999). Figure 38.34 shows the effect of subjecting the tapes to a shuttle test against a MIG head in a rotary drive, on head output, friction force, and number of dropouts. The head output and friction force for digital ME tape appear to fluctuate more than that of digital MP tape. These fluctuations are believed to
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Digital ME tape RMS = 4.04 nm, Sk = 0.48, K = 4.7, P-V = 47 nm, β* = 0.7 µm AFM
Optical Profiler 10.0
Height (nm)
7.5 50
30.0 nm
0
15.0 nm
60
10.0 5.0
7.5
25
0.0 nm 120
5.0 0 0
2.5
2.5 2.5
5.0
7.5
0 10.0 0
2.5
Distance (µm)
5.0
7.5
179
0 10.0
3
64
124
184
239
245
Distance (µm)
Distance (µm)
Digital MP tape RMS = 5.98 nm, Sk = -1.85, K = 12.8, P-V = 99 nm, β* = 0.5 µm 10.0
Height (nm)
7.5
30.0 nm
15.0 nm
0
60
50
10.0
5.0
0.0 nm 120
7.5
25
5.0 0 0
2.5
179
2.5 2.5
5.0
7.5
0 10.0
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2.5
5.0
7.5
239
0 10.0
3
64
184
245
Distance (µm)
Distance (µm)
Distance (µm)
124
Hi-8 ME without DLC tape RMS = 3.51 nm, Sk = 0.15, K = 2.9, P-V = 64 nm, β* = 0.7 µm 10.0
7.5
30.0 nm
15.0 nm
0
Height (nm)
2.5 60
50
10.0
5.0
0.0 nm 0
7.5
25
120
5.0 0 0
2.5 179
2.5 2.5
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Distance (µm)
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0 10.0
0
2.5
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Distance (µm)
7.5
0 10.0
3
64
239
124
184
245
Distance (µm)
FIGURE 38.33 AFM and optical profiler maps of virgin Digital ME (for mini DV recorder and data storage applications), Digital MP and Hi-8 ME without DLC tapes. RMS, Sk, K, P-V, and β* are based on AFM data. (From Luk, A. and Bhushan, B. (2001), Durability and failure mechanisms of digital tapes in a rotary tape drive, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
be associated with burnishing of the tape surface, changes in the head contour, and generation of loose debris and head stain during the experiment. Tape burnishing and the formation of a favorable contour on the head rubbing surface during running-in results in decreased head/tape spacing and leads to an increase in head output and an increase in contact area, which leads to an increase in friction (Patton and Bhushan, 1995, 1996a, 1997a, 1998; Kattner and Bhushan, 2000a,b). Loose debris and head stain results in an increase in spacing and consequently an increase in head output, whereas the loose debris decreases contact area and leads to low friction. Some stains are lubricious which reduces friction (but a thick stain may increase contact area and consequently the friction) (Kattner and Bhushan, 2000a,b). The number of dropouts for digital ME and MP tapes were comparable. The higher number of dropout counts at the beginning could be explained by the wear of tape asperities during the running-in period (Patton and Bhushan, 1996a, 1997a, 1998; Luk and Bhushan, 2001). Anderson and Bhushan (1996) have
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FIGURE 38.34 Head output, friction force, and number of dropouts as a function of shuttle cycles for Digital ME and Digital MP tapes against a metal-in-gap (MIG) head [with single-crystal Mn-Zn ferrite core and Sendust metal alloy (Fe-Si-Al) film and SiO2 gap] in a digital camcorder at 22°C and 45% RH condition (vertical arrows indicate drive stoppage). A 5-minute long shuttle cycle involves moving the tape segment (~5.9 m) round trip over the head surface. (From Luk, A. and Bhushan, B. (2001), Durability and failure mechanisms of digital tapes in a rotary tape drive, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
shown that the debris on the tape surface or generated at the interface can stick to the head gap and result in an intermittent signal loss (dropout) and a friction spike. Optical and AFM maps of worn head surfaces taken periodically during the test are shown in Figure 38.35 (Luk and Bhushan, 2001). These show evidence of debris on the heads tested with ME tape. The debris is believed to be mainly Co-O magnetic material and DLC coating from the tape. Most of the debris resides on the trailing side of the ferrite surface. It is observed that debris exists at the interface intermittently. Much less debris exists on the surface of the head tested with the MP tape. Figure 38.36a indicates the traces of debris found on the surface of worn digital ME (top) and digital MP (middle) tapes. Crack lines were found near the tape edge of digital ME tape. They originated from the tape edge, where pre-existing cracks were found in the virgin tape (Figure 38.36b). The pre-existing cracks were believed to first occur when the slitting process took place during tape manufacturing (Topoleski and Bhushan, 2001). Cracks may lead to a more serious tape corrosion problem by trapping moisture on the tape (Scott and Bhushan, 2000a). Cracks were not found near the edge of MP tape when the tape was virgin, nor after the shuttle test. The digital ME tape surface is more brittle than an MP tape, so cracks form more easily on the ME tape surface. It is found that cracks are more easily formed in the DLCcoated ME tapes. Therefore, the fracture toughness of the magnetic and DLC-coatings of an ME tape needs to be optimized. Metal core recession (MCR) is defined as the height difference between the ferrite and metal core surfaces of the head. Luk and Bhushan (2001) reported that heads tested with MP tape showed higher MCR than those tested with ME tape. The formation of a stain layer on the head surface was found to be responsible for less recession in the case of heads tested with ME tape.
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FIGURE 38.35 (a) Debris and stains formation; and (b) AFM maps on head surfaces after different shuttle cycles with Digital ME and Digital MP tapes at 22°C/45% RH condition. (From Luk, A. and Bhushan, B. (2001), Durability and failure mechanisms of digital tapes in a rotary tape drive, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
Figure 38.37 schematically illustrates the evolution of tape wear and head-to-tape contact condition during use with ME and MP (particulate tape in general) tape (Patton and Bhushan, 1997a, 1998, 1999). High asperities on the virgin tapes are severed off during the record pass and many remain on the tape surface as loose wear debris. More loose debris is generated by the sliding action of the severed asperities and decreased head-to-tape spacing during the first few play/rewind cycles. Typically, abrasive wear (associated with high friction and fluctuating head output) due to loose wear debris in the head/tape interface is followed by mild abrasive wear in the absence of loose debris. For MP tape, head-to-tape spacing after 1000 play/rewind cycles in streaming mode has been reported to be 15 nm less than it was initially (Patton and Bhushan, 1996b, 1997a). For DLC ME tape, head-to-tape spacing is not usually less than it is originally. In ME tapes, tape failure occurs by lateral crack formation (cracks often propagate through coating defects), driven by longitudinal tape tension or flexing of the tape in the transport, which cause the coating to flake. As stated before, it is easier to form cracks in the DLC-coated ME tapes. Patton and Bhushan (1995) studied the effect of interchanging tapes and head contour on the durability of particulate and ME tapes. They reported that interchanging ME and particulate tapes caused excessive head and tape wear. The fundamental cause of this phenomenon was that the tapes formed different head shapes during tape recorder operation. (Also see Tsuchiya and Bhushan, 1994; Patton and Bhushan, 1996a, 1997a.) Each tape formed a different steady-state head contour because each tape has a different bending stiffness. Tape bending stiffness can be measured using a simple mechanical bending method developed by Scott and Bhushan (1997), in which a tape loop is pressed against a load cell. It is
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FIGURE 38.35
1453
(continued)
recommended that the same kind of tape be used in a tape drive to avoid excessive wear due to this head contouring phenomenon. 38.5.1.1.1 Effect of Environment The operating envelope for data recording applications includes temperature (typically ranging from about 15.6°C to 32.2°C) and relative humidity (from about 20% to 80% RH), with a maximum wet bulb temperature of about 25.6°C (to avoid condensation on the drive components). The operating envelope for consumer drives is broader, typically ranging from 5°C to 38°C and relative humidity from 10% to 80% RH. For humidity effects at various temperatures, data are normally plotted as a function of specific humidities (or SH, equal to the ratio of the weights of water vapor to dry air in the mixture), rather than the relative humidity, because SH gives the amount of water present in the environment regardless of temperature, which is more relevant. The amount of water at a given relative humidity increases with an increase in temperature.
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FIGURE 38.36 (a) Wear marks on Digital ME tape surface and cracks found near the edge of the Digital ME tape (top); wear marks on Digital MP tape surface and debris particles found on worn Digital MP tape surface after 965 cycles of shuttle test at 22°C/45% RH condition (middle); and (b) tape edges of the virgin Digital ME and Digital MP tapes (bottom). (From Luk, A. and Bhushan, B. (2001), Durability and failure mechanisms of digital tapes in a rotary tape drive, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
The effect of environment (temperature and humidity) on tape tribology has been studied by several investigators by conducting tests at different conditions of the operating envelope used in data recording applications (Tsuchiya and Bhushan, 1994; Bhushan and Khatavkar, 1996; Patton and Bhushan, 1996c, 1997b, 1998; Anderson and Bhushan, 1997; Luk and Bhushan, 2001). Capillary consideration of water between head and tape surfaces form menisci, which introduce meniscus forces and influence the stability of the tape. Figure 38.38 shows the real-time response of head output and friction force to changes in RH for a Hi-8 ME tape with DLC at a temperature of 22°C (Patton and Bhushan, 1998). In these nonequilibrium
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FIGURE 38.37 Schematic illustrations of the evolution of tape wear and head-to-tape contact condition during play/rewind cycling with (a) an ME tape with a DLC coating, and (b) an MP tape.
experiments, the first minute of the experiment was in an equilibrium condition at 45% RH, and then RH was modulated in one cycle of a square wave (unless tape failure occurred during modulation) before finally being held again for 1 minute at 45% RH. Note that head output and friction force modulated in
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FIGURE 38.38 Head output (left) and friction force (right) as a function of nonequilibrium changes in relative humidity for Hi-8 ME tapes with a DLC coating at 22°C during the first play/rewind cycle in streaming mode (note 0 dB is the initial playback RMS voltage for each tape and vertical arrows indicate tape failure).
phase with RH. Thus, in addition to the changes in the amount of water vapor in real time, the amount of water vapor in the air and condensed on the interface components directly affected head-to-tape spacing and the tribological behavior of the interface as a result of meniscus formation, which is responsible for changes in head output and friction force. In these nonequilibrium experiments, tape failure occurred when RH was increased to about 80%. More menisci are formed between head and tape surfaces as RH is increased. Menisci heights on the order of 30 to 40 nm at 80% RH have been reported (Patton and Bhushan, 1997b). Pause and shuttle test durability of digital (mini DV) and MP tapes in a rotary drive under different environmental conditions are presented in Figure 38.39a (Luk and Bhushan, 2001). Pause test durability of MP tape at 22°C/45% RH was slightly higher than that at low humidity at the two temperatures tested (5°C/10% RH and 35°C/10% RH); whereas the durability of ME tape is much higher at moderately high humidity than at either low or very high humidity conditions. The durability of ME tape was high at moderate to hot temperatures. Variation in temperature and humidity seemed to affect durability much less than that of ME tapes. The optimum operating envelope for the ME tape shown in Figure 38.39a, is moderate to hot temperature (22°C to 35°C) and moderate relative humidity (45 to 58% RH). The best and worst operating conditions are found to be 35°C/58% RH (hot and moderate humidity) and 5°C/10% RH (cold and dry), respectively. Specific humidity is critical to ME tape performance. The availability of lubricant film with proper viscosity has a significant effect on the durability. Under cold and dry conditions, lubricant solidification, thermal stresses between different layers, and lack of desirable water film (which acts as a lubricant) can lead to low durability. At hot to moderate humidity conditions, the abundance of moisture, in addition to decreased viscosity at higher temperatures, leads to lower friction and higher tape durability. Patton and Bhushan (1997b) reported a streaming-mode optimum operating envelope for MP tapes in a rotary drive, based on head output and friction force (Figure 38.39b). The MP tapes function best at low to moderate temperatures and a range of humidities. Tape instability and low head output at higher temperatures and high specific humidities were reported. Softening of the tape binder and/or meniscus formation are believed to be responsible for poor performance. Anderson and Bhushan (1997) reported that Co-γ Fe2O3 tapes in a rotary drive performed poorly at low humidity (10%) at temperatures ranging from 10°C to 38°C. A low relative humidity environment increases the propensity for debris to persist over the head gap and creates a loss in head signal. High temperature further increases the propensity for dropouts in a low relative humidity environment. The propensity for dropouts is reduced by increasing the relative humidity.
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MP tape (b)
Optimum operating envelope Data processing operating envelope 0.025 Saturation line
Specific humidity
0.020
RH = 80% RH = 50%
0.015
RH = 20%
0.010
0.005
0
0
10
High dropout frequency and low head output
20 30 Temperature (°C)
40
FIGURE 38.39 (a) Optimum operating envelope for Digital ME (mini DV) tape and MP tape during pause and shuttle mode; and (b) optimum operating envelope for MP tape during streaming mode.
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FIGURE 38.40 Wear of Mn-Zn ferrite head as a function of sliding distance for various magnetic tapes. (From Bhushan, B. and Lowry, J.A. (1995), Friction and wear studies of various head materials and magnetic tapes in a linear mode accelerated test using a new nano-scratch wear measurement technique, Wear, 190, 1-15. With permission.)
38.5.1.2 Effect of Magnetic Tapes To study the relative abrasivity of various tapes, Bhushan and Lowry (1994, 1995) ran various particulate (Co-γ Fe2O3, CrO2, MP, and barium ferrite [BaFe]) and ME tapes in an accelerated wear test against MnZn ferrite simulated heads. Head wear rates for various tapes are summarized in Figure 38.40. Note that head wear rate decreases with an increase in the sliding distance because of blunting of tape asperities (Bhushan, 1996a). CrO2 tape was found to be more abrasive than the other tapes; ME tape has a wear rate of nearly zero. Because the magnetic layer of the CrO2 tape had no head cleaning agents, abrasive wear of the ferrite head surface was dominated by the hard magnetic particles (Bhushan, 1985b). This tape wore a coarse polish into the head surface. Co-γ Fe2O3 particles are known to be less abrasive than CrO2 particles (Bhushan and Martin, 1988). Because of the higher ductility of the metal particles and relatively small size of the BaFe particles, abrasive wear of the ferrite surface was probably dominated by the head cleaning agents for these tapes. MP and BaFe tapes wore a smooth polish onto the ferrite head surface at lower wear rates relative to the Co-γFe2O3 and CrO2 tapes. The abrasivity of the ME tape was negligible compared to the other tapes, but showed an undesirable tendency to transfer debris to the head surface. The debris was a combination of an agglomeration of small ferrite wear particles and lubricant transfer. In addition to head cleaning agents, tape surface roughness, isolated asperities on the tape surface, tape stiffness, tape tension, and tape sliding speed can affect wear. Head wear increases with surface roughness of tapes and with an increase in the number of isolated asperities on the tape surface (Hahn, 1984a,b; Bhushan, 1985b; Bhushan and Khatavkar, 1995; Bhushan et al., 1996b; Bhushan, 1996a; Xie and Bhushan, 1996a,b). 38.5.1.3 Effect of Head Materials Bhushan and Lowry (1995) ran various head materials against the most abrasive tape sample, CrO2 tape, in a linear tape drive for evaluation of their wear characteristics (Figure 38.41). Wear rates appeared to be inversely related to their hardness. Because the wear mechanism is primarily abrasive, the wear rate is expected to be inversely proportional to the head material hardness (Bhushan, 1996a, 1999c). Head wear also depends on the grain size of the head material. The wear rate slightly decreases with an increase in the grain size (Bhushan, 1996a). The wear rate increases above 40 to 60% relative humidity (Kelly, 1982; Bhushan, 1996a; Bhushan and Khatavkar, 1996). Figure 38.42 shows the effect of relative humidity on friction and wear of Mn-Zn ferrite heads run against CrO2 tapes in a linear tape drive. Friction and wear of the ferrite increased steadily up to 65% RH and then increased catastrophically. It was determined that static fatigue of the ferrite grains at high humidity yields fine particles, which are responsible for high friction and wear.
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FIGURE 38.41 Wear rates of various head materials sliding against CrO2 tape as a function of material hardness. (From Bhushan, B. and Lowry, J.A. (1995), Friction and wear studies of various head materials and magnetic tapes in a linear mode accelerated test using a new nano-scratch wear measurement technique, Wear, 190, 1-15. With permission.)
FIGURE 38.42 Wear rate and coefficient of friction as a function of relative humidity for Mn-Zn ferrite sliding against CrO2 tape. (From Bhushan, B. and Khatavkar, D.V. (1996), Role of water vapor on the wear of Mn-Zn ferrite heads sliding against magnetic tapes, Wear, 202, 30-34. With permission.)
38.5.1.4 Pole-Tip Recession (PTR) In the case of thin-film heads, in addition to head staining, pole-tip/gap recession in thin-film heads or metal core recession in MIG heads is a serious concern as it also increases spacing between head elements and magnetic medium (Scott and Bhushan, 2000b). MCR growth was studied by Tsuchiya and Bhushan (1995) in a linear tape drive using MIG heads in sliding against Co-γFe2O3 and MP tapes. Core recession was about the same for three different core metals, and reaches a steady-state value with increased sliding distance, which may be either higher or lower than initial values as shown in Figure 38.43. Core recession caused by MP tape was larger than that caused by oxide tape. The mechanism of core recession was studied Tsuchiya and Bhushan (1995) using an optical interference technique. It was found that the tape had little contact with recessed areas of the head, and core recession is likely caused by loose wear debris particles trapped between the tape and head core. Oxide tape produced a more severe head stain than MP tape. Nickel-iron (NiFe) films and cobalt-zirconium-tantalum (CoZrTa) amorphous films are the most commonly used pole-tip materials for thin-film heads for tape and disk drives, but are softer than the hard head substrate material and insulating layers used in the head construction. This difference in hardness leads to PTR. Iron-aluminum-nitride (FeAlN) is a promising alternative pole-tip material with
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FIGURE 38.43 Metal core recess (measured using non-contact optical profiler) as a function of sliding distance for various MIG heads against oxide and MP tapes. (From Tsuchiya, T. and Bhushan, B. (1995), Metal core recession and head stain studies of MIG heads sliding against cobalt doped-gamma iron oxide and metal particle tapes, Tribol. Trans., 38, 941-949. With permission.)
FIGURE 38.44 Pole-tip recession as a function of sliding distance for NiFe, CoZrTa, and FeAlN heads run against MP tape. (From Patton, S.T. and Bhushan, B. (1996d), Micromechanical and tribological characterization of alternate pole tip materials for magnetic recording heads, Wear, 202, 99-109. With permission.)
higher saturation magnetization to write onto high coercivity media. FeAlN is harder than the other two pole tip materials (Patton and Bhushan, 1996d). In a study to examine growth in PTR in thin-film heads with various pole-tip materials and Al2O3-TiC substrate sliding against MP tape, Patton and Bhushan (1996d) reported that FeAlN pole tips exhibited a low (~10 nm) and constant PTR over 1000 km of tape sliding distance, whereas the NiFe and CoZrTa poles exhibited growth in recession to about 30 and 40 nm, respectively, over the same sliding distance, as shown in Figure 38.44. Scott and Bhushan (1999b) studied the differences in growth in PTR in thin-film Al2O3-TiC and Ni-Zn ferrite heads. They reported that no significant differences exist in the PTR of Al2O3-TiC compared with Ni-Zn ferrite heads. In the case of the Ni-Zn ferrite heads, the softer Ni-Zn ferrite substrate has mechanical properties close to those of the poles, suggesting that PTR growth should be low. However, additional third-body wear particles from the ferrite substrate result in additional pole-tip wear. Linear tape drive heads have slots to control flying characteristics in the vicinity of the head elements. Blind-slotted heads (with slots in the direction of tape motion) have been in common use in IBM 3490/STK4490 type computer tape drives since 1985 (see schematic presented earlier). Transverse-slotted heads (with slots in the direction transverse to tape motion) were introduced in 1999. Scott et al. (2001) reported that the PTR was higher for blind-slotted heads than for transverse-slotted heads. More tape debris was found on the surface of transverse-slotted heads, but most of the debris resided in the slots rather than on the bearing surface. The slots in the transverse-slotted heads act as tape cleaners, which accounts for the large debris buildup in the slots. This leaves fewer loose debris particles at the interface
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Uncoated
Coated
100
Pole tip recession (nm)
25nm 75
Uncoated
Virgin
25nm
5 km
5 km
Coated
Virgin
20 km 20 km 100 km
50
100 km
500 km
500 km
1000 km
25 25 µm 0
0
250
500
750 1000
Sliding distance (km)
Ni-Zn fertile
Ni-Fe Al2O3 Ni-Za fertile
Ni-Fe/ Al2O3
25 µm Ni-Zn fertile Ni-Fe/ Al2O3
Ni-Fe Al2O3 Ni-Za fertile
25 µm
FIGURE 38.45 Pole-tip recession as a function of sliding distance (left), AFM scans across the thin-film structure (center), and optical micrographs of the coated thin-film structure at various sliding distances for uncoated and ionbeam carbon-coated Ni-Zn ferrite heads run against MP tape (right). (From Bhushan, B., Patton, S.T., Sundaram, R., and Dey, S. (1996d), Pole tip recession studies of hard carbon-coated thin-film tape heads, J. Appl. Phys., 79, 5916-5918. With permission.)
for the transverse-slotted heads. They suggested that the greater amount of loose debris available at the interface for use in three-body abrasive wear, which is believed to cause PTR, results in higher PTR in blind-slotted heads. One approach to minimize PTR is to deposit a thin hard coating over the entire ABS and thin-film region of the head. The 100-nm thick CrOx coatings are applied over the ABS of the digital compact cassette (DCC) heads (Bhushan et al., 1997b). Ultra-thin (3.5 to 5 nm) hard DLC coatings are commonly used for protection of disk MR heads. To study the effectiveness of hard carbon, thin-film heads with and without hard carbon coatings were run against MP tape in a linear tape drive (Bhushan et al., 1996d; Scott et al., 2000). Hard carbon coatings were deposited by cathodic arc and direct ion-beam deposition techniques on thin-film Al2O3-TiC heads and by the latter technique on thin-film Ni-Zn ferrite heads. The ion-beam deposited carbon coating substantially reduced the pole-tip recession observed with uncoated heads, as shown in Figure 38.45. Cathodic arc beam coated heads performed better than uncoated heads, but were less effective than the ion-beam coating (Bhushan et al., 1996d). Pole-tip recession increased only if carbon was removed from the pole tip (Bhushan et al., 1996d). 38.5.1.5 Effect of Tape Path Materials Tapes come into contact with various drive components in the tape path. There is potential for debris generation at the various contacts. To study the effect of commonly used materials in tape path components on friction and wear, tests with various magnetic tapes mated with various tape path materials were conducted in pure sliding and rotary/sliding modes (Bhushan and Monahan, 1995). Co-γFe2O3, CrO2, MP, BaFe, and ME tapes were run against acetal plastic, aluminum, 303 stainless steel, and MnZn ferrite, all of which commonly come into contact with tapes in both linear and rotary tape drives. Figure 38.46 shows damage index bar charts for various tapes and tape path materials slid against each other in rotary/sliding mode. Damage of tape path materials decreased with increased hardness of a material, and damage to tapes was greatest when run against aluminum and stainless steel, followed by plastic, with negligible damage occurring with the ferrite.
38.5.2 Head/(Thin-Film) Rigid Disk Interface Smoother surfaces and lower flying heights in modern disk drives result in higher friction during startstop cycles and increased potential of head-to-disk interactions during flying. During normal drive operation, the isolated contacts of asperities on head slider and disk surfaces result in adhesive and impact wear and generation of wear debris. In addition, any asperity contacts introduce maximum shear stress
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Plastic D,P,S
3
D,P
D,P
D,P
D,P
2 1
S
D,S
D,S
0
Damage Index
Co-γ Fe2O3
CrO2
MP
BaFe
Me
Aluminum 3
DSO, P,S
D
D,P
P,S
D,S,O D,P,S
D,P
D,S
2 D,S,O
1 0 Co-γ Fe2O3
CrO2
MP
BaFe
Me
Stainless Steel 3
D,P,S
D,S
D,S
D,S,O D,S
2 1
P
D,P
D,P
D
D,P
0 Co-γ Fe2O3
CrO2
MP
BaFe
Me
Mn-Zn Ferrite 3 D
2 1 0 Co-γ Fe2O3
CrO2
MP
0 - No Apparent Damage 1 - Small Damage
Tape Damage
2 - Medium Damage 3 - Heavy Damage
Material Damage
BaFe
Me D - Deposits P - Polishing S - Scratching P - Pullouts
FIGURE 38.46 Damage index bar chart for various tapes and tape path materials in rotary/sliding mode. (From Bhushan, B. and Monahan, J.A. (1995), Accelerated friction and wear studies of various particulate and thin-film magnetic tapes against tape path materials in pure sliding and rotary sliding modes, Tribol. Trans., 38, 329-341. With permission.)
at the disk subsurface, which may initiate a crack. Repeated contacts would result in crack propagation (subsurface fatigue), leading to delamination of the overcoat and magnetic layer. The wear eventually results in high friction and head crash (Bhushan, 1996a). External contamination readily abrades the overcoat and results in localized damage of the disk surface by three-body abrasion. Wear debris invades the spacing between the head slider and the disk and/or transfers to the head slider, making it unstable. This leads to additional debris and head crash, both in the start-stop and flyability modes. With alumina contaminant particles, Koka and Kumaran (1991) observed buildup of particulates in the leading-edge taper of the slider, which degraded the flyability of the slider and resulted in abrasive wear on the disk (also see Hiller, 1995). 38.5.2.1 Wear Mechanisms During drive use, the head track follows or accesses the data tracks. Because a track on a disk surface can be used for a large number of passes, disk durability becomes important. Head slider materials are very hard and their wear is generally small and less important than disk wear. During initial development, accelerated drag tests are conducted with the slider dragging on a disk surface and the coefficient of friction is monitored. In the CSS tests that simulate start-stop operation of the drive, the drive is programmed to accelerate to full speed (typically 3600 RPM) from rest, stay at full speed for a short time (~10 s), decelerate to zero speed, and then stop for typically 30 s for the desired number of CSS cycles. A CSS test cycle lasts about 60 s. During the test, coefficient of friction, acoustic emission, particle count, and/or some optical reflectance measurements are generally made; these measurements are used to better understand precursors to failure and to synthesize the wear mechanisms (Bhushan and Forehand, 1997; Forehand and Bhushan, 1997; Xu and Bhushan, 2000).
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FIGURE 38.47 The results of a CSS test for a laser-textured disk with sombrero-shaped bumps: (a) coefficient of friction, AE signal RMS, and number of particles as functions of CSS cycles; (b) optical reflectance across the wear track at various CSS cycles; and (c) AFM maps of laser bumps at various CSS cycles. (From Xu, J. and Bhushan, B. (2000), Studies of failure mechanisms for head-disk interface using in-situ instrumentation, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214, 189-199. With permission.)
Figure 38.47 shows typical CSS data for an Al2O3-TiC nanoslider against a laser textured disk. The static friction and kinetic friction increase significantly with an increase in CSS cycles after about 400 CSS cycles; this indicates depletion of the lubricant. The AE signal shows spikes after about 13,000 cycles. The number of particles increases after the occurrence of these spikes. The optical reflectance data show that wear tracks begin to be detectable from about 15,000 cycles. This evolution of wear, shown schematically in Figure 38.48, can be divided into four steps. These consist of depletion of lubricant on laser bumps, uniform wear of the carbon coating on laser bumps, failure of the carbon coating on laser bumps and abrasive wear of the underlying layers. Similar evolution of interface wear for mechanically textured disks has also been reported by Xu and Bhushan (2000).
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FIGURE 38.47
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(continued)
Calabrese and Bhushan (1990) and Hedenqvist et al. (1992) conducted in situ drag tests of various head/disk combinations in the scanning electron microscope to identify the initiation of particle removal. Calabrese and Bhushan reported that first a little debris was deposited on the rail edges followed by some damage to the slider edges, light burnishing of the disk surface and then catastrophic failure. According to them, the most significant parameter that influences the initiation of particle removal is the condition of the slider rail edges which contact the disk. Engel and Bhushan (1990) developed a head/disk interface failure model for thin-film disks based on topography of the wearing surfaces. Principal variables include sliding speed, surface topography, mechanical properties, coefficient of friction, and wear rate. Surface asperities and debris particles induce impact and sliding encounters, which represent a damage rate. Failure occurs when a specific damage rate, a characteristic for the system, is reached. 38.5.2.1.1 Effect of Particulate Contamination Contamination inside a disk drive affects the reliability of the drive. It can cause an increase in stiction, head and/or disk damage, or a head crash. With ever-decreasing flying heights and smooth disk surfaces, the analysis and control of disk drive contamination become even more crucial. The contamination can be in the form of static or airborne particulate matter, organic contamination, corrosion from residual anions (chloride and sulfate), or outgassed vapor (Cooper, 1996; Mee et al., 1997). A variety of techniques are used by disk drive manufacturers for contamination analysis of disk drives (Mee et al., 1997). A liquid wash technique is used to collect and measure static particles (Bhushan et al., 1999). Bhushan and Chandra (1999) focused on aerosol sampling instruments for detection of airborne particles and discussed various methodologies that can be used for both drive-level and component-level studies. Laser particle counters are most commonly used. Contaminants can come from the manufacturing or assembling environment or can be generated during disk drive operation. To determine shape, size, concentration, composition, and properties of the static particles, a liquid wash technique was used by Bhushan et al. (1999) to extract the particles in commercial drives. Aluminum, an elemental constituent of many drive components, was found to be
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200
400 nm
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400 nm
Virgin
200
30.0
0
20.0 10.0 0
10.0
20.0
30.0
0 µm
400 nm
13 k CSS cycles
200
30.0
0
20.0 10.0 0
10.0
20.0
30.0
0 µm
400 nm
14 k CSS cycles
200
30.0
0
20.0 10.0 0
10.0
20.0
18 k CSS cycles (c)
FIGURE 38.47
(continued)
30.0
0 µm
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FIGURE 38.48 Summary of the proposed failure mechanism for head/disk interfaces with laser-textured disks in CSS tests against Al2O3-TiC nanoslider. (From Xu, J. and Bhushan, B. (2000), Studies of failure mechanisms for head-disk interface using in-situ instrumentation, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214, 189-199. With permission.)
FIGURE 38.49 Schematic of the range of particle size that can reside at the interface. dmax and dmin are the flying heights at the leading edge and the trailing edge, respectively.
the predominant element in the particles detected. The number of particles increased with drive usage, which suggests that particles were generated during initial run-in. The number of airborne particles generated during flying or CSS tests are very few and difficult to track (Bhushan and Chandra, 1999). The air flow at the disk surface, and underneath and over the slider, govern particle motion. The particles that are important for interface durability are the ones whose size is equal to or less than the flying height at the leading edge of the slider (Figure 38.49) (Yoon and Bhushan, 2000). Larger particles never enter the interface. To study the effect of particles on the wear performance of the head/disk interface, Chandra and Bhushan (2000) and Yoon and Bhushan (2000) injected particles at the interface and studied their effect on interface durability. They reported that durability increases and the coefficient of friction decreases as the disk speed is increased in a contaminated environment. An increase in particle hardness and particle size made the interface fail early. Figure 38.50a shows the effect of particle concentration and particle size on interface durability (Yoon and Bhushan, 2000). Durability decreases with an increase in particle concentration and particle size. Figure 38.50b reveals the effect of slider size on durability. Durability with the picoslider is longer than that with the nanoslider. The time for one particle to encounter at the leading edge of the slider is believed to affect the interface durability, which is given as inverse of the product of particle concentration, width of slider, flying height at the leading edge, and disk speed. Because the width of the picoslider is less than that of the nanoslider, the time for encounter
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FIGURE 38.50
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Durability as a function of concentration for (a) alumina particles with two sizes; and (b) two sliders.
is shorter and, consequently, durability is longer for the picoslider. Yoon and Bhushan (2000) proposed a mechanism of interface failure as a result of particulate contamination. 38.5.2.2 Effect of Slider Materials Chandrasekar and Bhushan (1991), Chu et al. (1992), Koka (1994), and Xu and Bhushan (1997) studied the effect of slider materials on the durability of the head/disk interface. Chu et al. (1992) reported that, among the slider materials tested, the slider materials that exhibited a slow and steady increase in friction include Mn-Zn ferrite, Ni-Zn ferrite, and SiC; the slider materials that exhibited a slow as well as rapid increase in friction include Al2O3-ZrO2, Al2O3-TiC, and Al2O3-TiO2; and CaTiO3 exhibited a rapid increase in friction. It appears that single-phase slider materials are more consistent in wear behavior than multiphase slider materials; all multi-phase materials showed both slow and rapid increases in friction. In general, the single-phase slider materials showed lower wear than multi-phase materials, with the exception of CaTiO3. The poor behavior of CaTiO3 can be attributed to poor processing conditions of the material. In situ SEM studies showed that CaTiO3 disintegrated easily during sliding (Calabrese and Bhushan, 1990). The differences in wear behavior of materials are attributed to microstructural flaws present in the multi-phase system. In addition, differences in thermal and mechanical properties between the two phases may lead to cracking during processing and machining.
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FIGURE 38.51 Durability of various slider materials at various levels of relative humidity in drag tests. (From Xu, J. and Bhushan, B. (1997), Friction and durability of ceramic slider materials in contact with lubricated thin-film rigid disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 303-316. With permission.)
Chandrasekar and Bhushan (1991) conducted tests on various slider materials in contact with lubricated thin-film disks with carbon overcoat. Among the ceramics tested, single-crystal diamond had the lowest coefficient of friction (~0.12), followed by partially stabilized zirconia (~0.15); the remaining ceramics (Mn-Zn ferrite, Al2O3-TiC, and CaTiO3) all had an initial coefficient of friction of about 0.2. Although the coefficient of friction increased with the number of passes, this increase was small for single-crystal diamond even after 5500 passes. The rate of increase in the coefficient of friction was highest for CaTiO3 and Al2O3-TiC sliders; Mn-Zn ferrite and ZrO2-Y2O3 sliders exhibited a smaller increase. CaTiO3 (1200 kg/mm2) showed poor durability because it cracks readily. Al2O3-TiC is hardest (2300 kg/mm2) and burnished the disk more than the Mn-Zn ferrite slider. The Mn-Zn ferrite slider was scratched, which suggests that it is slightly softer than the disk and is gentle to the disk surface. Matching of ceramic slider and disk hardness is essential for low wear. Xu and Bhushan (1997) conducted tests with Mn-Zn ferrite, CaTiO3, Al2O3-TiC, and SiC sliders against the mechanically textured thin-film disks in drag tests and CSS tests at various humidities. Figure 38.51 shows that, in drag tests, SiC has the longest durability, even at higher relative humidities. Following SiC, long durability is observed with Mn-Zn ferrite and Al2O3-TiC, with that of CaTiO3 being the shortest. The latter three sliders have decreased durability with increasing humidity level. The superior friction and wear performance of SiC is attributed to lubricant transfer from the lubricated disk to the slider surface and formation of tribochemical films (Figure 38.52). A lubricant layer on the slider surface protects the slider from wear and also increases the contact angle with the water film, resulting in a low meniscus contribution leading to low stiction. The tribochemical reaction forms a gel-like hydroxide layer on the SiC slider surface that performs as a boundary lubricant, leading to a low coefficient of friction and low wear. There is a growing interest in SiC as a substrate for MR-type picosliders and femtosliders. SiC has a high thermal conductivity, which provides better cooling during powering of the MR heads. In addition, its high thermal conductivity leads to lower interface temperatures, which generally results in less degradation of the interface. SiC is also a preferable substrate for small sliders because it machines with less edge-rounding, fewer pullouts, and high smoothness. Chu et al. (1992) studied the effect of slider curvature on interface durability. They reported that sliders with positive crown were superior in performance to those with negative crown. The sharp edges in the negative crown sliders scrape and damage the disk surface. There is an interest in horizontal, thin-film head designs in which the plane of the read/write magnetic films is parallel to the ABS (Bhushan et al., 1992a). Horizontal head sliders can be inexpensively mass produced using integrated circuit (IC) technology, thus eliminating the need for labor-intensive slicing and precision lapping of the rows. There is concern about head wear in horizontal heads that can be minimized by the use of wear-resistant films. Bhushan et al. (1992a) and Bhushan and Venkatesan (1993) have shown that the horizontal slider with about 3-µm thick PECVD SiO2 coating performs as well as
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FIGURE 38.52 Schematic model for lubricant transfer from a lubricated disk to a SiC slider. (From Xu, J. and Bhushan, B. (1997), Friction and durability of ceramic slider materials in contact with lubricated thin-film rigid disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 303-316. With permission.)
or better than conventional thin-film heads with ABS made of Al2O3-TiC material. Because SiO2 is transparent, it prevents the use of commonly used optical interference techniques for flying height measurements and thus is undesirable. A 0.5-µm thick sputtered DLC coating has been successfully used. 38.5.2.3 Pole-Tip Recession (PTR) As stated earlier, growth in PTR is undesirable as it results in an increase in spacing between head elements and magnetic medium. For ultra-low flying heights, any increase in the magnetic spacing due to PTR becomes a concern and needs to be minimized. Mechanisms of PTR growth and effects of various ABS and pole-tip region designs and DLC have been studied in detail by Xu and Bhushan (1998a,b). Manufactured head sliders may either have recession or protrusion of their pole tips. Figure 38.53 shows coefficient of friction and PTR growth as a function of CSS cycles for various uncoated MR-type negativepressure nanosliders and a carbon-coated slider. For the uncoated head slider, the coefficients of both static and maximum kinetic friction increase with an increase in CSS cycles. The MR shields and inductive pole recess slowly with increasing CSS cycles and approach saturated values of about 28 nm, 28 nm, and 16 nm for Co-Zr-Ta shield, NiFe shield, and NiFe pole, respectively. For the carbon-coated slider, the coefficients of both static friction and maximum kinetic friction increase very slowly, with no apparent increase in PTR with CSS cycles. Xu and Bhushan (1998a,b) proposed the following growth mechanism for PTR growth for initially protruded poles. First, the protruded parts of the pole tips are knocked off by disk texture through adhesive wear and two-body abrasive wear within first few hundred CSS cycles. Continued contacts at the interface result in the wear of A12O3-TiC ABS and various thin films present in the thin-film region,
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FIGURE 38.53 Coefficients of friction (top) and PTR growth (bottom) as a function of CSS cycles for uncoated and carbon-coated MR-type nanoslider against a laser-textured disk. (From Xu, J. and Bhushan, B. (1998b), Pole tip recession studies of thin-film rigid disk head sliders. II. Effects of air bearing surface and pole tip region designs and carbon coating, Wear, 219, 30-41. With permission.)
which generate additional wear particles that act as an abrasive. These wear particles result in three-body abrasive wear, which selectively removes soft metal poles and leads to PTR growth. The mechanism for initially recessed poles is the same except there is no initial step of pole-tip wear for initially recessed poles. This observation suggests that initially protruded poles may not be a good design choice because the knocking-off process may potentially damage the poles. Furthermore, to minimize or eliminate the PTR, the efforts should be made to minimize the generation of the abrasive particles through improved pole-tip region and ABS designs. DLC coating minimizes or eliminates the PTR growth by reducing friction and wear during takeoff and landing. Xu and Bhushan (1998b) reported the effects of ABS and pole-tip region designs. They found that the detailed mechanism of PTR growth is a function of ABS and pole-tip region design. It is also reported that as compared to laser-textured disks, PTR reaches the saturated value more quickly in the case of mechanically textured disks (Xu and Bhushan, 1998a). 38.5.2.4 Effect of Overcoat Materials As stated, almost exclusively used as the overcoat for rigid disks is sputtered hydrogenated DLC. Very few disks use sputtered SiO2. MR sliders are also coated with a hydrogenated DLC, generally deposited by sputtering and less commonly by ion-beam deposition. DLC is a metastable amorphous carbon (a-C) material, but includes a micro- or nanocrystalline phase with no long-range order. Coatings are a random network of covalently bonded carbon in hybridized tetragonal — sp3 (diamond) and trigonal — sp2 (graphite) local coordination, with some of the bonds terminated to hydrogen (Bhushan and Gupta, 1991; Bhushan, 1999d). These coatings have been successfully deposited by a variety of vacuum deposition techniques on variety of substrates at or near room temperature and they reproduce substrate topography. These coatings adhere best to silicon substrates because silicon forms carbide during initial deposition, which is responsible for good adhesion. For deposition on other substrates, an interlayer of silicon is usually required, except in the case of cathodic-arc deposition. The DLC coatings for demanding wear applications can be deposited by DC/RF sputtering, RF-plasmaenhanced chemical vapor deposition (RF-PECVD), electron-cyclotron resonance chemical vapor deposition (ECR-CVD), direct ion-beam (IB) deposition, and filtered cathodic-arc (FCA) deposition. The
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structure and properties of these coatings are dependent on the deposition techniques and the deposition parameters. High-energy deposition processes produce harder and denser coatings. It is reported that sp3/sp2 fractions are in the following decreasing order: FCA deposition, IBD, PECVD, and sputtering (Bhushan, 1999d). FCA, ECR-CVD, and IB deposition processes are energetic, that is, carbon species arrive with an energy significantly greater than that represented by the substrate temperature. The resultant coatings are amorphous in structure, with hydrogen content up to 50%, and display a high degree of sp3 character (Cho et al., 1990; Bhushan et al., 1992b). It is known that deposition of sp3-bonded carbon requires the deposition species to have kinetic energies on the order of 100 eV or higher, well above those obtained in thermal processes such as evaporation (~0.1 eV). The species must then be quenched in metastable configuration. Deposition conditions need to be optimized for best mechanical and tribological properties (Cho et al., 1990). Carbon coatings with low porosity and high electrical resistivity offer better electrochemical corrosion resistance (Bhushan, 1996a). In the studies by Bhushan and Koinkar (1995d), Gupta and Bhushan (1995a,b), Li and Bhushan (1999a,b,c), and Sundararajan and Bhushan (1999), DLC coatings, ranging in thickness from 3.5 to 20 nm, were deposited on single-crystal silicon, Ni-Zn ferrite, and A12O3TiC substrates by FCA, IB, ECR-CVD, PECVD, and DC planar magnetron sputtering (SP) deposition techniques. Screening of coatings includes mechanical characterization, accelerated wear tests, and functional tests. Mechanical properties of interest are hardness, elastic modulus, and fracture toughness. The scratch technique is commonly used to study adhesion and scratch resistance (mechanical durability) of hard coatings. In a scratch test, the cracking or delamination of a hard coating is signaled by a sudden increase in the coefficient of friction at a load referred to as critical load (Bhushan, 1999a). Residual stresses need to be controlled for strong adhesion and mechanical durability. Selected properties for various DLC coatings are summarized in Table 38.2. These properties are known to vary over a wide range with sp3-to-sp2 bonding ratio, which depends on the kinetic energy of the carbon species and amount of hydrogen (Bhushan, 1999d). FCA and ECR-CVD, followed by IB, exhibit high hardness and fracture toughness as compared to commercially used SP coatings. Macroscale accelerated wear tests are conducted in a ball-on-disk apparatus in which a sapphire ball is slid against the sample in a reciprocating mode. Based on optical micrographs of worn samples in Figure 38.54, FCA, IB, and ECR-CVD are superior in wear resistance to SP coatings. The thickness of the coating affects the wear performance (Li and Bhushan, 1999a, b). It appears that coatings with 3.5-nm TABLE 38.2 Hardness, Elastic Modulus, Fracture Toughness, Critical Load Estimated from an Abrupt Increase in Friction and Average Values of Coefficient of Friction During Accelerated Wear Testing, and Residual Stress of Various DLC Coatings
Sample Cathodic-arc carbon coating (a-C) Ion-beam carbon coating (a-C:H) ECR-CVD carbon coating (a-C:H) DC sputtered carbon coating (a–C:H) Bulk graphite (for comparison) Diamond (for comparison) Single-crystal silicon substrate a
Hardnessa (GPa)
Elastic Modulusa (GPa)
24 19 22 15
280 140 180 140
Very soft 80-104 11
9–15 900–1050 165
Fracture Toughnessb KIc (MPa-m1/2)
Critical Loadc (mN)
Coefficient of Friction During Accelerated Wear Testingc
Residual Stressd (GPa)
11.8 4.3 6.4 2.8
3.8 2.3 5.3 1.1
0.18 0.18 0.22 0.32
12.5 1.5 0.6 2.0
— — —
— — 0.5
— — 0.55
— — 0.02
Measured on 100-nm thick coatings on single-crystal silicon substrates at a peak load of 0.2 mN with an indentation depth of 10 to 30 nm. b Measured on 100-nm thick coatings on single-crystal silicon substrates. c Measured on 20-nm thick coatings on single-crystal silicon substrates slid against 3-mm diameter sapphire ball at a normal load of 200 mN. d Measured on 400-nm thick coatings on single-crystal silicon substrates.
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FCA
IB
ECR-CVD
SP
20 nm, 200 mN 200 µm 10 nm, 200 mN 200 µm 5 nm, 150 mN 200 µm Si Si, 150 mN
3.5 nm, 150 mN 200 µm
200 µm
FIGURE 38.54 Optical micrographs of wear tracks and debris formed on the various DLC coatings of different thicknesses on silicon substrate when slid against a sapphire ball after a sliding distance of 5 m. The end of the wear track is on the right-hand side of the image.
thickness provide no wear protection. Rankings of coatings obtained based on mechanical characterization and accelerated wear testing are similar and compare well with functional tests (Bhushan et al., 1996d). It is reported that coatings as thin as 5 nm are continuous on microscale (Bhushan, 1999d; Bhushan and Koinkar, 1995d; Sundararajan and Bhushan, 1999). Bhushan and Gupta (1994) reported that ion implantation of the DLC coating on a rigid disk improved its wear resistance. 38.5.2.4.1 Effect of DLC Overcoat on Sliders For sliders with DLC overcoats, a lower static friction and higher CSS durability are obtained as compared to those of sliders without DLC overcoats (Figure 38.55) (Zhao and Bhushan, 1999). The DLC-coated slider is less abusive to the DLC-coated disk surface as compared to the hard A12O3-TiC slider, resulting in a better performance. The effect of the DLC coating is more significant at high humidity. In addition, degradation by the interaction of lubricants with A12O3-TiC, to be described in the section on lubrication (Section 38.6), does not occur in the case of carbon-coated sliders (Zhao and Bhushan, 1999). Zhao and Bhushan (2000c) conducted drag and CSS tests using the uncoated sliders and sliders coated with various DLC coatings. They reported that the durability of a DLC coating deposited by FCA, ECRCVD, or IB deposition techniques is superior to that of a sputtered coating. Coatings as thin as 5 nm provided protection. However, their durability generally increased with an increase in thickness. These results are consistent with the trends observed from the micromechanical and accelerated wear test studies presented previously. 38.5.2.4.2 Effect of Environment Marchon et al. (1990) and Strom et al. (1991) studied the wear behavior of unlubricated thin-film disks with a DLC overcoat sliding against ceramic sliders in various environments. In sliding experiments with Mn-Zn ferrite or CaTiO3 sliders and unlubricated thin-film disks with DLC overcoats, Marchon et al. (1990) reported that there is gradual increase in the coefficient of friction with repeated sliding contacts performed in air. However, in pure nitrogen, no friction increase is observed; the coefficient of friction remains constant at 0.2. The alternate introduction of oxygen and nitrogen elegantly showed the role of these gases (Figure 38.56). Contact start-stop tests exhibited the same effect. It is well-known that the wear process in on oxygen environment involves oxygen chemisorption onto the DLC surface and a gradual loss of DLC through the formation of CO/CO2 due to the action of the slider (Zhao et al., 2000; Zhao and Bhushan, 2001).
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FIGURE 38.55 CSS durability comparison between Al2O3-TiC sliders with and without DLC overcoats, and a lubricated disk at (a) 45% RH and (b) 80% RH. The σ roughness of the disk is 10.5 nm.
FIGURE 38.56 Coefficient of friction as a function of number of revolutions during sliding of Mn-Zn ferrite slider against an unlubricated thin-film disk at a normal load of 100 mN and a sliding speed of 60 mm/s in various dry gases. (From Marchon, B., Heiman, N., and Khan, M.R. (1990), Evidence for tribochemical wear on amorphous carbon thin films, IEEE Trans. Magn., 26, 168-170. With permission.)
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FIGURE 38.57 Durability measurements in drag tests on lubricated disks with two types of overcoats in various environments, measured at 0.5 to 0.75 m/s speed and 100 mN load. Vacuum refers to 2 × 10–7 Torr.
To understand basic failure mechanisms, it is of interest to study the effect of gaseous composition on durability (Bhushan and Ruan, 1994a; Bhushan et al., 1995a). Figure 38.57 shows friction profiles for lubricated disks with an Al-Mg substrate and sputtered DLC overcoat, and a glass substrate and sputtered SiO2 overcoat in various environments. Disk durability was determined from these data. In the case of disks with DLC overcoats, wear lives are in the following order (from best to worst): argon and nitrogen, Ar + H2O, ambient air, Ar + O2, vacuum. From this order of wear performance, it is seen that having oxygen and water in an operating environment worsens the wear performance of the disks, but having nothing in it (vacuum) is the worst of all. In vacuum, intimate contact between disk and slider surfaces results in significant wear. In ambient air, Ar + O2, Ar + H2O environments, tribochemical oxidation of the carbon overcoat is responsible for disk failure. In pure argon and nitrogen environments, wear performance is very good. For the disks with sputtered SiO2 overcoats, life in vacuum was the shortest; life in humid atmospheres (ambient air and Ar + H2O) is the highest, followed by N2, Ar, and Ar + O2. Humidity plays a beneficial role in the durability of SiO2 overcoats. A tribochemical reaction of oxide and non-oxide ceramics with water present as liquid or vapor in a humid environment forms amorphous hydrated surface layers {Si(OH)4}, which in many interfaces reduces friction and prolongs wear life at high humidities. A tribochemical reaction of the silica overcoat with ambient humidity is believed to be responsible for the longer life in ambient and humid environments as compared to a nonhumid environment. These data show that oxygen and water in an operating environment worsen the wear performance of disks, but no gaseous environment (vacuum) is the worst of all. In vacuum (~5 × 10–7 Torr), intimate contact between disk and slider surfaces results in significant wear. In ambient air, Ar + O2, and Ar + H2O, tribochemical oxidation of the DLC overcoat was responsible for shorter durability. Outgassing products in a drive affect lubricant degradation. For example, during sliding of the silicon seal, siloxanes start to desorb due to tribochemical degradation. The outgassing products degrade the lubricant on the disk surface and result in higher stiction/friction and shorter interface durability.
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FIGURE 38.58 Coefficient of friction as a function of the number of revolutions for slider on Al2O3-TiC unlubricated and lubricated disks. (From Chu, M.Y., Bhushan, B., and De Jonghe, L. (1992), Wear behavior of ceramic sliders in sliding contact with rigid magnetic thin-film disks, Tribol. Trans., 35, 603-610. With permission.)
38.5.2.5 Role of Lubricant Film A lubricant film on the disk surface is essential for acceptable disk life. Figure 38.58 shows the friction behavior of an A12O3-TiC slider on unlubricated and lubricated disk surfaces. It is observed that the coefficient of friction increases much more rapidly for the unlubricated disk than for the lubricated disk. It was reported in the section on friction and adhesion (Chapter 38.3) that the interplay of surface roughness and thin films of the lubricant needs to be optimized for low static and kinetic friction and durability. The lubricant should be partially bonded to the DLC on the disk surface to allow a thicker film of lubricant for long durability without increasing the stiction, and to minimize sensitivity to humidity. A partially bonded film provides a mobile fraction to protect any exposed regions during sliding. As will be discussed later, the PFPE lubricant is bonded to the disk surface by thermal prebaking of the lubricated disk surface. Zhao et al. (1999b) reported that interfacial sliding also results in partial bonding of lubricant film. 38.5.2.5.1 Effect of Degree of Chemical Bonding of Lubricant Film The effect of degrees of chemical bonding on static and kinetic friction and durability has been studied by several investigators (Gao and Bhushan, 1995; Zhao and Bhushan, 1996, 1998; Bhushan and Zhao, 1999). Figure 38.59 shows normalized static friction force (Fs/W) as a function of rest time for disks with two roughnesses with untreated, partially bonded, and fully bonded films of Z-DOL lubricant. Static friction increases with increasing rest time only in the case of the untreated lubricant film at the composite σ roughness of 3.0 nm, and it levels off after a rest time of about 105 s. The static friction force remains constant and does not change for all other types of lubricant films. The reason for a low static friction force, even for the untreated film, for the rough disk is that the lubricant thickness of 2 nm for a head/rough disk interface is not thick enough to produce a significant amount of meniscus force. To study the effect of film thickness on tribological performance, the disks with two roughnesses were lubricated with different film thicknesses (Zhao and Bhushan, 1996). Static and kinetic friction forces and durability as a function of the ratio h/σ for disks with different bonding levels of lubricant films are shown in Figure 38.60. The film thickness h is a total lubricant film thickness in all cases. At low ratios of h/σ (≤0.7), the values of Fs/W and Fk/W for untreated, partially bonded, and fully bonded films are low and almost the same. This is because the meniscus effect is not significant at a short rest time of 100 s. The benefit of using partially bonded and fully bonded films is clear in long-term stiction, as shown in Figure 38.59, where untreated film at the composite roughness σ of 3.0 nm would develop severe stiction. At a medium ratio of 0.7 < h/σ ≤ 1.0, the values of Fs/W and Fk/W for untreated and partially
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FIGURE 38.59 Normalized static friction force as a function of rest time for disks lubricated with untreated, partially bonded, and fully bonded Z-DOL lubricant films. (From Zhao, Z. and Bhushan, B. (1996), Effect of bonded-lubricant films on the tribological performance of magnetic thin-film rigid disks, Wear, 202, 50-59. With permission.)
bonded films are similar. Again, partially bonded film is expected to produce a lower stiction compared to that of untreated film after a long rest time. In the case of durability, the disk with a fully bonded lubricant exhibits a low wear life because there is no replenishment of the lubricant on the disk surface. The durability of the partially bonded film appears to be marginally better than that of the untreated film at a low film thickness. (This effect is discussed in the following section in connection with the effect of humidity, where the difference is more significant.) At a large ratio of h/σ (>1.0), however, the static and kinetic friction and durability are comparable for partially bonded and untreated films. The reason is that for a larger lubricant thickness, the bulk of the lubricant is unbonded, which is responsible for large values of the meniscus forces; this leads to high values of Fs /W and Fk /W and a low value for durability. To summarize, the partially bonded film provides low stiction and high durability among three types of lubricant films. 38.5.2.5.2 Effect of Environment Disk surfaces exposed to a humid environment can adsorb a layer of water film. The total liquid film on the disk surface consists of the lubricant and adsorbed water. Uniformity of the liquid film is necessary for a uniform value of friction (Bhushan and Zhao, 1997; Zhao and Bhushan, 1997). A summary of Fs /W during the first cycle of CSS tests and durability in terms of disk revolutions in drag tests and CSS cycles in CSS tests, as a function of relative humidity, is presented in Figure 38.61. Static friction is low for unlubricated disks and disks lubricated with a fully bonded lubricant film at various levels of humidity, whereas disks lubricated with untreated and partially bonded lubricant films have a higher static friction; it increases rapidly between 50% and 80% RH. For the unlubricated disk, the durability increases with an increase in the relative humidity, and the effect is more pronounced in CSS tests than it is in drag tests. It is expected that the water film acts as a lubricant at high humidities. For three types of lubricated disks, the effect of humidity on durability is different. For fully bonded disks, the durability in the drag tests is insensitive to humidities; and at high humidity, it is equivalent to that of the unlubricated disk. In the CSS tests, the durability decreases with an increase of the relative humidity and levels off at a lower level, which is equivalent to that of the unlubricated disk at moderate to high humidities. For partially
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FIGURE 38.60 Normalized static (top) and kinetic (middle) friction forces and durability (bottom) as a function of the ratio of total lubricant film thickness to composite σ roughness (h/σ) for disks lubricated with untreated, partially bonded, and fully bonded lubricant films.
bonded and untreated disks, the durability generally decreases from low to moderate humidities and drops in all cases at high humidity. In the case of partially bonded and untreated disks, lubricant permeability results in lubricant displacement at high humidity, which is responsible for poor durability. For partially bonded and untreated disks at 5% and 50% RH in drag tests, a higher durability is achieved by the partially bonded disk, followed by the untreated disk. At high humidities, the durability in drag tests is comparable to that of the fully bonded and unlubricated disks. In the CSS tests, the durability of partially bonded and untreated disks is comparable at all humidity levels. Thus, the partially bonded disk is the best in the drag tests and is as good as the untreated disk in CSS tests. The existence of a mobile fraction of a lubricant film improves durability at intermediate levels of humidity. At low humidities, the presence of an immobile fraction improves durability in the case of CSS tests, whereas both mobile and immobile fractions are important in the case of drag tests. The mobile fraction of lubricant film allows the exposed areas to be protected, and the immobile fraction can prevent the film from being disturbed by the adsorbed water molecules. Besides, the immobile fraction will not form meniscus forces in a long-term stiction test. It is clear that the degree of bonded fraction is key to the static and kinetic friction and durability of the disks in different environments.
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FIGURE 38.61 Normalized static friction force (top) and durability in drag (middle) and CSS (bottom) tests as a function of RH for unlubricated and lubricated disks with lubricant Z-DOL. The composite σ roughness is 10.5 nm. (From Zhao, Z. and Bhushan, B. (1997), Effect of environmental humidity on the friction/stiction and durability of lubricated magnetic thin-film disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 295-301. With permission.)
38.5.2.5.3 Different Polar Lubricants Sensitivity to the humid environment varies from one lubricant to another (Bhushan and Zhao, 1997). Figure 38.62 shows long-term stiction results for the unlubricated disk and disks lubricated with lubricant Z-DOL or Demnum SA in the untreated and bonded conditions. For the unlubricated disk, the value of Fs /W remains about 0.2 at 5% and 50% RH; however, it begins to climb at 80% RH at a rest time of 103 s and then levels off at a rest time of 3 × 103 s. It is believed that a thick water film is adsorbed at the interface at 80% RH, which is responsible for an increase of the meniscus force. For the disks lubricated with untreated films, Fs /W begins to climb up after some rest time at 5 to 80% RH and then levels off after reaching the maximum, except for the case at 80% RH, where tests are performed at a rest time of no longer than 3.6 × 104 s because the friction force is too high for the strain-gage beam. The combined liquid from the lubricant film and water film at the interface increases the meniscus force. The disk lubricated with lubricant Demnum SA shows a lower value of Fs /W than the disk lubricated with lubricant Z-DOL after the same rest time. This is believed to be due to the lower affinity value of the water to lubricant Demnum SA. For disks lubricated with fully bonded films, Fs /W begins to build up at 80% RH at a rest time of 500 s for the disk with lubricant Z-DOL and then levels off after reaching the maximum. It remains low for disks with lubricant Demnum SA, even at 80% RH. Figure 38.63a shows static and kinetic friction and durability as a function of relative humidity of the unlubricated disk and disks lubricated with untreated films of lubricant Z-DOL or Demnum SA. For the disks with fully bonded films of lubricant Z-DOL or Demnum SA, results are presented in Figure 38.63b.
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FIGURE 38.62 Normalized static friction force as a function of rest time of the head slider for unlubricated and lubricated disks at 5%, 50%, and 80% RH. The composite σ roughness is 3.0 nm. (From Bhushan, B. and Zhao, Z. (1997), Friction/stiction and wear studies of magnetic thin-film disks with two polar perfluoropolyether lubricants, IEEE Trans. Magn., 33, 918-925. With permission.)
For the unlubricated disk, Fs /W remains constant with an increase in relative humidity. For the disks with untreated films of lubricant Z-DOL, Fs /W begins to climb at 50% RH and increases rapidly with an increase in relative humidity. The disk with lubricant Demnum SA shows a lower value of Fs /W than the disk with lubricant Z-DOL at a given relative humidity. The primary factor responsible for the difference is that lubricant Demnum SA is less susceptible to water than lubricant Z-DOL. If there is only a fully bonded film of lubricant Z-DOL or Demnum SA, Fs /W does not show any obvious increase at 5 to 80% RH at a rest time of 100 s (Figure 38.63b). At a longer rest time, however, Fs /W for the disk with a fully bonded film of lubricant Z-DOL is expected to grow as shown in Figure 38.62. For kinetic friction, little change is observed.
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FIGURE 38.63 Normalized static and kinetic friction forces and durability as a function of RH for unlubricated disks and disks lubricated with (a) untreated and (b) fully bonded lubricant films. The composite σ roughness is 3.0 nm. (From Bhushan, B. and Zhao, Z. (1997), Friction/stiction and wear studies of magnetic thin-film disks with two polar perfluoropolyether lubricants, IEEE Trans. Magn., 33, 918-925. With permission.)
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For disk durability (Figure 38.63a), tests reveal that for the unlubricated disk, the durability increases with an increase in relative humidity. For the disks with untreated films of lubricant Z-DOL, the durability increases with increasing RH up to 50%, then decreases with a further increase in relative humidity. The durability at RH > 60% is almost the same as that for the unlubricated disk at 80% RH. The durability of the disk with lubricant Demnum SA remains constant with increasing relative humidity. For the unlubricated disk, the adsorbed water film at increasing relative humidity improves its durability because the water film acts as a lubricant at the interface. For the disks with untreated films of lubricant Z-DOL, the adsorbed water at RH > 60% can displace the lubricant at some sites on the disk surface, which results in a durability similar to that of the unlubricated disk. An insensitivity of durability of the disk to humidity with lubricant Demnum SA occurs because of an insensitivity of the lubricant film to the water film. In dry environments, the lubricants behave similarly. If there is only a fully bonded film of lubricant Z-DOL or Demnum SA, the durability increases slightly with increasing relative humidity (Figure 38.63b). The adsorbed water film acts as a mobile layer of lubricant. However, the durability of the bonded films is somewhat poorer than that of untreated films. It is clear that for static and kinetic friction and durability, a disk with lubricant Demnum SA is relatively insensitive to a humid environment as compared to a disk with lubricant Z-DOL. Lubricant Demnum SA is insensitive to humidity because it has an OH group on one end that attaches to DLC, and the other end is nonpolar and unreactive to humidity. 38.5.2.5.4 Recommended Lubrication Approaches The effect of h/σ on static and kinetic friction forces and durability is summarized in Figure 38.64 (Bhushan and Zhao, 1999). Film thickness h is the total mobile fraction of the liquid film, which includes the lubricant film plus the water film (condensation of water vapor from the environment) on disk and head slider surfaces for static and kinetic friction, but h is the total liquid film for durability; and σ is the composite roughness of disk and head slider surfaces. The vertical axis indicates the normalized static friction (Fs /W), kinetic friction (Fk /W), and durability in terms of disk revolutions or CSS cycles. Note that a high h/σ (10), which is in the immersed region, is desirable for low static and kinetic friction and long durability, but at the intermediate value of h/σ (between ~0.7 and 6), stiction increases with an increase of h/σ; the ratio at the head/disk interface is typically in the range of 0.5 to 2. Durability is poor
FIGURE 38.64 Schematic showing the effect of h/σ on static friction, kinetic friction, and durability, and the associated mechanisms for a lubricated interface.
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Crowned slider
Pad Three pads on a slider
Small slider
FIGURE 38.65 Schematic showing various types of geometrical design (size and shape) of a slider for low stiction in near-contact recording applications.
at low h/σ, and gradually increases with h/σ up to about 1. It slightly decreases with increasing h/σ and then increases and approaches a high value at h/σ > 10. In general, smooth surfaces and surfaces with thick films result in low wear. Bonded and solid lubricants can be used to maintain low stiction, friction, and wear. Reduction in the slider size and load can also be used to reduce the stiction. Thick films have been known to be undesirable because of slider instability during accessing and contamination resulting from recirculation of the lubricant required for thick films. Therefore, partially bonded thin-film lubrication with h/σ (mobile fraction film/composite σ roughness) between 0.5 and 0.7 is recommended. Further optimization can be obtained with a smooth surface, small slider size, and low load. In a flooded interface, the apparent contact area needs to be reduced to reduce stiction. The apparent contact area between the disk and head slider surfaces can be reduced by either providing a crown on the slider, using three pads on the slider surface, or reducing the physical size of the slider (Figure 38.65) (Bhushan and Zhao, 1999). Wear of the interface can be high if the apparent contact area is reduced; thus, the slider shape and size need to be optimized.
38.6 Lubrication Mechanical interactions between the head and the medium are minimized by the lubrication of the magnetic medium. The primary function of the lubricant is to reduce the wear of the magnetic medium and to ensure that friction remains low throughout the operation of the drive. The main challenge, however, in selecting the best candidate for a specific surface is to find a material that provides acceptable wear protection for the entire life of the product, which can last for several years. There are many requirements that a lubricant must satisfy in order to guarantee an acceptable life performance. An optimum lubricant thickness is one such requirement. If the lubricant film is too thick, excessive stiction and mechanical failure of the head/disk are observed. On the other hand, if the film is too thin, protection of the interface is compromised and high friction and excessive wear will result in catastrophic failure. An acceptable lubricant must exhibit properties such as chemical inertness, low volatility, high thermal, oxidative, and hydrolytic stability, shear stability, and good affinity for the magnetic head and medium surfaces. Fatty acid esters are excellent boundary lubricants and esters such as tridecyl stearate, butyl stearate, butyl palmitate, butyl myristate, stearic acid, and myristic acid are commonly used as internal lubricants and make up roughly 1 to 7% by weight of the magnetic coating in particulate tapes and flexible disks.
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TABLE 38.3
Chemical Structure and Selected Properties of Perfluoropolyether Lubricants
Lubricant Z-15 Z-DOLa D-SAa
YR
Krytox 143 AD
a
Formula CF3-O-(CF2-CF2-O)m-(CF2-O)n-CF3 HO-CH2-CF2-O-(CF2-CF2-O)m-(CF2-O)n-CF2-CH2-OH (m/n ~ 2/3) F-(CF2-CF2-CF2-O)m-CF2-CF2-CH2-OH CF3 | CF3-O-(C-CF2-O)m-(CF2-O)n-CF3 (m/n ~ 40/1) | F CF3 | CF3-CF2-CF2-O-(C-CF2-O)m-CF2-CF3 | F
End Groups
Molecular Weight (Daltons)
Density (× 103 kg/m3 at 20°C)
Kinematic Viscosity (mm2/s)
-CF3 -OH
9100 2000
1.84 1.81
-OH
3600
1.87
-CF3
6800
1.91
1600@20°C 515@38°C
-CF3
2600
1.88
495@38°C
150@20°C 80@20°C 34@38°C 75@38°C
Functional or polar lubricants.
The fatty acids involved include those with acid groups with an even number between C12 and C22, and with alcohols ranging from C3 to C13. These acids are all solids with melting points above the normal surface operating temperature of the magnetic medium. This suggests that the decomposition products of the ester via lubrication chemistry during the head/flexible medium contact may be the key to lubrication. Silicone oils are also used in the construction of some magnetic tapes. Topical lubrication is used to reduce the wear of thin-film rigid disks and metal-evaporated tapes. Perfluoropolyethers (PFPEs) are chemically the most stable lubricants with some boundary lubrication capability, and are most commonly used for topical lubrication of rigid disks and metal evaporated tapes (Bhushan, 1993a, 1996a). The flexible molecular structure of the -CF2-O-CF2- ether bonds allows PFPEs to exhibit a low viscosity at a given molecular weight and to have a relatively constant viscosity over a wide range of temperatures. PFPEs consist of a unique combination of low surface tension, good thermal and oxidative stability, hydrophobicity, low volatility, chemical inertness, and good boundary lubrication properties. The performance of PFPEs depends on their molecular structure. Lubricants with polar end groups, known as functional or polar lubricants, are designed to provide enhanced adhesion to the DLC overcoats. Groups such as hydroxyl (-OH), carboxyl, -COOH, or piperonyl, -CH2-phe(O)2CH2 can react strongly with surfaces and bond the lubricant to the DLC surface. These lubricants form bonded lubricant films and are effective in reducing friction and increasing durability (Zhao and Bhushan, 1996; Bhushan and Zhao, 1999). The degree of chemical bonding of the lubricant film depends on the type of lubricant with or without polar end groups, post-treatment of the film, and the chemical activity of the overcoat on which the lubricant film is applied (Bhushan and Zhao, 1999). PFPEs commonly used over the years include Fomblin Z and Fomblin Y lubricants made by Ausimont (Milan, Italy); Krytox 143 AD made by Dupont (U.S.A.); and Demnum S-100 made by Diakin (Japan) and their difunctional derivatives containing various reactive end groups (e.g., hydroxyl [Fomblin Z-DOL and Demnum SA], piperonyl [Fomblin AM 2001], and isocyanate [Fomblin Z-DISOC]). See Table 38.3 for examples of nonpolar and polar molecules. The difunctional derivatives are referred to as reactive (polar) fluoroether lubricants. Note that the rheological properties of thin-film lubricants, particularly at high shear rates during takeoff and touchdown, are expected to be different from their bulk properties. Fomblin Z and Demnum SA are linear PFPEs, and Fomblin Y and Krytox 143 AD are branched PFPE wherein the regularity of the chain is perturbed by -CF3 side groups. The bulk viscosity of Fomblin Y and Krytox 143 AD is almost an order of magnitude higher than Fomblin Z. The molecular coil thickness
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1
Viscosity (Pa s)
Z-03 Z-15 Z-25 S-100 0.1
0.01 0.01
0.01
1
10
Shear Rate (x106 s-1)
Viscosity (Pa s)
1 143AY 143AB 143AD YR 0.1
0.01 0.01
0.01
1
10
Shear Rate (x106 s-1)
FIGURE 38.66 Measured absolute viscosity as a function of shear rate for a disk lubricated with various lubricants with 50 to 150-nm thick coatings. (From Hahm, C.D. and Bhushan, B. (1997), High shear rate viscosity measurements of perfluoropolyether lubricants for magnetic thin-film rigid disks, J. Appl. Phys., 81, 5384-5386. With permission.)
is about 0.8 nm for these lubricant molecules. The monolayer thickness of these molecules depends on the molecular conformations of the polymer chain on the surface. Fomblin Z-DOL and Demnum SA are most commonly used for lubrication of thin-film rigid disks. A mixture of polar perfluoropolyether and fatty acid/fatty acid ester is used for lubrication of metalevaporated tapes. The lubricant is partially chemically bonded to the DLC of magnetic medium by thermal prebaking, typically at 150˚C for 30 minutes.
38.6.1 Measurement of Viscosity at High Shear Rates In a conventional air-bearing design, during initial takeoff and landing of the slider or in the situation when the slider comes closer to the disk surface during flying such that it touches the disk lubricant, shearing of the lubricant would occur at high shear rates, on the order of 109 s–1 near ambient pressure. The viscosity of lubricants Fomblin Z-15, Demnum SA, and several others at shear rates up to about 107 s–1 were measured by Jonsson and Bhushan (1995) and Hahm and Bhushan (1997). A special rheometer with a head/disk interface configuration was designed so that viscosity measurements can be made using thin films at low sliding velocities such that viscous heating effects can be minimized. The viscosity data at different shear rates are presented in Figure 38.66. Note that lubricants show nearly Newtonian behavior up to shear rates of about 106 s–1 used in the studies. The viscosity of YR and Krytox lubricants shows a slight non-Newtonian behavior at high shear rates, which may be caused by the branched structure of YR.
38.6.2 Measurement of Localized Lubricant Film Thickness in Rigid Disks Uniformity of the lubricant film is critical for producing disks with consistent performance. Techniques to measure film thickness include Fourier transform infrared spectroscopy (FTIR), ellipsometry, angleresolved X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), optical surface analysis,
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and capacitance (Mate et al., 1990; Bhushan and Blackman, 1991; Novotny and Baldwinson, 1991; Leung et al., 1989; Meeks et al., 1995; Hahm and Bhushan, 1998; Bhushan and Dandavate, 2000). The first four techniques produce point measurements and require a substantial amount of time to map a surface, while optical surface analysis is best suited for determining a change in surface properties and is limited in vertical resolution as compared to the other methods. The capacitance technique can quickly, nondestructively, and accurately map lubricant film thickness and characterize lubricant depletion (Hahn and Bhushan, 1998). The AFM technique can allow measurements with nanoscale lateral resolution (Bhushan and Dandavate, 2000).
38.6.3 Lubrication Mechanisms in Particulate Magnetic Tapes 38.6.3.1 Lubricant Kinetics Magnetic particles are partially encapsulated in the cured polyester polyurethane binder, forming a porous and permeable medium. The pores that are not completely filled with the solid urethane polymer are filled with a fatty acid ester lubricant and other liquids associated with the formation of the coating. The liquid-filled pores are estimated to be 7 to 15 vol% of the magnetic coating (Bhushan and Phelan, 1986). The polyester polyurethane is a relatively elastic polymer that allows the rigid magnetic particles to distort elastically. Under a load on the coating surface, the compression of the magnetic coating will force the liquid trapped in the pores to flow to the surface. When the compressive stress is removed, the coating will return to its original position, allowing the liquid pushed out on the surface by the compression to reenter the pores of the coating. Under ideal conditions, the liquid circulating into and out of the pores would be the lubricant. The coating will behave as a stiff sponge in this model. The lubricants on the surface of the tape, after being forced out of the porous medium, can evaporate, transfer to the head, or be carried out to a new position on the tape by the shear forces (Klaus and Bhushan, 1985; Bhushan, 1996a). The lubricant in magnetic tapes ranges from 1 to 7 wt% of the magnetic coating, including the magnetic material. The lubricant contained in the coating is estimated to be on the order of 50 to 200 nm thick if it is to be considered to be a uniform film covering the total surface of the coating. It should be noted that the location of the lubricant in the porous coating reduces significantly the rate of loss by evaporation compared to a thin layer of lubricant exposed on the tape surface. Evaporation would appear to be the cause of a substantial amount of loss based on the high vapor pressure of fatty acid esters used as lubricants. A limited amount of data suggests that in a durability test, about 50% of the lubricant is lost in 2000 passes of the tape over the head (Klaus and Bhushan, 1985). This translates to a lubricant loss equivalent to 0.03 nm per pass. If the lubricant is transferred to the head or cleaner blade, the buildup of lubricant would be significant. 38.6.3.2 Lubricant Degradation Mechanisms The weakest link in ester-based lubricants is the acid-catalyzed degradation reaction that can be followed by oxidation or thermal or hydrolytic mechanisms. The esters have a good additive response for oxidation and lubricant behavior. In general, there are no additives in tape and flexible disks. All of the magnetic oxides show a catalytic level of activity accelerating the oxidative degradation of a typical fatty acid ester (Klaus and Bhushan, 1986, 1988; Bhushan 1996a). The magnetic oxides appear to react with the ester lubricant to produce a metal-organic lubricant soluble material capable of acting as a catalyst for both oxidation and polymerization. These authors have projected that the life of the lubricant, based on oxidative stability at 60˚C, is about 1 year. Running tape in high-humidity environments results in dramatic increases in both friction and wear. If a significant portion of this water layer is on the exposed surface of the coating, it would result in poor boundary lubrication and meniscus effects, leading to high friction and wear. The presence of water in contact with ester lubricants suggests hydrolysis as a lubricant degradation mechanism.
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38.6.4 Lubrication Mechanisms in Thin-Film Rigid Disks 38.6.4.1 Lubricant Bonding The adsorption of the lubricant molecules is due to van der Waals forces, which are too weak to offset the spin-off losses or to arrest displacement of the lubricant by water or other ambient contaminants. Considering that these lubricating films are on the order of a monolayer thick and are required to function satisfactorily for several years, the task of developing a workable interface is quite formidable. As mentioned earlier, there is a critical film thickness of total liquid film (accumulated from a mobile layer of lubricant film and/or condensation of water vapor from a humid environment) divided by the composite roughness that should remain below 0.7 to minimize stiction. A thicker film of lubricant is desirable for long durability. An approach that aims to alleviate the above shortcomings is to enhance the attachment of the molecules to the overcoat, which, in most cases, is sputtered carbon. The overcoat must be chemically active in order to attach lubricant molecules, whereas the lubricant molecules should be hydrophobic so that they repel water from the environment. Lubricants can attach to the carbon surface by one or more of the following mechanisms: physisorption, conformational rearrangement, and chemisorption. The type and degree of attachment depend on the molecular structure and end groups of the lubricants and surface groups on the carbon surface. A hydrogenated carbon surface is highly functional and consists of many oxygen-containing surface groups, including -C-O-C- (ether), CO (carbonyl), -COOR (ester), -COOH (carboxyl), and -OH (hydroxyl) groups, as well as unpaired electrons (dangling bonds); see Figure 38.67 (Yanagisawa, 1994). The carbon-oxygen bonds are known to be important for physical adsorption of functional as well as nonfunctional PFPE derivatives. Only a few of the functional groups, carboxyl and hydroxyl, present on the carbon surface show a strong affinity for the lubricant. Main adsorption sites are associated with the presence of dangling bonds. Figure 38.67 shows the schematic for the adsorption of the Z-DOL molecule on the carbon surface in an ambient environment (Yanagisawa, 1994). The C-O bond and the hydroxyl groups in the case of Z-DOL interact with functional groups and dangling bonds on the carbon surface. The functional groups behave as an anchor, that is, an immobile fraction of the lubricant film. The addition of an alcohol (-OH) end group to a lubricant molecule adds an interaction energy on the order of 20 kJ/mol, even if no chemical reaction occurs with the surface. The attachment of lubricant molecules with or without functional groups is enhanced after sliding, as long as lubricant chains are exposed to the disk surface (Zhao et al., 1999b). The perfluoropolyether backbone primarily interacts with surfaces through van der Waals forces. The van der Waals interaction energy of PFPE molecules with a DLC surface is on the order of 2 kJ/mol or less. This energy is strong enough to make molecules lie flat on the surface when the lubricant film thickness is comparable to the polymer chain diameter of 0.7 nm. There are two approaches for chemisorption that have been shown to be successful in chemically bonding the liquid monolayer to the overcoat. The first relies on exposure of the disk lubricated with neutral PFPE to various forms of radiation such as low-energy X-ray (Heideman and Wirth, 1984), electron or ion beam (Lee, 1991; Vurens et al., 1992a), nitrogen plasma (Homola et al., 1990), or farultraviolet (e.g., 185 nm) (Saperstein and Lin, 1990; Vurens et al., 1992a). The mechanism of the improved affinity of the lubricant for the surface by ultraviolet radiation is not yet well-understood. It is believed that ultraviolet radiation enhances the bonding by photochemical alteration of either the lubricant, the
FIGURE 38.67
Schematic for the Z-DOL molecules adsorbed on the carbon surface at 20°C.
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substrate, or the air-deposited organics. The PFPEs undergo dissociative electron attachment caused by photoelectrons that are generated by the interaction of the ultraviolet light with the substrate. This dissociative electron attachment results in the formation of a negative ion and a radical. It is suggested that subsequent radical propagation and termination steps crosslink the PFPE and bond it to the substrate. Another approach uses chemically active PFPE molecules through either the above-mentioned treatments or a post-thermal treatment, in which the various functional end groups offer the opportunity of strong attachments to a specific interface if a high-enough temperature is applied to overcome the activity barrier (Ruhe et al., 1992). The activation energy of the thermal attachment of Z-DOL to a carbon surface is on the order of 30 kJ/mol. Surface cleanliness and chemical activity of the overcoat affect the degree of bonding. The length of the thermal treatment and the temperature for PFPE lubricants with polar end groups are important factors in determining the adsorption level of lubricants to the disk surface (typically 150°C for 30 min.) (Zhao and Bhushan, 1996). For 100% bonding, the thermal-treated film is washed off with a solvent to remove any unbonded fractions. The main advantage of bonded lubricants is their ability to enhance durability without the problem of stiction usually associated with weakly bonded lubricants. As mentioned, it has been observed that partially bonded lubricants work best. 38.6.4.2 Lubricant Degradation Mechanisms Experimental evidence suggests that some of the lubricant loss occurs by its transfer to the slider or the surrounding medium (Hu and Talke, 1988; Novotny and Karis, 1991). During start-stops or flying, there is a displacement of lubricant to the outside of the track and a decrease of lubricant to the outside of the track and a decrease of lubricant in the track (Figure 38.68). Some of the lubricant loss in the track is recovered when the slider is stationary. As the lubricant film gets thinner, most of the lubricant loss is not by desorption of intact lubricant molecules, but requires prior breakdown. Figure 38.69 shows the coefficient of friction and mass spectra of the untreated lubricant Z-DOL (Zhao et al., 2000; Zhao and Bhushan, 2001). The sliding tests were conducted in a high vacuum environmental tribotester and desorbed species were monitored with a mass spectrometer. During the sliding process, nine gaseous species were produced. Three species — including H2(2), C2H5(29), and CO2(44) — came from the wear of carbon overcoat; the remaining six species came from the degradation of the lubricant Z-DOL; all of them contain fluorine atoms. The gaseous products H2, C2H5, and CO2 are believed to show evidence of wear of the DLC overcoat, as well as desorption of organic adsorbates and removal of oxygenated or hydrogenated surface groups from the surface. The results show that Z-DOL decomposes immediately when the sliding begins. Fluorocarbon fragments are generated from lubricants during the initial period of sliding with a low and stable coefficient of friction,
FIGURE 38.68 XPS cross-sectional profiles of lubricant thickness immediately after sliding of an Al2O3-TiC slider on a carbon-coated thin-film disk lubricated with 3 nm of Fomblin Y with a load of 150 mN and a sliding velocity of 1 m/s. (From Novotny, V.J. and Karis, T.E. (1991), Sensitive tribological studies on magnetic recording disks, Adv. Info. Storage Syst., 2, 137-152. With permission.)
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FIGURE 38.69 Coefficient of friction and mass spectra of untreated lubricant Z-DOL sliding against a laser-textured thin-film disk at a normal load of 30 mN and sliding velocity of 0.5 m/s. (From Zhao, X. and Bhushan, B. (2001), Studies of degradation mechanisms of lubricants for magnetic thin film rigid disks, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
followed by sharp rise in friction and generation of gaseous products of DLC overcoat material. The increase in friction is associated with lubricant depletion, leading to intimate contact of the slider with the DLC overcoat. It appears that decomposition of PFPE begins from the onset of sliding, and once most of the lubricant is depleted, the DLC overcoat starts to wear. Bhushan and Cheng (1997) and Li and Bhushan (1997) have reported that fully bonded lubricants are best for protecting the DLC, followed by partially bonded lubricants and then untreated lubricants. Several possible processes have been proposed to account for the degradation of PFPE lubricants, i.e., thermal decomposition, catalytic decomposition by head slider or disk materials, triboelectric reactions, and mechanical scission (Bhushan and Cheng, 1997; Zhao et al., 2000; Zhao and Bhushan, 2001). These will be discussed next. 38.6.4.2.1 Thermal and Catalytic Decomposition It has been reported that the thermal decomposition temperature of PFPE lubricants is above 350°C. However, transient temperatures up to 100°C are generated on a microsecond scale at typical conditions (Bhushan, 1992, 1996a). Zhao et al. (2000) reported that no degradation occurs up to 70°C. The decomposition can occur by oxidation and chemical breakdown at high interface temperatures under extreme operating conditions, such as asperity contacts at high speeds during flying. PFPE lubricants degrade at much lower temperatures in the presence of most metal oxides. Kasai et al. (1991) and Kasai (1992) reported that Lewis acid sites present on Al2O3 are catalytic, and cause PFPE lubricant molecules to decompose at temperatures as low as 200°C although the lubricant would normally degrade above 350°C. A Lewis acid is defined as a substance that can accept a pair of electrons. Their experiments were conducted with ground-up powders of Al2O3 in the presence of lubricant at high temperatures ranging from 200 to 300°C for a duration of 1 to 48 hr. The kinetics of these experiments is very different from that in the drive operation. Thus, this mechanism is not believed to be relevant (Zhao and Bhushan, 2001). 38.6.4.2.2 Triboelectric Decomposition It has been reported that tribo-emission of electrons may be a significant factor in tribochemical reactions in the contact zone (operating under lightly loaded conditions), in addition to temperature rise and the
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catalytic action of the sliding surface (Zhao et al., 1999a, 2000; Zhao and Bhushan, 2000a, 2001). It is known that a wide variety of materials become electron emitters after mechanical treatment. The term “exoelectron emission” originates from investigation of the emission in freshly formed metals that were produced as a consequence of an exothermal transformation process of the surface. As reported in the literature, exoelectron emission occurs when a material surface is disturbed by plastic deformation, abrasion, fatigue cracking, or phase transformation. The electron emission from freshly formed surface bursts almost immediately during sliding and then decays suddenly as sliding stops. Electron emission has been observed from both metals and non-metals. The energy of exoelectrons is considered to be very low, on the order of 1 to 3 eV. Vurens et al. (1992b) studied the decomposition of PFPE lubricants by means of mass spectrometry and FTIR. The gaseous products being generated during sliding (mechanical decomposition) were compared with products from thermal decomposition and from electron decomposition of the PFPE lubricants. They concluded that electron decomposition of perfluoropolyethers gives rise to a different set of products than thermal decomposition. Electron decomposition and thermal decomposition of the lubricants probably occur through different pathways. They suggested that electron decomposition occurs through the formation of a negative ion resistance state, and then a negative ion is formed through dissociative electron attachment and a reactive radical species is generated. Subsequently, gas products are generated from the reactive radical species as well as from the negative ions. The wear fragments suggest that the decomposition of the PFPE lubricants during sliding is an electron-mediated process because most of the product fragment distribution is very similar to the electron decomposition fragment distribution. The electrons necessary for this decomposition could be tribo-electrons generated during the sliding process. To study the effect of low-energy electrons, Zhao et al. (2000) and Zhao and Bhushan (2001) conducted sliding experiments in a high-vacuum environmental tribotester and monitored desorbed species with a mass spectrometer. They used a low-energy ultraviolet (UV) lamp to generate low-energy electrons (0 to 5 eV). The illumination of the far-UV light creates low-energy electrons by excitation of the disk surface by UV photons. The produced low-energy electrons then interact with the lubricant molecules and accelerate the decomposition of the lubricant during the sliding process. They reported that UV illumination decreased the durability of the interface; more gaseous fragments were generated; and the partial pressure of the gas fragments was increased because of UV illumination. These results clearly show that UV illumination, which generates low-energy electrons, accelerates the degradation of the lubricant. Thus, triboelectric reaction can be a dominant degradation mechanism. The interaction between the PFPE lubricants and low-energy electrons generated in sliding process is schematically shown in Figure 38.70 (Kajdas and Bhushan, 1999; Zhao and Bhushan, 2001).
FIGURE 38.70
Schematic showing the electron-induced degradation process of PFPE lubricants.
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38.6.4.2.3 Mechanical Scission Shear rates during start-stops and isolated contacts during flying are high, which can result in mechanical scission. The lubricant film thickness is typically 1 to 2 nm and at 1 to 20 m/s sliding velocity, the shear rate is 5 × 107 to 2 × 109 s–1. At such shear rates, there can be significant energy imparted to the polymer chain, inducing the chains to slide over one another. If the molecules are strongly interacting with the surface, the sliding may be hindered. Additional hindrance to interchain sliding can be the presence of a bulky side group such as the -CF3 group on the Y lubricant. The additional intermolecular friction of the chains with the side group can hinder the rapid configurational adjustments required to support such high shear rates. The chains can be broken by tearing bonds apart along the polymer backbone and reduced to volatile products that provide the route for the observed lubricant loss when contact occurs in sliding or flying. Moreover, potential differences of up to 0.1 V are measured on thin-film disk surfaces, between areas on and off the sliding tracks. Corresponding electric fields for slider/disk separations lead to alteration of organic materials when the localized currents pass between the disk and slider asperities. Novotny et al. (1994) compared the mass spectra obtained during sliding experiments with those obtained in thermal desorption and found that the spectrum during sliding at 0.5 m/s resembled the thermal spectrum at 300°C rather than that at 90°C. They speculated that the loss mechanism of the lubricants could be of two types: either transient interfacial temperatures were high enough to evaporate lubricant from the surface or polymer scission-produced fragments were small enough to be gaseous. They anticipated that PFPE lubricants were decomposed by the scission of polymer chains driven by several processes, including high mechanical shear rate, high interfacial temperature, and tribocharging. The effects of mechanical shear were studied by Zhao et al. (2000) and Zhao and Bhushan (2001) by changing the sliding velocity of the slider. The slider slid on different tracks at different sliding velocities, the sliding distance being kept constant at 9 m at different velocities. The test results are shown in Figure 38.71. The partial pressure of mass spectrum peaks in the top figure were produced at different velocities; the sliding velocities are noted at the peaks. The higher the sliding velocity, the stronger the signal peaks. The bottom plot in Figure 38.71 shows the partial pressure increase of four gaseous species as a function of sliding velocity. It is clearly seen that the partial pressure increases with sliding velocity. The partial pressure of the gaseous products is obviously affected by the sliding velocity or mechanical shear rate, and is not affected by the sliding distance or sliding time. These results indicate that mechanical
FIGURE 38.71 Partial pressure changes of selected species of lubricant Z-DOL at different velocities (top), and partial pressure increase of selected species with sliding velocity (bottom) for a sliding of 9 m at each velocity; lubricant film thickness is 2.2 nm. (From Zhao, X. and Bhushan, B. (2001), Studies of degradation mechanisms of lubricants for magnetic thin film rigid disks, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press.)
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FIGURE 38.72
1491
Schematic showing the degradation process of PFPE lubricants caused by mechanical shear.
scission is also a dominant degradation mechanism of the PFPE lubricants. A schematic showing PFPE degradation as a result of the mechanical scission is shown in Figure 38.72 (Kajdas and Bhushan, 1999; Zhao and Bhushan, 2001). 38.6.4.2.4 Dominant Degradation Mechanisms Although several possible mechanisms for decomposition of PFPE lubricants are possible, dominant mechanisms appear to be triboelectric decomposition and mechanical scission. Thermal decomposition may also play a role in contacts at high velocities. 38.6.4.2.5 X-1P Additives X-1P, a cyclic phosphazine lubricant, is commonly used as an additive to PFPE lubricants in thin-film disks. Studies show that lubricant X-1P as an additive increases interface durability, especially at high humidities (Zhao and Bhushan, 1999; Zhao and Bhushan, 2000a). Unlike the long, linear molecular structure of Z-DOL and Demnum lubricants, the X-1P molecule has a dense spherical structure, consisting of six benzene rings and one phosphazine ring. The benzene rings and phosphazine ring are tightly bonded together, forming a whole, firm and dense structure, which makes the X-1P molecule more stable than the Z-DOL molecule. It is difficult for it to be scissioned or to be attacked by low-energy electrons. X-1P’s higher viscosity, in addition to its spherical molecule structure, provide for a stronger lubricant film compared to Z-DOL. This minimizes direct solid/solid contact at the interface.
38.7 Micro/Nanotribology and Micro/Nanomechanics At most interfaces of technological relevance, contact occurs at many asperities. Consequently, the importance of investigating single asperity contacts in studies of the fundamental micromechanical and tribological properties of surfaces and interfaces has long been recognized. The recent emergence and proliferation of proximal probes, in particular the tip-based microscopies — the scanning tunneling microscope (STM) and the atomic force microscope/friction microscope (AFM/FFM) — and of computational techniques for simulation of tip/surface interactions and interfacial properties, have allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifications and manipulations of nanoscale structures. These advances have led to the appearance of the new field of micro/nanotribology and micro/nanomechanics, which pertain to experimental and theoretical investigations of interfacial processes on scales ranging from the atomic and molecular scales to the microscale occurring during adhesion, friction, scratching, wear, nanoindentation, and thin-film lubrication at sliding surfaces (Bhushan et al., 1995b; Bhushan 1996a, 1997, 1998b, 1999a,c,e,f). These studies are needed to develop a fundamental understanding of interfacial phenomena on a small scale and to study interfacial phenomena in magnetic storage devices.
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38.7.1 Description of AFM/FFM AFM/FFMs used in the tribological studies have been described in several papers (e.g., Bhushan, 1999a). Briefly, in one of the commercial designs, the sample is mounted on a PZT tube scanner to scan the sample in the x-y plane and to move the sample in the vertical (z) direction. A sharp tip at the end of a flexible cantilever is brought into contact with the sample. Normal and frictional forces being applied at the tip/sample interface are simultaneously measured using a laser beam deflection technique. For surface roughness and friction measurements, a microfabricated square pyramidal Si3N4 tip with a tip radius of about 30 nm attached to a cantilever beam (with a normal beam stiffness of about 0.5 N/m) is generally used at normal loads ranging from 10 to 150 nN. A preferred method of measuring friction and calibration procedures for conversion of voltages corresponding to normal and friction forces to force units, are described by Ruan and Bhushan (1994). The samples are typically scanned over scan areas ranging from 50 nm × 50 nm to 10 µm × 10 µm, in a direction orthogonal to the long axis of the cantilever beam (Ruan and Bhushan, 1994). The scan rate is on the order of 1 Hz. For example, for this rate the sample scanning speed would be 1 µm/s for a 500 nm × 500 nm scan area. In nanoscale wear studies, the sample is initially scanned twice, typically at 10 nN to obtain the surface profile, then scanned twice at a higher load of typically 100 nN to wear and to image the surface simultaneously, and then rescanned twice at 10 nN to obtain the profile of the worn surface. For magnetic media studied by Bhushan and Ruan (1994b), no noticeable change in the roughness profiles was observed between the initial two scans at 10 nN and between profiles scanned at 100 nN and the final scans at 10 nN. Therefore, any changes in the topography between the initial scans at 10 nN and the scans at 100 nN (or the final scans at 10 nN) are believed to occur as a result of local deformation of the sample surface. In picoindentation studies, the sample is loaded in contact with the tip. During loading, tip deflection (normal force) is measured as a function of vertical position of the sample. For a rigid sample, the tip deflection and the sample traveling distance (when the tip and sample come into contact) are equal. Any decrease in the tip deflection as compared to vertical position of the sample represents indentation. To ensure that the curvature in the tip deflection-sample traveling distance curve does not arise from PZT hysteresis, measurements on several rigid samples, including single-crystal natural diamond (IIa), were made by Bhushan and Ruan (1994b). No curvature was noticed for the case of rigid samples. This suggests that any curvature for other samples should arise from the indentation of the sample. For microscale scratching, microscale wear, and nanoscale indentation hardness measurements, a three-sided pyramidal, single-crystal, natural diamond tip with an apex angle of 80° and a tip radius of about 100 nm (determined by scanning electron microscopy imaging) is used at relatively high loads (1 µN to 150 µN). The diamond tip is mounted on a stainless steel cantilever beam with normal stiffness of about 25 N/m (Bhushan and Koinkar, 1994a; Bhushan et al., 1994b, 1996c). For scratching and wear studies, the sample is generally scanned in a direction orthogonal to the long axis of the cantilever beam (typically at a rate of 0.5 Hz). For wear studies, typically an area of 2 µm × 2 µm is scanned at various normal loads (ranging from 1 to 100 µN) for a selected number of cycles. Scratching can also be performed at ramped loads (Sundararajan and Bhushan, 2000a). For nanoindentation hardness measurements, the scan size is set to zero and then normal load is applied to make the indents. During this procedure, the diamond tip is continuously pressed against the sample surface for about 2 seconds at various indentation loads. Sample surface is scanned before and after the scratching, wear, or nanoindentation, to obtain the initial and the final surface topography, at a low normal load of about 0.3 µN using the same diamond tip. An area larger than the scratched, worn, or indentation region is scanned to observe the scratch, wear scars, or indentation marks. Nanohardness is calculated by dividing the indentation load by the projected residual area of the indents (Bhushan and Koinkar, 1994b). Nanohardness at very shallow depths of 5 nm or less is measured using a depth-sensing capacitance transducer system in an AFM (Bhushan et al., 1996c). Boundary lubrication studies are conducted using either Si3N4 or diamond tips (Bhushan et al., 1995c; Koinkar and Bhushan, 1996a,b).
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38.7.2 Friction Bhushan and co-workers (Bhushan, 1996a, 1999a) measured friction on a microscale. They reported that coefficient of friction on a microscale is lower than the macrofriction for typical values of coefficients of friction of MP, barium ferrite and ME tapes, PET tape substrate, and polished and textured thin-film rigid disks (Table 38.4). Friction values on the microscale are much lower than those on the macroscale, which is believed to be due to a lower plowing contribution (almost no damage on the disk surface as measured, implying negligible plastic deformation). When measured for the small contact areas and very low loads used in microscale studies, mechanical properties are higher than at the macroscale (to be discussed later). This reduces the degree of wear. In addition, the apparent area of contact reduces the number of particles trapped at the interface and thus minimizes the plowing contribution to the friction. Furthermore, it has been shown that the coefficient of friction decreases with a decrease in asperity radius; therefore, the fact that an AFM tip is sharp would result in less friction as compared to a macrocontact. Local variations in the microscale friction of rough surfaces can be significant. Figure 38.73 shows the surface map, the slopes of surface map taken along the sliding direction, and the friction force map for a thin-film disk (Bhushan and Ruan, 1994b; Bhushan et al., 1994b; Bhushan and Koinkar, 1995a,b,c; Koinkar and Bhushan, 1996c, 1997; Sundararajan and Bhushan, 2000b). Note that there is no resemblance between the coefficient of friction profiles and the corresponding roughness maps; for example, high or low points on the friction profile do not correspond to high or low points on the roughness profiles. By comparing the slope and friction profiles, one observes a strong correlation between the two. (For a clearer correlation, see gray-scale plots of slope and friction profiles for FFM tip sliding in either direction in Figure 38.74). It has been shown that this correlation holds for various magnetic tapes, silicon, diamond, and other materials. This correlation can be explained by a “ratchet” mechanism; based on this mechanism, the local friction is a function of the local slope of the sample surface (Bhushan, 1999a,c). The friction is high at the leading edge of asperities and low at the trailing edge. In addition to the slope effect, the collision of the tip encountering an asperity with a positive slope produces additional torsion of the cantilever beam, leading to a higher measured friction force. When encountering an asperity with a negative slope, however, there is no collision effect and hence no effect on friction. The ratchet mechanism and the collision effects thus explain the correlation between the slopes of the roughness maps and friction maps observed in Figure 38.73. To study the directionality effect on the friction, gray-scale plots of coefficients of local friction of the thin-film disk as the FFM tip is scanned in either direction are shown in Figure 38.74. Corresponding gray-scale plots of slope of roughness maps are also shown in Figure 38.74. The left-hand set of figures corresponds to the tip sliding from the left toward the right (trace direction), and the middle set corresponds to the tip sliding from the right toward the left (retrace direction). It is important to take into account the sign change of the surface slope and friction force that occurs in the trace and retrace directions. To facilitate a comparison of the directionality effect on friction, the last set of the figures in the right-hand column shows the data with sign of surface slope and friction data in the retrace direction reversed. Now compare trace and –retrace data. It is clear that the friction experienced by the tip is dependent on the scanning direction because of surface topography. The directionality effect in friction on a macroscale has also been observed in some magnetic tapes (Bhushan, 1999a). On the macroscale, the effect of surface asperities is normally averaged out over a large number of contacting asperities.
38.7.3 Scratching and Wear Bhushan and Ruan (1994b) conducted nanoscale wear tests on metal particle (MP) tapes at a normal load of 100 nN. Figure 38.75 shows the topography of the MP tape obtained at two different loads. For a given normal load, measurements are made twice. There was no discernible difference between consecutive measurements for a given normal load. However, as the load increased from 10 to 100 nN, material (indicated by an arrow) was pushed toward the right side, in the sliding direction of the AFM tip relative to the sample. The material movement is believed to occur as a result of plastic deformation
3.3 2.3 5.4 5.1 7.0 4.7 5.8
4.5 4.1 8.7 12.5 7.9 5.1 7.0
Scan area: NOP, noncontact optical profiler; AFM, atomic force microscope. Numbers are for polymer and particulate regions, respectively.
2.2 2.3 4.6 6.0 12.3 9.3 33
1 × 1 µma
AFM 10 µm × 10 µma 0.05 0.04 0.04 0.08 0.07 0.05 0.05
1 × 1 µma 0.06 0.05 0.05 0.06 0.03 0.03 0.04
10 × 10 µma
Coefficient of Microscale Friction
— — — 0.19 0.18 0.18 0.55
Mn-Zn ferrite
0.26 0.19 0.16 — — — —
Al2O3-TiC
Coefficient of Macroscale Friction
21/100 — — 0.30/50 0.25/25 0.7 to 4.3/75 0.3/20 and 1.4/20b
Nanohardness (GPa)/ Normal load(µN)
1494
b
a
Polished unlubricated disk Polished lubricated disk Textured lubricated disk Metal-particle tape Barium-ferrite tape Metal-evaporated tape PET tape substrate
Sample
NOP 250 × 250 µma
RMS (nm)
TABLE 38.4 Surface Roughness (RMS), Microscale and Macroscale Friction, and Nanohardness Data of Thin-Film Magnetic Rigid Disk, Magnetic Tape, and Magnetic Tape Substrate (PET) Samples
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Surface height 40
500 400
20
300 200
0 0
100 100
200
300
400
500 nm
Surface slope 0.75
500 400
0.00
300 200
-0.75 0
100 100
200
300
400
500 nm
Friction force 15 500
10
400
5
300
0 -5
200 0
100 100
200
300
400
500 nm
FIGURE 38.73 Surface roughness map (σ = 4.4 nm), slope of the roughness map taken in the sample sliding direction (the horizontal axis) (mean = 0.023, σ = 0.197), and friction force map (mean = 6.2 nN, σ = 2.1 nN) for a thin-film rigid disk at a normal load of 160 nN. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29. With permission.)
of the tape surface. Similar behavior was observed on all tapes. With disks, no deformation under a 100-nN normal load was observed. Scratch and wear studies have been conducted on various magnetic tapes, rigid disks, and slider materials (Bhushan et al., 1994b; Bhushan and Koinkar, 1995a,b,c; Koinkar and Bhushan, 1996c). Microscratches made on the MP tape and an unlubricated thin-film rigid disk at various loads are shown in Figure 38.76. All scratches were made with 10 cycles. Notice that the scratch depth increases with an increase in the normal load. Figure 38.77 shows the micro-wear profiles at 20 µN load and at various cycles of an unlubricated thin-film disk. Also note that wear is not uniform and the wear is largely initiated at the texture marks present on the disk surface. This suggests that surface defects act as initiation sites
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-Retrace
Retrace
Trace
500 nm
0
500 0 nm
500 0 nm
500 nm
0
Surface slope 500 nm 0
0
500 0 nm
500 nm
500 nm
0
500 nm
0
Friction force
FIGURE 38.74 Gray-scale plots of the slope of the surface roughness and the friction maps for a thin-film rigid disk with FFM tip sliding in different directions. Higher points are shown by lighter shades.
for wear. Figure 38.78a shows the wear depth as a function of the number of cycles for the unlubricated and lubricated thin-film disks at 10 and 20 µN loads. Wear initially takes place slowly, with a sudden increase after about 40 cycles at 10 µN and after about 10 cycles at 20 µN. The rapid increase is associated with the breakdown of the carbon coating. Similar behavior has been reported by Bhushan and Koinkar (1995b) for ME tapes. Wear rates for particulate tapes (Figure 38.78b) and PET (polyethylene terephthalate) tape substrates are approximately constant at various loads and number of cycles. PET tape substrate consists of particles sticking out on its surface to facilitate winding. Figure 38.79 shows the wear profiles as a function of time at 1 µN load on the PET film in the nonparticulate and particulate regions (Bhushan and Koinkar, 1995a). Note that polymeric materials tear in microwear tests. The particles do not wear readily at 1 µN. Polymer around the particles is removed but the particles remain intact. Wear in the particulate region is much smaller than that in the polymer region. Nanohardness of the particulate region is about 1.4 GPa, compared to 0.3 GPa in the nonparticulate region. Scratches and wear profiles can be produced with very shallow depths; thus, the AFM technique can be used to measure scratch resistance and wear resistance of ultra-thin films.
38.7.4 Indentation The mechanical properties of materials can be measured using AFM (Bhushan et al., 1994b; Bhushan and Koinkar, 1994a,b; Bhushan and Ruan, 1994b). Bhushan and Ruan (1994b) measured the indentability
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FIGURE 38.75 Surface roughness profiles of a calendered metal-particle magnetic tape. The applied normal force was (a) 10 nN and (b) 100 nN. Location of the change in surface topography as a result of microwear is indicated by arrows. (From Bhushan, B. and Ruan, J. (1994b), Atomic-scale friction measurements using friction force microscopy. II. Application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)
of magnetic tapes at increasing loads on a picoscale (Figure 38.80). In the figure, the vertical axis represents the cantilever deflection and the horizontal axis represents the vertical position (z) of the sample. The “extending” and “retracting” curves correspond to the sample being moved toward or away from the cantilever tip, respectively. The left portion of the curve shows the tip deflection as a function of the sample traveling distance during sample/tip contact, which would be equal to each other for a rigid sample. However, if the tip indents into the sample, the tip deflection would be less than the sample traveling distance — in other words, the slope of the line would be less than 1. In Figure 38.80, we note that line in the left portion of the figure is curved with a slope of less than 1 shortly after the sample touches the tip, which suggests that the tip has indented the sample. Later, the slope is equal to 1, suggesting that the tip no longer indents the sample. Because the curves in extending and retracting modes are identical, the indentation is elastic up to a maximum load of about 22 nN used in the measurements. Bhushan and Koinkar (1994b) and Bhushan et al. (1996c) have reported that indentation hardness with a penetration depth as low as 1 nm can be measured using AFM. Bhushan et al. (1994b) measured the hardness of thin-film disks at loads of 80, 100, and 140 µN. Hardness values were 21 GPa (10 nm), 21 GPa (15 nm), and 9 GPa (40 nm); the depths of indentation are shown in the parenthesis. The hardness value at 100 µN is much higher than at 140 µN. This is expected because the indentation depth is only about 15 nm at 100 µN, which is smaller than the thickness of the carbon coating (~30 nm). The hardness value at lower loads is primarily the value of the carbon coating. The hardness value at higher loads is
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FIGURE 38.76 Surface profiles for scratched unlubricated thin-film rigid disk and MP tape. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29. With permission.)
primarily the value of the magnetic film, which is softer than the carbon coating (Bhushan, 1996a). This result is consistent with the scratch and wear data discussed previously. For the case of hardness measurements made on magnetic thin film rigid disk at low loads, the indentation depth is on the same order as the variation in the surface roughness. For accurate measurements of indentation size and depth, it is desirable to subtract the original (unindented) profile from the indented profile. An algorithm has been developed for this purpose. Because of hysteresis, a translational shift in the sample plane occurs during the scanning period, resulting in a shift between images captured before and after indentation. Therefore, the image for perfect overlap needs to be shifted before subtraction can be performed. To accomplish this objective, a small region on the original image was selected and the corresponding region in the indented image was found by maximizing the correlation between the two regions. (Profiles were plane-fitted before subtraction). Once two regions were identified, overlapped areas between the two images were determined and the original image was shifted with the required translational shift and then subtracted from the indented image. An example of profiles before and after subtraction is shown in Figure 38.81. It is easier to measure the indent on the subtracted image. At a normal load of 140 µN, the hardness value of an unlubricated, magnetic thin-film rigid disk (RMS roughness = 3.3 nm) is 9.0 GPa and the indentation depth is 40 nm.
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FIGURE 38.77 Surface profiles of unlubricated thin-film rigid disk showing the worn region (center 2 µm × 2 µm). The normal load and the number of test cycles are indicated in the figure. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29. With permission.)
38.7.5 Lubrication AFMs have been used to measure film thickness of ultra-thin lubricant films (a couple of nanometers thick) with a lateral resolution on the order of the AFM tip radius (about 100 nm or less), which is not possible by other techniques (Mate et al., 1990; Bhushan and Blackman, 1991; Bhushan and Dandavate, 2000).
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FIGURE 38.78 Wear depth as a function of number of cycles for (a) unlubricated and lubricated, thin-film rigid disks at 10 µN and 20 µN loads, and (b) MP tape at a normal load of 2 µN. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29.; Bhushan, B. and Koinkar, V.N. (1995b), Microtribology of metal particle, barium ferrite and metal evaporated magnetic tapes, Wear, 183, 360-370. With permission.)
Bonded lubricants are commonly used to reduce friction and wear of sliding surfaces, such as in thinfilm magnetic rigid disks (Bhushan, 1996a). Blackman et al. (1990) and Mate (1992) studied the deformation of bonded lubricant using AFM. They reported that the bonded lubricants behave as soft polymeric solids while contacted with an asperity. To study lubricant depletion during microscale measurements, Koinkar and Bhushan (1996a,b) measured the microscale friction as a function of the number of cycles of virgin Si (100) surface and silicon surface lubricated with about 2-nm thick Z-15 and Z-DOL PFPE lubricants (Figure 38.82). These experiments were conducted in an AFM/FFM by sliding an Si3N4 tip against the samples. The lubricant film was thermally bonded at 150°C for 30 minutes and washed off with a solvent to provide a chemically bonded layer of the lubricant film. From Figure 38.82, one notes that the friction force in a virgin silicon surface decreases a few cycles after the natural oxide film present on silicon surface gets removed. In the case of the Z-15-coated silicon sample, the friction force starts out low and then approaches that of the
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0 1 µN 4.00 100 cyc. µm
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2.00
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0 1 µN 4.00 µm
100 cyc.
FIGURE 38.79 Surface profiles of a PET film showing the worn regions (center 2 µm × 2 µm) in the (a) nonparticulate and (b) particulate regions. The normal load and the number of test cycles are indicated in the figure. (From Bhushan, B. and Koinkar, V.N. (1995a), Microtribology of PET polymeric films, Tribol. Trans., 38, 119-127. With permission.)
Tip deflection -6 nm/div
Retracting Extending
A C B
D Z Position -15 nm/div
FIGURE 38.80 Indentation curve for an MP tape. The spring constant of the cantilever used was 0.4 N/m. (From Bhushan, B. and Ruan, J. (1994b), Atomic-scale friction measurements using friction force microscopy. II. Application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)
unlubricated silicon surface after a few cycles. The increase in friction of the lubricated sample suggests that the lubricant film gets worn and the silicon underneath is exposed. In the case of the Z-DOL-coated silicon sample, the friction force starts low and remains low during the 100-cycle test. This suggests that Z-DOL does not get displaced/depleted as readily as Z-15. Thus, AFM studies can be used to study the performance of lubricants in simulated single-asperity contact.
38.8 Closure The need for ever-increasing high recording densities requires that the surfaces be as smooth as possible and the flying height (head-to-medium spacing) be as small as possible. Very smooth surfaces and
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FIGURE 38.81 Images with nanoindentation marks generated on an unlubricated thin-film rigid disk at normal loads of 140 µN with an indentation depth of 40 nm (a) before and (b) after subtraction. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29. With permission.)
ultra-low flying heights present challenges and opportunities unparalleled in any other industry. For an increase in the recording density from 10 Gbits/in.2 to 100 Gbits/in.2, the flying height would need to be reduced from about 25 nm to a value of 5 to 8 nm. A flying height on this order would require that disk surfaces become even smoother than they are today. Thus, stiction during CSS would become even more critical than it is today. It is likely that a load/unload mechanism via a ramp loading mechanism may become prevalent in future drives. Furthermore, to reduce magnetic spacing, the thickness of DLC overcoat and lubricant film on the disk surface and DLC overcoat slider surface would have to be reduced further from current DLC thicknesses of 8 to 10 nm to about 3.5 nm, and lubricant film thicknesses of 2 nm to less than 1 nm. The development and characterization of the materials present major challenges. The ultimate goal is to eliminate the air bearing and move to contact recording. To minimize stiction/friction and wear, the slider would have to be extremely small (on the order of 100 µm), with operation at ultra-low loads (on the order of 50 mg). These small sliders would require semiconductor processing techniques to produce a monolithic slider suspension assembly. These nanodevices would present their own challenges. It is expected that the disk drive industry will continue the path of pseudocontact recording with decreasing flying heights. A fundamental understanding of the tribology of the head/medium interfaces from macro- to micro/nanoscales will continue to remain crucial for the continued growth of this industry.
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FIGURE 38.82 Friction force as a function of number of cycles for the unlubricated and lubricated silicon samples. (From Koinkar, V.N. and Bhushan, B. (1996a), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol., A 14, 2378-2391. With permission.)
It appears that analytical models and experimental data available for tribology of head/medium interface are available. Understanding the micro/nanotribology of ultra-smooth surfaces and small components in future head/medium interfaces is lacking. AFM/FFM studies are expected to play a major role in computer tribology.
References Albrecht, T.R. and Sai, F. (1999), Load/unload technology for disk drives, IEEE Trans. Magn., 35, 857-862. Anderson, R.M. and Bhushan, B. (1996), Concurrent measurement of in situ friction force and head signal amplitude during dropouts in rotary head tape drives, Wear, 202, 35-49. Anderson, R.M. and Bhushan, B. (1997), Effect of environment on drop-outs in rotary-head tape drives, Proc. Inst. Mech. Eng., Part J: J.Eng. Tribol., 211, 349-363. Bair, S., Green, I., and Bhushan, B. (1991), Measurements of asperity temperatures of a read/write head slider bearing in hard magnetic recording disks, ASME J. Tribol., 113, 547-554. Baumgart, P., Nguyen, T., and Tam, A. (1995), Laser texture: a new solution for stiction and durability in disk drives, IEEE Trans. Magn., 31, 2946-2951. Bhushan, B. (1984), Analysis of the real area of contact between a polymeric magnetic medium and a rigid surface, ASME J. Lubr. Tech., 106, 26-34. Bhushan, B. (1985a), The real area of contact in polymeric magnetic media. II. Experimental data and analysis, ASLE Trans., 28, 181-197. Bhushan, B. (1985b), Assessment of Accelerated Head-Wear Test Methods and Wear Mechanisms, Tribology and Mechanics of Magnetic Storage Systems, Vol. 2, Bhushan, B. and Eiss, N.S. (Eds.), SP-19, ASLE, Park Ridge, IL, 101-111. Bhushan, B. (1987a), Magnetic head-media interface temperatures, Part I — Analysis, ASME J. Tribol., 109, 243-251. Bhushan, B. (1987b), Magnetic head-media interface temperatures, Part II — Application to magnetic tapes ASME J. Tribol., 109, 252-256.
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Bhushan, B. (1990), Magnetic media tribology: state-of-the-art and future challenges, Wear, 136, 169-197. Bhushan, B. (Ed.) (1991-1999), Advances in Information Storage Systems, Vol. 1-5, ASME, New York (1991–1993); Vol. 6-10, World Scientific, River Edge, NJ (1995-1999). Bhushan, B. (1992), Magnetic head-media interface temperatures — Part 3: Application to rigid disks, ASME J. Tribol., 114, 420-430. Bhushan, B. (1993a), Magnetic recording surfaces, in Characterization of Tribological Materials, Glaeser, W.A. (Ed.), Butterworth-Heineman, Boston, 116-133. Bhushan, B. (1993b), Magnetic slider/rigid disk substrate materials and disk texturing techniques — Status and future outlook, Adv. Info. Storage Syst., 5, 175-209. Bhushan, B. (1994), Tribology of magnetic storage systems, in Handbook of Lubrication and Tribology, Vol. 3, CRC Press, Boca Raton, FL, 325-374. Bhushan, B. (1996a), Tribology and Mechanics of Magnetic Storage Devices, 2nd ed., Springer-Verlag, New York. Bhushan, B. (1996b), Tribology of the head-medium interface, in Magnetic Recording Technology, Mee, C.D. and Daniel, E.D. (Eds.), McGraw-Hill, New York. Bhushan, B. (1996c), Contact mechanics of rough surfaces in tribology: single asperity contact, Appl. Mech. Rev., 49, 275-298. Bhushan, B. (1996d), Methodology for roughness measurement and contact analysis for optimization of interface roughness, IEEE Trans. Magn., 32, 1819-1825. Bhushan, B. (1997), Micro/Nanotribology and its Applications, NATO ASI Series E: Applied Sciences, Vol. 330, Kluwer Academic, Dordrecht, The Netherlands. Bhushan, B. (1998a), Contact mechanics of rough surfaces in tribology: multiple asperity contact, Tribol. Lett., 4, 1-35. Bhushan, B. (1998b), Micro/nanotribology using atomic force microscopy/friction force microscopy: state of the art, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 212, 1-18. Bhushan, B. (Ed.) (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. Bhushan, B. (Ed.) (1999b), Journal of Information Storage and Processing Systems, Vol. 1–, Birkhauser Boston, Cambridge, MA. Bhushan, B. (1999c), Principles and Applications of Tribology, Wiley, New York. Bhushan, B. (1999d), Chemical, mechanical and tribological characterization of ultra-thin and hard amorphous carbon coatings as thin as 3.5 nm: recent developments, Diamond and Related Mater., 8, 1985-2015. Bhushan, B. (1999e), Nanoscale tribophysics and tribomechanics, Wear, 225–229, 465-492. Bhushan, B. (1999f), Wear and mechanical characterisation on micro- to picoscales using AFM, Int. Mat. Rev., 44, 105-117. Bhushan, B. (2000a), Mechanics and Reliability of Flexible Magnetic Media, 2nd ed., Springer-Verlag, New York. Bhushan, B. (2000b), Macro- and microtribology of magnetic storage devices, in Proc. 26th Leeds-Lyon Symp., Dowson, D. et al. (Eds.), Elsevier Science, Amsterdam, The Netherlands (in press). Bhushan, B. and Blackman, G.S. (1991), Atomic force microscopy of magnetic rigid disks and sliders and its applications to tribology, ASME J. Tribol., 113, 452-457. Bhushan, B. and Chandra, S. (1999), Detection and sizing of particulate contamination in rigid disk drives, IEEE Trans. Magn., 35, 956-962. Bhushan, B. and Cheng, Y. (1997), Wear and degradation mechanisms of magnetic thin-film rigid disks with different lubricants using mass spectrometry, J. Appl. Phys., 81, 5390-5392. Bhushan, B. and Chilamakuri, S. (1996), Non-Gaussian surface roughness distribution of magnetic media for minimum friction/stiction, J. Appl. Phys., 79, 5794-5796. Bhushan, B. and Dandavate, C. (2000), Thin-film friction and adhesion studies using atomic force microscopy, J. Appl. Phys., 87, 1201-1210. Bhushan, B. and Doerner, M.F. (1989), Role of mechanical properties and surface texture in the real area of contact of magnetic rigid disks, ASME J. Tribol., 111, 452-458.
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Bhushan, B. and Dugger, M.T. (1990a), Real contact area measurements on magnetic rigid disks, Wear, 137, 41-50. Bhushan, B. and Dugger, M.T. (1990b), Liquid-mediated adhesion measurements at the thin-film magnetic disk/head slider interface, ASME J. Tribol., 112, 217-223. Bhushan, B. and Forehand, S. (1997), In situ instrumentation for localized wear studies of magnetic thinfilm disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 249-262. Bhushan, B. and Gupta, B.K. (1991), Handbook of Tribology: Materials, Coatings and Surface Treatments, McGraw-Hill, New York (1991), Reprint, Krieger Publishing Co., Malabar, FL, 1997. Bhushan, B. and Gupta, B.K. (1994), Friction and wear of ion implanted diamondlike carbon and fullerene films for thin-film rigid disks, J. Appl. Phys., 75, 6156-6158. Bhushan, B. and Gupta, B.K. (1995), Micromechanical characterization of Ni-P coated aluminummagnesium, glass, and glass-ceramic substrates and finished magnetic thin-film rigid disks, Adv. Info. Storage Syst., 6, 193-208. Bhushan, B. and Hahn, F.W. (1995), Stains on magnetic tape heads, Wear, 184, 193-202. Bhushan, B. and Khatavkar, D.V. (1995), Role of tape abrasivity on friction, wear, staining and signal degradation in audio tapes, Wear, 190, 16-27. Bhushan, B. and Khatavkar, D.V. (1996), Role of water vapor on the wear of Mn-Zn ferrite heads sliding against magnetic tapes, Wear, 202, 30-34. Bhushan, B. and Koinkar, V.N. (1994a), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. Bhushan, B. and Koinkar, V.N. (1994b), Nanoindentation hardness measurements using atomic force microscopy, App. Phys. Lett., 64, 1653-1655. Bhushan, B. and Koinkar, V.N. (1995a), Microtribology of PET polymeric films, Tribol. Trans., 38, 119-127. Bhushan, B. and Koinkar, V.N. (1995b), Microtribology of metal particle, barium ferrite and metal evaporated magnetic tapes, Wear, 183, 360-370. Bhushan, B. and Koinkar, V.N. (1995c), Macro and microtribological studies of CrO2 video tapes, Wear, 180, 9-16. Bhushan, B. and Koinkar, V.N. (1995d), Microscale mechanical and tribological characterization of hard amorphous carbon coatings as thin as 5 nm for magnetic disks, Surf. Coat. Technol., 76–77, 655-669. Bhushan, B. and Lowry, J.A. (1994), Friction and wear of particulate and ME magnetic tapes sliding against a Mn-Zn ferrite head in a linear mode, IEEE Trans. Magn., 30, 4182-4184. Bhushan, B. and Lowry, J.A. (1995), Friction and wear studies of various head materials and magnetic tapes in a linear mode accelerated test using a new nano-scratch wear measurement technique, Wear, 190, 1-15. Bhushan, B. and Majumdar, A. (1992), Elastic-plastic contact model of bifractal surfaces, Wear, 153, 53-64. Bhushan, B. and Martin, R.J. (1988), Accelerated wear test using magnetic-particle slurries, Tribol. Trans., 31, 228-238. Bhushan, B. and Monahan, J.A. (1995), Accelerated friction and wear studies of various particulate and thin-film magnetic tapes against tape path materials in pure sliding and rotary sliding modes, Tribol. Trans., 38, 329-341. Bhushan, B. and Patton, S.T. (1998), Tribology in ultra-high-density tape drive systems: state of the art and future challenges, IEEE Trans. Magn., 34, 1883-1888. Bhushan, B. and Phelan, R.M. (1986), Frictional properties as a function of physical and chemical changes in magnetic tapes during wear, ASLE Trans., 20, 402-413. Bhushan, B. and Ruan, J. (1994a), Tribological performance of thin film amorphous carbon overcoats for magnetic recording disks in various environments, Surf. Coat. Technol., 68/69, 644-650. Bhushan, B. and Ruan, J. (1994b), Atomic-scale friction measurements using friction force microscopy: Part II — Application to magnetic media, ASME J. Tribol., 116, 389-396. Bhushan, B. and Tian, X. (1995), Contact analysis of regular patterned rough surfaces in magnetic recording, ASME J. Electonic Packaging, 117, 26-33.
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Bhushan, B. and Venkatesan, S. (1993), Friction and wear studies of silicon in sliding contact with thinfilm magnetic rigid disks, J. Mater. Res., 8, 1611-1628. Bhushan, B. and Zhao, Z. (1997), Friction/stiction and wear studies of magnetic thin-film disks with two polar perfluoropolyether lubricants, IEEE Trans. Magn., 33, 918-925. Bhushan, B. and Zhao, Z. (1999), Macro- and microscale studies of molecularly-thick boundary layers of perfluoropolyether lubricants for magnetic thin-film rigid disks, J. Info. Storage Proc. Syst., 1, 1-21. Bhushan, B. et al. (Ed.) (1984-90), Tribology and Mechanics of Magnetic Storage Systems, Vol. 1–7, STLE, Park Ridge, IL. Bhushan, B., Bradshaw, R.L., and Sharma, B.S. (1984a), Friction in magnetic tapes II: Role of physical properties, ASLE Trans., 27, 89-100. Bhushan, B., Sharma, B.S., and Bradshaw, R.L. (1984b), Friction in magnetic tapes I: Assessment of relevant theory, ASLE Trans., 27, 33-44. Bhushan, B., Nelson, G.W., and Wacks, M.E. (1986), Head-wear measurements by autoradiography of the worn magnetic tapes, ASME J. Tribol., 108, 241-255. Bhushan, B., Wyant, J.C., and Meiling, J. (1988), A new three-dimensional digital optical profiler, Wear, 122, 301-312. Bhushan, B., Dominiak, M., and Lazzari, J.P. (1992a), Contact-start-stop studies with silicon planar head sliders against thin-film disks, IEEE Trans. Magn., 28, 2874-2876. Bhushan, B., Kellock, A.J., Cho, N.H. and Ager, J.W. (1992b), Characterization of chemical bonding and physical characteristics of diamond-like amorphous carbon and diamond films, J. Mater. Res., 7, 404-410. Bhushan, B., Hinteregger, H.F., and Rogers, A.E.E. (1994a), Thermal considerations for the edge guiding of thin magnetic tape in a longitudinal tape transport, Wear, 171, 179-193. Bhushan, B., Koinkar, V.N., and Ruan, J. (1994b), Microtribology of magnetic media, Proc. Inst. Mech. Eng. J., J. Eng. Tribol., 208, 17-29. Bhushan, B., Yang, L., Gao, C., Suri, S., Miller, R.A., and Marchon, B. (1995a), Friction and wear studies of magnetic thin-film rigid disks with glass-ceramic, glass and aluminum-magnesium substrates, Wear, 190, 44-59. Bhushan, B., Israelachvili, J.N., and Landman, U. (1995b), Nanotribology: friction, wear and lubrication at the atomic scale, Nature, 374, 607-616. Bhushan, B., Miyamoto, T., and Koinkar, V.N. (1995c), Microscopic friction between a sharp tip and thin-film magnetic rigid disks by friction force microscopy, Adv. Info. Storage Syst., 6, 151-161. Bhushan, B., Chyung, K., and Miller, R.A. (1996a), Micromechanical property measurements of glass and glass-ceramic substrates for magnetic thin-film disks for gibabit recording, Adv. Info. Storage Syst., 7, 3-16. Bhushan, B., Anderson, R.M., and Koinkar, V.N. (1996b), Effect of tape burnishing and drive use on head wear in rotary tape drives, Adv. Info. Storage Syst., 7, 229-247. Bhushan, B., Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996c), Nanoindentation and picoindentation measurements using a capacitive transducer system in atomic force microscopy, Philos. Mag., A74, 1117-1128. Bhushan, B., Patton, S.T., Sundaram, R., and Dey, S. (1996d), Pole tip recession studies of hard carboncoated thin-film tape heads, J. Appl. Phys., 79, 5916-5918. Bhushan, B., Sundararajan, S., Chilamakuri, S., and Scott, W.W. (1997a), Stiction analysis of magnetic tapes, IEEE Trans. Magn., 33, 3211-3213. Bhushan, B., Theunissen, G.S.A.M., and Li, X. (1997b), Tribological studies of chromium oxide films for magnetic recording applications, Thin Solid Films, 311, 67-80; Erratum, 320, 330 (1998). Bhushan, B., Chandra, S., and Smallen, M. (1999), Analysis of drive-level contaminant particles, J. Info. Storage Proc. Syst., 1, 115-124. Blackman, G.S., Mate, C.M., and Philpott, M.R. (1990), Interaction forces of a sharp tungsten tip with molecular films on silicon surface, Phys. Rev. Lett., 65, 2270-2273.
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Weick, B.L. and Bhushan, B. (1995a), Shrinkage and viscoelastic behavior of alternative substrates for magnetic tapes, IEEE Trans. Magn., 31, 2937-2939. Weick, B.L. and Bhushan, B. (1995b), Viscoelastic and shrinkage behavior of ultra-thin polymeric films, J. App. Poly. Sci., 58, 2381-2398. Weick, B.L. and Bhushan, B. (1995c), Tribological and dynamic behavior of alternative magnetic tape substrates, Wear, 190, 28-43. Weick, B.L. and Bhushan, B. (1996a), Characterization of magnetic tapes and substrates, IEEE Trans. Magn., 32, 3319-3323. Weick, B.L. and Bhushan, B. (1996b), The relationship between mechanical behavior, transverse curvature and wear of magnetic tapes, Wear, 202, 17-29. Xie, Y. and Bhushan, B. (1996a), Effects of particle size, polishing pad and contact pressure in free abrasive polishing, Wear, 200, 281-295. Xie, Y. and Bhushan, B. (1996b), Fundamental wear studies with magnetic particles and head cleaning agents used in magnetic tapes, Wear, 202, 3-16. Xu, J. and Bhushan, B. (1997), Friction and durability of ceramic slider materials in contact with lubricated thin-film rigid disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 303-316. Xu, J. and Bhushan, B. (1998a), Pole tip recession studies of thin-film rigid disk head sliders I. Mechanisms of pole tip recession growth, Wear, 219, 16-29. Xu, J. and Bhushan, B. (1998b), Pole tip recession studies of thin-film rigid disk head sliders II. Effects of air bearing surface and pole tip region designs and carbon coating, Wear, 219, 30-41. Xu, J. and Bhushan, B. (2000), Studies of failure mechanisms for head-disc interface using in-situ instrumentation, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214, 189-199. Yanagisawa, M. (1994), Adsorption of perfluoro-polyethers on carbon surfaces, in Tribology and Mechanics of Magnetic Storage Systems Vol. 9, SP-36, STLE, Park Ridge, IL, 25-32. Yoon, E.Y. and Bhushan, B. (2000), Effect of particulate concentration, materials and size on the friction and wear of a negative-pressure picoslider flying on a laser-textured disk, Wear, in press. Yu, M.H. and Bhushan, B. (1996), Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact, Wear, 200, 265-280. Zhao, Z. and Bhushan, B. (1996), Effect of bonded-lubricant films on the tribological performance of magnetic thin-film rigid disks, Wear, 202, 50-59. Zhao, Z. and Bhushan, B. (1997), Effect of environmental humidity on the friction/stiction and durability of lubricated magnetic thin-film disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 295-301. Zhao, Z. and Bhushan, B. (1998), Effect of lubricant thickness, viscosity and rest time on long-term stiction in magnetic thin-film rigid disks, IEEE Trans. Magn., 34, 1708-1710. Zhao, Z. and Bhushan, B. (1999), Tribological performance of PFPE and X-1P lubricants at head-disk interface — Part I: Experimental results, Tribol. Lett., 6, 129-139. Zhao, X. and Bhushan, B. (2000a), Lubrication studies of head-disk interfaces in a controlled environment — Part I: Effects of disk texture, lubricant thermal treatment and lubricant additive on durability of head-disk interface, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214, in press. Zhao, Z. and Bhushan, B. (2000b), Studies of fly stiction, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press. Zhao, Z. and Bhushan, B. (2000c), Effect of head slider DLC overcoats produced by various deposition techniques on the interface failure, IEEE Trans. Magn., in press. Zhao, X. and Bhushan, B. (2001), Studies of degradation mechanisms of lubricants for magnetic thin film rigid disks, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., in press. Zhao, Z., Bhushan, B., and Kajdas, C. (1999a), Tribological performance of PFPE and X-1P lubricants at head-disk interface — Part II. Mechanisms, Tribol. Lett., 6, 141-148. Zhao, Z., Bhushan, B., and Kajdas, C. (1999b), Effect of thermal treatment and sliding on chemical bonding of PFPE lubricant films with DLC surfaces, J. Info. Storage Proc. Syst., 1, 259-264. Zhao, X., Bhushan, B., and Kajdas, C. (2000), Lubrication studies of head-disk interfaces in a controlled environment — Part II: Degradation mechanisms of PFPE lubricants, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214, in press.
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39 Macro- and Microtribology of MEMS Materials 39.1
Introduction ................................................................... 1515 Background • Tribological Issues
39.2
Experimental Techniques .............................................. 1525 Description of Apparatus and Test Procedures • Test Samples
39.3
Results and Discussion .................................................. 1527 Micro/nanotribological Studies of Virgin, Coated, and Treated Silicon Samples • Micro/Nanotribological Studies of Doped and Undoped Polysilicon Films, SiC Films, and Their Comparison to Single-Crystal Silicon • Macroscale Tribological Studies of Virgin, Coated, and Treated Samples • Boundary Lubrication Studies • Component-Level Studies
Bharat Bhushan The Ohio State University
39.4
Closure ............................................................................ 1544
39.1 Introduction 39.1.1 Background The advances in silicon photolithographic process technology since the 1960s have led to the development of microcomponents (or microdevices) known as microelectromechanical systems (MEMS). More recently, lithographic processes have been developed to process non-silicon materials. These lithographic processes are being complemented with nonlithographic micromachining processes for fabrication of milliscale components or devices. Using these fabrication processes, researchers have fabricated a wide variety of miniaturized devices, such as acceleration, pressure, and chemical sensors; linear and rotary actuators; electric motors; gear trains; gas turbines; nozzles; pumps; fluid valves; switches; grippers; tweezers; and optoelectronic devices with dimensions in the range of a couple to a few thousand microns (for an early review, see Peterson, 1982; for recent reviews, see Muller et al., 1990; Madou, 1997; Trimmer, 1997; and Bhushan, 1998a). MEMS technology is still in its infancy and the emphasis to date has been on the fabrication and laboratory demonstration of individual components. MEMS devices have begun to be commercially used, particularly in the automotive industry. Silicon-based high-G acceleration sensors are used in airbag deployment (Bryzek et al., 1994). Acceleration sensor technology is slightly less than a $1 billion-a-year industry, dominated by Lucas NovaSensor and Analog Devices. The digital micromirror devices (DMDs) provided by Texas Instruments are large-scale, integrated spatial light modulators (Hornbeck, 1989). These use deformable mirror arrays on microflexures as part of airlineticket laser printers and high-resolution projection devices.
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Potential applications of MEMS devices include silicon-based acceleration sensors for anti-skid braking systems and four-wheel drives; silicon-based pressure sensors for monitoring pressure of cylinders in automotive engines and of automotive tires; and various sensors, actuators, motors, pumps, and switches in medical instrumentation, cockpit instrumentation, and many hydraulic, pneumatic, and other consumer products (Fujimasa, 1996). MEMS devices are also being pursued in magnetic storage systems (Bhushan, 1996a, 2000), where they are being developed for supercompact and ultrahigh-recordingdensity magnetic disk drives. Horizontal thin-film heads with a single-crystal silicon substrate, referred to as silicon planar head (SPH) sliders, are mass-produced using integrated circuit (IC) technology (Lazarri and Deroux-Dauphin, 1989; Bhushan et al., 1992). Several integrated head/suspension microdevices have been fabricated for contact recording applications (Hamilton, 1991; Ohwe et al., 1993). Highbandwidth, servo-controlled microactuators have been fabricated for ultrahigh-track-density applications that serve as the fine-position control element of a two-stage, coarse/fine servo system, coupled with a conventional actuator (Miu and Tai, 1995; Fan et al., 1995). Millimeter-sized wobble motors and actuators for tip-based recording schemes have also been fabricated (Fan and Woodman, 1995). In some cases, MEMS devices are used primarily for their miniature size, while in others, as in the case of the air bags, because of their high reliability and low-cost manufacturing techniques. This latter fact has been possible because semiconductor-processing costs have decreased drastically over the last decade, allowing the use of MEMS in many fields. The fabrication techniques for MEMS devices employ photolithography and fall into three basic categories: bulk micromachining, surface micromachining, and LIGA (a German acronym for Lithographie Galvanoformung Abformung), a German term for lithography, electroforming, and plastic molding. The first two approaches — bulk and surface micromachining — use planar photolithographic fabrication processes developed for semiconductor devices in producing two-dimensional structures (Jaeger, 1988; Madou, 1997; Bhushan, 1998a). Bulk micromachining employs anisotropic etching to remove sections through the thickness of a single-crystal silicon wafer, typically 250 to 500 µm thick. Bulk micromachining is a proven high-volume production process and is routinely used to fabricate microstructures such as acceleration and pressure sensors and magnetic head sliders. Surface micromachining is based on deposition and etching of structural and sacrificial films to produce a freestanding structure. These films are typically made of low-pressure chemical vapor deposition (LPCVD) polysilicon film with 2 to 20 µm thickness. Surface micromachining is used to produce surprisingly complex micromechanical devices such as motors, gears, and grippers. LIGA is used to produce high-aspect ratio (HAR) MEMS devices that are up to 1 mm in height and only a few microns in width or length (Becker et al., 1986). The LIGA process yields very sturdy three-dimensional structures due to their increased thickness. The LIGA process is based on the combined use of X-ray photolithography, electroforming, and molding processes. One of the limitations of the silicon microfabrication processes originally used for fabrication of MEMS devices, is the lack of suitable materials that can be processed. With LIGA, a variety of non-silicon materials such as metals, ceramics, and polymers can be processed. Nonlithographic micromachining processes, primarily in Europe and Japan, are also being used for fabrication of millimeter-scale devices using direct material microcutting or micromechanical machining (such as micromilling, microdrilling, microturning) or removal by energy beams (such as microspark erosion, focused ion beam, laser ablation and machining, and laser polymerization) (Friedrich and Warrington, 1998; Madou, 1998). Hybrid technologies, including LIGA and high-precision micromachining techniques, have been used to produce miniaturized motors, gears, actuators, and connectors (Lehr et al., 1996, 1997; Michel and Ehrfeld, 1998). These millimeter-scale devices may find more immediate applications. Silicon-based MEMS devices lack high-temperature capabilities with respect to both mechanical and electrical properties. Recently, researchers have been pursuing SiC as a material for high-temperature microsensor and microactuator applications (e.g., Tong et al., 1992; Shor et al., 1993). SiC is a likely candidate for such applications because it has long been used in high-temperature electronics, and highfrequency and high-power devices such as SiC metal-semiconductor field effect transistors (MESFETS) (Spencer et al., 1994) and inversion-mode metal-oxide-semiconductor field effect transistors (MOSFETS).
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TABLE 39.1
Selected Bulk Properties of 3C (β- or cubic) SiC and Si(100)
Sample
Density (kg/m3)
Hardness (GPa)
Elastic Modulus (GPa)
β-SiC Si(100)
3210 2330
23.5–26.5 9–10
440 130
Fracture Toughness (MPa m1/2)
Thermal Conductivitya (W/m K)
Coeff. of Thermal Expansiona (× 10–6/°C)
Melting Point (°C)
Bandgap (eV)
4.6 0.95
85-260 155
4.5–6 2–4.5
2830 1410
2.3 1.1
Note: Unless stated otherwise, data shown were obtained from Bhushan and Gupta (1997). a Obtained from Shackelford et al. (1994).
Many other SiC devices have also been fabricated, including ultraviolet detectors, SiC memories, and SiC/Si solar cells. SiC has also been used in microstructures such as speaker diaphragms and X-ray masks. For a summary of SiC devices and applications, see Harris (1995). Table 39.1 compares selected bulk properties of SiC and Si(100). Because of the large bandgap of the SiC, almost all devices fabricated from SiC have good high-temperature electronic properties. This high-temperature capability of SiC, combined with its excellent mechanical properties, thermal dissipative characteristics, chemical inertness, and optical transparency, makes it an ideal choice for complementing polysilicon (polysilicon melts at 1400°C) in MEMS devices at temperatures above 600°C (Mehregany et al., 1998). Because MEMS devices need to be of low cost to be viable in most applications, researchers have found low-cost techniques of producing single-crystal 3C-SiC (cubic or β-SiC) films via epitaxial growth on large-area silicon substrates for bulk micromachining (Zorman et al., 1995) and polycrystalline 3C-SiC films on polysilicon and silicon dioxide layers for surface micromachining of SiC (Zorman et al., 1998). It is believed that these films will be well-suited for MEMS devices.
39.1.2 Tribological Issues In MEMS devices, various forces associated with the device scale down with the size. When the length of the machine decreases from 1 mm to 1 µm, the area decreases by a factor of a million and the volume decreases by a factor of a billion. The resistive forces such as friction, viscous drag, and surface tension that are proportional to the area, decrease a thousand times less than the forces proportional to the volume, such as inertial and electromagnetic forces. Because of the increase in resistive forces and the fact that these devices produce relatively low power, tribological concerns become important. The tribological issues become critical because friction/stiction (static friction), wear, and surface contamination affect device performance and, in some cases, can even prevent devices from working. Examples of two micromotors using polysilicon as the structural material in surface micromachining — a variable-capacitance side drive and a wobble (harmonic) side drive — are shown in Figures 39.1 and 39.2; both can rotate up to 100,000 RPM. The microfabricated, variable-capacitance, side-drive micromotor with 12 stators and a four-pole rotor shown in Figure 39.1 is produced using a three-layer polysilicon process; the rotor diameter is 120 µm and the air gap between the rotor and stator is 2 µm (Tai et al., 1989). It is driven electrostatically to continuous rotation (by electrostatic attraction between positively and negatively charged surfaces). The intermittent contact at the rotor/stator interface and physical contact at the rotor/hub flange interface result in wear issues, and high stiction between the contacting surfaces limits the repeatability of operation or may even prevent the operation altogether. Figure 39.2 shows the SEM micrograph of a microfabricated harmonic side-drive (wobble) micromotor (Mehregany et al., 1988). In this motor, the rotor wobbles around the center bearing post rather than the outer stator. Again friction/stiction and wear of the rotor/center bearing interface are of concern. There is a need for the development of bearing/bushing materials that are both compatible with MEMS fabrication processes and that provide superior friction and wear performance. Monolayer lubricant films are also of interest. Figure 39.3a shows the SEM micrograph of a gear train for an air turbine with gear or blade rotors, 125 to 240 µm in diameter, fabricated using polysilicon as the structural material in
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hub rotor
3rd polysilicon 2nd polysilicon
stator
SiO2 Si3N4
1st polysilicon
Si3N4 lubricant ground plane
FIGURE 39.1 (top) SEM micrograph, and (bottom) schematic cross-section of a variable capacitance side-drive micromotor fabricated of polysilicon film. (From Tai, Y.C., Fan, L.S., and Muller, R.S. (1989), IC-processed micromotors: design, technology and testing, Proc. IEEE Micro Electro Mechanical Systems, 1-6. With permission.)
surface micromachining. The two flow channels on the top are connected to the two independent input ports, and the two flow channels at the bottom are connected to the output port of an air turbine. Wear at the contact of gear teeth is a concern. In the micromachined flow modulator shown in Figure 39.4, eight micromachined flow channels are integrated in series with eight electrostatically actuated microvalves (Robertson and Wise, 1998). The flow channels lead to a central gas outlet hole drilled in the glass substrate. Gas enters the device through a bulk micromachined gas inlet hole in the silicon cap. The gas, after passing through an open microvalve, flows parallel to the glass substrate through flow channels and exits the device through an outlet. The normally open valve structure consists of a freestanding double-end-clamped beam that is positioned beneath the gas inlet orifice. When electrostatically deflected upward, the beam seals against the inlet orifice and the valve is closed. In these microvalves used for flow control, the mating valve surfaces should be smooth enough to seal, while maintaining a minimum roughness to ensure low friction/stiction (Bhushan, 1996b). Stiction is a major issue. Figure 39.5 shows an SEM micrograph of a micromechanical switch (Peterson, 1979). As the voltage is applied between the deflection electrode and the p+ ground plane, the cantilever beam is deflected and the switch closes, connecting the contact electrode and the fixed electrode; wear during contact is of concern. Figure 39.6 shows an SEM micrograph of a pair of tongs (Mehregany et al., 1988). The jaws
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FIGURE 39.2 SEM micrograph of a harmonic side-drive (wobble) micromotor. (From Mehregany, M., Nagarkar, P., Senturia, S.D., and Lang, J.H. (1990), Operation of microfabricated harmonic and ordinary side-drive motors, Proc. IEEE Micro Electromechanical Systems, Vol. 86, IEEE, New York, 1-8. With permission.)
FIGURE 39.3 SEM micrograph of a gear train with three meshed gears, in an air turbine. (From Mehregany, M., Gabriel, K.J., and Trimmer, W.S.N. (1988), Integrated fabrication of polysilicon mechanisms, IEEE Trans. Electron Devices, 35, 719-723. With permission.)
open when the linearly sliding handle is pushed forward, demonstrating the linear slide and the linearto-rotary motion conversion; for this pair of tongs, the jaws open up to 400 µm in width. Wear at the teeth is of concern. Figure 39.7a shows an exploded view of a digital micromirror device pixel for xerographic-type printers and digital projection displays (Hornbeck, 1989). It consists of an array of rotatable aluminum mirrors fabricated on top of a CMOS static random access memory integrated circuit. The surface micromachined array consists of a half a million to a million or more of these independently controlled, reflective, digital light switches. The electrostatically activated pixel strikes the electrode surface with a certain energy. The
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Silicon cap
Gas inlet Beam
Flow channel Pressure sensor
Sense plate Metal pull-down Gas outlet plate
Gas outlet
FIGURE 39.4 Schematic of a low-pressure flow modulator. (From Robertson, J.K. and Wise, K.D. (1998), An electrostatically actuated integrated microflow controller, Sensors and Actuators, A 71, 98-106. With permission.)
FIGURE 39.5 SEM micrograph of single-contact and double-contact (with two orientations of the fixed electrodes) designs of micromechanical switches. (From Peterson, K.E. (1979), Micromechanical membrane switches on silicon, IBM J. Res. Dev., 23, 376. With permission.)
FIGURE 39.6 SEM micrograph of a partially released pair of tongs. (From Mehregany, M., Gabriel, K.J., and Trimmer, W.S.N. (1988), Integrated fabrication of polysilicon mechanisms, IEEE Trans. Electron Devices, 35, 719-723. With permission.)
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FIGURE 39.7 Schematics of (a) DMD pixel exploded view, and (b) two DMD pixels (mirrors are shown transparent). (From Henck, S.A. (1997), Lubrication of digital micromirror devices, Tribol. Lett., 3, 239-247. With permission.)
pixel operates in a bistable mode where the equilibrium positions occur when the yoke with the mirror is rotated ±10° (with respect to the horizontal plane) into contact with the electrode surface (Figure 39.7b). Contact between the yoke and the electrode surface is required for true digital (binary) operation. In the silicon planar head slider for magnetic disk drives shown in Figure 39.8, wear and friction/stiction are issues because of the close proximity between the slider and disk surfaces during steady operation and continuous contacts during start and stops (Lazarri and Deroux-Dauphin, 1989; Bhushan et al., 1992). Hard diamond-like carbon (DLC) coatings are used as an overcoat for protection against corrosion and wear. The two electrostatically driven rotary and linear microactuators (surface-micromachined, polysilicon microstructure) for a magnetic disk drive shown in Figure 39.9, consist of a movable plate connected only by springs to a substrate, on which there are two sets of mating interdigitated electrodes that activate motion of the plate in opposing directions. Any unintended contacts can result in wear and stiction. As an example of non-silicon components, Figure 39.10a shows a DC brushless permanent magnet millimotor (diameter = 1.9 mm; length = 5.5 mm) with an integrated milligear box that is produced with parts obtained by hybrid fabrication processes, including the LIGA process, micromechanical machining, and microspark erosion techniques (Lehr et al., 1996, 1997; Michel and Ehrfeld, 1998). The
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Air bearing surface etched in SiO2 to a depth of 0.7µm, rail width = 0.28 mm
Thin-film head Si (100)
0.52 mm
Peripheral secondary surface etched in SiO2 Pre cut depth = 17 µm 0.52 mm
m
85
m
2.
Leading edge 2.25 mm The layout of the rails on a 5-µm thick SiO2 film
(a) gap layer
air bearing surface
coils second level first level
Insulator layers
magnetic layer conductive layer silicon substrate
through hole connection
(b) FIGURE 39.8 Schematics (a) of a silicon planar head slider, and (b) of cross-section of the slider for magnetic disk drive applications. (From Bhushan, B., Dominiak, M., and Lazarri, J.P. (1992), Contact start-stop studies with silicon planar head sliders against thin-film disks, IEEE Trans. Magn., 28, 2874-2876. With permission.)
motor can rotate up to 100,000 RPM and deliver a maximum torque of 7.5 µNm. The rotor, supported on two ruby bearings, consists of a tiny steel shaft and a diametrically magnetized rare-earth magnet. The rotational speed of the motor can be converted by use of a milli-gearbox to increase the torque for a specific application. Gears are made of metal (e.g., electroplated Ni-Fe) or injected polymer materials (e.g., POM) using the LIGA process (Figures 39.10b and c). Figure 39.11 shows the SEM micrograph of a gear train for an externally excited magnetic millimotor with gears made of electroplated Ni-Fe using LIGA. Studies have been conducted to measure the friction/stiction in micromotors (Tai and Muller, 1990), gear systems (Gabriel et al., 1990), and polysilicon microstructures (Lim et al., 1990) to understand friction mechanisms. Several studies have been conducted to develop solid and liquid lubricant and hard films to minimize friction and wear (Bhushan et al., 1995b; Deng et al., 1995; Beerschwinger et al., 1995; Koinkar and Bhushan, 1996a,b; Bhushan, 1996b; Henck, 1997; Maboudian, 1998). Optimum materials, and liquid and solid lubrication approaches for bearings and gears are needed. There are tribological issues in the fabrication processes as well. For example, in surface micromachining, the suspended structures can sometimes collapse and permanently adhere to the underlying substrate (Figure 39.12) (Guckel and Burns, 1989). The mechanism of such adhesion phenomena needs to be understood (Mastrangelo, 1997; Maboudian and Howe, 1997). Friction/stiction and wear clearly limit the lifetimes and compromise the performance and reliability of microdevices. Because microdevices are designed to small tolerances, environmental factors, surface contamination, and environmental debris affect their reliability. There is a need for development of a
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(a)
(b)
FIGURE 39.9 Schematics (a) of a microactuator in place with magnetic head slider, and (b) top view of two electrostatic, rotary and linear microactuators (electrode tree structure). (From Fan, L.S., Ottesen, H.H., Reiley, T.C., and Wood, R.W. (1995), Magnetic recording head positioning at very high track densities using a microactuatorbased, two-stage servo system, IEEE Trans. Ind. Electron., 42, 222-233. With permission.)
fundamental understanding of friction/stiction, wear, and the role of surface contamination and environment in microdevices (Bhushan, 1998a). A few studies have been conducted on the tribology of bulk silicon and polysilicon films used in microdevices (Bhushan and Venkatesan, 1993a,b; Gupta et al., 1993, 1994; Venkatesan and Bhushan, 1993, 1994; Gupta and Bhushan, 1994; Bhushan and Koinkar, 1994;
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FIGURE 39.10 Schematics of (a) permanent magnet millimotor with integrated milli-gear box; (b) of wolfrom-type system made of Ni-Fe metal (From Lehr, H. Abel, S., Doppler, J., Ehrfeld, W., Hagemann, B., Kamper, K.P., Michel, F., Schulz, Ch., and Thurigen, Ch. (1996), Microactuators as driving units for microrobotic systems, in Proc. Microrobotics: Components and Applications, Vol. 2906, Sulzmann, A. (Ed.), SPIE, 202-210.); and (c) of multistage planetary gear system made with microinjected POM plastic showing a single gear and the gear system. (From Thurigen, C., Ehrfeld, W., Hagemann, B., Lehr, H., and Michel, F. (1998), Development, fabrication and testing of a multi-stage micro gear system, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 397-402. With permission.)
Bhushan, 1996b). Mechanical properties of structures made of silicon and polysilicon films such as indentation hardness are not well characterized. Microtribological studies have been conducted using AFM/FFM on undoped and doped silicon and polysilicon films and SiC films that are used in MEMS
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FIGURE 39.11 SEM micrograph of a gear train made of nickel for a millimotor. (From Guckel, H., Skrobis, K.J., Christenson, T.R., and Klein, J. (1994), Micromechanisms for actuators via deep X-ray lithography, Proc. of the Symp. Microlithography, SPIE, Bellingham, WA, 39-47. With permission.)
Sacrificial/Spacer Layer
Microstructure Layer
Freestanding Microstructure
Isolation layer Silicon Substrate
Silicon Substrate
FIGURE 39.12 Schematics of microstructures during fabrication using surface micromachining before (left/upper) and after (right/lower) removal of sacrificial/spacer layer.
devices (Bhushan, 1996b, 1997, 1998a; Bhushan et al., 1994, 1997a,b, 1998; Li and Bhushan, 1999; Sundararajan and Bhushan, 1998). Young’s modulus of elasticity, fatigue strength, and fracture toughness of interest to tribological performance have been characterized in a few studies (Mehregany et al., 1987; Ericson and Schweitz, 1990; Schweitz, 1991; Guckel et al., 1992; Connally and Brown, 1993; Fang and Wickert, 1995; Mazza et al., 1996; Wilson et al., 1996; Bhushan, 1999a). This chapter presents a review of macro- and micro/nanotribological studies of single-crystal silicon and polysilicon, oxidized and implanted silicon, doped and undoped polysilicon films, and SiC films. A summary of limited component-level tests is also presented.
39.2 Experimental Techniques 39.2.1 Description of Apparatus and Test Procedures 39.2.1.1 Micro/Nanoscale Tests A modified AFM/FFM (Nanoscope III, Digital Instruments, Santa Barbara, CA) was used for the micro/nanotribological studies (Bhushan et al., 1995a; Bhushan, 1999a). Surface roughness and microscale friction measurements were simultaneously made over a scan size of 10 µm × 10 µm with an Si3N4 tip (tip radius ~ 50 nm; cantilever stiffness ~ 0.6 N/m) sliding over the sample surface orthogonal to the
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long axis of the cantilever at 25 µm/s. A coefficient of friction and conversion factors for converting the friction signal voltage to force units (nN) were obtained through the methods developed previously by Bhushan and co-workers (Bhushan, 1999a). The normal loads used in the friction measurements varied between 50 and 300 nN. The reported values are each an average of six separate measurements. For the scratch and wear tests, specially fabricated diamond microtips were used (Bhushan et al., 1997a; Sundararajan and Bhushan, 1998). These microtips consisted of single-crystal natural diamond, ground to the shape of a three-sided pyramid, with an apex angle of 60° and tip radius of about 70 nm, mounted on a platinum-coated stainless steel cantilever beam whose stiffness was 50 N/m. Samples were scanned orthogonal to the long axis of the cantilever, with loads ranging from 20 to 100 µN to generate scratch/wear marks. Scratch tests consisted of generating scratches in a reciprocating mode at a given load for ten cycles over a scan length (stroke length) of 5 µm at 10 µm/s. Wear marks were generated over a scan area of 2 µm × 2 µm at 4 µm/s, and the wear marks were observed by scanning a larger 4 µm × 4 µm area with the wear mark at the center. Imaging scans of both scratch and wear tests were done at a low normal load of 0.5. The reported scratch/wear depths are an average of three runs at separate instances. All measurements were performed in an ambient environment (21 ± 1°C, 45 ± 5% RH). Hardness and elastic modulus were calculated from load-displacement data obtained by nanoindentation using a commercially available nanoindenter (Bhushan et al., 1997b; Bhushan, 1999a; Li and Bhushan, 1999). The instrument monitored and recorded dynamic load and displacement of a threesided pyramidal diamond (Berkovich) indenter with a force resolution of about 75 nN and displacement resolution of about 0.1 nm. Multiple loading and unloading were performed to examine reversibility of the deformation and thereby ensuring that the regime was elastic. The fracture toughness measurements were made using a microindentation technique. A Vickers indenter (four-sided diamond pyramid) was used to indent samples in a microhardness tester at a normal load of 0.5 N. The indentation impressions were examined in an optical microscope to measure the length of radial cracks to calculate the fracture toughness (Li and Bhushan, 1999). 39.2.1.2 Macroscale Tests Macroscale studies were conducted using either a ball-on-flat tribometer under reciprocating motion or a magnetic rigid disk drive. In the ball-on-flat tribometer tests, a 5-mm diameter alumina ball (hardness ~ 21 GPa) was slid in a reciprocating mode (2 mm amplitude and 1 Hz frequency) under a normal load of 1 N in the ambient environment (Gupta et al., 1993). The coefficient of friction was measured during the tests using a strain gage ring. Wear volume was measured by measuring the wear depth using a stylus profiler. In the magnetic disk drive tests, a modified disk drive was used. The silicon pins or magnetic head slider specimens to be tested were slid in a unidirectional sliding mode against a magnetic thin-film disk under a normal load of 0.15 N and rotational speed of 200 RPM. The sliding speeds at track radii ranging from 45 to 55 mm varied from 0.9 to 1.2 m/s (Bhushan and Venkatesan, 1993a,b). At these speeds, the pin or slider specimen remained in contact throughout the period of testing. The coefficient of friction was measured during the tests using a strain gage beam. Samples were examined using scanning electron microscopy to detect any wear. Chemical analyses of the samples were also carried out to study failure mechanisms.
39.2.2 Test Samples Materials of most interest for planar fabrication processes using silicon as the structural material are undoped and boron-doped (p+-type) single-crystal silicon and phosphorous doped (n+-type) LPCVD polysilicon films. For tribological reasons, silicon needs to be coated with a solid and/or liquid overcoat or be surface-treated, which exhibits low friction and wear. Studies have been conducted on various types of virgin silicon samples including undoped (lightly doped) single-crystal Si(100); Si(111); and Si(110); and the following types of treated/coated silicon samples: PECVD-oxide coated Si(111), dry-oxidized, wet-oxidized, and C+-implanted Si(111) (Bhushan and Venkatesan, 1993b; Bhushan and Koinkar, 1994). Studies have also been conducted on heavily doped (p+-type) single-crystal Si(100), undoped polysilicon film, heavily doped (n+-type) polysilicon film, and
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3C-SiC (cubic or β-SiC) film (Bhushan et al., 1997a,b, 1998; Sundararajan and Bhushan, 1998; Li and Bhushan, 1999). A 10 mm × 10 mm coupon of each sample was ultrasonically cleaned in methanol for 20 minutes and dried with a blast of dry air prior to measurement. The undoped Si(100) was a p-type material grown by the CZ process. It had a boron concentration of 1.7 × 1015 ions/cm3 from intrinsic doping during the manufacturing process. The doped wafer (p+-type single-crystal silicon) was heavily doped with boron ions (from a solid source of oxide of boron) with concentration of 7 × 1019 ions/cm3 down to a depth of 5.5 µm using thermal diffusion. The grain size of polysilicon wafer was about 5 mm. The polysilicon film was produced as follows: 1. The substrate used was thermally oxidized Si(100) wafers with the oxide layer grown using a standard wet oxidation recipe to a nominal thickness of about 100 nm 2. The polysilicon film was grown on the substrate using an LPCVD process (deposition temperature, 610°C; silane flow rate, 285 sccm; deposition pressure, 230 mTorr), using the thermal decomposition of silane vapor. The films were about 3 µm thick, with columnar grains and a grain size of about 750 nm. X-ray diffraction and transmission electron microscopic characterization showed the film to be highly oriented (110). The n+-doped polysilicon film was obtained by doping the polysilicon film with phosphorus ions from a solid source of P2O5 by thermal diffusion at 875°C for 90 minutes. The 3C-SiC films were grown through an atmospheric pressure chemical vapor deposition (APCVD) process on an Si(100) substrate. To grow the SiC film on the wafer by carbonizing its surface, the wafer is placed on an SiC-coated graphite susceptor, which is induction-heated by an RF-generator to the growth temperature of 1360°C in the presence of propane and silane at 1 atm. Prior to film growth, the wafer is heated to 1000°C in the presence of hydrogen, which etches the native oxide from the wafer surface (Zorman et al., 1995). The films obtained were about 2 µm thick. Both as-deposited and polished versions of the undoped polysilicon and SiC films were studied. The polysilicon film was chemomechanically polished in a Struers Planopol-3 polishing machine using 100 mL colloidal silica dispersion (Rippey Corporation; particle size of 30 to 100 nm) mixed in 2000 mL deionized water at a force of 210 N for 15 min, with the pads running at 150 RPM in the same direction. The SiC and doped polysilicon films were polished in a Buehler Ecomet-3 polishing machine with diamond slurry (General Electric Company; particle size of 100 to 500 nm) for 30 min for SiC and 12 min for doped polysilicon film at a load of 50 N, with the pads running at 10 RPM in the same direction. Doped polysilicon film was polished using Fuji film lapping tape (LT-2), the main lapping agent being 37-µm-sized Cr2O3 particles. Boundary lubrication studies have been conducted on silicon samples coated with perfluoropolyether lubricants (Koinkar and Bhushan, 1996a,b) and Langmuir-Blodgett and chemically grafted self-assembled monolayer films (Bhushan et al., 1995b).
39.3 Results and Discussion Reviews of five studies are presented in this chapter section. The first study (Section 39.3.1) compares micro/nanotribological properties of various forms of virgin, coated, and treated silicon samples. The second study (Section 39.3.2) is composed of similar studies conducted on SiC film and compares this material to other materials currently used in MEMS devices. The third study (Section 39.3.3) compares the macroscale friction and wear data of virgin, coated, and treated silicon samples. The fourth study (Section 39.3.4) discusses various forms of boundary lubrication that may be suitable for MEMS devices. Finally, the fifth study (Section 39.3.5) presents a review of component-level studies.
39.3.1 Micro/nanotribological Studies of Virgin, Coated, and Treated Silicon Samples Table 39.2 summarizes the results of the studies conducted on various silicon samples (Bhushan and Koinkar, 1994). Coefficient of microscale friction values of all the samples are about the same. Table 39.3
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TABLE 39.2 RMS, Microfriction, Microscratching/Microwear, and Nanoindentation Hardness Data for Various Virgin, Coated, and Treated Silicon Samples
Material
RMS Roughnessa (nm)
Microscale Coefficient of Frictionb
Scratch Depthc at 40 µN (nm)
Wear Depthc at 40 µN (nm)
Nanohardnessc at 100 µN (GPa)
0.11 0.09 0.12 1.07 0.16 1.50 0.11 0.25 0.33
0.03 0.04 0.03 0.04 0.05 0.01 0.04 0.04 0.02
20 20 25 18 18 8 16 17 20
27 — — — 25 5 14 18 23
11.7 — — — 12.5 18.0 17.0 14.4 18.6
Si(111) Si(110) Si(100) Polysilicon Polysilicon (lapped) PECVD-oxide coated Si(111) Dry-oxidized Si(111) Wet-oxidized Si(111) C+-implanted Si(111)
Scan size 500 nm × 500 nm. Versus Si3N4 ball, ball radius of 3 mm at a normal load of 0.1 N (0.3 GPa) at an average sliding speed of 0.8 mm/s. c Measured using an AFM with a diamond tip of radius of 100 nm. a
b
TABLE 39.3 Surface Roughness and Coefficients of Micro- and Macroscale Friction of Selected Samples
Material Si(111) C+-implanted Si(111)
RMS Roughness (nm)
Coefficient of Microscale Frictiona
Coefficient of Macroscale Frictionb
0.11 0.33
0.03 0.02
0.33 0.18
a Versus Si N tip; tip radius of 50 nm in the load range of 10 to 150 nN (2.5 to 6.1 GPa) 3 4 at a scanning speed of 5 µm/s over a scan area of 1 µm × 1 µm. b Versus Si N ball; ball radius of 3 mm at a normal load of 0.1 N (0.3 GPa) at an average 3 4 sliding speed of 0.8 mm/s.
compares macroscale and microscale friction values for two of the samples. When measured for small contact areas and very low loads used in microscale studies, indentation hardness and elastic modulus are higher than that at the macroscale — this reduces friction. This, added to the effect of the small apparent area of contact reducing the number of trapped particles on the interface, results in a lower plowing contribution in the case of microscale friction measurements. Figure 39.13 and Table 39.2 show microscale scratch data for the various silicon samples (Bhushan and Koinkar, 1994). These samples could be scratched at 10 µN load. Scratch depth increased with normal load. Crystalline orientation of silicon had little influence on scratch resistance because the natural oxidation of silicon in ambient masks
FIGURE 39.13 Scratch depth as a function of normal force after 10 cycles for various silicon samples: virgin, treated, and coated. (From Bhushan B. and Koinkar, V.N. (1994), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. With permission.)
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the expected effect of crystallographic orientation. PECVD-oxide samples showed the best scratch resistance, followed by dry-oxidized, wet-oxidized, and ion-implanted samples. Ion implantation does not appear to improve scratch resistance. The microscratching experiments just described can be used to study failure mechanisms on the microscale and to evaluate the mechanical integrity (scratch resistance) of ultra-thin films at low loads. Wear data on the silicon samples is presented in Table 39.2 (Bhushan and Koinkar, 1994). PECVDoxide samples showed superior wear resistance, followed by dry-oxidized, wet-oxidized, and ionimplanted samples. This agrees with the trends seen in scratch resistance. In PECVD, ion bombardment during the deposition improves the coating properties such as suppression of columnar growth, freedom from pinhole, decrease in crystalline size, and increase in density, hardness, and substrate-coating adhesion. These effects may help in improving the mechanical integrity of the sample surface. The wear resistance of ion-implanted silicon samples was further studied (Figure 39.14) (Bhushan and Koinkar, 1994). For tests conducted at various loads on Si(111) and C+-implanted Si(111), it is noted that the wear resistance of implanted sample is slightly poorer than that of virgin silicon, up to about 80 µN; above 80 µN, the wear resistance of implanted Si improves. As one continues to run tests at 40 µN for a larger number of cycles, the implanted sample exhibits higher wear resistance than the unimplanted sample. Damage from the implantation in the top layer results in poorer wear resistance; however, the implanted zone at the subsurface is more wear resistant than the virgin silicon.
FIGURE 39.14 Wear depth as a function of (a) load (after one cycle), and (b) cycles (normal load = 40 µN) for Si(111) and C+-implanted Si(111). (From Bhushan B. and Koinkar, V.N. (1994), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. With permission.)
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Nanoindentation hardness values of all samples are also presented in Table 39.2. Coatings and treatments improved nanohardness of silicon. Note that dry-oxidized and PECVD films are harder than wetoxidized films as the latter may be porous. The high hardness of oxidized films may be responsible for the measured low wear on the microscale and macroscale (data to be presented later). Figure 39.15 shows the indentation marks generated on virgin and C+-implanted Si(111) at a normal load of 70 µN with an indentation of about 3 nm and hardness values of 15.8 and 19.5 GPa, respectively (Bhushan and Koinkar, 1994). Hardness values of virgin and C+-implanted Si(111) at various indentation depths (normal loads) are presented in Figure 39.16 (Bhushan and Koinkar, 1994). Note that the hardness at a small indentation depth of 2.5 nm is 16.6 GPa, and drops to a value of 11.7 GPa at a depth of 7 nm and a normal load of 100 µN. Higher hardness values obtained in low-load indentation can arise from the observed pressureinduced phase transformation during the nanoindentation (Pharr, 1991; Callahan and Morris, 1992). The additional increase in the hardness at an even lower indentation depth of 2.5 nm reported here might well arise from the contribution by complex chemical films (not from native oxide films) present on the silicon surface. At small volumes, there is a high probability that indentation would be made into a region that was initially dislocation-free. Furthermore, at small volumes, it is believed that there is an increase in the stress necessary to operate dislocation sources (Gane and Cox, 1970; Sargent, 1986). These are some of the plausible explanations for an increase in hardness at smaller volumes. If the silicon material is to be used at very light loads — such as in microsystems — the high hardness of surface films would protect the surface until it is worn. From Figure 39.16, the hardness value of C+-implanted Si(111) at a normal load of 50 µN is 20.0 GPa with an indentation depth of about 2 nm, which is comparable to the hardness value of 19.5 GPa at 70 µN; whereas the measured hardness value for virgin silicon at an indentation depth of about 7 nm (normal load of 100 µN) is only about 11.7 GPa. Thus, ion implantation results in an increase in hardness. Note that the surface layer of the implanted zone is much harder than the subsurface and may be brittle, leading to higher wear on the surface. The subsurface of the implanted zone is harder than virgin silicon, resulting in higher wear resistance, which will be shown later in macroscale tests conducted at high loads.
39.3.2 Micro/Nanotribological Studies of Doped and Undoped Polysilicon Films, SiC Films, and Their Comparison to Single-Crystal Silicon 39.3.2.1
Surface Roughness and Friction
The surface roughness of various samples obtained with the AFM is compared in Figure 39.17a (Sundararajan and Bhushan, 1998). Polishing of the as-deposited polysilicon and SiC films drastically affects the roughness as the values reduce by two orders of magnitude. Si(100) appears to be the smoothest, followed by polished undoped polysilicon and SiC films, which have comparable roughness. The doped polysilicon film shows higher roughness than the undoped sample, which is attributed to the doping process. The coefficients of microscale friction of the various samples are shown in Figure 39.17b (Bhushan et al., 1998; Sundararajan and Bhushan, 1998). Despite being the smoothest sample, Si(100) exhibits higher friction than the other samples. Doped polysilicon also shows high friction, which is due to the presence of grain boundaries and high surface roughness. In the case of the undoped polysilicon and SiC films, polishing did not significantly affect the friction values. From the data, the polished SiC film shows the lowest friction, followed by polished, undoped polysilicon film, which strongly supports the candidacy of SiC films for use in MEMS devices. Gray-scale top-view images of surface height and corresponding friction force of selected samples obtained with the AFM/FFM are shown in Figure 39.18. Brighter regions indicate higher height than darker regions in the case of the surface height images, and brighter regions indicate higher friction force experienced by the tip than the darker regions. The doped polysilicon film shows a large number of grain boundaries. It appears that regions of high and low surface height do not necessarily correspond to regions of high and low friction. The low microscale friction exhibited by SiC, compared to the other materials, agrees with the fact that many ceramic/ceramic interfaces generally show low friction on the macroscale. In this study, the Si3N4 tip/SiC film interface shows the same trend. In the case of ceramic materials, formation of tribochemical
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20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250
0 250
20.0 nm
0 500 nm
10.0
500
0
250
0 250
0 500 nm
(a)
20.0 nm
40.0 nm
10.0 nm
0.0 nm
20.0
500
0
250 0 250
0 500 nm
(b)
FIGURE 39.15 (a) Gray-scale plot and line plot of the inverted nanoindentation mark on Si(111) at 70 µN (hardness ~ 15.8 GPa); and (b) gray-scale plot of indentation mark on C+-implanted Si(111) at 70 µN (hardness ~ 19.5 GPa). The indentation depth of indent was about 3 nm.
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FIGURE 39.16 Nanohardness and normal load as function of indentation depth for virgin and C+-implanted Si(111). (From Bhushan B. and Koinkar, V.N. (1994), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. With permission.)
films on the surface due to sliding results in low values of friction. SiC can react with water vapor to form silicon hydroxide and oxide, which improve the frictional behavior (Xu and Bhushan, 1997). From this discussion, it can be seen that an obvious drawback with SiC is its readiness to form tribochemical films, which is environment dependent. Another factor that affects friction in ceramic materials is fracture, which leads to high friction because of the plowing contribution. But in the case of SiC film, fracture toughness is believed to follow the same trend as that of the bulk material; that is, the fracture toughness is higher than that of silicon (see Table 39.1), thereby resulting in a lower plowing contribution and hence lower friction. Macroscale friction measurements indicate that SiC film exhibits one of the lowest friction values as compared to the other samples. The doped polysilicon sample shows low friction on the macroscale as compared to the undoped polysilicon sample, possibly due to the doping effect. 39.3.2.2 Scratch/Wear Tests As explained, the scratch tests consisted of making scratches for ten cycles with varying loads. Figure 39.19a shows a plot of scratch depth vs. normal load for various samples (Bhushan et al., 1998; Sundararajan and Bhushan, 1998). Error bars are given for the Si(100) data. The variation was typically about 12%. Scratch depth increases with increasing normal load. Si(100) and the doped and undoped polysilicon film show similar scratch resistance. From the data, it is clear that the SiC film is much more scratch resistant than that of other samples. The increase in scratch depth with normal load is very small and all depths are less than 30 nm, while the Si(100) and polysilicon films reach depths in excess of 150 nm. Figure 39.20 shows three-dimensional images of the scratch marks. Wear tests were conducted on the samples for one cycle at normal loads ranging from 20 to 80 µN. The resulting wear depths are plotted against the normal loads in Figure 39.19b (Bhushan et al., 1998; Sundararajan and Bhushan, 1998). Again, the wear depth increases with increasing normal load. Similar to the scratch resistance data, Si(100) and the polysilicon samples also behave similarly in terms of wear resistance. The SiC film starts out showing comparable wear depth at 20 µN to all the other samples; but at higher loads, the SiC film shows superior wear resistance. Also, there is no significant increase in wear depth with increasing normal load in the case of SiC film. The evolution of wear on the various samples was also studied. This test was performed by wearing the same region for 20 cycles at a normal load of 20 µN, while observing wear depths at different intervals (1, 2, 10, 15, and 20 cycles) (Figure 39.21). This should give information as to the progression of wear of the material. The wear depths observed are plotted against the number of cycles in Figure 39.19b. For all the materials, the wear depth increases almost linearly with increasing number of cycles. This suggests that the material is removed layer by layer in all the materials. Here also, SiC film exhibits lower wear depths than other samples. Doped polysilicon film wears less than the undoped film. Not many debris particles are seen in the figures; this is due to the fact that the debris particles created are loose and are pushed outside the imaging area by the sliding
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Undoped Si(100) Undoped Polysilicon film (as-deposited) Undoped Polysilicon film (polished) n+-type Polysilicon film (as-deposited) n+-type Polysilicon film (polished) SiC film (as-deposited) SiC film (polished) 46
Rms roughness (nm)
50
(a)
40 30
25
20
12
10 0.09
0.86
1.0
0.89
0 0.1
Coefficient of friction
0.07 0.08
(b)
0.06 0.05
0.06 0.04 0.04
0.03 0.02
0.02
0.02 0
FIGURE 39.17 Comparisons of (a) RMS surface roughness, and (b) coefficient of microscale friction values for various samples. (From Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. With permission.)
tip during scanning. It can also be seen from the figure that the wear marks are uniform at the bottom, indicating that uniform wear has occurred with particle pileup on the edges of the wear mark. The wear tests clearly indicate that SiC film possesses an extremely wear-resistant surface compared to the other samples and, together with the scratch tests results, indicate that SiC film has better surface mechanical properties than Si(100) and the polysilicon films. Table 39.4 shows a summary of the various properties of the samples measured in this study (Bhushan et al., 1998; Sundararajan and Bhushan, 1998). The superior scratch/wear resistance of the SiC film is consistent with the hardness values near the surface measured with the nanoindenter. The higher hardness of SiC film is one of the factors responsible for its better scratch/wear resistance. Wear in ceramic materials in the case of asperity contacts occurs due to brittle fracture. As the AFM tip slides over the material surface, cracks can occur when the normal stress exceeds a critical value (Bhushan, 1999b). Friction (tangential) forces during sliding reduce this critical value. High fracture toughness and a low coefficient of friction of SiC film help in reducing the chances of brittle fracture, which results in low wear. Therefore, abrasive wear due to plastic deformation and fracture govern the wear process. In all of the samples, surface reactions result in the formation of
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Surface Height
0
2.5
5.0
7.5
Friction Force 10.0
5.0 nm
10.0
5.0 n N
7.5
2.5 nm
7.5
2.5 nN
5.0
0.0 nm
5.0
0.0 nN
2.05
Undoped Si(100)
2.05
0.0 10.0 µm
0
0
2.5
5.0
7.5
5.0
7.5
0.0 10.0 µm 5.0 n N
2.5 nm
7.5
2.5 nN
0.0 nm
5.0
5.0 nm
7.5
5.0
0.0 nN
2.05
Undoped Polysilicon Film
0.0 10.0 µm
0
2.5
5.0
7.5
0.0 10.0 µm
W = 68 nN, mean = 2.6 nN, σ = 0.28 nN
10.0
5.0 nm
10.0
5.0 n N
7.5
2.5 nm
7.5
2.5 nN
5.0
0.0 nm
5.0
2.05
2.5
7.5
10.0
10.0
σ = 0.79 nm, P-V = 6.3 nm
0
5.0
W = 155 nN, mean = 8.5 nN, σ = 0.76 nN
σ = 0.09 nm, P-V = 0.92 nm
2.05
2.5
2.05
n+-type Polysilicon Film
0.0 10.0 µm
0
σ = 0.85 nm, P-V = 7.6 nm
0.0 nN
2.5
5.0
7.5
0.0 10.0 µm
W = 340 nN, mean = 6.9 nN, σ = 0.53 nN 10.0
5.0 nm
10.0
5.0 n N
7.5
2.5 nm
7.5
2.5 nN
0.0 nm
5.0
5.0
0.0 nN
2.05
2.05
SiC Film 0
2.5
5.0
7.5
σ = 0.81 nm, P-V = 5.9 nm
0.0 10.0 µm
0
2.5
5.0
7.5
0.0 10.0 µm
W = 180 nN, mean = 3.8 nN, σ = 0.46 nN
FIGURE 39.18 Gray-scale maps of surface height and corresponding friction force maps of Si(100), undoped polysilicon film (polished), n+-type polysilicon film (polished), and SiC film (polished) samples. (From Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. With permission.)
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FIGURE 39.19 (a) Scratch depths for 10 cycles as a function of normal load, and (b) wear depths as a function of normal load and as a function of number of cycles for various samples. (From Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. With permission.)
tribochemical films that are different in nature from the underlying material. Therefore, at low loads and at the onset of wear, all samples would show similar wear depths as they all have comparable interfacial shear strengths and attack angles (attack angle is the included angle between the leading face of the asperity and the contact plane at the point of contact). This is seen in the case of the reported wear depths at 20 µN for 1 cycle (Figure 39.19b). In the case of the scratch test data (Figure 39.19a), SiC reveals slightly lower scratch depth at 20 µN because the data are for ten cycles, during which time it is possible that the bulk properties of the material start coming into play in addition to that of the tribochemical films. This is consistent with the wear depths at 20 µN for ten cycles and more (Figure 39.19b). As the normal load increases, Si(100) and polysilicon films show a sharp increase in degree of penetration (ratio of groove depth to radius of contact) and attack angle, which leads to higher wear (Hokkirigawa and Kato, 1988; Koinkar and Bhushan, 1997; Zhao and Bhushan, 1998). Higher fracture toughness and higher hardness of SiC as compared to Si(100) is responsible for its lower wear. In addition, the higher thermal conductivity of SiC (see Table 39.1) as compared to the other materials leads to lower interface temperatures, which generally results in less degradation of the surface (Bhushan, 1996a). Doping of the polysilicon does not significantly affect the scratch/wear resistance and hardness. The measurements made on the doped sample are affected by the presence of grain boundaries.
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100
60
40
20 µN
250 500 750 nm
80
5.00 2.50
0
Undoped Si(100) 0 2.50 5.00
100
60
40
20 µN
250 500 750 nm
80
0 µm
5.00
2.50
0
Undoped Polysilicon Film 0 0 µm
2.50 5.00
100
60
40
20 µN
250 500 750 nm
80
5.00 2.50
0
N+-type Polysilicon Film 0 2.50 5.00
80
60
0 µm
40
20 µN
250 500 750 nm
100
5.00 2.50
0
SiC Film 0 2.50 5.00
0 µm
FIGURE 39.20 Scratch profiles for various samples. (From Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. With permission.)
39.3.2.3 Hardness, Elastic Modulus, and Fracture Toughness Measurements Representative load-displacement curves of indentations made at 0.2 and 15 mN peak indentation loads on various samples are shown in Figure 39.22. Measured hardness, elastic modulus, and fracture toughness values are given in Table 39.4 (Bhushan et al., 1998; Li and Bhushan, 1998; Sundararajan and
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500 0
1.00 1.00
200
3.00
500
4.00 3.00
0
2.00
200
3.00
500
4.00 3.00
0
200
3.00
0 4.00 µm
1000 nm 500 0
4.00 3.00
W = 20 µN 5 cycles d = 50 nm
1.00 1.00
200
3.00
0 4.00 µm
4.00 3.00
0
1.00 1.00
200
3.00
W = 20 µN 20 cycles d = 365 nm
W = 20 µN 10 cycles d = 80 nm
0 4.00 µm
4.00 3.00 2.00
0
1.00 1.00
0
W = 20 µN 10 cycles d = 215 nm
0 4.00 µm
0 4.00 µm
2.00
2.00 0
3.00
0
1.00 1.00
1000 nm
0
200
2.00
W = 20 µN 5 cycles d = 116 nm
0 4.00 µm
1000 nm
0
W = 20 µN 1 cycle d = 18 nm
1.00 1.00
1000 nm
4.00 3.00 2.00
0
500
W = 20 µN 1 cycle d = 30 nm
0 4.00 µm
0
3.00
1000 nm
200
500
0
1.00 1.00
1000 nm
0
4.00 3.00 2.00
1000 nm
500
4.00 3.00 2.00
SiC Film
500
1000 nm
Undoped Polysilicon Film
0
1.00 1.00
200
3.00
0 4.00 µm
W = 20 µN 20 cycles d = 119 nm
FIGURE 39.21 Three-dimensional wear profiles of undoped polysilicon and SiC films (polished) after 1, 5, 10, and 20 wear cycles at 20 µN normal load. (From Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. With permission.)
Bhushan, 1998). Properties of undoped polysilicon films are comparable to that of bulk single-crystal silicon. Doping of the polysilicon film degrades its mechanical properties. SiC film shows hardness and elastic modulus higher than other samples. The higher hardness of SiC is believed to be responsible for its superior scratch/wear resistance compared to the other samples.
39.3.3 Macroscale Tribological Studies of Virgin, Coated, and Treated Samples To study the effect of ion implantation of silicon on friction and wear, single-crystalline and polycrystalline silicon samples were ion implanted by Gupta et al. (1993, 1994) and Gupta and Bhushan (1994) with various doses of C+, B+, N2+, and Ar+ ion species at 200-keV energy. The coefficient of friction and wear factor of C+-implanted silicon samples as a function of ion dose is presented in Figure 39.23 (Gupta et al., 1993). The friction and wear tests were conducted using a ball-on-flat tribometer (Gupta et al., 1993). Each data bar represents the average value of four to six measurements. The coefficient of friction and wear factor decrease drastically with ion dose. Silicon samples bombarded above 1017 C+ cm–2 exhibit extremely low values of coefficients of friction (typically 0.03 to 0.06 in air) and the wear factor (reduced by as much as four orders of magnitude). Gupta et al. (1993) reported that a decrease in coefficient of friction and wear factor of silicon as a result of C+ ion bombardment occurred because of formation of silicon carbide rather than amorphization of silicon. Gupta et al. (1994) also reported an improvement in friction and wear with B+ ion implantation. For magnetic disk drive applications, macroscale friction and wear experiments have been performed using a magnetic disk drive with unoxidized, oxidized, and implanted pins sliding against amorphous,
6 91 7 150 6
0.86 12 1.0 25 0.89
0.02 0.03 0.02
0.04 0.07
0.06 0.05
Microb
61 6
0.20
99
89
Scratch depthd (nm)
0.23
0.46
0.33
Macroc
Coefficient of Friction
16
51
140
84
Wear depthe (nm)
25
9
12
12
Nano-hardnessf (GPa)
395
95
175
168
Young’s Modulusf (GPa)
b
a
Measured using AFM over a scan size of 10 µm × 10 µm. Measured using AFM/FFM over a scan size of 10 µm × 10 µm. c Obtained using a 3-mm diameter sapphire ball in reciprocating mode at a normal load of 10 mN and average sliding speed of 1 mm/s after 4-m sliding distance. d Measured using AFM at a normal load of 40 µN for 10 cycles; scan length of 5 µm. e Measured using AFM at normal load of 40 µN for 1 cycle; wear area of 2 µm × 2 µm. f Measured using nanoindenter at a peak indentation depth of 20 nm. g Measured using microindenter with Vickers indenter at a normal load of 0.5 N.
0.9 340
P-V Distancea (nm)
0.09 46
RMS Roughnessa (nm)
Summary of Micro/Nanotribological Properties of the Sample Materials
Undoped Si(100) Undoped polysilicon film (asdeposited) Undoped polysilicon film (polished) n+-Type polysilicon film (as-deposited) n+-Type polysilicon film (polished) SiC film (as-deposited) SiC film (polished)
Sample
TABLE 39.4
0.78
0.89
1.11
0.75
Fracture Toughnessg KIc (MPa m )
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FIGURE 39.22
1539
Representative load displacement curves for various samples.
carbon-coated magnetic disks lubricated with perfluoropolyether (Bhushan and Venkatesan, 1993b; Venkatesan and Bhushan, 1993, 1994; Bhushan, 1999c). The data of silicon samples was compared with the commonly used slider materials in disk drives: Al2O3-TiC and Mn-Zn ferrite. Representative profiles of the variation of the coefficient of friction with number of sliding cycles for Al2O3-TiC slider and uncoated and coated silicon pins are shown in Figure 39.24. Friction data obtained from the various tests conducted in ambient air in terms of the initial coefficient of friction, the contact life (i.e., the number of revolutions before the coefficient of friction increased by a factor of two), and the maximum value of the coefficient of friction for cases when the increase was more than by a factor of two are presented in Table 39.5. For the case of oxidized samples, a significant increase (by a factor of two or more) was not observed and so the range of variation of the coefficient of friction for the duration of 50,000 cycles is indicated. It was found that crystalline orientation of silicon has no effect of friction and wear. For bare silicon, after the initial increase in the coefficient of friction, it drops to a steady-state value of 0.1 following the increase, as seen in Figure 39.24a. The rise in the coefficient of friction and damage on the pin surface for Si(111) is associated with the transfer of amorphous carbon from the disk to the pin, oxidationenhanced fracture of pin material, followed by tribochemical oxidation of the transfer film. The drop is associated with the formation of a transfer coating on the pin (Figure 39.25a). The mechanism of transfer and tribochemical oxidation was seen to be also operative for the friction increase for A12O3-TiC and Mn-Zn ferrite pin/slider materials tested in ambient air. As seen in Table 39.5 and Figure 39.24b, dryoxidized Si(111) exhibits excellent characteristics and this behavior has been attributed to the chemical passivity of the oxide and lack of transfer of DLC from the disk to the pin. The behavior of PECVD was comparable to that of dry oxide; but for the wet oxide, there was some variation in the coefficient of friction (0.26 to 0.4). The difference between dry and wet oxide has been attributed to the increased porosity of the wet oxide (Bhushan and Venkatesan, 1993b; Pilskin, 1977). Because tribochemical oxidation was determined to be a significant factor, experiments were conducted in dry nitrogen (Venkatesan and Bhushan, 1993, 1994). The variation of the coefficient of friction for a silicon pin sliding against a thin-film disk is shown in Figure 39.24a. For comparison, the behavior in ambient is also shown. It is seen that in a dry-nitrogen environment, the coefficient of friction of Si(111) sliding against a disk decreased from an initial value of about 0.2 to 0.05 with continued sliding. Similar behavior was also observed while testing with Al2O3-TiC and Mn-Zn ferrite pins and sliders. Based on SEM and chemical analysis, this behavior has been attributed to the formation of a smooth amorphouscarbon/lubricant transfer patch and suppression of oxidation in a dry nitrogen environment (Figure 39.25b).
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FIGURE 39.23 Influence of ion doses on the (a) coefficient of friction and (b) wear factor on C+ ion-bombarded single-crystal and polycrystalline silicon slid against an alumina ball. S and P denote tests that correspond to singleand polycrystalline silicon, respectively, and V corresponds to virgin single-crystal silicon. (From Gupta, B.K., Chevallier, J., and Bhushan, B. (1993), Tribology of ion bombarded silicon for micromechanical applications, ASME J. Tribol., 115, 392-399. With permission.)
Experiments in dry nitrogen indicated that low-friction conditions can be achieved in dry nitrogen, although transfer of carbon from the disk to the pin occurs. An experiment was performed with a hydrogenated amorphous carbon-coated (~18 nm thick) silicon pin sliding against a lubricated thinfilm disk in dry nitrogen. The friction variation with sliding for this experiment is shown in Figure 39.26. No damage for the pin and disk surfaces could be detected after this experiment. Based on macrotests using disk drives, it is found that the friction and wear performance of bare silicon were not adequate. With single and polycrystalline silicon sliding against an amorphous carboncoated magnetic disk, transfer of amorphous carbon from the disk to the pin/slider and oxidationenhanced fracture of pin/slider material followed by oxidation of the transfer coating (tribochemical oxidation) is responsible for degradation of the sliding interface and consequent friction increase in ambient air. With dry-oxidized or PECVD SiO2-coated silicon, no significant friction increase or interfacial degradation was observed in ambient air. In the absence of an oxidizing environment (in dry nitrogen), the coefficient of friction decreased from 0.2 to 0.05 following amorphous carbon transfer for the materials tested.
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COEFFICIENT OF FRICTION
1.00 AMBIENT AIR
0.80
DRY NITROGEN
0.60 0.40 0.20 0.00 0
1200
2400
3600
4800
6000
REVOLUTIONS
(a)
COEFFICIENT OF FRICTION
1.00 0.80 0.60 0.40 0.20 0.00 0
20
10
30
40 50 (Thousands)
REVOLUTIONS
(b)
FIGURE 39.24 Coefficient of friction as a function of number of sliding revolutions in ambient air for (a) Si(111) pin in ambient air and dry nitrogen, and (b) dry-oxidized silicon pin in ambient air. (From Bhushan, B. and Venkatesan, S. (1993b), Friction and wear studies of silicon in sliding contact with thin-film magnetic rigid disks, J. Mater. Res., 8, 1611-1628. With permission.) TABLE 39.5 Macrofriction Data for Various Hemispherical Pins with Radius of 100 mm Sliding Against Lubricated Thin-Film Rigid Disks in Ambient Air
Pin Material Al2O3-TiC Mn-Zn ferrite Single-crystal silicon Polysilicon PECVD-oxide-coated Si(111) Dry-oxidized Si(111) Wet-oxidized Si(111) C+-implanted Si(111)
Initial Coeff. of Friction
Cycles to Friction Increase by a Factor of 2
Max. or Ending Value of Coeff. of Friction
0.20 0.22 0.20 0.20 0.28 0.22 0.26 0.16
~2,200 ~5,500 ~1,200 ~3,000 >50,000 >50,000 >50,000 ~1,000
0.78 0.45 0.40 0.40 0.23–0.28 0.20 0.26–0.40 0.60
(Normal load = 0.5 N; sliding speed = 0.9-1.2 m/s; ambient air (RH 45±5%)
39.3.4 Boundary Lubrication Studies The classical approach to lubrication uses freely supported multimolecular layers of liquid lubricants (Bhushan, 1999a). The liquid lubricants are chemically bonded to improve their wear resistance. To study depletion of boundary layers, the microscale friction measurements were obtained as a function of
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FIGURE 39.25 Scanning electron micrographs of Si(111) after sliding against a magnetic disk in (a) ambient air for 6000 cycles, and in (b) dry nitrogen after 15,000 revolutions.
COEFFICIENT OF FRICTION
1.00 DRY NITROGEN
0.80 0.60 0.40 0.20 0.00 0
1200
2400
3600
4800
6000
REVOLUTIONS
FIGURE 39.26 Variation of the coefficient of friction with number of revolutions in dry nitrogen for a DLC-coated silicon pin sliding against a magnetic disk. (From Bhushan, B. and Venkatesan, S. (1993b), Friction and wear studies of silicon in sliding contact with thin-film magnetic rigid disks, J. Mater. Res., 8, 1611-1628. With permission.)
number of cycles on virgin Si(100) surface and silicon surface lubricated with about 2-nm-thick Z-15 and Z-DOL perfluoropolyether (PFPE) lubricants, the data of which are shown in Figure 39.27 (Koinkar and Bhushan, 1996a). Z-DOL is a PFPE lubricant with hydroxyl end groups. Its lubricant film was thermally bonded at 150°C for 30 minutes and washed off with a solvent to provide a chemically bonded
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FIGURE 39.27 Friction force as a function of number of cycles using an Si3N4 tip at 300 nN normal load for unlubricated and lubricated silicon samples. (From Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. With permission.)
2.00
25.0 50.0 nm
25.0 50.0 nm
layer for the lubricant film. In Figure 39.27, the unlubricated silicon sample showed a slight increase in friction force, followed by a drop to a lower steady-state value after 20 cycles. Depletion of native oxide and possible roughening of the silicon sample are believed to be responsible for the decrease in friction force after 20 cycles. The initial friction force for the Z-15 lubricated sample is lower than that of unlubricated silicon and increases gradually to a friction force value comparable to that of unlubricated silicon after 20 cycles. This suggests depletion of the Z-15 lubricant in the wear track. In the case of the Z-DOL-coated sample, the friction force starts out low and remains low during the cycle of 100 tests. This suggests that Z-DOL does not get displaced or depleted as readily as Z-15. Additional studies of freely supported liquid lubricants showed that either increasing the film thickness or chemically bonding the molecules to the substrate with a mobile fraction improves the lubrication performance (Koinkar and Bhushan, 1996a,b). For lubrication of microdevices, a more effective approach involves the deposition of organized, dense molecular layers of long-chain molecules on the surface contact (Bhushan et al., 1995b). Such monolayers and thin films are commonly produced by Langmuir-Blodgett (LB) deposition and by chemical grafting of molecules into self-assembled monolayers (SAMs). Based on measurements, SAMs of octodecyl (C18) compounds based on alkyl octadecyldimethylchlorosilane on oxidized silicon exhibited a lower coefficient of friction (0.018) and greater durability (Figure 39.28) than LB films of zinc arachidate adsorbed on a gold surface coated with octadecylthiol (ODT) (coefficient of friction 0.03) (Bhushan et al., 1995b). LB films are bonded to the substrate by weak van der Waals attraction, whereas SAMs are chemically bound
2.00 1.00
0
0
1.00 0
1.00 C18 double grafted/SiO2/Si 40 µN, 3.7 nm
0 0 2.00
1.00
0 2.00 µm
ZnA/ODT/Au/Si 200 nN,6.5 nm
FIGURE 39.28 Surface profiles showing worn region after one scan cycle for self-assembled monolayers of alkyl octadecyldimethylchlorosilane (C18) (left) and zinc arachidate (ZnA) (right). Normal load and wear depths are indicated.
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via covalent bonds. Because of the choice of the chain length and terminal linking groups that SAMs offer, they hold great promise for boundary lubrication of microdevices.
39.3.5 Component-Level Studies Friction and wear studies have been conducted on actual and simulated MEMS components. One of the MEMS devices in which friction and wear issues are critical is the micromotor. To measure in situ the static friction of a rotor-bearing interface in a micromotor, Tai and Muller (1990) measured the starting torque (voltage) and pausing position for different starting positions under a constant-bias voltage. A friction-torque model was used to obtain the coefficient of static friction. To measure the kinetic friction of the turbine and gear structures in situ, Gabriel et al. (1990) used a laser-based measurement system to monitor the steady-state spins and decelerations. Lim et al. (1990) designed and fabricated a polysilicon microstructure to measure in situ the static friction of various films. The microstructure consisted of shuttle suspended above the underlying electrode by a folded beam suspension. A known normal force was applied and the lateral force was measured to obtain the coefficient of static friction. Mehregany et al. (1992) developed a quantitative method for in situ wear measurements in micromotors. They used a wobble micromotor under electric excitation for quantitative wear measurement. Because the gear ratio of the wobble micromotor depends on the bearing clearance, changes in the gear ratio can be a direct measure of wear in the motor bearing.
39.4 Closure Silicon-based MEMS devices are made from single-crystal silicon, LPCVD polysilicon films, and other ceramic films. For high-temperature applications, SiC films are being developed to replace polysilicon films. Tribology in MEMS devices requiring relative motion is of importance. AFM/FFM and nanoindentation techniques have been used for tribological studies on the micro- to nanoscale on materials of interest. These techniques have been used to study surface roughness, friction, scratching/wear, indentation, and boundary lubrication of bulk and treated silicon, polysilicon films, and SiC films. Macroscale friction and wear tests have also been conducted using the ball-on-flat tribometer. Measurements of microscale and macroscale friction forces show that friction values on both scales of all the silicon samples are about the same among different silicon materials and higher than that of SiC. The microscale values are lower than the macroscale values as there is less plowing contribution in the microscale measurements. Surface roughness has an effect on friction. In microscale and macroscale tests, C+-implanted, oxidized, and PECVD oxide-coated single-crystal silicon samples exhibit much larger scratching and wear resistance when compared to untreated samples. Polysilicon films and undoped single-crystal silicon show similar friction and wear characteristics. Doping of polysilicon film does not affect its tribological properties. Microscratching, microwear and nanoindentation, and macroscale friction and wear studies indicate that SiC films are superior when compared to the other materials currently used in MEMS devices. Higher hardness and fracture toughness of the SiC film is believed to be responsible for its superior mechanical integrity and lower friction. Chemically grafted self-assembled monolayers and chemically bonded liquid lubricants show promising performance for boundary lubrication in MEMS devices.
References Becker, E.W., Ehrfeld, W., Hagmann, P., Maner, A., and Munchmeyer, D. (1986), Fabrication of microstructures with high aspect ratios and great structural heights by synchrotron radiation lithography, galvanoforming, and plastic moulding (LIGA Process), Microelectronic Eng., 4, 35-56. Beerschwinger, U., Albrecht, T., Mathieson, D., Rueben, R.L., Yang, S.J., and Taghizadeh, M. (1995), Wear at microscopic scales and light loads for MEMS applications, Wear, 181/183, 426-435. Bhushan, B. (1996a), Tribology and Mechanics of Magnetic Storage Devices, 2nd ed., Springer-Verlag, New York.
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Bhushan, B. (1996b), Nanotribology and nanomechanics of MEMS devices, Proc. 9th Annu. Workshop on Micro Electro Mechanical Systems, IEEE, New York, 91-98. Bhushan, B. (1997), Micro/Nanotribology and its Applications, Vol. E330, Kluwer Academic, Dordrecht, The Netherlands. Bhushan, B. (1998a), Tribology Issues and Opportunities in MEMS, Kluwer Academic, Dordrecht, The Netherlands. Bhushan, B. (1998b), Contact mechanics of rough surfaces in tribology: multiple asperity contact, Tribol. Lett., 4, 1-35. Bhushan, B. (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. Bhushan, B. (1999b), Principles and Applications of Tribology, Wiley, New York. Bhushan, B. (1999c), Chemical, mechanical and tribological characterization of ultra-thin and hard amorphous carbon coatings as thin as 3.5 nm: recent developments, Diamond and Rel. Mater., 8, 1985-2015. Bhushan, B. (2000), Mechanics and Reliability of Flexible Magnetic Media, 2nd ed., Springer-Verlag, New York. Bhushan, B. and Gupta, B.K. (1997), Handbook of Tribology: Materials, Coatings and Surface Treatments, reprint edition, Krieger, Malabar, FL. Bhushan, B. and Koinkar, V.N. (1997a), Microtribological studies of doped single-crystal silicon and polysilicon films for MEMS devices, Sensors and Actuators, A 57, 91-102. Bhushan B. and Koinkar, V.N. (1994), Tribological studies of silicon for magnetic recording applications, J. Appl. Phys., 75, 5741-5746. Bhushan, B. and Li, X. (1997b), Micromechanical and tribological characterization of doped single-crystal silicon and polysilicon films for microelectromechanical systems, J. Mater. Res., 12, 1-10. Bhushan, B. and Venkatesan, S. (1993a), Mechanical and tribological properties of silicon for micromechanical applications: a review, Adv. Info. Storage Syst., 5, 211-239. Bhushan, B. and Venkatesan, S. (1993b), Friction and wear studies of silicon in sliding contact with thinfilm magnetic rigid disks, J. Mater. Res., 8, 1611-1628. Bhushan, B., Dominiak, M., and Lazarri, J.P. (1992), Contact start-stop studies with silicon planar head sliders against thin-film disks, IEEE Trans. Magn., 28, 2874-2876. Bhushan, B., Israelachvili, J.N., and Landman, U. (1995a), Nanotribology: friction, wear and lubrication at the atomic scale, Nature, 374, 607-616. Bhushan, B., Kulkarni, A.V., Koinkar, V.N., Boehm, M., Odoni, L., Martelet, C., and Belin, M. (1995b), Microtribological characterization of self-assembled and Langmuir-Blodgett monolayers by atomic force and friction force microscopy, Langmuir, 11, 3189-3198. Bhushan, B., Sundararajan, S., Li, X., Zorman, C.A., and Mehregany, M. (1998), Micro/nanotribological studies of single-crystal silicon and polysilicon and SiC films for use in MEMS devices, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands. Bryzek, J., Peterson, K., and McCulley, W. (1994), Micromachines on the march, IEEE Spectrum, May, 20-31. Callahan, D.L. and Morris, J.C. (1992), The extent of phase transformation in silicon hardness indentation, J. Mater. Res., 7, 1612-1617. Connally, J.A. and Brown, S.B. (1993), Micromechanical fatigue testing, Exp. Mech., 33, 81-90. Deng, K., Collins, R.J., Mehregany, M., and Sukenik, C.N. (1995), Performance impact of monolayer coatings of polysilicon micromotors, in Proc. MEMS 95, Amsterdam, Netherlands, Jan–Feb. Ericson, F. and Schweitz, J.A. (1990), Micromechanical fracture strength of silicon, J. Appl. Phys., 68, 5840-5844. Fan, L.S. and Woodman, S. (1995), Batch fabrication of mechanical platforms for high-density data storage, 8th Int. Conf. Solid State Sensors and Actuators (Transducers ’95)/Eurosensors IX, Stockholm, Sweden, 25-29 June, 434-437. Fan, L.S., Ottesen, H.H., Reiley, T.C., and Wood, R.W. (1995), Magnetic recording head positioning at very high track densities using a microactuator-based, two-stage servo system, IEEE Trans. Ind. Electron., 42, 222-233.
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Fang, W. and Wickert, J.A. (1995), Comments on measuring thin-film stresses using bi-layer micromachined beams, J. Micromech. Microeng., 5, 276-281. Friedrich, C.R. and Warrington, R.O. (1998), Surface Characterization of Non-Lithographic Micromachining, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 73-84. Fujimasa, I. (1996), Micromachines: A New Era in Mechanical Engineering, Oxford University Press, Oxford, U.K. Gabriel, K.J., Behi, F., Mahadevan, R., and Mehregany, M. (1990), In situ friction and wear measurement in integrated polysilicon mechanisms, Sensors and Actuators, A 21-23, 184-188. Gane, N. and Cox, J.M. (1970), The micro-hardness of metals at very light loads, Philos. Mag., 22, 881-891. Guckel, H. and Burns, D.W. (1989), Fabrication of micromechanical devices from polysilicon films with smooth surfaces, Sensors and Actuators, 20, 117-122. Guckel, H., Skrobis, K.J., Christenson, T.R., and Klein, J. (1994), Micromechanisms for actuators via deep X-ray lithography, Proc. of the Symp. Microlithography, SPIE, Bellingham, WA, 39-47. Guckel, H., Burns, D., Rutigliano, C., Lovell, E., and Choi, B. (1992), Diagnostic microstructures for the measurement of intrinsic strain in thin films, J. Micromech. Microeng., 2, 86-95. Gupta, B.K. and Bhushan, B. (1994), Nanoindentation studies of ion implanted silicon, Surf. Coat. Technol., 68/69, 564-570. Gupta, B.K., Chevallier, J., and Bhushan, B. (1993), Tribology of ion bombarded silicon for micromechanical applications, ASME J. Tribol., 115, 392-399. Gupta, B.K., Bhushan, B., and Chevallier, J. (1994), Modification of tribological properties of silicon by boron ion implantation, Tribol. Trans., 37, 601-607. Hamilton, H. (1991), Contact recording on perpendicular rigid media, J. Mag. Soc. Jpn., 15(Suppl. S2), 483-481. Harris, G.L. (Ed.) (1995), Properties of Silicon Carbide, Inst. of Elect. Eng., London. Henck, S.A. (1997), Lubrication of digital micromirror devices, Tribol. Lett., 3, 239-247. Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge forming during abrasive wear, Tribol. Int., 21, 51-57. Hornbeck, L.J. (1989), Proc. Soc. Photo-Opt. Eng., 1150, 86. Jaeger, R.C. (1988), Introduction to Microelectronic Fabrication, Vol. 5, Addison-Wesley, Reading, MA. Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol., A14, 2378-2391. Koinkar, V.N. and Bhushan, B. (1997), Scanning and transmission electron microscopies of single-crystal silicon microworn/micromachined using atomic force microscopy, J. Mater. Res., 12, 3219-3224. Lazarri, J.P. and Deroux-Dauphin, P. (1989), A new thin film head generation IC head, IEEE Trans. Magn., 25, 3190-3193. Lehr, H. Abel, S., Doppler, J., Ehrfeld, W., Hagemann, B., Kamper, K.P., Michel, F., Schulz, Ch., and Thurigen, Ch. (1996), Microactuators as driving units for microrobotic systems, in Proc. Microrobotics: Components and Applications, Vol. 2906, Sulzmann, A. (Ed.), SPIE, 202-210. Lehr, H., Ehrfeld, W., Hagemann, B., Kamper, K.P., Michel, F., Schulz, Ch., and Thurigen, Ch. (1997), Development of micro-millimotors, Min. Invas. Ther. Allied Technol., 6, 191-194. Li, X. and Bhushan, B. (1999), Micro/nanomechanical characterization of ceramic films for microdevices, Thin Solid Films, 340, 210-217. Lim, M.G., Chang, J.C., Schultz, D.P., Howe, R.T., and White, R.M. (1990), Polysilicon microstructures to characterize static friction, Proc. IEEE Micro Electro Mechanical Systems, 82-88. Maboudian, R. (1998), Surface process in MEMS technology, Surf. Sci. Rep., 30, 209-269. Maboudian, R. and Howe, R.T. (1997), Stiction reduction process for surface micromachines, Tribol. Lett., 3, 215-221. Madou, M. (1997), Fundamentals of Microfabrication, CRC Press, Boca Raton, FL.
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Madou, M. (1998), Facilitating choices of machining tools and materials for miniaturization science: a review, Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 31-51. Mastrangelo, C.H. (1997), Adhesion-related failure mechanisms in micromechanical devices, Tribol. Lett., 3, 233-238. Mazza, E., Abel, S., and Dual, J. (1996), Experimental determination of mechanical properties of Ni and Ni-Fe microbars, Microsystem Technologies, 2, 197-202. Mehregany, M., Gabriel, K.J., and Trimmer, W.S.N. (1988), Integrated fabrication of polysilicon mechanisms, IEEE Trans. Electron Devices, 35, 719-723. Mehregany, M., Howe, R.T., and Senturia, S.D. (1987), Novel microstructures for the in-situ measurement of mechanical properties of thin films, J. Appl. Phys., 62, 3579-3584. Mehregany, M., Senturia, S.D., and Lang, G.H. (1992), Measurement of wear in polysilicon micromotors, IEEE Trans. Electron Devices, 39, 1136-1143. Mehregany, M., Nagarkar, P., Senturia, S.D., and Lang, J.H. (1990), Operation of microfabricated harmonic and ordinary side-drive motors, Proc. IEEE Micro Electromechanical Systems, Vol. 86, IEEE, New York, 1-8. Mehregany, M., Zorman, C.A., Rajan, N., and Wu, C.H. (1998), Silicon carbide MEMS for harsh environments, in Proc. of the IEEE, 86, 1595-1610. Michel, F. and Ehrfeld, W. (1998), Microfabrication technologies for high performance microactuators, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 53-72. Miu, D.K. and Tai, Y.C. (1995), Silicon micromachined scaled technology, IEEE Trans. Industr. Electron., 42, 234-239. Muller, R.S., Howe, R.T., Senturia, S.D., Smith, R.L., and White, R.M. (1990), Microsensors, IEEE Press, New York. Ohwe, T., Mizoshita, Y., and Yonoeka, S. (1993), Development of integrated suspension system for a nanoslider with an MR head transducer, IEEE Trans. Magn., 29, 3924-3926. Peterson, K.E. (1979), Micromechanical membrane switches on silicon, IBM J. Res. Dev., 23, 376. Peterson, K.E. (1982), Silicon as a mechanical material, Proc. IEEE, 70, 420-457. Pharr, G.M. (1991), The anomalous behavior of silicon during nanoindentation, in Thin Films: Stresses and Mechanical Properties III, Vol. 239, Nix, N.D., Bravman, J.C., Arzt, E., and Freund, L.B. (Eds.), Materials Research Soc., Pittsburgh, PA, 301-312. Pilskin, W.A. (1977), J. Vac. Sci. Technol., 14, 1064. Robertson, J.K. and Wise, K.D. (1998), An electrostatically actuated integrated microflow controller, Sensors and Actuators, A 71, 98-106. Sargent, P.M. (1986), Use of the indentation size effect on microhardness for materials characterization, in Microindentation Techniques in Materials Science and Engineering, Blau, P.J. and Lawn, B.R. (Eds.), STP 889, ASTM, Philadelphia, PA, 160-174. Schweitz, J.A. (1991), A new and simple approach to the stress-strain characteristics of thin coatings, J. Micromech. Microeng., 1, 10-15. Shackelford, J.F., Alexander, W., and Park, J.S. (Eds.) (1994), CRC Material Science and Engineering Handbook, 2nd ed., CRC Press, Boca Raton, FL. Shor, J.S., Goldstein, D., and Kurtz, A.D. (1993), Characterization of n-type β-SiC as a piezoresistor, IEEE Trans. Electron Devices, 40, 1093-1099. Spencer, M.G., Devaty, R.P., Edmond, J.A., Khan, M.A., Kaplan, R., and Rahman, M. (Eds.) (1994), SiC and Related Materials, Proc. Fifth Conf., Inst. of Physics Publishing Ltd., Bristol, U.K. Sundararajan, S. and Bhushan, B. (1998), Micro/nanotribological studies of polysilicon and SiC films for MEMS applications, Wear, 217, 251-261. Tai, Y.C. and Muller, R.S. (1990), Frictional study of IC processed micromotors, Sensors and Actuators, A 21-23, 180-183.
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Tai, Y.C., Fan, L.S., and Muller, R.S. (1989), IC-processed micro-motors: design, technology and testing, Proc. IEEE Micro Electro Mechanical Systems, 1-6. Thurigen, C., Ehrfeld, W., Hagemann, B., Lehr, H., and Michel, F. (1998), Development, fabrication and testing of a multi-stage micro gear system, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), Kluwer Academic, Dordrecht, The Netherlands, 397-402. Tong, L., Mehregany, M., and Matus, L.G. (1992), Mechanical properties of 3C silicon carbide, Appl. Phys. Lett., 60, 2992-2994. Trimmer, W.S. (Ed.) (1997), Micromachines and MEMS, Classic and Seminal Papers to 1990, IEEE Press, New York. Venkatesan, S. and Bhushan, B. (1993), The role of environment in the friction and wear of single-crystal silicon in sliding contact with thin-film magnetic rigid disks, Adv. Info Storage Syst., 5, 241-257. Venkatesan, S. and Bhushan, B. (1994), The sliding friction and wear behavior of single-crystal, polycrystalline and oxidized silicon, Wear, 171, 25-32. Wilson, C.J., Ormeggi, A., and Narbutovskih, M. (1996), Fracture testing of silicon microcantilever beams, J. Appl. Phys., 79, 2386-2393. Xu, J. and Bhushan, B. (1997), Friction and durability of ceramic slider materials in contact with lubricated thin-film rigid disks, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 211, 303-316. Zhao, X. and Bhushan, B. (1998), Material removal mechanisms of single-crystal silicon on nanoscale and at ultra-low loads, Wear, 223, 66-78. Zorman, C.A., Fleischmann, A.J., Dewa, A.S., Mehregany, M., Jacob, C., Nishino, S., and Pirouz, P. (1995), Epitaxial growth of 3C-SiC films on 4 in. diam Si(100) silicon wafers by atmospheric pressure chemical vapor deposition, J. Appl. Phys., 78, 5136-5138. Zorman, C.A., Roy, S., Wu, C.H., Fleischman, A.J., and Mehregany, M. (1998), Characterization of polycrystalline silicon carbide films grown by atmospheric pressure chemical vapor deposition on polycrystalline silicon, J. Mater. Res., 13, 406-412.
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40 Mechanics and Tribology of Flexible Media in Information Processing Systems 40.1 40.2 40.3
Introduction ................................................................. 1549 Introduction to Foil Bearings ..................................... 1550 A Simple Foil Bearing Model...................................... 1553 Inlet Region • Central Region • Exit Region
40.4 40.5 40.6 40.7 40.8
Richard C. Benson The Pennsylvania State University
Eric M. Mockensturm
40.9 40.10 40.11 40.12
The Pennsylvania State University
Other Foil Bearing Models.......................................... 1556 Air Reversers................................................................. 1558 Introduction to Wound Rolls ..................................... 1561 Air Entrainment in Wound Rolls ............................... 1562 Nip-Induced Tension and J-line Slip in Web Winding ........................................................................ 1565 Web Tenting Caused by High Asperities.................... 1570 Mechanisms that Cause a Sheet to Jam, Stall, or Roll Over in a Channel................................................ 1576 Micro-slip of Elastic Belts ........................................... 1579 Transport of Sheets Through Roller/Roller and Roller/Platen Nips........................................................ 1582
40.1 Introduction The modern office is filled with printers, copiers, scanners, fax machines, tape drives, and other machines that handle very flexible sheets and webs. The marketplace for such devices is highly competitive and, thus, designers must continually strive for increased speed, precision, and automation in the handling of paper sheets, magnetic tapes, and other flexible media. This presents both design opportunities and design challenges. The flexibility of paper, for example, makes it possible for the sheet to follow a circuitous path in a small amount of space, but it also makes the sheet vulnerable to a paper-jam. Likewise, a thin magnetic tape can use self-entrained air to lubricate its passage around a post, but air entrainment during roll-winding causes poor stacking of the laps. This chapter addresses some of the basic mechanical and tribological issues that affect the handling of flexible media in information processing systems. Specifically, it explores the following topics. • An introduction to foil bearings • A simple foil bearing model • Other foil bearing models 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
1549
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• • • • • • • •
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Air reversers Introduction to wound rolls Air entrainment in wound rolls Nip-induced tension and J-line slip in wound rolls Web tenting caused by high asperities Mechanisms that cause a sheet to jam, stall or roll over in a channel Micro-slip of elastic belts Transport of sheets through roller/roller nip or roller/platen nips
These topics are ones that the authors have found of particular research interest, and for which they have a modest depth of experience. Because of this personal perspective, the majority of the references are to publications very familiar to the authors, and is strictly for their convenience. The authors realize that many other references could have been used to make the same points. Those seeking a broad coverage of the field are referred to the section “For Further Information” at the end of the chapter.
40.2 Introduction to Foil Bearings A foil bearing is a type of bearing in which at least one of the x1 surfaces is flexible. In a typical foil bearing, a tensioned, extremely flexible, axially moving strip (foil) is wrapped around a stationary or rotating drum. Due to the motion of the strip or the drum, a thin air film develops between the R surfaces. Because the lubrication is provided by the air x2 entrained from the motion of the strip, such systems are often referred to as self-acting foil bearings. In externally pressurized foil bearings, the drum is porous and the air film is enhanced by pumping air into the gap through the drum’s surface. An illustration of the self-acting foil bearing analyzed here is shown FIGURE 40.1 Schematic of a self-acting foil bearing. in Figure 40.1. Externally pressurized foil bearings are discussed further in the chapter section on air reversers (Section 40.5). Self-acting foil bearings are found in a variety of systems. In some cases, such as when one wants to change the transport direction of a foil without contact, a foil bearing can be a benefit and is designed into the system. In other cases, such as in contact recording and winding operations, the self-acting effect often hinders the system performance and is deliberately thwarted by design. Because foil bearings form the foundation of so many problems in the mechanics and tribology of information processing systems, they are discussed below. The self-acting foil bearing is a classic example of a system with fluid/structure interaction. Because the fluid and structure are in contact, the pressure and shear stress in the fluid provides structural surface loading (traction), which causes the elastic body to deform. The deformation of the structure causes the boundary of the fluid domain to change, altering the stress state of the fluid. This couples the equations of motion governing the fluid and the structure. In the foil bearing, the air film is bounded on one side by a flexible structure. Thus, the pressure and shear loading on the strip are dependent on the strip’s motion through the motion of the fluid. The strong coupling of the equations of motion for the air film and flexible strip complicate the analysis considerably. Thus, it is important to use mathematical models for the two continua that are simple, yet robust enough to capture the relevant physics of the system. Consider a strip moving over a circular, cylindrical drum as shown in Figure 40.2. The drum is considered rigid, fixed in space, and has radius R. The strip has half-width b and is traveling with velocity V under tension T (force/length). The region where the strip wraps around the drum is characterized by the angle θ. The air film separating the drum from the strip has thickness h and viscosity µ. Because
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FIGURE 40.2
1551
End view of a self-acting foil bearing showing the inlet, central, and exit regions.
this air film is thin (h b and h Rθ), the variation through the thickness is integrated out of the analysis and the Reynolds equation (derived in a previous chapter) is used. In the present notation, this equation is:
∂ 3 ∂p ∂ ∂ 3 ∂p ∂ h p h p + hp + 12 µ hp = 6 µV ∂x1 ∂x1 ∂x2 ∂t ∂x2 ∂x 2
( )
( )
(40.1)
where p is the air film pressure, x1 is the coordinate in the transverse direction (i.e., the direction of the drum axis (Figure 40.1)), x2 is the coordinate along the foil centerline (Figure 40.2), and t is time. Considerably more detail will be given to the derivation of the equilibrium equations governing the strip, as this has not yet been examined. The derivation follows Barlow (1967a). In terms of the tangential stress resultants N11, N22, N12, and the moment resultants* M11, M22, M12, the equations governing the strip are:
∂M11 ∂x12
+2
∂M 22 ∂M12 ∂N 22 ∂N12 + − κ 22 + =0 ∂x2 ∂x1 ∂x1 ∂x2
(40.2)
∂N11 ∂N12 + =0 ∂x1 ∂x2
(40.3)
∂ 2h ∂ 2h ∂M12 ∂M 22 2 ∂v 2 κ ρ κ + + = − − + − N p p V − V 22 22 a m 22 2 ∂x1x2 ∂x22 ∂t ∂x2∂t R ∂t
(40.4)
where pa is the ambient pressure, κ22 is the strip’s curvature in the x2 direction, ρm is the mass per unit area of the strip, and in-plane and rotary inertia have been neglected. The bending moments are proportional to the strip’s curvatures κ22 and κ11, the curvature in the x1 direction, and given by:
M11 = −
Ed 3
(
12 1 − v 2
)(
κ11 + νκ 22
)
(40.5)
*Stress resultants are obtained by integrating the stress through the thickness of the foil. Moment resultants are obtained by integrating the stress times the radial coordinate, x3, through the thickness of the foil.
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M 22 = −
Ed 3
(
12 1 − ν2
)
(κ
22
+ νκ11
)
(40.6)
where E is the elastic modulus, d is the thickness, and ν is the Poisson ratio of the strip. The torsional moment is given by:
M12 = −
Ed 3
( )
12 1 + ν
κ12
(40.7)
The tangential stress resultants are proportional to the tangential strains in the strip and are given by:
N11 =
(
)
Ed ε11 + νε 22 + νT 1 − ν2
N 22 =
(
(40.8)
)
Ed ε 22 + νε11 + T 1 − ν2
N 22 =
Ed
( )
2 1+ ν
(40.9)
ε12
(40.10)
The strip or foil is assumed to be flat in its stress-free state. Thus, points on the deformed strip’s midsurface are given by:
[ (
)] [
)] [
(
(
)]
x = x1 + u x1, x2 , t Eˆ x + R + h x1, x2 , t Eˆ r + x2 + ν x1, x2 , t Eˆ β
(40.11)
where the vectors Êr , and Êβ are shown in Figure 40.2, Êx = Êr × Êβ , and u and v are the displacements in the transverse (Êx) and tangential (Êβ) directions, respectively. From Equation 40.11, the strain measures can be calculated. Assuming infinitesimal displacements:
ε11 =
κ11 = −
∂u 1 ∂v ∂u ∂v h + , ε12 = , ε 22 = + ∂x1 2 ∂x1 ∂x2 ∂x2 R
∂ 2h ∂ 2h 1 ∂v 1 ∂2h h 2 ∂v , = − + , = − + + κ κ 12 22 ∂x1∂x2 R ∂x1 R ∂x22 R2 R ∂x2 ∂x12
(40.12)
(40.13)
It is typical to replace h in Equation 40.12 with h(x1, x2) – h(0, x2) so that a uniform displacement of the strip away from the drum does not introduce additional longitudinal strain. The last term in Equation 40.13.b and the last two terms in Equation 40.13.c are usually neglected as small with respect to the remaining terms. These assumptions will be made hereafter. Combining Equations 40.2 through 40.13 and neglecting higher-order terms gives an equation for gap thickness in terms of the applied pressure, elastic constants, foil tension, and drum radius:
D∇2∇2h +
(
Ed h − h0 R
2
) = p− p − T −ρ V m
a
R
2
∂ 2h ∂ 2h ∂ 2h 1 − R 2 + ρm 2 + V ∂x2∂t ∂x2 ∂t
(40.14)
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where h0 is the gap at the foil centerline, h(0, x2, t),
∇2 ≡
Ed 3 ∂2 ∂2 + 2 , and D = 2 ∂x1 ∂x2 12 1 − v 2
(
)
(40.15)
Note that as R → ∞, Equation 40.14 reduces to the equation of a flat plate under tension. See Shames and Dym (1991) for further information. The Reynolds equation (Equation 40.1) and the strip equation (Equation 40.14) must be solved simultaneously to find the film thickness and pressure. It is possible to use numerical methods to solve variations of this problem, as did Ono and Mizukawa (1985), Heinrich and Connolly (1992), Lacey and Talke (1990), and Müftü and Benson (1996). Due to the strong nonlinearity in the Reynolds equation, much numerical effort is required. Ono et al. (1991) have reviewed various numerical techniques used to solve these equations. Wickert (1993) and Lakshmikumaran and Wickert (1996) used Green’s function and adaptive finite difference meshes to significantly reduce the computational effort, making parameter studies feasible. While one must resort to numerical methods for most foil bearing problems, many characteristics of the foil bearing can be deduced from the solution of a simplified (linear) problem in which the foil is considered perfectly flexible and the lubricant incompressible.
40.3 A Simple Foil Bearing Model Neglecting the dependence of all variables on the transverse coordinate x1, ignoring the bending stiffness of the strip, and assuming a steady solution and incompressible lubricant, the Reynolds equation and foil deflection equation reduce, respectively, to:
d 3 dp dh h = 6 µV dx2 dx2 dx2
p − pa =
T − ρmV 2 d 2h 1 − R 2 , R dx2
(40.16)
(40.17)
One can combine these equations to obtain what is normally referred to as the foil-bearing equation:
6 µV d 3 d 3h dh =− h 3 2 dx2 dx2 T − ρmV dx2
(40.18)
The nondimensional variables
δ=
6 µV T − ρmV 2
, ξ = δ −1 3
x2 h , and H = δ −2 3 R R
(40.19)
are introduced, reducing the foil-bearing equation to:
d 3H H − H = dξ 3 H3
(40.20)
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where H is a constant of integration. The dimensionless quantity δ is small, O(10–6), for most foil bearings with air lubrication. At this point, it is good to investigate some of the consequences of the equations that have been developed. First, note that Equation 40.16 can be integrated to give:
(
h−h dp = 6 µV dx2 h3
)
(40.21)
Recall that at the bearing inlet and exit, the pressure will be atmospheric. Unless the pressure is atmospheric throughout the domain, which one –knows it is not, there must be at least one point in the domain at which dp/dx2 = 0. –At this point, h = h and the pressure has reached either a local minimum or maximum. For h > 3 h/2, an increase in h will result in a decrease in the pressure gradient. Due to the flexibility of the foil, a decrease in the film pressure will cause a decrease in the film thickness. The result of the combination of these is that peaks in the pressure get smoothed, suggesting that the majority of the bearing surface has a constant pressure. Rearranging Equation 40.17 gives:
p − pa T − ρmV 2
=
1 d 2h − R dx22
(40.22)
where the right-hand side is recognized as the strip curvature. Through most of the bearing region, one suspects that p > pa and T > ρmV2, resulting in the left-hand side of Equation 40.22 being positive. Thus, the additional foil curvature d 2h/dx 22 will be less than the –drum curvature. If h is constant, then p = pa + (T – ρmV2)/R is constant, and from Equation 40.21, h = h. Equation 40.20 is a nonlinear equation that does not permit a closed-form, analytical solution. However, —much of the qualitative behavior of the foil bearing can be obtained by linearization. Assuming — H ≈ H, one can introduce the small function f —such that H(x2) = H [1 + f (x2)]. Inserting this into Equation 40.20 and linearizing gives d 3f/dx 32 + f/ H 3 = 0, which has solution:
3 3 f = A1e − ξ + A2e ξ 2 cos ξ + A3e ξ 2 sin ξ 2 2 –
(40.23)
—
where ξ = ξ/ H. Experimental observation suggests there are three distinct regions in the foil bearing: the inlet region where the pressure builds from atmospheric, the central region, in which the pressure and gap width are nearly constant; and the exit region where the pressure decays to ambient. These regions are shown in Figure 40.2 and are discussed individually.
40.3.1 Inlet Region In the inlet region, the pressure builds from atmospheric pressure as the lubricant gets squeezed by the narrowing gap. Because the pressure is growing in this region, the pressure gradient is positive. In addition, the film thickness is decreasing to its nearly constant value in the central region. From the onedimensional Reynolds equation (Equation 40.16), one notes that a positive pressure gradient is consistent – with the film thickness decreasing from infinity to h, its value in the central region. As noted previously, the combination of the strip and Reynolds equations smooth out any peaks in the film pressure. Additionally, boundary data is only propagated by the film in the direction of flow. The inlet region is thus extremely important as the system’s behavior in this region determines its behavior downstream, that is, in the central and exit regions.
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For the solution in the inlet region to remain bounded in the central region, A2 and A3 of Equation 40.23 must be zero. Thus, the gap decays exponentially and is given by:
δ1 3 H h = 1 + A1e − ξ or = 1 + A1 exp − x2 H h h
(40.24)
40.3.2 Central Region The central region extends over most of the strip’s wrap angle. In this region, H is constant. From the — observations above, one knows that the pressure is also constant and H = H. The constant of integration — H is now an important parameter in the system, the film thickness over most of the bearing region. Unfortunately, its value cannot be determined from the linear analysis completed above. Blok and Van Rossum (1953) first estimated this value to be 0.426. Eshel and Elrod (1965) numerically integrated — Equation 40.20 and found H = 0.643. In dimensional parameters,
6 µV h = 0.643 R 2 T − ρmV
2 3
(40.25)
and one sees that the film thickness grows with — the drum radius, film viscosity, and strip velocity; and diminishes with the strip tension. This value for H was obtained by introducing many assumptions into the foil-bearing equation. The importance of many of these assumptions has since been studied, and — according to Gross (1980), H does not deviate much from 0.643, provided that the following inequalities are met:
Stiffness: S =
D
(T − ρ V )R δ 2
2 2 3
< 0.8
m
Compressibility: α =
T − ρmV 2 < 0.12 p0 R
Fluid inertia: I =
1 ρRV 2 < 0.05 2 T − ρmV 2
Wrap angle: Θ =
θ >6 δ1 3
Foil width: 2b dR
40.3.3 Exit Region The analysis for the exit region is similar to that of the inlet region. In this region, the pressure must decrease from its constant value in the central region to its atmospheric level; that is, one expects that dp/dx2 < 0. In addition, the gap will increase as the foil peels away from the drum. Note, however, that this is not consistent with the one-dimensional Reynolds equation. Thus, there is not a smooth transition out from the central region as there is into it. As the foil enters the exit region and begins to peel away from the drum, the pressure initially rises. The pressure then quickly falls to a level below atmospheric and the tape is sucked back toward the drum, with the film thickness decreasing below that in the central region. This is illustrated in Figure 40.2. The foil can then move away from the drum with the pressure increasing to atmospheric. Both the minimum film thickness and the maximum and minimum pressures occur in the exit region.
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The described oscillatory behavior also shows up in the linearized solution (Equation 40.23). In the exit region, A1 must be zero and the solution is:
3 3 H ξ + A3 sin ξ or = 1 + e ξ 2 A2 cos H 2 2 13 h δ 3x2 x 2 sin δ1 3 = 1 + A5 exp + A4 h 2h 2h
(40.26)
40.4 Other Foil Bearing Models Even with the many simplifying assumptions used to arrive at Equation 40.20, the result is still a nonlinear differential equation that can only be solved numerically. Since the early studies in the 1950s and 1960s for highly idealized foil bearings, many authors have investigated the consequences of many of the assumptions used in the early models. In particular, the effects of foil bending rigidity, lubricant compressibility, foil wrap angle, finite width, fluid inertia, foil/drum contact, unsteady deformation, and mean free path of air molecules have been studied. The following discussion investigates the effect that some of these have on the film thickness in the central region. One of the first assumptions to be removed by Eshel and Elrod (1967) was that of the perfectly flexible foil. As all foils have a finite thickness, they will have some resistance to bending deformations. Including bending rigidity in the model alters the strip equation
D
(
)
T − ρmV 2 d 4h Ed h − h0 d 2h + = p − p − 1 − R a R dx24 R2 dx22
(40.27)
but does not change the simplified Reynolds equation (Equation 40.16). Solving for p and inserting into Equation 40.16 gives the stiff foil bearing equation:
D
(
)
3 d 5h Ed dh h−h 2 d h + − T − ρ V = 6 µV 3 m 5 2 3 dx2 R dx2 dx2 h
(40.28)
d 5H dH d 3H H − H + − = S dξ dξ 3 dξ 5 H3
(40.29)
or in nondimensional form:
S
where the stiffness parameter S was defined previously and
S=
(
Edδ 2 3
R T − ρmV 2
)
(40.30)
The second term on the left-hand side of Equation 40.29 is usually neglected as small compared to the remaining terms. The response predicted by this model is similar to that of the perfectly flexible foil model. There is again a smooth inlet region, a central region with constant film thickness, and an undulating exit region. When the stiffness parameter is greater than 0.326, there are also oscillations in the inlet region. The
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dimensionless gap thickness H —decreases as the stiffness parameter increases. When S = 0.8, H has decreased to 0.615. For S = 10, H = 0.525. When lubricant compressibility — but not foil bending rigidity — is included in the model, the foilbearing equation becomes:
d2H d 3H 1 + α1 − 2 H 3 3 + H = H dξ dξ
(40.31)
where the compressibility parameter α is as defined above. This model was studied by Eshel (1968), who found that the film thickness in the central region decreases significantly when α > 0.12. When α = 1, — — H has decreased to 0.475; when α > 100, H < 0.1. Another interesting consequence of including lubricant compressibility is that for α > 2.4, the exit region is monotonic (i.e., there are no foil undulations). Implicit in the discussion of the solution of the simple foil-bearing equation is that three regions exist. However, this is only true when the total wrap angle– θ is large. It is known that the lengths of the inlet – and exit regions are each of the order h/δ1/3. With h = 0.643Rδ2/3, the wrap angle covered by the inlet and exit regions is of order δ1/3. If the total wrap angle is small, the inlet and exit regions will converge and the central region will disappear. When the wrap angle goes to zero, the film thickness approaches infinity as the component of tension pulling the foil around the drum goes to zero. Barlow (1967b) numerically integrated Equation 40.20 to study the effect of wrap angle. For dimen— nominal value of 0.643 found by Eshel sionless wrap angles Θ = θ/δ1/3 > 6, H is nearly constant at the — H is within 5% of the value of 0.643. As the and Elrod (1965). For Θ as low as 2.5, the dimensionless gap — dimensionless wrap angle decreases from 6, H initially increases, reaching a maximum of approximately 0.66 at Θ = 4.25. Knowing the limiting value for zero wrap angle, one might expect the film thickness to continue to increase as the wrap angle decreases. However, this is not the case. For Θ between 1.4 and — — 4.25, H decreases, reaching a minimum of approximately 0.575. For Θ < 1.4, H monotonically increases. Assuming the foil has an infinite width simplifies the analysis considerably by removing all dependence on x1 from the system and reducing the governing equations from partial differential equations to ordinary differential equations. However, real foil bearings are not infinitely wide and many authors have studied the consequences of this assumption on the steady-state response of the foil bearing. Relaxing the assumption of infinite width introduces two important new phenomena to the problem. First, and most obvious, is the variation of the solution across the width of the bearing. Second is side leakage, where air entrained by the motion of the foil leaks along the foil’s free edges. While the full twodimensional equations must be solved to determine the solution’s dependence on the transverse coordinate, side leakage can be incorporated into one-dimensional models. One method of doing this is to assume the foil is permeable, allowing air to leak through it. Another method, used by Allaire and Benson (1987), is to approximate the cross-flow and integrate out the width coordinate, much like the thickness coordinate is integrated out in the derivation of Reynolds equations. Much like the foil profile in the running direction, the profile across the width contains a central region where the pressure and film thickness are nearly constant. The edges are effectively two exit regions where the pressure must drop from its elevated level between the drum and foil to ambient. Thus, one would expect the foil’s edges to be drawn toward the drum as there is no cross-width tension pulling the foil away from the drum. Because of this, contact between the foil and drum is most likely to occur near the foil’s free edges, and wear can be a significant problem here. In an extensive experimental study of foil bearings, Licht (1968) found this to be the case. Müftü and Benson (1996), who included foil-drum contact, and Lakshmikumaran and Wickert (1999), who used a more efficient numerical algorithm, predicted this theoretically. Because the foil is drawn toward the drum near its free edges, the foil acts to seal the bearing and prevent side leakage. When air leaks from the sides of the bearing, the pressure and film thickness decrease slowly through the central region. Licht (1968) showed that while translation speed has an effect on side leakage, the most important parameter is the foil width. Much like what happens for small wrap angles, as the foil width decreases, the two exit regions merge and significant side leakage can occur. For 2b > dR , side leakage can be neglected.
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Many other effects have been studied. The effect of fluid inertia was investigated by Eshel (1970b). Because the film thickness in many applications is of the same order as the mean free path of air molecules (67 nm), the Reynolds equation is often modified to include slip flow. Burgdorfer (1959) and Fukui and Kaneko (1987a) have included the effect of mean free path in their analyses of the Reynolds equation. Experimental investigations of slip flow were performed by Hsia and Domoto (1983) and Fukui and Kaneko (1987b). Eshel (1970b) included slip flow and also studied the effect of drum contour. Foil vibrations have been a topic of papers by Stahl et al. (1974), Wickert (1993), Lakshmikumaran and Wickert (1996), and Renshaw (1999). Effects specific to helical scan recorders have been investigated by Rongen (1990, 1994) and Kotera et al. (1991, 1992).
40.5 Air Reversers Air reversers are found in many applications. They are most x1 common in systems that process coated materials. When the traveling direction of the material needs to be changed, a regular roller cannot be used as it would damage the possibly wet pr coating. In these situations, an air reverser replaces the roller, R allowing the traveling direction of the material to be changed without contact. Air reversers accomplish this feat by providx2 ing a cushion of air between the solid drum surface and the coated material. This air cushion is primarily provided by air forced through small holes in the drum surface by the pressure inside the drum, pr (Figure 40.3). Air is also entrained by the FIGURE 40.3 Schematic of an air reverser moving material, much like a self-acting foil bearing; however, showing a typical hole pattern. this contribution is small compared to the forced air. In many aspects, air reversers are similar to externally pressurized foil bearings, which have been studied extensively; see Gross (1980). As mentioned previously, pressurized foil bearings are analyzed using the Reynolds equation modified to include a source term. The main operating difference between air reversers and pressurized foil bearings is the clearance between the drum and the traveling material. In foil bearings, the film thickness, h, is typically on the micrometer scale, while the air gap in air reversers is measured on the millimeter scale. In both cases, the gap would be considered small. However, the larger gap in the air reverser necessitates closer inspection of the assumptions used to develop the Reynolds equation. The modified Reynolds number, Re* = ρf Vh2/µL, is a ratio of the inertial to viscous forces in a narrow channel. In the development of the Reynolds equation, Re* is assumed small and inertial forces are neglected when compared to viscous forces. However, it is clear from the presence of h2 in the definition of Re* that the modified Reynolds number will be much larger in an air reverser than in a self-acting foil bearing. In fact, Re* = O(10) for a typical air reverser. Thus, in the present situation, the Reynolds equation cannot be used as inertial forces are not small compared to viscous forces. In fact, here one may consider neglecting viscous forces. This is what was done by Müftü et al. (1998). Following this work, the equations of motion for the incompressible fluid in the air reverser are
( ) ( )
∂h ∂ hv ∂ hu + = βV + ∂x2 ∂x1 ∂t ∂v 1 ∂p ∂v ∂v v +v +u + = −βV ∂t ∂x2 ∂x1 ρ f ∂x2 h 1 ∂p ∂u ∂u ∂u u +v +u + = −βV ∂t ∂x2 ∂x1 ρ f ∂x1 h
(40.32)
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–
–
where V is the fluid velocity through the holes (not the same as V, the material velocity), and u and v are the fluid velocities in the x1 and x2 directions, respectively. The factor β is the ratio of the area of the holes to the area of the drum. Implicit in Equation 40.32 are the noteworthy assumptions that the flow in the gap is two-dimensional, centrifugal effects from the curvature of the flow are negligible, and the in-plane fluid velocities and pressure are not functions of the radial coordinate. As the flow is turbulent in the gap, the flow through individual drum holes is not considered and they are modeled as a uniform, distributed flow source given by the right-hand sides in Equation 40.32. — The fluid velocity through the holes, V, is approximated from Bernoulli’s equation to be:
V =κ
(
2 pr − p ρf
)
(40.33)
where κ is an empirical (discharge) constant lying between zero and one, and accounts for the losses due to the contraction of the effective flow area near the hole and turbulence. Using Equation 40.33 and assuming no flow in or dependence of fields on the transverse direction, Müftü et al. (1998) were able to obtain an analytical expression for the steady-state axial fluid velocity and the pressure in the air gap. In most air reversers, the holes are not distributed uniformly over the drum. Holes are typically more densely spaced near the edges of the supported material. In most cases, there are no holes in the central region (see Figure 40.3). This situation can still be studied using the above analysis with x2 replaced by – x, a local coordinate for the porous region. The flow in the central region (with no holes) is then zero and the pressure is constant. The total solution is then constructed from the local solutions. With these assumptions and Equation 40.33, Equation 40.32 becomes:
( ) = βκ 2( p − p) ,
d hv
r
dx
ρf
v
(
)
dv 1 dp v 2 pr − p + + βκ =0 dx ρ f dx h ρf
(40.34)
If the gap thickness, h, is assumed to be constant, the gap pressure is, from Equation 40.34a:
p = pr −
ρ f h dv 2 βκ dx
2
(40.35) –
Substituting Equation 40.35 into Equation 40.34b gives a linear ordinary differential equation for v: 2
ακ d 2v − 2 v = 0 2 dx h
(40.36)
with solution 2 cosh mx l pr sinh mx l v= , p = pr 1 − ρ f cosh m cosh m
(
where m =
( )
)
2 βκl/h and l is the length of the porous region.
(
( )
)
(40.37)
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0.75
y(m)
0.5
0.25
0
0
0.4
x(m)
p(Pa) 200 150 100 0 50
0.25 0.5
0 0
0.75 0.2
1
0.4
x(m)
)
y(m
1.25
0.6 1.5
FIGURE 40.4 Theoretical results of the air velocity and pressure in the gap between the porous drum and the foil. (From Müftü, S., Lewis, T.S., Cole, K.A., and Benson, R.C. (1998), A two-dimensional model of the fluid dynamics of an air reverser, J. Appl. Mech., 65(1), 171-177. With permission.)
Müftü et al. (1998) also used numerical methods to solve the full two-dimensional equations with a constant gap thickness. Figure 40.4 shows the pressure and flow distributions for the case with holes distributed around the outer 20 cm of the domain. The hole density β was 0.0084 in the porous region and the supply pressure pr and gap thickness h were 800 Pa and 3 mm, respectively. Solutions from the one-dimensional model compared favorably with those from the two-dimensional model when hole densities were uniform in the outer region. The average pressure is overestimated by the one-dimensional model because it cannot predict the two-dimensional flow near the corners (Figure 40.4). The effect of various hole densities in the outer regions on the average pressure was studied using the two-dimensional model. When normalized by the supply pressure, it was found that the optimal configuration was one with a uniform hole density. From the one-dimensional solution which makes excellent predictions for this case, it is clear that the ratio βκl/h (l = 20 cm here) plays a key role in determining the pressure in the central, nonporous region of the air reverser. As this dimensionless parameter grows, the central and average pressures approach the supply pressure. Thus, to make the most efficient use of
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the supply pressure, air reversers should be designed with densely packed holes uniformly distributed over the outer region of the air reverser.
40.6 Introduction to Wound Rolls Winding material into a roll is an important process in many manufacturing systems and consumer products. During the mass production of thin materials such as paper, fabric, and plastic and metal films, the material is often wound into a roll for transport to other processes or to the consumer. These rolls can weigh several tons and measure hundreds of centimeters in diameter and several meters in length. Smaller, but no less important, wound rolls are found in many consumer products. The tape in cartridges for cassette players, VCRs, digital audio tape players, and computer backup devices is stored in wound rolls. Here, as the tape is unwound and rewound thousands of times during the life cycle of the product, it is especially important to understand the mechanics involved in the winding process and how entrained air trapped between layers can cause performance problems. There are fundamentally two ways of driving the wound roll. In center winding, a motor is connected to the spindle of the winding roll. As the motor turns the spindle, material is wound onto it. In this method, the rotational velocity of the roll is constant and the transport velocity of the material increases during winding as the roll radius increases. This is how the tape used in common devices such as VCRs and cassette and digital audio tape players is wound. In other applications such as material processing and high-density data storage, it is essential to maintain a constant transport velocity. This is called surface winding and is done by driving the outer edge of the roll. In material processing devices, a drive or nip roller is often used. Material passes around the drive roller onto the wound roll (Figure 40.5). The center of the driving roll is fixed, forcing the center of the wound roll to translate as material is added. In some high-density data cartridges, an elastic band is stretched around a portion of the wound roll (see Figure 40.6). A drive roller transmits power through the band to the wound roll. In this setup, both the drive and wound rollers can have their centers fixed. As the elastic band is also partially wrapped around the unwind reel, its length remains nearly constant as tape is transferred from one reel to the other. In winding applications, all relative motion between wraps or layers is to be avoided. Relative motion in either the winding (machine) direction or the lateral (cross-machine) direction can cause wear or damage a delicate material. Slip in the winding direction can reduce the wound-in tension that keeps the roll compact, produce axial compression and buckling of layers, and cause “roll collapse.” Slip in the lateral direction can damage the lateral edges, and cause uneven wraps and telescoping. In addition to causing damage to the material being wound, relative motion between layers can cause manufacturing problems during the unwind process.
Wound Roll TA
A
TB B Nip Roller
FIGURE 40.5 Schematic of a winding process with a nip roller. Either the nip roller is fixed and driven and the wound roll free (B fixed, TA = 0), or the wound roll is fixed and driven and the nip roller is free (A fixed, TB = 0).
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Tape Pack
Drive Belt
Drive Roller
Magnetic Tape R/W Head
Motor Drive Puck
FIGURE 40.6 Example geometry of a data cartridge showing the reel-to-reel magnetic tape path and the closedloop drive belt.
40.7 Air Entrainment in Wound Rolls In many applications, it is desirable to have an air film Air between two surfaces to reduce friction, drag, and wear. Leakage There are, however, many other applications in which R engineers want two surfaces to be in contact. Having two surfaces in direct contact is often desirable when attemptAir Entrainment ing to transmit force or power. It is also necessary when trying to prevent relative motion between two surfaces. V 2b In these applications, an air film can cause performance degradation of the system. Roll winding is one such application where air entrainment and films between layers FIGURE 40.7 Schematic of a wound roll showare unwanted. During winding, air is entrained by the material being ing air entrainment and leakage. transported; this is similar to what happens in a foil bearing and illustrated in Figure 40.7. There are, however, a few important differences between a foil bearing and a wound roll. First, in the wound roll, there is no exit region. Second, both surfaces are flexible in the wound roll. In this case the “drum” is composed of the previous layer of wound material, which may have a significant air film between it and the preceding layer. Third, in the present case, the drum is moving with the same velocity as the incoming material. Thus, while much of the knowledge about foil bearings can be applied to air entrainment in wound rolls, some modifications must be made to the mathematical models. In winding, because there is no exit region, the only place for air to escape is across the lateral edges of the material. Because the cross-width deformation of neighboring surfaces will be approximately equal, the deformation at the outer edge does not seal the bearing as with the foil bearing. Thus, more side leakage will occur; see Figure 40.7. However, roll guide flanges can hinder side leakage. For winding where air films are unwanted, side leakage is desirable. It is therefore essential to include side leakage in the model. During winding, a steady state is reached in which the entrained air coming into the roll is equal to the air leaking out. As the winding speed increases, more air is entrained. As increasing the winding speed does not reduce the speed at which air leaks from the roll, higher winding speeds will lead to a much larger region where adjacent wound layers are not in direct contact. At high winding speeds, a
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significant air film can exist several dozen wraps in from the outer edge. It can take several seconds after winding stops for all the air to leak out of the roll. Because one of the simplest methods to increase processing productivity, and possibly the only way to reduce seek times in tape recording devices, is to increase the winding speed, air entrainment can provide a formidable adversary to increased performance. Engineers have contrived many different ways to help alleviate this problem. Wind-on or nip rollers attached to spring-loaded dancer arms are used to press the incoming material against the roll, rapidly squeezing out the entrained air; see Figure 40.5. Highly elastic drive belts are sometimes stretched around the roll to compress the outer layers of the roll and force the entrained air out; see Figure 40.6. As many design concerns need to be considered and these methods can cause additional wear in the wound material, it is often not feasible to use them. There are a variety of ways that a wound roll with air entrainment can be modeled. Because side leakage is very important in the analysis, it would be best to use a two-dimensional model. However, adding the second dimension to the problem increases its complexity enormously. One could include side leakage in a one-dimensional foil bearing model by approximating the pressure distribution across the width of the wound material and using the Galerkin method to remove width dependence from the equations (Allaire and Benson, 1987). Another major modeling concern in winding that is also included in some foil bearing models is that of surface roughness of the wound-on material. In magnetic tape applications, the back surface, whose characteristics are not normally constrained by other considerations, is often textured with patterns to induce more rapid side leakage. Striations running across the width of the tape have been found to help. The Reynolds equation can be modified to include surface roughness through the use of flow factors, φ1 and φ2. For an incompressible fluid, it becomes:
∂ 3 ∂p ∂ 3 ∂p ∂h ∂h φ 2h φ1h + 12 µ + = 6 µ 2V ∂x2 ∂x2 ∂x1 ∂x2 ∂t ∂x1
( )
(40.38)
where 2V replaces V, and the shear flow factor (φu in Bhushan and Tønder, 1989) is neglected because both surfaces are moving with velocity V. For isotropic roughness, Bhushan and Tønder (1989) give:
( )
φ1 = φ2 = 1 + 0.85 σ h
2
(40.39)
where σ is the equivalent standard deviation for surface roughness of adjacent tape layers. For transverse roughness, Tripp (1983) finds:
( )
2
( )
φ2 = 1 − 6 σ h , φ1 = 1 + 3 σ h
2
(40.40)
where the factors impede flow in the transport direction and aid flow in the cross-width direction. For more about surface roughness factors, see Tønder (1984), Mitsuya (1986), Mitsuya and Fukui (1986), and Patir and Cheng (1978, 1979). Keshavan and Wickert (1997, 1998) have used Equation 40.38, a global form of mass conservation, and approximations for the two-dimensional, spatial pressure distribution to study air entrainment during steady-state winding and transient air discharge from a wound roll. In each study, symmetric, in which air leaks from both sides of the roll, and asymmetric, in which air leaks from only one side of the roll, cases were investigated. In the study of steady-state winding, the mass flows into and out of each wrap are equated to give recursive algebraic cubic equations for the thickness ratio, hn /hn – 1. For wrap n, the mass flow into the region is:
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(1)
M i = 2bVρh0 (40.41)
3 (n) = 2bV ρh − b ρhn −1 p ∂p , x , x = 2πRn dx , n > 1 ( )n −1 ∫ (1 2 ) 1
Mi
−b
12 µ
∂x 2
while the mass flow out of the region is:
(n )
ρhn ( )n ∫−b 12 µ
M o = 2bV ρh −
b
3
p
(
(
ρhn3 ∂p p , x1 = −b, x 2 dx 2 − + 2 πR (n −1) 12 µ ∂x1
∫
2 πRn
))
∂p , x1 , x 2 = 2πR n − 1 dx1 ∂x 2
(
)
∫
ρhn3 ∂p p , x1 = b, x 2 dx 2 2 πR (n −1) 12 µ ∂x1 2 πRn
(
)
(40.42)
for all n. The last two terms in Equation 40.42 are from side leakage. In this analysis, the film thickness in each layer is assumed constant and the thickness of the first layer, h0, is obtained from the classic foilbearing problem. The spatial dependence of the pressure is assumed known and separable, p = p1(x1)p2(x2). For the symmetric (asymmetric) case, p1 = 23 [1 – (x1/b)2] (p1 = 98 [1 – 23 (x1/b) – 13 (x1/b)2]). For both cases, p2 = T/2Rb( 12 + x1/2πR). With h0 known and using the ideal gas law to determine the density, the film thickness of each subsequent layer can be determined by setting Equation 40.41 equal to Equation 40.42. The simulation stops when the film thickness falls below the peak-to-valley asperity level of the wound material. In this way, the total air film thickness, Σh, is determined and compared with experimental results. While the cumulative air film thickness increases with δ, the foil bearing parameter, for both the symmetric and asymmetric cases, the thickness is always greater for the asymmetric case as less air leaks out. As illustrated in Figure 40.8 (reproduced from data in Keshavan and Wickert, 1997), the difference between the predictions of the two cases increases with δ. Over one order of magnitude of δ, the experimentally obtained values of Σh fall between the theoretical predictions from the two cases, as shown in Figure 40.8.
FIGURE 40.8 The cumulative air film thickness increases with the parameter δ. The theoretical results for the symmetric and asymmetric cases bound the experimental data.
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For the transient discharge of air from a wound roll, Equation 40.38 with V = 0 is used. In this analysis, ˆ , t) = Keshavan and Wickert (1998) used the pressure distributions given above and assumed h(x 2 h(x2)q(t), where h(x2) is the piece-wise constant function determined from the steady-state analysis. Inserting these assumed forms for the dependent variables in Equation 40.38 and using the Galerkin method gives a nonlinear ordinary differential equation for q, q· + C1q + C2q3 = 0, where the coefficients are functions of the system parameters and the known initial film thicknesses. The solution of this equation is:
C C q t = − 2 + 1 + 2 e 2C1t C1 C1
()
−1 2
(40.43)
The time history of the theoretically predicted cumulative thickness was compared with experimental results. Again, for all systems tested, the results from the asymmetric case bounded the experimental results from above, while the results from the symmetric case bounded them from below.
40.8 Nip-Induced Tension and J-line Slip in Web Winding In web handling processes, a nip roller is often used to remove entrained air and increase the wound-in tension. A schematic of this is shown in Figure 40.5. The material to be wound enters the system and is wrapped around the nip roller and then onto the wound roll. Equal and opposite forces are applied to the spindle of each roller to press the nip roller against the wound roll. The pressure generated at the nip by these forces squeezes entrained air out and increases the tension in the material wound onto the roll, producing a tighter, more compact roll. There are two fundamental ways the nip and winding rollers can be configured. In center winding, a motor drives the wound roll and the center of the nip roller translates to accommodate the increasing diameter of the wound roll. In surface winding, the nip roller is driven by a motor and the spindle of the wound roll is allowed to translate, usually in a guiding track. Each configuration has advantages and disadvantages. The decision to use one over the other is typically based on the type of material being wound and the convenience of changing the wound roll when it is full. How winding with a nip roller can force air out of the nip interface is clear. However, the reason the nip roller increases the wound-in tension is not as intuitive. This effect has been known to material processing engineers for many years. Scientists and engineers have, however, only recently investigated the mechanisms that cause it. In early experiments on wound rolls, it was discovered that if one used a chalked bow-string to mark a radial line on the end of a partially wound roll, this line would be curved when winding was finished. The final shape of the line resembled the letter “J” and was thus called a J-line; see the solid white lines (c) in Figure 40.9, reproduced from Gueldenberg and Welp (1999). For this initially straight line to become curved, relative motion between the layers of the wound roll must have occurred. Thus, the phrase “J-line slip” is used to describe this behavior. The originators of the terminology and method are unknown, but first public mention of it was by Laumer (1966). Lucas (1981) has a nice discussion of the history of J-line analysis. The bent portion of the J-line occurs at the outer section of the roll and always points in the direction of rotation of the roll. This indicates that the outer layers are shifting ahead of the previously wrapped inner layers. Thus, while the nip roller increases the tension of the material to be wound, there is an apparent loosening of the material after it is wrapped onto the roll. Pfeiffer (1968) and Good and Wu (1993) have investigated the mechanism that causes the increase in tension as the winding material passes through the nip (the point of contact of the nip roller and the wound roll). In both studies, experiments were done by placing flat sheets of material on a hard surface
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FIGURE 40.9 Photograph of a wound roll showing the slip of layers marked with ink (a) away from the reference line (b). J-lines (c) marked at three stages of winding are superimposed digitally to illustrate the difference between J-line measurements and ink-dot measurements.
and passing a roller over the material, much like a baker rolling dough. While not precisely the configuration of an actual wound roll, this setup provides a good simulation and much easier access for measurements. In a real wound roll, the ends of the adjacent layers in the stack of sheets would be connected. Thus, in the simulation, the tension at the ends of a sheet should be equal to the tension of the opposite ends of adjacent sheets. In the experiments performed by Pfeiffer (1968), stacks of paper sheets of varying thickness were used. A force gage was attached between one end of the top sheet and a rigid fixture to measure the tension in the sheet. A roller was moved over the stack, beginning near the force gage. There was an almost immediate increase in tension when rolling began. As the roller moved over the stack, the tension in the rolled material continued to increase until an asymptotic value was reached. This asymptotic value will hereafter be called the wound-in tension. It was found that the wound-in tension increased with the number of sheets in the stack. Pretensioning the top sheet to various levels appeared to have no effect on the additional wound-in tension produced by the nip roller. The wound-in tension decreased with increasing roll diameter and decreasing nip pressure. The wound-in tension also increased as the thickness of the individual sheets increased. Possibly the most interesting portion of Pfeiffer’s work was the result obtained when force sensors were connected to both ends of the underlying sheets in the stack. Pfeiffer found that while the tension in the top sheet, in contact with the nip roller, increases, the tension in the underlying sheets may decrease. Thus, while the nip roller increases the tension of the incoming material before it is wound onto the roll, the full increase in tension does not remain once more wraps are added to the roll. This also explains the J-lines that indicate the wrapped material relaxes as more material is wrapped over it. Interestingly, it is the same device (the nip roller) that both increases the tension of the incoming material and decreases the tension in the underlying, previously wrapped material. In the end, while the full effect of the initial tension increase caused by the nip roller is not maintained, the initial increase is greater than the subsequent decrease and nip rolling produces tighter wound rolls. Pfeiffer explained this interesting result by experimentally observing that the instant center of the nip roller was not at the contact point of the sheet and the roller. This was done by taking a collection of magnified time-lapse photographs of the roller/stack contact point as the roller moved across the stack. In the perfect case of a rigid drum rolling over a rigid surface, a particle on the edge of the drum should trace out a perfect cycloid that comes to an infinitely sharp point as the particle passes through the
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Wound Roll
Instant Center Nip Roller
FIGURE 40.10 Expanded view of the nip interface illustrating the experimental observation that the nip roller’s instant center is not at the nip roller/wound material interface but somewhere in the wound roll.
contact point. When the particle is at the point of contact of the two surfaces, it has no velocity in the direction the drum is rolling. Particles not on the drum’s edge will always have a component of velocity in the direction of travel. Pfeiffer noticed that when the steel roller was passed over the paper stack, no particle on the roller traced out a perfect cycloid, indicating that the instant center was below the contact point, in the paper stack. With an instant center below the contact point, sheets above the instant center will move in the direction of rolling, and sheets below will move in the opposite direction. This phenomenon is illustrated in Figure 40.10. Thus, there will be an increase in tension of the sheets above the instant center and a decrease in tension in the sheets below. In the work performed by Good and Wu (1993), a finite-element analysis was used to study the problem. Agreement between the model and experiments performed by the authors was demonstrated. The nip roller and wound roll were again modeled by passing a roller over a flat sheet of material pressed against a hard surface. In these experiments, a single aluminum strip was used instead of the paper stack used by Pfeiffer (1968). Initial tension was provided by attaching to one end of the horizontal strip a wire that bent over a pulley and supported a known mass. Strain gages were attached near the other end of the strip, which was rigidly clamped to a foundation. It was again found that as the roller, which was pressed against the strip with known force, moved away from the clamped end, the tension in the rolled portion of the strip increased. Rollers of different diameters and different nip loads were used to determine their effect on the nipinduced tension. In all cases, the tension immediately began to increase from its nominal level when rolling began. After approximately 10 cm of rolling, the tension reached a saturation value (the woundin tension), beyond which additional rolling had no effect on the tension. For the two rollers tested, the wound-in tension increased with increasing nip load as in Pfeiffer’s experiments. The increase in woundin tension with decreasing roll diameter seen by Pfeiffer was not seen in these experiments. If there is a tension change in the strip as the freely rotating roller passes over it, it must be caused by frictional forces between the strip and the underlying material. With this observation, Good and Wu (1993) modeled the system using finite elements with gap elements simulating the frictional interface between the aluminum strip and the steel foundation. A Hertzian parabolic pressure distribution was quasi-statically moved across the top of the finite-element mesh to simulate the nip load. To simulate the clamped and free edges of the strip, one vertical boundary of the mesh was constrained with spring elements while the other was free. In this analysis, the Poisson effect was determined to be the mechanism causing nip-induced tension. As the roller passes over the strip and compresses it vertically, the Poisson effect causes elongation (positive strains) of the strip at the foundation interface in both the length and width directions. The elongation strain is largest at a point directly under the roller and decreases away from this point. As this strain profile moves with the roller, material wants to advance in front of the roller and contract behind it. This can be readily seen when rolling dough. In this case, however, the material behind the roller is constrained by the clamp holding one end to the foundation and the friction between the foundation and the rolled material under the nip roller. Because of this, the rolled material cannot contract between the clamp and the roller as it would like and an increase in tension results.
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FIGURE 40.11 A wrap outlined in its initial state gets compressed by µr and stretched by ∆ut as more wraps are added to the roll.
The finite-element model was only able to accurately predict the nip-induced tension during the first few centimeters of roller travel. In this region, the stress increases nearly linearly with roller displacement. The finite-element model did an excellent job of predicting the slope of this line for the two cases studied. However, to get such good agreement, the authors had to use a coefficient of friction between the strip and foundation of 2, much higher than the value of 0.085 measured using standard ASTM testing methods. This was justified by noting that there is a high local contact pressure between the strip and the foundation directly under the roller. This high pressure, along with surface asperities, can cause a dramatic increase in the coefficient of friction (Bayer et al., 1969). The saturated tension values (wound-in tension) were accurately predicted using the measured coefficient of friction. The stress was calculated by simply multiplying this coefficient of friction by the nip load and dividing by the thickness of the strip. This method will obviously predict the same wound-in tension for all nip roller diameters. However, as noted previously, the experiments performed by Good and Wu, as opposed to those done by Pfeiffer, did not show a clear dependence of wound-in tension on nip roller diameter. Experiments on actual wound rolls were conducted by Gueldenberg and Welp (1999). In these experiments, a nip-driven configuration was used to provide a constant axial material velocity. Various papers were studied during winding. A rotary encoder was used in conjunction with an ink-jet printing head and digital camera to collect data from the wound roll. Each time the wound roll made one revolution, the printing head marked a spot on the incoming material. A digital image of the nip region was taken as each marked point passed through the nip. From these images, the tangential strain in each sheet was calculated. The tangential strain in a given wrap in a wound roll depends on the number of previously and subsequently wrapped layers and consists of two parts. The first is due to the radial displacement of the layer and the second is due to the tangential displacement. This is shown schematically in Figure 40.11. The original length of the layer (when it was initially wrapped) is 2πR. The present length of the layer is (2π + ∆ut /R) (R + ur), where ur is positive out from the center of the wound roll. Neglecting the term containing ∆utur , the tangential strain is:
εt =
∆ut + 2πur 2πR
(40.44)
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800
Previously Wrapped Layers
700
Tangential Displacement
1569
3 6 12 18 27 51 96
600
500
400
300
200
100
0 0
2
4 6 Subsequently Wrapped Layers
8
FIGURE 40.12 Experimental results showing the tangential displacement at various stages of winding as a function of subsequently wrapped layers.
In the experiments, ur is found by summing the change of thickness of all layers contained within the region of interest. The tangential displacement is measured from the separation of adjacent ink dots, which have also been compressed radially from the added wraps; see Figure 40.11. Figure 40.9 shows the layer displacements of the outer 300 layers of a wound roll. The dark ink line (a) consists of the ink dots marked during each rotation. The dashed line (b) is the reference line that denotes no tangential displacement. This line is not radial because of the specific experimental setup used. The solid lines (c) simulate the J-lines that would have appeared from lines drawn at three different times on the wound roll. The J-lines are different from the ink line because the J-line only measures displacement of the layers after it is marked. The only point in common between the J-lines and the ink line will be the end point of the J-line. This point is on the layer that was the outermost when the J-line was drawn. The tangential displacement ∆ut is the derivative of the ink line and is positive in the outer region of the wound roll. It grows from zero away from the outer edge and reaches a steady value before decreasing to zero at the core. The dependence of ∆ut on the number of previously wrapped layers is shown in Figure 40.12. In layers near the core, ∆ut is much smaller than in layers away from the core. If wrapped under constant tension, beyond about 50 wraps from the core, ∆ut is nearly independent of the number of previously wrapped layers. Thus, the tangential strain and stress caused by the tangential displacement are positive in this region. However, the tangential strain and stress caused by the radial displacement are negative throughout the roll. The magnitude of this portion of the tangential strain increases in from the edge of the roll, reaches a maximum, and decays to zero at the rigid core. This is expected as the roll is compressed further with each tensioned wrap added. This phenomenon has been modeled by Hakiel (1987) and Benson (1995). Thus, in the outer region of the wound roll, competing factors exist. In the experiments discussed here, it was found that the tangential stress increased for approximately the first 10 layers. The tangential stress then slowly decreased, due to the radial compression, falling below the stress in the incoming material beyond approximately 100 layers in from the edge of the roll. The experiments conducted by Gueldenberg and Welp (1999) clearly show how both radial and circumferential motions of the layers influence the stress in the wound roll. As stated previously, the
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radial compression of the roll has been modeled by Hakiel (1987) and Benson (1995). These models do an excellent job of predicting the interfacial pressure between two layers in the roll. However, the change in tension caused by tangential displacement in a wound roll has not, to the authors’ knowledge, been modeled. Good and Wu (1993) modeled a single, flat layer to better understand the importance of the Poisson effect on the problem. However, the actual system is much more complicated, with many interfaces and other phenomena involved. As noted by Good and Wu, frictional forces between the layers must play an important role in the analysis. However, these effects have yet to be included when attempting to predict the stress in a wound roll.
40.9 Web Tenting Caused by High Asperities In many imaging and data storage applications, a web is drawn around a circular cylinder or along a flat platen during processing. This includes magnetic tape passing over read/write head, paper on a xerographic photoreceptor during toner transfer, and photographic film during exposure to light. Such processes often suffer from severe quality degradation if the web is not flush to the intended surface. Take, for example, modern tape recorders. Wallace (1951) showed that the signal loss in magnetic recording is proportional to the spacing between the magnetic layer and the recording head, and inversely proportional to the wavelength of the recorded signal. Thus, in a typical high-density tape drive, there will be a 99% loss of signal strength at 1 micron spacing compared to what would have been achieved if the tape and head were in contact. Baker (1977) predicts the size of the “drop-out” area that is affected by an asperity in the interface of a digital tape recorder. A foreign particle lodged between a sheet of copier paper and a photoreceptor can also produce a drop-out area where the toner fails to be transferred from the photoreceptor to the paper. It is thus important to understand how a high asperity between a flexible web and a rigid foundation affects the conformity of the web to the foundation. Figure 40.13, from Benson (1991), shows the basic geometry. A flexible, elastic plate with Young’s modulus E, and Poisson ratio v is held up at its center by a “tentpole” of height c. (These variables are not depicted in the figure.) This causes a “tent” to form before the plate regains contact with the foundation. The contacting arc is assumed to be an ellipse with principal dimensions 2a and 2b. The plate carries a force per unit area of p, which could be due to weight or the “belt-wrap” pressure of holding a web under tension around a curved surface. (See ahead to Equation 40.57). Because this pressure cannot be supported by the foundation in the regions where there is a gap, a concentrated force F must be born at the tentpole. Less intuitive is the fact that there must also be a force per unit length, Q(θ), along the contact perimeter. Here, θ is the angle around the perimeter (not shown in the figure). Arbitrarily set θ = 0 from the point where the tent radius is length a. The elastic plate has in-plane stress resultants Tx and Ty . Also allow for a spring-like pressure between the plate and foundation of magnitude kw. Here, k is the “foundation stiffness” with units of pressure per unit distance, and w is the gap between the plate and the foundation. The foundation stiffness k can arise from such phenomena as electrostatic attraction between the plate and foundation, and also from shell effects caused by wrapping the plate around a curved surface. (See, again, Equation 40.57). P F k a
Q b
Ty
Tx
FIGURE 40.13 Geometry of a tented web. (From Benson, R.C. (1991), Plate tenting with a one-sided constraint, J. Appl. Mech., 58(2), 484-492. With permission.)
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Following Benson (1991), an approximate solution for the tented plate is found through the use of two assumed shape functions. The first is a contour function. It is assumed that the plate has a gap from the foundation that is constant along ellipses concentric to the contact ellipse. Thus, the contour indicator
( ) ( ) 2
2
s= x a + y b
(40.45)
ranges from s = 0 at the tentpole to s = 1 along the contacting arc. Here, x and y are the in-plane coordinates of the plate. They point, respectively, in the direction of the stress resultant arrows Tx and Ty shown in Figure 40.13. The gap at contour s is given by a second assumed shape function:
[
( )]
w = c 1 − s 2 + 2s ln s
(40.46)
where “ln” is the natural log function. The tentpole height c is known; thus, it remains to compute the principal diameters of the tent, 2a and 2b. Then, from Equations 40.45 and 40.46, the entire tent profile will be known. Using a Rayleigh-Ritz energy minimization technique (Shames and Dym, 1985), Benson (1991) calculated the most accurate choices for a and b. After some algebra, the solution can be presented in nondimensional form. First, define reference values for the tentpole force Fref , edge load Qref , in-plane stress resultants Tref , foundation stiffness kref , and lengths rref :
( )
Fref = 4 π Dcp
12
(
, Qref = Dcp 3 4
( ) (43c ),
kref = 180 p
)
14
(
, Tref = 9 Dp c
(
rref = 64Dc p
)
12
,
)
(40.47)
14
Here,
( ) [12(1 − v )]
D = Eh 3
2
(40.48)
is the bending rigidity of the plate.* From these reference values, the following nondimensional analogs are defined for the variables of the problem:
F = F Fref , Q = Q Qref , Tx = Tx Tref , Ty = Ty Tref k = k kref , a = a rref , b = b rref
(40.49)
Solution of the next two equations gives the major axes of the contact ellipse:
( )
γ2 = a b
2
( )
2 = 1 + 2Txa 2 + Tya 2
{( )[ ( )
a 4 = 3 8 1+ 2 3 γ 2 + γ 4
1 2
− Tya
]} (1 + k )
(40.50)
(40.51)
*The bending rigidity was also given in Equation 40.15, with d representing the thickness of the plate. Here, h denotes the thickness of the plate.
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and then the tentpole force and contact perimeter load can be found from the following formulae:
F=
T b T a 2kab ab b a 1 + 3+ 3+ + x + y + 3 4a 6ab a b 3 4b
2 2 cos θ sin θ Q θ = 2 + 2 a b
()
2 2 cos θ + sin θ a b
(40.52)
32
(40.53)
The values in Equations 40.50 through 40.53 are all nondimensional. Dimensional counterparts are found from Equations 40.47 through 40.49. This gives a general, albeit approximate, solution to the tented web problem. The accuracy of the solution is discussed in detail by Benson (1991). As a rule-of-thumb, results will be acceptable when the maximum deflection is less than one plate thickness. Figure 40.14 shows how tentpole force predictions compared with experiments made by Ono et al. (1980) and Benson (1991). Specifications are presented in Table 40.1. Cases A and B are taken from Ono (1980), and are representative of magnetic tape recording systems. Cases C and D are taken from Benson (1991), and are for a relatively thick polycarbonate plate wrapped around a rigid cylinder. (Cases E and F are examined later.) The match to experiment in Cases A and B is quite good, even beyond one plate thickness. The match to experiment in Cases C and D is also good, although a deviation starts to occur after one plate thickness of deflection. An even better match to the experimental data of Case C is made by Rongen (1994), who utilized a finite-element solution of the nonlinear Donnell-Mushtari-Vlasov shell theory to extend the range of the simple closed-form solution presented here. His graph for Case C is also presented in Figure 40.14.
12 0.03 0.025
"Tentpole" Force (N)
10
0.02 Case A Theory (Benson) Experiment
0.015 0.01
8
Case B Theory (Benson) Experiment
0.005 0.02
0.04
0.06
0.08
0.1
6
Case C Theory (Benson) Theory (Rongen) Experiment
4
Case D Theory (Benson) Experiment
2
0.25
0.5
0.75
1
1.25
1.5
Penetration (mm) FIGURE 40.14
Comparison of theoretical and experimental force-vs.-penetration graphs for tented webs.
1.75
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TABLE 40.1 Variable E ν h Tx Ty p k
Units 2
GN/m — µm N/m N/m N/m2 MN/m3
Case A
Case B
Case C
Case D
Case E
Case F
6.22 0.3 30 39.2 0 0 82.0
4.60 0.3 40 39.2 0 0 80.9
2.4 0.3 760 676 0 563 1.39
2.4 0.3 760 939 0 783 1.39
3.45 0.25 25 100 0 4000 147
3.45 0.25 14 157 0 523 0. 57
TABLE 40.2 Load/Deflection Results for Case E Variable
Unitsa
c a b γ F Qmax Qmin Qtotal W
µm mm mm — mN N/m N/m mN mN
a
← Results for Different Tentpole Heights → 1.0 0.536 0.515 1.04 1.89 0.560 0.499 1.75 3.47
5.0 0.813 0.750 1.08 4.69 0.909 0.713 3.99 7.66
10.0 0.973 0.872 1.12 7.17 1.155 0.831 5.78 10.67
25.0 1.225 1.048 1.17 13.27 1.666 1.042 9.73 16.13
Please note that “mN” denotes milli-Newtons, not meter-Newtons.
The specifications of Case E of Table 40.1 will next be used to demonstrate the sensitivity of the tented plate to the size of the asperity in the interface. Table 40.2 shows how the tented region grows as larger tentpoles are encountered: c = 1, 5, 10, and 25 µm. Note in Equation 40.50 that γ is the “aspect ratio” for the tented web. A value of γ = 1 denotes a perfectly circular tent. Also shown in Table 40.2 are the resultant loads at the tentpole, F, the maximum and minimum values of the line load on the contact perimeter:
()
( )
Qmax = Q 0 , Qmin = Q π 2
(40.54)
the resultant force around the perimeter:
∫ Q(l)dl
(40.55)
W = pA = πabp
(40.56)
Qtotal =
s =1
and the total weight lifted by the tent:
In the last two equations, dl is an element of arclength on the curve s = 1, and A is the area inside of this ellipse. A notable feature from Table 40.2 is the very large ratio of the lateral tent dimensions to the tentpole height. Consider the last column of the table, which is for a center deflection equal to the plate thickness, c = h = 25 µm. The ratio of a to c is approximately 50 to 1. The ratio is even greater for smaller tentpole heights. Thus, even a very small asperity in the interface can cause a very large region of the web to lose
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TAPE
h c
TENTPOLE DRUM
w
u
d
DATUM
x
R
CENTERLINE
FIGURE 40.15 Cross-section of a tented web wrapped around a cylinder. (From Benson, R.C., Smith, D.P., Madsen, D.M., and Fung, S. (1992), Magnetic tape tenting: modeling and experiments, Adv. Information Storage Systems, 4, 63-72, ASME Press. With permission.)
contact with the foundation. As noted above, this can lead to drop-outs, loss of signal, and defocusing, depending on the application. A potentially more serious problem is the load redistribution that occurs in the interface. A plate that lies flush with the foundation will have a uniformly distributed pressure p in the interface. For Case E of Tables 40.1 and 40.2 this pressure is p = 4000 N/m2. A tented web, however, will carry no load in the gapped region, and will, instead, have a concentrated force F at the center and a line load on the contact perimeter with resultant Qtotal. These more concentrated loads will lead to more severe wear and debris problems than if a flush contact had been maintained. Further, the combined value of F + Qtotal will be greater than the weight of the lifted tent, W. This overloading is due to combined effects from the inplane tension, Tx and Ty , and the spring stiffness k. Consider again the last column in Table 40.2. The tentpole force is 82% of the lifted weight, and the contact perimeter resultant is 60% of the lifted weight. Thus, there is 42% more load being carried at the center and perimeter of the tent, than if the same area had lain flush with the foundation. In many applications, tenting occurs in a web that is drawn under uniaxial tension, Tx > 0, Ty = 0 around a cylinder of radius R. Figure 40.15 shows a typical cross-section. In this case, the “belt wrap” pressure p and foundation stiffness k are found from classical elastic shell theory to be:
[ ( )]
p = Tx R , k = Eh R2 1 − v 2
(40.57)
Substituting these results into the preceding equations allows for a somewhat simpler solution for the tent dimensions and loading. First, the aspect ratio for the ellipsoidal tent, γ, is computed from the following implicit equation:
(γ − 1)
(5 18)(T Rh D) (c h) = + (2 3)γ + 1 15(T Rh D ) + 43(c h) 4
γ4
2
2
x
2
(40.58)
x
Note that the right-hand side of Equation 40.58 will be a known nondimensional quantity based on the loading and geometry of the web/cylinder system. Once γ has been computed, the tent dimensions are found from the following expression:
( )
2
(
)(
)
a 2 = γb = 36 D Tx γ 4 − 1
(40.59)
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The tented profile, w(x,y), is then computed from Equations 40.45 and 40.46. For comparison with experiment, however, it is usually necessary to convert from the displacement measured from the curved cylindrical surface, w, to one measured from a horizontal datum. See, again, Figure 40.15. For a large radius cylinder (i.e., R >> a), the following expression can be used:
( ) ( )
( )
u x , y = w x , y + h + d − x 2 2R
(40.60)
where d is the offset of the datum as measured below the tentpole. The tentpole force F and contact perimeter load Q(θ) are, respectively: 2 D F 2 c 9γ 4 + 2γ 2 − 3 γ 4 − 1 172 D c + + = 48 T Rh (40.61) πTx h 27 h γ γ 4 − 1 γ 5 Tx Rh h x
(
)
()
Qθ
(Dc a ) 3
cos2 θ + γ 4 sin2 θ = 16 2 2 2 cos θ + γ sin θ
32
(40.62)
Figure 40.16 shows how the displacements predicted by the present model correlate with an optical interferometric measurement (Benson et al., 1992). The web was a polyethylene terephthalate (PET) film drawn over a large radius drum of R = 0.3 m. An asperity of height c = 1.15 µm produced the tent. The other system specifications for this experiment are given by Case F of Table 40.1. Figure 40.16 shows the analytically predicted tent as a gray surface. The dots in Figure 40.16 are taken from the experimental measurement. One line of dots extends in the “running direction” of the web (i.e., along the circumference
m) (m ion 0.4 t c ire
D o ss Cr 0.2
0
s) (micron
1
Height
0.5
0
-0.5 -0.4
Ru -0.2 nn ing
FIGURE 40.16
Di
0 rec tio 0.2 n( mm )
0.4
Comparison to experiment for tented web geometry.
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R
∇
L/R
Ψ
F Ψ*
L
θ*
F
R
θ h
H Φ
FIGURE 40.17 Geometry of a curled sheet on first contact with a frictional surface (top) or wedged in a frictional channel (bottom).
of the underlying drum), and the other line of dots extends in the “cross-direction” of the web (i.e., along the axis of the drum). The tentpole is at the origin of Figure 40.16. For this figure, the tentpole height used in the model was established by the experimentally measured value. The correlation outward from the tentpole is excellent. The upward turn of the experimental data near 0.6 mm in the cross-direction in Figure 40.16 is due to the presence of a nearby asperity (i.e., a second tentpole). The running-direction discrepancy between model and experiment in Figure 40.16 appears to be due to a small 0.5 milliradian rotation of the interferometric measurement from a true horizontal datum.
40.10 Mechanisms that Cause a Sheet to Jam, Stall, or Roll Over in a Channel In many office machines, it is necessary to push the leading edge of a flexible sheet along a frictional surface. Whether the sheet sticks to or slides along the surface will affect the processing of the sheet. Take, for example, paper in a copier. In the process of making a copy, an individual sheet can be fed as a cantilevered beam against a photoreceptor, fuser rolls, and various guiding surfaces. The process grows even more complicated if the sheet is being imaged in color or if two-sided copying is being performed. Further, modern copiers all have two paper paths: one for the imaged sheet and one for the automatic handling of originals. This chapter examines how the elastic flexibility of the sheet, combined with the frictional rubbing against a guiding surface, can lead the sheet to “jam,” “stall,” or “roll-over” during processing. The upper drawing of Figure 40.17 shows a curved sheet being fed against a frictional surface, inclined at an angle ψ* with respect to the vertical. The sheet, which may be curled, has a radius R, thickness h, elastic Young’s modulus E, and Poisson ratio v. On first contact, the sheet has extended a length L past the driving rollers. The coefficient of Coulomb friction between the sheet and wall is µ. It is desired to know whether the sheet will: (1) slide up the surface, (2) stick to the surface, or (3) slide down the surface. That is determined by assuming that the sheet sticks to the wall, and then computing the magnitude ∆F and angle ψ of the small force that develops after a small additional length ∆L is pushed past the feeding rollers. Stick-or-slip is determined by the following frictional limits:
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() < arctan(µ ) ⇒ stick to the wall
1577
ψ − ψ ∗ > arctan µ ⇒ slide up the wall
() −arctan(µ ) > ψ − ψ
− arctan µ < ψ − ψ ∗
(40.63)
⇒ slide down the wall
∗
As the wall angle ψ* and friction angle arctan(µ) are both known, the problem is one of computing the reaction angle ψ. Benson (1982) uses the theory of the elastica (Frisch-Fay, 1962) to compute:
( ) ( ) ( )[ ( )] ( ) ( )[ ( )]
L R sin L R − 2 cos L R 1 − cos L R ≈ 5L ψ = arctan 8R cos L R + sin L R 1 − 2 cos L R
(40.64)
The approximation given above is very accurate for absolute values up to ψ = π/2 radians = 90°, so the simpler value from Equation 40.64 can be used in Equation 40.63 for most any conceivable sheet-handling application. The lower drawing of Figure 40.17 shows a second, common sheet-handling geometry involving frictional sliding of the leading edge. A curled sheet of radius R is pushed through a channel, for which the lower surface is flat and the upper surface may be curved. At any point along the channel, there will be a known channel height H and angle θ*, as depicted in the figure. As the leading edge of the sheet drags along the top frictional surface, it will generate a force with magnitude F and direction θ. This angle is known through the inclination of the surface and the coefficient of friction between the sheet and wall, µ:
()
θ = θ ∗ + arctan µ
(40.65)
Using the theory of the elastica (Frisch-Fay, 1962), Benson (1981) determined the reaction force through an implicit evaluation of the following elliptic integral:
H = R
∫
φ
0
() 2FR [( ) (bD)][sin(φ + θ) − sin(θ)] sin φ dφ
12
(40.66)
2
In the preceding, b is the width of the sheet (not depicted in Figure 40.17) and Φ is the slope angle of the sheet at its leading edge, given by:
[( ) (2FR )] + sin(θ) − θ
Φ = arcsin bD
2
(40.67)
where D is the bending rigidity of the sheet. Recall Equation 40.48. The results of Equation 40.66 are presented in Figure 40.18 for different values of:
F=
FR2 bD
(40.68)
which may be thought of as a nondimensional reaction force between the sheet and upper wall. Figure 40.18 is important for determining how the sheet will progress through the channel, and with
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1.5 Jam ope vel En
Channel Height / Sheet Radius of Curvature, H/R
Modern Tribology Handbook
1.0
Nondimensional Reaction Force Contours, (FR2)/(bD)
.6
0.5 .7 .8 .9 1.0
10
1.2 1.4
0
0
20
1.6 2.0 2.4
40
20 3
4 6
40
60
80
100
Reaction Angle, θ (degrees)
FIGURE 40.18 A graph for calculating the magnitude of the lead-edge reaction force retarding sheet motion through a frictional channel.
what amount of resistance. Recall that the reaction angle θ and height-to-radius ratio, H/R, are both known. Thus, from Figure 40.18 and Equation 40.68, one can determine what the magnitude of the reaction force F will be. The horizontal component of this force, Fsin(θ), resists the sheet motion through the channel. The vertical component of this force, Fcos(θ), leads to a wedging action in the channel. The combination of resistance and wedging can lead to three distinctly different types of sheet transport failure: namely, jam, stall, and roll-over. Jam describes what happens when the coordinate pair falls to the upper right of the “Jam Envelope” in Figure 40.18. In this case, the friction is sufficient to arrest the forward motion of the sheet’s leading edge. More material can be pushed into the channel through the drive roller, but the tip of the sheet will not progress. This is akin to the self-locking that occurs with a doorstop, although in this case the “doorstop” is a flexible beam. Pushing harder with the drive roller will not correct the problem — the sheet will simply jam faster. A second question arising from Figure 40.18 is how to interpret results when the coordinate pair lies to the lower left of the “Jam Envelope.” A close examination of the figure shows that every coordinate – pair admits two values for the nondimensional friction force F. For example, near H/R = 0.5 and θ = 20°, there is one solution with (FR2)/(bD) = 0.8, and another with (FR2)/(bD) = 15.2. Clearly, the latter sheet is receiving 19 times more drag force than the former sheet. Figure 40.19 depicts these two solutions for the case of a parallel channel, θ* = 0°, with a friction coefficient of µ = arctan (20°) = 0.346. The solution
200
{
{
µ = 0.346
FR2 = 0.81, Mode 1 bD 15.23, Mode 2
Mode 1 Mode 2
FIGURE 40.19
Depiction of two admissible modes of sheet transport through a parallel, frictional channel.
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labeled “Mode 1” in Figure 40.19 is to be preferred to that labeled “Mode 2.” Not only is the force of resistance much smaller, but the sheet lies flatter in the channel with its leading edge the furthest progressed through the channel. The Mode 2 beam is tightly wedged in the channel, and the furthest progressed point in the channel is not the leading edge, but rather a “knuckle” that is some distance back from the leading edge. This can present problems downstream in the channel, for example, in the approach to a pair of counter-rotating fuser rolls. The designer expects the leading edge of the sheet to enter the fuser first, but it may happen that the knuckle is grabbed, causing the sheet to be folded or mangled. Roll-over is used to describe the phenomenon of a sheet switching from a desired Mode 1 configuration to an undesired Mode 2 configuration. This can happen when the leading edge of the sheet encounters an anomalous rough spot on a channel wall. The sheet may temporarily jam, and then, as additional material is fed in at the drive roller, the leading edge sticks to the guide wall with increasing slope angle. If the sheet eventually breaks free of the rough spot, it may continue its travel through the channel in a Mode 2 configuration. Stall is used to describe what can happen when a sheet is pushed through the channel in a Mode 2 configuration. The drive roller may not be able to exert sufficient force to overcome the unexpectedly high drag force. (Recall the example of Figure 40.19.) In this case, the sheet will stall in the channel as the drive roller continues to turn. Unlike the case of the jammed sheet, which is entirely a problem of geometry, the stalled sheet can be made to move again with the application of a larger drive force. From Figure 40.18, one can extract design guidelines that help prevent jam, stall, and roll-over. The objective is to be as far from the “Jam Envelope” as possible (obviously to the lower left). That is achieved by: Reducing the steepness of the upper wall: Reducing the friction with the upper wall: Flattening the curvature of the sheet: Narrowing the channel height:
θ*↓ µ↓ R↑ H↓
The two examples of sheet stick and slip presented in this section are for commonly occurring geometries. A new analysis would have to be made if the boundary conditions or systems specifications changed; however, the same basic phenomena of jam, stall, and roll-over would still apply. It should also be noted that these analyses are for quasi-static motion of the sheet, for which inertial loads and impulse loads from striking a surface can be ignored. The dynamic sheet-feeding problem has been studied in depth by Stolte (1992) and Stolte and Benson (1992, 1993).
40.11 Micro-slip of Elastic Belts Many machines employ elastic webs running over rollers. Frequently, as in a belt-drive system, a moment is imparted to the roller with an equilibrating tension change imparted to the web. Figure 40.6 from Smith (1998) shows a typical data-cartridge geometry. There are two web systems: a reel-to-reel path for the transport of the magnetic tape, and a closed belt-loop that drives the tape. Figure 40.20 diagrams the simple two-roller geometry studied by Johnson (1985). The belt in the lower half of the figure is at tension T1, and moves at velocity V1. It wraps around the left-side roller, which is turning with angular velocity Ω1. A moment M is imparted to the roller. When the belt emerges at the top half of the figure, it has a higher tension T2 and faster speed V2. The belt then wraps around the right-side roller, which turns with angular velocity Ω2, and has a moment M imparted to it. And the loop repeats. It is assumed that all effects are constant across the width of the belt. Because the belt changes tension during its contact with the rollers, it must undergo a strain change in the “running” direction. Conversely, the rollers are rigid. Thus, it is impossible for the belt to exactly match the constant surface speed of the roller at all locations. In addition to the stick zone, there must be a slip zone where the belt overdrives the roller if a tension increase is to be achieved, or underdrives the roller if a tension decrease is to be achieved. This creates friction in the slip zone.
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Sl
T2
S
T2
=v 2 rc v ka tic
v>v 1 rc a ip
High Tension Side φ
Ω1
M
Stick a
Ω2
M
φ
T1
v
=v 1
Low Tension Side
2
rc v
T1
a Slip
rc
v>
FIGURE 40.20 Geometry showing roller/belt zones of stick and slip. (From Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press. With permission.)
First examine the belt/roller system at the left in Figure 40.20. The belt enters the roller at tension T1 and immediately sticks to the roller. This creates a pressure in the interface of the stick zone of an amount:
p1 =
T1 bR
(40.69)
Here, b is the width of the belt (not shown in Figure 40.20). As the belt is sticking to the roller, there is no tangential frictional stress in the interface. However, at some angle φ back from the exit, the belt begins to slip relative to the roller. The local tension T(s) will vary with the arclength s, which is measured from the start of the slip zone. The interfacial pressure will be:
T s ( ) bR( )
ps =
(40.70)
which yields a frictional drag stress on the web of an amount:
()
()
q s = µp s =
()
µT s
(40.71)
bR
Here, µ is the dynamic coefficient of friction between the belt and roller. It is assumed that a Coulomb friction law applies. The rate of increase of tension is proportional to this drag pressure:
()
µT s dT = bq s = bµp s = ds R
()
()
(40.72)
The solution to this simple differential equation is:
()
(
T s = T1 exp µs R
)
(40.73)
where “exp” is the function of raising e ≈ 2.718282 to the indicated power. It will be observed that T(0) = T1, as is required at the transition from the stick to the slip zone.
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The next question is: what is the extent of the slip zone, φ? That is found by setting T(s) in Equation 40.73 equal to the exiting value of T2 when s is equal to the exiting value of Rφ:
( )
( )
T Rφ = T1 exp µφ = T2 ⇒ φ =
(
ln T2 T1 µ
)
(40.74)
where “ln” is the natural logarithm function. Thus, the belt sticks to the roller for an angle (in radians) of θ = π – φ, and overdrives the roller in a slip zone of angle φ. Obviously, if φ is computed to be greater than the total wrap angle (π radians = 180° for the present example), then gross slippage will occur between the belt and roller. The wearing of the web and roller surfaces occurs from the micro-slip or “creep” in the slip zone. The difference in tension from the low-tension side to the high-tension side of the roller is used to find the moment acting on the roller:
(
M = R T2 − T1
)
(40.75)
A similar tension change takes place at the right-side roller, only this time it is to reduce the tension from T2 to T1. For a same-sized roller of radius R, the extent of the slip zone will again be φ, as given in Equation 40.74. The declining tension and interfacial pressure in the slip zone can be found from:
()
(
)
()
T s = T2 exp −µs R = bR p s
(40.76)
where the arclength s is again measured from the transition point between stick and slip. The pressure in the stick zone of the right-side roller will be:
p2 =
T2 bR
(40.77)
Next, one can focus on velocity ratios. Because of its increased strain, the velocity of the belt on the high-tension side, V2, will be faster than the velocity of the belt on the low-tension side, V1. The ratio will be proportional to the ratio of strains, which, in turn, is proportional to the ratio of tensions:
V2 T2 = V1 T1
(40.78)
The angular velocities of the left-side and right-side rollers are determined by noting that they stick, respectively, to the slack-side and tight-side belt segments:
Ω1 = RV1 and Ω2 = RV2
(40.79)
This present example is relatively simple in its geometry, but nevertheless reveals basic features of web/roller interaction. In a recent paper, Smith (1998) reports on experiments performed on rubbery belts under considerable tension. It is typical of the drive belts shown in Figure 40.6. By looking through a glass cylinder at the surface of the belt, which is textured, Smith was able to show the transition from low-tension to high-tension conditions, and vice versa, and he measured the cross-width dimensional change that occurs from Poisson contraction. Figure 40.21, based on Smith (1998), schematically shows how the belt will change its width while undergoing a tension change. Also embedded in Figure 40.21 is
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High Tension Side Smith’s photo of high strain belt
Belt creeps past roller
SLIP
Belt adheres to roller
S TIC K
Smith’s photo of low strain belt
Low Tension Side
FIGURE 40.21
Depiction of roller/belt stick and slip with Poisson contraction.
a pair of photographs taken by Smith that show a textured strip of the belt in its low-strain state and in its high-strain state. Each photograph shows a set of six microcylinder bumps running across the belt. In the unstressed state, these bumps had a diameter of 0.077 mm and were separated by a center-tocenter distance of 0.160 mm. It should be noted that even the “low-strain” belt in Smith’s experiment is highly deformed. Due to Poisson contraction, its width is approximately 52% of what it had been in the undeformed state. The “high-strain” belt in Smith’s experiment has approximately 42% of its original unstressed width. Note, as a rule, that whether the tension change is one of increase or decrease: The web sticks on entry to a roller and slips on exit. This is an essential factor in many web-handling applications. For example, when a pivoting roller is used to laterally steer a moving web, it is known that the web will stick on entry to a “downstream” roller, and then slip on exit for what has become the “upstream” roller for the next web span. The lateral dynamics of webs will not be treated here, but readers are referred to detailed studies by Shelton and Reid (1971a,b), Sievers (1988), Soong and Li (1979), Young et al. (1989a,b, 1993), and, in general, to the proceedings of the International Conference on Web Handling (see Chapter 40.1).
40.12 Transport of Sheets Through Roller/Roller and Roller/Platen Nips Figure 40.22, based on a calculation made by Stack (1995), shows how rollers operating in pairs, or pressed against a platen, can be used to move webs and sheets. The rollers are often made of an easily compressed elastic material in order to achieve a large “footprint” of contact with the sheet. The question then arises as to how fast the sheet will move through the contact “nip.” This is not a simple question to answer, as the nominal surface speed of the roller will be altered in the nip because of the circumferential straining of the roller. Surprisingly, the sheet may slow down or speed up, depending on the elastic properties of the roller(s). This chapter lays out some of the basic design issues concerning sheet transport through nips. As the rollers used in sheet transport are often highly deformed, it is difficult to produce
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Hub Rotation
Hub Rotation
FIGURE 40.22 Sheet transport through a roller/roller nip. (From Stack, K.D. (1995), A Nonlinear Finite Element Model of Axial Variation in Nip Mechanics with Applications to Conical Rollers, Ph.D. thesis, University of Rochester, New York.)
closed-form mathematical expressions, as has been done in the other sections of this chapter. Instead, one relies on numerical results, produced through nonlinear finite-element modeling and presented in two recent doctoral dissertations by Diehl (1995) and Stack (1995). The most important issue in nip transport is to know if the roller/roller or roller/platen geometry will lead to an “overdrive” or “underdrive” condition in the nip. If the nominal surface velocity of the undeformed roller is V0 and the velocity in the nip where the sheet sticks to the roller(s) is V, then the following “speed ratio” definitions are made:
V > 1 ⇒ Overdrive, V0
V < 1 ⇒ Underdrive V0
(40.80)
To explore the origins of overdrive and underdrive, first consider the case of a non-spinning roller pressed against a rigid surface. Figure 40.23 from Stack (1995) shows the deformation of two rollers that are identical in every respect, except for the Poisson ratio, v, of the elastic material. Stack’s two-dimensional nonlinear finite element model was used to analyze this nip problem. The contours in Figure 40.23 show how much displacement has taken place in the horizontal, or “transport,” direction. In the example at the top of Figure 40.23, the Poisson ratio is v = 0.45, which is indicative of a nearly incompressible material. As the roller is pressed against the platen, the nearly incompressible roller must swell circumferentially to help accommodate the radial straining. By contrast, in the example at the bottom of Figure 40.23, the Poisson ratio is v = 0. In this case, the radial straining, caused by pressing the roller against the floor, can be accommodated without any circumferential swelling. In fact, the
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FIGURE 40.23 Finite-element calculations of roller displacements leading to sheet transport overdrive (top) and underdrive (bottom). (From Stack, K.D. (1995), A Nonlinear Finite Element Model of Axial Variation in Nip Mechanics with Applications to Conical Rollers, Ph.D. thesis, University of Rochester, New York.)
circumferential strain in the nip is slightly compressive. This perhaps-unexpected contraction is a geometrical consequence of having pressed the circular surface of the roller against the flat surface of the platen. Johnson (1985) discusses the inward displacement of material in the case of a circular punch pressed against a half-space. The reverse of the patterns in Figures 40.23 (top) and 40.23 (bottom) gives quick evidence that the material particles in the respective nips have displaced in opposite directions. If the v = 0 roller of Figure 40.23 is used to transport a sheet, an underdrive will result. This can be appreciated in the following intuitive way. Consider the travel of a material particle on the surface of the roller from the time it first enters the nip to the time it exits the nip. The straight-line chord of contact in Figure 40.23 (bottom) is shorter than the circular arc that a material particle would have traveled had it not been compressed in the nip. The time of travel in each case is the same, so it can be concluded that the material particle on the roller’s surface slows down as it passes through the nip.
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This intuitive reasoning breaks down if the Poisson ratio of the roller is not zero. In this case, the compression of the roller against the platen is accompanied by circumferential swelling of the roller, and one can no longer approximate the width of the contact footprint as the straight-line chord cutting across the roller. The footprint will be wider than that. Indeed, the contact arc can actually swell to the point where it is longer than the original circumferential length in the undeformed roller. Such is the case for the v = 0.45 geometry of Figure 40.23 (top). In this case, the speed of a material particle through the nip is faster than along the undeformed surface of the roller, and an overdrive situation exists. Now turn to the more complicated case in which there is a sheet in a roller/platen interface. In an example from Stack (1995), an elastic roller with shear modulus 0.0689 MPa (10.0 psi) is used to transport the sheet. The outer radius of the roller is 25.4 mm (1.00 in.), and the radius of the rigid inner core is 6.35 mm (0.25 in.). The center of the rigid core is 20.3 mm (0.80 in.) away from the floor for a 20% “engagement.” The coefficient of friction between the roller and sheet is 1.0, and the coefficient of friction between the sheet and floor is zero. The wire-frame rendering of this roller was used to create Figure 40.22. Table 40.3, taken from Stack (1995), shows how the speed ratio will vary as a function of the Poisson ratio of the roller. Stack’s two-dimensional finite element model was used to make the calculations. It was found that the sheet speed matches the roller speed at the center of the nip, with micro-slip between the roller and sheet occurring on either side. (The point of matched speeds would have been shifted to the upstream side of the nip had the sheet/platen friction not been zero.) As anticipated from the preceding discussion, an underdrive condition prevails at low values of the Poisson ratio in Table 40.3. The change from underdrive to overdrive occurs at a Poisson ratio of about 0.28. Recall that the effective penetration, or “engagement,” of this example is 20%. The fact that a particular choice of Poisson ratio (v ≈ 0.28) could give a speed ratio of 1 (i.e., V/V0 = 1) for such a highly deformed roller suggests that, through a clever choice of roller material, one could render the nip relatively insensitive to variations in engagement. Figure 40.24 illustrates this concept. The speed ratio vs. penetration is graphically illustrated for three different materials. TABLE 40.3 Poisson’s Ratio, v
Speed Ratio, V/V0
0.0 0.1 0.2 0.3 0.4 0.475
0.88 0.91 0.95 1.01 1.08 1.19
Polyurethane Rubber Speed Ratio, V/V0
1.08 1.06 1.04 1.02
Foam Rubber
1.00 0.98 0.96 0.94
Open-Cell Foam Rubber
0.92 0.90 0.88
0
5
10
15
20
25
30
Engagement (%)
FIGURE 40.24 Speed ratio vs. roller engagement for three different roller materials. (From Stack, K.D. (1995), A Nonlinear Finite Element Model of Axial Variation in Nip Mechanics with Applications to Conical Rollers, Ph.D. thesis, University of Rochester, New York.)
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Right hand side is high engagement
Left hand side is low engagement
Roller Sheet Platen Sheet skew after one roller revolution o
-3.6
Roller
Polyurethane Rubber
0
o
+1.2 o
Roller
Roller
Foam Rubber
Open-Cell Foam Rubber
FIGURE 40.25 Media skew produced by nonuniform roller loading. (From Stack, K.D. (1995), A Nonlinear Finite Element Model of Axial Variation in Nip Mechanics with Applications to Conical Rollers, Ph.D. thesis, University of Rochester, New York.)
The geometry is the same as in the previous example: inner core radius of 6.35 mm, outer roller radius of 25.4 mm, roller/sheet coefficient of friction of 1.0, and sheet/floor coefficient of friction of zero. The two-dimensional nonlinear finite-element model of Stack (1995) is again used to compute results. Figure 40.24 reveals that as the open-cell foam roller is pressed more heavily against the platen (i.e., the engagement goes up), a pronounced underdrive results. At an engagement of 20%, the speed ratio is only 90%. This is because the open-cell foam roller compresses with no appreciable Poisson swelling. By contrast, the polyurethane rubber roller is nearly incompressible, and thus it swells appreciably when the roller/floor engagement is increased. At an engagement of 20%, the polyurethane roller is producing an overdrive of approximately 108%. The most interesting graph in Figure 40.24 is that for the foam rubber roller. Its Poisson ratio of v = 0.25 seems to be well chosen to produce a Poisson swelling that closely counteracts the chord-shortening that occurs as the roller is pressed against the floor. The graph in Figure 40.24 drops off slightly from a speed ratio of 1.0 and then holds nearly steady at 0.97 for a wide range of engagements. This can be very important in nip transport systems, as it may be difficult to hold the engagement of the nip rollers to very tight tolerances. The upper drawing of Figure 40.25 depicts a roller that is not perfectly aligned with the floor. On one side of the roller there is a “High Engagement” where the roller presses a bit more firmly against the floor than on the “Low Engagement” side. As seen from the previous results, one can expect the local speed ratio to be different along the axis of the roller, which means that a sheet will rotate or “skew” as it moves through the roller. Because of the Poisson influence on speed ratio, the choice of roller material will influence whether the sheet will rotate clockwise or counterclockwise in the imperfect system of Figure 40.25. Using the three-dimensional version of his finite-element model for nip transport, Stack (1995) analyzed a misaligned roller of the sort depicted in Figure 40.25. The roller had the same specifications listed in the second paragraph on page 1585. The engagement of the roller was 20% at the center, but with a 1.0° misalignment of the roller axis to produce the high/low engagement variation along the axis of the roller. The sheet had a width of 216 mm (8.5 in.), and the roller had a width of 32 mm (1.25 in.).
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TABLE 40.4 Material Class Polyurethane rubber Foam rubber Open-cell foam rubber
Shear Stiffness
Poisson Ratio
0.1723 MPa = 25.0 psi 0.0689 MPa = 10.0 psi 0.0345 MPa = 5.0 psi
0.45 0.25 0.00
CONIC ROLLER SIDEGUIDE
SHEET PLATEN
END OF TRAVEL
SIDEGUIDE START CONIC OF ROLLER TRAVEL CONIC
ROLLER
FIGURE 40.26 Side-registration of a sheet using a conic roller. (From Stack, K.D. (1995), A Nonlinear Finite Element Model of Axial Variation in Nip Mechanics with Applications to Conical Rollers, Ph.D. thesis, University of Rochester, New York.)
Using the same three materials as in Table 40.4, Stack (1995) predicted the “media skew” that would result after one complete revolution of the misaligned roller. The lower drawing of Figure 40.25 shows the results. In the case of the polyurethane rubber with the high Poisson ratio (v = 0.45), the sheet moves faster on the high engagement side of the roller, so the sheet rotates in the counterclockwise direction. A “media skew” of 3.6° is produced by each revolution of the roller. In contrast, the open-cell foam roller, with a Poisson ratio of v = 0, underdrives the sheet with increasing nip engagement. (Recall Figure 40.24.) Thus, for this type of material, the sheet will move more slowly on the high engagement side of the roller. After one complete revolution of the roller, the sheet had rotated 1.2° in the clockwise direction. Finally, note that the foam rubber roller with its relative insensitivity to roller engagement (see, again, Figure 40.24) transports the sheet with almost no “media skew.” Last, note that sheet skew can be exploited for design purposes. Figure 40.26 depicts how a conical roller can be used for side-registration of a sheet. The lower drawing in Figure 40.26 is based on a calculation by Stack (1995), and shows a sequence where a sheet is transported by a conical roller near a side-guide. The sheet starts 25.4 mm (1 in.) away from the side-guide. As the roller turns, pushing the sheet forward, the conical nature of the roller makes the sheet want to rotate counterclockwise in the figure. Soon, however, the trailing edge of the sheet presses against the side guide, which prevents further counterclockwise rotation. Indeed, the sheet begins to reverse its rotation, all the while moving forward. In approximately two thirds of a sheet length of forward travel, the sheet becomes fully registered with the side-guide.
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Defining Terms Air reverser: A device that allows the moving direction of a coated material to be changed without contact. Center winding: A process in which material is wound onto a roll by driving the center of the wound roll. Foil bearing: A device in which entrained or supplied air acts to lubricate a flexible foil moving over a rigid surface. Instant center: The instantaneous point about which a rigid body in planar motion rotates. J-line: The line formed by an initially radial line marked on a wound roll after further winding. Jam: A mechanism by which the motion of a bent flexible plate in a frictional channel is arrested by a self-locking geometry. Motion cannot be restored by an increase in the driving force. Micro-slip: A slight mismatch in speed between an elastic tape and a transporting roller caused by straining of the tape. Nip: The region of contact of two rollers, or between a roller and a platen. Overdrive: The condition that occurs when a sheet moves through a roller/roller or roller/platen nip with a speed that is faster than the nominal surface speed of the undeformed roller(s). Roll-over: A form of “snap-through” buckling in which a flexible plate, bent between channel walls, jumps from one configurated to another. Slip zone: The region over which an elastic tape and a transporting roller have different speeds. Stall: A mechanism by which the motion of a bent flexible plate in a frictional channel is arrested by frictional drag. Motion can be restored through an increase in the driving force. Stick zone: The region over which an elastic tape and a transporting roller have identical speed. Surface winding: A process in which material is wound onto a roll by driving the edge of the wound roll with a separate roller. Tentpole: A protrusion in the interface between a flexible plate and a rigid foundation that causes the plate to lose contact with the foundation in an area surrounding the protrusion. Underdrive: The condition when a sheet moves through a roller/roller or roller/platen nip with a speed that is slower than the nominal surface speed of the undeformed roller(s).
References Allaire, P.E. and Benson, R.C. (1987), A rapid solution method for the compressible Reynolds equation in magnetic recording applications, in Symp. Tribology and Mechanics of Magnetic Storage Systems, STLE Special Publication 22, 33-39. Baker, B.R. (1977), A dropout model for a digital tape recorder, IEEE Trans. Magnetics, MAG-13, 1196-1198. Barlow, E.J. (1967a), Derivation of governing equations for self-acting foil bearings, J. Lubr. Tech., 89, 334-340. Barlow, E.J. (1967b), Self-acting foil bearing of infinite width, J. Lubr. Tech., 89, 341-345. Bayer, R.G., Shalkey, A.T., et al. (1969), Design for Zero Wear, Mach. Des., 41(1), 142-151. Benson, R.C. (1981), The deformation of a thin, incomplete, elastic ring in a frictional channel, J. Appl. Mech., 48(4), 895-899. Benson, R.C. (1982), Stick/slip conditions for a thin, incomplete, elastic ring impinging on a frictional barrier, J. Appl. Mech., 49(1), 231-232. Benson, R.C. (1991), Plate tenting with a one-sided constraint, J. Appl. Mech., 58(2), 484-492. Benson, R.C., Smith, D.P., Madsen, D.M., and Fung, S. (1992), Magnetic tape tenting: modeling and experiments, Adv. Information Storage Systems, 4, 63-72, ASME Press. Benson, R.C. (1995), A nonlinear wound roll model allowing for large deformation, J. Appl. Mech., 62(4), 853-859. Benson, R.C., Stack, K.D., and Stolte, J. (1997), A review of computer simulation models for sheet transport through a copier, in Proc. Int. Conf. Information and Precision Equipment, Japan Society of Mechanical Engineers, Tokyo, 615-620.
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Bhushan, B. and Tønder, K. (1989), Roughness-induced shear- and squeeze-film effects in magnetic recording—part I: analysis, J. Trib., 111, 220-227. Blok, H. and Van Rossum, J.J. (1953), The foil bearing — a new departure in hydrodynamic lubrication, Lubr. Eng., 9, 316-320. Burgdorfer, A. (1959), The influence of molecular mean free path on the performance of hydrodynamic gas lubricated bearings, J. Basic Eng., 81, 94-100. Diehl, T., Stack, K.D., and Benson, R.C. (1993), A study of three-dimensional nonlinear nip mechanics, in Proc. of the Second Int. Web Handling Conf., Good, J.K. (Ed.), Oklahoma State University. Diehl, T. (1995), Two-dimensional and three-dimensional analysis of nonlinear nip mechanics with hyperelastic material formulations, Ph.D. thesis, Department of Mechanical Engineering, University of Rochester, Rochester, New York. Diehl, T. and Benson, R.C. (1995), Modelling foamed elastomeric tires with Ogden-Hill strain energy functions, in Numerical Implementation and Application of Constitutive Models in the Finite Element Method, ASME Applied Mechanics Division Book, Number 213, 79-94. Eshel, A. and Elrod, H.G. (1965), The theory of the infinitely wide, perfectly flexible, self-acting, foil bearing, J. Basic Eng., 87(4), 831-836. Eshel, A. and Elrod, H.G. (1967), Stiffness effects on the infinitely wide foil bearing, J. Lubr. Tech., 89, 92-97. Eshel, A. (1968), Compressibility effects on the infinitely wide, perfectly flexible foil bearing, J. Lubr. Tech., 90, 221-225. Eshel, A. (1970a), On controlling the film thickness in self-acting foil bearings, J. Lubr. Tech., 92, 359-362. Eshel, A. (1970b), On fluid inertia effects in infinitely wide foil bearings, J. Lubr. Tech., 92, 490-494. Frisch-Fay (1962), Flexible Bars, Butterworth and Company. Fukui, S. and Kaneko, R. (1987a), Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report — derivation of a generalized lubrication equation including thermal creep flow, in ASLE/ASME Tribology Conference, San Antonio, TX, ASLE/ASME. Fukui, S. and Kaneko, R. (1987b), Experimental investigation of externally pressurized bearings under high Knudsen number conditions, J. Tribol., 110(1), 144-147. Good, J.K. and Wu, Z. (1993), The mechanism of nip-induced tension in wound rolls, J. Appl. Mech., 60(4), 942-947. Gross, W.A. (1980), Fluid Film Lubrication, Wiley, New York. Gueldenberg, B. and Welp, E.G. (1999), Quantitative analysis of nip-induced tension by use of digital image processing, to appear in Proc. of the Fifth Int. Web Handling Conf., Good, J.K. (Ed.), Oklahoma State University. Hakiel, Z. (1987), Nonlinear model for wound roll stresses, J. Tech. Assoc. of the Pulp and Paper Industry (TAPPI), 70(5), 113-117. Heinrich, J.C. and Connolly, D. (1992), 3-Dimensional finite element analysis of self-acting foil bearings, Comp. Meth. in Appl. Mech. and Eng., 100(1), 31-43. Hsia, Y.-T. and Domoto, G.A. (1983), An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances, J. Lubr. Tech., 105, 120-130. Johnson, K.L. (1985), Contact Mechanics, Cambridge University Press. Keshavan, M.B. and Wickert, J.A. (1997), Air entrainment during steady-state web winding, J. Appl. Mech., 64(4), 916-922. Keshavan, M.B. and Wickert, J.A. (1998), Transient discharge of entrained air from a wound roll, J. Appl. Mech., 65(4), 804-810. Kotera, H., Kita H., Yohda H., and Mizoh Y. (1991), Finite element analysis of the interface phenomena between VCR tape and head, IEEE Trans. Consumer Electronics, 37(3), 224-227. Kotera, H., Kita H., Mizoh Y., and Yohda H. (1992), A new scheme for finite element analysis of an interface phenomena between VCR drum, head, and tape, IEEE Trans. Consumer Electronics, 38(3), 181-187.
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Lacey, C.A. and Talke, F.E. (1990), A tightly coupled numerical foil bearing solution, IEEE Trans. on Magnetics, 26, 3039-3043. Lakshmikumaran, A.V. and Wickert, J.A. (1996), On the vibration of coupled traveling string and air bearing systems, J. Vib. Acoustics, 118(3), 398-405. Lakshmikumaran, A.V. and Wickert, J.A. (1999), Equilibrium analysis of finite width tension dominated foil bearings, J. Tribol., 121(1), 108-113. Laumer, E.P. (1966), Minimizing wound-in paper defects within shipping rolls, TAPPI, 49(6), 127A-135A. Licht, L. (1968), An experimental study of elastohydrodynamic lubrication of foil bearings, J. Lubr. Tech., 90, 199-220. Lucas, R.G. (1981), Winder crepe wrinkles — their causes and cures, in Proc. of the Paper Finishing & Converting Conference, TAPPI Press, 91-98. Mitsuya, Y. (1986), Stokes roughness effects on hydrodynamic lubrication. II. Effects under slip flow boundary conditions, J. Tribol. Tech., 108(2), 159-166. Mitsuya, Y. and Fukui, S. (1986), Stokes roughness effects on hydrodynamic lubrication. I. Comparison between incompressible and compressible lubricating films, J. Tribol. Tech., 108(2), 151-158. Müftü, S. and Benson, R.C. (1995), Modelling the transport of paper webs including the paper permeability effects, in Advances in Information Storage and Processing Systems, Vol. 1, ASME, San Francisco, CA, 247-258. Müftü, S. and Benson, R.C. (1996), A study of cross-width variations in the two-dimensional foil bearing problem, J. Tribol., 118(2), 407-414. Müftü, S., Lewis, T.S., Cole, K.A., and Benson, R.C. (1998), A two-dimensional model of the fluid dynamics of an air reverser, J. Appl. Mech., 65(1), 171-177. Ono, K., Hara, S., and Murata, K. (1980), Magnetic tape deformation under a concentrated load, Bull. JSME, 23(175), 13-19. Ono, K. and Mizukawa, M. (1985), Study on spherical foil bearings. 3rd Report. Analysis for large bearing penetration, Bull. JSME, 28, 2097-2104. Ono, K., Kodama, N., and Michimura, S. (1991), A new numerical analysis method for 2-dimensional foil-bearing problems based on inverse analysis concept, JSME Vib. Cont. Eng. for Industry, 34(1), 82-90. Patir, N. and Cheng, H.S. (1978), An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, J. Lubr. Tech., 100, 12-17. Patir, N. and Cheng, H.S. (1979), Application of average flow model to lubrication between rough sliding surfaces, J. Lubr. Tech., 101(2), 220-230. Pfeiffer, J.D. (1968), Mechanics of a rolling nip on paper webs, Tappi J., 51(8), 77A-85A. Renshaw, A.A. (1999), Vibration considerations in foil-bearing design, J. Appl. Mech., 66(2), 432-438. Rongen, P. (1991), On numerical solutions of the instationary 2D foil bearing problem, in Proc. Trib. and Mech. of Magnetic Storage Systems, STLE SP-29, 130-138. Rongen, P. (1994), Finite element analysis of the tape scanner interface in helical scan recording, Ph.D. thesis, Eindhoven University, The Netherlands. Shames, I.H. and Dym, C.L. (1991), Energy and Finite Element Methods in Structural Mechanics, Taylor & Francis, New York. Shelton, J.J. and Reid, K.N. (1971a), Lateral dynamics of a real moving web, J. Dyn. Sys., Meas., and Control, 93(3), 180-186. Shelton, J.J. and Reid, K.N. (1971b), Lateral dynamics of an idealized moving web, J. Dyn. Sys., Meas., and Control, 93(3), 187-192. Sievers, L., Balas, M.J., and von Flotow, A. (1988), Modeling of web conveyance systems for multivariable control, IEEE Tran. on Automatic Control, 33(6), 524-531. Smith, D.P. (1998), Tribology of the belt-driven data tape cartridge, Tribol. Int., 31(8), 465-477. Soong, T.C. and Li, C. (1979), An elastic analysis of multiroll endless web systems, J. Dyn. Sys., Meas., and Control, 101(3), 308-313.
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Stack, K.D. and Benson, R.C. (1993), The effects of axial variation in nip mechanics, in Proc. 2nd Int. Conf. Advanced Mechatronics, Meiji University, Tokyo, Japan, 731-735. Stack, K.D., LaFleche, J.E., and Benson, R.C. (1995), The effects of nip parameters on media transport, in Proc. 3rd Int. Web Handling Conf., Oklahoma State University, 382-395. Stack, K.D. (1995), A nonlinear finite element model of axial variation in nip mechanics with applications to conical rollers, Ph.D. thesis, Department of Mechanical Engineering, University of Rochester, Rochester, NY. Stack, K.D., Perconti, J., LaFleche, J.E., and Benson, R.C. (1997), A nonlinear finite element model for stationary bar web spreading, in Proc. 4th Int. Web Handling Conf., Oklahoma State University, 446-460. Stahl, K.J., White, J.W., and Deckert, K.L. (1974), Dynamic response of self-acting foil bearings, IBM J. Res. Dev., 18, 513-520. Stolte, J. (1992), An extending, dynamic elastica: analysis with inertial loads and impact with a surface, Ph.D. thesis, Department of Mechanical Engineering, University of Rochester, Rochester, NY. Stolte, J. and Benson, R.C. (1992), Dynamic deflection of paper emerging from a channel, J. Vib. Acous., 114(2), 187-193. Stolte, J. and Benson, R.C. (1993), An extending dynamic elastica: impact with a surface, J. Vib. Acous., 115, 308-313. Tønder, K. (1984), Roughness effects on thin-film gas lubrication — A state-of-the-art review, in Tribology and Mechanics of Magnetic Storage Systems, Bhushan, B. (Ed.), ASLE SP-16, 183-192, Park Ridge, IL. Tripp, J.H. (1983), Surface roughness effects in hydrodynamic lubrication: the flow factor method, J. Lubr. Tech., 105, 458-465. Wallace, R.L. (1951), The reproduction of a magnetically recorded signal, Bell Systems Tech. J., 30, 1145-1173. Wickert, J.A. (1993), Free linear vibration of self-pressurized foil bearings, J. Vib. Acous., 115(2), 145-151. Young, G.E., Shelton, J.J., and Fang, B. (1989a), Interaction of web spans. I. Statics, J. Dyn. Sys., Meas., Control, 111(2), 490-496. Young, G.E., Shelton, J.J., and Fang, B. (1989b), Interaction of web spans. II. Dynamics, J. Dyn. Sys., Meas., Control, 111(2), 497-504. Young, G.E. and Reid, K.N. (1993), Lateral and longitudinal dynamic behavior and control of moving webs, J. Dyn. Sys., Meas., Control, 115(2), 309-317.
For Further Information Those seeking a broad coverage of the field are referred to a number of key proceedings: Tribology and Mechanics of Magnetic Storage Systems, Norman Eiss, Bharat Bhushan, et al., Editors. Nine symposium proceedings, 1984–1990, 1992, 1994, published by the Society of Tribologists and Lubrication Engineers, 840 Busse Highway, Park Ridge, IL 60068. Advances in Information Storage Systems, Bharat Bhushan, Editor. Volumes 1–5 published 1991–1993 by ASME Press, American Society of Mechanical Engineers, 3 Park Avenue, New York, NY 10016. Volumes 6–10 published 1995–1999 by World Scientific Publishing Company, P.O. Box 128, Farrer Road, Singapore 912805. International Conference on Web Handling, J.K. Good, Editor. Biennial conference proceedings beginning 1991 by the Web Handling Research Center at Oklahoma State University, Stillwater, OK 74078. Journal of Information Storage and Processing Systems, Bharat Bhushan, Editor. Published quarterly beginning January 1999 by Birkhäuser Verlag AG, P.O. Box 133, CH-4010 Basel, Switzerland.
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41 Biomedical Applications 41.1 41.2
Introduction ................................................................... 1593 Tribology in the Human Body...................................... 1594 The Cardiovascular System • Soft Tissues • The Skeletal System
41.3
Tribology of Artificial Organs and Medical Devices ..... 1596 Cardiovascular Devices • Soft Tissues • Hard Tissue Replacements
41.4
Natural Synovial Joint and Articular Cartilage............ 1599 The Functional Requirements • Articular Cartilage • Friction and Lubrication
John Fisher The University of Leeds
41.5 41.6 41.7
Total Replacement Joints ............................................... 1603 Wear and Wear Debris Induced Osteolysis .................. 1605 Joint Replacement and Repair in the Next Millennium..................................................................... 1607
41.1 Introduction The application of tribology in medicine and biology is a growing and rapidly expanding field. It necessarily builds upon the fundamentals of engineering tribology, and extends well beyond conventional boundaries. Biomedical tribological systems involve an extensive range of synthetic materials and natural tissues, which often operate in complex interactive biological environments. Their performance specifications and lifetimes often exceed that found in many engineering systems and frequently have to extend beyond the lifetime of the patient. Biomedical tribology involves natural human and animal systems and, of increasing importance, the development of replacement (prosthetic) devices to replace diseased tissues and organs. Over the last 30 years, studies of natural tissues have been used to define the functional tribological specification for prosthetic devices and biomaterials. During this period, prosthetic devices have primarily developed from an engineering science base. The current designs of prosthetic devices, such as total replacement joints, have demonstrated clinical lifetimes of well beyond 10 years. These successes have also led to new types of problems, relating to long-term tribological and biological interactions within the human body, that can limit the lifetime of many of these devices. As the average age of the elderly population increases, their expectations of both levels of activity and quality of life increase, the fundamental specification and long-term performance requirements of biomaterials and prosthetic devices are being extended. A new era of biomedical tribology is now emerging, in which the conventional approach of defining tribological requirements in terms of engineering functions is no longer adequate. Biological activity has now become a critical element of the engineering function. The future will embrace coupled interactive tribological and biological systems using both bioactive biomaterials and prosthetic systems and also novel viable biological systems and tissue engineered products. These developments will integrate existing
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experience of the tribology of natural human systems and conventional synthetic implant biomaterials, and involve scientists from biological and medical disciplines working more closely alongside engineers and physical scientists. In this chapter, aspects of the tribology of the natural human body, artificial organs, and medical devices are reviewed as an overview of the breadth of biomedical applications. Subsequently, the chapter focuses on the major areas of biotribology, the natural human joints and their artificial replacements. The natural synovial joint and artificial cartilage are initially described. The types of joint replacements used over the last 30 years are introduced and the major limitations that control their long-term survivorship in patients and adverse biological reactions to wear debris are discussed. Finally, the alternatives for joint replacement in the next millennium are described, including both functional biomaterials that are engineered to give improved biological activity and viable tissue engineered systems.
41.2 Tribology in the Human Body Tribology in the human body often focuses on the natural synovial joints in the lower limb — the ankle, hip, and knee. The ability of these joints to articulate freely with extremely low friction and wear for over 75 years, with frequently more than 1 million loading cycles per year, is a remarkable testament to nature’s design. The structure and function of the natural synovial joints and articular cartilage are reviewed in Section 41.4. There are many other examples of successful tribological designs and functions in the human body. It is valuable to study these applications, not just at the macroscopic or functional level, in order to determine functional design specification for prosthetic replacements, but also at the structural, microscopic, and micro-functional levels where there is potential to learn about novel tribology from natural solutions. Human tribology can be considered in three parts: the cardiovascular system, the soft tissues, and the hard tissue skeletal support structures, including synovial joints.
41.2.1 The Cardiovascular System The cardiovascular system, including the heart, arteries, veins (and for convenience in this review, the lungs), is a complex pumping system that transports blood, gases, nutrients, energy, and waste products around the body and controls temperature regulation (Figure 41.1). It consists of a primary pumping LUNGS
Left side of heart
Right side of heart
TISSUES
DIGESTIVE TRACT
LIVER
KIDNEYS
FIGURE 41.1
A schematic representation of the cardiovascular system.
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Pulmonary artery
Aor
ta
SVC
LA RA
A M P T
IVC RV
LV
Key : RA - right atrium, RV - right ventricle, LA - left atrium RV - left ventricle, T - tricuspid valve, P - pulmonary valve, M - mitral valve, A - aortic valve, SVC - superior vena cava IVC - inferior vena cava
FIGURE 41.2
An outline of the heart showing the two pumping chambers.
system, the heart, and a complex network of vessels distributing the blood to the major organs and tissues. The heart, like many pumping systems, has valves and moving components and, additionally, a network of vessels that are elastic and compliant. Some of these vessels, the major veins, also have a series of valves that, along with the peristaltic action of the vessel walls, result in an effective low-pressure pumping action for the return of blood to the heart. The flow of blood through small capillaries between the high-pressure arteries and veins offers interesting examples of low Reynolds number flow and of non-Newtonian multi-component fluids in very small diameter vessels (down to 10 µm in size). Equally important is an understanding of the pulsatile flow down the elastic small diameter arteries, such as the coronary arteries and the femoral arteries, which are frequently sites for disease and occlusion leading to heart disease and peripheral vascular disease, respectively. The heart is the most critical element of the cardiovascular system, and as with all pumping systems, the moving valves offer particular tribological challenges and in this case unique solutions. The heart has two independent pumping chambers, the left and right ventricles (Figure 41.2). The left ventricle operates at the high pressure, approximately 120 mmHg (15.6 kPa), and circulates blood to most of the body. The right ventricle operates at the lower pressure, approximately 4 kPa, and circulates blood to the lungs. The inlet and outlet valves to the left ventricle, the mitral and aortic valves, have to withstand a peak pressure of 120 mmHg (15.6 kPa) when closed, but additionally open at low pressure drops less than 1 kPa with little resistance to blood flow. Both valves consist of tissue flaps or flexible valve leaflets. The mitral valve has two leaflets that are supported along their free edge by chords attached to the ventricular wall. The aortic outlet valve has three leaflets and these are supported peripherally by the elastic wall of the aortic root. The valves open and close approximately 40 million times a year, and during each cycle the tissue deforms considerably. When closed, the free edges and inflow surfaces of the tissue flaps come together in apposition to prevent backflow. Wear and abrasion of the leaflets can occur as they come together along these free margins. This is reduced by the inherent lubrication of the blood and, additionally, in the center of the aortic valve the leaflets are thickened. The opening of the leaflets is facilitated by dynamic expansion of the aortic root, by the nonlinear elastic properties of the tissue, which has a low elastic modulus at low strain, and by a trilaminate structure in which the three layers
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of the leaflet can slide over each other during flexion, reducing the structural bending stiffness. The proteoglycan molecules in the middle layer (the Spongiosa) facilitate this shearing (Thurbrikar et al., 1983). The complex composite biological structure of the valve leaflets allows the valves to perform for up to 5 billion cycles in many people, in the absence of congenital abnormalities or diseases such as calcification or fibrosis. The tribological function of the natural heart valve has yet to be replicated by a prosthetic equivalent.
41.2.2 Soft Tissues Studies of soft tissues such as skin, tendons, ligaments, and other membranes have shown interesting tribological properties. These tissues comprise primarily collagen type I, cells, extracellular matrices, and water. The water is not tightly bound as in articular cartilage (see Section 41.4), but does act as an effective self-lubrication mechanism for limited or occasional motions. Skin often rubs on other external surfaces, particularly on hands, and the body has an effective self-repair or turnover for these living tissues. The eye, and particularly the movement of the eyelid over the eye, has generated considerable interest. The surfaces can be lubricated by tears and the role of boundary molecules in the tear film, including both lipids and proteins, is of current interest. This has emerged as an important area with the increase in the wearing of contact lenses in which additional tribological/biomaterial interfaces have been introduced. Internally, the soft tissues frequently slide against each other and in the case of tendons and ligaments, this occurs when the tissues are under high loads. The tissues are fibrous in nature and the fibers are aligned to give maximum strength along the axis of maximum load. The inherent natural lubrication assists in minimizing friction and wear when the tissues are sliding over other tissues.
41.2.3 The Skeletal System There are many joints in the musculoskeletal tissue in addition to the major weight-bearing joints in the lower limb. The upper limb — fingers, wrist, elbow, and shoulder — contains synovial joints and their function is described in Section 41.4. The forces in these joints may at first consideration seem quite low. However, the moment arm of the muscles across some of these joints is disadvantageous. For example, the moment arm of the muscles acting at the shoulder to raise a weight in the arm when fully extended is 1 in 12. Hence, to raise a 5-kg weight results in 600 N force at the shoulder joint, which is equivalent to the body weight of an average person. This type of loading and motion, although less frequent than in the lower limb, still requires the tribological properties of the natural synovial joints (Section 41.4). The spinal column has many flexible joints that are under compression loading. The properties of the cartilage in these joints is not dissimilar to that of cartilage in the lower limb, an important tribological feature being its high water content, the type II collagen and proteoglycan extracellular matrix that binds water, retaining it in the tissue over long periods of static loading. The role of chemically bound water, first described by McCutcheon (1959), is critically important in lubrication which was first described as a sponge hydrostatic or self-pressurized lubrication. However, the major tribological challenges of the muscular skeletal system lie in the natural synovial joints of the lower limb (Figure 41.3) and these are discussed in detail in Section 41.4.
41.3 Tribology of Artificial Organs and Medical Devices Tribological properties of biomaterials play an important role in the performance of many artificial organs and medical devices. Most important is the tribological performance of total artificial joints, particularly in the hip and knee, of which approximately 1 million replacements are carried out every year. The need for extended lifetimes, which is currently limited by tribological performance, is described fully in Section 41.5. It is also interesting to consider the tribological design challenges of other medical devices within the context of the three groups of tissues described in Section 41.2.
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Articular Cartilage
Bone
Synovial Fluid Capsule Bone
FIGURE 41.3
A schematic diagram of a natural synovial joint in the lower limb.
41.3.1 Cardiovascular Devices The total artificial heart, or indeed ventricular or heart assist pumps, have yet to be sufficiently developed to allow widespread clinical use. Currently, smaller elements of the cardiovascular system, heart valves, arterial grafts, and internal stents are implanted, and tribology plays an important role in the design and performance of these devices. Vascular stents are a relatively recent innovation but are being used in increasing numbers to dilate blocked or partially occluded small-diameter arteries or to repair or support arterial or aortic aneurysms — weaknesses of the vessel wall. These stents are flexible and expandable structures that can be delivered by minimally invasive surgery via small-diameter catheters typically inserted through the femoral artery. The devices are frequently metallic (some are shape memory alloys) and polymers, and are expanded at the vascular site to attach to the vessel wall, hence providing a new lining to the vessel. The materials directly contact the blood, so there is considerable interest in their surface characteristics and blood compatibility, along with the actual fluid flow field through the device. The tribological properties of the catheter systems that deliver them are also important as they too contact the blood, but additionally need a very low coefficient of friction to allow the surgeon a more precise “feel” for the placement of the device. The blood interactions with surfaces of small-diameter arterial grafts, the biochemistry, and the local fluid flow fields are critical in the long-term patency of the graft and its resistance to thrombolic occlusion. At present, synthetic grafts are not widely used for vessel diameters of less than 6 mm and yet much arterial disease occurs in vessels that are 4 mm or less. Currently, biological approaches are being considered to overcome these challenging interface problems. These include bioactive coating of synthetic vessels to give better blood compatibility and also the production of “living” tissue-engineered blood vessels in which the blood contacts natural autologous endothelial cells. Over 100,000 heart valves are implanted in the world every year and yet although they have been continuously developed over the last 40 years, the ideal valve still does not exist. Two types of valves are currently used: mechanical valves and bioprosthetic valves. Mechanical valves (Figure 41.4) are predominantly manufactured from pyrolytic carbon, either as a tilting disk or bileaflet valve, and generally have good durability. They do, however, require the patient to take long-term anticoagulation therapy to prevent blood clot formation or thromboemboli. The pyrolytic carbon valve occluders are rigid and cause disturbance to the flow, particularly around the hinge points, and this can cause blood damage and blood clot formation. Recent work has also shown them to cause cavitation in the blood. The carbon is a compatible and extremely hard-wearing material and attempts to replace it with alternative surfaces have not proved successful due to their poor tribological performance (King et al., 1996). It is likely that the
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FIGURE 41.5
Modern Tribology Handbook
A tilting disk mechanical heart valve.
A porcine bioprosthetic heart valve.
unnatural form of these rigid mechanical valves may well require that they will always require drug therapy to be given to the patient to prevent coagulation. Bioprosthetic tissue valves are made from chemically treated animal tissues (Figure 41.5). They do not usually require using anticoagulation therapy but their durability is currently limited to between 10 and 15 years (Schoen et al., 1983). These chemically treated valves are not viable and failures occur due to biodegradation (calcification), fatigue of the leaflets, and also abrasive wear of the flexible leaflets on their supporting synthetic frames (Fisher et al., 1989). The future of improved heart valve developments lies with synthetic, flexible leaflet valves with improved biostability and blood compatibility (Leat et al., 1995), or alternatively, in the longer term, tissue-engineered viable heart valves using the patient’s own cells and donor tissues. The interactions of the surfaces of the materials with the blood and the interface with the moving flexible leaflets requires careful tribological and biological studies and there are potentially many tribological problems in developing novel tissue valves still to be overcome.
41.3.2 Soft Tissues There is a clear need to replace or repair soft tissues in wound care, burn patients, in patients with ruptured ligaments or tendons, in ophthalmology, and other internal organ repairs. It is perhaps in the
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repair or replacement of tendons and ligaments that the tribological design is most important. These tissues transmit forces ranging from 100 to several thousand Newtons across articulating joints. The movement of these tissues against other joint tissues under load can lead to abrasive wear and failure, particularly close to bony attachments. Some of the early ligament replacements were made from carbon fiber, but the wear particles produced from abrasion produced acute inflammation and failure. More recently, polyester scaffold ligaments, which encourage host tissue ingrowth, have been used extensively. The fibrous tissue ingrowth forms a neo-ligament. However, its long-term strength and abrasive resistance is dependent on this biological ingrowth, and a high number of failures have been reported using this approach. Ligament repair is now most frequently carried out with host tissue grafts such as the patella tendon graft. The natural tribological properties of this tissue do not result in the same modes of failure found with the synthetic equivalents, although correct surgical attachment to bone remains a challenge. In the future, tissue engineering with host, cadaveric, or synthetic scaffolds and autologous patient cells may offer an alternative to the autologous graft.
41.3.3 Hard Tissue Replacements The tribology of articulating joint replacement is discussed in detail in Section 41.5. There are, however, many other interfaces in orthopedic surgery in which tribological considerations are becoming increasingly important. Many orthopedic implants are comprised of modular components to allow for ease of surgery, the correct sizing of the component to the patient, and more sophisticated designs. The modular junctions frequently involve taper locks or screws and although there are nominally fixed interfaces, there is increasing evidence of micromotion and fretting wear. Although the volumes of wear may be relatively small, the wear products from various metals can be released into small volumes of tissues in quite high concentrations and cause adverse toxic or inflammatory biological responses. All orthopedic devices have to be attached to bone. These purportedly fixed interfaces can have micromotion and produce fretting wear products. Soft polymers such as polyethylene produce very poor fixation to the bone, as the bone abrasively wears away the polyethylene, turning micromotion into macromotion. Bone cement, polymethylmethycrylate, is set within bone cavities and forms geometrical macroscopic and microscopic interlocks to the bone. Generally, this is a successful interface, but can result in fibrous soft tissue interface layers. Very hard inert ceramics such as alumina ceramic do not fix or integrate to the bone and translation of acetabular cups has been found in these situations. Metallic stems and surfaces were traditionally roughened to provide an interlock to the bone and this can prove a very effective micro-interlock. However, if these roughened surfaces do loosen, they can produce adverse biological reactions due to both bone and bone cement wear debris. More recently, metallic interfaces with bone have used porous coatings such as beads or meshes, and hydroxyapatite bioactive coatings on both to promote bone ingrowth or bone growth. In general, these provide good quality fixation to healthy bone with little micromotion or wear debris. However, if these surface coatings fail, the interface can fail and they can produce wear particles that are both biologically and mechanically damaging. The future of the interfaces of orthopedic implants with bone lies in more advanced bioactive surfaces to provide more secure long-term fixation.
41.4 Natural Synovial Joint and Articular Cartilage The tribology of the natural joint has been studied extensively over the last 30 years (Dowson et al., 1990). In the lower limb, loads of between four and five times body weight are transmitted during normal walking, with even higher loads during more vigorous activities. The loading regimes are complex and variable, and lifetimes frequently exceed 70 years or 100 million cycles. The tribological design of the natural joint is complex as it involves a number of different lubrication mechanisms. After over 30 years of research, there remains a considerable scientific challenge to fully understand the structure and functional relationships in both healthy and diseased natural joints. The major elements of the natural synovial joint are the underlying bone, the articular cartilage (in the knee, the meniscus), the synovial
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FIGURE 41.6
Modern Tribology Handbook
A representation of the peak forces across the hip joint during walking.
fluid, and the tissues that constrain and articulate the joint, the ligaments, tendons, and soft tissue capsule (Figure 41.3).
41.4.1 The Functional Requirements The loading patterns in the hip were first described by Paul in 1967. In the hip, the loading is time dependent and has two peaks during the stance phase of walking at heel strike and at toe-off. These peak forces reach four times body weight and are associated with muscle forces as well as dynamic effects of the body segments. During mid-stance, the force across the hip joint drops to approximately twice body weight and, during the swing phase of walking, drops to a low level of less than 200 N (Figure 41.6). The force fields in the hip are three dimensional as well as time dependent, and vary with stride length, speed of walking, and the nature of gait. The motions that occur at the hip are equally complex, with the major motion being flexion extension 45° to 60° per cycle that can result in sliding velocities of up to 50 mm/s for a 60-mm-diameter femoral head. Additionally, there are internal/external rotation and adduction/abduction motions that make the motion at the femoral head acetabular cup highly multi-directional. In many ways, the knee is more complex than the hip because it has less conformity and greater laxity. The forces at the knee include the muscle forces that react to ground reaction forces and moments and contribute substantially to the resultant forces that can rise to two to three times body weight. The tibial axis force field is characterized by three peaks during the stance phase of gait and has a much lower swing phase load, as in the hip (Figure 41.7). The major motion of flexion extension of the knee results in a combination of both rolling and sliding at the articular cartilage interface, associated with some rollback of the instantaneous center of rotation as the knee flexes. The tibia also rotates internally as the knee flexes, producing a greater backward displacement posterior to the femur on the lateral tibial surface. The amount of flexion extension during the stance phase is 0 to 25°, which is less than in the hip, but flexion angles of 60° to 70° are frequently achieved during the swing phase of walking. During other activities such as stair-climbing and squatting, a flexion angle of 90° to 120° occurs with very high joint reaction forces. The durability of the natural hip and knee joints depends primarily on their ability to articulate with low levels of friction and wear. This performance is reduced by pathological disease processes such as rheumatoid or osteoarthritis. However, the inherent mechanical properties of the articular cartilage, synovial fluids, and soft and hard tissues are critical to the successful long-term tribological function of these joints.
41.4.2 Articular Cartilage The low elastic modulus of articular cartilage is one of its most important and frequently overlooked properties. Its equivalent elastic modulus of 10 to 20 MPa is about 1000 times less than the underlying
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FIGURE 41.7
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A representation of the tibial axis force acting across the knee during walking.
cortical bone. It is integrated and fully bonded to the bone and behaves as a thin-layer cushion contact. It is able to deform to accommodate complex geometries and increasing areas, reducing stress. Typically, in the natural hip, the contact area of 500 mm2 results in a stress of approximately 5 MPa. The ratio of the contact half-width to cartilage thickness is frequently greater than 2, and the contact mechanics give rise to high shear stresses at the interface with the underlying bone, a reasonably uniform compressive hydrostatic stress field in the center of the contact, and tensile stresses at the periphery of the surface. However, consideration of the cartilage as a simple thin elastic layer bonded to a rigid substrate is an inadequate model. Articular cartilage comprises 80% water with the remaining 20% being made up of a type-2 collagen fiber network and hydrophilic proteoglycan matrix. It is a highly viscous/elastic/biphasic material. The retention of water by the proteoglycans, and resistance to fluid flow through the porous solid, provide unique properties that resist deformation and lubricate the joint even under extensive periods of compressive loading. The biphasic properties and nature of articular cartilage have been extensively researched by Mow et al. (1986), and this has led to considerable understanding of its response to loading and pressure, both macroscopically and also intrinsically. The latter is important in understanding the cell (chrondrocyte) matrix interactions. The most critical lubrication mechanism, biphasic lubrication, was originally described by McCutcheon (1959) as self-pressurized lubrication and more recently demonstrated by Forster and Fisher (1997) (Figure 41.8). When the cartilage is initially loaded, most of the load is carried by the fluid phase as the pressure forces the fluid out of the contact, the flow being resisted by the hydrophilic proteoglycans. As the load is continuously applied over an extended period of up to 60 minutes, fluid continues to be lost but at a lower rate, and a greater proportion of the load is carried by the solid phase. After an extended period of time, the biphasic cartilage reaches an equilibrium deformation state, dependent on the applied stress, at which no further flow occurs. The load is then carried by the solid phase, and the material characterized by an aggregate modulus. On removal of the load, the hydrophilic proteoglycan matrix attracts water, swelling the cartilage to its original fully hydrated state. The displacement and pressurization of fluid in articular cartilage under load provides a very unique lubrication mechanism.
41.4.3 Friction and Lubrication The lubrication of articular cartilage and the resulting low levels of coefficient of friction are extremely important in the survivorship of the natural joint. Increased levels of friction cannot only increase wear
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FIGURE 41.8
Modern Tribology Handbook
The increase in coefficient of friction with loading time as described by Forster and Fisher (1997).
and surface damage, causing fibrillation, but can also cause subsurface damage at the interface with the subchondral bone. Coefficients of friction of less than 0.1 are necessary and as low as 0.01 desirable. Over the last 40 years, there have been a number of lubrication mechanisms proposed for articular cartilage, often with a single mechanism being championed to the exclusion of other mechanisms. In reality, the operating conditions of the natural joint are varied and complex and all the proposed mechanisms can make a contribution to lubrication. It is now recognized that multi-mode lubrication is necessary to fulfill all the functional requirements (Murakami et al., 1990). The various lubrication mechanisms are discussed below, their roles and conditions during which they operate described, and their relative contributions indicated. 41.4.3.1 Weeping Lubrication McCutcheon (1959) proposed that because cartilage has such a high water content, it was self-lubricating. The term “weeping” lubrication was introduced, which conceptually described the flow of water out of the cartilage into the contact at the surface to lubricate it. This was readily understood and accepted by many, although it was challenged by proponents of fluid film lubrication who indicated that it was not possible for fluid to flow into the area of maximum pressure at the center of the contact. Indeed, it was more appropriate for fluid to flow away from this area. Indeed, it has been shown that a porous material can actually deplete fluid film thickness. Perhaps the disparity is resolved by recognizing the role of weeping lubrication once the contact has entered the mixed regime. It was unfortunate that the term “weeping” was adopted because the term “self-pressurization” introduced by McCutcheon perhaps more accurately reflected the lubrication function currently described by the term “biphasic lubrication.” 41.4.3.2 Elastohydrodynamic Fluid Film Lubrication Elastohydrodynamic fluid film lubrication is a mechanism supported by many engineering tribologists working in this area (Dowson et al., 1986). Both the squeeze film action and entraining action can contribute during the stance and swing phase of walking, respectively (Figure 41.9). Fluid films of between 0.5 and 2 µm thick are required to separate the articular cartilage surfaces in which roughnesses can approach 0.5 to 1 µm (Jin et al., 1992, 1993). These are only achieved with high-viscosity synovial fluid. The non-Newtonian behavior of synovial fluid, thinning at high shear rates, and reduction of viscosity in diseases such as rheumatoid and osteoarthritis diminish the capacity to produce full fluid film lubrication. Although fluid film lubrication can be achieved during activities with high sliding velocities and dynamic loading such as walking, this is not the case for over 95% of the time for our natural joints in which there is limited sliding and often constant loading. Other mechanisms are necessary to protect articular cartilage during the majority of its working life.
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FIGURE 41.9 Prediction of the fluid film lubrication due to squeeze action in the stance phase and entraining action during the swing phase of walking.
41.4.3.3 Boosted lubrication or Ultrafiltration Boosted lubrication (or ultrafiltration) has been proposed as a mechanism for protection of articular cartilage when fluid film lubrication breaks down. Essentially, the water in the synovial fluid can enter the porous cartilage, leaving higher-molecular-weight proteins on the surface as a viscous gel lubricating layer (Walker et al., 1968). 41.4.3.4 Boundary Lubrication Boundary lubrication has also been cited as an effective mechanism, with both phospholipids (Hills and Butler, 1984) and glycoprotein complexes playing a role. In practice, both have been shown to combine to give some level of protection (Pickard et al., 1998) over short- to medium-term periods of loading when the fluid film was not present. 41.4.3.5 Biphasic Lubrication Biphasic lubrication theories, which are consistent with the original self-pressurized concept of McCutcheon (1959), are now emerging as one of the most important mechanisms. Current understanding, that the load is carried by the fluid phase of the cartilage, has been reinforced by an extensive study of friction in different conditions with extended loading periods (Forster et al., 1997). However, just as a consensus of views is emerging, there remains contradictory evidence. Recent work has shown that degradation of the proteoglycan content of articular cartilage changes its deformation response with time but does not alter the frictional properties. The processes and micromechanisms of lubrication in articular cartilage are very complex and although it has not yet been possible to replicate most of them with synthetic materials, the moves toward more bioactive and tissue-engineered products will require a fuller understanding of the biological/tribological interactions at a molecular level.
41.5 Total Replacement Joints Joint replacements have proved to be one of the most successful applications of biomaterials over the last 30 years. Currently, over 1 million devices are implanted annually in patients worldwide and about 1% of the population in Western countries benefit from these therapies. There is clear evidence that many devices last well beyond 10 years. However, with prostheses now being implanted in younger patients with more active lifestyles, a life expectancy of over 20 years is required in many cases. After the widespread introduction of hip and knee prostheses in the 1970s (Willert, 1977), little attention was paid to the tribological function of these devices during the 1980s because it was felt that the majority would not wear out or fail mechanically. During this period, concern was expressed about causes of loosening, such as stress shielding or cement failure (see Section 41.3). It has only been in the last 10 years that it has become recognized that wear is the major cause of long-term failure of joint replacements
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FIGURE 41.10
Modern Tribology Handbook
Schematic diagram of the artificial hip joint.
(Schmalzried et al., 1992). Although joints do not wear out, they produce many millions of wear particles, and it is the adverse biological reaction to these particles that leads to bone resorption and to loosening and failure (Shanbharg et al., 1994; Howie et al., 1993). Currently, there is considerable attention focused on the wear, wear debris, and adverse biological reactions in artificial joints (Fisher, 1994) and this is discussed in Section 41.6. Over the last 40 years, several different bearing couples have been used in joint replacements: metal on metal, ceramic on ceramic, polytetrafluoroethylene (PTFE) on metal and, polyethylene on metal. By far the most frequently used bearing couple has been ultrahigh-molecular-weight polyethylene (UHMWPE) articulating on ceramic or metal femoral heads in the hip (Figure 41.10), and metal femoral condyles in the knee. There has been good agreement between the clinical measurement of wear and in in vitro simulators in UHMWPE cups in the hip. For smooth polished metal femoral heads, wear rates of about 40 mm3/year have been recorded both in vivo and in vitro, and this corresponds to a linear penetration of 0.1 mm/year. Hence, with this wear rate, it would take an 8-mm-thick cup 80 years to wear out. Wear is, however, accelerated by damage to the femoral head, oxidative degradation of the UHMWPE, and also by the use of larger-diameter heads and cups. Clinical and laboratory studies have shown that damage to the femoral head and aging of the polyethylene can independently accelerate the wear by a factor of 2; and hence, with these combined effects, it is possible to obtain wear rates of between 100 and 200 mm3/year clinically (Livermore et al., 1990). Explant studies have shown osteolysis associated with cumulative wear volumes of 500 to 1000 mm3 and therefore it is not surprising that the incidence of wear debris-induced osteolysis increases markedly after 10 years. Clinical evidence indicates that the wear rate of UHMWPE in the knee is not so high due to less multi-directional kinematics; nevertheless, other wear-related failure mechanisms, such as fatigue and delamination, can lead to early revision. Alternative bearing materials for the hip, such as alumina ceramic on alumina ceramic (Sedel, 1992) and cobalt chrome alloy pairings (Muller, 1995), have been used clinically in the hip in limited numbers. The wear volumes are typically 10 to 100 times less than UHMWPE clinically and this has prompted renewed interest in the development of second-generation hard-on-hard bearings (Figure 41.11). It has
FIGURE 41.11 Volumetric wear rates of UHMWPE on ceramic metal on metal and ceramic on ceramic in a hip joint simulator.
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to be recognized however, that failure is caused by adverse biological reactions to wear debris (not wear volume alone), and the next section describes the current understanding of wear, wear particles, and adverse biological reactions.
41.6 Wear and Wear Debris Induced Osteolysis Wear debris induced osteolysis is caused by adverse cellular reactions to micrometer- and submicrometersized wear particles (Figure 41.12). Essentially, the particles generated in the joint are dispersed into the surrounding fluids and tissues, where they are phagyocytosed by macrophages. These activated macrophages release cytokines such as TNF-alpha, which act upon osteoblasts and osteoclasts to cause bone resorption. Work by Green et al. (1998) has shown that macrophage activation is dependent on the volumetric concentration of wear particles and also their size, with particles in the size range 0.1 to 7 µm being the most biologically active (Figure 41.13). Therefore, in considering the wear of artificial joints, it is necessary to study the wear particles generated and ideally their biological activity at functional levels and concentrations.
FIGURE 41.12
Representation of particle cell interactions.
FIGURE 41.13
An example of the dependency of cellular reactions on particle size.
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Ultrahigh-molecular-weight polyethylene acetabular cups, when articulating against smooth femoral heads under ideal conditions in vivo or in vitro, have been shown to wear at a rate of approximately 40 mm3/year/106 cycles. Tipper et al. (2000) have shown that this corresponds to between 500 and 1000 × 109 particles per year, with the majority of particles being submicrometer in size. The cumulative tolerance level for these polyethylene particles lies between 1012 and 1013 particles. Roughening the femoral head has been shown to double the rate of wear and particle generation rate in vivo and in vitro. Similarly, oxidative aging of polyethylene after it has been gamma-irradiated in the presence of air has been shown to markedly increase the wear volume and the number of particles generated (Besong et al., 1998). It is now recognized that the use of ceramic damage-resistant femoral heads and sterilization by irradiation in an inert atmosphere can remove these factors that accelerate wear and bring the volumetric wear rate down below 40 mm3/year. Inert atmosphere irradiation is now also being combined with post-irradiation inert annealing of polyethylene to provide further stabilization and resistance to oxidative degradation (Kurtz, 1999). However, this will still produce hundreds of billions of wear particles per year in the biologically active size range. In the knee, there is evidence that the wear volume is less than in the hip. Nevertheless, there remain concerns about wear debris induced osteolysis in the knee. This has produced a demand for alternative bearing materials. In the last 2 years, three alternative materials have emerged to the forefront for the hip prosthesis: highly crosslinked polyethylenes, metal-on-metal bearings, and ceramic-on-ceramic bearings. Highly crosslinked polyethylenes have been developed by irradiation at high doses between 5 and 10 Mrad in an inert atmosphere. These have shown a reduction in wear of between two and four times with smooth femoral heads (Muratoglu, 1999). However, some of this advantage is lost in the presence of third-body damage and damaged femoral heads. There are concerns that the crosslinked polyethylene will produce a larger proportion of submicrometer biologically active particles, but this remains to be determined. These materials are now entering clinical trials and this will provide further evidence of their true benefit. Metal-on-metal prostheses have been clinically shown to have wear rates of approximately 1 mm3/year, or 1 to 5 µm linear penetration. In vitro under ideal conditions, wear rates as low as 0.1 to 2 mm3/106 cycles have been found with very small wear particles on the order of 20 to 50 nm in diameter, which produces over 1013 particles/mm3 of debris (Figure 41.14). Thus, although the wear rate is substantially less than for polyethylene, the number of wear particles generated is greater (Figure 41.15). Perhaps the next concern lies with the biological activity of these particles, and their release and distribution around the body (Tipper et al., 1999).
FIGURE 41.14 The approximate number of particles per mm3 of debris in ceramic-on-UHMWPE and metal-onmetal hip prostheses.
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FIGURE 41.15 The approximate number of wear particles generated per million cycles in ceramic-on-polyethylene and metal-on-metal hip prostheses.
Alumina/alumina hip prostheses have also been shown to generate very low wear rates in vivo (1 mm3) (Nevelos et al., 1999) and even lower (0.1 mm3) in vitro. The particles are less well-defined, being on the order of 0.1 to 1 µm from some in vivo explants but being substantially smaller, 10 to 100 µm, from laboratory tests in which the wear rate is lower. Their biological activity remains to be determined. From measurements of wear volumes, these new bearing materials appear to offer considerable benefits, but the long-term clinical outcome will be determined by the biological response to the wear debris, which can be defined by further in vitro and in vivo studies.
41.7 Joint Replacement and Repair in the Next Millennium The year 2000 brought in the start of the Bone and Joint Decade and also a wider recognition of the role of functional biomaterials, biological activity, and tissue engineering in the replacement and repair of diseased tissues. Recent advances in biological science, molecular biology, and cellular engineering have provided the building blocks for the development of novel biologically engineered products. These will involve functional biomaterials with improved biocompatibility such as conventional joint replacements, bioactive biomaterials, and tissue-engineered products. Although biology provides the basic scientific building blocks for these developments, it will be engineers who develop the devices, structures, and systems to deliver this technology to patients. Interfaces, surfaces, and material interactions, which are fundamental to tribology, will play a key role in this new area of medical and biological engineering and will create a greater need to understand the tribological and biological reactions in natural systems (Figure 41.16). In joint replacement and repair, one will not only see novel functional biomaterials with improved biocompatibility and reduced adverse reactions to wear particles, but also bioactive coatings and interfaces to integrate with bone for improved fixation. There will be an increased use of injected artificial lubricants for the natural joint and, most importantly, a substantial growth in the development of viable tissueengineered products for articular cartilage, bone, ligaments, and tendons. These will involve synthetic and natural biomaterials matrices and scaffolds integrated with host autologous cells and tissues. The challenges in understanding the tribological function of biological systems is enormous and will involve macroscopic- and molecular-level studies, in vivo and in vitro simulations, and the formation of multi-disciplinary research. The biological tools and building blocks that are now available in biomedical engineering are extensive, and it is the responsibility of the engineers and tribologists to ensure that they are applied and delivered to the patient effectively.
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FIGURE 41.16
Modern Tribology Handbook
Requirements and inputs to joint replacement in the next millennium.
References Besong, A.A., Tipper, J.L., Ingham, E., Stone, M.H., Wroblewski, B.M., and Fisher, J. (1998), Quantitative comparison of wear debris from UHMWPE that has and has not been sterilised by gamma irradiation. J. Bone Joint Surg., 80B, 340-344. Dowson, D. (1990), Biotribology of natural and replacement synovial joints, in Biomechanics of Diarthroidal Joints, Vol. II, Mow, V.C., Ratcliffe, A., and Wood, S.L.Y. (Eds.), Springer-Verlag, New York, Part IV, 305-345. Dowson, D. and Jin, Z.M. (1986), Micro-elastohydrodynamic lubrication of synovial joints, Proc. Inst. Mech. Eng., J. Eng. Med., 15(H), 63-65. Fisher, J. (1994), Wear of ultra high molecular weight polyethylene in total artificial joints, Curr. Orthopaed., 8, 164-169. Fisher, J., Spyt, T.J., and Wheatley, D.J. (1989), Failure and hydrodynamic testing of explanted bioprostheses, Proc. Inst. Mech. Eng., J. Eng. Med., 203H, 65-70. Forster, H. and Fisher, J. (1997), The influence of loading time and lubricant on the friction of articular cartilage, Proc. Inst. Mech. Eng., J. Eng. Med., 210H, 109-119. Green, T.R., Fisher, J., Stone, M.H., Wroblewski, B.M., and Ingham, E. (1998), Polyethylene particles of a ‘critical size’ are necessary for the induction of cytokines by macrophages in vitro, Biomaterials, 19, 2297-2302. Hills, B.A. and Butler, D. (1984), Surfactants identified in synovial fluid and their ability to act as boundary lubricants, Ann. Rheumatic Des., 43, 641-648. Howie, D.W., Haynes, D.R., Rogers, S.D., Mcgee, M.A., and Pearcy, M.J. (1993), The response to particulate debris, Orthopaed. Clin. N. Am., 24, 571-581. Jin, Z.M., Dowson, D., and Fisher, J. (1992), The effect of porosity of articular cartilage on the lubrication of a normal hip joint, J. Eng. Med., 206(H), 117-124. Jin, Z.M., Dowson, D., and Fisher, J. (1993), Fluid film lubrication in natural hip joints, Thin Films in Tribology, Tribology Series 25, Elsevier, Amsterdam, 545-555. King, M.J., Olin, C.L., and Fisher, J. (1996), An initial investigation into the wear and damage of three types of heart valve, J. Heart Valve Dis., 5, 5111-5114. Kurtz, S.M., Muratoglu, O.K., Evans, M., and Edidin, A.A. (1999), Advances in the processing sterilisation and crosslinking of UHMWPE in joint arthroplasty, Biomaterials, 20, 1659-1688. Leat, M.E. and Fisher, J. (1995), The influence of manufacturing methods on the function and performance of a synthetic leaflet heart valve, Proc. Inst. Mech. Engs., J. Eng. Med., 209(H), 65-69.
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Livermore, J., Duane, I., and Murray, B. (1990), Effect of femoral head size on the wear of the polyethylene acetabular component, J. Bone Joint Surg., 72-A, 518-528. McCutcheon, C.W. (1959), Sponge hydrostatic and weeping bearings, Nature, 184, 1284-1285. Mow, V.C. (1986), Biomechanics of articular cartilage, in Basic Biomechanics of the Musculoskeletal Systems, Leafekeyer, London, 31-58. Muller, E.M. (1995), The benefits of metal on metal hip replacement, Clin. Orthop., 311, 54-59. Murakami, T. (1990), The lubrication of natural synovial joints, Japan Soc. Mech. Eng., 33, 465-47. Muratoglu, O.K., Bragdon, C.R., O’Connor, D.O., Jasty, M., and Harris, W.H. (1999), Unified wear model for highly crosslinked UHMWPE, Biomaterials, 20, 1463-1470. Nevelos, J.N., Ingham, E., Doyle, C., Nevelos, A.B., and Fisher, J. (1999), The influence of acetabular cups angle on the wear of alumina ceramic bearing couples in a hip simulator, J. Mat. Sci. Mat. Med., (in press). Nevelos, J.N., Ingham, E., Doyle, C., Nevelos, A.B., and Fisher, J. (1999), Analysis of retrieved alumina alumina ceramic components from Mittlemeir total hip prostheses, Biomaterials, 20, 1833-1840. Paul, J.P. (1967), Forces transmitted by joints in the human body, Proc. Inst. Mech. Eng., 181, 8-21. Pickard, J., Ingham, E., Egan, J., and Fisher, J. (1998), Investigation into the effect of proteoglycan molecules on the tribological properties of cartilage joint tissues. Proc. Instn. Mech. Engs., J. Eng. Med., 21(H), 177-182. Shanbhag, A.S., Glant, T.T., Gilbert, J.L., Black, J., and Galante, J.O. (1994), Composition and morphology of wear debris in failed uncemented total hip replacement, J. Bone Joint Surg., 76B, 60-67. Schmalzried, T.P., Jasty, M., and Harris, W.H. (1992), Periprosthetic bone loss in total hip arthroplasty, J. Bone Joint Surg., 74A, 849-963. Schoen, F.J. and Hobson, C.E. (1983), Anatomical analysis of removed prostheses, Hum. Pathol., 16, 549-559. Sedel, L. (1992), Ceramic hips, J. Bone Joint Surg., 74, 331-332. Thubrikar, M.J. (1983), The role of mechanical stress in the calcification of the aortic valve, J. Thoracic Cardiovasc. Surg., 86, 115-125. Tipper, J.L., Firkins, P.J., Ingham, E., Stone, M.H., Farrar, R., and Fisher, J. (1999), Quantitative analysis of wear and wear debris from cobalt chrome alloys used in metal on metal hip replacements, J. Mat. Sci. Mat. Med., 10, 353-362. Tipper, J.L., Ingham, E., Besong, A.A., Wroblewski, B.M., Stone, M.H., and Fisher, J. (2000), Quantitative analysis of polyethylene wear debris, wear rate and head damage in retrieved Charnley hip prostheses, J. Mat. Sci. Mat. Med., 13, 117-124. Walker, P.S., Dowson, D., Longfield, M.D., and Wright, V. (1968), Boosted lubrication, in Synovial Joints by Fluid Entrapment and Enrichment, Ann. Rheumatic Dis., 27, 512-520. Willert, H.G. (1977), Reactions of circular capsule of wear products from polycetal and UHMW polyethylene, J. Biomed. Mat. Res., 21, 459-466.
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42 Technologies for Machinery Diagnosis and Prognosis 42.1 42.2
Introduction ................................................................... 1611 Failure Prevention Strategies......................................... 1611
42.3
Condition Monitoring Approaches .............................. 1616
Learn from History • Study the Asset • Maintain the Asset
Richard S. Cowan Georgia Institute of Technology
Vibration Monitoring • Oil Monitoring • Thermal Monitoring • Nondestructive Evaluation • Corrosion Monitoring • Performance Monitoring
42.4
Fluid Film Bearings • Rolling Element Bearings • Gears • Seals
Ward O. Winer Georgia Institute of Technology
Tribo-Element Applications .......................................... 1634
42.5
Equipment Asset Management ..................................... 1639
42.1 Introduction For as long as there have been engineered structures and mechanical systems, there have been maintenance issues, uncertainties regarding reliability, and failures. Yet, the impact of such occurrences has significantly changed as manufacturing has moved away from the manual labor of the Industrial Revolution to the machinery of today’s technology-driven society. With an ever-increasing reliance on expensive and complex machines, machinery failures significantly affect company profits, largely due to the loss of equipment availability, the cost of spare componentry, the risk of injury to people, and the possibility of damage to the environment. The response of such pressures from industrial concerns and government agencies has been to demand that maintenance systems minimize the risks of equipment failure. In turn, this has spurred technology advances in providing a means to monitor and assess the condition of tribological elements and mechanical systems, rather than waiting until failures occur or replacing parts as a matter of routine. The aim of this chapter is to present these technologies for machinery diagnosis and prognosis in terms of failure prevention strategies and condition monitoring approaches, and suggest how they can be applied so as to lead to the effective management of equipment assets.
42.2 Failure Prevention Strategies Machine failures happen in many different ways and for many different reasons. To prevent their occurrence at an inopportune time, a strategy can be employed, based on learning from past events, understanding present performance, and adopting a cost-effective maintenance approach.
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42.2.1 Learn from History When something fails, the limitations of a design can be quickly understood. While success enables one to see the possibilities for reducing conservatism by subjecting machinery to more demands, it is only in failure that boundaries are defined, and much can be learned to increase safety and reliability and decrease manufacturing and operating costs. Failure analysis methodologies have progressed to the point of becoming somewhat routine, simple, and straightforward (Bloch and Geitner, 1994). It is imperative that evidence is catalogued and all steps and parts are fully documented to preserve a thorough record. Before defining the analytical steps required for a failure investigation, one must first determine what will be done with the information gained. For example, will the failure mode information be used to model the failure, such that time-to-failure can be predicted for other, similar designs? This may enable the implementation of a more effective maintenance schedule. Or, is how the component behaves in its environment the objective? This may lead to a longer service life. Perhaps, results from a study may suggest that the component or system needs to be redesigned. Given the right objective, there are many different techniques available for an analysis, and someone trained in conducting one will know which are best suited for a particular cause. By probing failures to their root-cause, the results should ultimately impact some aspect of product manufacture and/or use. Areas of significance include the development of new design approaches, the creation of redesigned configurations for improved safety and reliability, and the justification for service life extension.
42.2.2 Study the Asset To have confidence that a machine will carry out its intended purpose, one must establish its fitness for use as determined through its quality of design and quality of conformance. Quality of design infers reaching a level of attainment in performance, reliability, serviceability, and/or function, as determined through deliberate engineering and management decisions. Quality of conformance infers a systematic reduction of variability and elimination of defects until every unit produced by the machine is identical and defect-free. Understanding and improving upon quality can minimize the likelihood of catastrophic failure, and lead to lower costs, higher productivity, increased customer satisfaction, and ultimately higher profits. Insight can be readily obtained through statistical control and reliability engineering methods (Hines and Montgomery, 1990). 42.2.2.1 Statistical Control Statistical control can be broadly defined as those mathematical and engineering methods useful in the measurement, monitoring, and improvement of quality. It dates back to the 1920s with the development of statistically based sampling and inspection methods at Bell Telephone Laboratories, and matured during World War II as the techniques spread to other U.S. industries. In evaluating the possibility of failure, one may wish to compare a set of measurements for a given product to a set of specifications. The designer or the customer determines these specifications, usually called tolerance limits. Mathematically, tolerance limits are a set of bounds between which one can expect to find any given proportion of a population. If one knows or assumes that a parameter is normally distributed with mean µ and variance σ2, then tolerance limits can be constructed at any level of confidence for a proportion of the population using the tables of the cumulative normal distribution. Measurements recorded outside the bounds would likely be symptomatic of a problem. Theoretically, all processes can be characterized by a certain amount of variation if measured with an instrument of sufficient resolution. When this variability is confined to chance variation only, the process is said to be in a state of statistical control. However, a situation may exist in which the process variability is also affected by some assignable cause, such as a worn machine component. The power of a control chart lies in its ability to detect assignable causes.
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Upper control limit
Centerline
Lower control limit
1
2
3
4
5
6
7
8
9
10
11
12
Sample number FIGURE 42.1
A typical control chart.
A control chart, whether for measurements or attributes, consists of a centerline corresponding to the average quality at which the process should perform when statistical control is exhibited, and two control limits, called the upper and lower control limits. A typical control chart is shown in Figure 42.1. The control limits are chosen so that values falling beyond them can be taken to indicate a lack of statistical control. The general approach consists of periodically taking a random sample from the process, computing some appropriate quantity, and plotting that quantity on the chart. Other graphical tools that can be used to gage system performance include the histogram, Pareto diagram, cause-and-effect diagram, and defect-concentration diagram. Each uniquely contributes to performance improvement through a systematic reduction of variability. The key task in the application of statistical control is determining the appropriate variables on which to apply control. The number of control charts used is not as important as having the correct chart present at the right time and place to enable operators and management to find and remove the source of a problem. 42.2.2.2 Reliability Engineering Reliability engineering (Kececioglu, 1991) originated in the aerospace industry during the 1950s when failure rates of military electronic systems resulted in limited supply and high life-cycle costs. With an emphasis on data collection, statistical analysis, and risk assessment, this engineering discipline has since achieved significant credibility in providing the probability that a component or system will perform a required function without failure under a given set of circumstances. This is predicated on knowing what failures to expect, and how they will become evident over time. The failure process is usually complex, consisting of at least three types of failures: initial failures, wearout failures, and those that fail in between. Figure 42.2, the so-called bathtub curve, represents a typical failure pattern. In a well-designed system, the majority of failures are completely random. These would be depicted by the bathtub curve shown during the period when the failure rate is lowest, and for most purposes can be regarded as constant. Other common forms of failure patterns are shown in Figure 42.3. Line A can usually be applied to parts that seldom fail, but are subjected to damage at any time. Line B represents a failure pattern for an item that has a finite life, with the majority of failures occurring before that life is doubled; for example, a light bulb guaranteed for a certain number of hours. Line C exhibits a gradual increase of failures, true of many mechanical moving parts subjected to gradual wear. Line D demonstrates that when early-age failures have been removed by burn-in, the time to occurrence of wearout failures is very large (as with electronic parts).
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Random-Failure
Wear-out
Probability of failure
Burn-in
Time The “bathtub” curve.
Probability of failure
FIGURE 42.2
C D
C B B
D
A
A
Time FIGURE 42.3
Common failure patterns.
Mathematically, it is appropriate to model the anticipated failure pattern with a distribution formula to predict the likelihood of failure, and hence determine the extent of reliability testing required before endorsing a system or structure of interest. In situations where most failures are due to wear, the normal distribution may very well be appropriate. The gamma-distribution is frequently used to model components that have an exponential time-to-failure distribution. When a system is composed of a number of components, and failure is due to the most serious of a large number of possible defects, the Weibull distribution seems to perform particularly well as a model. Should complex and competing failure modes exist, modeling should be supplemented with results from statistically based experiments. In forming a statistical design of experiments, judgment is needed in determining a factorial set of computer simulation tests and/or actual hardware tests. Upon performing these tests, results are analyzed using variance techniques. Through the mathematics, an understanding of the sensitivity of the design to each factor or interaction of factors results. By being attentive to the identified characteristics that significantly impact the system or structure of interest, reliability improvement and or life extension can be achieved. As reliabilities improve, test times correspondingly increase. Thus, demonstration testing becomes less practical. An alternative to testing is to continuously monitor the structure of interest during its development stage so that weaknesses are quickly identified. The process enables misapplied parts to be found
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and replaced, design errors to be corrected, and defects associated with workmanship or manufacture to be eliminated. Accumulating test data from different environments during the design process is not simple, but necessary to ferret out any unintended performance attributes.
42.2.3 Maintain the Asset If equipment is not looked after, the impact is not immediately noticed. As a result, it is conceivable that a “not broke, don’t fix it” attitude can prevail in an industry, with the inherent benefit of making shortterm profit by saving monies earmarked for upkeep. Yet, given the complexity in the design and operation of most machines, breakdown is inevitable and has an ever-increasing impact on profitability due to factors such as loss of availability, cost of spares, cost of labor, cost of secondary damage, and risk of injury to people and the environment. The engineering challenge has therefore become one of identifying the optimum means for ensuring against catastrophic failure, while avoiding needless expenditure. Approaches taken to maintain systems have evolved as industry has changed, as shown in Table 42.1. Given product demand, historical behavior, and management attitude, the maintenance plans of today will likely be unique to the system of interest, incorporating one or more maintenance philosophies based on failure mode, timing, reliability, or condition. 42.2.3.1 Failure-Based Maintenance Failure-based maintenance requires little if any advanced planning. It typically takes the form of waiting until a failure occurs, at which time the reaction is to repair the damage. This is the simplest approach to maintenance and is very effective if the cost of failure and cost of repair are both low. The drawbacks depend on the consequence of failure. Unexpected failures are disruptive to existing activities, requiring plans to be altered and may cause a loss in productivity. The means to implement this approach is extremely simple. The failure is defined and catalogued to provide information for future use, and assigned a priority as to the urgency of repair. Upon assembling the necessary resources, the system is restored to its original condition. 42.2.3.2 Time-Based Maintenance Time-based maintenance evolved due to the economic impact of failure-based maintenance. It is a system of addressing upkeep at fixed periods of time, independent of the condition of the equipment. It is very effective when the performance and condition of equipment are related to the passage of time, and where the maintenance tasks can be carried out simply and quickly, such as an oil or filter change. Often, an annual cycle is used for shutdown, disassembly, and mechanical inspection of the various elements of the system. One disadvantage of this maintenance philosophy is associated with the random nature of failures. As with failure-based maintenance, an unanticipated malfunction can lead to high repair costs and a heavy TABLE 42.1 Period
History of Maintenance Approaches Manufacturing Characteristics
Dominant Maintenance Approach
Up to WWII
Overdesigned Reliable
Failure-based maintenance Lubricate and service
WWII–1970
Increased mechanization Downtime issues
Time-based maintenance Fixed-time overhauls
1970–1980
Worldwide competition Increasing costs (inflation) Just-in-time inventory
Time-based maintenance Introduction of reliability-centered maintenance (RCM)
1980–Present
Highly automated equipment Safety/environmental issues Computer technology
Time-based maintenance Reliability-centered maintenance Pursuit of condition-based maintenance (CBM)
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loss in productivity. A second disadvantage is that at the designated time for inspection, perfectly good equipment can be disassembled. This is not only expensive because of downtime and labor, but exposes the equipment to be at risk upon reassembly due to human error and/or the introduction of foreign elements. 42.2.3.3 Reliability-Centered Maintenance Reliability-centered maintenance (RCM) is a technique that originated in the aircraft industry to develop maintenance schedules on the principle that the reliability of systems and structures and the performance achieved are a function of design and build quality. Two separate methodologies are used: one for systems and the other for structures (Smith, 1993). For systems, RCM begins with a top-down failure modes and effects analysis (FMEA). The objective of the FMEA is to identify all plausible means of failure for each item of a system based on its function. Criticality analysis is sometimes employed to rank the modes according to probability of occurrence and severity. The modes are then categorized as being evident to or hidden from the operator in the normal performance of duty, and further differentiated as to consequences sensitive to a particular sector of industry (e.g., safety, environment, operations, economics). From the resulting list, a set of questions is asked to determine the most effective maintenance task to address each failure mode. The outcome may dictate at a specified time interval whether to determine the condition of the item, rework the item, discard the item, or do nothing. It may even suggest that the failure mode cannot be addressed through a maintenance task and must be redesigned. For structures, RCM methods were developed to establish inspection regimes to ensure structural integrity and thereby safety. Operational and economic consequences do not apply. The methodology is based on the assumption that structure either has a safe life, normally related to the fatigue process, or is designed so that it incorporates the use of redundant load paths. For inspection purposes, structurally significant items are identified and rated in accordance with their risk of damage due to fatigue, environmental deterioration, and accidental damage using a table of structural rating factors developed specifically for each application. For non-significant areas, a low-cost visual inspection plan is implemented. RCM is being used effectively over a wide range of industries, as well as in commercial and military aviation where its use is now accepted practice. Normally, it is necessary to cost-justify the process as it has a cost of its own, including the time it takes to acquire the necessary skills for implementation. 42.2.3.4 Condition-Based Maintenance Condition-based maintenance (CBM) is safer and economically more attractive than either the failurebased or time-based methods. The fundamental concept behind CBM consists of evaluating the system or structure from many aspects and assessing the current state of operation or performance. Maintenance plans and requirements are then driven by the anticipated workload. The key to CBM is being able to perceive or assume a condition as a result of sensing, observation, or test. Evaluation based on condition requires management support, as resources must be allocated for the devices used to obtain information about the behavior of the system or structure, as well as establish documentation and historical information for comparative use. Trained personnel are required to implement and sustain the effort. In an effectively run program, the savings incurred from reduced maintenance should offset these costs. Success or failure is dependent on good knowledge of the condition of the item of interest, necessitating that condition monitoring is a prerequisite. The tools and techniques required for the implementation of condition monitoring are discussed next in Section 42.3.
42.3 Condition Monitoring Approaches Any engineering system will fail to operate satisfactorily at some time in its useful life, induced by many, potentially unrelated, factors. As a result, there are a variety of approaches commonly used to assess machine behavior, the technical requirements of which are very different, as noted in this chapter section.
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42.3.1 Vibration Monitoring Vibration is defined as a periodic motion about an equilibrium position. Its duration and magnitude depend on the degree of damping the affected materials possess, and the phase relationships between the mechanism that perturbs the system and the response that is obtained. Vibration may be forced through unbalance, rub, looseness, and misalignment, or freely self-excited through internal friction, cracking, and resonance. Once generated, vibration can be transmitted from its source to other components or systems. When it reaches unacceptable levels, tribological wear-and-tear processes are accelerated, which in turn initiate various failure mechanisms. Hence, by monitoring for the presence and change of vibration patterns through the methods of signature analysis or shock pulse, the consequences of avoidable breakdowns can be prevented (Eisenmann, Sr. and Eisenmann, Jr., 1998). 42.3.1.1 Signature Analysis As vibration exhibits a unique pattern or signature of motion, analysis aims to provide information concerning its amplitude and predominant frequencies using data transmitted from sensor pickup. The means to accomplish this may vary from direct measurement in the time domain to the sophisticated application of several mathematical methods in both the time and frequency domains. 42.3.1.1.1 Sensors The first step in the monitoring of vibration is to capture an accurate recording of it, normally over a period of time. The devices typically used for this task are electronic sensors, or transducers, which convert numerous types of mechanical behavior into proportional electronic signals. Transducer outputs are usually converted into voltage-sensitive signals that can be processed with various electronic instruments. Industrial transducers used for measuring dynamic characteristics fall into the three distinct, yet mathematically related, categories of acceleration, velocity, and displacement. Selection of a sensor proportional to these parameters depends on the frequencies of interest and the signal levels involved. Accelerometers are preferred for most vibration monitoring applications. These acceleration measuring devices are fully contacting probes mounted directly onto a mechanical element (e.g., a bearing housing). They are useful for detecting low to very high frequencies (3 to 30,000 Hz) and are available in a wide variety of general-purpose and application-specific designs. The piezoelectric accelerometer is versatile, reliable, and the most popular vibration sensor for machine monitoring. It contains a piezoelectric crystal that emits an electrical charge when a mechanical load is applied. It also contains a mass that, when accelerated by vibration, imposes a definable force against the crystal. The resulting output charge from the crystal, being proportional to the force, which is proportional to the acceleration, is converted by an integrated circuit to a voltage signal that can be interpreted by a recording instrument. The rugged, solid-state construction of industrial piezoelectric sensors enables them to operate under harsh environmental conditions, unaffected by dirt, oil, and most chemical atmospheres. Standard transducers can be purchased for operation up to 300°C and custom accelerometers have been built to withstand temperatures in excess of 650°C. Most piezoelectric sensors contain internal electronics that can amplify a small acceleration signal, and if desired, convert it into a velocity or displacement signal. Velocity sensors, generally used for low- to medium-frequency measurements (1 to 1500 Hz), obtain absolute velocity measurements of machine elements. Traditional velocity coil sensors or vibrometers use an electromagnetic (coil and magnet) system to generate the velocity signal without the need for an external power source. They are fully contacting probes mounted directly onto the structure to be monitored. During recent years, piezoelectric velocity transducers (internally integrated piezoelectric accelerometers) have replaced these devices due to cost and durability in applications where velocity remains the preferable measurement. Displacement sensors are typically used to measure changes in position and clearance. An LVDT (linear-variable differential transformer) converts the rectilinear motion of an object to which it is
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attached into a corresponding electrical signal by means of a series of inductors positioned in a hollow cylindrical shaft and a solid cylindrical core. An RVDT (rotary-variable displacement transformer) similarly senses angular position. Piezoelectric transducers (doubly integrated accelerometers) have also been used to measure displacement, yielding an output proportional to the absolute motion of a structure. Non-contact proximity probes, such as eddy-current sensors, can monitor the relative motion between the proximity sensor mounting point and a target surface. These devices are generally used to sense shaft vibration relative to bearings or some other support structure. When selecting a vibration sensor, many factors must be addressed so that the best sensor is chosen for the application. Questions to ask include: • • • • •
What is the temperature range required? Are any corrosive chemicals present? Is the atmosphere combustible? Are intense acoustic or electromagnetic fields present? Are there sensor size and weight constraints?
For a piezoelectric sensor, two key parameters to consider include sensitivity and frequency range. To select the optimum frequency range, it is necessary to determine the frequency requirement of the application. This may already be known from vibration data collected from similar systems or applications; otherwise, the best approach is to place a test sensor at various locations on the machine of interest and evaluate the data collected. Given that most high-frequency sensors have low sensitivities, and conversely, most high-sensitivity sensors have low frequency ranges, it is generally necessary to compromise between the two. 42.3.1.1.2 Signal Acquisition The collection, transmission, and recording of vibration information should be done efficiently to avoid signal degradation. Signals must be protected from the many forms of interference generated by electrical and mechanical components during normal circuit operation. Transmission lines should be shielded from magnetic and electrostatic fields with appropriate materials. Questions to consider in assembling the electronics needed for signal acquisition include: • What cable lengths are required? • What temperatures will the cable be exposed to? • What are the power supply requirements? The degree of difficulty in acquiring quality vibration signal information increases with the complexity of the conditioning and recording devices used. Such instrumentation may include an oscilloscope, tape recorder, real-time signal analyzer, and a dedicated digital computer. The machine diagnostician may find it useful to convert the continuous analog signal measured by a transducer to a discrete form stored at equal time intervals in computer memory. This analog-to-digital conversion of data, known as digitizing, is carried out by a microprocessor. An electronic filter may also be of use in rejecting unwanted portions of the signal being transmitted. Both analog and digital filters are commonly used. 42.3.1.1.3 Data Interpretation The output from vibration sensors generally requires some degree of conditioning and statistical interpretation to provide meaningful information that can be used by the machine diagnostician to detect a potentially detrimental change in machine performance. In addition to associating a given waveform to its arithmetic mean, geometric mean, root mean square (rms), standard deviation, kurtosis, and skewness, a variety of other parameters have found favor in the maintenance community, including: 1. Frequency: the repetition rate of a periodic event within a specific unit of time. 2. Phase: a timing measurement between two signals.
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3. Peak value: the maximum magnitude measurement of periodic dynamic motion within a given time interval. 4. Crest factor: the ratio of the peak value of a periodic signal to its rms value. 5. Power Spectral Density (PSD): the power of random vibration intensity, in mean-square acceleration per frequency unit. When the vibration signature is composed of a mixture of sinusoidal waveforms of different amplitudes, frequencies, and phase differences, it is usually necessary to transform the data from the time domain into the frequency domain. This can be accomplished through a Fast Fourier Transform (FFT), which is a mathematical operation that decomposes the signal into a finite number of discrete frequency components. To remove some of the unwanted noise from a signal, enveloping can be used. This technique identifies the bursts of high frequencies that occur at a regular rate and passes them through highfrequency filters to eliminate low-frequency components. Wavelet analysis provides an alternative approach to traditional signal processing methods, for example, Fourier analysis, in breaking a signal up into its constituent parts (Newland, 1993). Wavelets are mathematical functions that divide data into different frequency components, and then study each component with a resolution matched to its scale. The driving impetus behind wavelet analysis is its ability to localize portions of signals in time (space) as well as scale (frequency), which provides an advantage over Fourier methods in that situations can be more accurately represented when the signal contains discontinuities and sharp spikes. The technique is ideal for analyzing signals that show time delays between pulses or pulse shape changes. In addition to interpreting data mathematically, the machine diagnostician can use visual techniques to identify a potential problem, viewed via an oscilloscope or PC monitor. Lissajous figures are a series of patterns traced by displaying time-based waveforms from two transducers whose outputs are phase shifted by 90°. For vibration measurements on rotating machinery, these are normally referred to as orbit plots. From a distinct pattern, information including amplitude, frequency, and phase angle can be extracted as an indication of wear, misalignment, unbalance, and rub. Analysis can also be carried out using Bode and polar plots that simultaneously display vibration amplitude and phase angle as a function of machine speed. Data of this type is essential for identifying rotor critical speeds and the influence of various resonances. To ensure that a system will not be operated at or near resonant frequencies, which are known to cause catastrophic failure, a cascade or waterfall diagram can be of use. This is a three-dimensional graph providing the frequency content of vibration signals as a function of machine operating speed. A successful vibration monitoring program using signature analysis requires a commitment to collecting a sufficient amount of vibration data, well in advance of having to take corrective action. Whether using visual or numerical techniques, data representing satisfactory machine performance must first be established and trended to establish satisfactory levels of maintenance alarm and response. 42.3.1.2 Shock Pulse Method The shock pulse method (SPM) is a technique that utilizes signals from rotating elements in contact as the basis for efficient condition monitoring of machines. It cannot be used to determine which part is at fault, but can be used to detect a lack of lubricant and/or the presence of wear when there is no physical deformation present. This method does not measure the vibration itself, but the shock wave or pulse created from impact. When two bodies collide, a mechanical shock or pressure wave spreads through the material of both bodies. Its peak amplitude is a function of the impact velocity. The frequency of this vibration is a function of the mass and the shape of the colliding bodies (e.g., a rolling element and bearing raceway). When the wavefront is detected by a transducer, the transducer’s reference mass reacts to the weak shock pulses with an amplitude oscillation. Electronic filtering is used to ensure that the transducer maintains a 32-kHz natural frequency to avoid being influenced by other sources. For bearing analysis, a microprocessor evaluates the signal using input data defining the bearing size and rotational velocity, and provides a decibel scale measurement of the shock pulse strength. Over time,
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a rise of up to 35 dB indicates developing damage; 30 to 50 dB indicates visible damage; and above 50 dB indicates risk of failure. Readings can be translated into measurements of relative oil film thickness or surface damage, whichever applies.
42.3.2 Oil Monitoring Oil is required to perform a number of functions in machinery, including reducing friction, cooling components, and cleaning load-bearing surfaces. Over time, it is likely to degrade, losing its lubrication properties due to chemical breakdown, and become contaminated by a buildup of particles caused by component wear. A number of techniques are available for analyzing the condition of an oil and any wear particles that are present (Hunt, 1996). Results can provide information that is very useful in determining the actual state of machine performance, and lead to improved efficiencies and cost savings in equipment operation. 42.3.2.1 Chemical and Physical Testing The chemical and physical testing of oil necessitates that a representative sample of the oil supply be taken for analysis. In circulating oil systems, the best location to obtain this sample is at a live zone, upstream of filters where wear debris particles are likely to concentrate. Usually, this means sampling from fluid return or drain lines. The sample should ideally be taken while the machine is running at its normal load, speed, and work cycle with the lubricant at normal operating temperature. Because an important objective in oil analysis is to obtain results of integrity, considerable care must be taken to avoid contaminating the contaminant. Sampling intervals are commonly scheduled at a frequency that can be keyed to recommended drain intervals or operating hours. A number of parameters are available for describing the condition of oil. Those identified in the following list can be tested for by the user, but special instrumentation and skill is often required. For this reason, analysis is commonly performed by lubricant companies or outside laboratories, offering fast and relatively inexpensive service. 42.3.2.1.1 Viscosity Viscosity is a measure of flow resistance. Its value is dependent on the viscometer used for the measurement and the temperature of the fluid being measured. The test is usually performed at 40°C and 100°C. A change in viscosity generally indicates a problem, which could be attributed to contamination by water, coolants, fuels or other lubricants, or degradation upon contact with oxygen (oxidation). It could also be the result of the addition of an incorrect grade of lubricant. 42.3.2.1.2 Total Acid Number The total acid number, in milligrams of potassium hydroxide per gram of oil, is a measurement of the level of acid in the oil. An increase in this reading is symptomatic of oil degradation through oxidation. Clean oil usually has a measurable acid number as a response to some of its antioxidant and antiwear additives. As the additives deplete over time, the reported acid number may drop, go through a minimum, and then rise. It drops because the additives are being depleted, bottoms out when they are gone, and rises again because there is now genuine acidic material in the oil. Maintenance action is generally advised before hitting the bottom of the curve by replacing the oil completely or refortifying it with concentrated additives. 42.3.2.1.3 Total Base Number The total base number is an aggregate measure of the concentration of the additives in the oil that counteract acid buildup. It is measured in equivalent milligrams of potassium hydroxide per gram of oil. This test is generally performed for oils taken from internal combustion engine crankcases, affected by the sulfur content of fuels that form sulfuric acid during the combustion process. Some proponents advocate changing oil when the total base number depletes to 50% of the total base number of the virgin stock.
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42.3.2.1.4 Specific Gravity Specific gravity is the mass of a fluid per unit volume referenced to a standard temperature. Oil, contaminated by coolants, fuels, or other lubricants, will have a specific gravity different from that of clean oil. 42.3.2.1.5 Flashpoint The flashpoint is the temperature to which a combustible liquid must be heated to give off sufficient vapor to momentarily form a flammable mixture with air when a small flame is applied under specified conditions. For used oil, a change in the value of this parameter over time may be indicative of contamination. 42.3.2.1.6 Pour Point The pour point is the lowest temperature at which a fluid is observed to flow when cooled under specified conditions. For used oil, a variation in this reading when compared to that of its original state, may be indicative of contamination. 42.3.2.1.7 Water Content The presence of water in oil (25 ppm or greater) can be harmful. It can affect the oil by significantly reducing its load-carrying capacity and negatively react with its oil additive package. In a free state, water can cause corrosion. The Karl Fischer method is the standard laboratory test to measure the water content of oil. It is based on the chemical reaction of water with iodine, which is either added volumetrically in a special “Karl Fischer” titrant or generated electrochemically via a titration cell. This relatively inexpensive method can determine water in a wide concentration range from 100% to as low as 1 ppm. 42.3.2.1.8 Gravimetric Analysis Gravimetric analysis is a measure of the dry weight of solid material present in a specific volume of fluid, usually 100 mL. As the amount of debris in a filtered system can be very low, the results are subject to variability, sometimes necessitating that a much larger volume of sample oil be used. Measurements are given in milligrams of contaminant per liter of fluid. The technique is commonly used for verifying the cleanliness levels provided by some other method. 42.3.2.2 Spectrography Spectrography is an analysis method that identifies the presence of particular elements within an oil. Results can be compared to those of an as-new oil sample in identifying deleterious particles and the rate in which they generate. A typical report from this test would summarize the results for the customer and recommend remedial action. Table 42.2 provides a summary of metals that can be identified using any of the following spectrographic techniques with an indication as to their possible origin. TABLE 42.2
Wear Metal Origins
Wear Metal
Possible Origin
Aluminum Antimony Chromium Copper Iron
Bearings, blocks, compressor blades, impellers, pistons, pump vanes, rotors Bearings, grease Exhaust valves, gears, liners, rings, rods, rolling element bearings, seals, shafts Bearings, bushings, cylinder liners, thrust washers Bearings, blocks, camshafts, clutch, cylinders, crank shafts, gears, liners, pistons, pumps, rings, shafts, valve train Bearings, oil additives, seals, solder Oil additives, shafts, valves Oil additives, piston rings Gears, rolling element bearings, shafts, turbine blades Gaskets, ingested dirt/sand, sealant Rolling element bearings, shafts, solder Bearings, bushings, seals, solder, worm gears Bearings, compressor blades, turbine blades Bearings, coolant, oil additives
Lead Magnesium Molybdenum Nickel Silicon Silver Tin Titanium Zinc
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42.3.2.2.1 Atomic Absorption Spectroscopy Atomic-absorption (AA) spectroscopy uses the absorption of light to measure the concentration of particular elements. The oil sample is first vaporized in a flame or furnace, producing atoms that absorb particular wavelengths of light for a given element. Concentration is determined from the strength of absorption. AA spectrometers use monochromators and detectors for ultraviolet and visible light. The main purpose of the monochromator is to isolate the absorption line from background light due to interference. Simple, dedicated AA instruments often replace the monochromator with a bandpass interference filter. Photomultiplier tubes are the most common detectors for AA spectroscopy. Concentration measurements are usually determined from a working curve after calibrating the instrument with standards of known concentration. 42.3.2.2.2 Atomic Emission Spectroscopy Atomic emission spectroscopy (AES) uses a quantitative measurement of the optical emission from excited atoms to determine the presence of particular elements and their concentrations. An oil sample with debris is introduced into a flame or plasma where vaporization and atomization occur. When the activated metal atoms cool and revert to their former stable state, light is emitted in a burst. The light has a unique wavelength signature for each element present, with a magnitude proportional to quantity. Because all atomic elements in a sample are excited simultaneously, they can be detected simultaneously using a polychromator with multiple detectors. This ability to simultaneously measure multiple elements is a major advantage of the AES technique. When AES is limited by its ability to detect coarse particle sizes (greater than 10 microns), the oil can be prefiltered through a rotrode. A rotrode is a porous carbon disk that is pressed onto the end of a rotating hollow shaft. Upon drawing an oil sample through its outer circumference when a vacuum is applied to the inside, the particles in the oil form a thin line around the outside edge of the disk. In collecting these particles, a much larger volume of oil is used than is normally analyzed by a traditional spectrometer, thus increasing the sensitivity of the method. A spark, formed between the top of the disk and the tip of a carbon rod electrode, atomizes the particles for detection. Multi-element analysis using the AES method can be accomplished in 30 to 40 seconds. Preparation time can be as short as 4 or 5 minutes for relatively clean used-oil samples. Engine oil samples with high soot levels require the longest filtration times (sometimes 30 minutes or more). 42.3.2.2.3 XRF Spectroscopy XRF (X-ray fluorescence) spectroscopy is similar to AES in that both techniques require an excitation of atoms followed by an analysis of the emitted light that results. Whereas the AES method excites the outer electron shells of the atoms using an electrical discharge or flame, XRF uses an X-ray, gamma-ray, or charged particle beam to stimulate characteristic X-ray emission from the elements in the sample. These atomic X-rays are detected, sorted into energy bins, and counted. The result is an energy spectrum that is effectively a fingerprint of the sample. The intensities of the various energy peaks in the spectrum are roughly proportional to the concentration of the corresponding elements. Commercial XRF spectrometers are designed to be operated safely without any requirement for radiation certification of the operator. Several studies suggest that its use is superior to atomic spectroscopy in the detection of failure modes involving large particles (greater than 10 microns). 42.3.2.2.4 Infrared Spectroscopy Infrared (IR) spectroscopy can be used to determine oil contamination levels and additive depletion based on how IR radiation interacts with materials on a molecular level. Molecules in a sample absorb IR radiation at specific wavelengths in the IR spectrum. An increase in the number of molecules that are present for a given element will result in an increase in measured absorption. Results from an analysis are usually provided in graphical form, using an experience-based algorithm to process the signal. This method is noted for monitoring the depleting concentration of antioxidants and antiwear components. If the sample is from an internal combustion engine, it also measures ethylene glycol and soot
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levels. It should be noted that the mixing of different oils renders this method nearly worthless as a valid diagnostic tool. As with all spectrographic methods, it is advised that tests be run on the same spectrograph to eliminate hardware-specific differences. 42.3.2.2.5 Raman Spectroscopy Raman spectroscopy is the measurement of the wavelength and intensity of inelastically scattered light from molecules. The Raman effect is generated when an intense beam of light, usually generated by a laser, is directed onto a fluid sample, exciting molecules that subsequently scatter a fraction of this excitation light. While most of this scattered light is at the same wavelength as the incident light, some is shifted to different wavelengths, corresponding to different energy levels in the material. Several different Raman shifted signals will often be observed, each being associated with different motions of molecules present in the sample. A study of this scattered light, referred to as the Raman spectrum, can provide both qualitative and quantitative information about the sample under investigation. The mechanism of Raman scattering is different from that of IR absorption; hence, Raman and IR spectroscopy can provide complementary information concerning the condition of a fluid. 42.3.2.3 Ferrography Ferrography is an analysis method that identifies the presence of ferrous wear particles suspended in an oil using a magnetic field to separate them according to their size. Two techniques are used: direct reading and analytical. 42.3.2.3.1 Direct Reading Ferrography Direct reading (DR) ferrography provides a direct measure of the amount of ferrous wear metals present in a sample of oil. The particles are separated and measured by drawing a sample of oil through a collector tube that lies over a magnetic plate. Larger particles in the oil (greater than 15 microns) are strongly attracted to the magnet and accumulate at the entrance of the collector tube. Smaller particles, which are only weakly attracted by the magnet, deposit equally along the length of the collector tube. By measuring the blockage of light using fiber optics, one at the entrance of the collector tube, and the other just further up the collector tube the quantities of large particles (denoted DL) and small particles (denoted DS) are determined. Trending of the DL and DS readings reveals changes in the wear mode of the system. For example, an increase in the DL value indicates that the system has entered into an abnormal wear mode. In comparison, an increase in the DS value can indicate an increase in system corrosion (corrosion wear particles are typically less than 3 microns in size). When an abnormal wear mode is detected, analytical ferrography is used for more detailed analysis. 42.3.2.3.2 Analytical Ferrography Analytical ferrography allows an analyst to visually examine the wear particles present in an oil sample by use of a microscope. The oil is passed over a glass slide that rests on a magnetic plate. The ferrous particles line up from the largest wear particles to the smallest in rows along the length of the slide, called a ferrogram. Nonferrous wear particles can be easily distinguished from ferrous particles because they are deposited randomly across the length of the slide. Under high magnification, the particles are readily identified and classified according to their morphology (size, shape, texture, etc.). A trained analyst can differentiate between a variety of wear particle types and assess the cause of such wear. Used in conjunction with spectroscopic oil analysis, ferrography verifies the wear condition of a machine. The test is neither inexpensive nor quick because there is a great deal of handling required. 42.3.2.4 Magnetic Chip Detectors As the name implies for this oil analysis method, a magnetic plug is inserted into the lubrication system before the filter to pick up ferrous chips created due to material wear and tear. The rate at which particles
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appear and the size of the particles can give an indication as to the likelihood of a machine malfunction. Larger particles are often generated near failure. In systems where the consequences of failure can be severe, continuous monitoring may be appropriate. Visual inspection and cleaning of the magnet at regular intervals are advised. 42.3.2.5 Particle Counting A system of oil cleanliness classification was initially ratified in 1974 by the International Standards Organization (ISO) and later updated in 1987. Identified as ISO 4406, this standard is used to describe a theoretically infinite range of contamination levels in oil via a three-class code representing the total number of particles per milliliter oil greater than 2, 5, and 15 microns, respectively. To manually count, size, and evaluate the types of particles present in an oil, oil is drawn through a membrane of known pore size and the trapped particles are counted by viewing the membrane under a microscope at various magnifications. The technique is tedious and time-consuming. Statistical counting techniques are usually employed. In an attempt to overcome the labor-intensive nature of particle counting by human sight, automatic particle counters have been developed, which have certain limitations and give erroneous counts if not used correctly. One approach uses the principle of fluid flow decay in which oil is passed through a screen of known mesh (usually 10 or 15 microns). The presence of contaminant gradually blocks the pores of the screen. By knowing the number of pores in the screen and the volume of oil that passes, the number of particles greater than the pore size per unit volume can be inferred by the degree of blockage. The disadvantage of using this technique is that it assumes a predetermined size distribution without actually measuring the number of particles. The most common approach in automatic particle counting uses a light blockage principle. Typically, a known volume of oil (usually 5 mL) is injected through a very small sampling cell. On one side of the cell is a beam of laser light and on the other side, a detector. As particles pass through the cell, they are counted as they block the beam of light by casting a shadow on the detector. The drop in light intensity received by the detector is proportional to the size of the particle blocking the light beam. In this way, both the number and size of the particles can be measured. An instrument is usually set up to measure particles in five different micron size ranges: 5 to 15, 15 to 25, 25 to 50, 50 to 100, and greater than 100. Results are expressed as the total number of counts (particles) per milliliter oil. 42.3.2.6 Image Analysis Image analysis, also referred to as image processing, provides information to the machine diagnostician through visually understood means. One of the simpler methods of image analysis in assessing used oil is the patch test, a method by which a specified volume of fluid is filtered through a membrane filter of known pore structure. All particulate matter in excess of an average size, determined by the membrane characteristics, is retained on the surface. Thus, the membrane is discolored by an amount proportional to the particulate level of the fluid sample. Visually comparing the test filter with standard patches of known contamination levels determines acceptability for a given fluid. The membrane could also be scanned using a video camera, with the resulting image being converted into a signal for processing by an image analyzing computer (IAC). Particles are identified in relation to their gray scale or color contrast with the surface of the membrane. The computer then applies the logic to provide particle count and a host of shape parameters, including dimension, area, and circumference. Potentially, this method overcomes the tiresome task of visual inspection; however, the technique has some shortcomings. If particles cluster together, editing is necessary to avoid interpreting the mass as a single particle. If there is a similarity between the color of the particle and background, incorrect sizing usually occurs. The U.S. Navy is developing a real-time online optical sensor called Lasernet for detecting and classifying suspended particles in lubricating oil flow systems (Reintjes et al., 1998). The optical imaging technology is designed to detect and classify particles according to specific mechanical faults. The system
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is capable of detecting ferrous, nonferrous, and nonmetallic particles such as sand or debris from advanced ceramic bearings and can distinguish between fault-related and non-fault-related particles. By measuring the size, rate of production, and shape of the debris particles, Lasernet can determine the type and severity of a fault. The Lasernet monitor is a full-flow inline monitor that detects and classifies debris particles. It examines all of the oil flow and can distinguish between debris particles and air bubbles. The Lasernet monitor is based on laser diode illumination of the oil column, high-speed optical imaging at frame rates up to 1000 per second, real-time image processing with a dedicated image processor, and neural net classification of the debris. It is designed to provide cumulative health monitoring of engines and gearboxes, recommend action for ground maintenance and, if necessary, provide early warning of potential catastrophic failure.
42.3.3 Thermal Monitoring The successful use of a machine often requires a thorough understanding of how it will thermally respond to being used. Temperature-dependent material properties, thermally induced deformation, and temperature variations may be important considerations in establishing safe limits of operation. Thermal energy is often generated and transferred when a machine begins to experience trouble, possibly attributed to friction, overloading, chemical reactivity, and/or insulation damage. Manifested as an unexpected temperature rise, action is warranted to determine the cause. Thermal monitoring methods (Omega, 1998) available to help diagnose a situation fall into two categories: contact and non-contact. 42.3.3.1 Contact Methods Contact methods for measuring temperature infer that something is placed on or within the surface of the component being assessed. Thermal paints and crayons fall in this category. They are easy to apply on the surface of interest and change color when a particular temperature range is reached, giving an observer a quick indication of a thermal event. Thermometers, such as the sealed liquid-in-glass-type, consist of a glass tube containing liquid. If the temperature increases, the liquid expands and rises in the tube. The temperature is then read on an adjacent scale. Mercury is commonly used as the liquid for measuring temperatures ranging from –15°C to +540°C. Other instruments, often used in permanent temperature control and measurement systems, include the thermocouple, RTD, and thermistor. 42.3.3.1.1 Thermocouple A thermocouple is a temperature transducer consisting of two wires of different metals (e.g., iron/constantan) joined at both ends. If the two junctions between the metals are at different temperatures, an electric current will flow around the circuit at a voltage directly proportional to the difference in temperature between the two junctions. When used for measuring temperature, one of the two junctions is placed in contact with the material whose temperature is to be monitored. The temperature of the second junction must be either known or controlled to at least the accuracy expected for measurement. A meter used to measure the voltage of the circuit can be calibrated directly to read in degrees of temperature, or provide the user a direct voltage reading to be converted into temperature via a standard thermocouple chart. Thermocouples are self-powered, rugged, and capable of measuring within a large temperature range (–200°C to +1800°C). 42.3.3.1.2 Resistance Temperature Detector A resistance temperature detector (RTD) is constructed with a wire coil or a thin layer of metal to form a precision resistor. The resistance value changes very accurately and repeatedly in a positive direction when heated. By incorporating the resistor in an electric circuit and attaching it to the material whose temperature is being measured, temperature can be determined from the change in resistance with the use of an equation relating the two variables.
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RTD assemblies can be used in a wide variety of configurations to give the highest accuracy of temperature measurement. An RTD is considered to be very stable, measuring temperatures in the range of –260°C to +850°C. It tends to be expensive and requires a current source. Platinum is usually used as the resistive material because it is chemically inert and exhibits repeatable resistance-temperature characteristics. 42.3.3.1.3 Thermistor A thermistor is generally described as a thermally sensitive resistor constructed with metal oxides formed into a bead and encapsulated in epoxy or glass. Its resistance exhibits a nonlinear, large negative change as it is heated. Used in the same way as an RTD, the change in resistance recorded during a small temperature change of a thermistor is several times greater than an RTD, making measurement easier. The device tends to be low in cost, yet fragile. Its temperature range is limited (–80°C to +300°C). 42.3.3.2 Non-contact Methods The non-contact approach to measuring temperature uses the principle that all objects emit electromagnetic waves from their surface in proportion to their warmth. By focusing this form of radiation from its source onto a sensor, its intensity can be interpreted and displayed as a temperature. The main advantage of this method, applied in pyrometers and infrared imaging, is that large areas can be quickly surveyed at a safe distance. 42.3.3.2.1 Pyrometer A pyrometer is a device with sensors that accept a range of radiant energy wavelengths from the visible light portion to the IR portion of the electromagnetic spectrum. A detector, usually focused on a select point of the surface of interest through a suitable lens, converts the radiant energy emitted by the surface into an electrical signal that is interpreted to provide a temperature reading. One type of pyrometer, the optical or brightness pyrometer, requires manual adjustment based on what is viewed through a sighting window. A second type, the two-color ratio pyrometer, compares the spectral radiance at two wavelengths to identify the temperature. Both devices are complex and are usually used in a laboratory setting. The total radiation pyrometer is commonly used for industrial applications, where temperature measurement from –150°C to +4000°C is needed. It responds reliably to all wavelengths in both the visible and IR portions of the spectrum, with exception to those altered by components of the system (e.g., lenses, filters, and atmosphere). Calibration of the instrument is required, typically using a blackbody, which is an object having a surface that does not reflect or pass radiation. Temperature limits and speed of response are dependent on the type of radiation detector used. 42.3.3.2.2 Infrared Imaging Thermal images are pictures of heat using the radiated energy emitted from an object. They are created by an IR thermal imager, a device that captures a portion of the radiated energy through a variety of scanning camera techniques, yielding a spatial map of temperatures. The instrument typically incorporates a cooling system to avoid the effects of system noise created by the sensing of its own temperature. Infrared imaging systems are available with a wide range of capabilities, features, and prices. Scan speeds range from real-time to seconds per image. Detectors range from being simple, single-element, and thermoelectrically cooled to state-of-the-art, multi-element focal plane detector arrays, incorporating closed cycle Sterling coolers. Spot temperature measurement accuracy as high as ±1% can be achieved in a range from –20°C to +2000°C when adequate compensation is given for the emissivity of and distance to the target region, and a reliable method is used to locate the point of interest in the image. Measurements are taken in real-time, and processing takes only a few minutes. The latest trend in infrared imaging systems is the mating of the imaging camera to a personal computer. The electronics are contained on a card that can plug directly into the computer and take advantage of its high-resolution display, processing capability, and mass storage. New focal plane array detectors have resulted in higher-resolution cameras that can be fabricated in significantly smaller configurations and at much lower cost.
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42.3.4 Nondestructive Evaluation Raw materials, advanced engineering components, and fully assembled systems are all potential reservoirs of hidden faults and defects that can cause tribological failure and impaired machine performance. Safety issues, legal requirements, and economic goals fuel the desire to correct, reject, or monitor these irregularities at the earliest opportunity. Nondestructive evaluation (NDE) is an interdisciplinary field of study that is concerned with the development of analysis and measurement technologies for the quantitative characterization of materials by noninvasive means. A wide variety of inspection and detection techniques are available to provide users with the speed, accuracy, and cost-efficiency needed to probe, identify, and diagnose features of import in validating quality control and product fitness (Bray and Stanley, 1997). 42.3.4.1 Visual Inspection Visual inspection is an NDE method used extensively to evaluate the condition or the quality of a material, element, or structure. It can be used to locate and position points of interest, track the flow of parts, and validate output for quality and consistency. It is most effectively applied in pass/fail circumstances where quick detection and the correction of flaws or process-related problems can result in significant cost savings. When performed with human sight, visual inspection is easily carried out, is relatively inexpensive, and does not require special equipment. Good eyesight, good lighting, and the knowledge of what to look for are required. Visual inspection can be enhanced by various methods, ranging from the use of magnifying glasses to optical probes or boroscopes. Preparation can range from wiping the surface of interest with a cloth to blast-cleaning and treating it with chemicals to show detail. To aid in identifying defects that are not easily tracked by the human eye, replication techniques and other surface treatment methods often enhance the inspection process. In response to situations where items need to be monitored quickly or with tolerances too small to be analyzed by the human eye, machine vision has emerged. In a typical machine vision application, items undergoing inspection are positioned under proper lighting in front of one or more video cameras. A lens forms an image of the item on the camera sensor, which generates an analog signal that is subsequently digitized into pixels that represent light intensity at points on the item, and collectively form an image of the item. The image is processed by specialized digital computers to select or amplify key features, or convert the image into measurements such as size and location. From these measurements, the machine vision system can qualify, accept, or reject an item based on decision thresholds or classifications established by the operator through experience. A machine vision system can inspect objects accurately even within complex or confusing scenes. Calibration is required to minimize distortion from the lens and camera sensor. It can be an economical way to precisely monitor repetitive and high-speed situations. 42.3.4.2 Liquid Penetrant Inspection Liquid penetrant inspection is a method that is used to reveal a surface-breaking flaw by the release of a colored or fluorescent dye. The surface of the part under evaluation is coated with a penetrant in which a visible or fluorescent dye is dissolved or suspended. The penetrant is pulled into surface defects by capillary action. After a waiting period, the excess penetrant is cleaned from the surface of the sample. A white powder or developer is then sprayed or dusted over the part. The developer lifts the penetrant out of the defect, and the dye stains the developer. By visual inspection under white or ultraviolet light, the visible or fluorescent dye indications, respectively, are identified and located, thereby defining the defect. Penetrant inspection can be used on any material with a relatively smooth, nonporous surface and usually takes less than an hour to accomplish for most parts. It is essential that the material is carefully cleaned; otherwise, the penetrant will not be able to get into the defect. If the surface penetrant is not fully removed, misleading indications will result.
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42.3.4.3 Magnetic Particle Inspection Magnetic particle inspection is a method that can be used to find surface and near-surface flaws in ferromagnetic materials. The technique uses the principle that magnetic lines-of-force or flux will be distorted by the presence of a flaw in a manner that will reveal its presence. Upon magnetizing the item of interest, iron particles are dusted over it or flowed over it if they are suspended in a fluid such as kerosene. A surface defect will form a magnetic anomaly, which attracts and holds the particles, giving a visual indication of a defect. An inspector views the object being evaluated, and makes a decision of acceptance or rejection. As surface irregularities and scratches can give misleading indications, it is necessary to ensure careful preparation of the surface before magnetic particle inspection is undertaken. Under optimum conditions, the probability of detecting a flaw as small as 2 mm is extremely likely. Typically, the evaluation time is a few minutes for relatively small parts (10 kg or less). Large parts must be done in sections, extending evaluation time. As the part must be ferromagnetic, this technique cannot be used on most stainless steels. While magnetic particle inspection is primarily used to find surface-breaking flaws, it can also be used to locate sub-surface flaws. Its effectiveness, however, quickly diminishes, depending on the flaw depth and type. 42.3.4.4 Eddy Current Inspection Eddy-current inspection is an electromagnetic approach to flaw detection that can only be used on conductive materials. A coil, bearing an alternating current (typically 10 Hz to 10 MHz), creates an alternating magnetic field that is used to induce circulating electric currents (eddy currents) in the component to be inspected. These currents flow in a thin skin beneath the surface adjacent to the coil. The thickness of this skin, between 5 µm and 10 mm, is dependent on the shape, size, and operating frequency of the coil, the proximity of the coil to the component, and the conductivity of the targeted material. As the coil scans a region of interest, the impedance in the coil is altered when the eddy currents are distorted by the presence of defects or material variations. This change is measured and displayed in a manner that indicates the type of flaw or condition of the material. Eddy-current evaluations can be made at different material depths using coils of differing size at a range of frequencies. Given that eddy currents are established through induction, there is no need for the coil to contact the component. Therefore, the surface can be painted or coated. Depending on surface condition, it is usually possible to find cracks as small as 0.1 mm deep. In automated applications, where scanning speeds can be as high as 1 m/s, best results are obtained when the scan direction is normal to flaw orientation. 42.3.4.5 Acoustic Emission Detection Acoustic emissions (AEs) are stress waves produced by sudden changes in the internal structure of a material. Possible causes are crack initiation and growth, crack opening and closure, dislocation movement, and material phase transformation. As most of the sources of AEs are damage related, the detection and monitoring of these emissions are commonly used to predict material failure. Figure 42.4 presents the setup of a typical AE monitoring system. Wideband transducers (typically 50 kHz to 1 MHz) are normally used to detect the minute random bursts of deformation, characteristic of an AE event. Made of a thin film of piezoelectric material, such as lead zirconate titanate (PZT), these sensitive devices emit an electric charge proportional to the applied stress. As AE signals are generally very weak, a charge amplifier is connected to the AE transducer to minimize noise interference and prevent signal loss. The amplified signal, which is in analog form, can then be sent via coax cable to a filter for noise removal and routed to a signal conditioner and/or computer for further analysis. AE signals can be recorded continuously by one or more relatively small sensors mounted on the surface of the structure being examined for progressive damage. When the AE transducer senses a signal over a certain level (i.e., the threshold), an AE event is captured. The amplitude of the event is defined at the peak of the signal. The number of times the signal rises and crosses the threshold is the count of
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AE Pre-amplifier Transducer
Filter Signal Conditioner Crack
Computer Post-processor
FIGURE 42.4
Acoustic emission monitoring system.
the AE event. The time period between the rising edge of the first count and the falling edge of the last count is the duration of the AE event. The time period between the rising edge of the first count and the peak of the AE event is called the rise time. The area under the envelope of the AE event is the energy. These features and others are correlated with defect formation and failure. The advantages of using acoustic emissions for assessing machinery health include: 1. 2. 3. 4. 5.
The whole structure can be monitored from a few locations. The structure can be tested in use (without taking it out of service). Microscopic changes can be detected if sufficient energy is released. Source location can be estimated using multiple sensors. Continuous monitoring with alarms is possible.
The main disadvantages are that AE systems can only estimate qualitatively how much damage is in the material and approximately how long the components will last. Hence, other NDE methods are still needed to do more thorough examinations and provide quantitative results. Moreover, service environments are generally very noisy, and the AE signals are usually very weak. Thus, signal discrimination and noise reduction are very difficult, yet extremely important for successful AE application. 42.3.4.6 Ultrasonic Inspection Ultrasonic inspection is an approach that uses high-frequency waves to evaluate the quality of a material. Pulses of ultrasonic energy, commonly emitted via a piezoelectric transducer placed on the object of interest, penetrate the material and are subsequently altered as they travel through it due to attenuation, reflection, and scattering. The resulting output pulse is detected, processed, and interpreted based on its relation to the input pulse. This can be accomplished through a pulse-echo arrangement, where one transducer is used to emit and receive ultrasound, or through a pitch-catch mode, where one or more transducers are strategically placed to catch the output pulse. For potentially hazardous and hostile environments, laser-based technology can be used for generating the ultrasonic signal. A laser beam targeted at the material of interest some meters away can produce broadband ultrasonic vibrations up to frequencies of about 100 MHz without damaging the surface. These vibrations act as sources of compression, shear, and Rayleigh surface waves that pass through the object of interest. Non-contact detection of these waves can be realized using interferometry to monitor the induced surface for resulting effects. Hence, no contact medium is required for ultrasonic inspection. Ultrasonic inspection can be applied to metals as well as carbon composites and ceramics. It is most often used to search for flaws within materials, for example, cracks, voids, porosity, and delamination. As the ultrasonic wave penetrates the object, defects will reflect the signal in a characteristic manner, which can be interpreted by observing the amplitude of the received pulse and the time taken to arrive.
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Whenever the configuration of the object under examination permits, a two- or three-dimensional image of the interior of the object can be made, showing reflections of the ultrasound for use in locating regions for concern. Flaw-size resolution (typically 1 mm in length) is dependent on both the speed of sound in the material and the frequency of the ultrasonic wave. Because this approach to nondestructive evaluation is complex, considerable training and skill are required. Best results are obtained if the object being evaluated is flat, or has spherical or cylindrical symmetry. As ultrasonic waves can attenuate rapidly in certain materials, pulse-echo measurements on thick (more than a few inches) parts can be difficult to perform. A high-resolution scan of large parts and scans of parts with odd shapes or convoluted surfaces can take many hours. Setup time typically takes less than an hour. 42.3.4.7 Radiographic Inspection Radiographic inspection uses radiation as the source for identifying abnormal characteristics within a material. A source of radiation (X-ray or gamma-ray) is directed toward the part under evaluation with a sheet of radiographic film placed behind it. This film is then processed and a semi-transparent image of the object is obtained as a series of shades between black and white. The density of the image that results is a function of the quantity of radiation transmitted through the object, which in turn is inversely proportional to its atomic number, density, and thickness. The largest single image is typically 17 by 22 in.; however, larger film is available if required. The image can reveal internal defects such as voids, cracks, or inclusions in the material. It can also expose internal clearances between parts in an assembly and any displacement of internal components. Laminations, tight cracks, or cracks parallel to the film plane are not readily discernible. The method is limited by material thickness to approximately the equivalent of 4 in. of lead, 10 in. of steel, or 2 ft of concrete. Given that the sources of radiation are hazardous to living tissue, special precautions must be taken when performing radiography. The operator must use a protective enclosure or appropriate barrier and provide warning signals to ensure there are no hazards. Setup typically takes a few minutes, the exposure typically 1 to 10 minutes, and film processing 10 minutes. Direct digital processing is available to provide a publication-quality image in one tenth the exposure time required for conventional film.
42.3.5 Corrosion Monitoring Corrosion is a major cause of the deterioration and premature failure of machinery. It can occur wherever a structural material such as steel is exposed to an environment of moisture, salts, and pollutants. Failures due to corrosion can be costly to repair, costly in terms of lost or contaminated product, costly in terms of environmental damage, and ultimately it may be costly in terms of human safety. Therefore, it is wise to look for it and be prepared to prevent it once a tendency to corrode is discovered. This can be done either electrochemically or by physical measurement (Moran and Labine, 1986). 42.3.5.1 Electrochemical Methods Corrosion takes place because the surface of a component undergoes a chemical reaction with its environment. There is an anode reaction, in which a material goes into solution as an ion, leaving electrons to be absorbed by a dissimilar element in the environment that acts as a cathode. This electron flow can be measured as a voltage, the magnitude of which is dependent on the elements involved. Corrosion monitoring methods, such as polarization and galvanic/potential monitoring, assess the electrochemical activity associated with corrosion. Results can be used to identify situations that are likely to promote corrosion, or to estimate the rate at which deterioration is occurring so that corrective action can be taken in a timely manner. 42.3.5.1.1 Linear Polarization Resistance Linear polarization resistance (LPR) is used to estimate the rate of corrosion occurring at a metal/fluid interface. Metal samples, immersed in the fluid, serve as electrodes to which a small voltage (or polarization
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potential) is applied. The resulting current needed to maintain a specific voltage shift (typically 10 mV) is directly related to the corrosion current, which in turn is directly proportional to a corrosion rate. This technique can be used as a quality control tool to compare the performance of a material with a well-established standard. Its advantage is that the measurement of corrosion rate is rapid. Using the standard setup, it takes less than 10 minutes. The disadvantage of the LPR method is that it can only be successfully performed in fluid that is conductive, which in practice limits it to aqueous solutions. LPR will not work in environments where the electrodes can become coated in oil or covered with scale. 42.3.5.1.2 Galvanic/Potential Monitoring Galvanic monitoring is a passive electrochemical technique that requires no polarizing current, but measures the naturally occurring electrochemical potential and current flows that are due to corrosion activity. For bimetallic corrosion, when two electrodes of dissimilar metals are immersed in solution, a natural voltage (potential) difference exists between them. The current generated due to this potential difference relates to the rate of corrosion that is occurring on the more active of the electrode couple. 42.3.5.2 Material Loss Methods Corrosion is a chemical attack that can, over time, destructively alter the shape, strength, and stiffness of a machine element. Hence, by physically or electrically monitoring for a physical change, such as weight, one can make an informed decision as to when to repair or replace the affected material. 42.3.5.2.1 Weight Loss Coupons The weight loss technique is the simplest of all corrosion monitoring methods. A sample (coupon) of material of known weight is exposed to a process environment for a given duration and then removed for analysis. Upon being carefully cleaned, the coupon is weighed. The change in weight per time of exposure defines the corrosion rate. The coupon requires a relatively long exposure to yield accurate results. This is partly due to the accelerated rate of corrosion of a new coupon and the small loss of uncorroded material from the coupon during the process of cleaning. The significance of both of these errors is proportionally reduced by greater material loss due to normal corrosion. In a typical monitoring program, coupons are exposed for a 90-day duration before being removed for laboratory analysis. This technique is most useful in environments where corrosion rates do not significantly change over long time periods. Weight loss coupons can be fabricated from any commercially available alloy. The technique is applicable to all environments and can provide a useful correlation with alternative electrochemical measurements (e.g., LPR). In addition to determining corrosion rate, the coupon can be examined to provide valuable clues as to the type of corrosion that has occurred. This is particularly useful if the mechanism is of a nonuniform type such as pitting. 42.3.5.2.2 Electrical Resistance Probes Electrical resistance (ER) probes provide a basic measurement of metal loss from corrosion; but unlike weight loss coupons, the value of metal loss can be measured at any time. The ER technique uses the change in electrical resistance of a corroding metal element exposed to the process stream to estimate the degree of corrosion. The action of corrosion on the surface of an element produces a decrease in its cross-sectional area, with a corresponding increase in its electrical resistance. The increase in resistance can be related directly to metal loss. By taking the results of a series of measurements at timed intervals, a corrosion rate can be calculated. To compensate for any temperature-induced change in resistivity, ER probes are constructed with a protected reference element. ER probes can be used in all working environments and remain installed in-line until the operational life is completed. They are available in a variety of geometries, metallurgies, and sensitivities. Actual metal loss must occur before a response is obtained; hence, this technique is somewhat slower than electrochemical equivalents.
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42.3.6 Performance Monitoring Performance monitoring uses process information to quantify or characterize normal machine behavior and highlight abnormal characteristics that often indicate deterioration. Information, representative of parameters identified through observation and measurement, is collected over time for interpretation and benchmarking using manual and computer methods. 42.3.6.1 Process Parameters Detailed observation provides the foundation for effective machine diagnosis. In addition to using sight, touch, and hearing to pick up such obvious faults as leaks, noise, overheating, and decay, the senses are of use in determining the optimum location for the mounting of gages. A large number of process parameters can be monitored (Rao, 1996), which will vary with the sophistication of the machine. Many have been discussed in this chapter, including temperature. Other common variables that can be easily monitored include flow rate and current. 42.3.6.1.1 Flow Rate The flow rate of a fluid entering or exiting a component is one of the basic parameters of a hydraulic system, and is often a direct measure of its performance. A variation in flow can be indicative of leakage or internal wear. Numerous types of flowmeters are available for closed-piping systems, of which differential pressure and velocity meters are commonly used (Omega, 1990). The differential pressure flowmeter is based on the premise that pressure drop across the meter is proportional to the square of the flow rate. It has a primary element that causes a differential pressure in the closed-piping system, and a secondary element to measure the differential pressure and provide the readout that is converted to an actual flow value. Orifices and venturi tubes are examples of differential pressure meters. The former is a flat piece of metal with a specific-size hole bored in it. It is installed in the pipe between two flanges and constricts the flow of fluid to produce a differential pressure across the plate. The latter is a section of pipe with a tapered entrance and straight throat. As the fluid passes through the throat, its velocity increases, causing a pressure differential between the inlet and outlet regions. In each device, pressure taps at the entrance and exit are used to measure the pressure difference used to calculate flow rate. Velocity meters operate linearly with respect to the flow rate. The most adaptable velocity meter is the turbine meter, which consists of a multiple-bladed rotor mounted within a pipe, perpendicular to the fluid flow. The rotor, or turbine, rotates as the fluid passes through the blades. The rotational speed is directly related to flow rate and can be sensed by either a capacitive, inductive, or magnetic pickup. Flow rates from 0.5 to 1000 L/min have been accurately measured using this device. A second type of velocity meter uses ultrasonics to determine the flow rate in a piping system. One method uses a piezoelectric crystal mounted on the outside of the pipe to emit an ultrasonic signal of known frequency into the flow stream. Upon contacting contaminant particles, bubbles, or discontinuities, the signal is reflected back to a receiver element. Because the fluid causing the reflection is moving, the frequency of the returned pulse is shifted. The frequency shift is proportional to the fluid velocity. This portable technique is very accurate in measuring flow velocities from 0 to 10 m/s. A second ultrasonic approach uses two transducers mounted on opposite sides of the pipe at a 45° angle to the direction of fluid flow. The speed of a signal traveling between the transducers increases or decreases with the direction of transmission and the velocity of the fluid being measured. A timedifferential relationship proportional to the flow velocity can be obtained by alternating the signal transmission in either direction. A limitation of this time-of-travel meter is that the fluid being measured must be relatively free of particles to minimize signal scatter and absorption. 42.3.6.1.2 Current Signature Analysis In motor-driven rotating equipment, current signature analysis provides a nonintrusive method for detecting mechanical and electrical problems (Tavner and Penman, 1987). The current signal can be measured using an ammeter, either installed in the machine control panel or clipped to the motor circuit
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(operating through magnetic induction). A spectrum analyzer and/or commercial computer with signal conditioning capability is needed to process the signal and provide diagnoses. When an electric motor drives a mechanical system, it experiences variations in load caused by gears, bearings, and other conditions that may change over the life of the motor. The variations in load caused by each of these factors in turn causes a variation in the current supplied to the motor. These variations, although very small, modulate the 60 Hz (or 50 Hz) carrier frequency. Upon demodulating the signal from the carrier using Fourier techniques, abnormal signal characteristics can be identified, representing a variety of failure precursors including rotor bar deterioration, stator phase imbalance, and increased friction forces. A single measurement of current is not likely to be informative, but comparison with prior readings can give immediate results. Hence, recording the current at regular intervals is advised in order to identify changes or trends toward failure. 42.3.6.2 Data Interpretation Data interpretation is a diligent process when used for assessing machine behavior. This activity includes assimilating information concerning mechanical configuration, process and maintenance history with performance data, and any supportive calculations. Normally, this commits the diagnostician to some type of database for trending and correlating the information. Computer programs offering artificial intelligence for the diagnosis and prognosis of machinery problems can provide significant time and accuracy advantages. 42.3.6.2.1 Trending To address the onset of failure, sufficient performance data must be collected to carry out an assessment that provides enough time to provide an opportunity for corrective action. This necessitates that reliable documentation be kept to establish a pattern of performance related to the machine element of interest and its mode of failure. To warn of changes in condition, alert levels can be set for the purpose of highlighting potential faults that can be corrected before any failure occurs. These are usually based on some percentage of change from the norm, and highlighted automatically, either by generating reports in software or triggering hard-wired alarms. Upon being advised of an abnormal trend, a decision is needed to determine what type of corrective action should be taken. When encountering an alarm, being too quick to initiate repairs can be wasteful, and being too slow can result in expensive breakdown. Factors to consider include the present reading, the rate of change in the reading, the maximum allowable reading, and the time needed to diagnose and correct the problem. If the data collected are numeric, and the degradation process is well-understood, the diagnostician can use the trend in the data to develop a mathematical model of use in projecting a time for corrective action. Although such projections can be used for alert purposes, it is rarely the case that the failure mechanism is understood well enough to predict the exact point in time when failure will occur. 42.3.6.2.2 Correlation One of the advantages of collecting data through a number of different technologies is the ability to correlate the data — that is, to compare the output of one technology to the output of another. This is particularly useful in determining whether an alert from one technology is truly representative of a deteriorating situation, or whether the alert has been triggered because the alarm level was too sensitive, or a false reading was encountered. The confidence level for a decision that may, for example, affect productivity can increase substantially when a fault is supported by more than one source of information. 42.3.6.2.3 Knowledge-Based Systems Knowledge-based systems are information processing machines that attempt to mimic the reasoning behavior of humans. They can operate on the basis of rules, capturing the decision-making process of an expert, or be trained in a manner to recognize and respond to patterns of data. Acquiring diagnostic recommendations through a rule-based approach to analyzing information relies on prodding, interpreting, and representing knowledge from human experts. Care must be exercised to
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X1
X2
X3
X4
Hidden layer
Z1 FIGURE 42.5
Z2
Neural network structure.
avoid misinterpretation, gaps, or errors in programming the logic used to arrive at an outcome. The benefit of using this method of artificial intelligence is that results are quickly provided to a diagnostician through a consistent path of directives based on a fixed sequential order. The downside is that the process cannot readily adapt to changes because of its rigid structure. Thus, the expert system must be periodically reprogrammed as experience is gained, which can be time-consuming and expensive. In an attempt to apply a more human-like way of thinking in the programming of computers, fuzzy logic can be used to describe how to execute decisions or control actions without having to specify process behavior through complex equations. Fuzzy logic is a superset of conventional Boolean logic that has been extended to handle the concept of partial truth when traditional true/false logic cannot adequately address situations that present a number of ambiguities or exceptions. Viewed as a formal mathematical theory for the representation of uncertainty, which is crucial to the management of equipment assets, fuzzy logic permits notions like “rather warm” or “pretty cold” to be formulated for computer use. Research activity has been undertaken into the possible use of neural networks in condition monitoring and diagnostics, modeled on the nerve cells of the brain (Kosko, 1992). This knowledge-based system learns to recognize complex patterns through a set of processing elements (or nodes) that are interconnected in a network that looks something like that in Figure 42.5. The top layer represents the input layer, in this case with four inputs labeled X1 through X4. In the middle is the hidden layer (or layers), with a variable number of nodes that perform much of the work of the network. The output layer in this case has two nodes, Z1 and Z2, representing conclusions to be determined from the inputs. Each node in the hidden layer is fully connected to all inputs. This hidden layer is where the network learns interdependencies. The network is repeatedly shown observations from available data related to the problem to be solved, including both inputs and desired outputs. It then tries to predict the correct output for each set of inputs by gradually reducing error through algorithms that involve an iterative search for a proper set of weights that will accurately predict the outputs. Hence, raw data are used and manipulated to update the system and draw the best conclusion based on all experience the network has encountered to date. As knowledge is not explicitly declared, the method is limited in justifying its chain of reasoning. The most recent development in knowledge-based systems is hybrid intelligence, combining the best features of expert systems, neural networks, and fuzzy logic. Object-oriented programming provides the necessary structure to enable these techniques to work together, so as to complement their strengths and to provide justification of the decision-making process. This is of prime value to diagnosticians who want to understand and decide for themselves whether the recommendations that result are sound.
42.4 Tribo-Element Applications As summarized in Table 42.3, there are several different types of measurements that can be used to facilitate the diagnosis and prognosis of machines, containing such tribo-elements as bearings, gears, and seals. The technical requirements of each of these are very different, and as a result, there is a tendency
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TABLE 42.3
Condition Monitoring Methods
Monitoring Technique
Elements Monitored
Machine Diagnosis
Measurement
Vibration Signature analysis Shock pulse method
Bearings Gears Rotors Shafts
Imbalance Looseness Misalignment Wear
Displacement Velocity Acceleration Spike energy
Oil analysis Chemical/physical testing Spectrography Ferrography Magnetic chip detection Particle counting Image analysis
Bearings Gears Rotors Lubricant
Contamination Degradation Fracture Wear
Composition Contaminants
Thermal monitoring Contact methods Non-contact methods
Bearings Coolant Gears Lubricant Motors
Chemical reaction Fracture Friction Overload Wear
Temperature
Nondestructive evaluation Visual inspection Penetrant/particle inspection Eddy current inspection Acoustic emission monitoring Ultrasonic monitoring Radiography
Rotating equipment Structures
Cracks Decay Leakage Wear
Flaw size Frequency
Corrosion monitoring Electrochemical methods Material loss methods
Structures
Chemical reaction
Dimensions Resistance Voltage Weight
Performance monitoring Flow Current monitoring
Filters Seals Motors
Blockages Failed rotor bars Worn brushes
Current Flow rate Pressure
to view the technologies in competing roles — yet best results are realized if the technologies can be used to complement each other.
42.4.1 Fluid Film Bearings A fluid film bearing is used in a wide variety of machines to support and guide a rotating shaft. In its most basic form, the shaft is contained within a stationary close-fitting partial or full cylinder separated by a film of fluid. The fluid, most commonly oil, is supplied to the clearance space between the surfaces to create a wedge support that prevents metal-to-metal contact as rotation occurs. Many application-dependent bearing designs have been created, each developed to use the fluid film to position the shaft or rotor at an optimum location relative to the bearing housing. Application of a disturbing force will move the shaft from this position, altering the pressure field within the fluid and hence the forces within the bearing. The forces generated normally tend to restore the shaft to its optimum position, but sometimes they can lead to an unstable motion or self-excited vibration. For an oil film bearing, the vibration, often referred to as oil whirl, usually coincides with the average oil velocity, which is typically less than half of the shaft rotational frequency. When this whirl frequency coincides with a rotor resonance, a severe vibratory state can occur. Known as an oil whip condition, the fluid film support becomes unstable, leading to severe bearing and shaft deterioration from metal-to-metal contact.
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To be assured that a machine maintains balance, stability, and proper alignment with the bearing supports, vibration monitoring is needed to assess the relative motion between shaft and bearing. A non-contacting proximity probe, such as an eddy-current transducer, is typically used. On small, less critical machines, one probe per bearing may be adequate, which will measure radial vibration for the plane in which the shaft moves away from and toward the mounted probe. On larger machines, two probes per bearing mounted 90° apart from each other are advised to assess the total radial vibration by measuring the shaft displacements within their respective planes. An additional probe can be used to assess the axial movements associated with thrust loading. To complement vibration analysis, the fluid used to support the shaft should be periodically monitored. Its physical and chemical properties must be evaluated and maintained to ensure that the film performs as designed and provides sufficient damping to limit vibration transmission. An increase in temperature and/or the presence of such elements as aluminum, tin, lead, copper, zinc, or iron, commonly used as bearing materials, may indicate the onset of wear from metal-to-metal contact.
42.4.2 Rolling Element Bearings Rolling element bearings utilize the rolling action of balls or rollers to permit constrained motion of one body relative to another with minimal friction. Most are employed to permit rotation of a shaft relative to some fixed structure. If properly lubricated, properly aligned, and kept free from abrasives or moisture, failure is most likely to be attributed to material fatigue, manifested as a flaking off of metallic particles from the raceways and/or rolling elements. Vibration analysis is one of the most common methods used to monitor for an indication of pending rolling element bearing failure in machines. A sizable local defect often characterizes the beginning of progressive bearing damage on one of the bearing components. When this occurs, subsequent rolling over the damage can cause repetitive measurable shocks, the frequency of which will be dependent on the rotational speed and the geometry of the bearing, which includes the number of rotating balls or rollers n, ball or roller diameter d, bearing pitch diameter D, and the contact angle between the rolling element and races α. It can be shown (Harris, 1991) that a defect in the bearing outer race will generate a frequency, fo , that can be computed with the following expression:
( )[ ( )
fo = n f 2 1 − d D cos α
]
(42.1)
where f is the angular velocity of the inner ring relative to the outer. Likewise, for bearing defects on the inner race, the emitted frequency, fi , can be determined from:
( )[ ( )
fi = n f 2 1 + d D cos α
]
(42.2)
and for a ball or roller defect, the emitted frequency, fb , can be calculated from:
( ) ( ) ( )(
)
2 fb = f D d − d D cos α
(42.3)
Note that a rolling element defect will contact both raceways in one revolution, such that fb is twice the rate of rotation of the ball or roller about its own axis. The fundamental train frequency, more commonly referred to as the cage defect frequency, fc , can be determined from:
( )[ ( )
fc = f 2 1 ± d D cos α
]
where the “+” is used for outer ring rotation and the “–” is used for inner ring rotation.
(42.4)
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Acceleration (g)
Technologies for Machinery Diagnosis and Prognosis
6
x10
4 2 0 0 3
Acceleration (g)
(a) Good bearing
-10
x10-09
100
200
300
400
500
600
(b) Outer bearing race defect (0.003 inch by 0.14 inch)
2
164 Hz = outer race characteristic frequency
1 0 0
Acceleration (g)
1.5
x10-07
100
200
300
400
500
600
500
600
(c) Outer bearing race defect (0.06 inch by 0.14 inch)
1 0.5 0 0
100
200
300
400
Frequency (Hz)
FIGURE 42.6 Frequency spectra of failing bearing: (a) good bearing; (b) outer bearing race defect (0.003 in. × 0.14 in.); (c) outer bearing race defect (0.06 in. × 0.14 in.).
Bearing dimensional data are often available from the bearing manufacturer for use in computing the defect frequencies. It must be recognized that the equations assume that the balls or rollers are rolling and do not slide. In real machines with reasonable loads, the elements do slip; as a result, the calculated and measured frequencies will probably not be identical. A new bearing will exhibit some or all of the defect frequencies at very low amplitudes. As defects occur, the amplitudes at the associated defect frequencies will increase and may shift as the load distribution changes and the rolling elements begin to slide. When the vibration measurements exceed a level predetermined by experience, the unit should be shut down for bearing replacement. Figure 42.6 illustrates the changes that a frequency spectrum, obtained from vibration accelerometer readings, will undergo as an outer race spall develops for a bearing with an outer race defect frequency of 164 Hz. Oil debris monitoring can provide a good backup to vibration monitoring, especially when vibration levels are high enough to render conventional vibration analysis ineffective. Quantity of debris (especially ferrous debris) and size range of the debris can indicate the rate of degradation. Studying debris morphology adds the ability to determine the kind of failure (e.g., skidding, spalling) and potentially the cause (e.g., high-temperature discoloration of debris indicates a lubrication-source failure). Temperature measurement can be useful in supporting preventive maintenance actions, such as lubricant change or addition.
42.4.3 Gears The frequencies associated with gear meshing usually dominate any vibration spectra measured on a typical gearbox due to the loads transmitted through the gear teeth (Smith, 1983). These forces are relatively high in comparison to other gearbox components such as bearings. Although vibrations can be measured at any location within or on the gearbox, it is common to place the recording sensors (e.g., accelerometers) on bearing housings to avoid resonance of the gearbox casing and to ensure the most direct path from their source, the gear teeth. The technique of trending vibration data relies on observing a change in vibration over time. This necessitates the recording of base levels of vibration after the gearbox has been run-in. When the measurements exceed a level, predetermined by experience to indicate the onset of problems, all changing frequencies should be itemized for diagnostic use.
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With a well-meshed pair of gears, the fundamental gear meshing frequency, fm , is likely to be observed. For a single contact and no loss of power:
fm = ω1N1 = ω 2 N 2
(42.5)
where ω is the angular velocity and N is the number of gear teeth of each gear, differentiated by subscript as gears 1 and 2. As the gears wear, the amplitude of the fundamental gear meshing frequency will increase. Harmonic frequencies (noise and vibration at integer multiples of the gear meshing frequency) will usually be present. The first two or three harmonics,
f(2 ) = 2 fm , f( 3) = 3 fm , and so on
(42.6)
may make significant noise contributions. Harmonics can occur when the loading and unloading of gear teeth is uneven, or when gear misalignment or scuffing alters the path of contact such that the gear teeth no longer follow a true involute curve. Pitting on the surfaces of gear teeth from a breakdown in lubrication or overloading also gives rise to harmonics. If a single tooth on a gear is poorly cut, chipped, or otherwise damaged, it will generate a noise impulse once every shaft revolution. This will be observed as a fundamental tooth-error frequency equal to the angular velocity of the affected gear. In addition, the tooth-error frequency may be observed if the shaft centerline is not straight, or if the gear is not concentric with the shaft centerline. For gears 1 and 2, these causes may result in sideband frequencies, fs , of the fundamental gear meshing frequency, given by:
f s1 = fm ± ω1
(42.7a)
f s 2 = fm ± ω 2
(42.7b)
Given that gearboxes are noisy and generate significant levels of vibration, it can be difficult to differentiate the source of an abnormal machine condition with a high degree of confidence in a timely manner. Therefore, it is often useful to supplement the vibration data with information obtained through other monitoring techniques. For example, oil debris analysis is useful in detecting a breakdown in material. A recorded increase in oil temperature is indicative of an increase in friction or power loss. Both approaches would be of value in diagnosing the fracture of an individual gear tooth from fatigue or sudden overload. Such an occurrence can be very difficult to observe through frequency analysis given that impacts occur only once per gear revolution, which is an infrequent number of impacts in comparison with all other gear meshing events.
42.4.4 Seals In tribology, a seal is a mechanical device designed to prevent the movement of fluid or contaminant from one chamber to another. It can be classified as either being static or dynamic, referring to the motion the seal experiences. Static seals such as O-rings and gaskets are used between machine joints. O-rings are typically made of polymers, whereas gaskets are available in a variety of materials, ranging from cork to metals such as copper. Some, such as room-temperature vulcanizing (RTV) silicone rubber, can be formed in place. Operating temperature, chemical compatibility, and differential pressure drive material selection and design. Dynamic seals, such as lip seals and mechanical face seals, experience either rotary and/or reciprocating motion. Lip seals are widely used to seal low-pressure differentials and are limited to relatively small amounts of radial motion. The lips are loaded against a shaft by the pressure differential, or by springs interacting with the lips. When relative velocities and lip loads are high, a considerable amount of heat is generated, leading to the need for some form of lubrication. Mechanical face seals are usually used for
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high-pressure differential applications such as centrifugal pumps, compressors, and turbines. Ideally, the sealing faces operate on a hydrodynamic film that is just thick enough to prevent asperity contact so as to minimize wear, leakage, and heat generation. Squealing is often indicative of dry operation, likely due to a lack of fluid at the sealing faces. Leakage is the most obvious clue that tells that a seal needs rebuilding or replacement. This could be a catastrophic leak or simple weepage that has gotten to the point of becoming a nuisance. An upper limit of leakage is usually set for a specific seal and system, and depends on system size, the fluid being sealed, and equipment disassembly and seal replacement cost. In some cases, the leaked fluid can be collected and measured volumetrically or weighed to establish leakage per unit time. Oil monitoring can be extremely useful in detecting seal degradation. Wear debris can result from the pitting, blistering, flaking, and/or peeling of seal face materials caused by chemical attack, contamination, and/or serious misalignment. Ceramic materials can chip or break from thermal and mechanical shock. Elastomeric materials can disintegrate from chemical incompatibility or excessive heat. Often, the pressure differential across the seal can be measured as a means of diagnosing a seal problem using standard pressure transducers. These readings can be recorded over time to provide a history of any degradation of performance. Less frequently, temperature, vibration, and/or friction torque can be measured to assist in the evaluation of performance. It should be noted that seals might leak when instrumentation suggests there is nothing apparently wrong. In troubleshooting, it is important to inspect all the sealing elements, using a procedure that keeps all pieces tied together and tagged with any information that may offer insight. Any evidence of a wear pattern can be very useful in diagnosing a problem that may be related to design, assembly, or operation.
42.5 Equipment Asset Management In selecting the technologies needed for machinery diagnosis and prognosis, the decision must often be justified by comparing the benefits that will result to the expenses that will be incurred. The economic tools of equipment asset management can therefore be employed — consisting of a combination of engineering, financial, management, and other practices — to fully understand what the technologies will really cost to implement over a number of years, and how they will impact company profits. Upon purchasing a machine, the investment can be considered as profitable when accumulated revenue exceeds the sum of accumulated operating costs and annualized capital expense. This is shown as a simplified model in Figure 42.7 (top), which excludes inflation, the variance of day-to-day transactions, and planned outage periods. As shown in Figure 42.7 (bottom), the consequence of any machine failure that results in downtime can have a large impact on overall profitability. Until the machine is brought back into service, no revenues are generated, yet operating costs continue with potentially large machine repair costs. Once production has been lost, lifetime profit can only be regained by improving efficiency or extending operating life. Failure prevention strategies and condition monitoring technologies are intended to achieve these objectives, as well as yield one or more of the following benefits. 1. Reduced repair time and costs. With advance knowledge of the repair requirements gained from a condition monitoring system, part replacement and labor costs can be minimized. 2. Avoided revenue loss. By detecting machine deterioration in advance of failure, process output can be maintained until machine repair is conducted at a convenient off-peak time. 3. Reduced maintenance expenses. With an advance indication of what should be maintained as opposed to what could be maintained, reductions in planned outage periods, repair parts inventory, and maintenance-induced failures can be realized. 4. Improved safety and reliability. By minimizing the possibility of catastrophic failure, greater confidence is gained in the credibility of the machine environment, thereby lowering insurance premiums and decreasing litigation and hospitalization costs.
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Revenue/Costs
e nu ve Re
Profit Breakeven Operating cost
st
Total Co
Annualized cost
Time
Revenue/Costs
e nu ve Re
Breakeven
Profit
Operating cost
st
Total Co
Annualized cost Failure Outage
Time FIGURE 42.7
Economic consequences of failure.
5. Enhanced sustainability. By minimizing the wastes of unwarranted maintenance and the environmental consequences of primary and secondary damage from machine failure, society benefits in that the needs of the present are met without compromising the ability of future generations to address their own needs. 6. Improved profitability. By combining process parameters with condition monitoring, production efficiencies can result through understanding the impact of design changes and tolerance requirements. When a condition monitoring system is activated, a real monetary benefit is obtained when the savings from avoiding spending exceed the costs of investment. A savings is realized when scheduled maintenance is reduced and in-service repairs are avoided because the run-to-failure strategy has been averted. The costs of investing in failure prevention technology are dependent on the complexity of the method needed to address the relevant failure mode and the frequency of sampling required. Table 42.4 provides an indication of relative costs. In determining actual values, the purchase price of the monitoring equipment and the cost of installation and operation must be considered. Capital costs of condition monitoring vary according to the data collection method employed. This expense could include the cost of sensors, cabling, signal conditioning software, and computer hardware with allowances for future upgrades. For determining installation costs, manpower rates are needed with
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TABLE 42.4 Cost
Condition Monitoring Method
Low
Manual inspection Leak detection Contact thermal monitoring Nondestructive evaluation Flow rate monitoring Shock pulse method Oil analysis Vibration signature analysis Current monitoring Non-contact thermal monitoring Corrosion monitoring
High
Cumulative maintenance cost
Relative Costs of Condition Monitoring
Overhaul cost A
Machine life FIGURE 42.8
Economic effect of maintenance action.
time estimates for sensor attachment and calibration. Ongoing operational costs will also be incurred, including the cost to train staff to operate the system. The consequences of severe damage from failure may be detrimental to employee morale and lead to significant replacement and compensation costs. Therefore, upon arriving at a baseline cost-benefit for justifying the use of condition monitoring, multiplication factors may be applied to take into account safety, technical, and operational issues using probabilities of occurrence and informed judgments. Determining a suitable technology for machinery diagnosis and prognosis can only be complete if a strategy for the disposal and replacement of the technology and the machine it is intended to monitor is taken into consideration. Factors that will influence this decision include technological advances, reduced operating efficiencies, the obsolescence of replacement parts, a product design change, and ease of machine overhaul. In Figure 42.8, the typical cumulative annual maintenance costs of a machine have been plotted, showing an increasingly steep curve as time progresses. In many cases, overhauling the equipment can extend the life of the machine by delaying the steep rise associated with its deterioration. The effect of this is shown at point “A.” Finally, the uncertainty of the future necessitates that to effectively manage the utility of an equipment asset, one must be flexible and resourceful in choosing and using a failure prevention technology. Upon identifying where and how often to take measurements, collect readings, and set alarm levels, a review process should be devised to allow for the replacement or adjustment of the technology based on operating experience. Possibly the most important part of such a review is that it can result in updating the sensitivity of the technology in order to avoid the stigma of its having reported a false alarm, or having missed an
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indicator that would have avoided failure. With this accomplished, methods for machinery diagnosis and prognosis will continue to develop and prosper, driven by their contribution in ensuring that performance commitments will be profitably and reliably met.
References Bloch, H.P. and Geitner, F.K. (1994), Machinery Failure Analysis and Troubleshooting, 2nd ed., Gulf Publishing, Houston, TX. Bray, D.E. and Stanley, R.K. (1997), Nondestructive Evaluation: A Tool in Design, Manufacturing and Service, CRC Press, Boca Raton, FL. Eisenmann, Sr., R.C. and Eisenmann, Jr., R.C. (1998), Machinery Malfunction Diagnosis and Correction, Prentice-Hall, Upper Saddle River, NJ. Harris, T.A. (1991), Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, New York. Hines, W.W. and Montgomery, D.C. (1990), Probability and Statistics in Engineering and Management Science, 3rd ed., John Wiley & Sons, New York. Hunt, T. (1996), Condition Monitoring of Mechanical and Hydraulic Plant: A Concise Introduction and Guide, Chapman & Hall, New York. Kececioglu, P. (1991), Reliability Engineering Handbook, Prentice-Hall, Englewood Cliffs, NJ. Kosko, B. (1992), Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall, Englewood Cliffs, NJ. Moran, G.C. and Labine, P. (Eds.) (1986), Corrosion Monitoring in Industrial Plants Using Nondestructive Testing and Electrochemical Methods, ASTM, Philadelphia, PA. Newland, D.E. (1993), An Introduction to Random Vibrations, Spectral and Wavelet Analysis, John Wiley & Sons, New York. Omega Engineering, Inc. (1990), The Flow and Level Handbook, Stamford, CT. Omega Engineering, Inc. (1998), The Temperature Handbook, Stamford, CT. Rao, B.K.N., (Ed.) (1996), Handbook of Condition Monitoring, 1st ed., Elsevier Science, Oxford, U.K. Reintjes, J. et al. (1998), LASERNET optical oil debris monitor, in 1998 Technology Showcase Proc. of JOAP Condition Monitoring Conference, Humphrey, G.R. and Martin, R.W. (Eds.), Joint Oil Analysis Program Technical Support Center, Pensacola, FL, 110-116. Smith, A.M. (1993), Reliability-Centered Maintenance, McGraw-Hill, New York. Smith, J.D. (1983), Gears and Their Vibration: A Basic Approach to Understanding Gear Noise, Marcel Dekker, New York. Tavner, P.J. and Penman, J. (1987), Condition Monitoring of Electrical Machines, John Wiley & Sons, New York.
For Further Information Condition-Based Maintenance Technical Committee, ASME Tribology Division, ASME International, Three Park Avenue, New York, NY 10016-5990. Organized to facilitate the interchange of mechanical system health monitoring and maintenance information. Condition Monitoring & Diagnostic Engineering Management (COMADEM), 307 Tiverton Road, Selly Oak, Birmingham B29 6DA, U.K. International organization addressing all aspects of condition monitoring technology and maintenance management. Offers annual conferences and publishes the International Journal of COMADEM. Condition Monitoring — Predictive Maintenance Technical Committee, STLE Headquarters, 840 Busse Highway, Park Ridge, IL 60068. Serves as an advocate for reducing the incidence of critical, inservice tribological failures. Coxmoor Publishing, P.O. Box 72, Chipping Norton, Oxford, Oxon OX7 6JU, U.K. Publishes Condition Monitor (a monthly newsletter) and Machine, Plant and Systems Monitor, a magazine issued in alternate months that focuses on monitoring techniques used by engineers.
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Joint Oil Analysis Program (JOAP) Technical Support Center, 296 Farrar Road, Pensacola, FL 325085010. Chartered to provide coordinated fluid analysis and technical support for the Army, Navy, and Air Force. Offers biennial conferences to exchange ideas and technology among the equipment maintenance, condition monitoring, diagnostics, and reliability communities. Machinery Information Management Open Systems Alliance (MIMOSA), 4259 Niagara Avenue, San Diego, CA 92107. A non-profit corporation organized as a trade association advocating the open exchange of equipment condition-related information. Society for Machinery Failure Prevention Technology, 4193 Sudley Road, Haymarket, VA 20169-2420. A division of the Vibration Institute, formed to facilitate the interchange of information concerning the processes of mechanical failures. Offers annual conferences with published proceedings. Vibration Institute, 6262 S. Kingery Highway, Suite 212, Willowbrook, IL 60514. A nationally recognized not-for-profit organization dedicated to the exchange of practical information about vibration and condition monitoring. Publishes the quarterly magazine Vibrations. Institutions focused on performing basic and applied research in machinery diagnosis and prognosis include the following. Center for Integrated Diagnostics, Georgia Institute of Technology, Woodruff School of Mechanical Engineering, Atlanta, GA 30332-0405,
Center for Nondestructive Evaluation, Iowa State University, 1915 Scholl Road, Ames, IA 50011-3042, . Organizer of the annual conference Review of Progress in Quantitative Nondestructive Evaluation (QNDE), and publisher of its proceedings. Condition-Based Maintenance Department, Applied Research Laboratory, Pennsylvania State University, North Atherton Street, State College, PA 16804, . Condition Monitoring Research Group, University of Wales, Swansea, Mechanical Engineering, Singleton Park, Swansea, SA2 8PP, U.K. . Maintenance and Reliability Center, University of Tennessee, 103 Estabrook Hall, Knoxville, TN 379962351, . Process Diagnostics & Evaluations Center, Oak Ridge National Laboratory, P.O. Box 2009, Bldg. 9737, Oak Ridge, TN 37831, . Systems and Integrity Maintenance Group, Monash University, Mechanical Engineering, Wellington Road, Clayton, Victoria, Australia 3168, .
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Glossary Francis E. Kennedy Dartmouth College
Peter J. Blau Oak Ridge National Laboratory
A abrasion, n. A process in which hard particles or protuberances are forced against and move along a solid surface. Note: This term sometimes is used to refer to abrasive wear. See also: abrasive wear. abrasive erosion, n. Erosive wear caused by the relative motion of solid particles that are entrained in a fluid, moving nearly parallel to a solid surface. See also: erosion. abrasive wear, n. Wear due to hard particles or hard protuberances forced against and moving along a solid surface. actual contact area, n. See: real area of contact. additive, n. In lubrication, a material added to a lubricant for the purpose of imparting new properties or enhancing existing properties. Main classes of additives: viscosity index (VI) improvers, anticorrosive, anti-foam, antioxidant, anti-wear, detergent, dispersant, extreme-pressure (EP), and boundary lubrication additives. adherence, n. The physical attachment of material to a surface by either adhesion or by other means of attachment that results from the contact of two solid surfaces undergoing relative motion. Note: Adhesive bonding is not a requirement for adherence because such mechanisms as mechanical interlocking of asperities can also provide a means for adherence. See also: adhesion. adhesion, n. In frictional contacts, the attractive force between adjacent surfaces. Notes: (1) In physical chemistry, adhesion denotes the attraction between a solid surface and a second (liquid or solid) phase. This definition is based on the assumption of a reversible equilibrium. (2) In mechanical technology, adhesion is generally irreversible. adhesion, mechanical, n. Adhesion between surfaces produced by the interlocking of protuberances on those surfaces. See also: adherence. adhesive wear, n. 1) Wear by transference of material from one surface to another during relative motion due to a process of solid-phase welding. Note: Particles that are removed from one surface are usually either permanently or temporarily attached to the other surface. 2) Wear due to localized bonding between contacting solid surfaces leading to material transfer between the two surfaces or loss from either surface. See also: transfer. air bearing, n. A bearing using air as a lubricant. See also: gas lubrication. angle of contact, n. In a ball bearing, the angle between a diametral plane perpendicular to a ball bearing axis and a line drawn between points of tangency of the balls to the inner and outer rings. angle of incidence, n. The angle between the direction of motion of an impinging liquid or solid particle and the normal to the surface at the point of impact. angular-contact bearing, n. A ball bearing of the grooved type, so designed that under no load, a line through the outer and inner raceway contacts with the balls forms an angle with a plane perpendicular to the bearing axis. anti-friction bearing, n. 1) Commonly, a bearing containing a solid lubricant. 2) Roller bearings or rolling element bearings. apparent area of contact, n. In tribology, the area of contact between two solid surfaces defined by the boundaries of their macroscopic interface. (Contrast with real area of contact.) Syn: nominal area of contact. See also: real area of contact, Hertzian contact area. 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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Archard wear law, n. Introduced in 1953 by J.F. Archard, the Archard wear law expresses a proportionality between the sliding wear volume (V), the normal load (W), the total sliding distance (S), and the hardness (H) of the wearing surface:
V = kWS/3H where k, the constant of proportionality, is often referred to as the “Archard wear constant,” the “Archard wear coefficient,” or simply, the “wear coefficient” or the “wear constant.” asperity, n. In tribology, a protuberance in the small-scale topographical irregularities of a solid surface. atomic force microscope (AFM), n. A surface analysis device in which a specimen surface is scanned by a sharp, microscopic tip on a thin cantilever beam. The deflection of the tip is measured, enabling determination of the microscale surface roughness and the forces between tip and surface. atomic wear, n. Wear between two contacting surfaces in relative motion attributed to migration of individual atoms from one surface to the other. attitude angle, n. In a bearing, the angular position of the line joining the center of the journal to that of the bearing bore, relative to the direction of loading.
B ball bearing, n. A rolling-element bearing in which the rolling elements are spherical balls. ball complement, n. The number of balls contained in a ball bearing. basic dynamic load capacity (of a bearing), n. The radial load that a rolling element bearing can support for a rating life of 1 million revolutions. See also: basic load rating. basic load rating (C), n. The radial load that a ball bearing can withstand for 1 million revolutions of the inner ring. basic static load rating (of a bearing), n. A load that, if exceeded on a non-rotating rolling element bearing, produces a total permanent deformation of rolling element and race at the most heavily stressed contact point of 0.0001 times the ball or roller diameter or greater. bearing, n. A support or guide by means of which a moving part is located with respect to other parts of a mechanism. bearing area, n. The projected bearing or load-carrying area when viewed in the direction of the load. bearing area curve, n. Introduced in 1933 by E.J. Abbott and F.A. Firestone and sometimes called the “Abbott-Firestone curve,” the bearing area curve is a plot of depth below a reference level parallel to a solid surface (ordinate) vs. the percent bearing area intercepted by a horizontal line at that depth (abscissa). bearing characteristic number, n. A dimensionless number that is used to evaluate the operating conditions of plain bearings. See also: Sommerfeld number. Beilby layer, n. The altered surface layer formed on a crystalline solid during a wear process or by a mechanical polishing, and originally described by Sir George Beilby. The damaged or otherwise altered surface layer resulting from wear is often referred to as the Beilby layer without any implication as to its actual structure or nature. bellows seal, n. A type of mechanical seal that utilizes a bellows for providing secondary sealing. bonded solid lubricant, n. A solid lubricant dispersed in a continuous matrix of a binder, or attached to a surface by an adhesive material. Syn: bonded-film lubricant. boundary lubricant, n. A lubricant suitable for use in boundary lubrication conditions. Note: Fatty acids and soaps are commonly used as boundary lubricants. boundary lubrication, n. A condition of lubrication in which the friction and wear between two surfaces in relative motion are determined by the properties of the surfaces, and by the properties of the lubricant other than bulk viscosity. Brinell hardness test, n. Invented by Swedish engineer J.A. Brinell, it is a measure of penetration hardness obtained by forcing a hard sphere (typically 10 mm diameter) into a surface under a normal load
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P so as to produce an impression of diameter d in the surface of the testpiece. The Brinell Hardness Number (BHN or HB) is a measure of the average indentation pressure. Brinelling, n. Indentation of the surface of a solid body by repeated local impact or impacts, or static overload. burnish, v. 1) To alter the original manufactured surface of a sliding or rolling surface to a more polished condition. 2) To apply a substance to a surface by rubbing. bushing, or bush bearing, n. A plain bearing in which the lining is closely fitted into the housing in the form of a bush, usually surfaced with a bearing alloy.
C cage, n. In a bearing, a device that partly surrounds the rolling elements and travels with them, the main purpose of which is to space the rolling elements in proper relation to each other. See also: separator. cavitation erosion, n. 1) Progressive loss of original material from a solid surface due to continued exposure to cavitation. 2) Wear of a solid body moving relative to a liquid in a region of collapsing vapor bubbles that cause local high impact pressures or temperatures. chatter, n. Elastic vibrations resulting from frictional or other instability. checking, n. Irregular surface cracking associated with thermal cycling, often oriented perpendicular to the sliding direction. Note: This term is used more in the U.S. than in the U.K., where the term “craze cracking” is used instead. chemical conversion coating, n. A coating produced by chemical or electrochemical treatment of a metallic surface, resulting in a superficial layer containing compounds of the metal. Such coatings are usually pretreatments onto which fluid or solid lubricants can be applied, but may themselves have lubricating properties. clearance ratio, n. In a bearing, the ratio of radial clearance to shaft radius. coefficient of adhesion, n. The ratio of the normal force required to separate two bodies to the normal load with which they were previously placed together. coefficient of friction, n. In tribology, the dimensionless ratio of the friction force (F) between two bodies to the normal force (N) pressing these bodies together.
µ (or f ) = (F / N) Note: Two symbols f and µ are commonly used for designating the coefficient of friction, but subscripts may be added to further specify static or kinetic friction conditions. Syn: friction coefficient. compatibility (frictional), n. In tribology, materials that exhibit good sliding behavior, including resistance to adhesive wear, are termed frictionally compatible. Note: Under some conditions, materials that are not normally considered compatible in the metallurgical sense (e.g., silver and iron) may be very compatible in the frictional sense. compatibility (metallurgical), n. A measure of the extent to which materials are mutually soluble in the solid state. compensation, n. In a hydrostatic bearing, the use of flow resistances between the supply and the entry to the bearing. compressibility number, n. A dimensionless group used in gas-bearing calculations. Note: The definition of compressibility number depends on the geometry of the bearing; it differs between thrust and journal bearings. conformal surfaces, n. Surfaces whose centers of curvature are on the same side of the interface. See also: counterformal surfaces. constriction resistance, n. In electrical contact theory, the resistance that arises from the constriction of current flow lines in order to pass through small areas of contact at the interface of two contacting bodies.
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contact angle, n. In lubrication, the angle at which the surface of a liquid drop meets the surface of a solid on which it is placed. contact fatigue, n. Removal of material from a solid surface caused by fracture arising from material fatigue. See also: spalling contact resistance, n. The electrical resistance between two contacting bodies, which is the sum of the constriction resistance and the film resistance. contact stress, n. That stress which results near the surfaces of two contacting solid bodies when they are placed against one another under a non-zero normal force. corrosive wear, n. A wear process in which chemical or electrochemical reaction with the environment predominates. See also: oxidative wear. Coulomb friction, n. A term used to indicate that the frictional force is proportional to the normal load. counterformal surfaces, pl. n. Surfaces whose centers of curvature are on the opposite sides of the interface, as in rolling element bearings or gear teeth. Syn: non-conformal surfaces. crater wear, n. The wear that occurs on the rake face of a cutting tool due to contact with the material in the chip that is sliding along that face. craze cracking, n. See: checking. cutting wear, n. See: abrasive wear.
D delamination wear, n. A wear process in which thin layers of material are removed from the wear surface. detergent additive, n. In lubrication technology, a surface-active additive that helps to keep solid particles in suspension in an oil. diamond film, n. A carbon-composed film, usually deposited by chemical vapor deposition or related process, that has the following three characteristics: (1) a crystalline morphology that can be visually discerned by optical microscopy; (2) a single-phase crystalline structure identifiable by X-ray and/or electron diffraction; and (3) a Raman spectrum typical for crystalline diamond. See also: diamond-like film. diamond-like (or diamond-like carbon) film, n. A hard, noncrystalline carbon film, usually grown by chemical vapor deposition or related techniques, that contains predominantly sp2 carbon-carbon bonds. See also: diamond film. DN value, n. The product of bearing bore diameter (in millimeters) times speed (in revolutions per minute). drip feed lubrication, n. A system of lubrication in which the lubricant is supplied to the bearing surfaces in the form of drops at regular intervals. droplet erosion, n. Erosive wear caused by the impingement of liquid droplets on a solid surface. See also: erosive wear. dry-film lubrication, n. Lubrication which involves the application of a thin film of solid lubricant to the surface or surfaces to be lubricated. dry friction, n. Typically, friction which occurs between two bodies in the absence of lubrication. dry lubricant, n. See: solid lubricant. dry sliding wear, n. Sliding wear in which there is no intentional lubricant or moisture introduced into the contact area. Syn: unlubricated sliding wear. durometer reading, n. An index that is used for ranking the relative hardness of elastomers. dynamic load, n. An imposed force that varies with time; that is, one that shows transient variation in magnitude, sense, and/or direction. dynamic seal, n. A seal that has rotating, oscillating, or reciprocating motion between its components, in contrast with a static seal such as a gasket. dynamic viscosity, n. See: viscosity.
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E eccentricity, n. In journal bearings, the radial displacement of the journal center from the center of the bearing liner. eccentricity ratio, n. In a bearing, the ratio of the eccentricity to the radial clearance. elastohydrodynamic lubrication, n. A condition of lubrication in which the friction and film thickness between two bodies in relative motion are determined by the elastic deformation of the bodies, in combination with the viscous properties of the lubricant at the prevailing pressure, temperature, and rate of shear. embeddability, n. The ability of a bearing material to embed harmful foreign particles and reduce their tendency to cause scoring or abrasion. emulsion, n. A dispersion of globules of one liquid in another in which it is insoluble, (e.g., oil in water). equivalent radial load, n. That constant radial load on a rolling element bearing that, when stationary with respect to the outer-race, will produce the same rating life as a given combination of radial and thrust loads under the same conditions of operation. erosion (erosive wear), n. 1) Loss of material from a solid surface due to relative motion in contact with a fluid that contains solid particles. 2) Progressive loss of original material from a solid surface due to mechanical interaction between that surface and a fluid, a multi-component fluid, or impinging liquid or solid particles. See also: cavitation erosion. erosion-corrosion, n. A conjoint action involving corrosion and erosion in the presence of a corrosive substance. extreme-pressure (E.P.) lubricant, n. A lubricant or additive that imparts increased load-carrying capacity to rubbing surfaces under severe operating conditions, generally through the creation of a sacrificial reaction film by chemical reaction with the solid surface. extreme-pressure lubrication, n. A condition of lubrication in which the friction and wear between two surfaces in relative motion depend on the reaction of the lubricant with a rubbing surface at elevated temperature.
F face seal, n. A device that prevents the leakage of fluids along rotating shafts. Note: Sealing is accomplished by a stationary primary-seal ring bearing against the face of a mating ring mounted on a shaft. Axial pressure maintains the contact between seal ring and mating ring. false Brinelling, n. Damage to a solid bearing surface characterized by indentations not caused by plastic deformation resulting from overload but thought to be due to other causes such as fretting corrosion. Note: The appearance is generally similar to that produced by Brinelling, but corrosion products are usually visible. See also: Brinelling. fatigue wear, n. Removal of particles detached by fatigue arising from cyclic stress variations. fatty acid, n. An organic acid of aliphatic structure originally derived from fats and fatty oils. ferrograph, n. An instrument used to determine the size distribution of wear particles in lubricating oils of mechanical systems. Note: The technique relies on the debris being capable of being attracted to a magnet. film resistance, n. The electrical resistance that results from films at contacting surfaces, such as oxides and contaminants, that prevent pure metallic contact. See: contact resistance, constriction resistance. film thickness, n. In a bearing or dynamic seal, the thickness of the fluid film separating the two solid surfaces. fixed-pad bearing, n. A thrust or radial (journal) bearing equipped with fixed pads, the surfaces of which are contoured to promote hydrodynamic lubrication. flank wear, n. The loss of relief on the flank of a cutting tool behind the cutting edge due to rubbing contact between the work and the tool during cutting; measured in terms of linear dimension behind the original cutting edge.
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flash point, n. The lowest temperature at which the vapor of a lubricant can be ignited under specified conditions. flash temperature rise, n. The maximum local temperature rise generated at some point of close approach in a sliding contact. Notes: (1) The flash temperature rise occurs at areas of real contact, due to the frictional heat dissipated at those areas. (2) The duration of the flash temperature rise is often on the order of a microsecond. flood lubrication, n. a system of lubrication in which the lubricant is supplied in a continuous stream at low pressure and subsequently drains away. fluid friction, n. Frictional resistance due to the viscous or rheological flow of fluids. Syn: viscous friction. foil bearing, n. A bearing in which the housing is replaced by a flexible foil held under tension against a portion of the journal periphery, the lubricant being retained between the journal and the foil. fretting, n. 1) Small-amplitude oscillatory motion, usually tangential, between two solid surfaces in contact. 2) Wear phenomena occurring between two surfaces having oscillatory relative motion of small amplitude. fretting corrosion, n. A form of fretting in which chemical reaction produces reaction products, particularly oxides, that dominate the wear process. fretting fatigue, n. The progressive damage to a solid surface that arises from fretting. See also: fretting wear. fretting wear, n. Wear arising as a result of fretting. friction, n. The resisting force tangential to the common boundary between two bodies when, under the action of an external force, one body moves or tends to move relative to the surface of the other. See also: coefficient of friction, dry friction, fluid friction. friction polymer, n. An amorphous organic deposit that is produced when certain metals are rubbed together in the presence of organic liquids or gases. full-film lubrication, n. A type of lubrication wherein the solid surfaces are separated completely by a hydrodynamic or elastohydrodynamic fluid film. See also: thick-film lubrication. full journal bearing, n. A bearing in which the journal is surrounded a full 360°.
G galling, n. A severe form of scuffing associated with gross damage to the surfaces or surface failure. gas lubrication, n. A system of lubrication in which the shape and relative motion of the sliding surfaces causes the formation of a gas film having sufficient pressure to separate the surfaces. gasket, n. A static seal, usually made of a deformable material, that is used between two relatively stationary surfaces to prevent leakage. grease, n. A lubricant composed of an oil thickened with a soap or other thickener to a semi-solid or solid consistency.
H half journal bearing, n. A journal bearing extending 180° around a journal. hardness, n. The characteristic of a solid material that expresses its resistance to penetration or abrasion by other bodies. Note: Hardness is not a basic property of a solid because it depends on the method of its measurement and the scale used to express it. heat checking, n. A process in which fine cracks are formed on the surface of a body in sliding contact due to the buildup of excessive frictional heat. See also: checking. herringbone bearing, n. Any plain, sleeve, or thrust bearing with herringbone-shaped oil grooves. Hertzian contact area (diameter, radius), n. The apparent contact area (also, diameter or radius of contact) between two bodies, calculated according to Hertz’ equations of elastic deformation.
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Hertzian contact pressure, n. The pressure at a contact between two solid bodies calculated according to Hertz’ equations of elastic deformation. high-stress abrasion, n. A form of abrasion in which relatively large cutting forces are imposed on the particles or protuberances causing abrasion, and which produces significant cutting and deformation of the wearing surface. highly-deformed layer, n. In tribology, a near-surface layer of severely plastically deformed material that results from the shear stresses imposed on that region during sliding contact. hydraulic fluid, n. A fluid used for transmission of hydraulic pressure or traction, not necessarily involving lubricant properties. hydrodynamic lubrication, n. A system of lubrication in which the shape and relative motion of the sliding surfaces cause the formation of a fluid film having sufficient pressure to separate the surfaces. See also: elastohydrodynamic lubrication, full-film lubrication, gas lubrication. hydrostatic bearing, n. A bearing in which the solid bodies are separated and supported by a hydrostatic pressure, applied by an external source to a compressible or incompressible fluid interposed between those bodies. hydrostatic lubrication, n. A system of lubrication in which the lubricant is supplied under sufficient external pressure to separate the opposing surfaces by a fluid film.
I impact wear, n. Wear of a solid surface resulting from repeated collisions between that surface and another solid body. incubation period, n. In cavitation and erosion, the initial stage of the erosion rate-time pattern during which the erosion rate is zero or negligible compared to later stages. indentation hardness, n. Resistance of a solid surface to the penetration of a second, usually harder, body under prescribed conditions.
J journal, n. That part of a shaft or axle that rotates or oscillates relative to a radial bearing. journal bearing, n. A sliding-type bearing in which a journal rotates or oscillates relative to its housing under radial loading.
K kinematic viscosity, n. See: viscosity. kinetic friction, n. Friction under conditions of macroscopic relative motion between two bodies. Knoop (microindentation) hardness number, n. Developed by F.C. Knoop in the late 1930s, it is the numerical value of microindentation hardness obtained using the Knoop indenter (diamond).
L L10 life, n. See: rating life (of a bearing). Langmuir-Blodgett film, n. A thin film of accurately controlled thickness produced by floating an insoluble monolayer on the surface of water and then transferring it to the surface of a solid. lapping, n. A surface finishing process involving motion against a fine abrasive embedded in a soft metal. layer-lattice material, n. Any material having a layer-like crystal structure, but particularly solid lubricants of this type. L/D ratio, n. In bearing technology, the ratio of the axial length of a plain bearing to its diameter. Lennard-Jones potential, n. One of the most commonly used models for the interatomic forces between adjacent atoms or molecules. This potential is often used in molecular dynamics simulations. Syn: 6-12 potential.
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load-carrying capacity, n. The maximum load that a sliding or rolling system can support without wear exceeding the design limits for the particular application. low-stress abrasion, n. A form of abrasion in which relatively low contact pressures on the abrading particles or protuberances cause only fine scratches and microscopic cutting chips to be produced. lubricant, n. Any substance interposed between two surfaces in relative motion for the purpose of reducing the friction or wear between them. lubrication, n. The reduction of frictional resistance and wear, or other forms of surface deterioration, between two load-bearing surfaces by the application of a lubricant. lubricious, adj. - relating to a substance or surface condition that tends to produce relatively low friction. Syn: lubricous. lubricity, n. The ability of a lubricant to reduce wear and friction, other than by its purely viscous properties.
M macrohardness test, n. A term applied to such hardness testing procedures as the Rockwell, Brinell, or macro-Vickers (high load) hardness tests to distinguish them from microindentation hardness tests such as the Knoop or Vickers tests. macroslip, n. A type of sliding in which all points on one side of the interface are moving relative to those on the other, in a direction parallel to the interface. See also: microslip. magnetic bearing, n. A type of bearing in which the force that separates the relatively moving surfaces is produced by a magnetic field. magneto-hydrodynamic lubrication (MHD lubrication), n. Hydrodynamic lubrication in which a significant force contribution arises from electromagnetic interaction. mechanical wear, n. Removal of material due to mechanical processes under conditions of sliding, rolling, or repeated impact. Note: The term “mechanical wear” includes adhesive wear, abrasive wear, and fatigue wear. melt lubrication, n. Lubrication provided by a steady melting of the lubricating species. Syn: phase change lubrication. metallic wear, n. Typically, wear due to rubbing or sliding contact between metallic materials that exhibits the characteristics of severe wear; e.g., significant plastic deformation, material transfer, and the possibility that cold welding of asperities has taken place as part of the wear process. See also: severe wear, adhesive wear. microindentation, n. 1) In hardness testing, the small, residual impression left in a solid surface when an indenter, typically a pyramidal diamond stylus, is withdrawn after penetrating the surface. 2) The process of indenting a solid surface, using a hard stylus of prescribed geometry and under a slowly applied normal force, usually for the purpose of determining its microindentation hardness number. See: Knoop microindentation hardness number, Vickers microindentation hardness number. microscale friction, n. Friction between contacting surfaces that is caused by microscopic mechanisms, including interatomic forces and microasperity interaction. microslip, n. Small relative tangential displacement in a contacting area at an interface, when the remainder of the interface in the contacting area is not relatively displaced tangentially. See also: macroslip. mild wear, n. A form of wear characterized by the removal of material in very small fragments. See also: severe wear. mineral oil, n. A refined hydrocarbon oil without animal or vegetable additives. mist lubrication, n. Lubrication by an oil mist produced by injecting oil into a gas stream. mixed lubrication, n. A loosely defined regime of thin-film lubrication wherein a combination of boundary and hydrodynamic lubrication occurs. Mohs hardness, n. The hardness of a body according to a scale proposed by Mohs, based on ten minerals, each of which would scratch the one below it.
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molecular dynamics simulation, n. A numerical simulation of atomic-scale interactions between contacting surfaces. The simulations are involve models of interatomic forces in classical equations of motion to determine the spatial and temporal motion of atoms and molecules for a given set of initial and boundary conditions. multi-grade oil, n. An oil having relatively little change in viscosity over a specified temperature range.
N nanohardness test, n. An indentation hardness testing procedure, usually relying on indentation force vs. tip displacement data to make assessments of the resistance of surfaces to penetrations on the order of 10 to 1000 nm deep. Note: Most nanohardness testing procedures use three-sided pyramidal diamond indenters first described by Berkovich. Navier-Stokes equations, n. Basic equations of hydrodynamic fluid flow. needle bearing, n. A bearing in which the relatively moving parts are separated by long, thin rollers that have a length-to-diameter ratio exceeding 5.0. Newtonian fluid, n. A fluid exhibiting Newtonian viscosity, wherein the shear stress is proportional to the rate of shear. nominal area (of contact), n. The area bounded by the periphery of the region in which macroscopic contact between two solid bodies is occurring. Note: This is often taken to mean the area enclosed by the boundaries of a wear scar although the real area of contact, in which the solids are touching instantaneously, is usually much smaller. See also: apparent area of contact, real area of contact. non-conformal surfaces, n. Surfaces whose centers of curvature are on the opposite sides of the interface, as in rolling element bearings or gear teeth. Note: Examples of non-conformal contact are sphereon-flat, crossed-cylinders, and flat block-against-ring (tangent to the circumferential surface). non-contact seal, n. A seal in which no solid contact occurs between relatively moving surfaces. non-Newtonian viscosity, n. The apparent viscosity of a material for which the shear stress is not proportional to the rate of shear.
O Ocvick number, n. A dimensionless number used to evaluate the performance of journal bearings. oil, n. A liquid of vegetable, animal, mineral, or synthetic origin feeling slippery to the touch. oil groove, n. A channel or channels cut in a bearing to improve oil flow through the bearing. oil starvation, n. A condition in which a bearing, or other tribocomponent, receives an inadequate supply of lubricant. oil whirl, n. Instability of a rotating shaft associated with instability in the lubricant film. Note: Oil whirl should be distinguished from shaft whirl, which depends only on the stiffness of the shaft. oxidative wear, n. A corrosive wear process in which chemical reaction with oxygen or oxidizing environment predominates.
P partial (journal) bearing, n. A bearing that extends over not more than half the circumference of the journal. partial hydrodynamic lubrication, n. See: mixed lubrication. penetration (of a grease), n. The depth that a standard cone penetrates a grease sample in a standard cup under prescribed conditions of weight, time, and temperature. The results can be quoted as penetration number or penetration value. Petroff equation, n. An equation describing the viscous power loss in a concentric bearing full of lubricant. phase-change lubrication, n. See: melt lubrication.
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pin-on-disk machine, n. A tribometer in which one or more relatively moving styli (i.e., “pin” specimens) are loaded against a flat disk specimen surface such that the direction of loading is parallel to the axis of rotation of either the disk or the pin-holding shaft, and a circular wear path is described by the pin motion. plain journal bearing, n. A plain bearing in which there is relative angular motion between cylindrical surfaces and the force between the surfaces acts radially. plain thrust bearing, n. A plain bearing of the axial-load type, with or without grooves. plasto-hydrodynamic lubrication, n. A condition of lubrication in which the friction and film thickness between two bodies in relative motion are determined by plastic deformation of the bodies, in combination with the viscous properties of the lubricant at the prevailing pressure, temperature, and rate of shear. ploughing (plowing), n. The formation of grooves by plastic deformation of the softer of two surfaces in relative motion. plowing, n. See: ploughing. Poise (P), n. The cgs unit of dynamic viscosity. Notes: 1) Because the poise is a rather large value of viscosity, the centiPoise (cP) has been more commonly used. 2) The SI unit of dynamic viscosity is Pascal-second (Pas = N s /m2). 1 Pas = 10 P = 1000 cP. polishing, n. A surface finishing process utilizing successive grades of abrasive. polishing wear, n. An extremely mild form of wear whose mechanism may involve extremely fine-scale abrasion, plastic smearing of micro-asperities, and/or tribochemical material removal. porous bearing, n. A bearing made from porous material such as compressed and sintered metal powder. Note: The pores can act as reservoirs or passages for supplying fluid lubricant, or the bearing can be impregnated with solid lubricant. pour point, n. The lowest temperature at which a lubricant can be observed to flow under specified conditions. pressure-viscosity coefficient, n. The slope of a graph showing the variation in the logarithm of viscosity with pressure. profiler (or profilometer), n. A device for measuring the roughness of a surface. Among the most common are stylus profilometer, optical (interferometric) profiler, and atomic force microscope (AFM). pseudoplastic behavior, n. A decrease in viscosity with increasing shear stress. PV factor, n. The product of bearing pressure and surface velocity. PV limit, n. The maximum permissible PV factor for a bearing.
Q quasi-hydrodynamic lubrication, n. See: mixed lubrication.
R race (or raceway), n. The groove or path in which the rolling elements in a rolling contact bearing operate. radial lip seal, n. A radial type of seal that features a flexible sealing member referred to as a lip, usually made of an elastomeric material. rating life, n. Currently, the fatigue life in millions of revolutions or hours at a given operating speed at which 90% of a group of substantially identical rolling element bearings will survive under a given load. Note: The 90% rating life is frequently referred to as L10-life or B10-life. Rayleigh step bearing, n. A stepped pad bearing having only one step in each pad. real area of contact, n. In tribology, the sum of the local areas of actual contact between two solid surfaces, formed by contacting asperities, that transmit the interfacial force between the two surfaces.
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Rehbinder effect, n. Modification of the mechanical properties at or near the surface of a solid, attributable to interaction with a surfactant. retainer, n. See: cage. Reyn, n. The former English unit of dynamic viscosity. Reynolds equation, n. The basic equation of hydrodynamic lubrication. ring seal, n. A piston-ring-type seal that assumes its sealing position under the pressure of the fluid to be sealed. Rockwell hardness number, n. A macrohardness number derived from the net increase in the depth of impression as the load on a penetrator is increased from a fixed minor load to a major load and then returned to the minor load. roller bearing, n. A bearing in which the relatively moving parts are separated by rollers. rolling contact fatigue, n. The process of repeatedly stressing a solid surface due to rolling contact between it and another solid surface or surfaces. rolling element bearing, n. A bearing in which the relatively moving parts are separated by balls, rollers, or needles. rotary seal, n. A mechanical seal that rotates with a shaft and is used with a stationary mating ring. roughness average (Ra), n. One of the most common parameters for quantifying surface roughness; it is defined as the arithmetic mean of the absolute values of vertical deviation of the surface from the mean line through the surface profile. Syn: centerline average (CLA), arithmetic average (AA). rubbing bearing, n. A bearing in which the relatively moving parts slide without deliberate lubrication. run-in, n. In tribology, an initial transition process occurring in newly established wearing contacts, often accompanied by transients in coefficient of friction, or wear rate, or both. v. In tribology, to apply a specified set of initial operating conditions to a tribological system in order to improve its long-term frictional or wear behavior, or both. running-in, n. The process by which machine parts improve in conformity, surface topography, and frictional compatibility during the initial stage of use.
S Saybolt Universal Viscosity, n. A commercial measure of viscosity expressed as the time in seconds required for 60 cm3 of a fluid to flow through the orifice of the Standard Saybolt Universal Viscometer at a given temperature under specified conditions. scoring, n. The formation of severe scratches in the direction of sliding. See also: scuffing. scratch, n. A groove produced in a solid surface by the cutting and/ or plowing action of a sharp particle or protuberance moving along that surface. scratch hardness test, n. A form of hardness test in which a sharp-pointed stylus or corner of a mineral specimen is traversed along a surface so as to determine the resistance of that surface to cutting or abrasion. scratching, n. The formation of fine scratches in the direction of sliding. Scratching is to be considered less damaging than scoring. See also: abrasion, scoring. scuffing, n. Localized damage caused by the occurrence of solid-phase welding between sliding surfaces, without local surface melting. Notes: (1) In the U.K., scuffing implies local solid-phase welding only. (2) In the U.S., scuffing may include abrasive effects. (3) In the U.S., the term “scoring” is sometimes used as a synonym for scuffing. See also: galling, scoring. seal, n. A device designed to prevent leakage between relatively moving parts, or to exclude contaminants. seal nose, n. The part of the primary seal ring of a face seal that comes in closest proximity to the mating surface and that, together with the mating surface, forms the primary seal. secondary seal, n. A device, such as bellows, piston ring, or O-ring, that allows axial movement of the primary seal of a mechanical face seal without undue leakage. seizure, n. The stopping of relative motion as the result of interfacial friction.
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self-aligning bearing, n. A rolling element bearing with one spherical raceway that automatically provides compensation for shaft or housing deflection or misalignment. self-lubricating bearing, n. A bearing independent of external lubrication. self-lubricating material, n. Any solid material that shows low friction without application of a lubricant. Note: Examples are graphite, molybdenum disulfide, and polytetrafluoroethylene. separator, n. In rolling-element bearings, the part of a cage that lies between the rolling elements. See also: cage. severe wear, n. A form of wear characterized by removal of material in relatively large fragments. See: mild wear. shaft run-out, n. Twice the distance that the center of a shaft is displaced from the axis of rotation; i.e, twice the eccentricity. shake-down (of surface layers), n. The establishment of a state of stress in which no further plastic flow occurs. shear stability, n. The ability of a lubricant to withstand shearing without degradation. shear thickening, n. An increase in viscosity with an increase in shear stress or time. See also: shear thinning. shear thinning, n. A decrease in viscosity with an increase in shear stress or time. See also: shear thickening. skidding, n. A form of nonuniform relative motion between solid surfaces due to rapid, periodic changes in the traction between those surfaces. sleeve bearing, n. A cylindrical plain bearing used to provide radial location for a shaft, which moves axially. Note: A sleeve bearing is a journal bearing. See also: journal bearing, sliding bearing. slide-roll ratio, n. The ratio of sliding velocity to sweep velocity, e.g., in a pair of gears. Syn: slide-sweep ratio. sliding bearing, n. A bearing in which predominantly sliding contact occurs between relatively moving surfaces. sliding velocity, n. The difference between the velocities of each of the two surfaces relative to the point of contact. sludge, n. A coagulated mass formed at low temperature in combustion engines from oil oxidation residues, carbon and water, often containing foreign material. slurry abrasion response (SAR) number, n. A measure of the relative abrasion response of any material in any slurry, as related to the instantaneous rate of mass-loss of a specimen at a specific time on the cumulative abrasion-corrosion time curve, converted to volume or thickness loss rate. slurry erosion, n. Erosion produced by the movement of a slurry past a solid surface. soap, n. In lubrication, a compound formed by the reaction of a fatty acid with a metal or metal compound. solid-film lubrication, n. Lubrication by application of solid lubricants. solid lubricant, n. Any solid used as a powder or thin film on a surface to provide protection from damage during relative movement, and to reduce friction and wear. soluble oil, n. A mineral oil containing additives that enable it to form a stable emulsion with water. Sommerfeld Number, n. A dimensionless number that is used to evaluate the performance of journal bearings. See also: Ocvick number. spalling, n. Separation of particles from a surface in the form of flakes. Spalling is usually a result of subsurface fatigue, and more extensive than pitting. See also: fatigue wear, contact fatigue. specific sliding, n. The ratio of the algebraic difference between the surface velocities of two bodies in relative motion, to their sum. spherical bearing, n. A bearing that is self-aligning by virtue of its partially spherical form. spherical roller bearing, n. A roller bearing containing barrel-shaped or hourglass-shaped rollers riding on spherical (concave or convex) races to provide self-aligning capability. spin, n. In rolling element bearings, rotation of a rolling element about an axis normal to the contact surfaces.
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spindle oil, n. An oil of low viscosity used to lubricate high-speed, light spindles. splash lubrication, n. A system of lubrication in which the lubricant is splashed onto the moving parts. squeeze effect, n. The persistence of a fluid film between two surfaces that approach each other in the direction of their common normal. static coefficient of friction, n. The coefficient of friction corresponding to the maximum friction force that must be overcome to initiate macroscopic motion between two bodies. static equivalent load, n. In rolling element bearings, the static load which, if applied, would give the same life as that which the bearing will attain under actual conditions of load and rotation. static load rating, n. In rolling element bearings, the maximum static load which can be applied under defined operating conditions before plastic deformation occurs at the most heavily loaded contact within the bearing. static seal, n. A seal, usually made of a deformable material, that is used to prevent leakage between two relatively stationary surfaces. See also: gasket, dynamic seal. stave bearing, n. A sleeve bearing consisting of several axially held slats or staves on the outer surface of which the bearing material is bonded. stepped bearing, n. A thrust bearing in which the working face consists of one or more shallow steps. See also: Rayleigh step bearing. stick-slip, n. A relaxation oscillation usually associated with a decrease in the coefficient of friction as the relative velocity increases. stiction, n. A term sometimes used to signify the condition in which the static frictional resistance is sufficient to prevent macroscopic sliding. Stoke (S), n. The cgs unit of kinematic viscosity. Notes: 1) Because the Stoke is a rather large value of kinematic viscosity, the centiStoke (cS) has been more commonly used. 2) The SI unit of kinematic viscosity is m2/s. 1 S = 100 cS = 0.0001 m2/s. Stribeck curve, n. A graph showing the relationship between coefficient of friction and the dimensionless number (ηN/P), where η is the dynamic viscosity, N the speed (revolutions per minute for a journal), and P the load per unit of projected area. surface damage, n. In tribology, damage to a solid surface, resulting from mechanical contact with another substance, surface, or surfaces moving relative to it, which involves the displacement or removal of material. surfactant, n. A chemical substance characterized by a strong tendency to form adsorbed interfacial films, when in solution, emulsion, or suspension, thus producing effects such as low surface tension, penetration, boundary lubrication, wetting, dispersing, etc. See also: Rehbinder effect. sweep velocity, n. The mean of the surface velocities of two bodies at the area of contact. Note: In rolling, the sweep velocity is also called the rolling velocity. synthetic oil, n. Oil produced from chemical synthesis rather than from petroleum. Examples are esters, ethers, silicons, silanes, and halogenated hydrocarbons.
T tapered land bearing, n. A thrust bearing containing pads of fixed taper. tapered roller bearing, n. A rolling element bearing containing tapered rollers. thermal (thermomechanical) wear, n. Removal of material due to softening, melting, or evaporation during sliding or rolling. Note: Thermal shock may be included in the general description of thermomechanical wear. thermoelastic instability (TEI), n. In sliding contact, sharp variations in local surface temperatures and stress with the passing of asperities leading to stationary or slowly moving hot spots of significant temperature and contact stress. thickener, n. A solid material dispersed in a liquid lubricant to produce a grease. Note: Silica, clays and metallic soaps are widely used as thickeners.
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thick-film lubrication, n. A condition of lubrication in which the film thickness of the lubricant is appreciably greater than that required to cover the surface asperities when subjected to the operating load, so that the effect of the surface asperities is not noticeable. See also: thin-film lubrication. thin-film lubrication, n. A condition of lubrication in which the film thickness of the lubricant is such that the friction and wear between the surfaces is determined by the properties of the surfaces as well as the viscosity of the lubricant. See also: boundary lubrication, mixed lubrication, thick-film lubrication. thixotropy, n. The property of recovering consistency after a decrease as result of shearing. thrust bearing, n. A bearing in which the load acts in the direction of the axis of rotation. tilting-pad bearing, n. A pad bearing in which the pads are free to take up a position at an angle to the opposing surface according to the hydrodynamic pressure distribution over its surface. transfer, n. In tribology, the process by which material from one sliding surface becomes attached to another, possibly the result of interfacial adhesion. Note: Transfer is usually associated with adhesion but the possibility of mechanical interlocking adherence, without adhesive bonding, exists in certain occurrences. traction, n. In rolling contacts, the tangential stress transmitted across the interface. tractive force, n. The integral of the tangential surface stress over the area of contact. transition diagram, n. In tribology, a plot of two or more experimental or operating variables that indicates the boundaries between various regimes of wear or surface damage. tribo-, pref. A prefix indicating a relationship to interacting surfaces in relative motion. tribochemistry, n. That part of surface chemistry dealing with interacting surfaces in relative motion. tribology, n. The science and technology of interacting surfaces in relative motion and of the practices related thereto. tribometer, n. Any device constructed for or capable of measuring the friction, lubrication, and/or wear behavior of materials or components.
U unlubricated sliding, n. Sliding without lubricant, but not necessarily under complete dry conditions.
V vapor-phase lubrication, n. A type of lubrication in which one or more gaseous reactants are supplied to the vicinity of the surface to be lubricated and which subsequently react to form a lubricious deposit on that surface. VI improver, n. An additive, usually a polymer, that reduces the variation of viscosity with temperature, thereby increasing the viscosity index of an oil. Vickers (microindentation) hardness number, n. The numerical value of microindentation hardness obtained using the Vickers (diamond) indenter. viscometer, n. A device for measuring the viscosity of a fluid. Capillary viscometers give a measure of kinematic viscosity, whereas rotational and falling-ball viscometers measure dynamic or absolute viscosity. viscosity, n. The bulk property of a fluid, semifluid, or semisolid substance that causes it to resist flow. Notes: (1) Viscosity is defined as the ratio of shear stress to the rate of shear. (2) Newtonian viscosity is often called dynamic viscosity, or absolute viscosity. (3) Kinematic viscosity (υ) is the ratio of dynamic viscosity (η) to density (ρ) at a specified temperature and pressure (υ = η/ρ). viscosity index (VI), n. A commonly used measure of the change in viscosity of fluid with temperature. viscous, adj. Possessing viscosity.
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W wear, n. (1) Damage to a solid surface, generally involving progressive loss of material, that is due to relative motion between that surface and a contacting substance or substances. (2) The progressive loss of substance from the operating surface of a body occurring as a result of relative motion at the surface. wear coefficient, n. In sliding wear, a dimensionless number that usually represents the proportionality factor k in the Archard wear law. wear debris, n. Particles that become detached in a wear process. wear rate, n. There is no single, standard way to express wear rate. The units used depend on the type of wear and the nature of the tribosystem in which wear occurs. Wear rate can be expressed, for example, as (1) volume of material removed per unit time, per unit sliding distance, per revolution of a component or per oscillation of a body (i.e., in sliding wear); (2) volume loss per unit normal force per unit sliding distance (mm3/N m, which is sometimes called the wear factor); (3) mass loss per unit time; or (4) change in a certain dimension per unit time. wear resistance, n. The resistance of a body to removal of material by wear processes, expressed as the reciprocal of wear rate. wear scar, n. The portion of a solid surface that exhibits evidence that material has been removed from it due to the influence of one or more wear processes. wear transition, n. Any change in the wear rate or in the dominant wear process occurring at a solid surface. wedge effect, n. The establishment of a pressure wedge in a lubricant. wedge formation, n. In sliding metals, the formation of a wedge or wedges of plastically sheared metal in local regions of interaction between sliding surfaces. Note: This type of wedge is also known as a prow. It is similar to a built-up edge. whirl (oil), n. Instability of a rotating shaft associated with instability in the fluid film. white layer, n. In tribology, a white-etching layer, typically associated with ferrous alloys, that is visible in metallographic cross-sections of bearing surfaces. See also: Beilby layer, highly deformed layer. wick lubrication, n. A system in which the lubricant is delivered to the bearing surface by means of a wick.
Acknowledgments Many of the definitions contained in this glossary are based on the “Glossary of Terms” compiled by P.J. Blau in ASM Handbook, Vol. 18, Friction, Lubrication, and Wear Technology (1992), ASM International, Materials Park, OH, pp. 1-21. Some definitions were suggested by the “Terminology Standard Wear and Erosion,” ASTM Standard G-40, Annual Book of ASTM Standards, ASTM, West Conshohocken, PA.
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Index A Abrasive wear, 277-278, 278, 281, 494, see also specific tribosystem of brittle material, 288-290 data generation in, 526-527 of ductile material, 281 abrasive asperity shape, 284 abrasive wear mode, 284-288 hardness ratio, 284 wear volume estimation, 281-284 testing, 502-504 Acoustic emission detection, 1628-1629 ACTIS, 523 Adaptive coatings, 857-858 Additives, in lubricating liquids, 365-366, 462 antioxidants, 463 antiwear additives, 462 corrosion inhibitors, 463 detergent/dispersive additives, 462-463 extreme-pressure additives, 462 friction modifiers, 462 viscosity index improvers, 463 Adhesion, 163, 1423-1425, see also specific tribosystem and cold welding, 197 and controlled rupture, 168-169 and crack propagation, 188-197 Dupré energy of, 165 energy dynamics of, 167-169 force measurements, 617-618, see also Atomic force microscopy (AFM); Friction force microscopy (FFM) force-distance curves in, 627-630 importance of, 618 pulsed force mode in, 631-633 surface topography in, 626-627 tapping mode in, 630-631 tip properties in, 624-626 forces/properties of, 164-167, 572-573, 587-589, 618-624 capillary forces, 572-573 friction, 215, 589-590, see also Interfacial friction; Thin films Griffith's criterion of equilibrium, 167-168 historical background of study of, 195-197 hysteresis and, 589-590
interfacial friction and, 587-589 in liquid meniscus, 183 and mechanical stress, 171-175, see also Stress(es) of metals, 197-198, see also Metal(s) of microcontacts, 197 of solids, 167-175, see also Ceramics; Surface(s), solid and liquids, 183-186, see also Boundary lubricating films; Interfacial friction rough elastic, 186-188 of spheres, 175-183, 573-574, see also Spheres surface effects in, 33-36 theoretical stress in, 164-166 Adhesion coefficient, 33 Adhesion field, 164 Adhesion parameter, 186-188 Adhesive wear, 277-279, 494, see also specific tribosystem adhesive wear mode, 280-281 wear volume estimation, 279-280 Adsorbed monolayers, 728-734 AFM, see Atomic force microscopy Air reversers, 1558-1561 Alcohols, 914-915 Aldehydes, 915 Alloys, see also Ceramics; Metal(s); specific material; specific metal aluminum bearing materials, 1033 for slider bearings, 1029 copper, 774 bearing materials, 1032 for slider bearings, 1028-1029 metals and ceramics, 781-782 soft bearing, 772-774 Aluminum alloys bearing materials, 1033 for slider bearings, 1029 Amides, 916 Amines, 916 Amontons' law, 641 in nanotribology, 646-648 Amplitude parameter, for roughness, 52-55 Amplitude probability distribution, and density functions, 56-59 Amplitude probability function moments, 59-61 Analysis, of surfaces, see also specific tribosystem Auger emission spectroscopy (AES), 24-27
1661
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1662 chemical, 23-24 infrared spectroscopy (IRS), 29-30 secondary ion mass spectroscopy (SIMS), 29 thermal desorption spectroscopy (TDS), 30-31 x-ray photoelectron spectroscopy, 27-28 Angular velocity, of roll, 131-132 Angular wedge, indentation by, 138-139 Annular thrust bearings, 418-422, see also Thrust bearings Annular thrust pad, 392-394 Antioxidants, 463 Antiwear additives, 462 Arbitrary shape, tribology of, 126-127 Articular cartilage, 1600-1601 Artificial organs, 1596 Asperity contacts, see also specific tribosystem in boundary lubrication, 485-486, see also Boundary lubricating films; Microtribology; Nanotribology friction between, 213-214, see also Friction; Interfacial friction probability distribution of, 72-75 single adhesion expression for, 692-694 computer simulation, 737-740 friction expression for, 692-694 Asset management, 1639-1642 Atomic force microscopy (AFM), 102-107, 669, 727-728, 1492 adhesion expression for single asperity contact, 692-694 adhesion force measurements, 617-638, 673-674, see also Adhesion atomic scale friction studies, 678 boundary lubricating film studies by, 678, 708-712 in fabrication/machining, 674-675, 702-703 force-distance curves in, 627-630 friction expression for single asperity contact, 692-694 in indentation measurements, 675-678, 703-708 microscale friction studies, 678-687 macroscale data compared to, 687-688 in nanotribology, 667-669 pull-off force measurements, 617-638 pulsed-force mode in, 631-633 in scratching, wear measurement, 674-675, 694-702 in surface potential measurements, 675 in surface roughness and friction force measurements, 669-673 surface topography in, 626-627 tapping mode in, 630-631, 671 tip properties in, 624-626, 672 tip radii and humidity effects on friction/adhesion, 688-692 in wear testing, 508-509, 674-675, 694-702
Modern Tribology Handbook Aubry transition, 725-726 Auger emission spectroscopy (AES), surface analysis by, 24-27 Autocorrelation function, spatial, 66-68 Autocovariance function, spatial, 66-68 Automatic transmission fluid, automobile, 1220 composition, 1220-1221 current specifications, 1222-1223 evaluating automatic transmission fluids, 1221 oxidation tests, 1221 physical and chemical tests, 1221 plate friction and band friction tests, 1221 road testing, 1222 shudder and stick-slip test, 1222 transmission cycling test, 1221 Automotive tribology, 1187 brakes, 1209-1210 contact pressure, 1210 friction, 1211 materials, 1211 shear traction, 1210 wear, 1212 constant-velocity joints, 1201-1202 continuously variable transmission (CVT), 1199-1201 drive chains, 1202-1203 engine components, 1188-1189 engine bearings, 1190-1191 engineering developments, 1196-1197 lubrication regimes, 1189-1190 piston assembly, 1191-1194 valve train, 1194-1196 lubricants, 1213 air conditioning lubricant, 1223 automatic transmission fluid, 1220-1223 brake fluid, 1224 development of, 1225 engine oil, 1213-1220, see also Engine oil, automobile fuel, 1224-1225 functional fluids: engine coolant, windshield washer fluid, 1224 gear and axle lubricants, 1223 grease, 1223-1224 power steering fluid, 1224 shock absorber fluid, 1224 tires, 1203 construction of, 1203-1204 contact area, 1205-1206 hydroplaning, 1208 load transfer mechanics, 1204-1205 pressure distribution, normal, 1205-1206 shear traction, 1206-1208 slip, 1206-1208 wear characteristics, 1208-1209
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Index traction drive, 1199-1201 transmission, 1197-1199 universal joints, 1201-1202 wheel bearings, 1202 windshield wipers, 1212-1213 Axisymmetric punch, flat rigid, 138, see also Flat punch Axle bearings, rail transport, 1321 Axle loads, rail transport, 1274-1275
B Babbits babbit fatigue, wear debris, 310 composition of, 1031 for slider bearings, 1028 Ball bearings, 1042, see also Rolling bearings angular contact ball bearings, 1043 deep groove ball bearings, 1042-1043 double row ball bearings, 1043 thrust ball bearings, 1043 Barenblatt model, of stress, 174 Base oils group I, 367 group II, 368-369 group III, 369 vs. PAO performance, 370-372 group IV, 369-370 Base stock categories, API, 367 Bearing area curves, 65-66 Bearing ratio, 65 Bearing volume subtraction, in wear testing, 508-509 Bearings in automobile engines, see Automotive tribology ball bearings, 1042-1043, see also Rolling bearings in diesel engines, see Diesel engine tribology externally pressurized, 391-398, see also Externally pressurized bearings journal bearings, 399-415, see also Journal bearings; Slider bearings in rail transport, see under Rail transport tribology roller bearings, 1043-1045, see also Rolling bearings rolling bearings, 1041-1090, see also Rolling bearings slider bearings, 969-1035, see also Slider bearings thrust bearings, 984-996, see also Slider bearings; Thrust bearings Bench test, 497, 514, see also Testing Bevel gears, 1097, see also Gears full film lubrication, 1107-1109 Biological debris sampling, 310-312 Biomedical tribology, 1593-1594, 1596 articular cartilage, 1600-1601
1663 artificial organs, 1596 bone replacement, 1599 cardiovascular devices, 1597-1598 cardiovascular system, 1594-1596 diamond-like carbon (DLC) films, 896 future developments, 1607-1608 hip prostheses, 1605-1607 joint replacement, total, 1603-1605 medical devices, 1596 orthopedic devices, 1599 particle induced osteolysis, 1605-1607 skeletal system, 1596 soft tissue repair/replacement, 1598-1599 soft tissues, 1596 synovial joints, 1599-1600 articular cartilage, 1600-1601 friction, 1601-1602 functional requirements, 1600 lubrication, 1602-1603 wear debris induced osteolysis, 1605-1607 wear mechanisms, 1605-1607 Body-centered cubic (bcc), 6-10 Bonding, and friction, 215 Bone replacement, 1599 Boric acid, 803-806 Boundary additives, 209 Boundary friction, 576, 582, see also Interfacial friction Boundary layer, thermal, 245 Boundary lubricating films, 209, 362-363, 468-470, see also specific tribosystem adsorbed monolayers, 728-734 appearance of, 470, 471, 472 chemical composition of, 470 computer simulation of, 740-744 and contact temperature, 237 defined, 456 depletion of, measurement of, 708-712 descriptive dynamics of, 422-424 spring and damping coefficients, linearized, 424-429 formation of, 219-220, 455 framework of, 478 and oxidation reactions, 464-467 friction forces and, 582-587, see also Interfacial friction measurement of, 476-479, 678 mechanical properties of, 474-476 metals and, 467, see also Metal(s) modeling, 479 asperity-asperity interaction, 485-486 flash temperatures, 480-485 molecular dynamics, 486-487 wear, 479-480 organometallic chemistry of, 467, 472-474
8403cIndex Page 1664 Monday, November 6, 2000 10:00 AM
1664 oxidation reactions, 464 metal catalyzed oxidation reactions, 464-465 oxidation and thermal reactions, 464 polymerization reactions, 465-467 performance of, 363-364 physical properties of, 470 self-assembling monolayers, 924-927 applications of, 909-912 organization of, 917-921 tribologic properties of, 921-924 tribochemistry of, 467, 468, 472-474 viscosity of, 582-587 Boundary monolayer, see Boundary lubricating films Brakes, automobile, 1209-1210 contact pressure, 1210 friction, 1211 materials, 1211 shear traction, 1210 wear, 1212 Bravais lattices, 6-10 Bronzes, for slider bearings, 1028-1029 Bulk dissipations, 192-193 Bulk forming operations, 1399 drawing, 1404, 1406 extrusion, 1404-1406 forging, 1402 cold, 1403-1404 hot, 1402-1403 rolling, 1399-1401 cold, 1401-1402 hot, 1401 sheet metal forming operations, 1407 friction modeling, 1407-1408 galling, 1408-1409 lubricants, 1408 orange peel, 1408-1409 smudge, 1408-1409 Bushings, diesel, 1253-1255
C Cantilever tips, 669-670 atomic force microscopy, 624-626 friction force microscopy, 642-644 Capillary forces, and adhesion, 572-573 Capillary restrictor, 396-398 Carbon nitride films, 871-872, 898-899, 942-943 future studies of, 899-900 Carboxylic acids, 915-916 Cardiovascular devices, 1597-1598 Cardiovascular system, 1594-1596 Cast irons, 774-776 Catalytic dewaxing, 368 Catastrophic stage, of wear, 495
Modern Tribology Handbook Cavitation erosion damage, 1019-1020, 1025-1026 large end bearings, 1020-1022, 1024-1025 main bearings, 1023-1024, 1024-1025 oil in connecting rod drilling, 1020-1022 oil in crankshaft drilling, 1023-1024 rapid shaft motion, 1024-1025 CBN, see Cubic boron nitride (CBN) films Center winding, 1561 Central moments, 59 Ceramics, 778-781, see also Coatings; Composite coatings boundary lubrication, 467 metals and alloys, 781-782 compared, 782-783 wear mapping, 324-325 alumina, 325-326 silicon carbide, 328 silicon nitride, 328 wear modeling using, 343-347 zirconia, 326-328 wear of, 319 mechanical, in elastic contact, 296-298 oxidative, 296 Cermets, 781-782 Chains extraction, 193-195 Characteristic frequency, of system, 385 Characteristic nucleation time, of films, 607 Chemical analysis, of surfaces, 23-24 Chemical imaging, 649-650 Chemical vapor deposition (CVD) diamond film synthesis by, 873-874 of diamond-like carbon (DLC) films, 889-890 Chemically passivated surfaces, 735-737 Chlorotrifluoroethylene fluids (CTFEs), 378-379 Chlorotrifluoroethylene polymers, 378-379 Clutch bearings, 1045 Coatings, 768-770, 827-828, see also specific tribosystem brittle, abrasive wear of, 288-290 carbon nitride, see Carbon nitride films ceramics, 771-784, see also Ceramics; Coatings; Composite coatings composite, see Composite coatings in contact measurement, 148 contact mechanics, 830-833 energy accommodation in surface, 840-843 fracture toughness in material response, 843-844 hard coating on softer substrate, 836-838 load-carrying capacity, 838-839 material response, 839-840 nanotribologic, 834-835 soft coating on hard substrate, 835-836 cracks, surface and subsurface, 844-847 cubic boron nitride, see Cubic boron nitride (CBN) films
8403cIndex Page 1665 Monday, November 6, 2000 10:00 AM
Index diamond, see Diamond films diamond-like carbon, see Diamond-like carbon (DLC) films ductile, abrasive wear of, 281-288 duplex, 943 friction between, 831-832, see also Coatings, contact mechanics layers formed, 844 reaction layers, 850-852 transfer layers, 850 metals, 771-784, see also Composite coatings; Metal(s) multicomponent, 852, 944, see also Composite coatings adaptive coatings, 857-858 functionally graded coatings, 856-857 multilayer coatings, 852-855 nanocomposite coatings, 855-856 multilayered, 943-944 nanocrystalline, 944 reaction layers, 850-852 superlattice, 944 transfer layers, 850 tribochemical properties of, 833-834 wear debris from, 844, 847-849 agglomeration of, 849-850 wear mechanisms of, 831-832 Cobblestone model, of interfacial friction, 587 Coefficient of friction, 206 kinetic, 221 models of, 230-232 static, 221 values of, 206-207 Cold welding, 197 Collection interfaces, rail transport, 1314 earth brushes, 1314-1316 pantographs, 1319-1321 registration arms, 1321 shoe and gear, 1316-1319 Commensurability effect, 734-735 Component test, 497, 515, see also Testing Composite coatings, 810-811, 931-933 carbon nitride, 942-943 component design, 945 load carrying capacity improvement, 946-947 stress considerations, 945-946 topography, 946 wear resistance improvement, 947 cubic boron nitride coatings, 942 current coatings, 936-938, 939-941 design of, 938-939 for cutting tools, 948 for forming tools, 948-949 for machine components, 948-949 diamond coatings, 942
1665 duplex coatings, 943 evaluation parameters, 949-950 failure analysis, 958-959 failure mechanisms, 933-934 gradual wear failure, 936 premature failure, 934-936 future studies of, 959 materials and strengthening, 941-942 multicomponent coatings, 944 multilayered coatings, 943-944 nanocrystalline coatings, 944 properties of adhesion, 950 coating properties, 950 mechanical, 950-955 tribologic, 955-958 self-lubricating new coatings and structures, 814-815 traditional materials, 813-814 superlattice coatings, 944 testing of, 958 Composite roughness, 75-76 Computer simulations, 717-718 constant temperature maintenance, 720-722 crystalline surfaces, dry sliding asperity contacts, single, 737-740 chemically passivated surfaces, 735-737 commensurability effect, 734-735 irreversible tribologic processes, 755-758 load, 722 lubricated surfaces, 740 flow boundary conditions, 740-744 phase transitions of thin films, 744-748 rough surfaces, 750-752 submonolayer lubrication, 748-750 viscosity changes in thin films, 744-748 model potentials, 719-720 molecular dynamics, 718-719 plastic deformation, 755 shear, 722 stick-slip dynamics, 752-755 tribochemistry, 756-758 wear, 755-756 wearless friction in low-dimensional systems, 722 adsorbed monolayers, 728-734 atomic force microscopy, 727-728 Aubry transition, 725-726 crystalline surfaces in direct contact, 722-723 Frenkel-Kontorova model, 723 Frenkel-Kontorova model, in two dimensions, 728-734 Frenkel-Kontorova-Tomlinson model, 726 kinetic friction, 726-727 Matsukawa-Fukuyama model, 726 metastability, 723-727
8403cIndex Page 1666 Monday, November 6, 2000 10:00 AM
1666 quartz crystal microbalance experiments, 728-734 static friction in one dimension, 723-726 Tomlinson model, 726-727 Tomlinson model, in two dimensions, 727-728 Condition monitoring, 1616 methods, 1635 Cone, indentation by, 139-140 Constant-velocity joints, 1201-1202 Contact, between surfaces, 121, see also Adhesion; Friction; Surface(s), solid Hertzian contact, 122-137, see also Hertzian contact layered solids, 157-159 loading beyond elastic limit, 153-156 non-Hertzian, 137-140, see also Non-Hertzian contact numerical methods in mechanics of, 140-144, see also Contact mechanics; Stress(es) repeated contact, 156-157, see also Wear; Wear mapping; Wear mechanisms rough surfaces, 150-153, see also Roughness Contact fatigue rolling, rail transport, 1299-1301 service experience, 1302 small scale tests, 1301-1302 wear and, 1302-1303 rolling bearings, 1083-1085 wear debris from, 310 Contact mechanics, see also specific tribosystem of coated surfaces, 828-831, 835-839, see also Coatings; Composite coatings hard coating on softer substrate, 836-838 load-carrying capacity, 838-839 soft coating on hard substrate, 835-836 in elastohydrodynamic lubrication, 438-441 experimental methods in, 144, see also Computer simulations; Simulation modeling real and nominal area measurement, 144-148 stress analysis, 148-150 in nanotribology, 644-646 numerical methods in, 140 finite element method, 143-144 matrix inversion method, 140-142 variational method, 142-143 Contact methods, thermal monitoring, 1625-1626 Contact temperatures, 235-238, see also Temperature, surface Contact value theorem, 592 Continuity, equation of, 384 Continuously variable transmission (CVT), 1199-1201 Controlled rupture, 168-169, 179 Copper alloys, 774
Modern Tribology Handbook bearing materials, 1032 for slider bearings, 1028-1029 Correlational wear parameters, 348-352 Corrosion inhibitors, 463 Corrosive wear, 277-278, 295, 494, see also specific tribosystem monitoring, 1630 electrical resistance probes, 1631 electrochemical methods, 1630-1631 galvanic/potential monitoring, 1631 linear polarization resistance, 1630-1631 material loss methods, 1631 weight loss coupons, 1631 oxidative wear of ceramics, 296 oxidative wear of metals, 295-296 Coulomb friction, 206, 587, 641 Coulomb's laws, 641 Crack(s), see also specific tribosystem extension energy dynamics of, 167-169 mechanical aspects of, 171-175 propagation, adhesion forces in, 188-189 additivity of dissipations, 192-195 branch with negative resistance, 191-192 bulk dissipations, 192-193 chains extraction, 193-195 fibrils extraction, 193-195 fixed crosshead velocity, 189-191 hysteresis, 195 viscoelastic solids, 189 viscous drag, 192 Critical pad mass, 434-438 Crystal-chemical approach, to high-temperature solid lubrication, 811-813 Crystalline surfaces, 722-723 asperity contacts, single, 737-740 chemically passivated surfaces, 735-737 commensurability effect, 734-735 Cubic boron nitride (CBN) films, 871-872, 897-898, 942 future studies of, 899-900 Current signature analysis, 1632-1633 Curved surfaces, see Hertzian contact; specific tribosystem Cutting tools, composite coatings, 948 Cutting wear debris, 309 CVD, see Chemical vapor deposition Cylinders engine, see under Automotive tribology; Diesel engine tribology tribology of, see also Hertzian contact with inclined axes, 124-126 with parallel axes, 123-124 sliding perpendicular to axes, 132-137
8403cIndex Page 1667 Monday, November 6, 2000 10:00 AM
Index
D Dampers, for train suspension systems, 1321, 1323-1324 Damping coefficients, 424-429 Data interpretation, 1633-1634 Database, tribo-materials, 523, 532-561 abrasive wear data, 529 data types, 529 definitions of data fields, 529-531 field definitions, 529-531 material data, 529 material types, 527 carbon-graphites, 528 metals, 527-528 nonmetallic material, miscellaneous, 529 plastics, 528 porous metals, 528 sources of data, 523-527 tribologic data, 529 Deborah number, 594 Deformation, wear debris, 309 Demnum™, 1164, 1483-1484, see also Perfluoropolyether (PFPE) lubricants Density distribution function, 568 Density functional theory, 10-12 Design quality, 1612 Detergent/dispersive additives, 462-463 Dewaxing, catalytic, 368 Diamond films, 871-873, 942 applications of, 883-884 industrial machining, 884-887 mechanical seals, 887 microelectromechanical systems (MEMS), 887-888 chemical vapor deposition (CVD) synthesis, 873-874 friction studies, 878-883 future studies, 899-900 high pressure/high temperature (HPHT) synthesis, 872-873 microcrystalline structure, 873-874 nanocrystalline diamond (NCD) films, 874-876 tribology of, 876-877 early studies, 877-878 Diamond-like carbon (DLC) films, 871-872, 888 applications, 896 classification, 888-889 deposition methods for, and microstructure, 889-891 friction studies, 892-893 future studies, 899-900 nanotribology, 893-896 properties, structure and compositional influences, 891
1667 tribochemistry, 894-896 tribology, 891-892 Diesel engine tribology, 1231-1233 bearings, 1009-1011, 1253-1255 bushings, 1253-1255 development of, 1267 engine valves, 1249 materials selection criteria, 1251-1253 valve stem/guide wear mechanisms, 1250-1251 valve/seat wear mechanisms, 1249-1250 filtration, 1261 air system, 1264-1265 cooling system, 1266-1267 fuel system, 1266 lubricating system, 1265-1266 fuel injectors, 1258-1261 fuel pumps, 1261 fuels, 1261-1262 lubricants, 1261, 1262-1264 marine engines, 1374-1375 high-speed diesel engines, 1380 medium-speed diesel engines, 1378-1380 slow-speed diesel engines/crankcase, 1377-1378 slow-speed diesel engines/cylinders, 1375-1377 overhead components, 1246-1247 cam/cam followers, 1247-1248 crossheads, 1248 push rods, 1248 rocker levers, 1248 power cylinder components, 1233 base stocks and additives effects, 1241 engine deposits effects, 1241 friction, 1237 fuel sulfur effects, 1240 liner wear mechanisms, 1244-1246 liners/bores, 1233-1235 oil cleanliness effects, 1243-1244 oil film thickness effects, 1241-1243 piston pin/connecting rod, 1237 pistons, 1236-1237 ring wear mechanisms, 1244-1246 ring/liner interface, 1238-1240 rings, 1235-1236 tribologic systems, 1237-1238 rail transport diesel engines, 1308 combustion air supply, 1312 design of, tribologic issues, 1309-1311 drives, electric, 1313 drives, mechanical and hydraulic, 1312-1313 four-stroke engine, 1309 mechanical power generation, 1308 transmissions, 1312 two-stroke engine, 1308-1309
8403cIndex Page 1668 Monday, November 6, 2000 10:00 AM
1668 turbomachinery, 1255-1257 used oil analysis, 1264 Diffuse reflection (scattering) methods, in roughness measurement, 89-93 Digital optical profiler, 97-100 Dissipative processes, 18-19, 593-594, see also specific tribosystem additivity of, 192-195 bulk, 192-193 molecular model of, 593-594 DLC, see Diamond-like carbon (DLC) films DMT (Derjaguin, Muller, Toporov) solution, 179-180, 620 Drive chains, automobile, 1202-1203 Drives, magnetic storage devices, 1415 Dugdale model, of stress, 174 JKR-DMT transition, 180-182 Duplex coatings, 943 Dupré energy, of adhesion, 165 Dynamic loading, 1011-1013 Dynamic seals, 1131 mechanical seals, 1131-1132 analysis, 1141-1146 analysis, computational procedure, 1144-1146 configurations, 1132-1134 contact mechanics, 1143 deformation, 1143-1144 face materials, 1134 floating seal, face, 1134-1136 fluid mechanics, 1142-1143 gas seals, 1140-1141 hydrodynamic seals, 1138-1140 hydrostatic seals, 1136-1137 hydrostatic seals, contacting, 1138 hydrostatic seals, non-contacting, 1137-1138 sealing region, 1134 thermal analysis, 1144 two-phase effects, 1141 nomenclature, 1154-1155 rotary lip seals, 1146-1147 analysis, 1154 bidirectionality, 1151 configurations, 1147 converse mounting, 1151 lip macrogeometry, 1149-1150 lip materials, 1147 lip microgeometry, 1148-1149 modeling, 1152-1154 reverse pumping, 1148 sealing region, 1147-1148 shaft surface microgeometry, 1150-1151 terminology, 1155-1156 tribo-element monitoring, 1638-1639 Dynamic thermocouples, temperature measurement, 261-262
Modern Tribology Handbook
E Earthmoving tribology, 1331-1333, see also Mining and mineral processing tribology abrasive wear classification, 1347-1349 contact conditions, 1353-1355 mechanisms, 1349-1352 parameters, 1352-1353 wear material properties, 1355-1358 equipment used in, 1339 bucket wheel excavator, 1344 bulldozers, 1340 dragline, 1342 dump truck, giant, 1343-1344 excavators, 1341 front-end loaders, 1342 graders, 1341 large-scale earthmoving, 1342 scrapers, 1340 small-scale earthmoving, 1339-1340 stripping shovel, 1342-1343 financial costs of, 1366-1368 Eddy current inspection, 1628 Effective viscosity, 390-391 Elastic belt microslip, 1579-1582 Elastic fretting, 166 Elastic friction, 210 Elastic shakedown, 156-157 Elasticity, limit of, 153-154 Elastic/plastic contact, 154-156 and fractal modeling of surfaces, 1428-1430 Elastohydrodynamic lubrication (EHL), 438, 456, 580, see also specific tribosystem contact mechanics description, 438-441 dimensional analysis, 441-443 film thickness, minimum, 443-450 film thickness design, 443 nomenclature of, 451-453 Electrical resistance, contact measurement by, 144-145 Electrical resistance probes, 1631 Electrochemical corrosion monitoring, 1630-1631 Electron microscopy high-resolution (HREM), 20-22 reflection, 109 in roughness measurement, 109-110 scanning (SEM), 109 of surface structure, 20-22 transmission (TEM), 696-702 Electronegativity/polarity, 912-913, 916-917 Elliptical contact, 130-131 Ellipticity, 440 Embedded atom method (EAM), 720 Embedded subsurface thermocouples, 259-261 Energy accommodation concept, 841-843
8403cIndex Page 1669 Monday, November 6, 2000 10:00 AM
Index Energy equation, 388-390 Engine oil, automobile composition, 1213-1214 fuel efficiency, 1218-1219 functions, 1214-1215 modeling engine oil performance, 1219-1220 oil properties, assessed in standard tests, 1215 oil properties, effects of service on, 1215-1216 city service, 1217-1218 extreme short trip, cold start, 1218 freeway service, 1216 high load service, 1216-1217 oil properties, monitoring devices, 1219-1220 Engine tribology automobile engine, 1188-1189 engine bearings, 1190-1191 engineering developments, 1196-1197 lubrication regimes, 1189-1190 piston assembly, 1191-1194 valve train, 1194-1196 diesel, see Diesel engine tribology Erosion, see Cavitation erosion damage; Corrosive wear Ester lubricants, 375-376, 461 in magnetic storage devices, 1482-1483 in space tribology, 1163 Esters, 915-916 Ethers, 914-915 External load, and interfacial friction, 590-593, see also specific tribosystem Externally pressurized bearings, lubrication, 391-392 annular thrust pad, 392-394 capillary restrictor, operation with, 396-398 optimization, 394-396 Extreme-pressure additives, 462
F Fabrication/machining, using AFM, 674-675, 702-703 Face-centered cubic (fcc), 6-10 Fatigue wear, 277-278, 290, 494, see also Contact fatigue characteristics of, 310 rolling/sliding elastic contact, 290-292 sliding plastic contact, 292-295 FFM, see Friction force microscopy (FFM) Fibrils extraction, 193-195 Field ion microscopy (FIM), of surface structure, 22-23 Field tests/trials, 497, 514, see also Testing; Tribosimulation(s) Films, 216-219, 422-438, see also Coatings; Composite coatings; Liquid lubricants; Monolayers; Solid lubricants; specific material
1669 boundary lubricating films, 456, see also Boundary lubricating films carbon nitride films, 871-872, 898-900, 942-943 chemical vapor deposition diamond film synthesis, 873-874 diamond-like carbon (DLC) films, 889-890 contact pressure pads, stress analysis, 150 cubic boron nitride (CBN) films, 871-872, 897-900, 942 diamond films, 871-873, 942 applications of, 883-884 industrial machining, 884-887 mechanical seals, 887 microelectromechanical systems, 887-888 chemical vapor deposition, 873-874 friction studies of, 878-883 future studies of, 899-900 high pressure/high temperature method, 872-873 microcrystalline structure of, 873-874 nanocrystalline diamond (NCD) films, 874-876 tribology of, 876-878 diamond-like carbon (DLC) films, 871-872, 888 applications of, 896 classification of, 888-889 deposition methods for, and microstructure, 889-891 friction studies of, 892-893 future studies of, 899-900 nanotribology of, 893-896 properties of, structure and compositional influences, 891 tribochemistry of, 894-896 tribology of, 891-892 film thickness calculations nominal line contact, 443-446 nominal point contact, 446-450 fluid films, 362-363, 585, see also Elastohydrodynamic lubrication; Hydrodynamic lubrication; Liquid lubricants; Microtribology friction and, 594-600, see also Friction; Interfacial friction gas films, 1029 materials combinations for various temperatures, 1034-1035 in gear tribology, see Gears intermediate, 581-582 liquid films, 585, see also Elastohydrodynamic lubrication; Hydrodynamic lubrication; Liquid lubricants; Microtribology magnetic storage devices diamond-like carbon (DLC) films, 896 monolayer films, 909-912
8403cIndex Page 1670 Monday, November 6, 2000 10:00 AM
1670 in mechanical seals, 887, see also Mechanical seals microelectromechanical systems (MEMS) diamond films, 887-888 monolayer films, 909-912 nanocrystalline diamond (NCD) films, 874-876 nanotribology of, see specific film rheology of, 576-582 in slider bearings, see under Slider bearings solid films, see Coatings; Monolayers; Solid lubricants surface force apparatus studies of, 745-748 temperature sensors in, 262-263 thick films, 577-580 thin films, see Coatings; Monolayers; Thin films tribochemistry of, see Boundary lubricating films; specific film; Tribochemistry viscosity of, 582-587, see also Viscosity Filtration systems, diesel, 1261 air system, 1264-1265 cooling system, 1266-1267 fuel system, 1266 lubricating system, 1265-1266 Finishing operations, 1398 chemical mechanical polishing, 1399 coated/bonded abrasives, 1398-1399 electrochemical machining, 1399 lapping, 1399 Finite element codes ABAQUS, 143 ANSYS, 143 DYNA3D, 143 MARC, 143 NASTRAN, 143 RADIOSS, 143 Finite journal bearings, 406-411 Fixed crosshead velocity, crack propagation in, 189-191 Fixed geometry (pad) bearings, 977, 984, see also Thrust bearings hydrodynamic lubrication, 418 Rayleigh step bearing, 986-989 recurrent-grooved bearings, 989-994 tapered land slider, 984-986 Fixed type journal bearings, externally pressurized, 405 Flash temperatures and boundary lubrication modeling, 480-485 calculations of rise, 239 flash temperature transients, 246-248 moving heat source on stationary body, 243-246 nominal surface temperature rise, 249-251 partition of frictional heat, 251-255 stationary heat source on moving body, 243-246 stationary heat source on stationary body, 239-243 summary of, 246
Modern Tribology Handbook Flat punch(es) adherence of, 169-171 axisymmetric, 138 non-Hertzian contact, 137-138 planar, 137-138 Flexible media tribology, 1416-1418, 1549-1550 air reversers, 1558-1561 elastic belt microslip, 1579-1582 foil bearings, 1550-1553 central region, 1555 exit region, 1555-1556 inlet region, 1554-1555 models, 1553-1558 sheet transport in channel, 1576-1579 roller/roller or roller/platen nips, 1582-1587 terminology, 1588 web tenting, 1570-1576 web winding J-line slip, 1565-1570 nip-induced tension, 1565-1570 wound rolls, 1561-1562 air entrainment, 1562-1565 Flexible rotor stability, 429-433 Flow boundary conditions, 740-744 Flow factors, Patir-Cheng, 388 Flow rate, 1632 Fluid film bearings, see Journal bearings Fluid film lubrication, 362-363, 585, see also Films Foil bearings flexible media, 1550-1553 central region, 1555 exit region, 1555-1556 inlet region, 1554-1555 models, 1553-1558 journal bearings, 1005-1006 advantages of, 1008 applications of, 1009 bending-dominated (continuous), 1007-1008 bending-dominated (segmented), 1006-1007 disadvantages of, 1009 materials used for, 1009 tension-dominated, 1006 Fomblin™, 1164, 1483-1484, see also Perfluoropolyether (PFPE) lubricants Forming tools, composite coatings, 948-949 Fractal modeling and elastic/plastic contact, 1428-1430 of surface roughness, 76-77 Fracture mechanics, 167-198, 213, see also Adhesion Free rolling, 135-136 Frenkel-Kontorova model, 723 in two dimensions, 728-734 Frenkel-Kontorova-Tomlinson model, 726 Fretting, 134-135, see also specific tribosystem
8403cIndex Page 1671 Monday, November 6, 2000 10:00 AM
Index elastic, 166 wear debris, 310 Friction, 1423-1425, see also specific tribosystem and adhesion, 167-175, 215, see also Adhesion and adhesion hysteresis, 589-590, see also Hysteresis asperities causing, 213-214, see also Boundary lubricating films; Interfacial friction atomic mechanism, 652-658 atomic-scale studies, 641-642, 678, see also Atomic force microscopy; Friction force microscopy; Nanotribology bonding and, 215 boundary, 576, 582 boundary lubricating films, 583-585, see also Boundary lubricating films coated surfaces, 831-832, see also Coatings; Composite coatings coefficient of friction, 206, 221 concepts of, 213-215, 1423-1425 continuum models of, limits of, 576-577 Coulomb friction, 206, 587 data generation for, 523-531 database of, 532-561 diamond films, studies of, 878-883, see also Diamond films diamond-like carbon (DLC) films, studies of, 892-893, see also Diamond-like carbon (DLC) films elastic friction, 210, 1428-1430 energy dissipation, 18-19, see also Dissipative processes forces measurements, 669-673, see also Atomic force microscopy (AFM); Friction force microscopy (FFM) fracture properties and, 213, see also Adhesion heat of, 235-238, see also Temperature, surface partition of, 251-255 and tribologic surfaces, 236-237 interfacial, 576, 582-590, see also Interfacial friction and intermediate films, 581-583 kinetic, 726-727 levels of friction, 205-206 lubrication and, 207-209, see also Boundary lubricating films; Lubricants/lubrication measuring, 220-227, see also Atomic force microscopy (AFM); Friction force microscopy (FFM); Testing; Tribosimulation(s) mechanisms, 219-220, see also Contact mechanics; specific tribosystem microscale studies, 678-687, see also Atomic force microscopy (AFM); Friction force microscopy (FFM) macroscale study data comparisons, 687-688
1671 models, 12-18, 230-232, see also Simulation modeling plastic friction, 210-211 qualitative ranges of, 208 elastic friction, 210 lubricated friction, 208-209 plastic friction, 210-211 rolling friction, 209-210 viscoelastic friction, 211-213 rolling friction, 209-210 self-assembling monolayers, studies of, 921-924 static, 231-232, 1425-1428 static, in one dimension, 723-726 stick-slip, 600-601, see also Stick-slip friction Stribeck curve in representation of, 232, 577-578 and surface chemical composition, 648-652 surface effects, 33-36, 216-219, 648-649, see also specific tribosystem surface temperatures and, 235-238, see also Temperature, surface test machine design and, 227-229 testing, 220-227, see also Testing; Tribosimulation(s) machines for, 221 thin film lubrication and, 594-600, see also Films; Thin films vibration and, 207, see also Vibration viscoelastic friction, 211-213 viscosity and, 362-363, see also Viscosity effective, 390-391 of intermediate films, 581-582 of thick films, 577-580 wear and, see Wear; Wear mapping; Wear mechanisms wearless, in low-dimensional systems, 722 adsorbed monolayers, 728-734 atomic force microscopy, 727-728 Aubry transition, 725-726 crystalline surfaces in direct contact, 722-723 Frenkel-Kontorova model, 723 Frenkel-Kontorova model, in two dimensions, 728-734 Frenkel-Kontorova-Tomlinson model, 726 kinetic friction, 726-727 Matsukawa-Fukuyama model, 726 metastability, 723-727 quartz crystal microbalance experiments, 728-739 static friction in one dimension, 723-726 Tomlinson model, 726-727 Tomlinson model, in two dimensions, 727-728 welding and, 215 Friction force microscopy (FFM), 642-644, 669, 1492 adhesion expression for single asperity contact, 692-694
8403cIndex Page 1672 Monday, November 6, 2000 10:00 AM
1672 adhesion force measurements, 673-674 atomic mechanism of friction, 652-658 atomic scale friction studies, 678 boundary lubricating film studies, 678, 708-712 chemical imaging, 649-650 in fabrication/machining, 674-675, 702-703 friction expression for single asperity contact, 692-694 indentation measurements, 675-678, 703-708 microscale friction studies, 678-687 macroscale data compared to, 687-688 in nanotribology, 642-644, 667-669 scratching, wear measurement, 674-675, 694-702 surface potential measurements, 675 surface roughness and friction force measurements, 669-673 tip radii and humidity effects on friction/adhesion, 688-692 velocity dependence of friction, 658-659 Friction modifiers, 462 Frictional anisotrophy, 649 Frictional heating, see Friction, heat of Fuel injectors, diesel, 1258-1261 Fuel pumps, diesel, 1261 Full tribocouple tests, 498, 515, see also Testing Functionally graded coatings, 856-857
G Galvanic/potential corrosion monitoring, 1631 Gas film lubrication, slider bearings, 1029 materials combinations for various temperatures, 1034-1035 Gas turbine engines marine, 1380-1381 rail transport, 1313-1314 Gears, 1095-1096, 1124 failure modes, 1097, 1099 macro-pitting, 1099 micro-pitting, 1099 mild wear, 1100-1101 scuffing, 1099-1100 failure modes, modeling, 1115 pitting life model, conventional, 1115-1116 pitting life model, prospective, 1116-1117 scuffing model, conventional, 1117-1119 scuffing model, prospective, 1119-1121 failure testing, 1122-1128 full film lubrication, 1101-1102 helical gears, 1105-1107 hypoid gears, 1107-1109 spiral bevel gears, 1107-1109 spur gears, 1102-1105 worm gears, 1109-1110
Modern Tribology Handbook mixed lubrication, 1110-1111 asperity contact pressure, 1111, 1114-1115 asperity contact simulation, 1111-1113 fluid film pressure simulation, 1111-1113 macro-micro method, 1113-1114 tribo-element monitoring, 1637-1638 types of, 1096 bevel gears, 1097 helical gears, 1096-1097 hypoid gears, 1097 spur gears, 1096 worm gears, 1097 wear modeling in spur gears, 1121-1122 Geometry, of surfaces, 6-10 Glossmeters, 88-89 Granato-Lucke effect, 188 Graphite, 799-802 Gray staining, see Cavitation erosion damage; failure modes, under specific tribosystem Griffith's criterion, of equilibrium, 167-168 Gross sliding, 132-134 Group I base oils, 367 Group II base oils, 368-369 Group III base oils, 369 vs. PAO performance, 370-372 Group IV base oils, 369-370 Gümbel boundary conditions, 402
H Halogenated compounds, 461 Heads magnetic, 1420-1423 rigid disk, 1420-1423 tape, 1420 Head/tape interface wear mechanisms, 1448-1449 head materials effects, 1458-1459 magnetic tape effects, 1458 particulate and metal-evaporated tapes, 1449-1453 environmental effects, 1453-1458 pole-tip recession effects, 1459-1461 tape path materials effects, 1461 Head/thin-film rigid disk interface thin film lubricant, 1475 chemical bonding effects, 1475-1476 environmental effects, 1476-1478 polar lubricant effects, 1478-1481 recommended lubrication approaches, 1481-1482 wear mechanisms, 1461-1464 DLC overcoat materials effects, 1472 environmental effects, 1472-1475
8403cIndex Page 1673 Monday, November 6, 2000 10:00 AM
1673
Index overcoat materials effects, 1470-1472 particulate contamination effects, 1464-1467 pole-tip recession, 1469-1470 slider materials effects, 1467-1469 Heat source equations, see Temperature, surface Height distribution functions, surface, 61-65 Helical gears, 1096-1097, see also Gears full film lubrication, 1105-1107 Herringbone-grooved journal bearings, 1004-1005 Herringbone-grooved thrust bearing, 992-994 Hertz stress, 123 Hertzian contact, 122, see also specific tribosystem adhesion properties and, 618-620 bodies of arbitrary shape, 126-127 cylinders, sliding perpendicular to axes, 132-137 cylinders with inclined axes, 124-126 cylinders with parallel axes, 123-124 elastic contact between rough surfaces, 152-153 elliptical contact, 130-131 free rolling, 135-136 gross sliding, 132-134 incipient sliding (microslip), 134-135 nominal line contact, 129-130 nominal point contact, 127-129 sliding contact, 131-132 sliding spheres, 132-137 spheres, 122-123, 175-176 stresses in, surface and subsurface, 127-131 surface traction in, 131-132 tractive rolling, 136-137 Hexagonal boron nitride, 802-803 High pressure/high temperature (HPHT) method, 872-873 High-resolution electron microscopy (HREM), 20-22 High-temperature solid lubricants, 808 composites, 810-811 crystal-chemical approach, 811-813 oxides, fluorides, sulfates, 808-810 Hip prostheses, 1605-1607 Hydrocarbon adsorption, surface effects in, 36-39 Hydrocarbon lubricants, see also Synthetic lubricants Hydrocarbons, 913-914 Hydrocracking, 368 Hydrodynamic lubrication, 398-399, 456 journal bearings, 399-405 finite journal bearings, 406-411 fixed type, 405 nomenclature, 404 performance of short and long bearings, 405 pivoted-pad journal bearings, 411-415 nomenclature of, 451-453 thrust bearings, 415 annular thrust bearing, 418-422 plane slider, 415-418 Hydroisomerization, 368
Hydrotreatment, 367 Hypoid gears, 1097, see also Gears full film lubrication, 1107-1109 Hysteresis (effect), 195, 232 adhesion, 574-576 and boundary friction, 589-590
I Incipient sliding (microslip), 134-135 Indentation, 675-678, 703, see also specific tribosystem angular wedge, 138-139 cone, 139-140 nanoindentation, 704-708 picoindentation, 703-704 rolling bearing, 1056 Industrial machining, see Machining; Manufacturing tribology Infrared detectors, temperature measurement, 265-269 Infrared imaging, 1626 Infrared photography, temperature measurement, 264-265 Infrared spectroscopy (IRS), surface analysis, 29-30 Interfacial friction, 576, 582-583 adhesion force and, 587-589 adhesion hysteresis and, 589-590 external load and, 590-593 monolayer coated surfaces, 583-585 theories of, 587 thin liquid films, 585 transition to normal friction, 585-587 Interlocking asperity model, 587 Intermediate films, viscosity, 581-582 Irons, cast, 774-776 Irwin formula, 174 ISODEWAXING technology, 369-370
J Jam envelope, 1578-1579 JKR (Johnson, Kendall, Roberts) solution, 176-179, 573-574, 620 Joint replacement, total, 1603-1605 Joints, synovial, 1599-1600 articular cartilage, 1600-1601 friction, 1601-1602 functional requirements, 1600 lubrication, 1602-1603 Journal bearings, 399-405, 996-1000, see also Slider bearings advantages and disadvantages, 981-983 cavitated flow characteristics, 999-1000
8403cIndex Page 1674 Monday, November 6, 2000 10:00 AM
1674 diesel engine bearings, 1009-1011 dynamic loading, 1011-1013 finite journal bearings, 406-411 fixed type, 405 flow balance, 999-1000 foil bearings, 1005-1009 helical grooved bearings, 1004-1005 hydrodynamic lubrication, 399-405 finite journal bearings, 406-411 fixed type, 405 nomenclature, 404 performance of short and long bearings, 405 pivoted-pad journal bearings, 411-415 lubricant supply arrangements, 1000-1004 nomenclature, 404 performance of short and long bearings, 405 pivoted pad, hydrodynamic lubrication, 411-415 plain, 996-1000 reciprocating load bearings, 1009-1013 shaft whirl, 1013 steady-state pressure distribution, 998-999 tribo-element monitoring, 1635-1636 vibrational loading, 1013 whirl inhibition, designs for, 1013-1019
K Ketones, 915 Kinetic friction, 726-727 Kohn-Sham equations, 10-12 Kolmogorov-Smirnov test, 58 Krytox™, 1164, 1483, see also Perfluoropolyether (PFPE) lubricants Kurtosis, 60-61
L Lamellar solid lubricants, 792-794 boric acid, 803-806 graphite, 799-802 hexagonal boron nitride, 802-803 lubrication mechanisms, 806-808 monochalcogenides, 798-799 transition metal dichalcogenides, 794-798 Lateral force microscopy (LFM), 643, see also Friction force microscopy Lattice trapping, 166 Lattices, Bravais, 6-10 Layered solids tribology, 157-159, see also Lamellar solid lubricants multilayered coatings, 943-944 Lennard-Jones potential, 164, 719-720
Modern Tribology Handbook Light sectioning method, of roughness measurement, 87 Line contact, nominal, 129-130 Linear polarization resistance, 1630-1631 Liquid bridges, 183-186, see also Adhesion; Interfacial friction; Thin films Liquid lubricants, 361, 740, see also specific tribosystem additives in, 365-366, 462-463 API base stock categories, 367 base stock categories, 460 biodegradability, 365 compared to solid lubricants, 788 compatibility, 365 film lubrication, 362-363, see also Films; Microtribology of slider bearings, 1027-1035 fire resistance, 364-365 formulation, 463 mineral oil based, 366, 460 additive improvements, 367 catalytic dewaxing, 368 early processing methods, 366 evolution of future lubricants, 372 group I base oils, 367 group II base oils, 368-369 group III base oils, 369 group III vs. PAO performance, 370-372 hydrocracking, 368 hydroisomerization, 368 hydrotreatment, 367 selection of, 361-362 solvent refining methods, 366-367 unconventional base oils, 369 reactions, 459 selection, 361-362 stability, 364 synthetic based, 369-370, 373, 461-462 chlorotrifluoroethylene polymers, 378-379 esters, 375-376 group IV base oils, 369-370 PAO (polyalphaolefin) fluids, 369-370 PAO vs. group III performance, 370-372 perfluorinated fluids, 380 phosphate esters, 376 polyphenylethers, 379-380 reasons for use of, 373-374 silahydrocarbons, 378 silicate esters, 377 silicon-containing fluids, 376-377 silicones, 377-378 synthetic hydrocarbons, 374-375 toxicity, 365 viscosity, 362-363
8403cIndex Page 1675 Monday, November 6, 2000 10:00 AM
1675
Index Liquid meniscus, adhesion forces, 183, see also Liquid bridges Liquid penetrant inspection, 1627-1628 Liquid structure, stick-slip sliding, 597-600 Loading beyond elastic limit, 153-156 dynamic, 1011-1013 vibrational, 1013 Local density approximation (LDA), 10-12 Low-energy electron diffraction (LEED), of surface structure, 19-20 Lubricants/lubrication, 383-384, 445 automobile engine, 1213-1225, see also Automatic transmission fluid, automobile; Automotive tribology, lubricants; Engine oil, automobile boundary, 209, see also Boundary lubricating films cold working, 1387-1389 compressible, 974-975 vs. incompressible, 975-977 computer simulation of, 740-752, see also Computer simulations; Simulation modeling description of approximation, 385-386 basic equations, 384-385 effective viscosity, 390-391 energy equation, 388-390 Reynolds equation, 386-387 surface roughness, 388 turbulent flow, 387-388 diesel engine, 1261, 1262-1264, see also Diesel engine tribology of dynamic seals, 1131-1156, see also Dynamic seals of earthmoving equipment, 1331-1333, see also Earthmoving tribology elastohydrodynamic, 438-450, see also Elastohydrodynamic lubrication of externally pressurized bearings, 391-398, see also Externally pressurized bearings films, 422-438, see also Coatings; Composite coatings; Films and friction, 207-208, see also Adhesion; Friction of gears, 1095-1128, see also Gears hot working, 1389-1390 hydrodynamic, 398-422, see also Hydrodynamic lubrication liquids, see Liquid lubricants of magnetic storage devices, 1482-1491, see also Magnetic storage devices in manufacturing operations, 1385-1409, see also Manufacturing tribology in marine engines/equipment, 1371-1380, see also Marine engine/equipment tribology
in mining and mineral processing, 1331-1333, see also Mining and mineral processing tribology nomenclature, 451-453 in rail transport systems, 1271, 1325-1326, see also Rail transport tribology regimes, 457, see also specific tribosystem of rolling bearings, 1041-1090, see also Rolling bearings of seals, dynamic, 1131-1156, see also Dynamic seals of slider bearings, 974-977, see also Slider bearings solid, see Coatings; Solid lubricants of space tribologic systems, 1159-1161, see also Space tribology of synovial joints, 1602-1603, see also Biomedical tribology synthetic, see Synthetic lubricants Lubricated friction, 208-209 Lubrication regimes, 457, 577, see also specific tribosystem
M Machine components, composite coatings, 948-949 Machinery diagnosis/prognosis, 1611, 1612 asset management, 1639-1642 condition monitoring, 1616 condition monitoring methods, 1635 corrosion monitoring, 1630 electrical resistance probes, 1631 electrochemical methods, 1630-1631 galvanic/potential monitoring, 1631 linear polarization resistance, 1630-1631 material loss methods, 1631 weight loss coupons, 1631 historical records, 1612 maintenance of equipment, 1615 condition-based maintenance, 1616 failure-based maintenance, 1615 reliability-centered maintenance, 1616 time-based maintenance, 1615-1616 nondestructive evaluation, 1627 acoustic emission detection, 1628-1629 eddy current inspection, 1628 liquid penetrant inspection, 1627-1628 magnetic particle inspection, 1628 radiographic inspection, 1630 ultrasonic inspection, 1629-1630 visual inspection, 1627 oil monitoring, 1620 atomic absorption spectroscopy, 1622 atomic emission spectroscopy, 1622 chemical and physical testing, 1620-1621
8403cIndex Page 1676 Monday, November 6, 2000 10:00 AM
1676 ferrography, 1623 flashpoint, 1621 gravimetric analysis, 1621 image analysis, 1624-1625 infrared spectroscopy, 1622-1623 magnetic chip detectors, 1623-1624 particle counting, 1624 pour point, 1621 raman spectroscopy, 1623 specific gravity, 1621 spectrography, 1621-1623 total acid number, 1620 total base number, 1620 viscosity, 1620 water content, 1621 x-ray fluorescence (XRF) spectroscopy, 1622 performance monitoring, 1632 current signature analysis, 1632-1633 data interpretation, 1633-1634 flow rate, 1632 process parameters, 1632-1633 quality of design, 1612 reliability engineering, 1613-1615 statistical control, 1612-1613 thermal monitoring, 1625 contact methods, 1625-1626 infrared imaging, 1626 noncontact methods, 1626 pyrometer, 1626 resistance temperature detector, 1625-1626 thermistor, 1626 thermocouple, 1625 tribo-element applications, 1634-1635 fluid film bearings, 1635-1636 gears, 1637-1638 rolling bearings, 1636-1637 seals, 1638-1639 vibration monitoring, 1617 shock pulse method, 1619-1620 signature analysis, 1617-1619 wear metal origins, 1621 Machining, see also Manufacturing tribology diamond films in industrial, 884-887 using atomic force microscopy, 674-675, 702-703 MACs, see Multiply alkylated cyclopentanes (MACs) Magnetic heads, 1420-1423 Magnetic media, 1415 Magnetic particle inspection, 1628 Magnetic storage devices, 1413-1415, 1416 adhesion, liquid-mediated, 1432-1433 components, 1415-1423 contact area measurement, 1430-1432 developments in, 1501-1503 diamond-like carbon (DLC) films, 896 experimental observations, 1440-1445
Modern Tribology Handbook fly stiction in rigid disk drives, 1445-1446 heads magnetic, 1420-1423 rigid-disk, 1420-1423 tape, 1420 head/tape interface wear, 1448-1449 head materials effects, 1458-1459 magnetic tape effects, 1458 particulate and metal-evaporated tapes, 1449-1453 environmental effects, 1453-1458 pole-tip recession effects, 1459-1461 tape path materials effects, 1461 head/thin-film rigid disk interface thin film lubricant, 1475-1482 wear, 1461-1475 lubrication, 1482-1484 particulate magnetic tapes, 1485 thin film rigid disks, film measurement, 1484-1485 thin-film rigid disks, 1486-1491 viscosity at high shear rates, 1484 media flexible, 1416-1418 magnetic, 1415 microtribology, 1491 friction, 1493 indentation, 1496-1499 lubrication, 1499-1501 scratching/wear, 1493-1496 monolayer films, 909-912, see also Thin film rigid disks particulate magnetic tapes lubrication, 1485 wear mechanisms, 1449-1458 stiction, 1432-1433 stiction modeling, 1433-1440 temperatures, interface, 1447-1448 thin-film rigid disks, 1415, 1418-1420 film thickness measurement, 1484-1485 fly stiction, 1445-1446 lubrication mechanisms, 1486-1491 Magnetron sputtering, deposition of DLC films, 889-890 Maintenance, equipment, 1615, see also Machinery diagnosis/prognosis condition-based maintenance, 1616 failure-based maintenance, 1615 reliability-centered maintenance, 1616 time-based maintenance, 1615-1616 Maintenance records, 1612 Manufacturing tribology, 1385 bulk forming operations, 1399 drawing, 1404, 1406 extrusion, 1404-1406
8403cIndex Page 1677 Monday, November 6, 2000 10:00 AM
Index forging, 1402-1404 rolling, 1399-1402 sheet metal forming operations, 1407-1409 finishing operations, 1398 chemical mechanical polishing, 1399 coated/bonded abrasives, 1398-1399 electrochemical machining, 1399 lapping, 1399 lubricants, 1386-1387 cold working lubricants, 1387-1389 hot working lubricants, 1389-1390 metal cutting, 1394-1395 cutting fluids, 1397-1398 cutting tool materials, 1395 cutting tool wear, 1395-1397 processes, 1386 surfaces, 1390 other surface effects, 1393-1394 surface flattening, 1390-1392 surface roughening, 1392-1393 unique aspects, 1385-1386 Marine engine/equipment tribology, 1371 diesel engine lubrication, 1374-1375 high-speed diesel engines, 1380 medium-speed diesel engines, 1378-1380 slow-speed diesel engines/crankcase, 1377-1378 slow-speed diesel engines/cylinders, 1375-1377 emissions/environmental concerns, 1372-1374 fuel/oil chemistry, 1371-1372 fuel/oil rheology, 1371-1372 gas turbine engines, 1380-1381 oil maintenance equipment, 1382-1383 pumps, 1382 rigging equipment, 1382 steam turbine engines, 1380-1381 stern tube lubrication, 1381-1382 Material(s), tribologic coatings, 768-770, see also specific tribosystem brittle, abrasive wear of, 288-290 ductile, abrasive wear of, 281-288 metals and ceramics, 771-784, see also Ceramics; Coatings; Composite coatings; Metal(s) database of, 523, 532-561 abrasive wear data, 529 data types, 529 definitions of data fields, 529-531 field definitions, 529-531 material data, 529 material types, 527-529 sources of data, 523-527 tribologic data, 529 loss methods, corrosion monitoring, 1631 response, in coated surfaces, 832-833, 839-840
1677 energy accommodation in surface, 840-843 fracture toughness in material response, 843-844 transfer mechanism, 850 coatings, 850 load, tire, 1204-1205 material transfer from countersurface, 497 Material normalization, 348 in wear modeling, 349-352 Material ratio, 65 Matsukawa-Fukuyama model, 726 Maugis, adhesion theory of, 621 Measured height distribution analysis, 110 Mechanical seals, 1131-1132 analysis, 1141-1146 analysis, computational procedure, 1144-1146 configurations, 1132-1134 contact mechanics, 1143 deformation, 1143-1144 diamond films, 887 face materials, 1134 floating seal, face, 1134-1136 fluid mechanics, 1142-1143 gas seals, 1140-1141 hydrodynamic seals, 1138-1140 hydrostatic seals, 1136-1137 hydrostatic seals, contacting, 1138 hydrostatic seals, non-contacting, 1137-1138 sealing region, 1134 thermal analysis, 1144 two-phase effects, 1141 Mechanical stress, 171-175, see also Stress(es) Mechanical stylus method, of roughness measurement, 81-85 Media flexible, 1416-1418, see also Flexible media magnetic, 1415, see also Magnetic storage devices Medical devices, 1596, see also Biomedical tribology MEMS, see Microelectromechanical systems Meniscus forces, 183, 216-218 Metal(s), 771, see also Metal manufacturing operations; specific metal adhesion of, 197-198 cold welding, 197 at high temperatures, 197-198 microcontacts, 197 aluminum alloys, 1028-1029 boundary lubrication, 467 cast irons, 774-776 ceramics and alloys of, 781-782 compared, 782-783 copper alloys, 774, 1028-1029 -insulator contact, surface effects in, 39-42 manufacturing processes, see Metal manufacturing operations
8403cIndex Page 1678 Monday, November 6, 2000 10:00 AM
1678 pure metals, 771-772 soft bearing alloys, 772-774 soft metals, 772-774, 815-817 steels, 776-778 wear, 319 oxidative, 295-296 wear modeling, using wear mapping, 341-343 Metal manufacturing operations, 1385, 1386 bulk forming operations, 1399 cutting, 1394-1395 cutting fluids, 1397-1398 cutting tool materials, 1395 cutting tool wear, 1395-1397 drawing, 1404, 1406 extrusion, 1404-1406 finishing, 1398 chemical mechanical polishing, 1399 coated/bonded abrasives, 1398-1399 electrochemical machining, 1399 lapping, 1399 forging, 1402 cold metal, 1403-1404 hot metal, 1402-1403 lubricants, 1386-1387 cold working lubricants, 1387-1389 hot working lubricants, 1389-1390 rolling, 1399-1401 cold metal, 1401-1402 hot metal, 1401 sheet metal forming, 1407 friction modeling, 1407-1408 galling, 1408-1409 lubricants, 1408 orange peel, 1408-1409 smudge, 1408-1409 surfaces, 1390 flattening, 1390-1392 other surface effects, 1393-1394 roughening, 1392-1393 unique aspects, 1385-1386 Metallographic techniques, temperature measurement by, 269 Metastability, 723-727 Michell and Kingsbury bearings, 994-996 Microelectromechanical systems (MEMS), 1515-1517, 1544 boundary lubrication studies, 1541-1544 component level studies, 1544 diamond films, 887-888 macroscale testing, 1526 silicon samples: virgin, coated, treated, 1537-1541 micro/nanoscale testing, 1525-1526 materials tested, 1526-1527 polysilicon films, doped and undoped, 1530-1537
Modern Tribology Handbook polysilicon films vs. single crystal silicon, 1530-1537 SiC films, 1530-1537 silicon samples: virgin, coated, treated, 1527-1530 monolayer films, 909-912 tribology of, 1517-1525 Microscale tribology, see Microtribology Microslip, 134-135, see also specific tribosystem elastic belt, 1579-1582 Microtribology, 564-565, 587, see also specific tribosystem adhesion forces, 572-574 of coated surfaces, 832-833 computer simulations, 717-758, see also Computer simulations hysteresis, 574-576 interfacial friction, 582-587 interfacial friction theories, 587-594 molecular tribology, 582-587 nanorheology, 576-581 nanotribology, 564-565 Amontons' law, 646-648 atomic mechanism of friction, 652-658 contact mechanics, 644-646 friction and surface structure, 648-652 scanning force microscopy, 642-644, 667-669, see also Atomic force microscopy; Friction force microscopy velocity dependence of friction, 658-659 scanning probe microscopy, 667-714, see also Atomic force microscopy; Friction force microscopy solvation forces, 568 stick-slip friction, 600-609 theories of interfacial friction, 587-594 thin films, rheology, 576-581 thin liquid films, friction, 594-600 Mineral oil based lubricants, 366, 460 additive improvements, 367 catalytic dewaxing, 368 early processing methods, 366 evolution of future lubricants, 372 group I base oils, 367 group II base oils, 368-369 group III base oils, 369 group III vs. PAO performance, 370-372 hydrocracking, 368 hydroisomerization, 368 hydrotreatment, 367 selection, 361-362 solvent refining methods, 366-367 in space tribology, 1162 unconventional base oils, 369 Mining and mineral processing tribology, 1331-1333, see also Earthmoving tribology
8403cIndex Page 1679 Monday, November 6, 2000 10:00 AM
1679
Index abrasive wear classification, 1347-1349 contact conditions, 1353-1355 mechanisms, 1349-1352 parameters, 1352-1353 wear material properties, 1355-1358 equipment, 1344-1345 classifiers, 1346-1347 crushers, 1345-1346 flotation machines, 1347 grinding equipment, 1346 magnetic separators, 1347 sand pumps, 1346 financial costs, 1366-1368 tribologic losses, 1359 ore processing/related processes, 1364-1366 shaft mining/drilling, 1362-1364 surface mining, 1359-1362 wear processes/mechanisms, 1333-1335, 1337 in conveying/handling/storage, 1338 in crushing, 1338 in digging/loading, 1335, 1337 in grinding, 1338-1339 in haulage, 1337 in mineral separation and concentration, 1339 in screening, 1338 in size classification, 1339 Model test, 497, see also Testing Molecular dynamics, 718-719 Molecular tribology, see Microtribology Moments, of amplitude probability functions, 59-61 Monochalcogenides, 798-799 Monolayers, see also Boundary lubricating films; Films; specific tribosystem adsorbed, 728-734 self-assembling, 924-927 applications of, 909-912 organization of, 917-921 tribologic properties of, 921-924 Multicomponent coatings, 944 Multilayered coatings, 852-855, 943-944 Multiply alkylated cyclopentanes (MACs), 1163-1164, 1165 space applications boundary lubrication, 1170-1172 elastohydrodynamic performance, 1166-1170 viscosity-temperature, 1166 volatility, 1166 wear characteristics, 1172-1173
N Nanocomposite coatings, 855-856 Nanocrystalline coatings, 944
Nanocrystalline diamond (NCD) films, 874-876 Nanorheology, 576-581 Nanotribology, 564-565, see also Microtribology; Tribochemistry Amontons' law, 646-648 of coated surfaces, 834-835 contact mechanics, 644-646 of diamond films, 883 of diamond-like carbon (DLC) films, 893-896 of friction, 652-658 and surface structure in, 648-652 velocity dependence, 658-659 scanning force microscopy, 642-644, 667-669, see also Atomic force microscopy; Friction force microscopy Navier-Stokes equation, 384 Nip roller, 1561 Nominal line contact, 129-130, 439 film thickness calculations, 443-446 Nominal point contact, 127-129, 439 film thickness calculations, 446-450 Nominal surface temperature rise, 249-251 Nominally flat rough surfaces, 150-152 Noncontact methods, thermal monitoring, 1626 Nondestructive evaluation, of machinery, 1627 acoustic emission detection, 1628-1629 eddy current inspection, 1628 liquid penetrant inspection, 1627-1628 magnetic particle inspection, 1628 radiographic inspection, 1630 ultrasonic inspection, 1629-1630 visual inspection, 1627 Non-Hertzian contact, 137 angular wedge, indentation by, 138-139 axisymmetric punch, flat rigid, 138 cone, indentation by, 139-140 planar punch, flat rigid, 137-138
O Oil, see Mineral oil based lubricants; specific tribosystem; Synthetic lubricants Oil monitoring, 1620 atomic absorption spectroscopy, 1622 atomic emission spectroscopy, 1622 chemical and physical testing, 1620-1621 ferrography, 1623 flashpoint, 1621 gravimetric analysis, 1621 image analysis, 1624-1625 infrared spectroscopy, 1622-1623 magnetic chip detectors, 1623-1624 particle counting, 1624 pour point, 1621
8403cIndex Page 1680 Monday, November 6, 2000 10:00 AM
1680 raman spectroscopy, 1623 specific gravity, 1621 spectrography, 1621-1623 total acid number, 1620 total base number, 1620 viscosity, 1620 water content, 1621 x-ray fluorescence (XRF) spectroscopy, 1622 Optical interference measurement, roughness, 93-95 digital optical profiler, 97-100 phase shifting interferometry, 95-96 vertical scanning coherence peak sensing, 96-97 Optical interferometry, wear testing, 508-509 Optical measurement of contact, 145-147 of roughness, 85-86 diffuse reflection (scattering) methods, 89-93 light sectioning method, 87 optical interference methods, 93-100 speckle pattern method, 93 specular reflection methods, 87-89 taper sectioning method, 86-87 of temperature (optical photography), 264-265 Organic chemistry, 912 electronegativity/polarity, 912-913 organic compounds classification and structure, 913-916 polar and nonpolar groups, 916-917 Organic compounds classification and structure, 913-916 polar and nonpolar groups, 916-917 Organometallic chemistry, 467 boundary lubricating films, 472-474 Orthopedic devices, 1599 Oscillatory forces, 568-570 Overhead components, diesel, 1246-1247 cam/cam followers, 1247-1248 crossheads, 1248 push rods, 1248 rocker levers, 1248 Oxidation reactions, boundary film formation, 464 metal catalyzed oxidation reactions, 464-465 oxidation and thermal reactions, 464 polymerization reactions, 465-467 Oxides, fluorides, sulfates, 808-810
P Pad resonance, 434 PAO (polyalphaolefin) lubricants, 369-370, see also Synthetic lubricants in space tribology, 1163-1164 vs. group III performance, 370-372 Particle counting, 309-310
Modern Tribology Handbook Particle induced osteolysis, 1605-1607 Particulate magnetic tapes lubrication mechanisms, 1485 wear mechanisms, 1449-1458 Passivated surfaces, chemically, 735-737 Patir-Cheng flow factors, 388 Peclet number, 244-246 Pennzane, 1163, see also Multiply alkylated cyclopentanes (MACs) Perfluoropolyalkylether (PFPAE) lubricants, 380 Perfluoropolyether (PFPE) lubricants in magnetic storage devices, 1483-1484 space tribologic applications, 1164, 1165, 1173 compared to MACs, 1165-1173 Performance monitoring, 1632 current signature analysis, 1632-1633 data interpretation, 1633-1634 flow rate, 1632 process parameters, 1632-1633 Phase shifting interferometry, 95-96 Phase transitions, thin film, 744-748 Phenols, 914-915 Phosphate ester lubricants, 376 Pin-on-disk machine, 221-222, 502-503 Pin-on-drum machine, 502-503 p bonding, 215 Pitting, see Cavitation erosion damage; Corrosive wear; specific tribosystem Pivoted pad bearings, 994, see also Thrust bearings hydrodynamic lubrication, 419 lubricating films, 433-438 Michell and Kingsbury bearings, 994-996 Planar punch, see Flat punch Planck's law, 263-264 Plane slider bearings, 415-418, see also Thrust bearings Plastic deformation, see also specific tribosystem computer simulation of, 755 Plastic friction, 210-211 Plastic ratchetting, 157 Plasticity index, 152 Point contact in nanotribology, 648 nominal, 127-129 Polarity, 912-913, 916-917 Polyalphaolefin (PAO) lubricants, 369-370, see also Synthetic lubricants in space tribology, 1163-1164 vs. group III performance, 370-372 Polycrystalline diamonds (PCD), 872-873 Polyether lubricants, 461 Polymer lubricants, 817-818 Polyphenylether (PPE) lubricants, 379-380 Power cylinder components, diesel, 1233 base stocks and additives effects, 1241 engine deposits effects, 1241
8403cIndex Page 1681 Monday, November 6, 2000 10:00 AM
Index friction, 1237 fuel sulfur effects, 1240 liner wear mechanisms, 1244-1246 liners/bores, 1233-1235 oil cleanliness effects, 1243-1244 oil film thickness effects, 1241-1243 piston pin/connecting rod, 1237 pistons, 1236-1237 ring wear mechanisms, 1244-1246 ring/liner interface, 1238-1240 rings, 1235-1236 tribologic systems, 1237-1238 Power spectral density function, spatial, 68-72 Principal curvatures, 439 Probability distribution functions, roughness, 56-61 Process parameters, 1632-1633 Prostheses, see Biomedical tribology Pull-off force measurements, by AFM, 617-638 Punch, see Flat punch(es) Pure metals, 771-772 Pure model test, 498 Pyrometer, 1626
Q Quartz crystal microbalance experiments, 728-734
R Radiation detection techniques, temperature measurement, 263-264 Radiographic inspection, 1630 Rail transport tribology, 1271, 1325-1326 axle bearings, 1321, 1322-1323 axle load increases, 1274-1275 axle loads, 1274 collection interfaces, 1314 earth brushes, 1314-1316 pantographs, 1319-1321 registration arms, 1321 shoe and gear, 1316-1319 dampers, for suspension systems, 1321, 1323-1324 diesel engines, 1308 combustion air supply, 1312 design of, tribologic issues, 1309-1311 drives, electric, 1313 drives, mechanical and hydraulic, 1312-1313 four-stroke engine, 1309 mechanical power generation, 1308 transmissions, 1312 two-stroke engine, 1308-1309 gas turbine engines, 1313-1314 historical context, 1271-1274
1681 rolling contact fatigue developments, 1324 friction modifiers, 1324 individually driven/controlled wheels, 1324-1325 integrated study of, 1325 wheelset steering, 1324-1325 traction motor bearings, 1321 wheel/rail interface, 1274, 1275 adhesion/traction, 1277-1288 braking, 1287-1288 contact patch forces, 1276-1277 grinding, 1303-1307 locomotive adhesion control, 1283-1287 materials, 1275-1276 materials rupture, 1293-1294 plasticity, 1288 rail corrugation, 1307-1308 ratcheting, 1288 repeated contact, 1288 rolling contact fatigue, 1299-1303 shakedown, 1288-1293 wear, 1294-1297, 1302-1303 Rayleigh step bearing, 986-987 pocket step bearing, 987-989 semicircular step bearing, 987 triangular step bearing, 987 Reduced Reynolds number, 385 Reflection electron microscopy, 109 Regimes, tribologic, 457, 577, see also specific tribosystem Reliability engineering, 1613-1615 Residual stress, 156-157 Resistance, electrical and thermal, 144-145 Resistance temperature detector, 1625-1626 Resistive microtransducers, in stress analysis, 150 Reworked wear debris, 312 Reynolds equation, 386-387 Reynolds number, reduced, 385 Rice J-integral, 174 Rigid disks, 1418-1420, see also Thin film rigid disks Rigid-disk heads, 1420-1423 Ring bearings, 1002-1004 Roller bearings, 1042, see also Rolling bearings cylindrical roller bearings, 1043-1044 roller thrust bearings, 1045 spherical roller bearings, 1045 tapered roller bearings, 1044-1045 Rolling free, 135-136 tractive, 136-137 Rolling bearings, 1041-1042 ball bearings, 1042 angular contact ball bearings, 1043 deep groove ball bearings, 1042-1043
8403cIndex Page 1682 Monday, November 6, 2000 10:00 AM
1682 double row ball bearings, 1043 thrust ball bearings, 1043 clutch bearings, 1045 contact mechanics, 1048 ball bearings, 1051-1053 edge stress, 1055-1056 Hertzian contact, 1048-1051 indentation, 1056 line contact, 1050-1051 non-Hertzian contact, 1055 point contact, 1048-1050 roller bearings, 1053-1054 roller crowning, 1055-1056 roller-end and flange contact, 1054-1055 roughness, 1057 surface scratching, 1056 elastohydrodynamic lubrication, 1063-1064 endurance testing, 1082-1083 failure analysis, 1083 contact fatigue, 1083-1085 corrosion, 1089 discoloration, 1089 electric arc damage, 1089 modes, and possible causes, 1090 overheating, 1089 surface depression, 1085-1086 surface fracture, 1085-1086 wear, 1086-1088 internal load distribution, 1057 general load conditions, 1057, 1060-1062 pure eccentric thrust load, 1062-1063 kinematics, 1067-1070 inner raceway control, 1070-1071 minimum differential spin, 1071 outer raceway control, 1070 life prediction, 1072-1073 adjustment factors, 1073-1074 load ratings, basic, 1071-1072 lubricant starvation, 1064-1065 lubrication methods, 1065-1066 circulating oil systems, 1066 greases, 1066-1067 oil bath, 1066 oil jet, 1066 oil mist, 1066 solid lubricants, 1067 materials, 1046-1048 roller bearings, 1042 cylindrical roller bearings, 1043-1044 roller thrust bearings, 1045 spherical roller bearings, 1045 tapered roller bearings, 1044-1045 running torque ball bearings, 1076-1077 tapered roller bearings, 1077-1079
Modern Tribology Handbook smart bearings, 1045-1046 spin motion effects on lubrication, 1064 starting torque angular contact ball bearings, 1075 tapered roller bearings, 1076 temperature analysis, 1079-1080 heat generation, 1080-1081 heat transfer, 1081-1082 torque calculation, 1074-1075 tribo-element monitoring, 1636-1637 Rolling contact fatigue, rail transport, 1299-1301 developments, 1324 friction modifiers, 1324 individually driven/controlled wheels, 1324-1325 integrated study of, 1325 service experience, 1302 small scale tests, 1301-1302 wear and, 1302-1303 wheelset steering, 1324-1325 Rolling friction, 209-210 Rolling velocity, 131-132 Rotary lip seals, 1146-1147 analysis, 1154 bidirectionality, 1151 configurations, 1147 converse mounting, 1151 lip macrogeometry, 1149-1150 lip materials, 1147 lip microgeometry, 1148-1149 modeling, 1152-1154 reverse pumping, 1148 sealing region, 1147-1148 shaft surface microgeometry, 1150-1151 Rotor stability, flexible, 429-433 Rough elastic solids, adhesion of, 186-188 Rough surfaces, lubrication of, 750-752 Roughness, 49-50, 114-116, 459 analysis of, 50-52 definition, 50 fractal characterization, 76-77 measurement, 81, 669-673 comparison of methods, 110-114 electrical methods, 107-108 electron microscopy methods, 109-110 fluid methods, 107 measured height distribution analysis, 110 mechanical stylus, 81-85 optical, 85-100, see also Optical measurement, of roughness scan size in, 80-81 scanning probe microscopic, 100-107 short and long wavelength filtering, 77-80 parameters amplitude, 52-55 spacing (spatial), 55
8403cIndex Page 1683 Monday, November 6, 2000 10:00 AM
Index pictorial display, 51 statistical analysis, 56-75 amplitude probability density and functions, 56-59 amplitude probability function moments, 59-61 asperities and valleys, probability distribution, 72-75 bearing area curves, 65-66 composite roughness, 75-76 spatial functions, 66-72 surface height distribution functions, 61-65 wear surface, 274 Run-in stage, wear, 494-495
S SAMs, see Self-assembling monolayers Scan size, in roughness measurement, 80-81 Scanning electron microscopy (SEM), 109 Scanning force microscopy (SFM), see Friction force microscopy Scanning probe microscopy (SPM), 100 atomic force microscopy, 102-107 measurement of boundary lubricating films, 476-477 microtribologic use, 667-669, see also Atomic force microscopy; Friction force microscopy scanning tunneling microscopy, 100-102 Scanning tunneling microscopy (STM), 100-102 Schallamach waves, 212-213 Scratching, microscale, 674-675, 694-695, see also specific tribosystem Seals, see Dynamic seals Secondary ion mass spectroscopy (SIMS), 29 Self-acting finite bearings, 977 Self-assembling monolayers (SAMs), 924-927 applications of, 909-912 organization of, 917-921 tribologic properties of, 921-924 Self-lubricating composites, see also Composite coatings new coatings and structures, 814-815 traditional materials, 813-814 SEM (scanning electron microscopy), 109 Severity index(es), in wear modeling, 348 historical, 348-349 SFA, see Surface force apparatus SFM (scanning force microscopy), see Friction force microscopy Shakedown elastic, 156-157 wheel/rail interface, 1288-1290 roughness and shakedown limit, 1290-1293 surface engineering, 1288-1290
1683 Shear thinning, 582 Sheet transport, flexible media in channel, 1576-1579 roller/roller or roller/platen nips, 1582-1587 Shock pulse method, vibration monitoring, 1619-1620 Signature analysis, vibration monitoring, 1617-1619 Silahydrocarbon lubricants, 378 in space tribology, 1164-1165 Silicate ester lubricants, 377 Silicon-containing fluids, 376-377 Silicone lubricants, 377-378 Silicone polymer lubricants, 461-462 SIMS (secondary ion mass spectroscopy), 29 Simulation modeling computer, 717-718, see also Computer simulations tribosimulation, 514-516, see also Tribotest(s), classification of tribosystems, 512-514 wear, 320, see also Testing; Tribosimulation(s); Tribotest(s) Skeletal system, human, 1596 Skewness, 59-61 Slider bearings, 969-971 advantages and disadvantages of types, 977 journal bearings, 981-983 thrust bearings, 978-980 alloys, fluid film performance characteristics, 1030 failure modes, 1019 cavitation erosion damage, 1019-1026, 1025-1026, see also Cavitation erosion damage wear from contaminants, 1026-1027 journal bearings advantages and disadvantages, 981-983 diesel engine bearings, 1009-1011 dynamic loading, 1011-1013 foil bearings, 1005-1009 helical grooved bearings, 1004-1005 lubricant supply arrangements, 1000-1004 plain, 996-1000 reciprocating load bearings, 1009-1013 shaft whirl, 1013 vibrational loading, 1013 whirl inhibition, designs for, 1013-1019 materials composition and testing results, 1030-1035 gas film materials, 1029 liquid film materials, 1027-1029 self-acting finite bearings, 977 thrust bearings, advantages and disadvantages, 978-980 thrust bearings, fixed geometry, 977, 984 Rayleigh step bearing, 986-989 recurrent-grooved bearings, 989-994 tapered land slider, 984-986
8403cIndex Page 1684 Monday, November 6, 2000 10:00 AM
1684 thrust bearings, pivoted pad, 994 Michell and Kingsbury bearings, 994-996 types of, 971-974 Sliding contact, 131-132, 594-595, see also Adhesion; Contact mechanics; Friction; specific tribosystem; Wear; Wear mechanisms data generation in, 525-526 directional dependence of, 650-652 gross, 132-134 incipient (microslip), 134-135 interfacial, 576, see also Interfacial friction simulation of, see Computer simulations; Tribosimulation(s) smooth, 595-597 stick-slip, 595-597, see also Stick-slip friction molecular shape and liquid structure in, 597-600 velocity of, 131-132 Slip line field technique, 154 Smart bearings, 1045-1046 Snoek effect, 188 SOAP (spectrographic oil analysis program), 301, 306-308 Soft bearing alloys, 772-774 Soft metals, 772-774, 815-817 Soft tissue(s), 1596 repair/replacement, 1598-1599 Solid lubricants, 787-789 characteristics, 790-791 classification, 792 compared to liquid lubricants, 788 future development, 818-819 high-temperature solid lubricants, 808 composites, 810-811 crystal-chemical approach, 811-813 oxides, fluorides, sulfates, 808-810 lamellar solid lubricants, 792-794 boric acid, 803-806 graphite, 799-802 hexagonal boron nitride, 802-803 lubrication mechanisms, 806-808 monochalcogenides, 798-799 transition metal dichalcogenides, 794-798 polymers, 817-818 recent advances, 791-792 self-lubricating composites new coatings and structures, 814-815 traditional materials, 813-814 soft metals, 815-817 Solid surfaces, see Surface(s) Solvation forces, 568-570 surface curvature and geometry, 572 surface structure and, 570-571 Solvent refining methods, 366-367 Sommerfeld number, 400-401
Modern Tribology Handbook Space tribology, 1159 greases, 1173 liquid lubricants, 1162, 1165 esters, 1163 mineral oils, 1162 perfluoropolyethers, 1164, 1165, 1173 properties required, 1165-1173 silahydrocarbons, 1164-1165 synthetic hydrocarbons, 1163 lubrication regimes, 1159-1161 mechanical components, 1161-1162 PFPE lubricants compared to MACs, 1165 boundary lubrication, 1170-1172 creep, 1166 elastohydrodynamic performance, 1166-1170 viscosity-temperature, 1166 volatility, 1166 wear characteristics, 1172-1173 solid lubricants, 1162, 1173-1175 ion-plated lead, 1175 molybdenum disulfide, 1175 testing, accelerated life, 1175-1177 eccentric bearing test apparatus, 1177 spiral orbit rolling contact tribometer (SOT), 1177-1179 vacuum four-ball tribometer, 1179-1181 vacuum pin-on-disk tribometer, 1181 Spalling, see Cavitation erosion damage; Corrosive wear; specific tribosystem Spatial functions, 66-72 Spatial parameter, for roughness, 55 Speckle pattern method, roughness measurement, 93 Spectrographic oil analysis program (SOAP), 301, 306-308 Specular reflection methods, roughness measurement, 87-89 Spheres, tribology of, 122-123 adhesion, 175 DMT (Derjaguin, Muller, Toporov) solution, 179-180 Hertz solution, 175-176, see also Hertzian contact JKR (Johnson, Kendall, Roberts) solution, 176-179 JKR-DMT transition in Dugdale model, 180-182 sliding, 132-137 Spinning motion, 131-132 Spiral-grooved journal bearings, 1004, see also Slider bearings Spiral-grooved thrust bearing, 989-992, see also Slider bearings SPM, see Scanning probe microscopy Spring coefficients, 424-429 Spur gears, 1096, see also Gears full film lubrication, 1102-1105 wear modeling, 1121-1122
8403cIndex Page 1685 Monday, November 6, 2000 10:00 AM
Index Static friction, 1425-1428 in one dimension, 723-726 Statistical control, 1612-1613 Steady-state conditions, wear, 495 Steam turbine engines, marine, 1380-1381 Steels, 776-778 Stefan-Boltzmann law, 263 Stereomicroscopy, 109-110 Stick-slip friction, 207, 595-597, 600-601, see also Vibration adhesion forces, 191-192 atomic mechanism, 652-658 computer simulation, 752-755 model(s) distance dependent, 602-604 phase transition, 606-607 rough surfaces, 601-602 velocity dependent, 604-606, 658-659 molecular shape and liquid structure, 597-600 and static friction, 231-232 surface structure and chemical composition, 648-652 velocity of, critical, 607-608 Stiction, 598, 1423-1425, 1432-1433 fly stiction in rigid disk drives, 1445-1446 modeling, 1433-1440 STM (scanning tunneling microscopy), 100-102 Strain capacity, 154 Stress(es), see also specific tribosystem analysis, photoelasticity and caustics, 148-150 Irwin formula, 174 mechanics, 171-175 models, 174-175 residual, 156-157 Rice J-integral, 175 shear, 582, 661 stress intensity factors, 171-174 surface and subsurface, 127-131 tensile, adhesion and, 621-624 theoretical, 164-166 Stribeck curve, 232, 577-578 Stribeck formula, 443 Structure function, spatial, 68 Submonolayer lubrication, 748-750 Subsystem test, 497, 515, see also Testing Supercells, 12 Superlattice coatings, 944 Surface(s), solid, see also Cylinders; Flat punch(es); specific tribosystem; Spheres adhesion, 163-199, see also Adhesion adhesion, bonding and welding, 215-216 analysis, 23-31, see also Analysis, of surfaces coated, see Coatings; Composite coatings films on, 216-218, see also Coatings; Composite coatings; Films; Monolayers fractal modeling, 76-77, 1428-1430
1685 friction between, 33-36, 205-232, see also Boundary lubricating films; Friction; Interfacial friction geometry of, 6-10 Hertzian contact, 122-137, see also Hertzian contact layered solids, 157-159 loading beyond elastic limit, 153-156 non-Hertzian, 137-140, see also Non-Hertzian contact numerical methods for mechanics, 140-144, see also Contact mechanics; Stress(es) passivated, chemically, 735-737 repeated contact, 156-157, see also Microtribology; Tribochemistry; Wear; Wear mechanisms rough, 150-153, see also Roughness rough elastic, adhesion, 186-188, see also Roughness structure, see Analysis; Roughness; Surface structure temperature, 235-238, see also Temperature, surface texture, see Roughness tribology of, 32-33, 121, see also Adhesion; Contact mechanisms; Friction; Interfacial friction; Simulation modeling; specific tribosystem; Testing; Wear wear, 273-299, see also Wear; Wear mechanisms Surface coatings, see Coatings Surface engineering, 768-770 Surface films, see Films Surface force apparatus (SFA), 476, 668-669 in thin film studies, 745-748 Surface potential measurements, 675 Surface structure, 457-458, see also specific tribosystem chemical composition, and friction, 648-652 determining, 19 field ion microscopy (FIM) in, 22-23 high-resolution electron microscopy (HREM) in, 20-22 low-energy electron diffraction (LEED) in, 19-20 energy emission under stress, 458-459 energy of, 458 friction and, see also Adhesion; Friction in nanotribology, 648-652 reactivity, 458, see also Boundary lubricating films; Tribochemistry roughness, 459, see also Roughness solvation forces, 570-571 Surface theory, 10-12 Surface traction, 131-132 Surface winding, 1561 Swift-Stieber boundary conditions, 402
8403cIndex Page 1686 Monday, November 6, 2000 10:00 AM
1686 Synovial joints, 1599-1600 articular cartilage, 1600-1601 friction, 1601-1602 functional requirements, 1600 lubrication, 1602-1603 Synthetic base oils, 369-370, 461-462 Synthetic lubricants, 369-370, 373, see also specific tribosystem chlorotrifluoroethylene polymers, 378-379 esters, 375-376 group IV base oils, 369-370 hydrocarbon, 374-375, 461 PAO (polyalphaolefin) fluids, 369-370 PAO vs. group III performance, 370-372 perfluorinated fluids, 380 phosphate esters, 376 polyphenylethers, 379-380 reasons for use, 373-374 silahydrocarbons, 378 silicate esters, 377 silicon-containing fluids, 376-377 silicones, 377-378 synthetic hydrocarbons, 374-375
T Tackiness, adhesion forces, 189-191 Tape heads, 1420 Taper sectioning method, roughness measurement, 86-87 Tapered-land slider, 984-986 TDS (thermal desorption spectroscopy), 30-31 Temperature, interface, in magnetic storage devices, 1447-1448 Temperature, surface analysis, 238-239 flash temperatures and boundary lubrication modeling, 480-485 calculations of rise, 239 flash temperature transients, 246-248 moving heat source on stationary body, 243-246 nominal surface temperature rise, 249-251 partition of frictional heat, 251-255 stationary heat source on moving body, 243-246 stationary heat source on stationary body, 239-243 summary of, 246 measurement, 259 dynamic thermocouples, 261-262 embedded subsurface thermocouples, 259-261 infrared detectors, 265-269 infrared photography, 264-265
Modern Tribology Handbook metallographic techniques, 269 optical photography, 264-265 radiation detection techniques, 263-264 thin film temperature sensors, 262-263 numerical methods of determination, 255-256 finite element methods, 256-258 hybrid methods, 258-259 integral transform method, 256 Tensile stress, adhesion and, 621-624 Testing, see also Friction; Tribosimulation(s); Tribotest(s) abrasive wear, 502-504 composite coatings, 958 design of testing machines, 227-229 erosive wear, 504-505 evaluation of wear, 500-501 friction effect reduction, 229-230 importance of, 493-494 mild wear, 508 rolling contact wear, 505-507 sliding contact wear, 505-507 space applications, 1175-1181 topological methods, 508-510 unsteady data and testing machines, 221-227 Theoretical stress, 164-166 Thermal boundary layer, 245 Thermal desorption spectroscopy (TDS), surface analysis, 30-31 Thermal monitoring, 1625 contact methods, 1625-1626 infrared imaging, 1626 noncontact methods, 1626 pyrometer, 1626 resistance temperature detector, 1625-1626 thermistor, 1626 thermocouple, 1625 Thermal resistance, contact measurement, 144-145 Thermistor, 1626 Thermocouple(s), 1625 dynamic, 261-262 embedded subsurface, 259-261 Thermoelasticity, 188 Thermohydrodynamic (THD) theory, 390 Thermomechanical wear theory, 237 Thick films, viscosity, 577-580 Thin film(s), see also Adhesion; Coatings; Composite coatings; Monolayers; specific tribosystem characteristic nucleation time, 607 friction, 594-600, see also Friction; Interfacial friction liquid, 183-186, 585, see also Elastohydrodynamic lubrication; Hydrodynamic lubrication; Liquid lubricants phase transitions, 744-748 rheology, 576-582
8403cIndex Page 1687 Monday, November 6, 2000 10:00 AM
Index solid, see Coatings; Solid lubricants surface force apparatus studies, 745-748 temperature sensors, 262-263 viscosity, 582-587, 744-748 Thin film rigid disks, 1415, 1418-1420 film thickness measurement, 1484-1485 fly stiction, 1445-1446 head interface, wear mechanisms, 1461-1464 DLC overcoat materials effects, 1472 environmental effects, 1472-1475 overcoat materials effects, 1470-1472 particulate contamination effects, 1464-1467 pole-tip recession, 1469-1470 slider materials effects, 1467-1469 head/thin film lubricant interface, 1475 chemical bonding effects, 1475-1476 environmental effects, 1476-1478 polar lubricant effects, 1478-1481 recommended lubrication approaches, 1481-1482 lubricant bonding, 1486-1487 lubricant degradation mechanisms, 1487-1488 dominant mechanisms, 1491 mechanical scission, 1490-1491 thermal/catalytic decomposition, 1488 triboelectric decomposition, 1488-1489 X-1P additives, 1491 Thiols, 914-915 Thrust bearings, 415, see also Slider bearings advantages and disadvantages, 978-980 annular thrust bearing, 418-422 fixed geometry (pad) bearings, 977, 984 hydrodynamic lubrication, 418 Rayleigh step bearing, 986-989 recurrent-grooved bearings, 989-994 tapered land slider, 984-986 hydrodynamic lubrication, 415 annular thrust bearing, 418-422 plane slider, 415-418 pivoted pad bearings, 994 hydrodynamic lubrication, 419 lubricating films, 433-438 Michell and Kingsbury bearings, 994-996 plane slider bearings, 415-418 Tilting pad bearings, see Thrust bearings, pivoted pad bearings Tires, automobile, 1203 construction of, 1203-1204 contact area, 1205-1206 hydroplaning, 1208 load transfer mechanics, 1204-1205 pressure distribution, normal, 1205-1206 shear traction, 1206-1208 slip, 1206-1208 wear characteristics, 1208-1209
1687 Tomlinson model, 653-655, 726-727 two dimensional, 727-728 Topographical difference method, in wear testing, 508-509 Topographical image subtraction, in wear testing, 508-509 Traction, surface, 131-132 Traction drive, 1199-1201 Traction motor bearings, train, 1321 Tractive rolling, 136-137 Transfer layers, coatings, 850 Transfer mechanics coatings, 850 load, tire, 1204-1205 material transfer from countersurface, 497 Transition metal dichalcogenides, 794-798 Transmission, automobile, 1197-1199 Tresca maximum shear stress criterion, 153-154 Tribochemistry, 468, see also Boundary lubricating films; Corrosive wear; Interfacial friction; Nanotribology coated surfaces, 833-834, 850-852 computer simulations, 756-758 diamond-like carbon (DLC) films, 894-896 Tribocouple tests, full and semi, 498, 515, see also Testing Tribo-element monitoring, 1634-1635 fluid film bearings, 1635-1636 gears, 1637-1638 rolling bearings, 1636-1637 seals, 1638-1639 Tribology, 5 of automobile engines, 1187-1226, see also Automotive tribology of bearings ball bearings, 1042-1043, see also Rolling bearings externally pressurized, 391-398, see also Externally pressurized bearings journal bearings, 399-415, see also Journal bearings; Slider bearings roller bearings, 1043-1045, see also Rolling bearings rolling bearings, 1041-1090, see also Rolling bearings slider bearings, 969-1035, see also Slider bearings thrust bearings, 984-996, see also Slider bearings; Thrust bearings of biomedicine, see Biomedical tribology of coatings, see Coatings; Composite coatings of diesel engines, 1231-1267, see also Diesel engine tribology of dynamic seals, 1131-1156, see also Dynamic seals of earth moving equipment, 1331-1368, see also Earthmoving tribology
8403cIndex Page 1688 Monday, November 6, 2000 10:00 AM
1688 of flexible media, 1549-1588, see also Flexible media tribology of gears, 1095-1124, see also Gears lubrication regimes, 457, 577, see also Lubricants/lubrication; specific tribosystem machine failure prevention, 1611-1642, see also Machinery diagnosis/prognosis of magnetic storage devices, 1413-1503, see also Magnetic storage devices of manufacturing operations, 1385-1409, see also Manufacturing tribology of marine engine/equipment, 1371-1383, see also Marine engine/equipment tribology materials/coatings, 768-770, see also specific tribosystem brittle, abrasive wear of, 288-290 ductile, abrasive wear of, 281-288 metals and ceramics, 771-784, see also Ceramics; Coatings; Composite coatings; Metal(s) of microelectromechanical systems, 1515-1544, see also Microelectromechanical systems microscale, 564-565, see also Microtribology of mining and mineral processing, 1331-1368, see also Mining and mineral processing tribology molecular, 582-587, see also Microtribology; Nanotribology of rail transport, 1271-1326, see also Rail transport tribology regimes, 457, 577 simulation modeling computer, 717-718, see also Computer simulations tribosimulation, 514-516, see also Tribotest(s), classification of tribosystems, 512-514 wear, 320, see also Testing; Tribosimulation(s); Tribotest(s) of space exploration systems, 1159-1181, see also Space tribology Tribo-materials database, see Database, tribo-materials Tribosimulation(s) baseline testing, 517 case studies, 518 gravure rollers on doctor blades, 519-520 oil pump gear in several wear modes, 518-519 piping, erosive wear, 522 plastic parts in optical disk drive, 521 rotary slitter knife blades, 521-522 spur gears, scoring of, 520 metrics, 516 refining, 517 physical and computerized, 511-512 physical simulations, 511-512
Modern Tribology Handbook level 1, 514 level 2, 515 level 3, 515 level 4, 515 problem definition, 512-514 scales of simulation, 514-516, see also Tribotest(s), classification of test apparatus selection/construction, 517 Tribosystem(s), 497-498 closed and open, 512 simulation testing, 512-514 TriboSystem Analysis (TSA), 513-514 Tribotest(s), see also Tribosimulation(s) classification, 497-498 examples, 501 level of realism, 499 planning, 498-500 purposes, 499 reference materials, 500 reproduction of wear mechanisms, 499 wear rates, 500 Turbomachinery, diesel, 1255-1257 Tyres, see Tires
U UHMWPE (ultrahigh molecular weight polyethylene), 1604-1605 Ultrasonic inspection, 1629-1630 Ultrasonic reflection methods, contact measurement, 147-148 Unconventional base oils, 369 Universal joints, 1201-1202 Unsteady testing data and interaction with test machine, 224-227 sources, 223-224 and vibration of test machine, 221-223 Upper bound method, 154
V Valleys, probability distribution, 72-75 Valves, diesel engine, 1249 materials selection criteria, 1251-1253 valve stem/guide wear mechanisms, 1250-1251 valve/seat wear mechanisms, 1249-1250 Velocity jump, adhesion forces, 191-192 Vertical scanning coherence peak sensing, 96-97 Vibration, and friction, 207 Vibration monitoring, 1617 shock pulse method, 1619-1620 signature analysis, 1617-1619 Vibrational loading, 1013
8403cIndex Page 1689 Monday, November 6, 2000 10:00 AM
Index Viscoelastic friction, 211-213 Viscoelastic solids, crack propagation, 189 Viscosity, 362-363 effective, 390-391 at high shear rates, in thin film rigid disks, 1484 of intermediate films, 581-582 of thick films, 577-580 of thin films, 582-587, 744-748 Viscosity index, 363 Viscosity index improvers, 463 Viscous drag, 192 Visual inspection, 1627 von Mises stress, 142 energy criterion, 153-154
W Wavelength filtering, roughness measurement, 77-80 Wear, 273-274, 317, 494-497, see also specific tribosystem abrasive, 277-278, see also Abrasive wear adhesive, 277-278, see also Adhesive wear and boundary lubrication modeling, 479-480, see also Boundary lubricating films catastrophic stage, 495 of ceramics, see Ceramics characterizing, 274 computer simulation, 755-756, see also Computer simulations corrosive, 277-278, 496, see also Corrosive wear cracking, 496, see also Crack(s) data from literature, 318 data generation, 523-531 database, 532-561, see also Database, tribo-materials debris of, 301, see also Wear debris defined, 273 descriptive terminology, 276-278 evaluations, 274-276, 500-501, see also Testing; Tribotest(s) fatigue, 277-278, 290, 494, see also Contact fatigue characteristics, 310 rolling/sliding elastic contact, 290-292 sliding plastic contact, 292-295 mapping, 320-322, see also Wear mapping; Wear maps material transfer from countersurface, 497 measurement, 674-675, see also Atomic force microscopy (AFM); Friction force microscopy (FFM); Testing mechanisms, 278-298, see also Wear mechanisms of metals, see Metal(s); specific tribosystem microscale wear, 694-702, see also Microtribology modeling, using wear mapping, 341-354, see also Wear mapping
1689 plastic deformation, 496 precursors of, 699-702, 712-714 prediction of, 319-320 process, 494-497, see also Wear mechanisms rates of, 274-276, see also Testing; Tribosimulation(s); Tribotest(s) run-in stage, 494-495 scratching, 674-675, 694-695, see also specific tribosystem simulation modeling, 320, see also Testing; Tribosimulation(s); Tribotest(s) steady-state conditions, 495 structural alterations, 496, see also Atomic force microscopy; Friction force microscopy; Surface(s), solid; Wear mechanisms testing materials, 320, 493-494, see also Testing; Tribosimulation(s); Tribotest(s) types, 277-278, 494-497 Wear debris, 301, 312-314 agglomeration of, 849-850 characteristics of, 309-310 babbit fatigue, 310 contact fatigue, 310 cutting, 309 deformation, 309 fretting, 310 wear-in conditions, 309 from coated surfaces, 844, 847-849 collection of, 306-308 delamination, 848-849 diagnostic analysis, 308-309 biological debris sampling, 310-312 particle counting, 309-310 reworked wear debris, 312 generating mechanisms, 302-306 osteolysis induced by, 1605-1607 particle crushing, 849 particle embedding, 847 particle entrapping, 848 particle hiding, 848 removal of, 497 Wear mapping, 320-322 advantages and limitations, 354-356 of ceramics, 324-328 classification system, 322-324 correlation of data, 348-352 future research, 356 materials comparisons, 328 advantages of, 337 in dry sliding conditions, 328-331 materials design and selection, 339-341 in paraffin oil lubricated conditions, 331-332 in water lubricated conditions, 332-334 wear mechanism maps, 337-339 wear transition diagrams, 334-337
8403cIndex Page 1690 Monday, November 6, 2000 10:00 AM
1690 modeling wear using, 341, 352-354 approaches to, 347 ceramics, 343-347 correlation parameters in, 349 materials normalization in, 348, 349-352 metals, 341-343 severity index in, 348 severity indexes in, historical, 348-349 uses of comparative, 337 Wear maps, 320-322, see also Wear mapping classification by, 322 forms used, 322-324 parameters of, 322-324 Wear mechanism maps, 237, 273, 337-339 Wear mechanisms, 278, 318-319, see also specific tribosystem abrasive wear, 281 brittle material, 288-290 ductile material, 281-288 adhesive wear, 278 adhesive wear mode, 280-281 wear volume estimation, 279-280 of ceramics, see also Ceramics in elastic contact, 296-298 of coated surfaces, 831-832, see also Coatings; Composite coatings corrosive wear, 295 ceramics, 296 metals, 295-296 of diamond films, 878-883 of diamond-like carbon (DLC) films, 892-893 fatigue wear, 290 rolling/sliding elastic contact, 290-292 sliding plastic contact, 292-295 of metals, see Metal(s) self-assembling monolayer studies, 921-924 Wear metal origins, 1621 Wear rate(s), 274-276, see also Testing; Tribosimulation(s); Tribotest(s) measurement, in steady-state conditions, 495 Wear surface roughness, 274 Wear surfaces, 274-276 Wear transition diagrams, 334-337 Wear volume, 274 Wear-in conditions, wear debris, 309 Web tenting, 1570-1576 Web winding J-line slip, 1565-1570 nip-induced tension, 1565-1570 Weight loss coupons, 1631 Welding, and friction, 215 Wheel bearings, automobile, 1202
Modern Tribology Handbook Wheel/rail tribology, 1274, 1275 adhesion/traction, 1277-1278 contaminant effects, 1281-1283 dry conditions, 1278-1279 improvement, 1287-1288 water lubrication, 1279-1281 braking, 1287-1288 contact patch forces, 1276-1277 grinding, 1303 curative/corrective, 1305 preparative, 1303-1304 preventive, 1304-1305 surface roughness, 1305-1307 locomotive adhesion control, 1283-1287 materials, 1275-1276 rupture, 1293-1294 plasticity, 1288 rail corrugation, 1307-1308 ratcheting, 1288 repeated contact, 1288 rolling contact fatigue, 1299-1301 service experience, 1302 small scale tests, 1301-1302 wear and, 1302-1303 shakedown, 1288 roughness and shakedown limit, 1290-1293 surface engineering, 1288-1290 wear, 1294-1295 and rolling contact fatigue, 1302-1303 wear mechanisms, 1295 wear tests service tests, 1297-1299 small scale tests, 1295-1297 Whirl inhibition designs, 1013-1014 elliptical bearings, 1016 lobed bearings, 1018-1019 offset elliptical bearings, 1016-1018 pressure dam bearing, 1016 steps and grooves, 1014-1015 Windscreen wipers, 1212-1213 Windshield wipers, 1212-1213 Worm gears, 1097, see also Gears full film lubrication, 1109-1110 Wound rolls, 1561-1562 air entrainment, 1562-1565
X X-ray photoelectron spectroscopy, surface analysis, 27-28
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