Mechanics and Chemistry in Lubrication (Tribology Series)

MECHANICS AND CHEMISTRY IN LUBRICATION

TR IBOLOGY SERl ES Advisory Board W.J. Bartz (Germany, F.R.G.) R. Bassani (Italy) B. Briscoe (Gt. Britain) H. Czichos (Germany, F.R.G.) D. Dowson (Gt. Britain) K. Friedrich (Germany, F.R.G.) N. Gane (Australia)

W.A. Glaeser (U.S.A.) M. Godet (France) H.E. Hintermann (Switzerland) K.C Ludema (U.S.A.) G.W. Rowe (Gt. Britain) T . Sakurai (Japan) W.O. Winer (U.S.A.)

Vol 1 Tribology - A Systems Approach to the Science and Technology of Friction, Lubrication and Wear (Czichos) Vol. 2 Impact Wear of Materials (Engel) VOl. 3 Tri bology of Natural and Artificial Joints (Dumbleton) Vol. 4 Tribology of Thin Layers (Iliuc) VOl. 5 Surface Effects in Adhesion, Friction, Wear, and Lubrication (Buckley) Vol. 6 Friction and Wear of Polymers (Bartenev and Lavrentev) VOl. 7 Microscopic Aspects o f Adhesion and Lubrication (Georges, Editor) Vol. 8 Industrial Tribology - The Practical Aspects of Friction, Lubrication and Wear (Jones and Scott, Editors) VOl. 9 Mechanics and Chemistry i n Lubrication (Dorinson and Ludema)

TRIBOLOGY SERIES, 9

MECHANICS AND CHEMISTRY IN LUBRICATION A. DORINSON Senior Research Associate (Retired), Harvey Technical Center, Atlantic Rich field Co., Harvey, IL, U.S.A.

K.C LUDEMA Professor of Mechanical Engineering, University of Michigan, Ann Arbor, MI, U.S.A.

ELSEVIER Amsterdam

- Oxford - New York - Tokyo

1985

E L S E V I E R SCIENCE PUBLISHERS B.V. Molenwerf 1 P.O. Box 21 1, 1000 A E Amsterdam, T h e Netherlands Distributors for the United States and Canada: E L S E V I E R SCIENCE P U B L I S H I N G C O M P A N Y INC. 52, Vanderbilt Avenue New York, N Y 10017

Library of Congress Cataloging in Publication Data L b r i n s o n , A. M e c h a n i c s and c h w i s t r y i n l x b r i c a t i o n . ( T r i b o l o g y s e r i e s ; 9) B i b l i o g r a p h y: p. I n c l u d e s index. 1. L u b r i c a t i o r and l u b r i c a n t s . 11. T i t l e . 111. S e r i e s .

~~1075.~64 1985 ISBN 0-444-42492-X

~21.0'9

I.

Ludem,

K.

C

85-6885

ISBN 0 4 4 4 4 2 4 9 2 - X ( V o l . 9) ISBN 0 4 4 4 4 1 6 7 7 - 3 (Series)

0 Elsevier Science Publishers B.V., 1985 A l l rights reserved. N o part of this publication may be reproduced, stored in a retrieval system o r transmitted in any f o r m o r b y any means, electronic, mechanical, photocopying, recording o r otherwise, w i t h o u t the prior w r i t t e n permission of the publisher, Elsevier Science Publishers B.V./Science & Technology Division, P.O. B o x 330, 1000 A H Amsterdam, T h e Netherlands. Special regulations for readers i n t h e U S A - This publication has been registered w i t h the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts, I n f o r m a t i o n can be obtained f r o m the CCC about conditions under which photocopies of parts o f this publication may be made in t h e U S A . A l l other copyright questions, including photocopying outside of the USA, should be referred t o the publisher Printed in The Netherlands.

V

PREFACE

Although it is widely recognized that friction, wear and lubrication are linked together in a single interdisciplinary complex of scientific learning and technological practice, this recognition does not seem to have resulted in a truly accepted, integrated union. Fragmented and specialized points of view still predominate, and books o n the subject are still restricted in outlook. To a large number of engineers lubrication still means only full separation of surfaces by a fluid film of oil. An important purpose of this book is to break down such isolationist attitudes by examining lubrication from a broad, inteidisciplinary point of view. When we do so, we find that in order to understand lubrication we must understand its interrelation with friction and wear, both fundamentally and empirically. The study of friction, wear and lubrication is no longer an obscure, minor topic in physics or a severely restricted, specialized discipline in engineering. Its modern status is a field of knowledge that has acquired the designation t t i i b o l a g y as characteristically its own. Its fundamental fabric is an amalgam cf basic concepts from various branches of physics and chemistry, and a wide array of sophisticated investigative techniques are used to elucidate its nature. It is in this sense that the term i n i e t i d i n c i p L i n a & y characterizes tribolOgY.

The traditional fluid film viewpoint that dominated the engineering treatment of lubricaticn in the past used only meager support from associated general concepts in physics and chemistry. Once the treatment of lubrication is released from the confines of the flbid film viewpoint, the interdisciplinary approach comes into full play. The modern concept of lubrication has expanded to take cognizance of behavior that was not example, the inclusion of recognized by the older points of view-for controlled lubricated wezr under extreme-pressure conditions as a valid case of lubrication. Such a shift in viewpoint requires the utilization of collateral information from various scientific and technical disciplines not directly connected with lubrication. I n this book the relation of lubrication to the broader aspects of tribological behavior is examined from two major points of view: ( 1 ) the mechanical principles that govern the properties and behavior cf the lubricant and also of the surfaces being lubricated; ( 2 ) the chemical factors in the composition and behavior of the lubricant, of the surfaces being lubricated, and of the ambient environment. It is in the emphasis on such basic mechanical

VI

and chemical processes that this book differs from conventional ments of lubrication.

treat-

The authors have elected to begin their examination of lubrication with a brief treatment of the classical full fluid film behavior, followed by some considerations of the role of elastohydrodynamics in fluid film lubrication at high pressures. The line of thought from these beginnings leads to examination of the breakdown of the fluid film and its consequences: contact and friction. From there the path goes to consideration of boundary and extreme-pressure lubrication and to lubricated wear. The greater the departure from full fluid film lubrication, the more prominent the interdisciplinary treatment of the various modes of mechanical and chemical interaction becomes. The first fourteen chapters of the book constitute a fairly orderly progression along these lines. The other five chapters do not f i t this sequence so neatly: some 3 f them have a recognized fundamental significance, and some examine the technological practice of lubrication from the interdisciplinary point of view. The authors have two classes of readers chiefly in mind. One is the practising engineer or lubrication specialist who may be skilled in the specifics of his vocation but, because of intense preoccupation with his immediate problems, may have lost touch with the recent basic advances. This book should serve such readers as an organized guide to the interdisciplinary aspects of lubrication, of h7hich they may be aware but which they have never got around to examining in detail. The other class of readers to whom this book is particularly directed is the advanced student of engineering. The teaching of lubrication in many engineering curricula is limited to classical hydrodynamics: the treatment of friction is shamefully inadequate and wear is mentioned only in passing. The authors have tried t 3 open the f d l vista of the science and art of tribology and lubrication t o these readers and thus give them insight into the rational and unified nature of the subject. In order to hold the book to a reasonable length, many of the quantitative derivations are not given in full. In all cases the reader is referred to the primary sources where the full development is available. It is taken for granted that the reader is familiar with the basics of the various fundamental disciplines involved o r knows where they are explained. References are cited for descriptive details of apparatus or procedures not given in the text and also as sources of concepts, theories and experimental results. Much of the data in the literature of tribology was obtained when sophisticated equipment used in present day experimentation was not available. Many of the concepts at the heart of the modern view of tribology are not newcomers to traditional physics and chemistry. The authors often found the older data better suited to the

purposes of this book than more recent publications, where at times the basic significance of the work was obscured by the emphasis on refinement of technique. In conformity with the policy of the major scientific and technical periodicals, quantitative units are SI iSyntc?mr I n t e f i n a t i o n a L c l wherever feasible. However, much of the data cited in this book goes back prior to the adoption of SI units, and in many instances it has not been possible to make the conversions o r else it has proved excessively laborious to do so. In such cases the data have been left in their original units. Also, the results of many studies of friction, wear and lubxication are reported in arbitrary units which cannot be converted to SI under any circumstances. The sheer bulk of the quantitative treatments in this book makes the assignment of multiple meaning to symbols inevitable. Within a given chapter, however, each symbol carries only a single meaning which is defined when the symbol is first introduced. Two symbols have only a single meaning throughout the book. The coefficient of friction is alis reserved for dynamic viscosity only. ways denoted by u. The Symbol A.

DORINSON

K. C LUDEMA

This Page Intentionally Left Blank

IX

ACKNOWLEDGEMENTS

A work of this scope would not be possible without recourse to data published in the open literature of science and technology. The authors are grateful to the following copyright owners of the figures arid tables reproduced with their permission in this book: Academic Press, publisher of J o u h n a L c6 C o i t o i d a n d l t i t e h 6 U C e S c i e n c e ; the American Chemical Society, publisher of A i ~ ~ i y t i cC h~Elm i 6 R h y , l n d u n t a i a l a n d E n y i n c c ~ t i n y C h e m i n t h y , 7 n d u h X h i a b and E n y i n e e s i f l g ChemihRhy P h o d u c t Reneahch and D c v e l o p m e n t , J o u h n a e c ! j C h e r n i c a t Ei.ig.itieehiny D a t a , and J c u h n a l 0 6 P i I q 4 i c a t C h e m i n t h y ; the American Institute of Physics, publisher of J u u h t i a i 0 6 A p p L i e d P h y n i c n , and l o u r i n a l 0 4 C h e m i c a L P k y h i c n ; the American Society for Metals, publisher of ble c hc nic ab Weah; the American Society of Lubrication Engineers, publisher of L u b h i c a t i o n E n y i n e e h i n g , and ASLE T z a n n a c k i o n n ; the American Society of Mechanical Engineers, publisher of T h a n h a c t i o t i n 0 6 t h e A m e h i c a f l S o c i e t y 0 6 b l e c h a n i c a t E n y i n c c h n , (i’ncluding J o u h n a l 06 B U h i C E n y i n e e h i t i g , J o u h n a L 06 E n g i n e e n i n 5 i o n I n d u n t h y , and J o u h f l a l 06 L u b t i c a t i o n T e c h n a L o g y ) , and P h o c e e d i n y h 0 6 l n t e h n a t i c 7 n c l C a n 6 c h e n c e n on Weah a 6 h f a t e h i a b n ; Sutterworth Scientific, Ltd., publisher of T h i b u l o y y l n t e h n a t i o n a l ; Chemical Publishincj Co., Inc., publisher of F h i c t i o n a t Phenomena by A. Gemant; the Design Council, publisher of E n yineehiny; the Division of Chemical Education, American Chemical Society, publisher of J o u ~ t n a L 0 0 C h e m i c a e E d u c a t i o n : Elsevier Publishing Co. (Elsevier Scientific Publishers), publisher of A h p e c t h 06 t h e C o n h t i t u t i o n 0 6 M i n e m b O i L 4 by K. van Nes and H. A. van Westen; Elsevier Sequoia, publisher of Wean; Industrieverlag von Hernhaussen, publisher of E h d & und KohLe. E h d g a n - P e t h o c h e m i e : the Institute of Petroleum, publisher of Jou.tnaL 0 6 t h e I n n t i t u t e o d P e t h o L e u m ; the Institute of Physics, publishers of J o u h n a l c6 P h i j n i c n , and P h o c e e d i n y h oh t k e P h y b i c a l S o c i e t y ; the Institution of Mechanical Engineers, publisher of P h a c e e d i n 5 h 06 t h e 1 f l h t i t U t h f l 06 M e c h a n i c a l E n y i n e e h h I w o L . l b 3 1 1 9 6 b J 1 9 6 9 ) , 3 P p p . 7 - 1 4 ! ; the Japan Petroleum Insticute and Frofessor T. Sakurai, publisher of B u L L e t i n 0 6 t h e J a p a n P e t h o l e u m I n s t i t u t e ; Macmillan Journals, Ltd., publisher of N a t u h e ; National Aeronautics and Space Adminstration, publisher of NASA S P - 2 7 7 . Weah and F h i c t i a n i n Vacuum by D. H. Buckley; National Lubricating Grease Institute, publisher of NLGl Spubenmar.; Oxford University Press, publisher of T h e F h i c t i o r l a n d L u b , t i c a f f i o n 0 6 Sotid4 hy F. P. Bowden and D. Tabor: the Royal Society of London, publisher of P h o c e o d i f l g n 06 t h e Roijad S o c i e t y ; the Royal Society of New South w a l e s , publisher of P ~ o c e e d i n g 0~6 t h e R o y a L S o c i e t y c 6 Neiu

X S o u t h W a k e s ; Curt A. Vincent2 Verlag, publisher of T h i b c t o 5 ~ c u n d S c h m i e t u n g ~ t e c h n i k ; World Petroleum Congresses, publisher of Phuceedinyn 06 t h e 1 5 t h WohLd Pethoeeum COngheAA.

The source of each item reproduced is acknowledqed in the text by a reference number and its corresponding listing at the end of each chapter.

XI

CONTENTS 1

2

.

.

Introduction 1.1. What Is Friction? 1.2. Friction and Wear 1.3. Tribology 1.4. Some Further Statements about Lubrication References

. . . . . . . . . . . . . . . .

. . . . . .

. . . . .

Simple in Two 2.1. 2.2.

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. . . .

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.

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. . . . . .

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. . . . . .

Hydrodynamic Theory: The Reynolds Equation Dimensions Beauchamp Tower's Bearing Experiments A n Engineering Derivation of the Two-Dimensional Reynolds Equation 2.3. The Reynolds Equation in Use: The Plane Siider Bearing 2.4. Energy Losses in the Hydrodynamic Lubrication ofBearings 2.5. The Pivoted Slider Bearing: Design Variables 2.6. The Full Journal Bearing 2.6.1. Application of the Reynolds Equation to the Full Journal' Bearing 2.6.2. Friction in the Full Journal Bearing References Appendix

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

. . . . .

Some 3.1.

3.2. 3.3. 3.4. 3.5.

. . . . . . . . . . . . . . . . . . . . . . . . . . Advanced Aspects of Hydrodynamic Lubrication . . . . The Classical Fluid . . . . . . . . . . . 3.1.1. Stress Analysis of a Fluid . . . . . . 3.1.2. The Simple Visccus Fluid . . . . . . . The Navier-Stokes Equations . . . . . . . . . The Generalized Reynolds Equation . . . . . . . Squeeze F i h s . . . . . . . . . . . . . Elastohydrodynamic Lubrication . . . . . . . . 3.5.1. Elastohydrodynamic Theory . . . . . . . 3.5.2. 3.5.3. 3.5.4.

. . . . .

. . . . .

4.4. 4.5. 4.6. 4.7. 4.8.

1

2 3 4 7 8 8 10 14 17 18 19 20 21 25 26

27 27 27 33 35 37 40 42 43 Some Elastohydrodynamic Solutions: Line Contact 46 Elastohydrodynamic Solutions for Point Contact 51 Experimental Observations of Elastohydrodynamic 53 Lubrication 57

. . . . . . . . . . . . . . . . . . . . . . . . . 4 . The Nature and Properties of Liquids . . . . . . . 4.1. The Properties of Liquids and Lubrication . . . 4.2. Newtonian and Non-Newtonian Viscosity . . . . 4.3. Capillary Viscometry . . . . . . . . . . 4.3.1. Newtonian Flow through a Capillary . . . 4.3.2. Non-Newtonian Capillary Flow . . . . . . References

1

. . . . . . . .

.

59 59 60 61 62 64 65 66 61 69 72 72 75 76 78 79

. . . . . . . . . . . . . . . . . .

79 80

.. . .. .. .

4.3.3. Sources of Error in Capillary Viscometry Capillary Viscometers 4.4.1. The Cannon-Fenske Viscometer 4.4.2. Capillary Viscometry Under Pressure Rotational Viscometry and Viscometers 4.5.1. The Couette Viscometer 4.5.2. The Cone-and-Plate Viscometer Rolling-Ball and Falling-Sinker Viscometers Orif ice Viscometers Influence of Temperature and Pressure on Viscosity 4.8.1. The Walther Equation and ASTM ViscosityTemperacure Charts 4.8.2. The Viscosity Index

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XI1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lubrication . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

4.6.3. Pressure and Viscosity Theories of Viscosity and the Molecular Structure of Liquids 4.10. Compressibility and Bulk Modulus 4.1!. The Role of Compressibility in Lubrication References 4.9.

5

.

. . . .

. . . . . . Lubricating Fluids .

Gases as 5.1. Fundamentzls of Gas Film 5.2. Gas-Lubricated Bearings 5.3. Properties of Gases Re f e r ences

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6

.

. . . . . . . . . .

Measurement of Fluid Film Thickness and Detection of Film Failure 6.1. Electrical Methods 6.1.1. Film Thickness by Electrical Resistance 6.1.2. ?ilm Thickness by Electrical Capacitance 6.2. ODtical Interferometry 6.3. X-Ray Transmission 6.4. Summarizing Discussion of Film Thickness Measurement 6.5. The Meaning of Film Failure 6.6. Electrical Methods of Detecting Film Failure 6.7. Detection of Fluid Film Failure by Friction or by Examination of Surface Condition References

83 87 92 99 100 102 102 103 106 108

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.. . . . . . . . . . . . . . . . . . . . .

7

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. . . . . . . . . . . . . . . . . . . . . . . . . . Phencmenology. Detection and Measurement .

. . . . .

Friction: 7.1. Basic Phenomenology of the Friction of Solid Bodies 7.2. Simple Behavioral Aspects of Static and Kinetic Friction 7.3. Experimental Arrangements f o r Detection and Measurement of Friction 7.3.1. Devices Utilizing Elastic Deflection 7.3.2. Dead-Weight Tangential Traction Devices 7.3.3. Inclined Plane Method for Static Friction 7.3.4. Damping of Oscillatory Motion References

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. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 8 . Friction: Mechanisms and Analysis . . . . . . . 8.1. A Simple Mechanism f o r the Friction of Solid Metallic Bodies . . . . . . . . .

. . . .

. .

. . . .

Extension of the Adhesive-Junction Model f o r Fricti on Intermittent Motion in Frictional Sliding: Stick-Slip Oscillation 8.4. Frictionally Induced Quasiharmonic Vibration 8.5. The Nature of Static and Kinetic Friction 8.6. Sliding Speed and Friction 8.7. Non-Adhesional Mechanisms for Friction Re f e renc e s 8.2. 8.3.

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. . . . . . . . . . . . . 9 . Lubricated Friction . . . . . . . . . . . 9.1. The Contact and Friction of Clean Surfaces . 9.2. The Influence of Oxides on the Friction of Metals . . . . . . . . . . . . Lubricated Friction: The Behavioristic View A Theoretical View of Lubricated Friction References 9.3. 9.4.

.

. . . . . . . . . . . . . 1 0 . Lubricant Additive Action . 1 . Basic Categories and Mechanisms . . . . . . . . . . . . . 10.1. What is a Lubricant Additive? . . . . . 1C.2. Classification and Nomenclature . . . . . 10.3. Interposed Adsorption Films . . . . . . 10.3.1. 10.3.2.

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Simple Absorbed Films Chemisorbed Films

109 110 110 114 117 121 122 123 125 128 133 134 134 139 140 141 144 146 147 147 149 149 152 159 162 165 172 175 177 178 178 183 185 193 197 198 198 200 2C3 203 214

XI11

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The Additive Action of Adsorbed Films 10.4.1. Durability of Films 10.4.2. Influence of Temperature cn Adsorbed Films and Friction 10.4.3. Thermodynamics of Adsorption and Lubrication 10.4.4. Other Physicochemical Influences in Adsorbed Film Behavior 10.5. Chemically Deposited Films 10.5.1. Polymeric Condensation Films 10.5.2. Surface Resin ("Friction Polymer") 10.6. Interaction Films 10.7. Asperity Junction-Growth Inhibition References 10.4.

. . . .

. . . .

. *

. . . . . . . . . . . . . . . . . . . . 1 . LuSri:ant Additive Action . I 1 . Chemical Reactivity and Additive Functionality . . . . . . . . . . . 11.1. A Basic View of Reactions between Additives and Metal Surfaces . . . . . . . . . . 11.2. Chemical Structures in Additives and Mechanisms of Additive Action . . . . . . . . . . 17.2.1. Sulfur Compounds: Chemical Reactions . 11.2.2. 11.2.3. 11.2.4. 11.2.5.

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. . . . .

Contact of Solid Bodies . . . . . . . . . 12 1 . Surfaces and Surface Roughness 12.1.1. Descriptive Surface Topography 12.1.2. The Metrics of Surface Roughness 12.2. Contact and Adhesion 12.2.1. Simple Deformation Models of Contact 12.2.2. Adhesion and Separation 12.3. Characterization cf Surfaces from Profile Data 12.4. Surface Topography and the Mechanics of Asperity Contact 12.5. Experimental Studies cf Contact and Adhesion 12.6. The Tribological Significance of Contact and Adhesion References

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. .

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.

Wear: 13.1. 13.2.

13.3.

255 255

276

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13

231 235 236 238 241 250 252

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.

226

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.

224

261 261 268 272 274

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Sulfur Compounds: Lubricant Additive Action Chlorine Compounds: Chemical Reactions Chlorine Compounds: Lubricant Additive Action PhosDhorus COmDOundS: Chemical Reactions and Additive Action 11.2.6. Phosphorus and Other Key Elements: Dithiophosphates (Phosphorodithioates). etc 11.3. The Action of Multicomponent Additives 11.3.1. Multicomponent Additives with Sulfur and Chlorine 11.3.2. Multicomponent Additives with Phosphorus and Chlorine 11.3.3. Sulfur and Fatty Esters in Multicomponent Additives 11.3.4. Interference Effects with Multicomponent Adlitives References

12

219 219

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles and General Behavior . . . . A Basic Definition of Wear . . . . . . . Phenomenological Wear . . . . . . . . . 13.2.1. Wear in Pure Sliding . . . . . . 13.2.2. Mixed Sliding and Rolling . . . . . 13.2.3. Pure Rolling . . . . . . . . . 13.2.4. Impinging Contact . . . . . . . 13.2.5. Dry and Lubricated Wear . . . . . 13.2.6. Wear of Non-Metals . . . . . . . Mechanistic Processes in Phenomenological Wear 13.3.1. Adhesion and Transfer . . . . . .

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...

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286 295 296 299 301 304 305 308 309 309 312 314 316 319 320 327 337 343 347 349 349 350 351 359 359 361 362 363 365 365

XIV

.. .. .. .. . . .. .. . . . . . .. .. .. . . .. .. ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 . Aspects of Lubricated Wear . . . . . . . . . . 14.1. Lubricated Wear by Penetration of the Fluid Film . 14.1.1. Wear and Partial Elastohydrodynamic . . . . . . . . . . Lubrication 14.1.2. Wear and Mixohydrodynamic Lubrication . . 14.2. Compounded Lubricants and Wear . . . . . . . 14.2.1. Reaction-Rate Theories of Wear in the Presence of Compounded Lubricants . . . 14.2.2. Reaction Rate Processes and Phenomenological Wear . . . . . . . . . . . . . . 14.3. The Control of Scuffing . . . . . . . . . . References . . . . . . . . . . . . . . . . 15 . Temperature Effects in Friction. Wear and Lubrication . . 15.1. Interfacial Temperature and Rubbing . . . . . . 15.1.1. A Descriptive Model for Interfacial Plastic Deformation Processes Fatigue Mechanisms Chemical Reaction Processes Combinations of Mechanistic Processes 13.4. Nomenclature 13.5. Wear Models 13.5.1. Wear Models and Asperity Contact 1 3 . 5 . 2 . Models for Constant Wear Rate 1 3 . 5 . 3 . Wear with Variable Rate 13.5.4. Geometrical Influences in Wear Models 13.5.5. Physical Parameters in Wear Models 13.6. Catastrophic Wear Damage References 13.3.2. 13.3.3. 13.3.4. 13.3.5.

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. . . . . . . . . . .

Temperature in Rubbing Calculation of Interfacial TemDerature by Continuum Heat Conduction Tkeory 15.1.3. A Stochastic Model for Interfacial Temperature Generated at Discrete Sites 15.2. Experimental Observations of Interfacial Temperature 15.2.1. The Dynamic Thermocouple 1 5 . 2 . 2 . The Embedded Thermocouple 15.2.3. The Strip Thermistor 15.2.4. Emission of Infrared Radiation 15.3. Ambient Temperature Effects 15.4. Effects of Temperature on Friction and Wear 15.5. Effects of Temperature on Lubrication and Lubricants References 15.1.2.

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16

.

. . . . . . . . . . . . . . . . Lubricating Oils . . . . . . . . . . .

Petroleum 16.1. Processing of Petroleum Lubricants 16.2. Nomenclature and Classification of Petroleum Oils 16.3. Structure in Lubricating Oils by Direct Techniques 16.3.1. Extraction, Chromatographic Adsorption, Distillation and Mass Spectrography 16.3.2. Distillation, Extraction, Chromatographic Adsorption, Thermal Diffusion and Mass Spectrography 16.3.3. Mass Spectrography of Refinery-Run Fractions 16.3.4. Nature of the Alkyl and Aromatic Structures 16.4. Type Structures in Lubricating Oils by Correlation with Physical Properties: Indirect Methods 16.5. Type Structures in the Performance of Petroleum Oils as Lubricants References

.

400 40 1 401 404 410 41 1 416 420 428 429 429 429 430 437 440 441 446 447 448 453 456 464 469

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472 472 476 480

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480

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484 487 488

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491

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17

366 367 367 368 375 379 379 381 388 390 392 395 397

. . . . . . . . . . . . . . . . Liouids as Lubricants . . . . . . . .

Non-Petroleum 17.1. Chemical Types and Structures 17.2. Chemical Types and Properties of Synthetic Lubricants

. . . . . . . .

495 499 501 50 1 507

xv

. . . . . . . . . . . . . . . . . . 18 . Lubricating Grease . . . . . . . . . . . . 18.1. Basic Aspects of Lubricating Grease Structure . 18.2. The Manufacture of Lubricating Grease . . . 18.3. Further Consideration of Grease Structure . . 18.3.1. Bleeding and Permeability . . . . . 18.3.2. Consistency and Penetration . . . . 18.4. The Flow of Greases . . . . . . . . . 18.5. Grease as a Lubricant in Service . . . . . References . . . . . . . . . . . . . . 19 . Lubrication by Solids . . . . . . . . . . . 19.1. Classification and Terminology . . . . . . 17.3. Applications of Synthetic Lubricanrs References

518 520 521 52 1 526 528 528 532 535 538 547 549 549 55 1

Layer-Lattice Inorganic Solids as Lubricants . 19.2.1. Molybdenum Disulfide a s a Luricating Lamellar Solid 1 9 . 2 . 2 . Graphite as a Solid Lubricant 19.2.3. Graphite Fluoride as a Solid Lubricant 19.2.4. Boron Nitride as a Solid Lubricant 19.2.5. Other Layer-Lattice Inorganic Solids as Lubricants 19.3. Lubrication by Non-Lamellar Inorganic Solids and by Soft Metals 19.4. Oraanic Solids as Lubricants Th; Technological Utilization of Solid Lubricants 19.5. References

581 589 594 610

Author Index

615

19.2.

. . . . . . . . . . .

Subject Index

. .

552 566 572 577

. . . . . . . . .

579

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . .

. . . . .

. . . . .

. . . . . . . .

621

This Page Intentionally Left Blank

1

Chapter 1 INTRODUCTION

1.1.

WHAT IS LUBRICATION?

The art of lubrication no doubt goes back past recorded history. I t can be cocjectured that the first use of the wheei predated the earliest historical records we have end it can be assumed that the practice of lubrication is almost a s old a s the use of the wheel. An Egyptian mural dating back to c a . 1 9 0 0 B.C. shows the runners of a sledge carrying a large block of stone being lubricated to decrease friction. A chariot found in a tomb of c a . 1 4 0 0 B.C. still had some of the original lubricant on its axle. The English word "lubricate" comes from the Latin Lubnicub, which means slippery. This tells us that the early concept of lubrication was slipperiness and that a lubricant was regarded as a substance which promoted the sliding of o n e body against another. A modern dictionary that will when interposed between defines a lubricant as "a substance moving parts of machinery make the surface slippery and reduce friction, eliminate asperities and prevent cohesion." This definition is not 2 s informative as it appears at first glance. From common experience one can readily form a mental image of interposing something between rubbing surfaces to make their movement easier, but the concepts of asperities and cohesion are derived from a more sophisticated level of experience.

...

I t is doubtful i f a satisfactory, all-inclusive definition of lubrication can be formulated a phiah;. In that case, we might a s well fall back on comnon experience and see whether we can identify and describe the modes of behavior we propose to designate as lubrication. Let us take a typical case where lubricants are unquestionably useful: namely, the operation of machinery with members that move against one We readily observe that lubricated operation differs from unanother. lubricated operation by the exertion of less force, the consumption of less energy, and the slower alteration of the shape and size of the contacting parts in the sustained course of the operation of the machinery. In the accepted terminology of engineering, lubrication results in the

reduction of friction and wear. This reads like a paraphrase of the dictionary definition quoted abcve. There is, however, an important difference. The description of lubrication as the mitigation of friction and wear-and i t should be

2

regarded as a description rather than a definition-is in terms of two modes of behavior that are well recognized in common experience. Thus we are not forced to begin our study of lubrication with a categorical definition. Instead we can start with familiar behavior and from i t build a systematic ideological structure. 1.2.

FRICTION AND WEAR

Any study of lubrication in the broad sense cannot be separated from a basic consideration of the nature and the phenomenology of friction and wear. The word "friction" stems from a Latin root which means "to rub," and no doubt the concept of friction came from observations of rubbing action. The earliest observations must have been naive: there would have been a sense of varying effort required to slide a given body under varying conditions of contact; furthermore, given the antiquity of the firestick and the fire-drill, the associat on of heat with rubbing must have been known in early primitive cultures. By the end of the fifteenth century as the notebooks of Leonard0 da Vinci attest [l], a quantitative relation was recognized between the weight of a body and the force required to make it slide. This relation was restated and amplified by Amontons in 1699 and by Coulomb in 1781. Except for historical interest, there is no need to go back to the older sources in tracing the development of modern knowledge about friction. In looking for the emergence of the modern viewpoint, one need not go back any farther than the third decade of the present century: prior to that, data and observations are sparse and for the most part of restricted significance. What might be termed the first flowering of the 20th-century studies of friction occurred in the 1930's. The work of R. Holm at the Siemens laboratories in Berlin is summarized in his monograph of 1946 on electrical contacts [2]. The work of F.P Bowden and h i s collaborators at Cambridge also dates from the 1930's but did not appear until 1950 [31. The key to the modern concept of the friction of solids is the demonstration that the topography of the overwhelming preponderance of real surfaces is rough and that true contact occurs at the high spots (asperities). The area of this true contact is only a small fraction of the apparent surface area, and the load forcing the two solid bodies together produces local pressures at the contacting asperities great enough to deform them elastically or even plastically. Friction is the interaction at the deformed asperities that we observe phenomenologically as a force opposing the motion when one body slides past another. Quantitative interpretation of observed macroscopic behavior in terms of measurable microscopic behavior at che contacting asperities is the characteristic feature of the modern viewpoint of friction.

3

Wear is another phenomenon associated with the rubbing of solids. The observation of common experience which identifies wear is the loss of material from one o r both of the rubbing bodies. There is no difficulty in showing the compatibility of the concept of contact and interaction at asperities with this overtly observable behavior, especially i f particulate wear debris is generated. But also, close examination of the rubbing surfaces often reveals evidence of interaction and damage long before any measurable debris is found. Thus we can enlarge the concept of wear to include any alteration of surface topography o r condition arising from contact interaction; and we see that friction and wear are two aspects of such interaction, the one being detected and measured as a force and the other by loss of material or change of surface condition.

1 .3.

TRI BOLOGY

From the foregoing discussions we can understand why friction, wear and lubrication have become associated a s related components of a recogAs this recognition nized scientific and technological specialty. developed, it became apparent that there was a need for a convenient and appropriate appellation which would emphasize the unified rather than the tripartite character of the subject. The past 15 years have seen the adoption of the term tniboeogy for that purpose. The word "tribology" comes from the Greek t f i i b e i n , which means "to rub." This derivation is evidence of the psychological conditioning that influenced the choice of nomenclature. Rubbing is the action associated by common experience with friction and wear. But the sophisticated experience of the present day has revealed instances of friction and wear behavior which do not have their origin in rubbing as ordinarily understood. Therefore the concept of tribology has been expanded, so that the definition now given by the English dictionary department of the Oxford University Press reads: "the science and technology of interacting surfaces in relative motion and the practices related thereto" [ 4 ] . The element of indeterminateness in this definition is to a certain extent advantageous, as the borderline between surface interactions which can be regarded as tribological and those which cannot is not firmly established. For example, the interaction between two charged surfaces as they approach each other is ordinarily thought of as electrical behavior. However, as we shall find when we come to the examination of contacting surfaces, the ultimate theory of van der Waals forces in such contacts is electrical in nature. Thus, we can regard contact between two surfaces from several points of view: that of gross mechanics, that of surface physics, o r that of charged particle interactions on a molecular scale. Expanding this point of

view

into

broad

language,

we

say

that

tribology has become an interdisciplinary study. The engineer's interest in friction might not go further than macroscopic measurement of the applied load and the tangential force, whereas the physicist might wish to characterize the fine structure of the surfaces, establish the distribution of asperity size and location, and compute the relation between the true area of contact and load: both might say they were studying friction. In the study of lubrication, one investigator might be satisfied to measure only the decrease in wear, while another might wish to relate it to the chemical interaction of the lubricant with the ambient atmosphere and the rubbing surfaces. The interdisciplinary approach is indispensable in order to understand tribology, in its large sense and in the fine details of specialized problems. 1.4.

SOME FURTHER STATEMENTS hBOUT LUBRICATION

The need for lubrication arises from the utilitarian demands of engineering for the mitigation of damage incurred by solid bodies sliding against one another. I t might be supposed that the study of lubrication should therefore be based on a thorough knowledge of friccion and wear and that the comprehensive understanding of unlubricated friction and wear is a prerequisite to the understanding of lubrication. However, the course of dry friction and wear under drastic conditions has little relation to lubricated rubbing under the same conditions because of the rapidity and the extent of damage in dry rubbing, a state of affairs which lubrication is intended to alleviate. Interactions amcng basic mechanisms assume much different proportions in destructive wear than in mild wear. And since the function of successful lubrication is to keep wear under controi, a thorough study of severe damage in dry friction and wear is not necessary in order to understand lubrication. Instead, we need to know the basic principles governing friction and wear and to be familiar with those aspects of tribological behavior which have direct bearing on lubricated rubbing. It simplifies things considerably i f we think of friction, wear and lubrication in terms of common experience: namely, the rubbing of solid bodies. We note the involvement of three basic conditions: ( 1 ) each body has a bounding surface: ( 2 ) the bodies are put into contact with each other at the surface by a load: ( 3 ) the bodies are in relative motion. Under these conditions the system composed of the solid bodies will experience friction and wear. We wish to eliminate or at least reduce the friction and wear, and we propose to do this by introducing an appropriate substance between the bounding surfaces. In other words, we propose to lubricate the rubbing system. Let us examine the problem for a familiar engineering device, namely the plain journal bearing, shown in diagrammatic cross-section in The bearing n is fixed in position and supported; its bounding Fig. 1 - 1 .

5

Figure 1 - 1 . Lubrication of a journal bearing. Journal stationary Journal rotating

-.

----.

surface has the radius R , . The journal b , of radius R 2 < R,, rotates with angular velocity U and carries the load W. In the absence of rotation the journal would come in contact with the bearing in the attitude indicated by the dashed line in Fig. 1-1. We seek by lubrication to prevent or mitigate the unfavorable consequences of such contact. Broadly there are three methods for accomplishing this. One i s to introduce a film of fluid to separate the surfaces of the journal and the bearing so that essentially the rubbing or sliding occurs within the fluid rather than at the contacting surfaces of the solid bodies. The laws governing the flow of a viscous fluid between two bounding surfaces are such that rotation of the journal about its axis can generate a fluid film which will support the applied load and will keep the journal and Its effect is the bearing apart. This is hydfiodgnamic Lubtication. shown by the position of the journal represented by the f u l l line in k second course of action is to coat the bounding surfaces Fig. 1 - 1 . with a substance so that even though macroscopic contact is not eliminated, contact on a microscopic scale is altered to reduce friction and strongly suppress wear. This type of action has acquired the designation of boundaty .tubtication. The third method is to introduce a substance into the rubbing boundary which reacts at the interface to produce a coating on the surface or to change the character of the surface so that wear is reduced to a tolerable level. This has come to be known as e x t f i e m e - p t e b b u f i e Lubtication. W e need not probe very deeply into these three types of lubrication for their interdisciplinary nature to become apparent. Hydrodynamics is a well-established branch of the physics of fluids, and for the most part the solution of hydrodynamic lubrication problems con-

6

sists of manipulating mathematical relations. But in those cases where the problem includes the response of the viscosity and the density of the fluid to pressure and temperature, the tribologist calls on physical chemistry to supply the appropriate relation. The interdisciplinary character of boundary lubrication has several aspects: the nature of the surface structure which governs the microcontacts ( i . e . , the physics of the fine surface structure); the condition of the surfaces participating in the microcontacts (surface chemistry); the interaction of the lubricant substance with the surface, both at rest and during rubbing (adsorption, desorption). Extreme-pressure lubrication is much like boundary lubrication, with the additional factor of chemical reaction during rubbing. In this book we shall begin with an examination of hydrodynamic lubrication. If there is a mode of real lubrication behavior which approaches the ideal, i t is simple hydrodynamic lubricat,ion. There is no

contact of the solid surfaces and therefore no wear in the generally cepted sense: the friction is that arising from the viscous shear of lubricating fluid. The part that the viscosity and the density of lubricating fluid plays in hydrodynamic lubrication leads us from gineering physics to the physical chemistry of liquids.

r3cthe the en-

A logical path by which we can go from hydrodynamic lubrication to the friction of solid bodies starts with an examination of the breakdown of lubrication by liquid films as generally understood. By this we mean that the film thickness and the pressure distribution are no longer described by either the simple hydrodynamic or the elastohydrodynamic relations and that there is no macroscopic separation of the solid boundary surfaces. Among the various overtly observable consequences of sliding under such conditions is the behavior commonly designated as friction. Discussion of the phenomenology and the nature of friction brings us to a detailed examination of boundary lubrication and this in turn involves us in the details of real contact. Wear, dry o r lubricated, has some aspects in parallel with friction and some which are different. Both friction and wear are characterized by a temperature rise at the contact interface. As we study these and other interrelationships involved in lubricated rubbing we see that broad, systematic knowledge of lubrication rests on a foundation derived from basic chemistry and physics

.

Most of the physics of lubrication is traditional mechanics and mechanical engineering. But there are also topics such as interfacial temperature, electrical resistance and capacitance of lubricant films, optics as applied to surface contact and surface topography, etc., as well as aspects which cannot be distinguished from physical chemistry. However, it is not with the formal classification of the interdisciplinary components that this book is concerned but rather with their mutual

7

interaction in the phenomenology of lubrication. Certain subjects which figure prominently in

practical

lubrication

do not fall neatly into the pattern outlined above but nevertheless warrant treatment in interdisciplinary terms, something which has been badly neglected in the past. Several chapters in this book are devoted to such topics. Included are chapters on petroleum oils, liquid lubricants other than petroleum, chemistry of additives, greases, and solid lubricants. REFERENCES 1.

2.

3.

4.

The Notebooks of Leonard0 da Vinci, arranged and rendered into English and introduced by Edward MacCurdy, George Braziller, New York, 1954. R. Holm, Electric Contacts, Hugo Gebers Forlag, Stockholm, 1946, Sections 3 3 - 3 8 . F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, Part I 1950, Part I1 1964. K. H. R. Wright, Tribology, 2 (1969), 152-161.

8

Chapter 2

SIMPLE HYDRODYNAMIC THEORY: THE REYNOLDS EQUATION IN TWO DIMENSIONS

If two solid bodies that are in relative motion can be kept from contacting each other, there will be no danger of either wear or seizure of the system and thus its running life will be long. Separation of the surfaces can be maintained by interposing a film of fluid between them. 8. fluid film can have the further advantage of reducing the energy loss during sliding below that possible without the fluid, as the loss due to viscous drag in the fluid is almost always less than the frictional loss of contacting solid surfaces. When an interposed fluid film acts to reduce wear or energy loss and to prevent seizure, it is called a lubricant. As will be seen later, the lubricating fluid can be either a liquid or a gas. Solids can also act as lubricants but by an entirely different mechanism than fluids. A fluid film can be interposed between the load-carrying areas of solid surfaces by one or a combination of two methods: by pumping the fluid in from the outside, or by immersing a properly designed and operating system of surfaces in the fluid. The first method is called hydrostatic lubrication, and it is recommended for systems that start and stop frequently or move very slowly. The second method is called hydrodynamic lubrication and is often preferred because the sliding system is self-acting and does not require auxiliary pumps and reservoirs. But the hydrodynamic method does require greater care in designing, since proper choice must be made of geometry, applied load , sliding speed and fluid properties. The science of hydrodynamic lubrication has been highly developed, both theoretically and technologically. A simple basic presentation of the analytical and mathematical approach to the relations among the necessary variables, illustrated by a few elementary cases, will be given in this chapter. I t is helpful to keep in mind that the engineer's goal is two-fold: to calculate the minimum spacing between the sliding bodies that insures adequate separation under operating conWe ditions, and to calculate the energy loss in the sliding system. shall begin with an examination of the experiments of Beauchamp Tower which led to the theoretical work of Osborne Reynolds. A simplified version of Reynolds' equation will be used to illustrate the application of hydrodynamic theory to bearing lubrication.

2.1.

BEAUCHAMP TOWER'S BEARING EXPERIMENTS In 1 8 8 3 and 1885 Beauchamp Tower reported his experimental investiga-

9

tion on bearings as a member of the Committee on Friction of the InstituThese were partial bearings, 0.102 m tion of Mechanical Engineers [l]. ( 4 inches) in diameter and 0.152 m ( 6 inches) long, with an arc of conformity approximately 2.74 radians (157'). Figure 2-1 shows the arrangement which resulted in successful lubrication of the bearing. In the

Figure 2-1.

Beauchamp Tower's experimental bearing.

course of the experiments a hole was drilled in the bearing for the installation of a lubricator. For unknown reasons, before the lubricator was inserted, the bearing was reassembled and put into operation, whereupon oil flowed from the hole drilled in the bearing. The shaft acted as a pump, transporting oil from the bath through the hole in the bearing. When attempts were made to stop up the hole with a cork or a wooden plug, the plug was slowly forced out by the oil pressure. When a 2 pressure gage of 1.379 MN/m2 ( 2 0 0 lb/in ) capacity was connected to the lubricator hole, the indicator was driven past the limit of the scale, even though the average unit load for the entire bearing was only 0.6895 MN/m2 ( 1 0 0 lb/in2). Tower's next step was to carry out a systematic exploration of the pressure distribution over the tearing surface by drilling nine holes in the bearing ( 3 rows of 3 holes spaced circumferentially) and connecting them to pressure gages. Assuming that the pressure was distributed symmetrically along the axis of the journal (thus requiring a row of holes at the midline and to one side only), he obtained the pressures for 15 points on the bearing surface. Figure 2-2a shows three pressure distribution curves along the bearing surface in the direction of journal rotation, while Fig. 2-2b shows three curves for pressure distribution as a function of location axially along the bearing. The curves marked A , B and M in Fig. 2-2b are the pressure

distribu-

10

I

I

I

I

lii ifi (a) F lm pressure distribution over the bearing surface. pressure distribution: B bearing width. ( b ) Axial pressure distribut on: L bearing length.

Figure 2-2.

C i rcumferent i a

tions in the planes perpendicular to the plane of Fig. 2-2a at the locations correspondingly marked there. The relation between the curves in Figs. 2-2a and 2-2b is therefore obvious. When the load carried by the bearing was computed from the area under the pressure curves, it was found to be 35.789 kN ( 7 9 8 8 lb), which was very close to the actual load of 35.876 kN ( 8 0 0 8 lb). This experiment demonstrated that a fluid film of finite thickness can be maintained in a loaded bearing by rotation of the shaft without the need for an external pump. 2.2. AN ENGINEERING DERIVATION OF THE TWO-DIMENSIONAL REYNOLDS EQUATION The year after Tower's second report appeared, Osborne Reynolds of the Manchester College of Technology published an explanation of these By making results on the basis of classical hydrodynamic theory [21. certain assumptions and by simplifying the Navier-Stokes equations for the flow behavior of viscous fluids, Reynolds obtained a differential equation for the pressure developed in a fluid film between bearing surfaces in motion. However, the same equation can be derived from the fundamentals of engineering mechanics without recourse to the complications of an analysis of fluid behavior. The simplifying assumptions required are given below. (1)

The lubricant fluid is Newtonian; i . e . shear stress tional to rate of shear.

is

propor-

( 2 ) Flow of fluid is laminar, with no vortex flow or turbulence.

( 3 ) The weight of the fluid is negligible.

11

(4) Fluid inertia terms are negligible. ( 5 ) The fluid is incompressible.

( 6 ) The fluid film is so thin that the pressure, p , remains constant

across its thickness. ( 7 ) The viscosity of the fluid, q , is uniform throughout the film.

(8) There

is

no

slip

between the lubricant and the bounding sur-

faces. (9) There is no end leakage (equivalent to the assumption bearing is of infinite length).

that

the

( 1 0 ) The

fluid film is so thin compared to bearing dimensions that the curvature of the bearing can be ignored and rotational velocities can be replaced by translational velocities.

(11)

The two bounding surfaces are not parallel.

Consider a lubricant film between two plane converging surfaces, as shown in the cross-sectional diagram of Fig. 2 - 3 , where x , rj and z are coordinate directions and u , w and w are velocities. Take an element of

U-

Figure 2-3. surfaces.

Analysis of the hydrodynamic film between

converging

plane

lubricant dxdydz within this film. Because of the limiting assumptions we have used, the forces acting on this element are reduced to the two normal forces

on the left and right-hand faces respectively, and the two shear forces

12

aTX

i X d x d z and

( T ~+

- dy ay

)

dxdz

on the top and bottom faces.

(

pdydz +

a-r,

T~

+

- dy ay

)

dxdz

-

Neglecting inertial forces, for equilibrium

(

p

+

dydz ax

-

1,dxdz

= 0

(2-1)

which reduces to ap

-

31,

ax

ay

From

the

(2-2)

definition

of Newtonian viscosity (see Eqn 4-2, Chapter 4) we

get au l X = T I -

ay

On introducing this value for

(2-3) T~

into Eqn 2-2

(2-4)

(2-5) It has already been postulated that p is not a function of y (assumption 6, above); on applying the additional assumption that p does not depend on z , the partial derivative ap/ax in Eqn 2-5 can be replaced by a simple derivative dp/dx. Then the integration is carried out twice with respect to y:

The boundary conditions u = U when y = 0 and u = 0 when y serted into Eqn 2-6b to give

=

h

are

in-

which reduces to

(2-8) Equation 2-8 gives the velocity distribution across any section of the oil film, subject to the restrictions implicit in Eqns 2-6.

13

Going back to the three-dimensional point of view, since the fluid has been assumed incompressible, the quantity of fluid leaving the element d x d y d z must equal the quantity entering it: au

udydz + v d x d z

+

wdxdy

=

(u

+

- dx ax

)

dydz

+

av

(,v

+

- dy ay

)

dxdz

whence au

av

aw

ax

ay

az

- + - + - =

0 (2-9)

which is the well-known volume-continuity equation The assumption of no end-leakage gives

fluid

of

mechanics.

aw

- =

0

az so that

av

au

aY

ax

- = - _

(2-10)

On introducing u from Eqn 2 - 8 ,

with the restrictions imposed there,

(2-1 1 )

Since

fluid cannot pass through solid surface aw/ay from y = 0 to g = h is zero, so that

-

hy)

+

A

or

B, the integral of

U ( v ) ] d g

= 0

(2-12)

is a

In Eqn 2 - 1 2 the limit h relationship can be used:

4(x)

1 f(x,y)dy ax

=

a $(X) -j ax

funct on

f(x,y)dy

-

$ 1

x;

of

l x i f [X,$IXl]

4(x)

In our case 41x1 = 0 ,

JI'lxi

$lxl = h,

ah

=

-,

+"x)

= 0

ax

and since u = 0 when y = h

hence

flx,yl

=

u

+

the

following

4 ' I x l f [X,$(X)]

14

Therefore

which means that we can integrate Eqn 2-12 with respect to y before differentiating with respect to x. This gives us

(2-13)

or

ah ax

(2-14)

Since by our assumption h is a function of x only and

% ( h3 s)

= 6Tlu

is constant

dh

az

(2-15)

Equation 2-15 is the Reynolds equation in two dimensions for the pressure p developed by hydrodynamic action in a film of incompressible fluid lubricant with no side leakage. The other variables are h, the film thickness, and x , the distance along the length of the bearing. For example, in Fig. 2-1 x is the distance along the circumference from the inlet to the outlet. 2.3.

THE REYNOLDS EQUATION IN USE: THE PLANE SLIDER BEARING

The application of the Reynolds equation to a simple problem in lubrication is illustrated by an examination of the plane slider bearing, which is basically a combination of two plane surfaces, one of which is inclined relative to the other. Figure 2-4 is a diagrammatic cross-

Figure 2-4

Diagram of plane slider bearing with fixed shoe.

sectional sketch in which the angle of inclination between the fixed memand the moving member (the heidea or h U n f l e h ) as well as ber (the hhoe

15

the film thickness are greatly exaggerated. 2.3.1.

Integration of the Reynolds Equation

The geometry of the system as shown in Fig. 2 - 4 is oriented with the origin at the vertex of the angle a. To make the bearing operate, the slider must move toward the converging wedge; hence the sense of U is opposite to that of x . The film thickness at any point along the shoe is given by the relation h = x t a n cr

(2-

16a)

is very small, i a n cr is practically equal to cr and we can write

Since h = ax

( 2 - 16b)

When cr is fixed, h is functionally governed by x , and integration Eqn 2 - 1 5 gives

2

=

-

(7 1

6qU

+

of

3)

(2- 17a)

(2-17b) The negative sign in the solution comes from the fact that the sense of U is opposite to the sense of x . Substitution of a x for h in Eqn 2-17b and integration gives p=6qU

(’

T + -

a x

k3 32+k4) 2cr x

From the boundary conditions that p is zero when x is x 1 or x2, together with x 1 = h1/a and x2 = h,/cr, we get

2hlh2 fig=--

hl

+

h2

1

(2-20)

Figure 2-5 is a plot of the pressure distribution as a function of the fractional distance x/B for a plane slider bearing of length B = 50.8 mm, angle of inclination a = 0 . 0 0 0 1 4 5 rad, minimum film thickness h2 = 7.62 urn, sliding with a velocity U = 8.13 m / s and lubricated with an oil of 0 . 0 7 3 Pa-s viscosity.

16

60

I

0

0.2

I

0.4

I

0.6

I

0.8

1.0

X/B

Figure 2-5. Pressure distribution f o r plane slider bearing. Length 8: 5 0 . 6 mm. Width L : 50.6 mm. Velocity U : 6.13 m / s . Angle a : 0 . 0 0 0 1 4 5 rad. Minimum film thickness h 2 : 7.62 urn. Viscosity q: 0.073 Pa-s.

Load Capacity of the Plane Slider Bearing

2.3.2.

The load carried by the bearing is the product pressure and the bearing area and is given by

W

=

of

the

integrated

i Jh l pdx h2

An equivalent expression is

(2-21 b)

The first term of the right-hand side of Eqn 2-21b is zero because p zero at both x 1 and x 2 . By evaluating dp/dx from Eqn 2-17a we obtain

is

hl xdx

(2-22 ) Then by using the relation

h2(a h = c u x =

-

1) X

B where a = hl/h2, first to s o l v e Eqn 2-22 in cerms of h and eliminate a we get f o r the load capacity of the bearing

(2-23)

and then to

(2-24a)

17

An equiva ent expression in which

w=

01

is retained is

6qUL

2

(2-24b)

Either of the two equations above can be used to explore the effects of changing the angle of inclination 01 and of reducing the minimum film thickness h 2 on load capacity. From a practical point of view, the minimum safe film thickness h 2 for a given value of 01 must be compatible with the surface roughness of the bearing members and be larger than the particle sizes of contaminants which might be carried along by the lubricant. 2.4.

ENERGY LOSSES IN THE HYDRODYNAMIC LUBRICATION OF BEARINGS

In the expressions for bearing lubrication we have examined so far, the viscosity of the fluid was an important parameter in determining the separation between the moving surfaces. Unfortunately from an engineering point of view the viscosity also represents an irreversible consumption of energy in shearing the fluid. The result is a loss of useful energy and heating of the bearing. The bearing engineer usually treats this energy consumption either as a frictional l o s s or a s a power loss. To calculate friction from the Reynolds equation, we begin by differentiating Eqn 2-8 with respect to y, keeping in mind the restrictions imposed on p which make d p / d x a simple derivative:

Using this result in Eqn 2-3 gives TX =

2 (y - $

-

T1

+)

(2-26)

The total frictional force is

(2-27)

In the plane slider bearing the shear stress on the surface y = h is with the convention used for the direction of the velocity give the expression below for the frictional force in the oil film between two surfaces: ( T ~ and ) ~ on the surface y = 0, ( T ~ ) ~ .These conditions, together

fh,o = L J h l h2

(2 $

+

i)dx

On introducing Eqn 2 - 2 3 for the relation between h and x into Eqn 2 - 2 8 and then integrating each term by parts,

18

(2-29) Replacing B by its equivalent in Eqn 2-23 gives us Fh,o =

w 2

VULU

+

-

(2-30)

ci

The first term is the horizontal component of the vertically integrated pressure acting on the shoe. The second term is the viscous frictional shear in the oil film and is the one that is dominant in lubricated siiding systems which can be treated by the Reynolds equation. Another way to treat the loss problem is to compute the power which is lost as the product of friction force and the shearing velocity at the I f the force is in newtons and the velocity in meters moving boundary. per second, the power loss is in watts. In English engineering units, if the force is in ibs and the sliding speed in inches per second, the loss expressed as horsepower is: H(horsrpower) =

2.5.

F(lbs) x U(in/s) 6600

THE PIVOTED SLIDER BEARING:

DESIGN VARIABLES

In optimizing the design of a bearing the object usually is to have the system carry a designated load while losing the least energy in shearing the lubricant and to tolerate sudden overloads should they be expected. One way of increasing the load-carrying capacity of a slider bearing system is to increase the viscosity of the lubricant. But, as examination of Eqns 2-24b and 2-30 reveals, this increases energy loss by

Figure 2-6. Pivoted slider bearing with diagram of pressure profile in lubricant film.

19

shear of lubricating fluid. The problem of flexibly meeting the varying needs of slider bearing geometry can in part be solved by designing a bearing shoe which pivots about the proper point. Figure 2 - 6 shows the basic features of a pivoted slider bearing that adjusts automatically to partially compensate for changing operating conditions. The integrated moments about the peak of the pressure distribution will act on the shoe to maximize the load capacity. The shoe is held in position by the equilibrium between the load it carries and the counterthrust generated by the flow of the lubricating fluid. Each element of thrust has a moment with respect to the origin of the coordinate system such that

xw

=

Jh' pxdx (2-31)

h2

where 2, the center of pressure, is the r-coordinate at which the total load would act if it were ali concentrated at that location. There are the various notations in which the solution to this problem is written; one shown below is adapted from that of Pinkus and Sternlicht 1 3 1 : x =

8

ad

- 1

-

2a e n a

-

( a 2 - 1 ) en a

2[

a2 - 1

2a

-

( a 2 - 1 ) en a

2(a

2a en

-

-

1)

2

a

2(a -1) 21

The pressure distribution is asymmetric the midpoint of 8, the projected length of designed so that the pivot is located at x p , cording to the load to shift the inclination moments about the pivot. 2.6.

(2-32)

(2-33)

x

and does not coincide with the shoe. If the bearing is the angle a will adjust acof the shoe and equalize the

THE FULL JOURNAL BEARING

A full journal bearing consists of a shaft (journal) surrounded by a bearing having a diameter slightly greater than that of the shaft. Usually the journal rotates and the bearing is fixed, but there are instances of the reverse arrangement. A diagrammatic view of a full journal bearing is shown in Fig. 2 - 7 , with clearance dimensions greatly exaggerated. The clearance space is filled with a film of fluid lubricant, which in practice is supplied externally by means of an oil hole o r the like. When operating under load the shaft moves into an eccentric posiNote that there is a tion relative to the bearing, as shown in Fig. 2 - 7 . "converging geometry" over the left lower-half of the bearing and a "diverging geometry" over the right lower-half. The lubricant film in any practical journal bearing is very thin relative to the radius of the

20

Figure 2 - 7 .

The full journal bearing.

bearing, which satisfies one of the basic assumptions for the validity o f the Reynolds equation. 2.6.1.

Application of the Reynolds Equation to the Full Journal Bearing

In applying the Reynolds equation to a real bearing, the film thickI n the ness h is expressed as a function of position in the bearing. journal bearing this is done as follows. Let n be the radius of the shaft and let us define the radial clearance c between the shaft and the bearing by the relation JL +

c =

O'A

as shown in Fig. 2 - 7 . The eccentricity of the journal when the bearing is in operation is defined as

e

=

00'

I t can be shown that the following relation is valid: h

= c +

e cod e

(2-34)

where the meaning of c a n 0 is apparent from Fig. 2 - 7 . I t is convenient to use the non-dimensional quantity E = e / c , which is generally called the eccentricity ratio or the attitude of the journal. Equation 2 - 3 4 then becomes h = ~

( +1

E

can

e)

2-35)

Equation 2 - 3 5 gives the thickness of the oil film in a journal bear ng at any point in terms of the angular distance of that point from F, where the film thickness is at a maximum (Fig. 2 - 7 ) . To use the Reynolds equation for a journal bearing

we

change

from

21

Cartesian to polar coordinates as follows: x = he

(2-36a)

d x = ad8

(2-36b)

whereupon Eqn 2 - 1 5 becomes (2-37

On integration with respect to 0 , (2-3Ba

where k,

is a constant of integration.

Evaluation from Eqn 2 - 3 5 gives

(2-39)

Equation 2 - 3 9 cannot be readily solved as it is written. Osborne Reynolds obtained a solution for it in the form of a Fourier series which converges for eccentricity ratios less than 0 . 5 and is therefore useful only for lightly loaded bearings. The exact solution of A . Sommerfeld, details of which can be found in most of the standard texts on hydrodynamic lubrication of bearings, yields the following expression:

(2-40)

where po is the pressure when 0 equals zero. From Eqn 2 - 4 0 by various treatments one can obtain information of engineering value, such as the distribution of pressure around the bearing, the response of journal attitude to load, the load-carrying capacity of the bearing, etc. Details of how such problems are handled can be found in texts specially devoted to the analysis and operation of bearings. 2.6.2.

Friction in the Full Journal Bearing

T o calculate the friction in a full jol;rnal bearing we have recourse to Eqn 2 - 2 6 , using the fact that at the surface of the journal the velocity is U and g = 0. The tangential stress at the journal surface is then (2-4 1 )

Changing to polar notation (see Eqns 2 - 3 6 ) gives

22

(2-42)

The friction force at the journal due to shear of the fluid is 2n

F , = Jo ~ , L n d e (2-43)

where L is the length of the bearing. This integral is evaluated by the use of Eqn 2 - 3 5 for h and the Sommerfeld treatment for d p / d e . An example of the type of solution thus obtained is given below:

(2-44)

The load carried by the bearing is obtained by integrating the pressure over its surface and setting the result equal to the force acting perpendicularly to the line 00' joining the centers: W sin B

=

J

2n

Lap s i n

8

de (4-45)

0

where B is the attitude angle of the journal. done by parts to yield

The integration can be

(2-46)

By our assumption, $ = n / 2 ;

hence

E

2 2 1/2 ( Z + E ) ( l - E )

(2-47)

The ratio F . / W consequently reduces to j

where 1 is a dnic.tion d a c t o n and not a coefficient of friction. Equation

2-47

can be transformed to

(2-49)

where N is the rotational velocity of the with U . On defining the quantity

p=-

journal

in

units

consistent

W 2hL

(2-50)

23

and substituting into Eqn 2 -49 ,

($; =

(2

+

E

2

)

(1 -

12n

2

E

we get

2 1/2 )

(2-51)

E

The dimensionless quantity

(2-52)

is known as the Sommerfeld number. function of the journal attitude.

As

is evident from Eqn 2-51, it is a

However, the assumption which gave us Eqn 2-47 is physically unA more rigorous approach, details of which can be found in realistic. the monograph by Pinkus and Sternlicht, enables the computation of the attitude angle B . Numerical methods are used for the most part. Once a value has been obtained for B the value of E is easily calculated. I t is customary to insert the value of E thus found into Eqn 2-51 to calculate the Sommerfeld number, although, as Pinkus and Sternlicht show, a more realistic relation is

(2-53)

where X ' is obtained by using Eqn 2-46. By plotting the quantity Xlnlcl against S as calculated by the righthand side of Eqn 2-52 the influence of various operating parameters found on the left-hand side of Eqn 2-52 can be evaluated by hydrodynamic theory. Curve A in Fig. 2-8 is a typical example of such a plot. But it

0

0.10

0.20

0.30

0.40

Figure 2 - 8 . Comparison of theoretical and experimental for the full journal bearing.

friction

curves

24

should be kept in mind that for physical reasons the quantities shown in Fig. 2 - 8 are not independently variable. For example, an increase in ~1 while N and P are kept unchanged does not necessarily mean an increase in S because c will also increase and make the ratio h l c decrease. Therefore the operation of each bearing must be explored by an adequate set of calculations, the effect of each parameter being evaluated in turn. The observed behavior of journal bearings shows a strong departure from that plotted in Curve A of Fig. 2-8. In actuality the value of X ( h / c ) rises very sharply in the low-value domain of the Somrnerfeld number, as illustrated by Curve B. The gently increasing course of the curve to the right of the minimum is ascribed to fluid film behavior which conforms with the predictions of hydrodynamic action. The sharp rise in X [ h / C ) to the left of the minimum is associated with marginal or boundary lubrication behavior: i . e . , the surfaces of the journal and the bearing are no longer separated by a full fluid film. Calculation of the Sornmerfeld number from the design input of a bearing is often a tedious process. Hence, in engineering investigations the coefficient of friction p is obtained from the measured friction force at the bearing surface, the dimensions of the bearing and the load it caris plotted against the factor I Z N I I P , where Z is ries. This measured the viscosity of the fluid in centipoise, N is the journal speed and P is the load per projected unit area of the bearing. In common practice N is in revolutions/minute and P in lb/in2. A set of such plots is shown in Fig. 2-9.

0.0024 c

0

.- 0.0016

t u0

c

c

.~0.0008 .. uc 0)

0

0

6 8 10 12 ZN P Experimental plots of coefficient of friction v n . ( Z N / P )

0

2

4

-

Figure 2-9.

the

Although the mixture of units in the factor I Z N l l P is not logical, course of the curves in Fig. 2-9 resembles Curve B in Fig. 2-8. The

25

interpretation of experimental curves such as B in Fig. 2-8 can reasonably be related to calculated curves such as A . By analogy, then, it is not difficult to relate the similarities between Curve B in Fig. 2-8 and the curves in Fig. 2-9. Thus critical examination of empirical [ZNIIP curves can yield useful information about the lubrication of bearings. In the steeply rising part of the curve, v responds sensitively to changes in any one of the factors comprising the quantity lZNl/ P. An increase in journal speed, a decrease in load or an increase in the viscosity of the lubricant will shift the operation of the bearing to the safe side of the minimum in the [ZNl/P curve.* To the right of the minimum v increases rather than decreases with increasing IZN)/P but the rise is much gentler than to the left of the minimum. Increase of u with increase of speed or load is readily understandable. The inverse effect of load on p may seem illogical, but it should be noted that in the hydrodynamic region a decrease in load permits greater film thickness; i.e., there is more lubricant to be sheared viscously. Therefore an attempt to introduce a margin of safety into the bearing operation by increasing the viscosity of the lubricant with the object of increasing film thickness will not necessarily succeed. The heat generated in the hydrodynamic film, in part governed by its thickness and in part by the viscosity of the lubricant, is dissipated to the surroundings by conduction, convection and radiation. The bearing will accept a share of this heat and attain an equilibrium operating temperature. There are some feed-back effects also to be considered , such as the influence of the equilibrium bearing temperature on the viscosity of the lubricant in the hydrodynamic film. The detailed treatment of such problems is complex and arduous, and the reader is referred to the the specialized texts, monographs and periodical literature on hydrodynamic bearings. REFERENCES 1.

2. 3.

4.

B. Tower, Proc. Inst. Mech. E n g . , 34 (1883) 632 i b i c l . , 36 (1885) 5 8 . Reynolds, Phil. Trans. Roy. S O C . London, 177 (1886) Part I , 157-234. 3 . Pinkus and B. Sternlicht, Theory of Hyd odynamic Lubrication, McGraw-Hill, New York, 1961, p. 58. 0. Pinkus and B. Sternlicht, up. ci R . , Chapters 3 and 4. 0.

*There are realistic limitations to such reasoning. For instance, i f the speed of the journal is in an extremely high domain or if the bearing is severely overloaded, one would not observe the sensitivity of response to amelioration of the other operating parameters as anticipated from the general trend of the plot of against iZNl/P.

26

APPEND1X The application of the Reynolds equation, even in its simplified twodimensional version, to specific bearing problems generally requires detailed, laborious computational treatments to arrive at usable solutions. The foregoing presentation in this chapter is intended to give the uninitiated reader an idea of the basic concepts of hydrodynamic lubrication. The limited space allotted to the subject does no: permit an extensive exposition. A large array of books and periodical literature is available to the student who wishes to develop skill in the fluid film aspect of lubrication engineering. A few of the texts and monographs which treat hydrodynamic lubrication and related problems in detail are listed below. E. I. Radzimovsky, Lubrication of Bearings, Ronald Press, New York, 1959. A text on the principles of hydrodynamic lubrication and their application to bearing problems; for the undergraduate engineering student.

A. Cameron, Principles of Lubrication, Longmans, Green and Co., don, 1966. This is also a text for the undergraduate student.

Lon-

M. C. Shaw and E. F. Macks, Analysis and Lubrication of Bearings, McGraw-Hill, New York, 1949. Suitable for the practicing engineer as well as the graduate engineering student. 0. Pinkus and B. Sternlicht, Theory of Hydrodynamic Lubrication, An advanced monograph in which many McGraw-Hill, New York, 1961. types of bearing problems are treated in extensive detail.

J. Boyd and A. A. Raimondi, Hydrodynamic Lubrication-Fundamental Requirements, Chapter 3 of Standard Handbook of Lubrication EngineerA digest ing, J. J. O'Connor, Editor, McGraw-Hill, New York, 1968. of the principal simple formulas of hydrodynamic lubrication.

21

Chapter 3

SOME ADVANCED ASPECTS OF HYDRODYNAMIC LUBRICATION

In Chapter 2 the Reynolds equation was derived directly from an engineering model. However, as a matter of history, Osborne Reynolds derived the equation which bears his name from the Navier-Stokes relations by making certain assumptions and simplifications. The NavierStokes equations are the general dynamic relations applicable to that special class of fluids which possess the property of viscosity. But in the broad view, hydrodynamic lubrication is only a small, highly specialized portion of this particular branch of fluid mechanics. The logical path that leads from the fundamentals of the dynamics of a fluid to hydrodynamic lubrication is too long and too involved to be rigorously presented here. Since some knowledge of the background of hydrodynamic theory is desirable, a brief synopsis will be given in this chapter. 3.1.

THE CLASSICAL FLUID

The fundamental property of a classical fluid, to cite Lamb's treatise on hydrodynamics [ I ] , is that it cannot be in equilibrium in a state of stress such that the mutual action between two adjacent parts is oblique to the common surface. In other w o r d s , the only stress that a surface of an element of fluid at rest can sustain is a normal pressure. Pressure oriented other than normally can be resolved into a component perpendicular to the surface and a tangential component, the latter of which will induce motion. One of the fundamental distinctions between the response of an elastic solid and a classical fluid to tangential stress is that there is a limited displacement within the solid which is proportional to the stress whereas the motion of a fluid continues as long as the stress is maintained. 3.1.1.

Stress Analysis of a Fluid

Let us select a point P within the body of the fluid located with respect to the Cartesian coordinate axes as shown in Fig. 3-1. We construct the plane ABC with direction cosines l , m and n relative to PA, PB, and PC. On applying the stress analysis to be found in any standard text on elasticity or rheology [ 2 ] , we obtain the orthogonally oriented system of stress components illustrated in Fig.3-1, where a symbol of the form aL denotes a tensile stress normal to the plane of reference, and a symbol T . . denotes a shear stress in that plane. Lcj

28

Figure 3-1.

Stress components in the body of a fluid.

Let F n be the resultant force acting outward nornal to the plane ABC, whose area we shall designate a s A . Then the areas of the faces PCB, P C A and P A B are LA, m A and nA respectively. The x-component of F n can be found by equating i t to the forces acting through and along the face PBC, as follows:

The components F Y and F 2 are found from similar relations, and dividing through by A then gives

Thus i f we know the six components of stress at a point P in the body of the fluid, we can calculate the components of the stress in any orientation by Eqns 3-1. Let u s examine the motion of the fluid in response to these stress I n general, i f the velocity components are u , v , and f i t at components. the point x , g , z , then the components of the velocity increment at x + A x , y + 6y, z + 62 are

(3-2a)

(3-2b)

29

a#

6lLj

- bx ax

=

+

a 11;

a U'

ay

az

- 6y + - 6z

(3-2c)

When we use the following notation: a = -

aw

au

c = -

az

ax aw

aw

ay

az

bl=--+-

au

aw

az

ax

d2=-+-

aw aw 51=--ay az

aw au 6 3 = -ax+ - ay

av au 5 3 = -ax- - ay

Eqns 3-2 become

The formal conversion of Eqns 3-2 to Eqns 3-3 is straightforward s u b stitution and simplification. The theoretical basis for this transformation as given in the treatment by M. Reiner [31 is in tensor matrix notation, the physical significance of which requires considerable experience to see. Let us therefore examine the parallelism between the expressions for elastic displacements of solids and for the flow of fluids. The flow derivatives in the expressions for a , b , c , etc. can be regarded as displacements occurring in the time interval 6 t . Consider a point 0 (x,y,z) in the body of the fluid and a neighboring point 0' a distance h away, as shown in Fig. 3-2, such that 6x =

Lh,

6y

=

mn,

Figure 3-2.

6z

= nh

Orientation of the flow vectors in a fluid.

30

While 0 is being displaced by the flow components u , v , w in the time interval 6 t , 0‘ is being displaced by the components u + 6u, w + 6v, w + 6w. The net effect is elongation of the element: and if we define 5 as unit elongation, then au

au

6X

+

-

6y

+

(

av

6g

+

+

-

av

6X

+

ax

- 6z az

ag

- 6g a9

+

-

62

az

aw

(3-4)

2Z

After dividing through by n 2 and using its components, remembering that second order infinitesimal quantities such a s squares and cross-products can be neglected, we eventually arrive at

By analogy with the treatments of strain as given in the texts on elasticity 1 2 1 , we define a radius vector to the point x , g , z such that k

9n substituting the appropriate equivalents into Eqn 3-5 we get k

k2

=

ax 2

+

by2

+

cz

2 +

dlgz

+

d2xz

+

d3xg

(3-6)

The physical meaning of Eqn 3-6 is this: as the plane ABC (c6. Fig. 3-1) rotates about the point P, the end of the vector R will always lie on the surface of the second degree given by Eq 3-6. I f the x - , g - and z-axes are chosen so that the cross-products disappear, then f k 2 = ax

2

+

by2

+

cz

2

(3-7)

and an element of volume with its center at x , g , z will not be subjected to any shearing velocity. But any other choice of axes introduces crossproducts in g z , xz, and xy, and the element will be subjected to the shearing velocities denoted in Eqn 3-6 by d , , d 2 and d 3 . Analysis of shear strains, which can be found in a standard text on elastic theory [2], shows that they result in rotations of linear elements along the lines of shear; hence an element of volume will experience rotations whose components are g l , g2 and y 3 . But, a s demonstrated by Reiner [31,

31

the expressions which define y , , y 2 and y 3 describe rotation of an element without deformation, and rigid rotation is of no interest in rheology. Hence in dealing with simple fluid behavior one can set y , , g 2 and y3 equal to zero, thus restricting this particular treatment of fluid flow to irrotational motion. Let us now examine the formulas of transformation necessary to deal with cases where the coordinate system for the equations of flow is not identical with the coordinate system for the stress components. At the point P let x ' , y' and z' be in the directions of the principal axes of distortion a s defined by Eqn 3-7 and let a', b', and c ' be the partial derivatives of flow along these axes. Let x , y and z be a set of orthogonal axes whose orientation is given by the matrix of direction cosines shown below: , x

Y

By the familiar transformations of vector analysis

By carrying out the analogous transformations f o r aw/ay and alu/az it will be seen that

b

= m2 l a ' + m2b' 2 + m2 3ct

c

=

2 n,a'

+

2 n2b'

+

2 n3c'

From the properties of direction cosines it follows that + b + c = a '

+ 6' +

c'

(3-9)

Expressions of the form aui

avi

awi

axi

ayi

azi

- + - + -

give the rate of dilation (the "expansion") of the fluid. From Eq 3-9 we see that the dilation remains unaffected by a change in the orientation of the coordinate axes of the system.

32

Application of the transformation relations to the shearing motions is exemplified below:

On carrying the complete transformation through we get

h2 d3

3- 10a)

+

m2n2b'

+

m3n3c')

(

= 2(Llnln' +

L2n2b'

+

L3n3c')

(3-lob)

2(Llmla'

L2m2b'

+

L3m3c')

(3-10~)

/J1 = S ( m l n l a '

=

+

I t is apparent that since x', y' and z' are the directions of the principal axes, the forces exerted at P per unit area across the y ' z ' , x'z' and x'y' planes in the directions of the deformations must be perpendicular to these planes. Let us denote these forces by o l , o2 and o 3 respectively. Let us take a triangular plane and orient it perpendicular to the x - , g - or z-axis, as the case may be. Thus i f the plane is perpendicular to x and its area is A , resolution of this area on the planes On adding y'z', x ' z ' and x'y' will give e l & , [,A and 1 3 A respectively. up all the forces parallel to the x-direction which act on a plane A'B'C' situated with respect to the axes x ' , y ' , z' as ABC is with respect to x , y , z (see Fig. 3-1), we find that

external impressed forces and acceleration forces being omitted. plying this analysis to the y - and z-directions as well, we get

ox =

o l e2l 2

Oy = o , m l

2 aZ = o l n l

2

+

+

a2L2

2

+

03L3

+

03m3

+

+

03n3

2 02n2

(3-1 la)

2

2 02m2

On ap-

(3-llb)

2

(3-llc)

and from the properties of direction cosines we get ax

ay

+

+

oz

=

al

+

o2

+

a3

(3-12)

I n a similar fashion we can derive the formulas below for the transformation of the shear forces from the coordinate syscem x ' , y ' , z' to the system x , y , z. T

YZ

T~~

=

almlnl

+

02m2n2

+

03m3n3

(3-13a)

=

olL,nl

+

02L2n2

+

a3L3n3

(3-13b)

33 T XY

o l L l m ,+ 5 2 k 2 m 2

=

+

a3L3m3

(3-1 3c)

The six components of stress given by Eqns 3-11 and 3-13 are sufficient to specify the stress on any set of mutually orthogonal planes y z , xz and x y in the immediate neighborhood of the point P. 3.1.2.

The Simple Viscous Fluid

The derivation of Eqns 3-11 and 3-13 followed the conventions of elastic theory: 0 . denotes tensile stresses, the positive senses of A which are oriented as shown in Fig. 3-1, where the positive senses of the shear components T . are also shown. The sense of a pressure component Af It follows from Eqn 3-12 that is that of a negative tension: 0 . = - p, A. whatever the orientation of the orthogonal coordinate axes is, the presFor the sure at point P in the body of the liquid remains unaffected. case of the ideal non-viscous fluid pi = p = pk for the components of 9 pressure, whatever the orientation of the coordinate axes with respect to P may be. From Eqns 3-1 we see that f o r such a fluid the shear stresses must be zero.

.

Since hydrodynamic lubrication depends on the behavior of real fluids with the property of viscosity, we cannot overlook the influence of shear stresses in the lubricant fluid even though they may be small compared to the normal pressures in the fluid. Each orthogonal component of tension, 0 . will differ from - p by quantities depending on the motion A' of distortion, which, as we have seen, are functions of G , b , and c only. Let us postulate that these functions are linear and write out the following relations [41:

ox

=

-p + i ( a + b + c ) + 2qG

(3-14a)

0

=

-p + i ( a + b + c )

(3-14b)

Y

o Z = -p

+

xta

+

b

+ c)

+ 2qb +

2qc

(3-14c)

TZX = 62

(3- 14e)

T x y = 63

(3-14f)

The postulate used in formulating the equations above is not wholly arbitrary: the format of these equations has a close analogy with the stressstrain relations for hydrostatic pressure in an elastic solid [51, the linearity of which follows directly from Hooke's law. The sum of the stress components a x , 5 and o Z Y' 3-14c e q u a l s -3p, from which it follows that 3x

+ 2q =

0

in

Eqns

3-14a

to

(3-15)

On writing out the partial differential equivalents, Eqns 3-14 become

34

ox

0

Y

0,

T YZ

=

-p -

= -p

=

av aw ;, i” + -+ \ax ay az

2 - 7,

- p - 7,

=,I-+-

ay

ag

az

au av - + - + ax ay

aw

az

(3- 16a)

ax av

(-+-+‘ax

aL:

azl

(3-16b)

aw

+ 2 n -

az

ZY

The quantity TI is the absolute o r dynamic viscosity of the fluid. derived here, viscosity is an adjustment to the hydrodynamic equations relating stress and flow in a fluid to make them f i t a postulated mode of behavior. But, a s shown in Chapter 4 , viscosity can also be defined will be used for directly in terms of a physical model. The symbol dynamic viscosity throughout this book in conformity with the usage of most of the modern texts on rheology and physical chemistry: in texts on hydrodynamics and fluid engineering viscosity is generally denoted by the symbol p. But is also widely used as a symbol for coefficient of friction, and the persistent retention of this symbol f o r viscosity by engineers reflects their interpretation of Newton’s original definition of viscosity as internal friction i n the liquid: “the resistance which arises from lack of slipperiness in a fluid-other things being equal - is proportional to the velocity by which parts are being separated from each other.”* At first glance it might seem that the resistance to shearing motion experienced by a plane element in a viscous fluid has more than a superficial resemblance to the resistance to shearing motion when a tangential force is applied to one solid resting on another. However, viscosity is the ratio between shear stress and the resulting velocity gradient-whether defined a s in Eqns 3-16 o r directly from a it has the dimensions physical model ( c 6 . Chapter 4, Eqn 4-1)-and ML-~T-’. Thus, viscosity is not a force o r a dimensionless ratio, and analogies between it and mechanical friction can lead to unfortunate conc l u s i on s. As

,

iResistentiam, quae oritur ex defectu lubricitatus partium Fluidi, caeteris paribus, proportionalem esse velocitati, quae partes Fluidi separantur ah in vicem. Isaac S. Newton, Philosophiae Naturalis Principia Mathematica, 1st Ed., 1687, Book 2 , Section IX.

35

3.2.

THE NAVIER-STOKES EQUATIONS

Having developed the relations between the components of stress and the components of velocity at a given point within the body of a simple Let viscous fluid, let u s consider the dynamical equations of motion. the center of the rectangular element 6 x 6 ~ 6be~ at the point x , y , z. Resolution of the internal forces parallel to the x-direction gives a traction of (aox/ax)6x*6y6z due to normal stress on the yz-plane and traction of ( 2 1 /ay)Gy*6xSz and (aTzx/az)6z*6y6x due to tangential XY stresses on the zx-and xy-faces respectively. To these force components must be added the component of external forces, pX6x6yGz where p is the density of the fluid. The sum of these forces must equal the force components given by p(Du/Dt)GxGy6z. Similar analyses can be carried out for the y- and z-directions, giving us Du

p

Dt

Dv

= px

aoX + -+ ax aT

p-=py+-+-+-

Dt

Dw p - =

Dt

XY

ax a1xz pz + - + - + ax

aTXY

a1xz

ay

az

-+ aay ay a1

YZ

ay

aT

( 3 - 17a)

YZ

az

(3-17b)

aoZ

az

(3- 1 7 ~ )

With the aid of Eqns 3-16, Eqns 3-17 can be reduced to a s e t of relations involving only the internal pressure p and the three components of velocity, u , v, and W.

(3-18a)

36

These are the general Navier-Stokes equations in Cartesian coordinates. There are only three equations for the four variables p , u , w , and w, but a fourth elation is supplied by the continuity equation: ap

a(pu

(3-19) I f the fluid is an incompressible liquid, a p / a x = 0, and

au ax

;jv

aw

ay

az

+ - + - = o (3-20)

Equations 3-18 can be simplified considerably by applying some restrictions derived from the physical properties of the fluid and the geometry of a lubricating film. These reduce the Navier-Stokes equations to a set of two differential equations from which a generalized version of the Reynolds equation is obtained. 1.

The height y of the fluid film is very small compared to the length of bearing action in the x-direction and the width of the bearing in the z-direction. Thus, in the case of curved bearing surfaces the curvature of the fluid film can be ignored and the Navier-Stokes equations in Cartesian coordinates can be used.

2.

There is no variation of pressure across fluid film, so that a p / a y = 0.

3.

The flow is laminar; there anywhere within the film.

4.

No external forces act on the film, so that X

5.

Fluid inertia (acceleration forces, centrifugal forces in curved films, fluid gravity) i s negligible compared to viscous shear and hence UulUt = U w I D R = h l U t = 0.

6.

There is no slip at the bearing surface.

7.

all Compared with the two velocity gradients au/*dy and aw/’ay, other velocity gradients are negligible. This assumption would not be valid without assumption 3 . Derivatives of higher order of all velocity gradients other than ;lu/ay and a w / a y and with respect to variables other than y will drop out.

is

no

the

thickness

of

the

vortex flow or turbulence

=

Y

=

Z = 0.

Since ap/ay = 0 and Eqn 3-18b contains no second-order differentials that do not drop out, this equation disappears from the scene entirely. What remains of Eqns 3-18a and 3-18c yields the following two relations: 2 .,ap-au

(3-21a)

37

Details of the derivation can hydrodynamic lubrication 1 6 1 . 3.3.

be found in a specialized monograph on

ThE GENERALIZED REYNOLDS EQUATION

Equations 3-21 can also be obtained from a direct engineering analysis of the forces on an element of fluid. Consider an element of fluid d x d y d z with its center at the point x , y , z . By summing up the forces i n the x - and z-directions (Fig. 3-3)* we get

aTz

( T +~ - __ d x ’i d y d z ax

aTz

( T +~ 3 - d y ) d x d z ay

+

(3-22b) which simplifies to

aTx

ap

- + - = ay az

ax

ZT,

aTz

- + - = ay ax

( 3-23a )

ap

az

(3-2333)

By introducing the relations for Newtonian viscosity du T

x

=

n

G

dw T z = q Z j

(3-24a) (3-24b)

we obtain

*The symbology of Eqns 3-22, 3-23 and 3-24 has been simplified strict tensor notation, since the meaning is clear from Fig. 3 - 3 .

from

38

Figure 3-3.

‘oLu

aLu

ap

- + - = - -

ay2 ayaz 2 2 aMi aLo -++ay2 axag

Forces acting on an element of fluid.

ax

TI

1 az

( 3-25a )

(3-25b)

On making use of assumption 7 which was employed in simplifying the Navier-Stokes equations (Section 3.2), the second term of each left-hand side of Eqns 3-25 drops out, leaving them identical with Eqns 3-21. By integrating Eqn 3-21a twice, using the boundary conditions u = U , at y = 0 u =

U2 at y

=

h

we get

(3-26) In the integration of Eqn 3-21b we use the boundary conditions UJ = 0 at y = 0 and at q = h , which implies that the bearing surfaces move only in the x-direction. We then get

(3-27) For a f l u i d whose density does not change with time the continuity equation can be written as

39

a(pu) --

a(pw)

- = -

a(pw)

ax

ay

az

(3-28)

Using the values of u and w given by Eqns 3-26 and 3-27, we get

a

h - g

ax

( 3-29)

Integrating with respect to g, with w gives

U at y

=

=

0 and v = 0 at

g

=

h,

(3-30) Since the upper limit h i s a function of the coordinates x and z, we can u s e the same mathematical device employed in deriving the simple Reynolds equation and perform the integration before differentiating to give

a (ph)

U2) ax

(U, -

+

(3-3l a )

which rearranges to

+ 6ph - ( U ,

+

U2)

+

12pV

ax

(3-31b)

It can be demonstrated by an analysis of

the

journal

bearing

[71

that

h

0

6ph - ( U , + U 2 ) + 12pV

ax

2

12p -

V

+ 12pV

R

where R i s the radius of the journal.

(3-32a) Equation 3-32a can be written a s

40

a

6pk - ( U , +

U2)

+

12pV

(3-32b)

ax

Since h/R is a quantity very much smaller than 1 , usually of the order of G.001, it follows that 6ph[a/ax(Ul + U2)l must also be very small and therefore can be neglected. The final form of the generalized Reynolds equation then becomes ;r (ph3 - -ap) 2x ax

+ -a - -( p h 3 a l - . \ ;z

Tl

a2

/

a(ph) = 6 ( U 1 - U2) -

12pv

2X

(3-33 1

For the case where the bearing surface s stationary and only the slider or the shaft is moving, the generalized Reynolds equation

(3-34)

Equation 3-34 holds for both journal and thrust bearings, and the velocity V 0 refers to the normal component that results from the motion of the shaft or the slider under a fluctuating load or non-steady state operation. For steady loading and an incompressible fluid, V o equals zero and p is constant, so that

(3-35)

SQUEEZE FILMS

3.4.

The squeeze film effect is the load-carrying capacity exhibited by a film of fluid between two surfaces which approach each other directly, in contrast to the dynamic film lubrication generated by sliding surfaces. A simple, easily visualized example is the case of a non-rotating shaft whose center moves linearly towards the center of an oil-filled journal bearing, as diagrammed in Fig. 3-4. It can be shown [81 that when Eqns 3-26 and 3-27 are integrated for the volume flow between the two surfaces and the results are transformed to polar coordinates, we get for a nonrotating shaft in a bearing of length 1 o = - - -

lh3 d p

1 2 v R d6

(3-36)

A l s o , from Fig. 3-4 the flow at any 8 due to the velocity V is

Q

=

v

L R nin 6

Combining these two equations and integrating we get

(3-37)

41

Figure 3-4.

Geometry of squeeze film in journal bearing.

where c h is the radial clearance of the bearing, E is the eccentricity ratio, and C , is an integration constant. When Eqn 3-38 is integrated to give the load W for a full bearing and V is replaced by its equivalent c n ( d ~ / d X ) we , obtain

(3-39) which when integrated again yields AX =

12nnLR

El

(3-40)

Equation 3-40 is the expression for the squeeze film behavior of a rotating shaft under a dynamically fluctuating load. In the time interval A t = t2 - t l , under the load k' the shaft changes from attitude c 1 to attitude c 2 . The influence of various parameters such a s rate of load cycling, rate of rotation, radial clearance, etc. must be explored numerically. The development above has been simplified to illustrate the principle involved. Detailed treatments of journal bearings with dynamically fluctuating loads can be found in texts by Pinkus and Sternlicht [8] and by Shaw and Macks [ 9 1 . Booth and Hirst [ l o ] examined the squeeze film problem for two rigid circular parallel plates of radius ho separated by an oil film of thickness h ( h < < h o ) ; see Fig. 3-5. Starting with the Navier-Stokes equations in cylindrical coordinates, they obtained the relations

Figure 3-5.

Cylindrical coordinate notation for squeeze film geometry.

(3-4la)

(3-41 b) dropping written as

the

by

inertial

force terms.

The equation of continuity was

These equations can be simplified. and solved; the original publication can be consulted for details. For an isoviscous liquid the integrated solution yields the Stefan equation: 4 3nnho dh

w=--

2h3

dt

where d h / d t 3.5.

13-43) =

V.

ELASTOXYDRODYNAMIC LUBRICATION

Journal bearings are conformal: that is, the curvatures of both bounding surfaces are in the same sense. It is to this type of geometry that the classical solutions of the Reynolds equation apply. Counterformal configurations are those in which the curvatures of the surfaces are in opposing senses. Rolling element bearings and gear teeth

43

are the two most important examples technology.

of

counterformal

configuration

in

Conformal bearing geometry is associated with the support of large loads by relatively thick lubricant films at relatively low maximum film pressures. Counterformal geometry, on the other hand, is associated with concentrated loading. The Reynolds equation has been solved for counterformal geometry with rigid boundary profiles, but the film thickness computed from these solutions for loads of realistic magnitude are much smaller than required for satisfactory lubrication of machine components o f average commercial surface roughness. However, it is known from operating experience that many heavily loaded counterformal interfaces are successfully lubricated by fluid films even when simple hydrodynamic theory contradicts their existence. I t can be shown that elastic deformation of highly loaded counterformal surfaces increases the area over which the load is distributed and thus reduces the pressure This approach to which a given length of lubricant film must sustain. the fluid film lubrication problem is known as e l a b , t o h q d k u d q n a m i c n . A l though elastic deformation of the bounding surfaces was recognized a s a factor in lubrication theory as early as 1935, the real beginning of Since then the elastohydrodynamics came with the work of Grubin [ll]. subject has developed rapidly and has acquired a considerable body of published literature. 3.5.1.

Elastohydrodynamic Theory

An elastohydrodynamic problem customarily involves the calculation of the pressure distribution in the lubricant film, allowing for the effects of pressure on the properties of the fluid and on the geometry o f the interface. The shape of the lubricant film and its thickness are functionally related to the pressure distribution. The technologically important solutions are for bounding surfaces of counterformal geometry, which in most cases can be approximated satisfactorily by two opposing circular cylinders. For simplicity let us first consider the problem for the following conditions: (a) the displacements of the boundaries are calculated for semi-infinite cylinders in a condition of plane strain; (b the lubricant is an incompressible fluid; (c) thermal effects are neglec ed. The equations to be solved are:

- (- GI d

h 3 dp

dx

TI

TI =

f ( p )

=

6 udhz (3-44)

(3-45) 2

h = h o + - + 2R

4J

(3-46)

44

The first of these is the Reynolds equation in its simplest form: the second equation covers the variation of viscosity as a function of pressure; the third expression gives the film thickness, where R is the radius of the equivalent cylinder and $ is the combined displacement of the two solid boundaries. The equivalent cylinder treatment is a way of generalizing and simplifying the geometry of curvilinear boundaries: i f x is small enough relative to R, 1 1 - = - + -

1

(3-47)

R2

R1

where R , and R 2 are the radii of curvature of the two bounding profiles. I n order to use Eqn 3-45 in conjunction with Eqn 3-44, an explicit expression must be found for f ( p ) . A relation frequently used is the exponential expression

where n o is the reference viscosity, usually at atmospheric pressure, and a is a constant of proportionality. However, as i s shown in the next chapter ( c 6 . Section 4.8.31, there are a significant number of lubricant liquids for which the simple exponential viscosity-pressure relation does not hold, especially at elevated temperatures. Equation 3-48 is used in the development below for the sake of simplicity. Integration of Eqn 3-44 gives

C a pdP -

=

6n0u

iz - h m ( 7)

dx

(3-49)

is the film thickness at the point of maximum pressure. The where h, left side of Eqn 3-49 can be thrown into a more workable format as follows:

(3-50)

where q is designated as the R e d u c e d phe55uhe.

Since 4:

=

0 when p

=

0,

3-5 l a ) 3-51b) In Eqn 3-46 I& i s the combined displacement of the two bounding surfaces a s calculated from elastic theory: 2 $ = - __ i42 p ( 4 ) bn

aE'

4,

(x -

4)2dn

+

conntant (3-52)

45 where

E'

2

\

El

E2

'

E being Young's modulus and u Poisson's ratio.

Figure 3-6 illustrates the displacement of the boundary of the equivalent cylinder by a simple Hertzian pressure distribution through the oil film of thickness h o . The geometrical coordinate x is measured from the center line in either direction. Each element of load p(n)dn along the entire line of the boundary from b , to b 2 acts at the location x to contribute to the normal displacement J, at that location as calculated by Eqn 3-52.

II

Figure 3-6.

I .

Elastic deformation of boundary and thickness of oil film.

The elastohydrodynamic solution requires that Eqns 3-44, 3-45 and 3-46 be satisfied simultaneously. A full analytical solution has not yet been found, but numerical methods have been developed f o r use with the aid of high-speed digital computers. I f the lubricant is a compressible fluid, the factor for its density cannot be dropped out of the Reynolds equation. Instead of Eqn 3-49, we get the following expression on integration:

(3-53) Fo,r further integration the first three terms of a Taylor expansion are used in a step-by-step numerical treatment:

(3-54) where dL4/dxL can be written as

(3-55)

46

The density p must be given as a function of the pressure p , and dp/dx is then replaced by dp/dp-dp/dx. The formidable task of including thermal effects in the elasThe tohydrodynamic problem was undertaken by Cheng and Sternlicht [ 1 2 ] . governing equations are the Reynolds equation and the film-thickness equation, as in the isothermal problem, to which must be added the energy equa t ion : au

2

P

dP

B

dx

(3-56)

where c d is the specific heat of the lubricant in the film, K d is the thermal conductivity of the lubricant, T is the temperature of the film and B is the bulk modulus of the lubricant fluid. The sources of energy (per unit of length and time) are the viscous flow and compression of the fluid as given by the right-hand side of Eqn 3-56. The partial derivative a u / a g is given by ;u

1

dp

- =

--

ay

2 n dx

1

(2y - h )

+

- ( U2 h

-

Ul)

(3-57)

where U 1 and U, are the velocities of the boundary surfaces. The tion of viscosity with temperature and pr ssure is represent d by

T

(3-58)

and the d e n s i t y - p r e s s u r e - t e i n p e r a t u r e

PC A ' + - + - -

3.5.2.

-

function [ 1 3 1 by

T o dp

pCg

po

quantities

no,

1 +

where the tions.

7

varia-

dT po

(3-59) and 7 0 refer to ambient atmospheric condi-

Some Elastohydrodynamic Solutions:

Line Contact

The elastohydrodynamic problem is a physical one and its solution should be thought of in physical terms, the mathematical technicalities notwithstanding. There are two broad cases of interest to the lubrication engineer: (a) "line" contact, i . c . the longitudinal contact of two cylinders or a cylinder against a flat; (b) "point" contact, e . 5 . the contact Of two spheres or a sphere against a flat. Actually, of course, the curved profiles are modified at the contact zone by pressure. Figure 3-7 is a diagrammatic representation of the boundary deformation and the pressure distribution for a cylinder against a rigid flat. Three regions conconcern us: the inlet region, where the fluid transported by the verging boundaries is fed into the pressure zone; the Hertzian region,

47

Inlet Region k H e r t z i o n R e g i o n 4 Outlet Region

Figure 3-7.

Elastohydrodynamic pressure and film profile.

where the pressure distribution and the film profile are dominated by the elastic deformation of the boundaries; and the outlet region, where the fluid returns to ambient pressure. wedeven [ 1 4 ] has published an instructive description of the physical events associated with these three regions. To some extent the way the computation is carried out is governed by the objectives. Usually information about one or nore of the following is sought: pressure distribution in the lubricant film; minimum thickness of the film; shape of the film. Items of input into the problem are load, radii of curvature of the boundaries, material properties (such as viscosity and density of the fluid together with their pressure and temperature dependence, elastic constants of the solid boundary material), and speed. A set of assumed initial conditions is used to

Pressure Y P Cornputing Hydrodynamic Elastic

(A)

Film Thickness

A’

(a) Low Load

(b) High Load Figure 3-8. Computing zones and computational pathways for pressure film thickness. After Dowson and Whitaker E151.

and

48

begin the computation. Grubin's contribution was to assume that the deformed shape of the boundaries of the high-pressure zone is the same as f o r dry contact and that a pressure has been established in the lubricant film at the entrance to the Hertzian zone. Much of the computational technique is concerned with finding iterations that converge to believable terminal values within an acceptable number of cycles and also f i t the transition from one region to the next smoothly. Dowson and Whitaker [ 1 5 1 have reviewed the computational methods for various problems involving counterformal boundaries. The lubrication of an elastic cylinder by a fluid with pressure-dependent properties divides into two cases. For relatively low loads and high speeds the pressure distribution is represented by Fig. 3-8a, which also shows the computational pathway. I n the region on the left, the hydrodynamic treatment f o r a rigid cylinder and an isoviscous, incompressible fluid suffices to compute the pressure distribution and the film profile. But as we go to the right, away from the inlet region, the elastic displacements of the bounding surfaces must be taken into account. The pressure obtained from the initial trial solution is fed into the elastic displacement computation and the result is used to start another cycle. Acceptable convergence is rapid. A s the load increases, so do the computational complexities, a s shown

in Fig. 3-8b. The inlet region is covered by the computing zones 1 and 2 , the region of Hertzian deformation by the computing zones 3 and 4. Zone 5 covers the transition from the Hertzian region and the outlet region. The computations for zone 1 are treated as in the low-load case, but the pressures computed for the junction of the inlet region and the Hertzian region by the pressure distribution and computational sequences

Location on Surface, m m

Figure 3-9. Elastohydrodynamically calculated pressure distribution and film thickness. Load: 100.3 kN/m. Speed 1.3 m/s. Data by Hamilton and Moore [ 1 8 ] .

49

must be adjusted to blend smoothly from zone 2 to zone 3. Computations in zone 4 are governed by the relatively gentle pressure gradients and the high pressure level. The pressure spike at the junction of zones 4 and 5 arises from the physical requirements associated with continuity of flow. The film shape is obtained by solving the inverse elastohydrodynamic the film thickness is calculated from the pressure. problem; i . e . , Figure 3-9 shows a calculated pressure distribution for a moderately heavy load and a slow speed, together with the corresponding profile of the film thickness. The pressure curve exhibits significant departures from the Hertzian pressure distribution for elastic deformation by dry contact. The minimum film thickness, h,, is not found in exactly the same location as the pressure spike. It is very cumbersome to investigate the influence of the various parameters by full solution of the elastohydrodynamic problem over an exthe minimum film tended range of conditions. I f interest lies in h,, thickness at the constriction in the outlet region, the formula Ii)o.7

h,

=

2.65

&0.54 Ro.34

(ll0

E'o.03 w,o.13

(3-60)

can be used with reasonable confidence for a practical range o f loads and From the point of view of lubrication, emphasis is on q speeds [ 1 6 1 . and c1, both of which pertain to the properties of the lubricating fluid, and an the speed and load parameters 0 and W ' , where 0 = 1 / 2 ( U , + U 2 ) , and w ' is the load per unit axial length of nominal contact. The film thickness is most sensitive c o velocity and fluid viscosity and is also strongly influenced by the coefficient a. The effect of the load parameter W' is small. in physical terms, increase of load produces an increase in bearing area by elastic deflection of the boundaries and also increases the viscosity of the lubricant by the pressure effect, both of which combine to carry the load with only minor alterations in h or h,. Direct evidence can be found in computations by Dowson and Higginson 1 1 7 1 , where a 600% increase in maximum pressure and a 600% increase in the breadth of the contact zone is accompanied by a 25% decrease in ho. An improved calculation by Hamilton and and Moore [ l a ] for a different set of operating parameters gave a 152% increase in peak Hertzian pressure, a 2795: increase in the pressure spike at the exit region, a 5.6% decrease in ho and a 6.3% decrease in It, for a 323% increase in load per axial length of contact. Elastohydrodynamic calculations are often presented in dimension format, which tends to obscure the physical interpretation of results. Figure 3-10, taken from the work of Archard, Gair and H [19], shows the influence of load on the pressure distribution in

ess the rst the

50

7--..-.

-_

\-

Hertzian Pressure

'

\

\

\

\

\

I

1

I

0.2

0.4

0.6

0.8

1.0

Surface Location, x / x ,

Figure 3-10. Effect of load on calculated outlet pressure. A: MK/m, po = 480 MPa. B: 0 . 2 8 2 MN/m, p, = 720 MPa. C: 0.50 M N / m , 960 MPa. Data by Archard, Gair and Hirst [ 1 9 ] .

0.125 po =

outlet region. The pressure is plotted non-dimensionally as the ratio p/ p o , where p 0 is the maximum Hertzian pressure, against the half-width distance x / x o . The Hertzian pressure distributions coincide on this scale for all the loads studied, but the magnitude and the location of the pressiire spike in the outlet region is load-dependent, even in dimenA similar situation is seen in Fig. 3-11 for the insionless form. fluence of speed on the pressure distribution in dimensionless terms [121. Cheng 1131 reported that for nearly pure rolling (U, = U 2 ) there was no significant thermal effect on either the pressure level or the film thickness, but for cases involving moderate or high slip the temperature

I

1

-2.0 -1.5

I

1

1

I

-1.0 -0.5 0 0.5 1.0 Surface Location, x / x ,

Figure 3-11. Zffect of speed on calculated outlet pressure. Load: 1252 ?ressure, = p* x 113.6 MPa. A : 7.841 m / s , B : 4.135 m / s , C: 1.989 N/cm. m/s, D: 0.810 m j s , E: C . 2 5 3 m/s. Data by Cheng and Sternlicht 1 1 2 1 .

51

effects are significant. Figure 3-12 by Cheng and Sternlicht El21 shows the comparison of an isothermal solution for pure rolling with the corresponding thermal case for 25% slip. The pressure spike in the thermal case is higher and is located closer to the Hertzian maximum. x

Q

6 1.0

1

I

I

I

I

1

1

-

M 0

-2.0 -1.5

-1.0 -0.5

0

1.0

0.5

Surface Location, x / x , Figure 3-12. Effect of temperature on calculated pressure distribution. Load: 1252 N/cm, Pressure = p* x 773.6 MPa. A : 2.013 m/s, 25% slip (thermal). B: 1.989 m/s, no slip (isothermal). Data by Cheng and Sternlicht [121.

3.5.3.

Elastohydrodynamic Solutions for Point Contact

I t will be recognized that the elastohydrodynamic problem as presented in Section 3.5.1 is formulated in terms of plane strain an2 collinear contact. Obviously the simple Reynolds equation i s not applicable to spherical geometry or crossed-axis contact. Geometrically both of these cases fall into the category of "p0ir.t" contact. In actuality, i f elastic deformation is involved, the contact region is a circle or an ellipse.

Treatments of the elastohydrodynamic problem for such cases have been published by krchard and Cowking [20], by Cheng [21] and by Hamrock and Dowson [22]. O f these, the work of Hamrock and Dowson is the most comprehensive. The general Reynolds equation is written as

at

(3-61)

where " = - Wl

+

"2

2 being the surface velocity of one o f the boundaries in the xdirection, u2 the surface velocity of the other boundary in the %til

52

direction; and U J , and U J ~are the surface velocities in the ?-direction. The coordinates R and 2 define the orientation of the plane perpendicular to the thickness of the lubricant film. Transformations may be employed to accommodate the geometry of the boundary surfaces or to throw the treatment into non-dimensional form. In solving the elastohydrodynamic problem for "point" contact, the Reynolds equation is coupled with the expressions for the elastic deformation of the bounding surfaces and for the influence of pressure and temperature on the viscosity of the lubricant, as in the solution for "line" contact. However, a single traverse across the contact zone does not suffice as the integration path in the case of "point" contact, where the contact area is elliptical or circular instead of rectangular. This brings into play the ellipticity parameter, b, = u , / b , , which is simply the ratio of the major and the minor axes of the contact ellipse. The ellipticity parameter controls the length of the integration path for a given traverse across the contact area and is introduced into the computation by way of its functional dependence on the geometry of the two solid surfaces. When k, = 1 , the area of contact is a circle, and as b e becomes very large the cor,tact area for all practical purposes approximates a rectangle. Hamrock and Dowson defined the following dimensionless groups by a numerical analysis of the parameters of the physical problem: the film the speed group o ' , the load group thickness R , the ellipticity b,, and the material group G . The dimensionless film thickness can then be written as

w'

R

= f(k,,

o', W',

G)

From the results of 34 different cases the following specific formula was obtained for the dimensionless minimum film thickness, ffm:

It

can be readily seen that

R m is less for a circular contact area

1 ) than for "line" contact between

values of ti', G and

cylinders

with

the

same

(he = effective

W'.

Since the dimensionless groups are defined in terms of real parameter5 such as radii of curvature, applied load, surface velocity, lubricant viscosity, Young's modulus, etc., it is possible to investigate the effect of a given group on the pressure distribution and the film profile over the contact area by fixing the value of the other groups. Figure 3-13 Shoh'S the contour plot5 of film thickness for ellipticity ratios of 1.25 and 8. The latter configuration closely approximates the rectangular area of "line" contact. Because of tne dimensionless

53

(b) k, = 1.25

(a 1 k, = 8

Figure 3-13. Contour plots of dimensionless film thickness for ellipticity ratios 8 and 1.25. Dimensionless film thickness R ( x 106 ) = h/R. (a): A 7.08, B 7.20, C 7.40, D 7.70, E 8.20, F 8 . 9 0 , G 9.80, H 11.00. (b): A 4.3, B 4.6, C 5.0, D 5.5, E 6.0, F 6.6, G 7.4, H 8.2. Hertzian deformation area ---Data by Hamrock and Dowson [22].

.

L+

lu

2 2.0 d

2ox10-6

C

;1.2 ul

$ 0.8

8

t

.%0.4 4

E o

.-

n

-2.4 -1.6-0.8 0 0.8

2

-

0

-

-2.4 -1.6-0.8 X

0

0.8

Figure 3-14. Influence of ellipticity ratio on pressure distribution and film thickness profile. Data by Hamrock and DoNson [221.

representation of the R and .? coordinates, the actual elliptical Hertzian contact area appears as a circle, regardless of the value of the ellipticity ratio. The thickness contour plot for the ellipticity ratio 1.25 is characterized by two side lobes where the film is thinner than is found along the median track. Figure 3-14 shows the effect of the ellipticity ratio on the dimensionless pressure and on the dimensionless film thickness along the median track. The pronounced pressure spike seen at the trailing edge for the lower ellipticity ratios i s absent for the ellipticity ratio 6. 3.5.4. Experimental Observations of Elastohydrodynamic Lubrication The usual verification of the validity of an elastohydrodynamic analysis o r the accuracy of the calculations is a n experimental pressure distribution profile or film thickness contour. This is difficult to ac-

54

complish because the pressure and contour changes must be evaluated over A. W . Crook [ 2 3 1 the short distance of the Hertzian deformation. developed a method of scanning the deformed zone for film shape by means of a capacitance probe which can also be used to determine film thickScanning the ness. Details of the technique are given in Chapter 6. elastically deformed zone for the pressure distribution was described by Kannel, Bell and Allen [ 2 4 1 and by Orcutt [ 2 5 1 . A thin, narrow strip of manganin is deposited across the edge of a glass disk which presses A s the against the edge of a steel disk in a rolling-disk apparatus. manganin strip traverses the deformed zone, its electrical resistance changes according to the pressure encountered there. Film contour results obtained by Crook I 2 3 1 , by Kannel e t at. [ 2 4 1 and by Orcutt 1 2 5 1 agree qualitatively with the predictions of elastohydrodynamic theory by showing a region of elastic deformation and a constriction at the exit. The pressure distributions, however, do not have the pressure spike in the exit zone [ 2 4 , 2 5 1 . By improving the construction of the pressure transducer, Hamilton and Moore [ 1 8 1 were able to demonstrate the existence of the pressure spike. But, as seen in Fig. 3 - 1 5 , the observed spike, which occurs at the location predicted by

al

0.2 ; 01 1 - 1

11

-0.4-0.2

I

1

0

' u\ -0.4 -0.2 0 0.2 Surface Location, mm

0.2

Figure 3 - 1 5 . Comparison of calculated and measured pressure distribution (b) Load 1 0 0 . 3 and film thickness. (a) Load 1 0 0 . 3 kN/m, speed 1 . 3 m/s. kN/m, speed 5 . 1 8 m/s. Data by Hamilton and Moore [ l a ] .

theory, is considerably lower than the calculated value. The film thickness profile, which was obtained experimentally by the capacitance method, agrees reasonably well with that calculated for low speed (Fig. 3 - 1 5 a ) but at higher speed the discrepancy between the observed and the calculated film profile is sericus (Fig. 3 - 1 5 b ) . A. Cameron and his co-workers developed an optical interferometric method of measuring film thickness and mapping film profiles, details of which are described in Chapter 6. The method is capable of resolving thickness to better than 100 nm and does not require empirical calibration. For reasons of technique, most of the published data are for a

55

rotating polished steel ball pressed against a stationary plate of glass, sapphire or diamond. For the circularly symmetrical geometry thus involved the computational treatment of Hamrock and Dowson [ 2 2 ] with an ellipticity ratio of l is applicable. Film profiles mapped from interferograms can be found in the work of Cameron and Gohar [ 2 6 1 , Wedeven, Evans and Cameron [ 2 7 1 , Gohar and Cameron [ 2 8 ] , and Sanborn and Winer [291.

(a) In the direction of rolling

(b) Transverse to roiling direction

200

100 0 100 200 z,km

Figure 3-16. Film profiles for sphere on plate by optical interData by Gohar and ferometry. Load: 717.7 N. Speed in cm/s a s shown. Cameron [28]. Figure 3-16 shows some diagrams of film profiles obtained by Gohar and Cameron [ 2 8 ] . The profiles along the median path in the x-direction (Fig. 3-16a) do not have the pronounced increase in film thickness just before the region of the pressure spike that is seen i n the calculated profile for an ellipticity ratio of 1.25 (Fig. 3-14). The observed film thicknesses along a median path in the z-direction show a better correspondence with the calculated profiles; in Fig. 3-16b we see the two tnin regions at the border of the contact zone and the thicker region at the center, as found in the contour plot of Fig. 3-13b. The correspondence between the observed and the calculated film shapes is particularly good at the highest rolling speed. The experimental evidence substantiates the general validity of elastohydrodynamic theory for circularly symmetrical contacts. What is particularly needed for technological purposes are quantitative comparisions of calculated and experimental results. Equation 3-63 below gives a relation for the dimensionless quantity ho/R in terms of the parameters c, qo, U , W , E ’ and R , the meanings of which have been established in previous discussions:

(3-63)

56

TABLE 3-1.

CONSTANTS FOR EQUATION 3-63

Cameron and Gohar 1261 Archard and Cowking[20] Cheng [211 Wedeven, Evans and Cameron [271

K

M

N

3 1.4 1.69 1.73

1 0.74 0.725 0.714

-0.33 -0.074 -0,058 -0.048

Table 3-1 shows values for K , bl and t i reported by Cameron and Gohar [261, Archard and Cowking [201, Cheng [Zll, and Wedeven, Evans and Cameron [271. Wedeven, Evans and Cameron plotted their experimental data against each of four versions of the equation. Over a range o f values of ho/’R from 1.2 x to 12 x the discrepancy between experiment and calculation was about l x lo-‘ for all except the formula of Cameron and Gohar [261. When the dimensionless ratios are converted to real film thickness, the average discrepancy between the observed and the calculated film thickness is about 100 nm for values of 11, in the range I 8 0 to 1800 nm. Iiertzian pressures ranged from 325 to 600 MPa (47,000-87,000 lb/in 2 ) : surface velocities were not explicitly given. Apparently plotting the dimensionless ratio h o / z against the dimensionless groups ( a n , U / R ) M and tends to suppress t h e sensitivity with which the response to individual parameters can be shown. Lee, Sanborn and Winer 1301 plotted ho/R against the Hertzian pressure over a

Hertzian Pressure, MPa Figure 3-17. Dimensionless film thickness as a function of Hertzian pressure for a polybutene fluid. Data by T e e , Ssnborn and Winer [ 3 0 1 .

51

2 range from 530 to 1550 MPa (77,000-225,000 lb/in ) at speeds from 35 to 229 cm/s (13.7-90 in/s). Figure 3-17 shows the data f o r a polybutene fluid compared with the line calculated from the theory of Archard and Cowking [20]. The experimental film thicknesses are significantly less that the theoretical values and have a distinctly non-linear trend downward at high pressures. Data obtained by Sibley and Orcutt [311 for a similar range of pressures but at much higher speeds showed analogous behavior. I t seems, therefore, that elastohydrodynamic calculations need refinement to make them represent actual lubrication performance accurately. REFERENCES 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 1 I.

12. 13. 14. 15. 16. 17. 16. i9. 20. 21. 22. 23. 24. 25. 26. 27.

28.

H. Lamb, Hydrodynamics, 6th Ed., Dover Publications, New York, 1945, p. 1. S. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd Ed., McGraw-Hill, New York, 1951, Chapter 8. F. R. Eirich, Editor, Rheology: Theory and Applications, Academic Press, New York, 1956, Volume I , Chapter 1 . H. Lamb, up. cit., Sections 325-326. S . Timoshenko and J. N. Goodier, op. c i t . , Section 6. 0. Pinkus and B. Sternlicht, Theory of Hydrodynamic Lubrication, McGraw-Hill, New York, 1961, Sections 1-2. 0. Pinkus and B. Sternlicht, o p . cit., pp. 9, 14. 0. Pinkus and B. Sternlicht, o p . cit., pp. 12, 221. M. C. Shaw and E. F. Macks, Analysis and Lubrication of Bearings, McGraw-Hill, New York, 1949, Chapter 6. M. J. Booth and W. Hirst, Proc. Roy. SOC. London, A316 (1970) 4 15-429. A. N. Grubin and i. E. Vinogradova, Investigation of the Contact of Machine Components, Central Scientific Research Institute for TechNauchno nology and Mechanical Engineering (Tsentral'nii Issled. Inst. Tekhnol. i Mashinostroen.), Moscow, 1949, Book No. 30. Translation No. 337, Dept. of Scientific and Ind. Res., London. H. S. Chena and B. Sternlicht. J. Basic Ens. (Trans. ASME). 87D (1965) 695I707. H. S. Chenq, ASLE Trans., 6 (1965) 397-410. L. D. WedeGen, Lubrication Eng., 31 (1975) 291-296. D. Dowson and A. V. Whitaker, ASLE Trans., 8 (1965) 224-234. D. Dowson, Proc. Inst. Mech. Engrs., 182 (1967/1968) Part 3A, 151- 167. D. Dowson and G. R. Higginson, J. Mech. Eng. Science, 1 (1959) 6-15. G. M. Hamilton and S. L. Moore, Proc. Roy. SOC. London, A322 (1971) 3 13-330. G. D. Archard, F. C. Gair and W. Hirst, Proc. Roy. S O C . London, A262 (1961) 51-72. J. F. Archard and E. W. Cowking, Proc. Inst. Mech. Engrs., '80 (1965/1566) Part 3 B , 47-56. H. S. Cheng, J. Lubrication Tech. (Trans. ASME), Q2F (1970) 155-162. B. J. Hamrock and D. Dowson, J. Lubrication Tech. (Trans. ASME), 98F (1976) 223-229, 375-383: 99F (1977) 264-276. A. W. Crook, Nature, 190 (1961) 1182-1183. J. W. Kannel, J. C. Bell and C. M. Allen, ASLE Trans., 8 (1965) 250-270. F. K . Orcutt, ASLE Trans., 8 (1965) 381-396. A. Cameron and R . Gohar, Proc. Roy. SOC. London, A291 (1966) 520-536. L. D. Wedeven, D. Evans and A. Cameron, J. Lubrication Tech. (Trans. ASME), 93F (1971) 349-363. R. Gohar and A. Cameron, ASLE Trans., 10 (1967) 215-225.

58

29. 33. 31.

S a n b o r n a n d W . 0 . W i n e r , J. L u b r i c a t i o n T e c h . (Trans. ASME), 93F ( 1 5 7 1 1 2 6 2 - 2 7 1 . D. L e e , D. M. S a n b o r n a n d W. 0. W i n e r , J . L u b r i c a t i o n T e c h . ( T r a n s . ASME), 95F ( 1 9 7 3 ) 3 8 6 - 3 9 0 . L. B . S i b l e y a n d F . K . O r c u t t , ASLE T r a n s . , 4 ( 1 9 6 1 ) 2 3 4 - 2 4 9 .

D. M.

59

Chapter 4 THE NATURE AND PROPERTIES OF LIQUIDS

4.1.

PROPERTIES OF LIQUIDS AND LUBRICATION

From the generalized Reynolds equation as developed in Chapter 3 (Eqn 3-31) we see that the specific influence of the fluid on the lubricating film is exercised through the density and viscosity. Since these properties stay constant at B fixed temperature for incompressible, isoviscous fluids, their effect on the film is obvious and straightforward in such simple cases. The viscosity and density of real fluids, however, alter in response to the changes in pressure and temperature encountered in hydrodynamically aenerated lubricating films. Therefore, in order to understand how real fluids behave in the lubrication process, we must learn something about the nature of fluids, in particular liquids, and of properties such as density and viscosity. The fluids most widely used f o r lubrication are the liquid oils. Each l i q u i d has its individual chemical composition, and consequently the way a liquid functions as a lubricant depends on how its chemical structure governs its density and viscosity behavior. Such influences are in part the subject of the discussions in this chapter. The general theory of fluids makes no distinction between liquids and gases. The basic relations for the flow of viscous fluids under pressure apply to both liquids and gases. However, there are overt differences between liquids and gases which are obvious from everyday experience. For example, under ordinary circumstances a liquid has a distinct interfacial boundary separating it from the ambient gaseous atmosphere. The deeper, fundamental difference between liquids and gases l i e s i n their internal structure, a subject of considerable complexity. The physicochenical differentiation of the liquid state from the gaseous and the solid states requires elaborate and formal treatment. But characterization of the liquid state in a fashion useful for lubrication problems can be made much simpler than is required by exact theory. I t will suffice f o r o u r purposes to begin with the treatment of liquid viscosity in descriptive terms. Then those constitutive and structural aspects of liquids and the liquid state which influence viscosity will be discussed. Similar treatment will be applied to the density and compressibility of liquids.

60

VISCOSITY AND VISCOMETRY 4.2.

NEWTONIAN AND NON-NEWTONIAN VISCOSITY

In deriving the equations for the flow of a simple viscous fluid the theoretical physicist uses a definition of viscosity based on a mathematical statement rather than a physical model. Let us define viscosity from a physical point of view. Consider two planes in the body of a fluid a distance dy apart, a s shown in Fig. 4-1. If we apply tangential stress T~~ along one of these planes and observe a rate of shear i , then we define the differential viscosity q a s

v

Equation 4-1 can in turn be used to define the unit of viscosity. In SI units, when the force F x is one newton, the area A one square meter and the velocity gradient one meter per second per meter, then the unit of viscosity is one newton-second per square meter, or alternately one pascal-second. The c.g.s. unit of viscosity, the poise, is one dynesecond per square centimeter. One pascal-second is therefore equal to 10 poise. The fundamental dimensions of viscosity are ML-lT-’.

Figure 4-1. Simple laminar shear between close parallel body of a fluid. What we have done in Eqn 4-1 is to define model applicable to any material which flows. is necessarily imply that the ratio volume of the fluid or during all the time many different modes of flow in nature, each w tion for 6 ~ /6+ . as illustrated in Fig. 4-2.

ST;^/&;

Lj

planes

in

the

viscosity by a rheological Note that Eqn 4-1 does not constant throughout the of flow. In fact, we find th a characteristic relaI f 6 ~. /. S ; is constant and

61

the shearing stress is zero when the rate of shear is zero, then we have a class of flow behavior designated a s Newtonian. The conditions for Newtonian flow are T.. h j

q = 7= constant Y

i.

=

o

when

T.. =

(4-2)

o

xj

Note that the designation N c l u t a n i a n refers to flow behavior and not to a generic type of liquid. However, liquids whose viscosity obeys Eqn 4-2 are frequently called Newtonian. Detailed and extensive discussions of Newtonian and non-Newtcnian rheological behavior can be found in specialized treatises and monographs 1 1 , 2 1 .

t

i c 0 0 c 0

a

Shearing Stress-

Fig ure 4-2. Flow curves for various ideal rheological bodies. A : NewD: Bingham ton ian liquid. E: Pseudoplastic fluid. C: Dilatant fluid. Pla stic ( J , is the yield value). E: Pseudoplastic material with a yield va 1ue. F: ililatant material with a yield value. The range of substances which exhibit flow behavior is truly amazing. For example, all the evidence for glass at roon temperature points to Newtonian flow at an extremely slow rate [ 3 ] . In this chapter it will be taken for granted that we are discussing liquids which can be recognized as such by their overt behavior. Even so, the problem of determining the kind of flow behavior is complex. Because of its technological importance, we shall turn our attention to the relation between basic flow behavior and the principles and methodology of viscometry. 4.3.

CAP1 LLARY V I SCOMETRY

The methodology of capillary viscometry of liquids rests on the laws of flow through a fine-bore tube. The viscosity is determined from the measured flow rate under a known applied pressure through a tube of known dimensions.

62

Let us examine the mechanics of viscous flow in a straight capillary tube of circular cross-section, subject to the following postulated conditions: ( 1 ) steady flow; ( 2 ) no radial or tangential components of velocity; (3) axial velocity a function of distance from the axis only; (4) no slip at the capillary wall; ( 5 ) end effects negligible; ( 6 ) incompressible fluid; ( 7 ) no external forces; ( 8 ) isothermal conditions throughout; ( 9 ) no appreciable change in viscosity with change of pressure along the length of the tube. Consider a cylindrical column of liquid (Fig. 4-3) in a capillary tube of radius R and length e. Let there

f

i

a

l7

Flow direction)

Figure 4-3. lary.

\

. \

Force balance on a column of liquid flowing through a capil-

be a difference in pressure AP between the ends of the capillary and let there be laminar flow in the direction shown. Now let U S look at a cylindrical column of liquid of radius n within the total column of liquid. For steady flow the viscous drag over the surface area 2nkL is equal to the driving force AP(nn 2 1 , s o that we may write the following expressions: 2lIhbT =

AP(iTh2 )

(4-3a)

APn T = - Z

(4-3b)

4.3.1.

Newtonian Flow through a Capillary

Equation 4-3b may be regarded as the basic equation of capillary viscometry. The properties of the liquid enter the equation by way of the rheological function which expresses the relation between rate of shear and shear stress. For Newtonian flow from Eqn 4-2 we get L

n = (4-4) Eqn 4-3b then gives us (4-5)

63

On integrating with respect to when h = R , we get

h

and using the boundary condition

0

=

M)

(4-6) I t is evident that the velocity function with respect to n is parabolic, with maximum velocity where h = 0.

The volumetric flow rate 2 can be obtained by a second inregration

(4-7) which yields (4-8) This is the Hagen-Poiseuille law for laminar flow in tubes. Its conversion to a form applicable to experimental measurements will be given later. For the present we note that the quantities 2 , R, AP and L can all be obtained by direct measurement and Eqn 4-8 therefore can be used in the absolute experimental method for the determination of the v i s cosity of a liquid in any physically rarional system of units. When the volume-rate 2 is divided by the area nR2 we get f o r the average flow velocity

The following relations then apply to the shear rate at the wall capillary:

Bi

of

the

(4-10)

(a)

k -

Velocity-

0

R

Distance from Center, rFigure 4-4. Parabolic velocity profile (a) and shear-rate for Newtonian flow in a capillary viscometer.

relation

(b)

64

Figure 4-4 shows graphical representations of the parabolic velocity distribution and the linear shear-rate relation characteristic of Newtonian flow. 4.3.2.

Non-Newtonian Capillary Flow

The non-Newtonian flow of liquids is too complex to be treated here at length, and we shall restrict ourselves to consideration of some cases specifically significant for lubrication science and technology. Curves such as B and C in Fig. 4-2 can be fitted to the de Waele-Ostwald power law

j,

= f(T) =

(1/cl)Tn

(4- 1 )

is the shear rate or where c 1 is a constant, T is the shear stress and the shear gradient. I t can be shown for both Newtonian and non-Newton an flow of liquids [41 that

(4-12) where T7? =

AP z

(4-13)

defiotes the shear stress at the interfacial wall of the capillary. stitution of Eqn 4-11 into Eqn 4-12 and integration gives

Sub-

(4-14) When n = 1 ,

Eqn

4-14 reduces to the Hagen-Poiseuille equation with c, =

n.

Velocity

Reduced Distance from Center , r / R

Figure 4-5. Velocity profiles (a) and approximate shear-rate relations (b) for Eon-Newtonian flow described by the de Waele-Ostwald power law.

puted

Velocity distributions within a capiiiary column of liquid as comby Metzner 151 for various values of n are shown in Fig. 4-Sa. F o r

65

pseudoplastic fluids, where n < 1 , the velocity profile flattens as n decreases. When n approaches zero the shear gradient is zero across most of the bore. When n > 1 the velocity profile becomes sharper with increasing n , and when n = m the shear gradient becomes linear across the bore. These relations must be taken into consideration when interpreting experimental data obtained by capillary tube viscometry. Figure 4-5b shows a non-dimensional plot of the various shear-rate relationships. A technique for the use of the power law model starts by putting Eqn

4-14 into logarithmic form:

(4-15) I f the plot of 1 0 5 2 against 1 0 5 (AP/21) is a straight line, its slope is I t then is possible to compute the value of c, from either Eqn 4-15 or Eqn 4-14. n.

The quantity using Eqns 4-4 and

is sometimes treated as an apparent viscosity by as shown below:

c, 4-11

But it is obvious that r)' is dimensionally different from the Newtonian This fact should be kept in mind in treating hydrodynamic viscosity 11. problems in which the viscosity of the liquid is non-Newtonian. 4.3.3.

Sources of Error in Capillary Viscometry

Before proceeding to a detailed examination of the techniques of capillary viscometry, we should consider the following list of ten potential sources of error. The first three apply to all viscometers and all fluids: Turbulence: departure from laminar flow.

(1)

( 2 ) Kinetic energy loss: loss of effective pressure because

of the kinetic energy retained by the stream of liquid which issues from the active part of the viscometer.

( 3 ) Heat effects: conversion of energy

arising

from

pressure

and

shear into heat energy. The next t icular :

four

sources

of error apply to capillary viscometers in par-

(4) Pressure losses prior to flow in the capillary: energy dissipated in the apparatus before the liquid enters the capillary; sticking of the piston in externally pressurized instruments. (5)

End

effects:

energy

losses

due to viscous o r elastic effects

66

when the liquid flow converges o r diverges on entering or ing the capillary. ( 6 ) Drainage:

liquid

adhering

to

the

leav-

walls of the reservoir and

capillary. ( 7 ) Surface tension: variations of surface tension from

one

liquid

to another. The remaining three sources of e r r o r are attributable primarily to the character of the parricular iiquid being tested: ( 8 ) Elastic energy: energy lost by elastic deformation, particularly

of viscoelastic liquids, not recovered during flow in the capillary. ( 9 ) Wall effects: changes in the liquid near the capillary wall

for

certain polyphase and Bingham fluids. (10)

Time-dependent effects: influence of residence time in the viscometer f o r thixotropic and rheopectic fluids.

Details of the nature of these errors and how they are dealt with in the actual determination of viscosity can be found in special works devoted to viscometry o r rheology [ 2 , 6, 71.

Figure 4-6. Cannon-Fenske viscometer for transparent liquids.

4.4. CAPILLARY VISCOMETERS

shall now proceed to the examination of some practical capillary viscometers and the methodology of their use. Only a few of the more important instruments will be discussed here; an extensive list of viscometers can be found in the monograph by Van Wazer e b at. 1 2 1 . Nor will we deal with the primary determination of viscosity from basic instrumental measurements. The viscometers described here are calibrated against standard liquids of known viscosity a s determined by primary reference i nst r umen t s We

.

67

The Cannon-Fenske Viscometer

4.4.1.

A s an example of a simple modern capillary viscometer let us examine the Cannon-Fenske modification of the Ostwald viscometer, illustrated in Fig. 4-6. A specified volume of liquid is charged into the viscometer in the bottom reservoir A , and the liquid is then carefully drawn up through the capillary into the bulb B. The volume between the markers I and I 1 is known precisely. The upper bulb T serves as a reservoir for the amount of liquid required to get the viscometer into steady-state operat ion.

The quantities involved in the determination of viscosity are related by the following expression, obtained from the Hagen-Poiseuille equation : nR4 h p y

dV =

dt

~

(4-17)

811.e

where dV is the volume of liquid which flows through the capillary in time dt, h is the hydrostatic head of liquid, p is density and 5 is the acceleration of gravity. In the integrated form we get vR4 h p y

t

TI=-

8LW

(4-18)

where h is the average hydrostatic head of the volume V and t is the time required for the meniscus to go from mark I to mark 1 1 . For a particular instrument, i f the total volume charged into it is a constant, h is constant, and Eqn 4 - 1 8 can be transformed to 11 = C , P t

(4-19)

where C , is the viscometer constant. To calibrate the viscometer, a liquid of known viscosity is required. Determination of the absolute viscosity with the aid of Eqn 4 - 1 8 is discussed in detail by Hatschek [ 6 1 and by Reilly and Rae 1 7 1 , with adequate descriptions of the apparatus and the techniques. Once Eqn 4 - 1 9 has been evaluated numerically for the calibrating liquid, the relation below follows directly:

T!

=

€LA-

no poto

(4-20)

where no is the absolute viscosity of the calibrating liquid, po its density and to the time of outflow. A l s o from Eqn 4 - 1 9 we get the relation v = 9 = C,t P

(4-21)

where v = n / p is designated a s the k i n e m a t i c vinconity. The SI unit of kinematic viscosity is the square meter per second. The absence of an explicit force factor distinguishes kinematic viscosity from d y n a m i c v i h -

68

conity (compare Eqn 4-21 with Eqn 4 - 1 8 ) . The c.g.5. unit of kinematic viscosity is the n t a k e , which is 0.0001 square meter per second. The magnitudes of both the stoke and the poise are inconveniently large for most of the liquids encountered in lubrication practice. Therefore the viscosities of such liquids are usually quoted in centistokes or centipoise. The magnitudes of the SI units are even more inconveniently large. One centistoke is square meter per second: one centipoise is 0.1 pascal-second. The determination of kinematic viscosity with a calibrated cometer rests on the following relation, derived from Eqn 4-20: R

Li=voG

vis-

(4-22)

Thus once the viscometer has been calibrated, the kinematic viscosity of the liquid can be obtained directly from the outflow time and the calibration constant. Glass capillary viscometers operating under the force of gravity are instruments of low shear stress and shear rate and are mostiy used in to 1 6 x dealing with liquids of relatively low viscosities (0.4 x square meter per second; 0.4 to 16,000 centistokes). Although this may seem like an enormous range, many lubricating oils have viscosities square meter per second (50,000 centistokes) at 253 well above 50 x K (-20 C ) . The limits on the magnitude of operating parameters inherent in gravity-actuated capillary viscometers makes it easy to correct the basic operating errors or else reduces them to negligible size. For instance, because the stream of flowing liquid in the Cannon-Fenske instrument originates in the upper bulb B and terminates in the lower reservoir A , the kinetic energy correction can be made insignificant by proper adjustments of the outflow time, the length of the capillary and the volume of the reservoir B. Low values of the shear stress and shear race diminish the influence of elasticity and heating corrections and eliminate t u r bulent effects. Viscosity is a sensitive function of temperature, and therefore viscosity determinations are carried out with the working parts of the viscometer in a constant-temperature environment. Hatschek [ 6 ] has pointed out that when gravity-operated instruments are filled with a predetermined volume of liquid, the filling operation should be carried out with the liquid at bath temperature because of the influence of temperature on density and hence on the driving head. Table 4-1 shows some of the dimensions and of Cannon-Fenske viscometers. These particular for flow times in the range 200-1000 seconds. flow time is governed partly by the acuity with

operating characteristics instruments are designed Capillary viscometer outwhich the transit of the

69

TABLE 4-1. DIMENSIONS AND VISCOSITY RANGES FOR CANNON-FENSKE GLASS CAPILLARY VISCOMETERS Approx. viscometer constant nm2s-2

cs/s

Viscosity range

Capillary diameter

llrn2s - 1

mm

(centistokes) 3 5 10 30 100 300

500 1000 3000 5000 10000 (a)

0.003 0.005 0.01

0.6-3 1-5

2-10

0.03 0.1 0.3 0.5 1 3 5

60-300 100-500 200- 1000 600-3000 1000-5000

10 (a)

2000-10,000

6-30

20- 100

0.31 0.42 0.63 0.78 1.02 1.26 1.48 1.88

f 0.02 f 0.02 f 0.02 f 0.02 f 0.02 f 0.02

f f 2.20 f 3.10 f 4.0

0.02 0.02 0.05 0.05

Volume of bulb B: 3 . 1 5 (f 0 . 1 5 ) mm 3 , except (a) 4 . 1 3 (f 0 . 1 ) mm 3 Length of capillary: 7 3 t 3 mm.

.

liquid menicus past the volume markers can be observed and partly by the capillary length-diameter ratio necessary to establish steady flow and eliminate end corrections. Under gravity only, shear stresses range from about one to 15 Nm-2. An externally applied driving pressure of 34.5 2 kNm-’ (5 lb/in ) could raise the shear stress to 460 Nm-’. The range of shear rates in glass capillary viscometers of the Cannon-Fenske type is from one to 20,000 s - l , based on 200-800 seconds efflux time. 4.4.2.

Capillary Viscometry under Pressure

For realistic application to lubrication problems, information on rheology of liquids at pressure levels greater than 0.6895 GPa 2 ( 1 0 0 , 0 0 0 lb/in ) and at high rates of shear is required. An elegant and versatile capillary viscometer operative under such conditions, as well as at elevated temperatures, has been described by Novak and Winer [ E l . The schematic illustration in Fig. 7 shows how the instrument works. The fluid whose viscosity is to be determined is contained in the system composed of rhe reservoir R 1 , the high-pressure tubing with the capillary in the test section, and the reservoir R 2 . The working pressure is generated by pumping hydraulic fluid into cavity I and venting cavity I 1 so that the pressure exerted on piston P1 is intensified 50 times by the movable ram which acts on the piston P2. Flow through the capillary in the test section is caused by creating a pressure difference between cavities I 1 1 and IV so that the translating piston moves relative to the fixed ram. Since the translating piston carries the system composed of the reservoirs R 1 and R2, the connecting tubing and the capillary with i t , such motion establishes the pressure which forces the test liquid the

70

Figure 4-7. and Winer Strain gage transducer. High-pressu

Schematic drawing of the high-pressure viscometer of Novak R 1 , R 2 : reservoirs. P1, P2, P3, PT: pistons. G1, G2, G3: transducers. a: Movable ram. b: Fixed ram. c: Displacement d: Capillary section. e: Constant temperature bath. f: e tubing. I , 11, 1 1 1 , IV: Cavities. 81.

through the capillary. The volume of liquid displaced is measured by the displacement transducer. Pressures are measured by strain gage transducers: G 1 measures the average pressure level in the test fluid, and G 2 and G2 sensitively measure the pressure difference across the capillary. The volume of the high-pressure tubing immersed in the constant-temperature bath is large enough to insure that liquid of known temperature flows through the capillary during the viscosity determination. The outputs from all the transducers are recorded on a strip chart which also carries the time-base signal. Thus it is possible to assure that all the data are acquired under steady-state conditions. Certain effects are inextricably bound up with the general technique of viscosity determination: e . g . , transient behavior of the liquid as it passes through the capillary under the driving pressure; changes in the capillary dimensions with changes in applied pressure and ambient temperature. For the conditions they used, Novak and Winer [ 8 1 found such changes to be negligible. A more serious source of error, theoretically unavoidable in the flow of a viscous liquid, is the generation of heat. Novak and Winer reduced rhis error to negligible levels by using short capillaries made of metal and by keeping the driving pressure low (7-14 MPa). Figure 4-8 shows data for b:s(2-ethylhexyl) sebacate, a liquid which exhibits Newtonian flow over a pressure range from atmospheric to 543 MPa (79,300 lb/in2). The shear stress limits of the viscoae:er are represented by the two vertical lines. The two lines with a slope of unity represent the range of shear rates over which the instrument was operated. Within the operating limits of the instrument the viscosity of the liquid was constant; i . c . , the flow was Newtonian.

71

-546.8 -463.4 -403.4

cn

*

.In

e

327.5

-257.2 0.10

.>

-

-

203.4

-

129.6 69.0 2

0.01

.

i

Figure 4-8. Flow curves for bis(2-ethylhexyl) sebacate with highpressure, high-shear viscometer at indicated pressures in MPa; temperature 311.0 K. Data by Novak a n d Winer [ E l ,

10 t

3

’

0.01 10

lo2

lo3

lo4

lo5

lo6

Shear Stress, N/m2 Figure 4-9. Change of flow behavior from Newtonian to non-Newtonian by addition of polymeric viscosity modifier. Temperature 311.0 K; pressure -1 See Table 4-2 137.9 MPa. Shear rates, in s : 1 , lo3; 2 , lo4; 3 , l o 5 . f o r identity of fluids. Data by Novak and Winer [El.

The shear stresses and the shear rates in Fig. 8 were computed by the appropriate formula for Newtonian flow at the capillary wall. But i f the results of such a computation indicate that the viscosity varies with shear rate, then the Rabinowitsch analysis is applied to determine the correct shear rate at the wall for non-Newtonian behavior ( c 6 . References 2 and 3 ) . Figure 4-9 illustrates how the addition of a polymeric viscosity modifier to a paraffinic petroleum base oil changes the viscosity behavior from Newtonian (Fluid B ) to non-Newtonian (Fluids C, D and E). The shear rates and the shear stresses have a hundred-fold range.

72

4.5. ROTATIONAL VISCOMETRY AND VISCOMETERS

A rotating body immersed in a liquid experiences a viscous drag or retarding force, and this principle can be applied to viscometry. The chief advantage of rotational viscometry is that continuous measurements at a given shear stress or rate of shear can be made over extended periods of time. Thus time-dependent changes in flow properties can be measured conveniently. Another advantage of rotational viscometry i s the ease with which shear rate can be altered. But though rotational viscometry seems simple in principle, in practice it turns out there are so many sources of error to consider and corrections to be made that an operating rotational viscometer of good accuracy is a rather complicated apparatus. Many commercial instruments, operating either on the continuous rotation principle o r the oscillating principle, are described in the monograph by Van Wazer ~t a L . [ 2 ] . To illustrate the application of the principles of rotational viscometry to operating instruments, we shall examine the details of two instruments: the first practical rotational viscometer, devised by Couette [ 9 1 , and the Ferranti-Shirley cone-and-plate viscometer.

A

Figure 4-10. Concentric cylinder rotational viscometer. (a) Basic scheme of operation. (b) Couette viscometer with guard rings and liquid seal.

4.5.1.

The Couette Viscometer

Figure 4-10a shows the basic schematic diagram for the operating parts of the Couette concentric cylinder viscometer. The liquid to be investigated is in a thin layer between two coaxial cylinders, the outer one with a radius R 2 rotating with angular velocity D and the inner one

13

with radius R, restrained by a filar suspension, the torsion of which indicates the angular momentum Ma imparted to the inner cylinder. I t can be shown by various analytical approaches [ 4 , 51 that

(4-23)

or alternatively

(4-24)

where 0 is the working height of the cylinder. The flow of the liquid is assumed to be Newtonian. Equation 4 - 2 4 is the Margules equation, which is the rotational analogue of the Hagen-Poiseuille equation. I n the analysis which gives Eqns 4 - 2 3 and 4 - 2 4 the following assumptions are made: (1) incompressible liquid; ( 2 ) non-turbulent flow; ( 3 ) streamline gradient in horizontal plane perpendicular to axis of rotation; ( 4 ) steady-state motion; ( 5 ) no slip at wall of either cylinder; ( 6 ) motion invariant in direction of axis of rotation. Assumption ( 3 ) neglects the effect of centrifugai forces, and this assumption a s well as assumption (2) implies small values of R. Assumption ( 6 ) means the end effect is neglected. To comply with assumption ( 6 ) in an operating instrument, the upper and lower surfaces of the stator are protected by guard rings o r liquid locks, a s shown in Fig. 4-10b, so that the liquid is interacting with only the cylindrical surfaces. Or the viscometer can be constructed with the depth of immersion variable, as shown schematically in Fig, 4 - 1 1 a . Equation 4-24 may then be written as an(.!

+

At) (4-25)

where A.! is the effective increases in length due to the viscous drag of the end effect. I t is obvious from Eqn 4-25 and the graph of Fig. 4-llb how to deal with the end effect experimentally. I n some instances it is also possible to treat the end effect analytically [41. Going back to Eqn 4-23, we

see

that

4nl

R 1 R 2 / ( R $ - R:)]

[ 2

may

be

regarded as an instrument constant; and since Ma and R are quantities which can be measured directly, it is possible to calibrate a rotational viscometer with liquids of known viscosities. This is usually done with liquids which show Newtonian flow over a range of shear rates, even

14

A1

I

Figure 4-11. Variable immersion cylindrical viscometer to eliminate end effects. (a) Scheme of construction. (b) Method of applying correction. though rotat anal viscometers are extensively employed to investigate non-Newtonian behavior. For Newtonian flow the rate of shear is given by

(4-26)

and its average value by

(4-27) I n practice most coaxial viscometers operate with

very thin films I n such case it is easy to show that liquid; i . e . (R2 - R,)/R, << 1. d h differs very little from (dw/dt),, and therefore the shear rate for all practical purposes be taken to be (dlu/dh)," anywhere across film.

of

dw/ may the

A correctly designed and constructed rotational viscometer is a convenient instrument f o r detecting departure from Newtonian viscosity behavior, since the rate of shear is readily computed by Eqn 4-27 from Barber, Muenger and easily measured quantities such as Q , R , and R2. Villforth 1101 discuss the design and construction of an instrument wnich has the desired attributes and in addition operates so that the temperature gradient in the sheared film of liquid is only one o r two degrees Kelvin.

Figure 4-12 shows the data obtained by rotational and by capillary viscometry for the non-Newtonian flow of a liquid lubricating oil containing a polymeric viscosity modifier 1 1 1 1 . There is no systematic dependence of viscosity on the type of viscometer used, but the decrease of viscosity with increasing rate of shear is unmistakably evident. The analytical approach Newtonian flow as presented Ostwald power law:

to by

the rotational viscometry of nonOka [41 is derived from the de Waele-

15

f 0.04

~

0

a 003-. t v1

8

002

-

u) .-

>

Base O i l 0.0076 Pa-s

0.01

0

0 Io2

lo3

lo4

lo5

lo6

Rate of Shear,sec-’

Figure 4-12. Viscosity v s . rate of shear for a Newtonian and a nonNewtonian liquid as measured by capillary and rotational viscometry. Data by W. Philippoff [ll].

._

R = 2n 12aZ)n

c2

(4-28)

Since both D and Adu are experimentally obtained quantities, the slope of the linear plot of Log v n . Lay hdu gives the value of the exponent n. The value of c 2 is then easily found from the intercept of the plot on the ordinate axis. 4.5.2.

The Cone-and-Plate Viscometer

Figure 4-13 illustrates the operating principle of the cone-andplate viscometer. The cone, which is driven at a rotational speed of R , has a radius R and makes an angle Q with the plate. The space between the cone and the plate is filled with the liquid to be investigated. Neglecting edge effects and secondary flow, we can obtain the following relation for Newtonian flow i f ,$ is small enough [ 3 1 : (4-29)

Figure 4-13.

Principle of the cone-and-plate viscometer.

76

The appealing feature of the cone-and ca. 0.052 rad) angles ( 4 less than everywhere along the radius of the cone tive approach leading to Eqn 4-29 is by

plate principle is that for small the rate of shear is uniform and is equal to C / + . An alternaway of the shear stress:

(4-30)

By combining Eqns 4-29 and 4-30 we get (4-31)

Therefore, i f G / $ is the true rate of shear and Eqn 4-30 gives the shear stress, a simple calculation suffices to obtain the viscosity, whether the flow is Newtonian or non-Newtonian. The most readily available cone-and-plate viscometer is Ferranti-Shirley instrument, described in detail by Van Wazer e R a!.

the [21.

4.6. ROLLING-BALL AND FALLING-SINKEZ VISCOMETERS

Rolling-ball viscometers are of interest because they have been used extensively to study the viscosity of liquids under high pressure [12,13,14,15]. Basically a rolling-ball viscometer is operated by observing the time required for a ball of radius R b and density p ' to roll a given distance down a tube of radius Rt inclined at a given angle to the horizontal and filled with the test liquid of density p . The use of a rolling ball in an inclined tube as a viscometer was first suggested in 1914 by Flowers [161. An extensive analysis of the theory and operation of this type of viscometer was published by Hubbard and Brown [ 1 7 1 . They showed that under the proper conditions the following equation holds:

il=c

dL2 'b

(4-32)

where the coefficient C 3 depends only on the dimensions of the instrument and the fact that i t operates under conditions of streamline flow; w h is the terminal rolling velocity of the ball. The coefficient C3 can be evaluated by calibrating the viscorneter with liquids of known viscosity and density. In another publication Hubbard and Brown [ 1 8 ] describe the construction and operation of a rolling-ball viscometer in detail. No rigorous hydrodynamic theory has been formulated for the rollingball viscometer. Hersey's original treatment of the determination of viscosity by means of a ball rolling down an inclined tube was a sketchy The work of Hubbard and Brown i s a more dimensional correlation [ 1 9 ! . elaborate dimensional analysis. The rolling-ball viscometer is a secondary instrument and can only give the viscosity of the test liquid relative to that of the calibrating liquid. Also the rolling-ball viscometer

77

does not give results for viscosity as a function of shear rate and therefore cannot demonstrate whether the viscosity of a liquid is Newtonian o r non-Newtonian. However, the instrument operates at such low rates of shear with lubricating oils that it is likely all the studies made with i t on such liquids were in the Newtonian domain.

Figure 4-14. High-pressure falling-sinker viscometer. Pressure is transmitted to the test liquid through the side arm and acts on the The instrument is bellows-like reservoir of the viscometer chamber. oriented vertically. Time of fall of the sinker i s monitored by electrical contact at the top and bottom pins. a: Viscometer tube. b: Sinker. c: Reservoir. d: Insulated lead. e: Insulated pin. f: End plugs. 9: Terminal plug. After Bradbury, Mark and Kleinschmidt [201.

Figure 4-14 illustrates the essential construction of the fallingsinker apparatus used by Bradbury, Mark and Kleinschmidt [201 in an important investigation of the viscosities and densities of lubricating oils up to pressures of 1.035 GPa (150,000 lb/in2) in the temperature range 273 to 491 K (32-425 F). A sinker falls vertically in a steel tube filled with the test liquid, pressure being applied through an external liquid acting on a compliant reservoir. The initiation and the termination of the passage of the sinker are detected by the break and make of electrical contact at pins in the plugs closing off the viscometer tube. The viscometer is used a s a comparison instrument, calibration being carried out at atmospheric pressure with liquids of known viscosity. The instrument is reliable with liquids of viscosity in the range from 0.0045 In normal operation shear to 540 Pa-s (4.5 to 540,000 centipoise). stress could be varied by a factor of about 40:1, but no information on the magnitude of the shear stresses was cited in the article describing the viscometer.

78

4.7.

ORIFICE VISCOMETERS

Orifice viscometers are capillary viscometers in which the length does not exceed 10 times the diameter of the tube and discharge of the liquid is into a separate reservoir. Their present use stems from the historical need in the oil industry for a simple, rugged device to measure viscosity. The Saybolt instrument is used in the United States, the Redwood viscometer in England, the Engler instrument in Germany and the Barbey viscometer in France. Flow in these viscometers does not obey the Hagen-Poiseuille law and che relation between efflux time and visA s is evident in Fig. 4-15, there is quite a large cosity is complex. variation in hydrostatic driving head from the beginning to the end of a run, and an appreciable fraction of the energy furnished by this head is consumed at the orifice entrance and by the kinetic energy of the spent liquid. The so-called viscosity a s determined by instruments of this

Saybolt univeral viscometer. a,a: Level of liquid in conFigure 4 - 1 5 . stant temperature bath. b: Overflow rim. c: Orifice. d: Bottom of bath. e: Cork. f: Graduation mark. g: Receiving flask.

type is expressed empirically in terms of efflux time: for example, the results of determinations with the Saybolt viscometer are reported a s Saybolt Universal Seconds ( S U S ) . To convert efflux time obtained with orifice instruments into kinematic viscosity we use the relation

(4-33)

But c 3 and c 4 are not true instrument constants, as C, is in Eqn 4-19, and therefore it is necessary to calibrate an orifice viscometer with liquids of known true viscosity for various ranges of efflux time. Since the arbitrary units of efflux time are useless in hydrodynamic calcula-

79

tions, it is necessary to publish elaborate tables of conversion. I n the United Silates the American Society for Testing and Materials has issued tables for conversion between centistokes and Saybolt seconds [ 2 1 ] . 4.8.

INFLUENCE OF TEMPERATURE AND PRESSURE ON VISCOSITY

I t is evidect from the discussions in Chapters 2 and 3 that the various aspects of hydrodynamic lubrication problems can range from the classical isoviscous, isothermal solutions of the simple Reynolds equation to short-time squeeze film behavior on impact. In dealing with elastohydrodynamic and impact problems, viscosity can no longer be taken as constant but instead must be introduced in a manner which correctly accounts for its response to temperature and pressure. A s background for the appreciation of the intricacies of such problems we shall examine the effects of temperature and pressure on the viscosity of liquids, particularly those which can be used as lubricants.

4.8.1.

The Walther Equation and ASTK Viscosity-Temperature Charts

Partington [ 2 2 ] lists 7 5 different expressions for the effect of temperature on the viscosicy of liquids; a few of them theoretical, most of rhem empirical. For many engineering applications it is adeqoate to know the viscosity of the lubricating liquid at the overall temperature of the operating parts, but for precise calculations the exact temperature of the lubricating film is required. I t is common industrial practice in the United States to determine the viscosity of the liquid at 1 0 0 Obviously it would F ( 3 1 1 . 0 K, 3 7 . 8 C) and at 2 1 0 F ( 3 7 2 . 0 K , 9 8 . 9 C).* be desirable to have a relation for the viscosity-temperature behavior of liquid lubricants which is reliably linear over a range wide enough so that the engineer can interpolate or extrapolate the measured viscosity of the lubricant into the temperature domain that concerns him. Such a relation is available in the Walther equation [ 2 3 1

L o g L o g (u

+

a ) = C,

- C5 Log T

(4-34)

where T is in degrees Kelvin. This equation is empirical. In an early version v was in centistokes and a was 0.8. Using essentially this type of log-log relationship, the American Society for Testing and Materials developed charts on which viscosity data for lubricating oils give straight lines when plotted against temperature [ 2 4 ] . The older version of the charts *The decision of the International Standards Organization (ISO) in 1972 to make 4 0 C ( 3 1 3 . 1 K) and 1 0 0 C ( 3 7 3 . 1 K) the reference temperatures has been adopted by the American Petroleum Institute (API), the American Society for Testing and Materials (ASTM) and the Society of Automotive Engineers (SAE) effective in 1978. The user of published viscosity data must therefore be alert to the existence of two sets of reference temperatures.

80

were available for viscosity in either centistokes or Saybolt seconds, with the temperature in degrees Fahrenheit. As revised in 1977 the charts are for viscosity in centistokes only, with the temperature scales in either Celsius or Fahrenheit.* In the development of the revised charts the Walther equation was modified to read

For viscosities in the range 2 to 20,000,000 centistokes the following empirical evaluation of Z is used:

Log t o g (u

+

0.7) = C4

- C5

La 5 1

(4-3513)

To carry the chart into the region of viscosities lower than 2.00 stokes the evaluation of Z must be modified:

centi-

(4-35c) where CCi is a polynomial function which changes when the low-end range of the viscosity scale shifts. Expressions for the specific evaluation of CCi can be found in the 1977 revision of ASTM Method D 341. Figure 4-16 shows plots of the viscosity-temperature behavior on the high-range ASTM chart for three different oils, the viscosities of which were measured at 37.8, 60.0 and 98.9 C. Within the range of the experimental values the linearity of the plots is excellent. I t should be noted that the log-log relationship compresses the scale for high values of the viscosity; hence in this region an error of only 0.1% in drawing the line could mean an error of 2 to 20 centistokes. I t can be seen in Fig. 4-16 that the viscosity of oil C is more sensitive to temperature than are the viscosities of the other two oils. The If importance of such behavior in hydrodynamic lubrication is obvious. the values of viscosity in the temperature range required by the hydrodynamic problem cannot be taken from the ASTM chart with precision, then analytical expressions such a s Eqns 4-352, o r 4-35c should be used.

4.8.2.

The Viscosity Index

We must perforce devote some time and attention to the concept known as the wibcanity index, which has become embedded in the terminology of technological lubrication with some unfortunate connotations. Whereas the Walther equation and the ASTM viscosity-temperature charts are frankly empirical devices used to linearize the viscosity-temperature relations for convenience and utility, the viscosity index is an attempt to impart the mystique of quality by assigning an evaluative aspect to the

*After withdrawn.

1978

official

recognition

of

the

Fahrenheit

scale

was

81

m x P c

E c

c

W 0

%

z .

0

Y

>

Temperature, degrees C

Figure 4-16. Viscosities of z h r e e o i l s plotted on t e m p e r a t u r e chart.

12

I

I

I

I

the

ASTM

I

10 -

H

U

L

20 40 60 80 100 120 Centlstokes at 40 C

Figure 4-17.

Basis of t h e v i s c o s i t y index computation.

viscosity-

82

effect of temperature on viscosity. The idea as originally proposed by Dean and Davis 1 2 5 1 rested on the fact that the viscosities of lubricant fractions from certain types of crude oil exhibited greater sensitivity to temperature change than did the viscosities of lubricant fractions from other types of crude stock. Therefore Dean and Davis carried out viscosity studies on lubricant fractions from two different sources. One was a naphthenic crude, and the oil fractions from it showed a more sensitive viscosity response to change of temperature than the fractions from the other source, a paraffinic crude. The naphthenic oils were assigned a viscosity index value of zero, the paraffinic oils a viscosity index of 100. Figure

4-17

illustrates the basis on which calculation of the vis-

cosity index of oils other than the reference fluids rests. The curve marked Series L is the reference plot of the viscosities in centistokes at 100 C of the standard naphthenic oils of viscosity index zero against the viscosities of these oils at 40 C. The curve labeled Series ff is a similar reference plot for the standard paraffinic o i l s of viscosity index 100. To compute the viscosity index of a new "unknown" oil, direct The determinations of its viscosity at 40 and at 100 C are required. formula below is then used for computation: L - U

-

v.1. =

L - H

where U =

100 (4-36)

the viscosity at 4 0 C of the new oil whose viscosity index is to be computed;

L

=

the viscosity at 4 0 C of an oil of zero viscosity index having the same viscosity at 100 C as the new oil whose viscosity index is to be computed:

H

=

the viscosity at 40 C of an oil of 100 viscosity index having the same viscosity at 100 C as the new oil whose viscosity index is to be computed.

an example let us take an oil with a viscosity of 7.30 cs at 1 0 0 C and cs at 4 0 C. A value of 8 4 . 5 3 cs is obtained from the abscissa where the 7.30 cs line intersects the Series L curve, as shown in A value of 6 8 . 0 6 cs for H is obtained similarly from the Fig. 4 - 1 7 . Series H curve. Substitution into Eqn 4 - 3 6 gives 50.3 as the viscosity index of this particular oil.

As

68.06

Suppose we have two oils with the same viscosity at 40 C but with different viscosities as 100 C. Then the individual lines for the 100 C viscosities will intersect the Series L and ff curves to give different values of L and ff for the two o i l s and consequently their viscosity indices will be different.

83

Detailed directions for computing the viscosity index are published by the American Society for Testing and Materials [261. For oils of viscosity not greater than 70 cs at 100 C and viscosity index not over 100 there is a table of values for L and H. For oils of viscosity greater than 70 cs at 100 C and for oils of viscosity index above 100, special computational formulas have been developed. These tables and formulas were adopted by ASTM in 1977. Prior to that the two fixed temperatures for the viscosity index were 100 and 210 F. Examination of Eqn 4-36 reveals that the value of the viscosity index does not depend on the units in which the viscosities are reported, since the factor for conversion to centistokes occurs in both the numerator and the denominator of the formula. The temperature interval and the viscosity-temperature characteristics of the series of reference oils are the two principal basic influences on the general nature of the viscosity index. 4.8.3.

Pressure and Viscosity

Although the study of the effect of pressure on the viscosity of lubricating liquids has a long history, as summarized in a report issued by ASME [271, the most trustworthy and self-consistent work is fairly recent. As an example we may take the data obtained by Bradbury, Mark and Kleinschmidt [20] with their falling-sinker viscometer for the following three liquids: (a) bis(2-ethylhexyl) sebacate, (b) a paraffinictype petroleum oil with a kinematic viscosity of approximately 53.9 x lo-' m2/s at 310.9 K (250 Saybolt seconds at 100 F), and (c) a naphthenic-type petroleum oil of approximately the same viscosity. These data are shown in Fig. 4-18 in their original form as semilogarithmic plots of dynamic viscosity against pressure at 32, 77, 100, 210 and 425 F (273.2, 298.2, 310.9, 372.0 and 491.4 K). Inspection of these graphs shows that the sensitivity of viscosity increase to pressure ranks in the following order: naphthenic oil > paraffinic oil > bis(2-ethylhexyl) sebacate. The effect of temperature on viscosity, which at atnospheric pressure is in the order naphthenic oil > paraffinic oil > bis(2ethylhexyl) sebacate, remains in the same order as pressure increases but with accentuation of effect. It is apparent in Fig. 4-18 that viscosity increases with pressure most strongly for the naphthenic oil and least for the synthetic sebacate fluid. I t is also apparent that for the most part increase of viscosity with pressure does not follow the exponential relation n p = v,eQP

(4-37)

In general, deviations from this relation are quite pronounced; but even when the departures from linearity on the semilogarithmic plots appear to

106

lo5 104 103

102

10'

I

L

1

lo-' 10-2

0 200 400 600 800 1000

0 200 400 600 8001000

0 200 400 600 800 1000

Pressure ,MPa Figure 4-18. V i s c o s i t y a s a f u n c t i o n of p r e s s u r e a t v a r i o u s t e m p e r a t u r e s . ( a ) : bis(2-Ethylhexyl) sebacate. ( b ) : P a r a f f i n i c petroleurn o i l . ( c ) : Nap!ithenic petroleum o i l . 1: 2 7 3 . 2 K . 2 : 291.2 K . 3: 3 1 0 . 9 K . 4: 372.0 K . 5: 4 9 1 . 4 K . Data by B r a d b u r y , M a r k and K l e i n s c h r n i d t [ 2 0 ] .

85

be minor, the viscosities at high pressure are of such large magnitude that small discrepancies in a can have a strong influence on the outcome of elastohydrodynamic calculations. Efforts have been made to overcome this difficulty by the development of other than the one-constant exFor practical purposes such efforts are in effect ponencial relation. empirical, requiring a great deal of specific experimental data for each individual lubricant fluid. However, studies of the influence of chemical structures in lubricant components on viscosity and on compressibility, which will be discussed later in this chapter (Sections 4.9 and % . l o ) , snow potential f o r reducing the amount of such data required. The work reported by Bradbury, Mark and Kleinschmidt [20], although reasonably adequate in pressure and temperature range ( 1-104 kPa, 273-491 K), suffered from the disadvantage of being carried out at a low shear stress ( 2 5 N/m 2 ) and at low shear rates. Novak and Winer f 8 1 with their high-pressure capil ary viscometer were able to attain shear rates as high a s l o 6 s-l and pressures up to 543 MPa (80,000 lb/in2) in the temperature range 3 1 to 422 K ( 1 0 0 to 300 F), under which conditions they investigated the viscosity behavior of the ten liquids listed in Table 4-2. Some of the data from this study appear in Figs. 4 - 8 and 4-9, which depict Newton an and non-Newtonian viscosity response to shear Each of the fluids listed in Table 2 gave a stress and shear rate. straight line for the temperature-dependent viscosity function plotted on :he ASTM viscosity-temperature chart over the range 311-422 K with pressure and shear stress held constant. Table 4 - 3 summarizes some of the additional findings. The viscosity-temperature coefficient, which i s the K), fractional decrease in viscosity between 100 and 210 F (311.0-372.1 shows a strong response to increase of pressure. The effect of the nature of the liquid is shown by the data for bis(2-ethylhexyl) sebacate (Fluid A ) and dimethylsiloxane (Fluid I). The data are given in their original units because insufficient information was published to convert all of them into SI units.

ly

The logarithm o f viscosity at 311.0 K was found to increase linearwith pressure for all the liquids listed in Table 4 - 2 except Fluids A

and I. The value of the viscosity-pressure coefficients shows some strong responses to the nature of the liquids, either through intrinsic structure in the case of bis(2-ethylhexyl) sebacate or naphthenic petroleum oil, o r else as the effect of additive in the case of petroleum oil with 8% high molecular weight polymer (Fluid D). Because of the exponential form of the viscosity-pressure relation, the magnitude of the viscosity increases at high pressures is very large and hence t h e decrease in the value of some of the viscosity-pressure coefficients at these pressures may be misleading.

86

FLUIDS STUDIED BY NOVAK AND WINER 181

TABLE 4-2.

bis(2-Ethylhexyl) sebacate B: Paraffinic petroleum oil C: B + 4% PMMA (a) D: B + 8% PMMA E: B + 4 % PBS (b) F: Naphthenic petroleum oil G: F + 4% PBS H: Polybutene I: Dimethylsiloxane J: Trifluoropropylmethylsiloxane

A:

(a) P W : polymethylmethacrylate, mol. wt. 560,000 (b) P9S: poly(t-butylstyrene), mol. wt. 375,000

TABLE 4-3. VISCOSITY-TEMPERATURE AND VISCOSITY-PRESSURE COEFFICIENTS ( a )

Fluid viscosity-temperature (see Table 4-2) coefficient (b)

Viscosi ty-presscre coefficient (c)

Atmospheric 50,000 lb/in2 Atmospheric 50,000 lb/in2 A

B C D E F G H I J !a)

0.740 0.845 0.823 0.843 0.876 0.873 0.837 0.906 0.620 0.833

0.913 0.965 0.950 0.975

-_--0.950 (e) 0.943 (e) 0.991 (d) 0.794 0.971

1.07 1.31 1.21 1.15 1.39 1.53 1.49 2.09 1.15 1.53

0.59 0.92 0.98 1.15 1.15 1.53 1.49 1.71 0.81 1.35

(d)

(e) (e) (d)

At 100 F (37.8 C), pressure 50,000 lb/in2 (344.75 MPa), T = 10 4 dynes/cm2 ( 1 O3 N/m2 )

( b ) Viscosity-temperature coefficient = 1

(2:

- -

;)P

(c) Viscosity-pressure coefficient

=

( d ) Pressure = 40,000 lb/in2 (275.80 MPa) (el Pressure = 20,000 lb/in2

Data by Novak and Winer [81.

(137.90 MPa)

in

cp per lb/in 2

87

4.9.

THEORIES OF VISCOSITY AND THE MOLECULAR STRUCTURE OF LIQUIDS

A theory which would tie together the phenomenology of the viscosity behavior of liquids with their molecular structure would be desirable not only as an intellectual accomplishment but also as a useful aid in predicting the behavior of liquids a s lubricants over a wide range of conditions. However, this goal is far from being attained because of basic deficiencies in present-day theories of liquids and because of the complex constitution of the hydrocarbon mixtures present in lubricating oils. An example of a study which attempts to correlate basic theories of the viscosity of liquids with experimental data is found in the work of Hogenboom, Webb and Dixon [ 1 5 ] . They worked with pure hydrocarbons which can be regarded a s representing structures found in petroleum oils. Viscosities and densities over the temperature range 288.7 to 4 0 8 . 2 K and the pressure range 0.1 to 360 MPa (14 to 101,000 lb/in 2 ) were determined. What gives particular significance to this work is that the data were used to test three basic theories of liquid viscosity: the Eyring-Ree significant-structure theory, the Cohen-Turnbull free-volume model, and the empirical free-volume model of Doolittle. The significant-structure theory of liquid viscosity developed by Eyring and his co-workers is discussed by Eyring and Marchi [ 2 8 ] well enough to bring out its important features. The liquid is thought of as being comprised of molecules of substance and intermolecular vacancies. In contrast to the relative immobility of molecules and vacancies characteristic of a solid, the interchange or mobility of molecules and vacancies within the body of a liquid is easy. By treating the molecules as though their behavior could be separated into two modes, one gas-like and the other like a solid, partition functions can be set up for calculating the fraction of molecules in each category. The equation for viscosity in terms of these two fractions is

where V is made up of V , , the molar volume of the solid portion, and - V , , the molar volume of the gaseous portion. The quantity 9 is a 9 gas-like viscosity term derived from kinetic theory: V

(4-39)

where m and b are molecular mass an3 diamete.r respectively, k is the Boltzmann constant and T is temperature in degrees Kelvin. From the data

88

n-dode,cane, n-pentadecane, n-octadecane, c i s - d e c a h y d r o n a p h t h a l e n e , trans-decahydronaphthalene, spiro(4,5)decane, spiro(4,5)undecane, cisoctahydroindene and trans-octahydroindene, Hoqenboom, Webb and Dixon 1151 were able to assign a value of 10 micropascal-seconds (0.01 cp) to the quantity ( V - W h ) q / V f o r rigid bicyclic compounds at 388.2 K (115 C ) ; Y i s approximately 2% of the maximum viscosity observed experimenA . E . qg tally in this group of compounds. This is well within the experimental uncertainty of the data, and therefore the burden of accounting for the observed viscosities falls on the term ( V , / V ) q , in Eqn 4-38. A usable expressioi: for r( is for

(4-40) which fits the data for argon, nitrogen, chlorine, methane and benzene 1291. In Eqn 4-40 N is Avoqadro's number, L is a constant representing 6 the free distance between nearest neighbors, C6 is a constant transmission coefficient, a ' is an adjustable constant, f ( d ) is an intermolecular pctential function, and C, is a constant equal to the number of nearest neighbors in the lattice. At atmospheric pressure everything in the expression for q, is constant except V and T , and by combining Eqns 4-38 and 4-40, remembering the practical restrictions on Eqn 4-39, we can wrire

(4-41) Hogenboom, Webb and Dixon I151 found that Eqn 4-41 accurately described the viscosity behavior of the nine compounds they studied at atmospheric pressure up to a temperature of 408.2 K. The Cohen and Turnbull free-volume model [ 3 0 1 assumes a liquid composed of hard-sphere molecules and voids in which diffusion occurs whenever a void larger than some minimum volume V * forms in the body of the liquid and a molecule jumps into it. The equation f o r the diffusion coefficient is

= c5b*ug e x p

[- 71 XV*

(4-42)

where c5 is a geometric factor, b* approximately equals the molecular diameter, u is the gas kinetic velocity, hV* closely approximates the 5

89

noleciilar volume, and V is the average free volume. The interpretation 5 given tc V d is crucial, and i t turns out . t i 1 practice that V represents I! the difference between the liqnid specific volume and the volume of a qiass-like condensed phase. Hence V o is very similar to the difference of specific volumes, V - V,, of the significant-structure theory. The Stokes-Einstein relation between the diffusion coefficient and absolute viscosity is

(4-43) and on substituting (3bT!m) ' I 2for u

TI

constant x T"*

exp

Y'

the Cnhen-Turnbull model yields

[y] Ir

(4-44b) where V d has been written as the difference between the liquid specific vclume and the specific volume of some reference state. By treating C l 0 , C , , and Vo a s adjustable constants, Hogenboom, Webb and Dixon 1 1 5 1 were able to obtain excellent fits of their viscosity data to E q n 4-4413. Vo cannot be regarded a s a basic property of the substance independent of pressure and temperature, for Eqn 4-44b predicts that at constant specific volume V o increases with increasing temperature. This implies that V, can be affected by pressure and temperature. By an extended and careful examination of n-alkanes over a long range of temperature at atmospheric pressure, Doolittle I 3 1 1 found the following expression suitable for the viscosity: 13"O .En

=

!4-45) The ratio Vo/(V - V o ) is a funcrion of the temperature. At first Doolittle regarded V o as the specific volume of the liquid extrapolated to absolute zero, but in a later paper [ 3 2 1 he treated V o a s a third adjustable constant. As might be expected, Eqn 4-45 also gives an excellent f i t to the atmospheric pressure data of Hogenboom, Webb and Dixon r151.

90

Insofar as fitting equations to temperature-dependent viscosity data at atmospheric pressure goes, the significant-structure theory (which is a modified reaction-rate model) does as well as the CohenTurnbull and the Doolittle equations, both of which are essentially freevolume models. Although Eyring and Marchi [ 2 8 ] claim that the significant-structure theory has no adjustable parameters, practically it turns out that some of the parameters of the solid cannot be calculated by theory and in effect the significant-structure theory is made to f i t the viscosity data by introducing assumptions about the intrinsic volume of the molecules in the solid state. The significant-structure free volume is the difference between the liquid specific volume and the specific volume of a crystalline lattice, and therefore it includes the volume change associated with melting. The Cohen-Turnbull free volume is the volume change associated with the thermal expansion from a reference state in which the material is a "glassy" liquid. As things stand now. the temperature dependence of V o remains a troublesome question and obscures extrapolation of viscosity data to temperatures which might resolve the distinction between V o and V , . The theoretical models can be applied to the pressure dependence of viscosity if appropriate physical interpretations can be assigned to the various quantities in the equations. The significant-structure expression (Eqn 4 - 4 0 ) becomes physically intractable at elevated pressures because of difficulties with the dependence of fl.4) on pressure. Matheson C331 assumed the Doolittle model to be valid and wrote the temperature dependence of viscosity as

(4-46)

where ( V o ) T refers to the temperature T . is given by the function

The pressure dependence of V o

(4-47)

where (Vo)p is the limiting specific volume at pressure P and AP = P The modified Doolittle equation then becomes

-

1.

When solved for f(P) Eqn 4-48 yields

- C12)

V ( t n 11

f(P)

=

( V o ) T ( L n 11

-

C,,

+

C13)

(4-49)

91

for a given temperature T . The original Doolittle equation has three empirically adjusted constants; Matheson's approach introduces the pressure-dependent function as still another adjustable constant in Eqn 4-40.

To modify the Cohen-Turnbull equation for use at elevated pressures we put it in the form

Ln (4-50)

in which f ( P ) applies to V ,- only, since V * represents a minimum void size which is approximately the unit of flow and has no interpretation as a "solid" phase. On solving Eqn 4-50 for f ( P ) the result is

(4-51)

where C , ,

= AV*

Hogenboom, Web and Dixon 1 1 5 1 used their experimental data at atmospheric pressure to evaluate the constants to be inserted into Eqns 4 - 4 9 and 4-50. They also computed experimental values of f(P) as the ratio of V , (experimentally determined) at elevated pressure to V o (also experimentally determined) at the atmospheric-pressure melting point. The

0.92

-

0.90

-

. I I I I 1000 2000 3000 4000 Pressure, bors

-d

Figure 4 - 1 9 . Variation of d l P l with pressure. The points o represent experimental values of b l P ) for cis-decahydronaphthalene. Points o are experimental values for n-pentadecane. Solid curves are calculated from the modified Doolittle equation, dashed curves from the modified CohenTurnbull equation. Data by Hogenboom, Webb and Dixon 1 1 5 1 .

results are illustrated in Fig. 4-19 f o r n-pentadecarie and cisdecahydronaphthalene. The fact that the function f ( F ' ) calculated by Eqn 4-51 falls somewhat below the experimental values may indicate that the "glassy" liquid is more compressible than the organic solid crystal. Petroleum oil lubricants are mixtures composed predominantly of polycyclic compounds (see Chapter 1 6 ) . Ring analysis is a widely used technique in studying such oils and in specifying types of oil for technological applications. A n inportant question is whether the viscosity behavior o f such oils of mixed structure is uniquely dependent on the particular mixture or whether i t reflects the average influence of the component structures. This question was investigated by Griest, &ebb and Schiessler 1131, who found that f o r the compounds they studied, the behavior of the mixtures corresponded closely to that of a single pure compound equivalent to the average structure of the mixture. This study covered a temperature range from 311.0 to 408.2 K (37.8-135 C ) and a pressure range from atmospheric to 345.0 MPa (3450 bars). Theories of liquid viscosity such as are presented in this chapter afford an insight into the mechanism of viscosity even when it becomes necessary to resort to adjustable constants in dealing with real liquids, other than those of the simplest molecular structure. The potential significance of such theories for practical lubrication lies in the development of general relations between viscosity behavior and molecular structure in lubricating liquids, relations which can take the prediction of the effect of temperature and pressure on viscosity out of the realm of the grossly empirical and permit confident extrapolation of easily obtained data for use in difficult circumstances.

COMPRESSION OF LIQUiDS 4.1C.

COMPXESSIBILITP AND BULK MODULUS

Suik modulus expresses the resistance of a fluid to compression: i t is the inverse of compressibility. F o r a fluid which experiences 071y normai stresses and normal strains ( i . e . no shear), bulk modulus is given by the basic relation [ 3 4 1

where B is the b u l k modulus, d i s the normal stress and E is the normai st:air,. When there is shear in the system, the defining equation becomes more complex [ 3 4 , 35, 361. Bulk

modulus may also be defined thermodynamically.

t a n g e n t b u l k r n o d a t ~ i 4 , BT is given by

The

i~athenmaZ

(4-53) where V is the v9Lum-s of the fiuid a: the thermoaynamic temperature T . Equation 4-53 implies the existence of ar, equation of state relating the volume V and the pressure P at the temperature T . I n engineerins practice it is customary to fix the reference volume V , at atmospheric presThe i h a t h e h m a e suze and to measure the increase in pressure by gage. n e c a n t b u L h m o d u l u n is then given by

i4-54)

where Pg is the gage pressure. lustrated in Fig. 4-20.

I

The

el tion between BT and BT is il-

\

Volume-

Figure 4-20. modulus.

Diagram

to illustrate isothermal tangent and secant bulk

The working data for E q n s 4 - 5 3 and 4 - 5 4 are obtained from experimental determinations of density. For the volume ( V o r V o ) we can use the specific volume of the liquid, i.c. the reciprocal of the density. The techniques of determining liquid densities at elevated temperatures and pressures can be found in the work of Bradbury, Mark and Kleinschmidt I 2 0 l , of Hopkins, Wilson and Bolze [37], or of Klaus and O'Brien [383. Correlations have been worked out for a number of lubricating fluids to reduce the amount of density data required to handle isothermal secant bulk modulus values over a range of pressures from atmospheric tG as high

94

as 3.447 GPa (500,000lb/in2) [39, 401. I t is a l s o shown how the correlation data for the isothermal secant bulk modulus at a given pressure and temperature can be used to find the corresponding isothermal tangent bulk modulus. An excellent study of the relation between hydrocarbon structure and compressibility was carried out by Cutler, McMickle, Webb and Schiessler [41]. The modification of Bridgman's method used to determine the compressibilities is described well and the specific volume data are given in detail over a pressure range from atmospheric to 1 GPa (10,000 bars) and a temperature range from 311.0 to 408.2 K (37.8 to 135 C). No attempt was made to develop a three-variable equation of state relating volume, pressure and temperature; however, the pressure-volume isotherms were examined analytically with respect to the Tait equation:

V o - 1' = c* ecy

i

1 +

2

(4-55)

c93

where V o is the specific volume at atmospheric pressure, V is the specific volume at pressure P, and c8 and c 9 are constants. By combining the data obtained in their study with other data on liquid hydrocarbons, Cutler e t aL. confirmed that c8/Vo was a constant independent of temperature. Thus c8 could be evaluated from any isotherm and then the corresponding value of c9 could be computed by a ieast-squares procedure. Some representative values of c8 and c9 are given in Table 4-4, where c8 is in cm 3/g and c9 in bars. Furthermore, the temperature dependence of the parameter c9 was found to be adequately described by a quadratic expression about the temperature 79.4 C: ( c ~ =) (~ c ~ ) +~ cl0(e ~ . ~- 79.4) + cl,(e - 79.4) 2 (4-56) Table 4-5 gives values of the parameters c l 0 and c l l obtained from the data in Table 4-4. Equations 4-55 and 4-56 afford a method of expressing

TABLE 4-5. TEMPERATURE-DEPENDENCE OF THE TAIT EQUATION PARAMETER c 9 FOR SELECTED LIQUID HYDROCARBONS

c9(79.4) bars 1-a-Naphthylpentadecane 1264 9(2-Phenylethyl)heptadecane 1048 9(2-Cyclohexylethyl)heptadecane 1019 n-Pentadecane 762.8

clo c1 1 bars/deg C bars/(deg -5.698 -5.916 -5.690 -4.805

0.0094 0.0121 0.0107 0.0116

From data by Cutler, McMickle, Webb and Schiessler [41].

CI2

TABLE 4-4, TAIT EQUATION PARAMETERS FOR SELECTED LIQUID HYDROCARBONS

37.8 C

8

c

60.0 C c9

79.4

c

98.9

c

115.0 C

8 c9 8 ' 9 1-a-Naphthylpentadecane

c9

0.2316 1378

0,2350 1264

0.2384 1160

135.0 C c9

0.2416 1061

c8

c9

0.2455 976.4

9(2-Phenylethyl)heptadecane

0.2438 1315

0.2481 1170

0.2520 1048

0.2560 941.3 0.2598 857.9 0.2645 756.6

9(2-Cyclohexylethyl)heptadecane

0.2502 1275

0.2551 1140

0.2590 1019

0.2632 907.6 0.2670 831.7 0.2717 736.0

~~

n-Pentadecane

0.2721 983.3 0.2778 876.5 0.2830 762.8 0.2884 676.7 0.2935 607.8 0.3000 532.0

c

8

i n cm 3/q

c9

in bars

From data by Cutler, McMickle, Webb and Schiessler 1411.

t;;e p r e s s u r e and temperazure ciependence of specific voiume functionaliy, once sufficierlt data have been obtained to evaluate the .Jarlous parameters

.

Proceeding directly from Eqr. 4-53, isothermal compressibility can be written as - ( l / V c ) ( 2 V / 2p). Since the Tait equation is a functional representation f o r most pressure-vclume isotherms within the experimectal accuracy of the data, compressibi-ities can be expressed functionally Sy c8 = differentiating. In the unics employed by Cutler e t at. [ 4 1 1 , 0.2058.V0, from which the following expression can be obtained f o r isothermal compressibility: 9.08936

cT

=

T-P

I n SI units Eqn 4--57would have the same form but with

(4-57)

different

values

for the constants. the result of their investigation Cutler, McMickle, Webb and Schiessler 1 4 1 1 came to the following conclusions abobt the compression an6 the compressibility of hydrocarbons: As

(a) For a given hydrocarbon, compressibility decreases with increasing pressure at constant temperature and increases with increasing temperature at constant pressure. !b) The compression and compressibility of liquid hydrocarbons are strongly dependent on molecular structure. Cyclization, which decreases the rotational freedom characteristic of open-chain hydrocarbons, decreases compressibility markedly. Furthermore, fused-ring cyclization ( 2 . y naphthyl and decalyl structures) has a greater effect in decreas ng compressibility than cyclization to a non-fused ring such as cyclopen~yl,cyclohexyl or phenyl, at equivalent percentage of carbon atoms occurring in ring strucLures. Figure 4 - 2 1 - s a concise illust ation of the influence of molecular structure on the c o r n p a e b b i o n of hydrocarbons as a function of pressure. Table 4-6 shows che influence of structure on the c a m p n c 5 b i b i L i t y of hydrocarbons with increasing pressure. The effect of structure tends to disappear with increase of pressure. Thus, in Table 4-6 the ccmpresof n-dodecane is 100% greater than that of 1-asibility naphthylpentadecane at atmospheric pressure, but it is only 1 2 % greater at 3446 bars (344.6 MPaj. This reflects the decrease i n free space as the pressure increases; the moiecules of the liquid have made all the steric adjustments possible by rotation around C-C bonds and the like, and further increase of pressure must thereafter work against intermolecular repulsive forces.

97

2000 4000

0

6000 8000

Pressure, bars Flgure 4-21. !nfluence of molecular stractsre on che compression of h.ydroz;rrmn liqui6s. 12: n-Dodecane. 1 5 : c-Pentadecane. 18: nCc:adecarie. N: 1 - a - N a p h t h y l p e n ~ a d e c a n e . C: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 1 3 , 1 4 , 1 5 , 1 6 Codecanydrochrysene. Data by Cutler, McMickle, Webb and Schiessler [ 4 1 ] .

TABLE 4-6. EFFECT OF PRESSURE ON COMPRESSIBlLITY FOR SOME LIQUID HYDROCARBONS AT 135 C

Pressure, bar 5

Compressi bi 1 i t y , bars1-a-haphthylpentadecane

Atmospheric

9.i4 x I P - ~

3446

2.03

x iO-5

6991 ~

~~~~

Y(2-Phenylethyljneptadecane

n-DDdecane

11.8

18.3

2.13

2.26 x

1. 18 x ~ i i - ~

1 , i i

x 1c-5

~~

Data by Cutler, McMickle, Webb and Schiessler [4'1.

Bulk modulus c a n be treated from the adiabatic as well as the isothermal point of vie^. Phenomenologically adiabatic compression or expansion are processes where heat is neither lost to ncr gained from the environment. I f the process o c c a r s under equilibrium conditions, then we have the thermodynamicaily tractable case at zero entropy change and we define the 1 4 c n t r , o p i c ouLk rnodlieun a s aP

3s

= -

" l; )

S

(4-55)

Whereas the isothermal bulk modulus can be determined by straightforward experimental methods, there is nc convenient direct tech-

98

nique available for the determination of isentropic bulk modulus. An ~ n direct technique depending on the velocity of ultrasonic waves in the medium is generally used, rhe local expansions and compressions being assumed to be adiabatic. The expression f o r adiabatic bulk modulus is pub

Es =

-7

(4-59)

where p i s the density of the liquid at the given pressure, v n the velocity of sound in the liquid and 5 is the acceleration of gravity, all in consistent units. Experimental methods of utiiizing Eqn 4-59 are described by Wostl, Buehler and Dresser 1421, by Barlow and Yazgan [ 4 3 ] , and by Yazgan 1441. among others. A frequently used relation is

Bs

cw

(4-60)

where C p and C v are the specific heats of the fluid at constant pressure and at constant volume respectively. This relation is hidden in the derivation of Eqn 4-59. Implicit in the use of Eqn 4-60 is the assumption that the behavior of the pressure P and the density p of the fluid obeys Boyle's law, an assumption not likely to hold if the fluid is a liquid, This is treated in some detail by Lindsay 1451. Kittel [ 4 6 ] has examined a case where the equation o f state for the liquid i s given as

P

3R7

= -jJ-

pl'

(4-61)

M being

molecular weight and p " a density factor representing the available volsme. This equation was used in a calculation of the temperature and pressure coefficients of the velocity of sound. The fact that both coefficients a s calculated were on the low side suggests that the available volume in the liquid was over-estimated in this model. The following relation, based on fundamental thermodynamics, may be used f o r the calculation of the isentropic bulk modulus from the isothermal bulk modulus [51: 1

Es

=

-1 87

[7

(

q2,b3cp)] aT

(4-62)

99

Implicit in this formula is the assumption that C P pressure.

4.11.

does

not

vary

with

THE ROLE OF COMPRESSIBILITY I N LUBRICATION

Much of the work on the compressibility and bulk modulus of liquids reported ir! the literature was motivated by problems i n mass hydraulic flow, such a s raising a hydraulic fluid to a pressure in the range 68.9-137.e MPa (10,000-20,000 lb/in2) and circulating it through the hydraulic system. In this type of problem most of the emphasis is on the isothermal compressibility of the fluid. The role of the liquid in lubrication is different and more complicated than this. Many lubrication problems deal with the behavior of the liquic! a s it is raised to a high pressure during rapid passage through a short conjunction. Some calculations have been made by Fein 1 4 7 1 for a f i l m of oil between gear teeth operating under moderately severe conditions. The duration of the transit of the oil through the conjunction iias 26 microseconds, in which time the pressure was rising at the rate of 1 0 9 TPa per second (250,000 lb/in2 per second) and the shear rate was changing a t the rate of 2 Ts-’. Obviously work was being done on the liquid lubricant as it passed through the conjunction. A question which should be considered is whether substantially all the work of compression is retained by the lubricant in its transit through the conjunction, to be reversibly returned as work of expansion on return to atmospheric pressure, or whether some of the input work is dissipated by processes . . xnich generate heat in the liquid. i t is also obvious that the liquid is being subjected to severe viscous shear i n its passage through the conjunction. I f the rate of passage is so rapid that essentially conditions in the liquid are adiabatic, : h e n the viscosity of the lubricant in the conjunction will be lower than t h e g r o s s temperature measured f o r the material bounding the conjunction would lead one to believe. I f the rate of compression significantly affects the behavior of the liquid, then its molecular structure has an important bearing on such behavior. F o r a hard-sphere liquid, the pressure generated by rapid compression will manifest itself as a larger driving head for viscous flow, but liquids which can reduce their volume by internal rearrangement during compression will exhibit elastic recovery. Booth and Hirst 1 4 8 1 made an elaborate study of the rheology of oils held between two parallel plates subjected to impact. They included effects such a s the analysis of thermal flow in the compressed liquid and deformation of the anvil plates. The total duration of impact was relatively long (0.5 millisecond) and the films were relatively thick, being compressed from

100

about 0 . i mm to about 0.02 mm. Booth and Hirst were mainly interested in the viscosity behavior of the liquid tinder impact, but they did detect eiastic recovery from compression in two liquids, one a high viscosity oil of low viscosi~y index and the other an aromatic extract. The other oils shoved no elastic recovery. REFERENCES 1.

2. 3. 4.

5. 6. 7.

8. 9. 10. 11. 12. 13.

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3 :

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-3 -1 ,

34.

--. 2E

?t. 37.

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->. 7 C

1s. 1 " 3s .

42.

W.

Wostl,

J.

('966) 43.

=*. " I 45. 46. 47.

4E

*

;.

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2.

R.

J.

Buehler and T. Dresser, Rev. S c i . Instr., 37

1665-1669.

Barlow and E. Yazgan, Brit. J. Appl. Phys., 17 ( 1 9 6 6 ) 807;

18

(1967) 645.

Yazgan, J . Inst. Petroleum, 5 6 ( 1 9 7 0 1 2 5 4 . R. B . Lindsay, Physical Mechanics, 3rd Edition, D. Van Nostrand, ?rinceton, N. J., 1 9 6 1 , Chapter 1 2 . 6 , pp. 3 7 3 - 3 8 0 . C. Kittel, J . Chem. Phys., 14 (1946) 6 1 4 . R. S . Fein, J. Lubrication Tech. (Trans. ASME), 90F , ( 1 9 6 8 ) 5 4 0 . .!b J . sooth and W. Hirst, Proc. Roy. Soc, London, A316 ( 1 9 7 0 )

'c.

391-4:3.

102

Chapter 5 GASES AS LUBRICATING FLUIDS

Gases as well as liquids belong to the general category of fluids, and like liquids, gases can sustain pressure and flow viscously. Hence it is possible to establish a film of gas for lubricating purposes by the same basic actions involved in liquid film lubrication. In Chapter 4 the difference between gases and liquids was touched upon briefly, from both the naked-eye, overt point of view and the subtle theoretical distinctions. These differences in properties between gases and liquids also become evident as differences in their behavior as lubricating fluids. For instance, there is no phase interface between the lubricating gas and the ambient atmosphere. A gas, with its low viscosity and low heat capacity, furnishes a more nearly isothermal and laminar lubricating film in a bearing than does a liquid lubricant. On the other hand, the higher compressibility of gases complicates the analysis of the gas lubrication problem. It is not the objective in the body of the chapter to follow to develop the analyses of lubrication by gases in detail. Such treatments can be found in the specialized monographs and papers published on the subject. Instead, it will be shown how the behavior of gases, as distinguished from the behavior of liquids, influences the outcome of the hydrodynamic analysis. It will also be seen how the specific values obtained in such analyses point to the technological benefits of the use of gases as lubricating fluids, although no individual cases will be described in detail. 5.1.

FUNDAMENTALS OF

GAS

FILM LUBRICATION

In Chapter 3 it was demonstrated that one form of the generalized Reynolds equation is given by the expression below (ci. Eqn 3-34),

a (p:3- ap) ax

ax

+ -a az

- -ap)

(0:’

az

a(ph)

= 6U

-+

12pv0

ax

where h is the film thickness variable, x and z are the bearing dimension variables, p is the density of the lubricating fluid, q its viscosity, U the velocity of the shaft or slider, and Uo is the velocity in the xdirection when y = 0. When the lubricant is a gas instead of a liquid, it can no longer be assumed that the fluid is effectively incompressible. Instead a functional relation between density and pressure must be found:

103

for example, the perfect gas law, which can be put in the following form, p = pRT

(5-1)

where R is the gas constant and T is absolute temperature. The generalized Reynolds equation then becomes the following function of pressure at constant temperature:

(5-2)

ax

When 0 , = 0 we get the analogue of Eqn 3-35

(5-3)

ax

If U = O , Eqn 5-3 becomes

(5-4)

In the absence of a relative velocity U between the two bounding surfaces, the gas film that separates them must be maintained by the flow of gas from a pressurized source external to the bearing system. 5.2.

GAS-LUBRICATED BEARINGS

In Section 5 . 1 above, the generalized Reynolds equation was made applicable to compressible gases by a straightforward formalistic application of the perfect gas law. As a result the variable of integration is p, the pressure of the lubricant gas film. The left-hand side of the equation ( e . g . Eqn 5-3) becomes non-linear in the variable of integration and no general analytical solution has been found for this problem. Much of the modern literature on the quantitative treatment of gas-lubricated bearings is devoted to manipulations for approximate solutions, either analytical or numerical. These manipulations involve specific restrictions on the physical input conditions, so that discussion of gas lubrication problems tend to be less general and more detailed than treatment of liquid film problems. The solution of Eqn 5-3 is greatly eased by adopting some physical assumptions regarding Eqn 5 - 1 . Ausman [ l ] treated the lubricating film as an isentropic gas, for which by straightforward thermodynamics we can write =

(q’y

where po is the ambient pressure of the gas in the unloaded bearing, PO the corresponding density, and y is the ratio C /C C and C, being the P v’ P specific heats of the perfect gas at constant pressure and constant

,~01ume respectively. *irite ~ q r ,5-5a .IS

Adoptinq

the

notation

i=

p/p,

and %,

=

p/gC, be

Furthermore, i f we define the quantities X = x/B and 5 = z/B f o r a ing of width 5 , we can put Eqn 5-6 into the non-dimensional form

h

Here

=

h/hm,

where h m 1 s the minimum clearance betweer! the bounding

surfaces; A = 6 ~ ~ U B / h $ p , ,where qo i s the viscosity at atmospheric sure; 6 = n / q o . Sternlicht and Elwell 1 2 1 generalized Reynolds equation,

started

il

U

=

pres-

with the following form of the

and used the transformations below to put it in applicable to a journal bearing:

k = -

bear-

a

non-dimensional

fcrm

TVN

2c

Here 9 is the bearing diameter, L its axial length, C the diametral clearance, q a u the average gas viscosity in the bearing , N the rotational speed of the journal in revolutions per second, and R the bearing radius, On substitution we get

which can be integrated numerically by a finite difference method. Figure 5-1 shows the experimentally observed pressure profiie arcun3 the circumference in the midplane of a self-acting gas-lubricated f u l l journal bearing. Sternlicht and Elwell [ 2 ] reported good agreement be-

105

Figure 5-1. Circumferential pressure distribution at the midline of a gas-lubricated journal bearing. N: 66.7 rev/s. V : 6 . 3 5 cm. L: 9.525 cm. C: 0 . 0 0 0 8 5 crn/cm. Gage pressure, kPa: a, 10; b, 20; c , 3 0 ; d , 40; 5 , 50; f , 60; g , 70; h, 80; i , 90. Load, newtons: j, 89; k , 1 3 3 ; 1, 1 7 8 ; rn, 222; n , 266. Pressure above ambient Pressure below ambient _-__ From data by Sternlicht and Elwell 1 2 1 .

.

.

tween these experimental results and the computed values. At the heaviest load imposed the ratio p/po ranged from 0.87 to 1.85. However, the speed at which the bearing was run was not exceptionally high for air lubrication. The data thus obtained show that the analysis and the method of computation are acceptable for the conditions investigated, but there are still questions open concerning the regime of extremely high speeds, where self-acting gas-lubricated bearings exhibit their best utility

.

Since gases are fluids of low density and viscosity, they can be moved at high speeds through very small gaps in applications where good dimensional stability and minimum perturbation from temperature effects are required. Total load capacity and operating stability of gaslubricated bearings under such circumstances are among the important concerns of design analysis and experimental testing i n terms of the principles outlined above. The self-acting gas-lubricated bearing cannot be used when precise location must be maintained with low friction and neg igible wear at very slow speed or when a low start-up torque is required, and it is then that the hydrostatic, externally pressurized bearing fin s application. Because of the variety of bearing configurations, the techniques of solving externally pressurized gas lubrication problems do not always have an obvious relation to Eqn 5-4. For instance, Laub [ 3 ] started his analysis of the circularly symmetrical step-pad bearing shown diagrammatically in Fig. 5-2 with the relation

106

44

Figure 5-2. ing.

I-

Scheme of externally pressurized gas-lubricated

step bear-

for the pressure gradient along the radius n when the volumetric gas flow rate is 2,. The value of 2, required to operate the bearing is

The radial pressure distribution is given by

P

=

Po

[

1 -

Ln ( h/Ro ) L n (R/Ro )

[,

-

I*);(

'I2

from which it is seen that there is a pressure drop from

=

Ro to n

=

R.

Analysis of the externally pressurized gas-lubricated journal bearing is involved, tedious and quite specific to the particular problem. Details can be found in the monograph by Pinkus and Sternlicht [ 4 1 . 5.3.

PROPERTIES OF GASES

From Eqn 5-3 it is evident that the two properties of a gas basically involved in its performance as a lubricating fluid are its pressure behavior and its viscosity. How they are involved depends on what aspect of gas lubrication is being examined. For most lubrication problems gases are regarded as obeying the ideal equation of state, pV = nRT

(5-91

107

where p is pressure, U is volume, R the molar gas constant, T the absolute temperature and n the number of moles of gas. Equation 5-1 follows directly from Eqn 5-9. Equations 5-1 and 5-9 obviously can be converted to units other than those dependent on moles and degrees Kelvin. It also follows from Eqns 5-1 and 5-9 that (5-10) The visccsity of an ideal gas by kinetic molecular theory is given by

(5-1 1 ) where a is the diameter of the spherical, perfectly elastic molecule of mass m and k is the Boltzmann constant. According to Eqn 5-11 the viscosity of an ideal gas increases as the square root of the absolute temperature and is independent of concentration ( i . e . pressure). This relation does not hold for a real gas; it can be shown that the viscosity of a monatomic gas such a s argon, for instance, is influenced by interatomic attraction as follows

(5-12) where H is the Hamaker constant and G is also a constant. The other quantities inside the brackets are constants too, and therefore the viscosity of argon should vary as the 5/6th power of the absolute temperature, which indeed it does. Carbon dioxide also obeys this relation but bromine and methane show significant departures. Another concentration effect, ascribed to the fractional volume occupied by real gas molecules, is given by

q = qo[l

+

(*) (5-13)

where v is a constant. and nitrogen gives: q:(H2 at 298.1 K ) q:(N2

=

Evaluation of Eqn 5-13 from the data for hydrogen

8.90 x 10-5(1

+

3.562

p)

at 2 9 8 . 1 K ) = 1 7 . 1 7 2 x 10-5(1 + 0.911

p)

Equations 5 - 1 2 and 5-13 both indicate departure from ideal gas behavior, the one by intermolecular attraction and the other by an occupied volume effect. Such departure from ideal behavior has a direct influence on density and hence on the transformation of the generalized Reynolds equation. An equation of state for the gas such as the van der Waals equation,

108

RT p = - - V - 6

a2 V2

is of little value in the analytical adaption of gas density to bearing pressure. It serves just as well to have straightforward recourse t2 an empirical pcwer series. Departure from ideal behavior is not likely to be a major source of e r r o r in the design and operation of gas-lubricated bearings. For one thing, the range of pressures is too low: not more than 3 atmospheres above ambient, a range in which deviation from ideal behavior is not of significant consequence. Also, in most cases gas-lubricated bearings operate pseudo-isothermally. The heat capacity of the gas in t h e lubricating film is so small, the body of the bearing i s such a large heat sink and the time available for heat transfer i s long enough so that although theoretically the primary process within the gas film is adiabatic, on a macrophenomenological scale the steady-state behavior is pseudo-isothermal. iience the temperature dependence of gas viscosity and density do not enter into consideration. This explains why Ausman [ l ] c n the one hand felt justified in manipulating the formal gas relations for the isentropic case and then later setting the exponent y equal to unity to make a pseudo-isothermal case.

FIEFERENCES

I. 2. 3.

4.

J. S . Ausman, Trans. ASMS, 7 9 (1957) 1218-1224. B. Sternlicht and R. C . Elwell, Trans. ASME, 80 (1958) 8 6 5 - 8 7 8 . J . H . Laub, 2 . Basic Enc;. (Trans. A S M E ) . 62D ( 1 9 6 0 ) 276-286. 0 . Pinkus and B. Sterniicht, Theory of Hydrodynamic Ldbrication, McGraw-Hill, N e w York, 1961, Dp. 1 7 8 - 1 9 6 .

Chapter 6 MEASUREMENT OF FLUID FILM THICKNESS AND DETECTION OF FILM FAILURE

It is obvious from scrutiny of the nature and mechanism of fluid film lubrication that in order for the 6 i L m to lubricate the rubbing of one solid surface against another i t must separate them. Hydrodynamic calculations will show whether or not a fluid film of the requisite thickness theoretically can exist under the given pressure distribution cver the opposing surfaces. We may therefore take a s an idealized criterion of fluid film failure a calculated film thickness of zero. The physical consequence implied by this criterion is that the solid surfaces can then come into direct contact. Rut in the world of material things the failure of fluid film lubrication is not that straightforward. In the first place, the real surfaces of engineering practice are not geometrically smooth. Instead they are ccmprised of peaks, ridges and valleys: and although a fluid film might theoretically be incapable of existing at asperity contacts, the fraction of the total bounding surfaces of the solids actually participating in the friction and wear at such contacts might be too small to detect by the means available. Secondly, the hydrodynamics of fluid lubrication is a continuum treatment. I t is unlikely that rhis treatmenr: would be valid when the film of lubricant substance decreases to a layer only a molecuie ar two thick. Thirdly, a s we shall see when we look further into contact, friction and wear, the practical attitude toward damage of surfaces by rubbing is flexible, and rubbing in the presence of a lubricant with minimal damage is often accepted as a substitute for totally effective lubrication. Such behavior can involve non-fluid films functioning as lubricants: e . 5 . oxide films on metallic surfaces. I f the idealized concept of fluid film failure proposed above is to have any significance in the world of experimental mechanics and enqineering, we must find a basis for its validity and utility. The study of fluid film failure in a practical sense then becomes the study of the behavior of the boundary surfaces of the solids and of the intervening fluid lubricant as the thickness of the lubricant film approaches zero. An important aspect is the reliability of the measurement technique f o r very thin films. We must be careful not to think of fluid film failure as rupture or breakdown by exceeding the intrinsic strength of the lubricant material. Bulk liquid films do not behave in that way. We know by hydrodynamic theory that the pressure a film of fluid is able to

110

sustain is a function of the motion of the system; let the system come to rest and the film cannot be maintained. In the study of the failure of fluid film lubrication we are confronted by two practical problems: (a) How do we determine the thickness of the fluid film? (b) How do we detect failure of the film? If we have a reliable method for film thickness as a function of some governing experimental parameter, for instance load or pressure, then extrapolation to zero thickness gives the conditions under which failure theoretically should occur. However, non-ideal behavior as the film thickness approaches molecular dimensions may invalidate the extrapolation; also, theoretical failure in the sense we have defined it may not be identical with tribological failure. The rubbing surfaces themselves might be capable of functioning acceptably even though in direct contact, or the fluid may contain constituents that interact with the solid surfaces to promote their tribological durability. With such exceptions understood, this chapter will deal with techniques for determining fluid film thickness and the relation of these determinations to the problem of fluid film failure.

MEASUREMENT OF FILM THICKNESS Methods of measuring film thickness are treated in the following sections according to the basic principles on which they depend. Cases in which the thickness of the lubricant film can be determined by gross measurement of the gap between the bounding surfaces or by gross displacement of these surfaces will be excluded as too obvious to require discussion.

ELECTRICAL METHODS

6.1.

For the most part in the study and practice of lubrication, the bounding surfaces are metallic and the film of oil or other lubricating fluid acts as an electrical insulator. The system can then be treated either as an electrical resistance or as a capacitance. Film Thickness by Electrical Resistance

6.1.1.

Let us consider the lubricant film between two metallic surfaces of length L and width w a distance h apart. The resistance of the lubricant film is given by peh

R = -

LW

where p, is the resistivity of the lubricant substance. voltage E drives a current I across the film,

(6-1)

If

an

applied

111 ELw

k = (6-2)

IP,

the resistance of the metallic bodies being regarded a s negligible. 7

'

,irnit :: .

7

i

However, there are many cheoretical and practical difficulties which the usefulness of the electrical resistance method for determining thickness. Consider the problem of the boundinq surfaces a s il~

~

lustrated in Fig. 6-la for the case of two loaded rings separated by a f i l m of fluid. When the rings are loaded lightly so that the circular periphery is essentialiy preserved, it is virtually impossible to f i x ex- L A y where the fluid fiim becomes so thick that its resistance may be

;?':

regarded as infinite; therefore an evaluation of L cannot be made to i n sert into Eqn 6-2. When the rings are loaded heavily enough to deform their surfaces elastically, then to a first approximation L can be calculated by the elastic thecry of dry contact. F o r a more precise evaluation of 1 , elastohydrodynamic computation of the surface profile could be employed, but in effect this amounts to assuming what one is trying to jetermine.

Figure 6-1. The oil film between two rotating rings. (a) Light load: undeformed periphery. (b) Heavy load: elastically deformed periphery.

The fact that real surfaces are not geometrically smooth inlrroduces a difficulty of considerable practical consequence, especially with thin films. For instance, a representative ground surface of a gear tooth might have asperities lying as much as 250-380 nm (10-15 microinches) above and below the average level of the surface. The lubricant film would thus be highly variable with location along the bounding surface; i t is possible (and in fact it happens) for the bounding surfaces to be i n contact through the lubricant film here and there. A . W. Crook 111 showed that the electrical resistance of two lubricated disks running against each other with combined rolling and sliding increased with time of running and related this to the progressive leveling of asperities by

112

wear to reduce the r.umber of metallic contacts. In the same investigation [ I ] Crook demonstrhted another effect in a dynamically lubricated system which has an important influence on the validity of film thickness determinations by electrical resistance. Direct measurement showed that the resistivity of a commercial turbine oil decreased from ohm-cm at 2 7 3 K ( 3 2 F ) to l o 9 ohm-cm at 5 4 9 K (530 F). I t was also demonstrated that the bulk of the metal in the rotating disks acted as such a large heat sink during a r u n that i t took considerable time for the temperature of the system to stabilize, and even then the temperature of the o i l film was not exactly known. Both of these influences cast doubt on the reliability of the electrical resistance technique for evaluating fluid film thickness. The usefulness of the resistance method is restricted to special circumstances such as light loads, very slow speeds and simple linear geometry. The "discharge voltage" method of A . Cameron and his co-workers is based on Ohm's law and can be regarded as a variant of the electrical resistance approach to the determination of fluid film thickness. Figure 6-2a shows the Ohm's law. behavior observed by Siripongse, Rogers and Cameron [ 2 ] for a steel ball resting directly o n a steel plate and for the ball separated from the plate by oil films of different thickness. The relation between the current passed and the driving e.m.f. when the ball rests directly on the plate is linear and the slope of the line is the ohmic resistance of the contact. When there is an oil film between the ball and the plate, the relation between the current and the e.m.f. is no longer monotonously linear; instead there are two linear segments joined by an intervening transition. The slope of the initial linear portion of the curve is greater for the thicker film and the terminal linear portion of each curve has the same slope as the straight line for metallic contact.

0

0.5

1.0

1.5

0

2

4

6

-3

Film Thickness, 10 cm

Amperes

Figure 6-2. Principle of the discharge voltage method for film thickness. (a) Calibration of discharge voltage. Discharge voltages for indicated film thickness denoted by (b) Relation between film thickness and discharge voltage for 1 ampere. Data by Siripongse, Rogers and Cameron 121.

*.

113

The initial slope is interpreted as the ohmic resistance of the oil film, which by Eqns 6-1 and 6-2 is proportional to the film thickness. This holds for only a small part of the overall behavior observed. At some critical voltage the electrical resistance of the system is no longer determined by the oil film thickness and there is a transition to behavior resembling Ohm's law for metallic contact. The critical voltage for the transition depends on the oil film thickness. At this voltage and above, the ohmic resistance of the film breaks down and the current is carried by a stream of ionized particles, the flux density of which depends on the voltage, analogous to the transport of electricity in low pressure discharge tubes. After passage of electrical current in this manner has been stably established, the difference between the linear voltage function and the Ohm's law line for metallic contact is independent of the current and is governed by the oil film thickness. This difference between the total voltage and the metallic contact voltage is called the "discharge voltage" by Cameron. In practice the method is based on the discharge voltage required to pass a current of one ampere through the oil film. Static calibration consists of plotting curves such as seen in Fig. 6-2a for a range of film thicknesses and then plotting the relation between the discharge voltage and film thickness, which is linear, as shown in Fig. 6-2b. Reliable data to establish the validity of the discharge voltage method for dynamically generated fluid films do not seem to be available; although MacConochie and Cameron [3] in a study of oil film thickness between operating gear teeth claim close agreement with the kind of results obtained by the electrical capacitance method ( q . w . 1 , details o f the comparison are not given. But even i f the absolute value of the film thickness as determined by the discharge voltage method is subject to question, the technique can be conveniently applied to follow the decrease in oil film thickness to scuffing failure, as illustrated in Fig. 6 - 3 by an example from the work of Askwith, Cameron and Crouch [41 with a four-ball lubricant testing machine. The rotating ball is connected to one side of the electrical circuit by a mercury slip ring and the three stationary balls are locked in a pot connected to the other side of the circuit (Fig. 6-3a). The voltage required to maintain a steady current of one ampere is regulated by a variable resistor and is read on a voltmeter. The voltage decreases with increasing load ( i . e . the oil film becomes thinner) until scuffing occurs, whereupon the system is short circuited and the discharge voltage drops to zero (Fig. 6-3b). At the same time the coefficient of friction shows a sharp increase. I t is apparent in Fig. 6-3b that the compounding of fatty acid additives in the base fluid complicates interpretation of the diagram as straightforward thinning of the oil film under load. However, Cameron and his co-workers carried out Some significant experiments on scuffing and oil film failure in this

114

5

I

a2

0.2

0,

0

c

9 W

p 0.1 0

c 0

??

n

0 0

2000

4000

Load, newtons

Figure 6 - 3 . Film thickness by the discharge voltage method. (a) The four-ball technique: 1. ball assembly; 2. ball pot (carries the friction torque arm); 3 . bearing; 4 . insulating base; 5. mercury slip ring. (b) Effect of load on film thickness by the discharge voltage method: I. cetane; 11. 0.03 M. lauric acid in cetane; 111. 0.03 M. stearic acid in cetane. Data by Askwith, Cameron and Crouch 1 4 1 . way as is discussed in Chapter 10; so even with its quantitative de f ciencies the discharge voltage method seems to be a useful technique for following changes in lubricant film thickness. 6.1

2.

Film Thickness by Electrical Capacitance

In principle the theory of electrical capacitance can be applied to the determination of lubricant film thickness between the bounding s u r faces of two solids, but in practice the geometrical difficulties for electrical resistance methods are even described in Section 6.1.1 more troublesome for capacitance. I f the solids are bounded by two flat surfaces parallel to each other, the electrical capacitance problem becomes that of a parallel-plate condenser, for which the formula is

c =E A o 4ah

(6-3)

where A, is the nominal area of the conjunctive zone, h is the separation of the flats and E is the permittivity of the lubricant in the gap be-

115

tween the flats. But i f the contour of the bounding surface is that of an undeformed ring, as depicted in Fig. 6-la, then the decision as to how much of the gap between the surfaces to include complicates the problem. Some illustrative computations for two parallel cylinders and for two spheres have been published by P. B r k e r [ 5 1 . When the rings are deformed elastically, the lubricant-filled gap in the loaded zone can be regarded as a parallel-plate condenser to which, ignoring the capacitances of the entry and the recess regions, Eqn 6-3 is and hence applied. From elastic theory A, is proportional to W2’3,

(6-4) where W is the applied load. However, the havior does not obey Eqn 6-4; instead

c

=

co

+ kW2’3

experimentally

observed

be-

(6-5)

as observed by Archard and Kirk 161, who worked with crossed cylinders. Figure 6-4 shows some of their results. The experimental lines for C - C o all pass through the origin, and therefore k can be evaluated from the slopes of these lines. Correcting for the capacity of the entry and recess regions puts Eqn 6-4 in the form

4nh

(6-6)

Interpreting C* as identical with Co gives

Figure 6-4. Electrical capacitance as a function of load in a crossedcylinders rubbing machine. Speeds in cm/s. Data by Archard and Kirk [61.

116

h = -

EK

(6-7)

4nk

Since k is obtained empirically and K can be evaluated by the Hertzian calculation, the thickness of the lubricant film can thus be found from capacitance measurements. The following technique for scanning the oil-filled gap between loaded disks was developed by Crook [ 7 1 . A chromium electrode is evaporated onto a glass disk, as shown in Fig. 6-5. A s the electrode traverses the region of the oil-filled gap, the potential across the resistor R is proportional to E / h . The potential as a function of the position of the electrode in the gap is displayed on an oscilloscope and a plot of the contour of the gap can be made. The gap thickness is calibrated statically by using measured spacers. I f the width of the electrode relative to the length of the conjunction zone is small enough, no elaborate theory or calculation is required.

Exit

Entry

Figure 6-5. Film thickness by capacitance with a scanning deposited chromium transducer. (a) Chromium electrode and electrical circuitry. (b) Oscilloscope trace of potential across resistance R.

Crook reported comparison of the results obtained by the scanning method [ 8 ] with those obtained by another, more complicated version of For average film thicknesses in the range the capacitance technique [ 9 ] . 50-150 pm, the results by both methods were substantially the same. Orcutt 1 1 0 1 used a capacitance scanning method in which the transducer was a platinum strip 0 , 0 25 mm wide across the edge of a glass disk. The circuitry was arranged to give a voltage signal on the oscilloscope of a commercial capacitance gaging system. The calibration relations between voltage and capacitance o r film thickness are shown in The relation between film thickness and voltage is nearly Fig. 6-6. linear in the range 2 03 0-3 05 0 nm ( 8 0 - 1 2 0 microinches) but voltage does not change rapidly in this region. Voltage is also linear in the range 350-75 0 nm ( 1 5 - 3 0 microinches) but here the voltage changes too rapidly for reliable evaluation of the film thickness. In the range 750-2030 nm the voltage function is such that a calibration curve must be used.

117 Capacitance, picofarads

15 10

65-

ul

c

3

4-

32I01 0

I

I

1

I

I

1

I

4 0 0 800 1200 1600 2000 2400 2800 Film Thickness, nrn

Figure 6-6. Calibration curve for film thickness by capacitance. by F. K. Orcutt [lo].

Data

Hamilton and Moore 1 1 1 1 described a refined version of the Beposited electrode technique in which the transducer is a very small strip of manganin. of dynamic film thickness determinations by The reliability capacitance measurements is an open question, principally because there are no absolute standards by which to judge. In their investigation of elastohydrodynamic lubrication, Archard and Kirk [ 6 ] determined film thicknesses over the range 2 0 to 1000 nrn; the uncertainty of their determinations ranged from 20 nm for films of the order of 20-50 nm thick to 250 nm for films 750-1000 nm thick. Crook’s comparisons of film thicknesses determined by his two capacitance methods indicated an uncertainty of 2 0 0 nm [81. Orcutt reported that the voltages required f o r his capacitance measurements exceeded the dielectric strength of the o i l film for thicknesses less than 1 5 0 nm [lo]. 6.2.

OPTICAL INTERFEROMETRY

The determination of oil film thickness in elastohydrodynamic lubrication by optical interferometry is disclosed in a series of communications by Cameron and his co-workers [ 1 2 , 13, 14, 1 5 1 . The principle of the method, as originally devised for the contact of a sphere against a flat plate, is illustrated in Fig. 6 - 7 . A carefully made steel ball B , 2.54 cm in diameter, is cemented to a conical chuck C which is driven by a quill shaft S. A light spring seats the ball against a stationary con-

118

Figure 6-7. Ball and plate apparatus for interferometry. After and Gohar [13].

\

Cameron

Incident Roy I

Fringe locolued here Glass

Plote

i Figure 6-8. fringe ,

Optical

path

difference for formation of an interference

ical bearing. The loading plate P carries a flat glass plate G. A microscope M is positioned over the ball and a collimated beam of light is incident on the glass plate and the ball as indicated by I. When the ball and the plate are loaded against each other in dry contact by the weight W, the elastic deformation area is a circle. Figure 6-8 shows in simplified form the optical path difference necessary to form an interference fringe. When the localized fringes are viewed

119

through the fringe order

ox

=

2t

5

microscope, a set of Newton's rings is seen, for which the is given by (6-8)

where 1 is the wave length of the light and .t is the distance between the plate and the ball that gives the required optical path difference for I f the space between the plate and the ball is filled with the fringe. oil of refractive index n, then the equation for the formation of a fringe becomes (6-9)

The central region, corresponding to the area of dry contact, is dark because of the phase change of half a period due to reflection at the ball surface. The first dark ring corresponds to a film thickness t = X/2n. By measuring the radial coordinates of the rings for a succession of values for 0 , a topographical map of the ball surface can be constructed

.

When the ball rotates, the Hertzian area of dry contact is replaced I f the increase in by an elastohydrodynamically generated oil film. rotational speed of the ball is regulated very carefully, the central region will change from the dark of dry contact to light. The interferometric condition for a light central region is t = 1/40. The interferometric equation for the first dark fringe is then t = 3X/40; i.e. the central region is filled with an oil film of thickness X/4 and the first dark fringe corresponds to a film of thickness 3X/4. Further controlled increase of the rotational speed will change the central area of the interferogram from the light to dark again. The governing condition for the first dark fringe then becomes t = 3X/2. By carefully keeping count of the number of changes from dark to light in the central area we can use the dark fringes as a measure of the oil film thickness by the relation II = 2 0 -ix a

(6-10)

Figure 6-9. Film thickness relations by interferometry of a fluid-filled gap.

120

where 11 = to + t' and to = iX/4, i being the count of the number of chanFigure 6-9 ges dark-light-dark as the speed of rotation is increased. shows the relation of h to to and 2 ' . Some points of experimental technique should be mentioned. The contact pressures under which the apparatus can be operated are increased by the use of diamond, which is mechanically stronger than glass, as the plate material. Furthermore, diamond has good thermal conductivity, so that heating of the contact zone as the experiment proceeds is easier to control. The average refractive index of the oil in the pressurized gap is computed from the Lorenz equation 1

canbtant (6-1 1 ) where dp is the density of the fluid at the pressure p. The constant is evaluated from the available data for atmospheric pressure. The value of n at the pressure p can then be found i f the relation between the density of the fluid and pressure is known. Figure 6-10 shows three interferograms for an experiment carried out under a load of 71.2 N (16 lb) which gave a maximum Hertzian pressure of 1517 MPa (223,000 lb/in2), average pressure 1 1 0 3 MPa (160,000 lb/in 2 ) .

X

(a) 0 cm/s

(b) 3.2 cm/s

(c) 28.6 cm/s

Figure 6-10. Interferograms: ball on plate. Load 71.2 N. Speed, cm/s: (a) 0, (b) 3.2, (c) 28.6. Arrow shows direction of rotation. After Gohar and Cameron [14].

Figure 6-10a is the interferogram for a non-rotating ball, stationary contact; the fringes are concentric circles. It can be demonstrated that if the radius h of a fringe is small compared to the radius R of the ball, the separation between two fringes is given by (6-12) From this we see where a . and ak are the orders of the fringes 1161. j n can be measured directly with the microscope or on a that photomicrographic interferogram. When the ball rotates and the inter-

121

ferograms are of the type illustrated in Figs. 6-lob and 6-10c, the fringes are contour lines for which h/X is constant. The absolute value of h is given by Eqn 6-10; but once h has been evaluated for a particular fringe by any means whatsoever, the thickness for other fringes can be obtained through Eqn 6-12. Figure 6-11 shows two film-thickness profiles constructed from an interferogram made with the lubricated ball rolling at the rate of 28.6 cm/s. One profile is in the direction of rotation, the other at a right angle to it. The self-consistency of the measurements is excellent.

ilJw 0.5

Entry L I

6.3.

1

1

I

I

I

I

I

Exit Entry I

I

I

Exit I

I

I

I

I

I

I

I

X-RAY TRANSMISSION

If a beam of X-rays is directed at an oil-filled gap bounded by material which is opaque to the X-ray beam, then a quantitative measurement of the X-ray flux transmitted through the gap can be used to assess The method as applied to two rollthe thickness of the oil film. ing disks by Sibley and Orcutt [171 is illustrated diagrammatically in Fig.. 6-12. A collimated monochromatic beam of X-rays is passed through a set of adjustable slits to deliver a square beam of known cross-section Lo.ad

Collimating slit,

ent beam

Figure 6-12. X-Ray method for film thickness.

122

to the conjunction region of the two rolling disks. Ideally only the radiation that impinges orthogonally on the oil-filled gap is passed through to be measured by the counter, the material of the disks being opaque to the radiation. The gap is scanned along the axis of rotation of the disks by moving the disk assembly on a carefully aligned set of tracks, the X-ray beam remaining stationary. The disks are mounted so that they may be loaded by an applied thrust force or else separated a known amount by a micrometer screw. The latter allows calibration of the A separate intensity of the X-ray beam in terms of film thickness. calibration is required f o r each kind of lubricating fluid used. This technique measures the minimum thickness of the oil film in a direction perpendicular to the hydrodynamically generated flow of oil through the gap between disks. Apparently it was one of the earlier methods developed for the precise experimental investigation of elastohydrodynamic lubrication. Prompted by the fact that the observed film thickness as measured by the X-ray technique was significantly less than predicted by a number of generally accepted expressions derived from elastohydrodynamic analysis, Kannel and Bell [ 1 8 1 examined the method critically. Although they found room for several refinements in the technique, none of these was of major significance. Bell and Kannel [ 1 9 ] ascribed the differences between the experimental observations and the theoretical computations to rheological factors not taken into account by the theory. 6.4.

SUMMARIZING DISCUSSION OF FILM THICKNESS MEASUREMENT

In the foregoing treatments of the methodology of film thickness determination, the experimental results have been examined with respect to lubrication theory rather than direct engineering application. Still, the ultimate utility of establishing the validity of a theoretical relation is practical: to predict the engineering limits for the existence of a fluid film, which in turn can be confirmed or tested by laboratory experiments amenable to close control and measurement, e . g . rolling/ sliding disk experiments. To be useful from both a theoretical and a practical viewpoint, the validity and accuracy of the film thickness measurements must be established on a primary basis. Direct measurement of oil film thickness by electrical conductivity has two basic drawbacks from the point of view of primary calibration. One is .the sensitive response of the resistivity of the oil to temperature. Unless the temperature of the oil under operating conditions is known accurately, it is uncertain that the calibration obtained under static conditions can be applied. Direct measurement of film temperatures by an infrared emission technique has shown temperatures within the oil film as high as 388 K ( 1 1 5 C ) [201. The other source of uncertainty to be considered is the increase in field intensity as the oil film be-

123

comes thinner under load or because of internal heating, This may bring about electrical breakdown while there is still a funct oning film of lubricant between the bounding surfaces. Electrical breakdown of very thin oil films is a bas c difficulty in the capacitance method also. The other difficulties assoc ated with applying static calibration to a dynamically generated film are chiefly manipulative: exclusion of o r compensation for stray capac ties, balancing the capacitance bridge, etc. The basic theory for the absorption of X-rays is the s mple exponential relation 1 = l o e -ae

(6-13)

where l o is the intensity of the X-ray beam incident on a film of length in the direction of propogation of the beam, 1 is the intensity of the The only emergent beam and a is the linear absorption coefficient. physical complication is the influence of the density of the fluid in the lubricant film on the absorption coefficient a. Sibley and Orcutt [ 1 7 ] reported that this effect is negligible. Therefore there is a straightforward relation between the cross-sectional thickness of the oil film and the attenuation of the X-ray beam. The chief experimental difficulty is manipulation and the method is unwieldy. Thus, the results already in the literature are probably acceptable as far as they go, but the X-ray technique seems to have disappeared from the scene, to be replaced by more convenient approaches such as strip transducers, even in the laboratory where X-ray transmission was developed.

L

The method which seems to be soundest and most free of empirical complications from the point of view of basic calibration is interferometry. The calibration is derived from fundamental optics. A technique for dealing with the effect of pressure on the refractive index of the fluid is available via the Lorenz equation. An implicit difficulty is the effect of temperature on the density of the fluid and thus on the evaluation of the Lorenz equation. The necessity of passing the light through a flat transparent plate to form the fringes imposes some limitations on the applicability of the method. DETECTION OF FILM FAILURE 6.5.

THE MEANING OF FILM FAILURE

In order that measurements of film thickness be tractable, the surfaces that bound the oil film should be substantially smooth, with no small-scale irregularities. Indeed, we would be unable to interpret the results of electrical conductance or capacitance for very thin films on any other type of surface. B u t in fact real surfaces do have small-scale irregularities and asperities, and it is only because the influence of

124

these irregularities averages out that the conductance and capacitance methods can be fitted to an analytical model. Conventional optical interferometry is responsive to surface irregularities as small as 50.8 nm ( 2 microinches). Thus the profile of a film 500 nm thick would be perturbed 10% by such surface irregularities. Let us examine the process of film failure conceptually by considering the progressive thinning of a fluid film bounded by two perfectly smooth solid surfaces. We might say that as long as there is a film of lubricant one molecule thick between these surfaces they are not in contact. But we cannot be sure the surfaces are truly isolated from each other in the sense that the atomic force fields of the surfaces do not interact through the molecular film of lubricant. However, the theoretical possibility of such interaction is not necessarily a criterion for film failure, for as we shall learn in subsequent chapters, there are types of adsorbed films only one or two molecules thick that function recognizably and satisfactorily a s lubricants. The crucial condition that characterizes failure of a monomolecular film is inability to persist in a state of structured adsorption on the bounding surfaces; consequently atoms in these surfaces can approach one another and interact directly. Molecules of non-polar liquids are not adsorbed as persistently at the bounding surfaces as are molecules of polar "boundary" lubricants and are more easily disoriented and desorbed under the influence of increased temperature and shear stress. However, this is not the process of film failure one would detect by an experimental technique such as electrical conductance, electrical capacitance or optical interferometry. None of these techniques, as described in the preceding sections of this chapter, is applicable to the evaluation of a monomolecular layer. Therefore, the indications of fluid film failure by these techniques are not those of the disorientation or the desorption of the final monomolecular film of lubricant; the phenomena to which they apply occur on a much coarser scale. There is no unequivocal basic standard for failure of a lubricant film, either a fluid film or an absorbed monomolecular film. Film failure is inferred from overt tribological behavior: high levels of friction or wear, destructive scuffing, etc. A s the film thins to dimensions which permit interaction between asperities, the structure of the bounding surfaces often becomes as much a part of the failure process as the thickness of the lubricant layer. Thus measurements of fluid film thickness by the methods described in the foregoing sections of this chapter cannot by themselves be used to predict lubrication failure; they must be employed in the full tribological context of the situation. Lubrication behavior in the presence of adsorbed "boundary" films and surface reaction products is reserved for subsequent chapters. In the present chapter discussion of lubrication failure will be in terms of thinning of the

125

fluid film. 6.6.

ELECTRICAL METHODS OF DETECTING FLUID FILM FAILURE

If the fluid film separating two metallic bounding surfaces is an electrical insulator, then loss of insulating behavior and appearance of conductance can be interpreted as contact between these surfaces. This is the premise behind the electrical conductance method of detecting lubricant film failure. A practical limit on the applicability of this premise is electrical breakdown of the fluid as thinning of the film concentrates the field intensity. Another complication arises from the fact that for the structured surfaces of every day experience first contact is at the highest asperities; rough surfaces may therefore come into initial contact sooner than indicated by the overall trend of the resistance measurements.

Some work carried out by C. M. Allen on the electrical measurement of oil film behavior in plain bearings s illuminating [ 2 1 ] . The study of a plain bearing has certain innate advantages because of the relative ease with which the theoretical oil film thickness can be calculated. The basic circuitry employed is illustrated in Fig. 6-13. The input is

Audio Frequency Oscillator

Figure 6-13.

I

Circuitry for detecting film failure in a plain bearing

.

delivered at a controllable voltage (up to 100 volts maximum) at a frequency of 20,000 Hz. As long as the oil film functions as an insulator, the cathode ray oscilloscope will display the wave form of the voltage source, as shown in Fig. 6-14a. Complete breakdown of the film unbalances the circuit and the oscilloscope then shows a straight line (Fig. 6-14b). The film thickness is calculated from the applied voltage required to show a condition of breakdown on the oscilloscope screen, a

126

(a)

(b)

(C)

Figure 6-14. Oscilloscope traces of film condition in a plain journal bearing. (a) Film intact. (b) Total film failure. (c) Intermittent failure. Data by C. M. Allen 1211.

value of 100 kilovolts per centimeter being assumed strength of the oil.

for

the

dielectric

The significance of this work is not in the accuracy of the determination of film thickness, for in fact the film thickness computed from the dielectric strength and the applied breakdown voltage was 152-254 nm (6-10 microinches), whereas the hydrodynamic computation gave a range of 2400-17,000 nm (95-670 microinches). When the bearing was operating under full hydrodynamic conditions and the sweep frequency of the oscilloscope was synchronized with the frequency of the input voltage, the display on the oscilloscope was the anticipated sine wave. As the load on the bearing was increased , eventually the oscilloscope display became a mixture of the sine wave curve characteristic of fluid film lubrication and an occasional horizontal line indicating film failure. The test voltage frequency was 2 0 , 0 0 0 Hz; the test journal rotated in the range 30-167 revolutions per second. The sweep speed of the oscilloscope could be adjusted to sample several locations on the journal for each revolution in the bearing. When the sweep of the oscilloscope was slowed down and synchronized with the rotational speed of the journal, it was observed, as shown by Fig. 6-14c, that at loads of borderline severity the film failed at identifiable locations on the bearing. The revelatory thing about this experiment is that the film failure observed in a real operating bearing was not a sudden go or no-go event but rather a process influenced by high spots on the journal or the bearing surface, accidental intrusion of grit or wear debris in the oil, etc. M. J. Furey 1 2 2 1 studied electrical contact during the lubricated rubbing of a ball against a ring, using the basic circuit shown in Fig. 6-15. The input voltage is dropped through the resistors R 1 and R 2 > R 1 ) so that only about 15 mV is applied across the b a l l and ring. (R2 When the oil film between the ball and the ring is intact, the oscilloscope trace indicates infinity. In actual practice the ratio R2/R1 is adjusted to give a convenient working midscale resistance by means of a

127

Figure 6 - 1 5 .

Basic circuitry for measuring "percent metallic contact."

Time, 10 ms

;"F(-=l E

8 0

c

U

0 Yo

loo/o

50%

90%

Figure 6 - 1 6 . Oscilloscope traces for "percent metallic by M. J. Furey 1 2 2 1 .

100%

contact."

Data

resistance switch box. When the oil film is no longer intact and there are locations at which metal-to-metal contact occurs, the current is shorted through the oscilloscope. Figure 6 - 1 6 shows how the oscilloscope traces are used to interpret "percent metallic contact." The circuit is balanced so that the oscilloscope responds to only two extreme conditions: full plate current for high resistance at the ball/ring conjunction or practically no current for low resistance at the conjunction. The "percent metallic contact" is calculated from the fraction of the sweep time that corresponds to low An integrating circuit (shown below the resistance ( 1 ohm or less). dashed line in Fig. 6 - 1 5 ) can be used to give direct readout of "percent metallic contact" on a recorder. It should be apparent that interpretation of the raw oscilloscope traces in terms of percent metallic contact is misleading. Since the response of the circuit is all or none, only

128

under carefully arranged experimental conditions can a valid distinction be made between a large contact and a small one. In general the method gives the kind of results anticipated from hydrodynamic lubrication theory. At a given load, "percent metallic contact" decreases with increasing speed; at a given speed it increases with load. "Percent metallic contact" is decreased for the oil of greater viscosity. Chu and Camercn I231 have shown that R 1 and R2 must be selected judiciously with respect to the total resistance of very thin oil films in the rubbing conjunction. If R 1 is too large, then a thin but continuous oil film of small area can act as a short in the circuit and give a spurious reading of 100% contact. 6.7. DETECTION OF SURFACE CONDITION

FLUID FILM FAILURE BY FRICTION OR BY EXAMINATION OF

Part of the difficulty of deciding from electrical measurements whether or not a fluid film is protecting the bounding surfaces from contact arises from uncertainty regarding the disruptive effect of the apIn theory this plied electrical field as the film becomes very thin. difficulty can be circumvented by looking for evidence of contact on the bounding surfaces themselves. In practice this expedient is not all that straightforward o r easy. At first glance it seems that one of the simplest ways to detect failure of a fluid film would be to watch for a sudden increase in the coefficient of friction. Classical hydrodynamic lubrication is characterized by coefficients of friction substantially lower than 0.01. Under confirmed conditions of elastohydrodynamic lubrication at contact pressures of c a . 690 MPa (100,000 lb/in2), Sanborn and Winer [24] observed traction coefficients (the equivalent of coefficients of friction) ranging from ca. 0.02 to 0.09. A sharp increase in the coefficient of friction to levels above 0.1 might be taken as phima 6acie evidence that the fluid film has thinned so that it no longer lubricates in the hydrodynamic sense. Examination of the condition of the bounding surfaces will usually confirm this. But the reverse is not necessarily true: that coefficients of friction less than 0.1 are indicators of simple hydrodynamic or elastohydrodynamic lubrication. Many instances of the action of "boundary" lubricants dissolved in oil are associated with coefficients of friction as low as 0.06 under conditions incompatible with simple hydrodynamic or elastohydrodynamic lubrication. Such cases will be treated in subsequent chapters devoted especially to this kind of behavior. In the discussion to follow in this chapter we shall examine the role of friction and surface damage, used in conjunction with electrical methods, in detecting the failure of hydrodynamic or elastohydrodynamic fluid film action. Let us re-examine the discharge voltage data of Askwith, Cameron and

129

Crouch [ 4 1 shown in Fig. 6-3b. Granted the criticisms of the method as a quantitative measure of film thickness, the discharge voltage can still be accepted as a valid indication of the existence of an electrically resistant film of lubricant. Evidence of scuffing when the discharge voltage dropped to zero is described as a sharp increase in friction and chattering of the spindle which held the rotating ball [ 4 1 . When the test machine was run at a load just below the scuffing level without any current flowing, no damage to the rubbing surfaces occurred; nor was there any damage when the discharge voltage appropriate to the load was then applied, showing that lubrication failure was not induced by the discharge voltage. By and large the influence of increasing load is that expected: however, a number of complications ascribed to purposely compounded fatty acid additives do arise, as described in the original work. Of particular interest is the lubricant behavior shown in Fig. 6 - 1 7 for two gas oils of commercial origin. In the load range 6 7 0 - 1 3 3 5 N the discharge voltage dropped to the small constant value of 0 . 0 1 volt and the balls did not scuff. This was ascribed to the additive effect of surface-active substances which are not removed from the gas oil by refining. The significance of these observations is that while a discharge voltage of zero can be accepted as an indication of film failure at the bounding surface, it cannot be accepted as evidence of 6Luid film failure without separate corroboration.

Load, new tons

Figure 6 - 1 7 . Discharge voltage behavior of films of gas oil. Askwith, Cameron and Crouch [ 4 1

Data by

Another approach to the detection of fluid film failure is the study of wear in relation to lubricant film thickness. Figure 6 - 1 6 shows observations by E. W. Landen [ 2 5 ] of the wear of two disks rubbing with The film thicknesses were calculated velocities in the ratio 1:1.25. from the operating parameters of the apparatus and elastohydrodynamic theory. A s shown by curve D , for an oil film 65 nm thick wear ceases after a break-in period of one hour. When the oil film is only 2 0 nm

130

D -

L

0 f 0,

c W

c

I50

c 0 U v-

h, nm A 19.6 B 28.4

al L

a cn

E

50

C 30.0

L

0

D 64.8

0

1

1

1

I

5

10

15

20

25

Hours

Figure 6-18. Wear of ground surfaces in relation to oil film Data by E. W. Landen [251.

thickness.

thick, wear proceeds at a steady rate over the entire 24 hours of the run. For intermediate film thicknesses there is a systematic transition between initial wear at a high rate and slower terminal wear. When the oil film is thick enough, selective wear of the asperities smooths the bounding surfaces of the disks until a full fluid film is established, If the oil film never becomes thick enough in stopping further wear. relation to the surface structure, the bounding surfaces do not wear smooth enough to permit establishment of a complete fluid film by hydrodynamic action. The interaction of film thickness and surface structure is not assessed by simply measuring surface roughness. The roughness of new disk surfaces was 125-250 nm, whereas the thickest film for which data are shown in Fig. 6-18 was 65 nm. Localized film failure is more complex than just penetration by the highest asperities. Tallian e t at?. [26, 271 combined Furey's concept of "percent metallic contact" with the measurement of wear and applied it to the study of thin films of lubricant between two surfaces of very small roughness in rolling contact. They carried out a detailed analysis of the contact voltage signals and the deduction of "no-contact time percentage" (the reverse of Furey's "metallic contact percentage"). Figure 6 - 1 9 shows the relation between the "no-contact time percentage" and a dimensionless film thickness parameter defined by 151

=

h0

6

(6-14)

-rq

a Ulh am d m C h om ..-I

U l -

am

cc

h

a s ,

roc m

131

132

where ho is the average film thickness computed from elastohydrodynamic theory and 6 is the surface roughness obtained by statisticai analysis of surface profile data. Experimentally the lubricant thickness was varied by adjusting the speed of a rolling ball apparatus, electrical contact data being obtained at the same time. When 151 = 1, i . e . when the surface roughness is equal to the film thickness, contact is assumed to be substantially permanent and constant, i . e . T / T o = 0. The minimum value actually seen for T/To in Fig. 6 - 1 9 is 0.1%, which for all practical purposes may be taken as zero. Contact is substantially zero ( T / T o = 99+ % ) when 151 is about 4. Thus T / T o = 99+ % may be taken as an indicator of the existence of a full fluid film. Since it prevents surface contact, a f u l l fluid film should not permit wear. This postulate was tested by making the driven ball of a rolling four-ball contact tester radioactive and monitoring the accumulation of wear debris in the lubricant. Figure 6 - 2 0 shows examples of wear rate, expressed as picograms of metal per meter of rolling distance, plotted against 151 in log-log coordinates. For I c l = 1 the wear rates are significantly greater than they are for 1 5 1 in the range 3-5; the type of oil has a strong influence on the wear rate function. Thus, for the two diester lubricants, wear increases by a~ factor of 7 5 - 1 6 5 as ( 5 1 decreases from 5 to 1 . For a mineral oil the relative increase is only about 12 for a load of 6 6 7 N on the balls and 70 for a load of 2 2 3 N. The RMS surface roughness of the balls in the test apparatus was nm (1-1.5 microinches). A value of 4 for 1 5 ) gives values of ho in the range 100-160 nm. The limit of reliability in the detection of wear is of the order of 1 4 - 1 6 picograms per meter of rolling distance. The experimental wear rate differences are more pronounced than they appear in the log-log plots of Fig. 6 - 2 0 . The logarithmic representation of the wear rate function reflects the distribution of asperity heights in the surface, as is shown in Chapter 12. At a value of 5 for 1 5 1 , the difference in wear rates with the two ester lubricants is negligible because the wear rate cannot be distinguished from zero within the limit of discrimination of the measurements. When 151 = 5 the wear rate with mineral oil under a load of 2 2 3 N is 4 5 pg/m, which is only three times the lower limit of discrimination , but under a load of 6 6 7 N the'wear rate is 2 4 0 0 25-40

pg/m, higher than anticipated by a factor of 5 3 . One of the key relations in this treatment is the definition of 1 5 1 , which in the ultimate analysis rests on the validity of the elastohydrodynamic computation of h,, the mean film thickness. The behavior of the mineral oil under 667 N load, which extrapolates to a film thickness of 1 1 5 5 nm f o r minimal wear, suggests that the contact parameters at the surfaces and the properties of the oil may not be known precisely enough for an accurate solution. The previously cited work of Landen

133

[25] indicates that a film 65 nm thick prevents contact after preliminary break-in running. This value comes reasonably close to the lower limit of 100 nm computed by Tallian e t a l . for 1c1 = 4. The wear measurements of Tallian e t a l . were more sensitive than those of Landen by a factor of 5 x 10”. It seems, therefore, that as means of detecting contact become more sensitive and subtle, especially for real surfaces which are not ideally smooth (even though the roughness may not be greater than 25 nm), the ability to establish the critical evidence for the existence of very thin, unbroken films of lubricant becomes less certain. We are thus driven to the expedient of reasonable conjecture from the behavior observed as a function of film thickness.

REFERENCES 1. 2.

3. 4.

A. W. Crook, Proc. Inst. Mech. Engrs., 171 (1958) 187-214. C. Siripongse, P. R. Rogers and A. Cameron, Engineering, 186

(1958) 146- 147. I. 0. MacConochie and A. Cameron, J. Basic Eng. (Trans. ASME), 82D (1960) 29-34.

T. C. Askwith, A. Cameron and R. F. Crouch, Proc. Roy. SOC.

London,

A291 (1966) 500-519. 5. P. Bruser, Schmiertechnik/Tribologie, 21, No. 4 (1974) 79-83. 6. J. F. Archard and M. T. Kirk, Proc. Roy. SOC. London, A261 (1961) 532-550. 7. A. W. Crook, Nature, 190 (1961) 1182-1183. 8. A. W. Crook, Phil. Trans. Roy. SOC. London, A255 (1963) 308-309. 9. A. W. Crook, Phil. Trans. Roy. SOC. London, A250 (1958) 387-409. 10. F. K. Orcutt, ASLE Trans., 8 (1965) 381-396. G . M. Hamilton and S. L. Moore, Proc. Roy. SOC. London, A322 (1971) 11. 313-330. 12. R. Gohar and A. Cameron, Nature, 200 (1963) 458-459. 13. A. Cameron and R. Gohar, Proc. Roy. SOC. London,‘A291 (1966) 520-536. 14. R. Gohar and A. Cameron, ASLE Trans., 10 (1967) 215-225. (1968) 15. C. A. Foord, W. C. Hammann and A. Cameron, ASLE Trans., 1 1 31-43. 16. S. Tolansky, An Introduction to Interferometry, Longmans, Green and Co., London, New York, Toronto, 1955, p. 66. 17. L. B. Sibley and F. K. Orcutt, ASLE Trans., 4 (1961) 234-249. 18. J. W. Kannel and J. C. Bell, J. Lubrication Tech. (Trans. ASME), 93F (1971) 478-484. 19. J. C. Bell and J. W. Kannel, i b i d . , pp. 485-496. 20. V. Turchina, D. M. Sanborn and W. 0. Winer, J. Lubrication Tech. (Trans. ASME), 96F (1974) 464-471. 21. C. M. Allen, in Mechanical Wear, J. T. Burwell, jr. (Editor), Am. SOC. for Metals, 1950, Chapter X. 22. M. J. Furey, ASLE Trans., 4 (1961) 1-11. 23. P. S. Y. Chu and A. Cameron, ASLE Trans., 10 (1967 226-234. (Trans. ASME), 24. D. M. Sanborn and W. 0. Winer, J. Lubrication Tech 93F (1971) 342-348. 25. E. W. Landen, ASLE Trans., 1 1 (1968) 6-18. 26. T. E. Tallian, Y. P. Chiu, D. F. Huttenlocher, J. A. Kamenshine, L. B. Sibley and W. E. Sindlinger, ASLE Trans., 7 1964) 109-126. 27, T. E. Tallian, E. F. Brady, J. I. McCool and L. B. Sibley, ASLE Trans., 8 (1965) 411-424.

134

Chapter 7 FRICTION:

PHENOMENOLOGY, DETECTION AND MEASUREMENT

The failure of a lubricant film between two solid surfaces implies contact between part or all of these surfaces. One of the consequences of such contact is overtly observable frictional behavior. Friction is a part of everyday experience, with antecedents reaching far back in time; but nevertheless it is still often misunderstood, both behavioristically and fundamentally. In Chapter 1 friction was described as a resistive force observed during rubbing; in Chapter 2 it was identified with the energy loss in a hydrodynamically generated lubricating film. Is there a genuine difference between these two points of view or are they linked by a generalization we have not yet examined? There is no categorically correct answer; it depends on how we choose to conceptualize friction. A . Gemant [ l ] defined friction thus: "Two bodies in mutual contact and in relative motion exert on each other retarding forces whose seat is the common boundary; these forces are called frictional forces and phenomena involving such forces are called frictional phenomena." Under the cover of this definition Gemant included such phenomena as the viscosity of liquids and gases, plastic flow in solids and internal friction (damping) in solids, in addition to the conventional external friction of solids. Instead of starting with an u p t r i a n i definition, we shall begin our examination of friction in this chapter on a phenomenological basis and then show that what is overtly observed can be explained in terms of the properties of matter. I n the main o u r point of view will be dominated by the friction of solid surfaces. 7.1.

BASIC PHENOMENOLOGY OF THE FRICTION OF SOLID BODIES

Let us examine the simple case, realizable in ordinary experience, Let B be a stationary solid body upon whose illustrated in Fig. 7 - 1 . surface the body A slides under load W with velocity U in the direction shown. I t is understood that body A is in contact with body B, although no details about the nature of the contact are given. Let us look at the force experienced by body A at the contact region by means of a probe which senses the frictional force F A in the orientation shown, i . e . in opposition to the direction of motion. An analogous probe in the surface of the body B senses an equal force in the opposite direction, such that F B = - FA'

135

W

1

~

---id

Figure 7-1.

FE

Friction force in the sliding of solid bodies.

I

I I

I I I I I

I

I

+

0 I1 Figure 7 - 2 .

J

Friction as an energy-consuming non-conservative force.

Another way of looking at frictional force is shown in Fig. 7-2. If the body A is at rest in position I , it has potential energy V 1 . If it were to fall freely in the potential field to position 1 1 , it would gain kinetic energy T and its potential energy would decrease to V 2 such that T = V1

-

V2

(7-1)

On raising the body back to position I , kinetic energy T is expended on it and its potential energy returns to V 1 . I f instead of falling freely, the body A slides a distance h with friction against the body B from position I' to position II', the kinetic energy of body A at position 11' will be less than the kinetic energy of free fall by the work expended in frictional sliding V1 -

v2

=

T ' + Fn

(7-2)

where F is the force of friction, The velocity of body A on arrival at The work exposition 1 1 ' is less than that for frictionless sliding. pended on frictional sliding has been consumed in a non-returnable manner and usually leaves the system as heat. The

concept

of

friction

as

a departure from the conservation of

136

mechanical energy does not require the sliding of two distinct bodies against each other. That the viscosity of liquids and the damping of vibrations in a solid body are often designated as frictional phenomena is a consequence of the physical models used to examine them. For instance, Newton's model of a liquid flowing viscously was a series of laminae of infinitesimal thickness which rubbed one against the next. When a lamina moves a distance dx (see Chapter 4, Fig. 4 - 1 ) the energy expended is idx, and the total energy lost by viscous flow in the system is the integral of all the shear stresses multiplied by the distances over which they act. It is on this basis that Newton came to regard viscosity as the friction of liquids in flow; by imprecise application of the concept the energy loss of a hydrodynamically lubricated bearing came to be designated as frictional loss of the bearing rather than as viscosity loss in the lubricant film. Extension of the concept of internal friction to material bodies other than liquids includes the energy lost by plastic deformation of solids, hysteresis loss of rubber, etc. in the category of frictional loss. Let us examine a simple idealized experiment by which we can detect and measure the sliding friction of two solid bodies in contact. In The movable Fig. 7-3a, M is a fixed flat bed that carries the post N. plate B is mounted on frictionless wheels o r rollers. Resting on the plate B is the block A under the load W . The block A is restrained by the spring E, one end of which is fastened to the post N and the other to the block. The extension of the spring is monitored by a pointer and a scale. When the plate B moves in the direction indicated by the arrow, it carries with it the block A , thereby extending the spring E as shown in Fig. 7-3a. At some critical force the block is no longer carried along by the plate B. Instead, as seen in Fig. 7-3b, the plate slides on the block, while the force exerted on the spring E remains constant.

n'"'

n"

W I

I!

L L Figure 7-3.

Detection and measurement of friction.

137 As long as the block A does not move relative to the plate B, the tractive force applied to the plate serves only to extend the spring E.* But when the block is sliding on the plate, the block-plate system can no longer be treated as a single body and an analysis of the forces at the sliding interface must be made. During steady-state sliding the block A is kept in position by two opposing forces: the tractive force exerted on it as the plate B slides past and the tension of the extended spring E. It is the convention in mechanics to assign the sense of the friction force opposite to the motion of the moving body; hence the force exerted by the extended spring is a measure of the friction force F.

Figure 7 - 1 is a simple, generalized representation of the friction of two sliding bodies but i t suffers from the drawback that conceptual probes must be introduced into the model in order to describe what occurs at the rubbing interface. Figure 7-3 depicts a direct experimental demonstration of frictional behavior and at the same time illustrates the basis of a method for the detection and measurement of the forces involved. The technique of elastic restraint shown there is not che only way to detect and measure friction, but it is the one used most frequently. The experiment illustrated by Fig. 7 - 3 introduces us to another aspect of friction: namely, the behavioristic differentiation of static No sliding is observed until the pull of the and kinetic friction. spring E exceeds a critical magnitude. This limiting value for the initiation of sliding is commonly identified as the force of static friction. The usual elementary demonstration of static friction is shown in Fig. 7-4. When a block of weight W rests on a plane with an inclination a , the limiting conditions for equilibrium are:

Figure 7-4. Illustration diagram.

of

static

friction

by

the

inclined

plane

*This statement involves two assumptions: that the motion of the system is steady (no acceleration or deceleration) and that the friction of the wheels or rollers is negligible. Both assumptions can very nearly be fulfilled in practice, and hence the experiment as described is a realistic one.

138

CFx

=

F + W

CFy = N

+

bin

a = 0

W cod a

=

0

from whence

F = - W

bin

a

- w

Cob

a

/d =

( 7-4a 1

(7-4b)

When W d i n a is greater than F , the block will accelerate in a direction opposite to the sense of F . For a given pair of surfaces there is a limiting value of a such that

w bin ~w con

a a

- t a n a = uA

(7-5)

where v d is the coefficient of static friction. Initiation of sliding involves basic theoretical considerations such as surface contact interactions, mechanical factors such as the inertia of the sliding body and the rate at which the angle 0: is altered, and the very practical matter of recognizing when sliding begins. Kinetic friction differs phenomenologically from static friction in that rather than being in a state of impending or beginning motion, the sliding body is moving overtly with respect to the stationary body. We write the following expression for the coefficient of kinetic friction Fk pk = -

N

where F k is the negative of slider moving at constant defining the coefficient of phenomenological fact. Its friction is

(7-6)

the tangential force required to keep the velocity. Equation 7-6 is a formal statement kinetic friction and also the expression of a counterpart for the coefficient of static

(7-7) where - F A is he tangential force required to initiate slid ng. Equation 7-7 is not tied to a particular apparatus as Eqn 7 - 5 is; in fact, Eqns 7-6 and 7-7 define u k and u, in generalized behavioristic terms and are applicable to any sliding pair or any type of apparatus. The magnitude of vn relative to uk is influenced by a number of factors that are scrongly empirical in character: the materials of which the rubbing surfaces are composed; their surface structure; the environment in which the rubbing takes place; the mechanical parameters of the device or ap-

139

paratus, particularly its elastic compliance.* 7.2.

SIMPLE BEHAVIORAL ASPECTS OF STATIC AND KINETIC FRICTION

As pointed out above, the arrangement depicted in Fig. 7 - 3 can be used as a simple apparatus for carrying out a friction experiment. Let us examine how it is used to investigate the behavior associated with static and kinetic friction. Consider the behavior cf the block as shown in Fig. 7-5a. The normal force N is equal to W and the friction force is

k",

4 I.

r,_

d3

1

2-342-3

Figure 7-5. Sliding behavior in static and kinetic friction. 1: Plate moving. 2 : Block moves with plate. 3: Block slides on plate. 4 : Plate and block stop. 5: Plate stops; block slides back.

therefore equal to u W . In Fig. 7 - 5 a the abscissa gives the distance the table moves and the ordinate shows the force F exerted by the spring. When the table moves forward, the block will move with the plate until F > F,, whereupon the block will slide on the plate. But when the block is From sliding, the spring pulls the block back until Eqn 7-6 is obeyed. this we conclude that F A > F k , i . e . U, > p k . The block moves with the plate over the distance d , , and then finds the equilibrium position where the force of the spring equals the force of kinetic friction. A s long as the plate keeps moving forward, the block will continue to slide against it and the spring will register the force Fk. Let the motion of the plate be stopped at some distance denoted as d 2 ; the block w i l l stop with

*The elastic compliance of the apparatus is discussed in detail in Chapter 8, Section 5.

140

it, and because p A > uk, the spring will be kept extended by the force When the plate is set in motion again, the block corresponding to Fk. will move with it and the spring will again extend to the length corresponding to F A > F k . This will occur at distance d 3 , where the block will begin to slide again and the spring will relax to the length corresponding to Fk. Now let us consider the behavior of the block as shown in Fig. 7-5b. As the plate moves from its original position of rest to the distance d,, it carries the block with it. When it moves beyond that position, the block slides in place and the extension of the spring shows the value of F = F k . When the plate is stopped at distance d2, the spring relaxes, pulling the block backwards: the extension of the spring then shows the On putting the plate in forward motion again, the block value of F = F,. will not begin to slide until the spring has been extended so that F = We conclude that in this case F A < Fk and p A < v k . Fk.

In terms of the behavior that actually would be observed with a simple apparatus of the kind described above, there is a direct and obvious phenomenological difference between static and kinetic friction. Close inquiry has revealed that in addition to theoretical considerations, the experimental methods and the instrumentation used to study and measure friction are an important aspect of the behavioristic manifestation of this difference. Therefore an examination of some7 of the more refined methods for the investigation of friction is in order. 7.3.

EXPERIMENTAL ARRANGEMENTS FOR DETECTION AND MEASUREMENT OF FRICTION

The American Society of Lubrication Engineers has issued a compilation of friction and wear devices [ 2 1 which describes 2 3 4 different pieces of apparatus. However, the measurement of friction is governed by only a few basic principles, and consequently an appreciation of the practical techniques employed is not difficult to acquire. To quote Bowden and Tabor [ 3 1 : ''Any method which will give at the same time a measure of the normal load between surfaces and of the tangential force necessary to cause sliding can be used to determine the coefficient o f friction. By far the greatest number of friction-measuring devices utilize the deflection of an elastic restraining member to sense the force of friction. The measurement of this deflection is carried out with the aid of accessory devices such as strain gages, linear variable differential transformers, optical levers, etc. Some of the devices employ the traction exerted by a mass under the influence of gravity ( e . g . , a weight on a cord over a pulley or a weight on an inclined plane). Other devices depend on the damping of simple harmonic motion o r on the deceleration of linear o r of rotational motion. Still other devices utilize the transfer

141

of momentum or of energy. 7.3.1.

Devices Utilizing Elastic Deflection

Elastic deflection can be used both to apply the load and to sense the response of the sliding body in a friction-measuring device. This was the principle employed by Bowden and Leben in their now classical research of the late 1 9 3 0 ' s [41. Today their apparatus is only of historic interest. A modern application of the elastic deflection principle is exemplified by the dual cantilever beam, such as is described by Bayer e t a L . 151 and illustrated in Fig. 7-6. Two independently acting elastic

Figure 7 - 6 . Dual cantilever beam for the measurement of friction. Bayer el: at. 151.

After

members are milled from a single bar, member I serving to apply the normal loading force while member I1 responds to the tangential friction force. Strain gages bonded to each member are used to measure the forces. The rider specimen R is carried in a head attached to member 1. Member I 1 is equipped with a means of attachment to any device that will put the rider in contact with the opposing specimen and apply the normal force. Bayer el: a.!. mounted the cantilever beam on the vertical feed column of a surface grinder, the highly precise and sensitive downward movement of which served to apply the loading force by deflection of member I. The moving specimen was held on the reciprocating table of the grinder, which was driven smoothly on hydrostatically lubricated ways by a precision hydraulic system. The device of Bayer e t aL. is a functional analogue of the Bowden-Leben apparatus. Morgan, Muskat and Reed 161 utilized the dual elastic member in conThe moving surjunction with rotary motion, as illustrated in Fig. 7 - 7 . face A is mounted on the carefully leveled rotating plate G. The rider B is coupled to the loading spring E held by the arm F, which also holds the elastic member D that responds to the friction force. Member D is positioned over the center of the turntable so that there are no tracking The mirror H errors when the assembly carrying rider B is deflected. reflects a beam of light which traces the friction signal on sensitive

142

Figure 7 - 7 . Dual-spring Muskat and Reed [ 6 1 .

apparatus

with rotary motion.

paper. The spring E is loaded by adjusting the position dual spring system with the screw K.

After Morgan,

of

the

entire

The dual elastic beam with strain gage instrumentation is an elegant means of carrying out friction experiments in special environments such as vacuum. Figure 7-8 shows the apparatus used by L. F. Coffin, jr. 1 7 1 . An adjusting screw operating through a sealed port in the vacuum chamber deflects the loading spring that presses the rider against the rotating disk. There is a class of friction-measuring devices in which the tangential force is sensed and measured by the deflection of a cantilever beam while the normal force is applied through a lever system. An apparatus of this type with versatile, sophisticated instrumentation was used by KO and Brockley 181, as shown schematically in Fig. 7-9. The moving specimen is a disk driven by a variable-speed DC motor through a speed reducer. Smooth rotation of the disk is ensured by applying a constant The slider is a countertorque through a cord-and-pulley arrangement. flat-surfaced button held in a self-aligning mount. The slider and its mount f i t in a holder at one end of the flexible cantilever beam, the other end of which is fixed firmly in a steel clamp-and-shaft assembly pivoted on two low-friction bearings. Load is applied by a weight-andpulley arrangement that puts moment on the beam system. The specimen holder is located so that displacement of the slider makes no tracking error with respect to the rotation of the disk. Elastic displacement of the cantilever beam is sensed by strain gages. Velocity of the tangential displacement of the beam is sensed by an electromagnetic transducer. The acceleration of the specimen holder is sensed by an electromagnetic accelerometer. This instrumentation gives a comprehensive picture of the

Figure 7-8. Dual-spring apparatus for vacuum. A: Disk. B: Rider. C: Beam and strain gage f o r normal force. D: Beam and strain gage for friction force. E: Adjusting screw for normal load. F: Srass bearings. G: Plate and cooling coils for temperature regulation. H: Sealing system. J: Metal envelope. K: Glass envelope. L: To vacuum. After L. F. Coffin, j r . [ 7 1 .

Figure 7-9, Spring and lever apparatus for friccion. A: Disk. B, B': Rider. C: Cantilever beam. D: Strain gage. E: Accelerometer. F: Velocity transducer. G: Speed reducer and turntable. H: Backlash take-up W: Loading weights. After KO and Brockley [ E l .

144

behavior of the specimen pieces and their supports and the course of rubbing. Buckley,

Swikert

and

Johnson

191

mountings

during

applied the principle of lever

loading and elastic deflection to the measurement of friction in high vacuum ( 1 3 . 3 VPa, lo-' torr). Their apparatus is illustrated diagrammatically in Fig. 7-10. The rotating specimen and its drive shaft are k

~DRIVE - SHAFT

/DISK AND RIDER SPECIMEN

. IAL

STRAIN A PC

*

Figure 7-10. Lever-loaded friction Buckley, Swikert and Johnson [ 9 ] .

'- BAKEOUT HEATERS apparatus

for

high

vacuum.

From

enclosed in the working chamber which is maintained at the required vacuum by continuously operating pumps. The rider is held on the end of a supporting rod which enters the chamber via a sealed bellows. The same assembly that carries the bellows also carries a gimbal mount which allows the rider support to move about two mutually perpendicular axes. Load applied by the dead-weight method exerts a moment about the horizontal axis. Friction force exerts a moment about the vertical axis which is sensed and measured by the elastic deflection of the strain gage assembly. The upper end of the working chamber is coupled to the drive motor, which is held in a separate evacuated chamber to minimize leakage through the seals. The other end of the working chamber is connected to the pumps that maintain the working vacuum. A large amount of data on the frictional behavior of materials in high vacuum has been obtained with apparatus of this type and published by the Lewis Research Center of NASA. 7.3.2.

Dead-Weight Tangential Traction Devices

At first glance dead-weight tangential traction devices of the type depicted in Fig. 7-11a appear to be well suited fo: the determination of the coefficient of static friction, the assumption being that the slider asseably is put in motion when the force exerted on it just exceeds the force of static friction. But experiments by Burwell and Rabinowicz [ l o ]

145

0.03

(a) T

E 0,

20.02

E

0)

0

go.01 .-

n

0 10 20 30 40 Time, days

Figure 7-11. Dead-weight tractive force method for measurement of friction. (a) Schematic diagram of apparatus. A: Plate. B: Block. T: Telescope. W: Loading weight. (b) Displacement as a function of time: steel on indium : load 2.94 N; tractive force 1.96 N. After Burwell and Rabinowicz [lOj.

have shown that the true initiation of sliding occurs at creep velocities, as illustrated in Fig. 7-llb f o r steel sliding on indium. The block carries three steel hemispheres that slide on the flat countersurface. Movement of the block is monitored by observing a fiduciary mark through a measuring microscope. Time-dependent displacement curves such as Fig. 7-llb obey relations of the form A

C

=

-

t

f

l

(7-8)

n

where t is time, C is a constant of proportionality and n is a numerical exponent. Differentiation of Eqn 7-8 gives the expression for the velocity of the slider; differentiation once more gives its acceleration. A force analysis of the system gives the following relations for the instantanecus coefficient of friction between the block and the countersurface: m5

-

m ' ; r - )I.m'5 A. m

i

u,=--*.

m'

= 0

(7-9a)

, g

(7-9b)

where m is the tractive mass, m ' the mass of the block, g the acceleration of gravity and the acceleration of the block and the tractive mass. F o r cases such as is illustrated by Fig. 7-llb, where the velocity of the slider decreases from an initial magnitude to a smaller terminal is negative and hence the steady-state level, the numerical value o f numerical value of ui increases from the initiation of sliding until steady-state sliding at a constant velocity is attained. But at the creep velocities depicted in Fig. 7-llb, the increase in u1-. is o f the order of 0.00001% at the most. No data are available for frictional be-

146

havior at macroscopic sliding velocities. Figure 7-12a shows the version of the dead-weight tangential force principle used by T. E. Simkins [ll]. The tractive force is regulated by admitting measured quantities of water into the container and is sensed by means of a strain ring that feeds its signal into the ordinate of an i l - Y plotter. Movement of the slider is followed by a fiber-optics displacement transducer that registers its signal a s the abscissa of the plot. Figure 7-12b shows the kind of diagram obtained. It is seen that

Y

x B

L

-Q-J--

0 200

600 1800 2200

Displacement, nm

Figure 7 tion. (a) placement (b) Tract placements

2. Dead-weight tractive force method for measurement of fricSchematic diagram o f apparatus. A: Plate. B: Block. D: Disransducer. W: Loading weight. X, Y: Leads to X-Y recorder. ve force vs. displacement. 1: Elastic portions of the dis2: microslips; 3: sliding. After T. E. Simkins [ 1 1 1 .

the gross sliding of kinetic friction slips and arrests. 7.3.3.

is preceded by a series of micro-

Inclined Plane Method for Static Friction

The inclined plane method for the coefficient of static friction utilizes the same principle that governs the dead-weight traction technique, and the results obtained by i t are subject to the same complications. The basis of the method is illustrated by Fig. 7-4. A sophisticated apparatus is described by W. E. Campbell [12]. The plane is tilted by a motor operating through a reduction gear, and when slip occurs between the slider and the plate, a switch is actuated to operate a solenoid brake on the motor so that movement of the plane is halted sharply; the angle of its tilt is then read on a vernier goniometer. Campbell observed that the coefficient of static friction was not influenced by variations in the rate at which the plane was raised over the range 0.083 to 0.333 cm/s. But it is obvious from more modern work that he would not have found this to be true i f the plane had been raised at a much slower rate. Another inherent difficulty in the method is skewing of the slider as the motion begins.

147 7.3.4.

Damping of Oscillatory Motion

The damping or deceleration principle as applied to the measurement of friction is illustrated in Fig. 7 - 1 3 by the pendulum apparatus of Tamai [ 1 3 1 . The moving specimen, which carries the pendulum, rests in a cradle formed by the stationary specimens. The damping of the pendulum is transduced by the variable capacitance of an inner plate moving with the pendulum relative to two fixed plates. This modulates the frequency of an electric oscillator that feeds its signal into a recorder as a sine wave. The friction force is obtained from the recorder traces by applying the logarithmic decrement calculation to the damping of the signal amplitude:

Damped pendulum method for measurement of friction. Figure 7-13. of the moving specimen in the cradle of the fixed specimens. Y. Tamai 1131.

A:

view After

(7-10)

where k is the damping constant, II is the period of the pendulum, a . is L the amplitude for the ith cycle and a . is the amplitude for the jth J cycle. The apparatus must be suitably calibrated to evaluate ai and a . J from the recorder traces, and the basic physical constants of the apparatus such as the mass of the pendulum, its length and its period must be known in order to evaluate the friction force from h . REFERENCES 1. 2.

3.

A. Gemant, in Frictional Phenomena, Chemical Publishing Co., Brooklyn, N. Y., 1950. Friction and Wear Devices, Revised and Enlarged Report of the Subcommittee on Wear, Lubrication Fundamentals Committee, 2nd Edition, American Society of Lubrication Engineers, Park Ridge, I l l . , 1976. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1950, Part I , p. 73.

148

4.

5. 6. 7. 8.

9. 10. 11. 12. 13.

F. P. Bowden and L. Leben, Proc. Roy. SOC. London, A169 (1939) 371-391. See also F. P, Bowden and D. Tabor, op. cit., Chapter 4. R. G. Baver. W. C. Clinton, C. W. Nelson and R. A. Schurnacher. Wear. 5 (1962)*376-391. F. Morqan, M. Muskat and D. W. Reed, J. Appl. Phys., 12 (1941) -_ 743-752: . L. F. Coffin, j r . , Lubrication Eng., 12 (1956) 50-59. P. L. K O and C. A . Brockley, J. Lubrication Tech. (Trans. A S M E ) , 92F (1970) 543-549. D. H. Buckley, M. Swikert and R. L. Johnson, ASLE Trans., 5 (1962) 8-23. J. T. Burwell and E. Rabinowicz, J. Appl. Phys., 24 (1953) 136-139. T. E. Sirnkins, Lubrication Eng., 23 (1967) 26-31. W. E. Campbell, Trans. ASME, 61 (1939) 633-641. Y. Tamai, Wear, 1 (1957/1958) 377-383.

149

Chapter 8 FRICTION:

8.1.

MECHANISMS AND ANALYSIS

A SIMPLE BASIC MECHANISM FOR THE FRICTION OF SOLID METALLIC BODIES

The treatment of friction in the preceding chapter was primarily phenomenological, with emphasis on the observation and measurement of frictional behavior. In this chapter our inquiry will be directed toward the basic mechanisms of friction, particularly how the properties of solid surfaces and the conditions of sliding govern observable friction phenomena. There are many different kinds of solids and their properties cover a wide range of categories. Therefore we shall begin with an inquiry into the basic mechanism of the friction of metallic solids, because the friction of metals is an important aspect of engineering practice and because the properties of metals stand in fairly simple relation to their constitution. Instead of becoming enmeshed in the intricacies of defining o r even describing what a metal is, we note that such commonly recognized metallic attributes as elasticity, ductility, electrical conductivity, etc. are important in the theory of the frictional behavior of metals. The frictional behavior we are concerned with is a consequence of rubbing contact and involves the interaction of surfaces. Real surfaces are neither geometrically nor molecularly smooth. Discussion of the complexities of contact theory and their influence on rubbing behavior is the subject of Chapter 12. But even a simple treatment of the basic theory of friction involves the role of surface structure. Bowden and Tabor [l] describe the application of electrical resistTwo pairs of ance to the study of the contact of metallic surfaces. ground and lapped steel flats were put in contact under equal loads: the nominal area of each member of one pair was 0.8 cm2 , of the other 21 cm2. Although their nominal contact areas were in the ratio 1:26, the electrical resistance was found to be the same for each set. It was shown by Bowden and Tabor [l] and by Holm [2] that this behavior can be explained by a model in which the real area of contact, as distinguished from the nominal or apparent area, is constant for a given load. True contact occurs at asperities on the nominal surfaces that are deformed plastically by the loading force. Assuming the yield pressure of the asperities to be that of the bulk metal, the constancy of real contact is given by the relation

150

(8-1)

where A is the real area of contact, W is the applied load and p, is the yield pressure for the fully developed state of flow under a hard indenter.

To make Eqn 8-1 useful in a physical sense we must answer the following questions: (a) How many individual asperities are in contact to add up to the area A ? (b) What are the sizes of the asperity contacts? Let us assume there are n asperities, all the same size and all situated at the same level in the nominal surface of the solid. The area A is then A = n-na

2

(8-2)

where a is the radius of a single asperity contact, assumed to be circular. The electrical resistance of the contact at these n asperities is substantially the constriction resistance, which is given by 1

R = -

2ana

(8-3)

where d is the conductivity.* The expression for evaluating n by contact resistance is derived by eliminating u from Eqns 8-2 and 8-3 and using the value of A given by Eqn 8 - 1 to obtain "Pm

n=-

4d2R2W

(8-4)

Elimination of n instead of a gives the following expression: 2aRW a = nprn

(8-5)

Figure 8-1 is obtained from the data reported by Bowden and Tabor for the ground and lapped steel flats 21 cm2 in nominal area. The direct experimental results are shown in the curve for the contact resistance R as a function of the load. Results calculated by Eqns 8-4 and 8-5 are shown by the curves for the number of asperities n and the average radius of an asperity contact u. When the load is increased 250 times, n increases 11.7 times and u 4.2 times. The true area of contact, which is obtained from Eqn 8-1, is, of course, a linear function of [l]

w.

Having

established

*SI nomenclature. opecidic conductivity.

the

relations

I t has the same

for

evaluating

meaning

as

the

the

more

number of

familiar

151 N

E 0 Y

0

5

[ A

R

1000

2000 3000

40005000a n

Lood,newtons

Figure 8-1. Asperity contacts in steel flats under load. Ground and 2 lapped flats, geometrical area 21 cm Data from Bowden and Tabor [ l ] .

.

asperity junctions and the average radius of a single junction, we introduce the physical assumption that each asperity junction becomes an asperity adhesion during the contact of the participating asperities as they encounter one another in the sliding of the two surfaces. Evidence for the self-adhesion of clean metals is cited by Bowden and Tabor 1 3 1 , and the data for the conductivity of metals in contact indicate that asperity adhesions can be regarded as clean-metal adhesions. The force of friction is identified with the force required to break the asperity adhesions. Assuming that the shear strength of each adhesion is equal to the shear strength of the bulk metal, we write for the force required to break the asperity adhesions

F =

rzna2.6 = A 6

(8-6)

where 6 is the force per unit area required to fracture the metal in shear and F is the macroscopic tangential force necessary to maintain the sliding of the moving member of the pair. Taking the value of A from Eqn 8 - 1 , we get W

F = -

'6

(8-7)

pm

and on rearranging

F A u = - = pm

(8-8)

152

the

The ratio F/W defines the coefficient of friction behavioristically; ratio A/P, defines it in terms of the shear strength of the metal in

the asperity junctions (A) and the yield pressure of the bulk metal (p,,,), and each asperity contact is treated as though it were being deformed independently by a rigid flat plane. In the aggregate the true area of contact is the statistical mean of the individual asperity areas is a over the time of sliding and remains constant because ideally p, constant property of a given metal. Ideally A is also a constant property of the metal. Then i f the second equality of Eqn 8-8 defines u, it follows that the coefficient of friction is constant for all loads applied to a given system, and this affords an explanation for the two classical observations regarding frictional behavior generally known as Amontons' laws: 1.

Friction force is directly proportional to the load applied.

2.

For a given load, friction force is independent of the a p p a h e n t area of the sliding surface.

illustration of Amontons' laws in operation is found in the data published by Bowden and Tabor [ 4 1 for steel sliding on electrolytically polished aluminum. They report a coefficient of friction 1-1 = 1.17 ? 0 . 1 0 for loads covering the million-fold range from 98 micronewtons to 98 N.

An

8.2.

EXTENSION OF THE ADHESIVE-JUNCTION MODEL FOR FRICTION

Many examples of departures from Amontons' laws of friction are And even though the value v = 1.17 cited recorded in the literature. above in Section 8.1 f o r the coefficient of friction of steel against aluminum conforms to Amontons' laws, it runs into another theoretical difficulty. As Tabor pointed out [51, i f the value of A in the ratio b/p, which defines u in Eqn 8-8 is the shear strength of the bulk metal, A,,,, then the coefficient of friction should fall in the vicinity of 1-1 = 0.2, because for an ideal plastic material p,,, is at least 5 times A,,,. But in fact the coefficient of friction observed in the unlubricated sliding of most ordinary metals in air falls in the range 0.5 to 1.6. Much higher values are observed in more severe environments: Bowden and Young [ 6 ] reported = 9 for out-gassed nickel i n wacuo; > 15 was measured by Brown and Burton [71 for copper i n wacuo at 533 K (500 F), and Buckley [ 8 1 found values of 1.1 as high as 40 for annealed copper in a specially clean high-vacuum environment. Neither departure from Amontons' laws of friction nor the occurrence of values greater than 0.2 for the coefficient of friction should be regarded as aberrations from a fundamentally ideal mode of frictional behavior. The theoretical basis of friction can be extended to these cases. To avoid the restrictions imposed by a limiting value of 0.2 for

153

the ratio 6,/p,, Tabor [ 5 1 developed a model for the friction of solid bodies based on the theory of plastic flow under combined normal and tangential stresses. The Huber-von Mises criterion for idealized twodimensional plastic flow under plane stress is p2

+

3A2

=

p,2

(8-9a) where p is the normal stress and A is the tangential stress in the metal at the location under investigation, and p, is the uniaxial flow stress of the bulk metal. For the case of three-dimensional asperities Eqn 8-9a is replaced by the postulated analogue p2

+

a*2 = p;

(8-9b)

where a is an empirical factor which releases the equations from the restrictions of the homogeneous stress state. Dividing Eqn 8-9b through by p 2 gives

I

+

a+

2

=

2 2 P,/P

(8-10)

where 4 = A/P is designated as the tangential d a m e coe6dicient. Since can be regarded as a constant characteristic property of the metal, when A increases p must decrease. Therefore i f the given total load W remains fixed throughout the deformation process, a decrease in p requires that the real area of contact increase from its original value of A to a new value A' such that p,

Tangential force coefficients can be determined by direct measurement of the tangential tractive force and the normal loading force of the system, but the ratio A'/A is usually obtained by indirect methods. McFarlane and Tabor 191 found that the adhesion of indium to steel under the influence of a normal preload was so strong that the tractive force to initiate sliding after removal of the preload was essentially a measure of the shear force in indium. From this measurement they calcu= 3 . 3 for indium. Courtney-Pratt and Eisner [ l o ] lated a value of evaluated A'/A by electrical resistance and obtained a value of a = 11.66 f o r platinum. I f , in Eqn 8-9b, p approaches zero f o r pure shear under an extremely light load and p, is assigned a value equal to 5n, [ 5 1 , then 6 = A, and a assumes the value 25. The following relation can then be obtained from Eqn 8-9b: p 2 + ao2 = 256, 2

(8-12)

154

Since the stresses in real asperities are not restricted to pure shear, 25 is probably too high a value for a. Tabor [51 argued that 3 . 3 , the value obtained from experiments with indium, is so low because of the experimental difficulty of measuring the adhesion and because of the plowing contribution to the force of friction for such a soft metal. The value of c a . 12 from the results of Courtney-Pratt and Eisner [ l o ] for platinum may be imprecise because of the influence of surface film error on the conductivity measurements. The value of 9 was selected for a as a useful magnitude representative of the metals usually encountered. Setting p, = 36, then gives

The exact value of a , so long as it is consistent with observed behavior, does not influence the logical conclusions drawn from the model. The physical condition for macroscopic sliding at an asperity junction in response to tangential traction is that the material in the junction interface be completely sheared. The shear strength of a junction depends on its composition. For example, the junction between two contacting asperities of an oxidizable metal such a s copper in ordinary ambient air might be mostly oxide with a few sub-regions of true metallic adhesion, in which case the shear strength of the junction will be less than the full shear strength of the bulk metal. On writing the expression for the effective shear strength over the area of as o A.. = ko

asperity

contact

(8-14)

where k lies between 0 and 1, Eqn 8-13 becomes (8-15a) (8-15b) from which we get

(8-16)

The relation of Eqn 8-16 to the coefficient of friction is seen in the equation below: A'eh. L

F!=-=-

W

A'*p

(8-17)

Thus the coefficient of friction can be plotted as a function of k , as is shown in Fig. 8-2 for three values of a. The magnitude of p increases

155

2

C

.-0 f

0

0 0 Figure 8 - 2 .

0.5 k

1 .o

Influence of the constant k on the coefficient of friction.

TABLE 8 - 1 . INFLUENCE OF THE SHEAR STRENGTH COEFFECIENT k ON THE COEFFICIENT OF FRICTION k

u

0.90000 0.95000 0.99000 0.99900 0.99990 0.99995 0.99996 0.99997 0.99999

0.688 1.014 2.340 7.454 23.569 33.332 37.267 43.032 74.536

Calculated from Equation 8 - 1 6 . very rapidly as k approaches unity: Table 8 - 1 gives some values computed using the right-hand side of Eqn 8 - 1 6 . Equation 8 - 1 6 by itself does not explain the part that asperity junction growth plays in the mechanism for high values of u. The basic tenet of the junction-growth mechanism is that the contacting interface transmits tangential stress to the bulk metal of the asperity so that it deforms plastically and thus enlarges the contact area prior to macroscopic sliding. The magnitude of the friction force is governed by both the area and the yield strength of the interface. Equation 8 - 1 6 does not show the interfacial area explicitly. To complete the physical picture

156

we must go to Eqn 8 - 1 1 , which informs us that the area of the interface increases with tangential traction. Figure 8 - 3 shows a plot of the tangential force coefficient $ against the ratio A ' / A , made by Tabor 151 from the data by Courtney-Pratt and Eisner [lo] for platinum. a

0.6

0.4 0 C

.c 0

E 0.2

I-

0

'5

1.o

2.0

A/A

Figure 8-3. Relation of the tangential traction coefficient to the area 0 Clean platinum. A Lubricated platinum. Data computed by ratio A ' / A . Tabor [5] from results by Courtney-Pratt and Eisner [lo]. TABLE 8-2. RESoONSE OF COEFFICIENT OF FRICTION TO ASPERITY JUNCTION GROWTH =

lim

+

A' / A

0.688 1.014 2.304 7.454 23.569 33.332 37.267 43.032 74.536

Calculated from Eqn 8-11 with

2.29 3.20 7.09 22.4 70.7 100 112 126 224 Q

= 9.

It is instructive to compare the influence o,f interfacial shear strength and of asperity junction area on the coefficient of friction. Table 8 - 1 shows that for p = 1.01 the shear strength of the junction interface is 95% of the shear strength of the bulk metal. From Table 8-2, which gives the ratios of the area after junction growth, we get a value of 3.20 for A ' / A . It is obvious that for the very high values of p the junction area cannot stay unchanged at the value corresponding to = 1.01: there is no credible way other than increase of the interfacial area by which the total shearing force at the junctions could increase to the values required for coefficients of friction in the range 75-100.

157

Our picture of the sliding process at an asperity contact is as follows. So long as the tangential stress at the junction interface is less than the shear strength of the material there, it is transmitted into the underlying metal of the asperity and produces junction growth. I f the shear stress in the material of the junction interface exceeds the critical strength h i , junction growth will cease and shearing will occur in the interfacial film, the manifestation of which will be gross sliding over the interface. I t can be seen from Tables 8-1 and 8-2 that interfacial junctions with almost the full strength of the bulk asperity metal are required for extensive asperity growth. The reason for the pronounced effect of surface contamination on the coefficient of friction is thus apparent. Courtney-Pratt and Eisner 1101 observed macroscopic sliding of platinum lubricated by lauric acid in cetane at a ratio of 1.6 whereas dry platinum did not slide macroscopically at A ' / A = for A ' / A , 2.5 (Fig. 8-3). However, the value of k is not necessarily a measure of the cleanliness of an interface. Certain metals, particularly those that crystallize in the hexagonal system like cobalt, were found by Buckley [ 1 1 1 to be highly sensitive to lattice orientation, exhibiting low adhesion and moderate friction on sliding in a hard vacuum of 1.33 nPa ( low1' torr). The characteristics of the junction interface of consequence in the sliding process are governed by a combination of surface condition and the intrinsic properties of the participating materials. The foregoing discussion has been in terms of contact

at

a

single

asperity, whereas the true contact of extended surfaces occurs at a number of 6iscrete regions in the nominal area of the specimen. Taking the data illustrated in Fig. 8-1 as an example, 50 asperities participate in the static contact under a load of 5000 N; the sum of their true contact areas comprises only 0.24% of the nominal 21 cm2 of the flat steel specimens. If the true contact area of the junctions increases by a factor of 225 via the asperity growth mechanism, the new contact area will be 54% of the nominal area. Thus the extensive enlargement of the asperity area required for coefficients of friction in the range 11 = 50-75 is not unrealistic in the physical sense. For most practical cases of sustained sliding in which the coefficient of friction exceeds the does not often go limit of 0.2 of the simple mechanism of Section 8.1, higher than 1.5-2. In such cases the fraction of the nominal surface area involved in true contact remains within modest limits The simple asperity area mechanism of Section 8.1 for friction can be brought under a common umbrella with the extended mechanism developed in the foregoing portion of this section. In the simple mechanism, the real area of contact is fixed by the relation 11 = h / p , ; the tangential shearing force over this area is F = A b = W ( b / p m ) and the coefficient of friction is 1.1 = A/P,. In the extended theory, tangential traction applied to the asperities causes them to grow so that the real contact area of

158

the sliding system is A ' = qW/p,, where q is the growth factor; the tangential shearing force is then F' = A'A = qW~/p,, and the coefficient of For Amontons' laws to apply-i.e. for p' to be friction is p' = qo/p,. q and A must be unaffected by the independent of the normal load-both I f either q or A changes with load magnitude of the loading force. -for instance, if the shear strength of the junction changes during asperity growth because an oxide film is disrupted-then Amontons' laws will not hold. Skinner and Gane [12] studied sliding friction under a negative load, as shown in Fig. 8-4: i . e . they obtained a negative c efficient of friction. These observations are cons stent with the asper ty adhesion

t 2 0,

4' n

2

0

8

k

z

-300

-200 -100 L o a d , JIN

0

Figure 8-4. Friction under negative load for gold and silver against diamond. Sliding speed 0.7 pm/s. Data by Skinner and Gane 1121.

mechanism of friction i f the special circumstances of the experimentation are kept in mind. The sliders were of relatively soft and ductile metals (lead, gold) with very small tips (radius 1 urn) and the manipulation of the extremely small forces involved (10-200 uN) was carried out in wacuo with great delicacy. After contact with the countersurface (diamond o r graphite) was established by sliding under positive load, the friction measurements were made as the positive normal load was progressively decreased to zero and then increased in the negative sense until contact with the countersurface could no longer be maintained. The friction force decreased linearly with increasingly negative normal loading. Skinner and Gane [12] attributed this to decrease in the magnitude of van der Waals forces with increasing separation of the opposing surfaces in the range 0.6-1.7 nm; an alternate physical explanation involves decrease in the number of adhesions between the surface material of the rider and the metal transferred to the countersurface during the initial-contact

159

phase of sliding. In this respecr: the findings of Gane, Pfaelzer and Tabor [ 1 3 1 for the adhesion of metals as the normal contacting load is backed off are significant. Unusual though the concept of a negative coefficient of friction seems at first glance, it is not at variance with the asperity adhesion mechanism of friction. In terms of customary nota= m ; in reality, the conventional formulation breaks tion, when W = 0, down for this case. 8.3.

INTERMITTENT MOTION IN FRICTIONAL SLIDING:

STICK-SLIP OSCILLATION

I n Chapter 7, Section 2 the treatment of static and kinetic friction was in simple behavioristic terms. Referring back to the experimental procedure illustrated in Fig. 7-3 and the frictional behavior shown in Fig. 7-5, we can now inquire into the mechanism that causes the block to be carried along by the plate in the initial phase of the experiment in terms of asperity adhesion. I t is obvious that in the block and plate experiment if the magnitude of the adhesive force as given by E q n 8-6 is greater than the force exerted by the restraining spring in the direction opposing the movement of the plate, the block will be carried along by the plate and the diagram of spring extension will be that shown in the initial part of Fig. 7-5a. Now let us consider the behavior of the elastically restrained rider in one of the sensitive, fast-acting devices for the measurement of friction ( e . 4 . Figs. 7-6 through 7-9). The deflection of the elastic restraining member in these devices is a measure of both the displacement of the rider from its neutral position and the force re-

quired to accomplish this. Figure 8-5 illustrates the sliding motion of the rider when its inertial mass is small relative to the stiffness of the restraining element and the translational velocity of the countersurface is very low compared to the period of the spring and rider system. Starting from rest, as the driven surface moves along with constant velocity it carries the adhering Y

4

'0

Figure 8 - 5 .

'1

Time

Stick-slip motion.

160

rider with it, and the trace of the displacement of the rider from its rest position is given by AB. At time t o ,corresponding to the arrival of the rider at position B, a rapid slip occurs and the rider moves back in the direction of its neutral position. This motion is opposed by the force of kinetic friction, which slows the rider down, and at time tt the rider sticks to the other surface again and is carried along with it, as indicated by CD. Thus a s the driven surface moves steadily forward, the motion of the rider is a series of alternate sticks and slips. The behavior of the rider along the path BC can be analyzed exactly. The equation is that of damped harmonic motion with a constant resisting force added:

where y is the displacement, rn is the mass of the moving rider assembly, X is the damping constant, K is the spring constant, F is the frictional This force of the rider against the opposing surface and t is time. equation has a well-known solution. However, since we are dealing here only with the motion of the rider along the path BC, the contribution to damping by 1 is negligible and the solution simplifies to

where u L = K/rn, and C and B are constants of integration which can be This evaluated by the conditions that when 1: = 0, y = yo and dy/dt = 0. gives us

from which y = (Y.

-

ot

*

F

-

(8-21)

The following expression is introduced into Eqn 8-21:

F A..

= Mgu.

A.

(8-22)

where Mg is the normal force due to a load of mass M and Fi and pi represent the frictional force and the coefficient of friction, static or kinetic as the case may be. At time to = 0 Mg

Yo

=

-

uh

(8-23)

Inserting this into Eqn 8 - 2 1 and evaluating F from the load and the coefficient of kinetic friction, we get

161

(8-24)

At the end of a slip ( i . e . when the rider is at C ) , d g / d t = 0. On difconferentiating Eqn 8 - 2 4 and setting the result equal to zero, the trolling condition is w t = T I , and hence

gives us

for the amplitude of the slip BC. The smaller the difference between uA and p b , the smaller the amplitude of the slip: when uA = uk the amplitude is zero and smooth sliding ensues. In the treatment above, stick-slip was discussed in terms of a real but very simple physical model. There are more sophisticated and detailed approaches which arise from the needs of engineering practice. For instance, B. R. Singh 1 1 4 1 represented the sliding system as shown in Fig. 8-6 and wrote the differential equation of motion during slip as

Figure 8 - 6 .

Elastically restrained sliding with two modes of damping.

Damping is divided into two categories, where X, represents the coefficient of viscous damping between the sliding mass and the drive system and X 2 represents the coefficient of viscous damping between the rubbing surfaces. FA-Fk is the difference between the forces of static and kinetic friction. A further proviso is that the damping ratios X 2, / 4 ~ m and X 2 / 4 ~ m are very much smaller than unity. By using the boundary conditions that y = 0 and = 0 when t = 0, Eqn 8 - 2 7 can be solved for y as a function of t , and this solution can then be differentiated to give the function for i . The parameters that govern the characteristics of the

4

162

solution for j are the damping ratios, the velocity of traction v and the quantity ( F , - F , , - ) / v ( K ~ ) ~ ’ ~ . There is a critical velocity v c above which the funct ion for j assumes a steady value with only a small ripple in the time interval t, equal to the duration of a slip, whereas at values of v less than v c , j rises to a maximum and then decays to zero. Figure 8-7 shows how j as a function of t responds to the magnitude of v . At tractive speeds less than v c , the velocity of the slider in slip will be slowed down to zero in time t, or less: i . e . a stick will occur.

Sliding velocity as governed by critical tractive Figure 8-7. After B. R. Singh [ 1 4 1 .

velocity.

I n engineering practice - e . y . in indexing machine tools or in the engagement of friction clutches - it is desirable to eliminate the stick-slip that is often associated with low tractive speeds. An analysis such as the one outlined above is valuable in two respects. It identifies those design parameters that govern stick-slip and it affords a quantitative approach to manipulating them. Singh [ 1 4 ] concluded that in order to keep the value of v c small, (a) F A - F h should be small: (b) K/m should be large: i . e . the stiffness of the elastic restraint relative to the mass of the sliding body should be large; and (c) the system should have sufficient viscous damping. Essentially the same conclusions were reached by Brockley, Cameron and Potter [ 1 5 1 in their analysis of Eqn 8 - 1 8 . 8.4.

FRICTIONALLY INDUCED QUASIHARMONIC VIBRATION

Sometimes the operation of machine elements such as brakes and clutches may result in audible sound, ranging from high-pitched squeals to low-pitched growls. It is often assumed that such sounds are manifestations of stick-slip sliding, but in reality they are the result of frictionally induced quasiharmonic vibration. This aspect of friction has been analyzed and studied experimentally by Brockley and KO [ 1 6 , 171. Typical stick-slip motion

is

the

combination

of

two

distinctly

163

resolvable events: sticking of the slider to the countersurface, followed by slip against the direction of the tractive motion until stopped by another stick. The typical trace observed by KO and Brockley [ 1 7 1 with transducer signals displayed on an oscilloscope is shown in Fig. 8-8a. One form of the equation for slip is given by Eqn 8 - 2 1 (Section 8 . 3 ) . The equation of traction after stick is

where Iz, is the constant angular velocity of deflection of the slider for steady tractive motion and L is the length of the elastic coupling of the slider; y, is the deflection at which stick occurs. Each stick-slip cycle has two discontinuities-one at stick ( y = y 6 ) and one at the ineach of which a new time count begins. itiation of slip (y = y,)-at To casual inspection traces of stick-slip motion such as Fig. 8-8a seem to be composed of linear segments, but Eqns 8 - 2 1 and 8-28 show that in actuality they are functions of the cosine or the sine of the angular displacement. Quasiharmonic oscillation gives the distinctly different type of trace shown in Fig. 8-8b. Brockley and KO 1 1 6 1 showed that a linear relation between kinetic friction and tractive velocity of the kind illustrated in Fig. 8-9a leads only to either stick-slip or smooth sliding; for quasiharmonic oscillation a humped curve such as is seen in Fig. 8-9b is required. The friction function that fulfills this requirement represented by a polynomial or by the exponential expression F k = [C,

+

C2

( W

-

j)] e x p [- C3

(V

- j)]

+

C4(v -

j)

+

C5

may

be

(8-29)

Equation 8-18 is coupled with this expression and manipulated to yield *

x+c4

Y+m

i -

c,

+ C2V

exp

[c3?l

+

m - e x p [C3w] c2

j * c x p [C,j]

2

+

w y =

C4"

m - e x p [C,V]

+

c5

m

(8-30)

Y

EYE Time, t

Figure 8-8. Oscilloscope traces of frictional vibration. (a). Stickslip. (b) Quasiharmonic vibration. After K O and Brockley [ 1 7 ] .

164

Fk

(b)

t

Velocity,

Y

Figure 8-9. Influence of tractive velocity on kinetic friction. (a) Stick-slip. (b) Quasiharmonic vibration. After Brockley and KO 1161.

The constant term on the right-hand side constitutes the static displacement of the vibration. Since we are interested only in the amplitude of the oscillations, this term can be omitted and the left-hand side of Eqn 8-30 can be set equal to zero. The solution of Eqn 8-30 is discussed by Brockley and KO [ 1 6 ] ; it requires considerable manipulation to put it in a form useful for computation. It can be shown there is a stable, cyclically repeated maximum amplitude of displacement of the rider, the value of which can be calculated i f the constants of the system such as w 2 , C,, etc. are known. In physical terms, the sliding body does execute frictionally induced harmonic vibration. Furthermore, it can be demonstrated that the curve representing kinetic friction as a function of tractive velocity (Fig. 8-9b) is consistent with the solutions for quasiharmonic vibration. Such a curve for the undamped case (1 + C4 = 0 ) is characterized by the following relations:

Fo

=

C,

+

C5

F

= ‘2

-

‘1‘3

‘2‘3

Quasiharmonic vibration will commence at a tractive velocity corresponding to the maximum of the friction curve at Fm. For the undamped case vibration will increase without limit a s the velocity of the tractive surface increases beyond this. But since in real life one cannot have an elastic coupling without damping loss, actual systems will have an upper velocity limit for sustained vibration. Figure 6 - 1 0 shows a comparison of the experimental results obtained by Brockley and KO [ 1 6 1 for the friction force and the amplitude of

165

r

6r

0.08

2

I 430 O 2 0.06

0.04 0.02 0

L

0

!"

I=

u120 8

10

Disk Velocity .cm/s

Figure 8 - 1 0 . Comparison of experiment and calculations for quasiharmonic vibration. Paper on steel, lubricated: m = 0 .5 4 5 kg, X = 0.0176 N/cm/s, K = 103.5 N/cm (see Eqn 8 - 1 8 ) . Data by Brockley and KO [ 1 6 1 . vibration with the results calculated by theory. The solutions for the amplitude of the damped system lie between A and B on the diagram. I t was observed experimentally that to the left of A the oscillations were of the stick-slip type. In theory and by experiment, quasiharmonic oscillation commences at a designated velocity A , with amplitude increasing linearly with velocity and suddenly decaying at B. The forced oscillations predicted to the right of B by theory were not observed experimentally. 8.5.

THE NATURE OF STATIC AND KINETIC FRICTION

The introduction to the concept of static and kinetic friction in Chapter 7 , Section 2 is admittedly simplistic. Familiarity with the experimental details of measuring friction leads to a more realistic view in behavioristic terms and also to some theoretical questions. In particular, the theory of stick-slip friction requires that u A be greater than and distinct from vk, and indeed Fig. 7-5a shows a discontinuity between static and kinetic friction. But the model for the fundamental adhesive mechanism of friction does not predict such a discontinuity. We have already seen in the foregoing treatments of stick-slip sliding and quasiharmonic vibration how the parameters of the experimental apparatus interact with the fundamental parameters that govern the sliding of the surfaces against each other to determine what is observed phenomenologically. Let us examine some evidence which supports the view that the distinction between static and kinetic friction is basically not categorical but rather the product of how the apparatus behaves. Several careful studies have been made of the initiation of sliding by the application of a tangential tractive force; that of Courtney-Pratt and Eis-

166

ner [ l o ] is particularly noteworthy because of the sensitivity with which the displacement of the slider was measured. The experimental method is The slider A is loaded against the stationary illustrated in Fig. 8 - 1 1 . surface B through the beam E by twisting the torsion bar D about the axis CC when thrust is applied on the arm R. The slider is held in a clamp to which the tangential traction is applied by a flexible cantilever J and link G when the micrometer screw H is advanced. The clamp also carries a silvered optical flat M which forms one side of a multiple beam interferometer capable of resolving a displacement of the order of 1 nm ( 1 0 2). With this sensitivity the apparatus could detect response to all six modes of motion (three translational and three rotational) ; however, the constraints imposed minimized all but the displacement in the direction of the traction. Normal loading and tangential tractive forces were varied over a range from 0.98 pN to 9 8 N to 104 grams of force); even at the highest loading the asperities had room to deform without mutual interference, as indicated by the electrical conductance behavior. The basic technique was to select a normal load and to apply increasing tangential traction in small increments; the corresponding displacement of the rider was monitored by the displacement of fringes of equal chromatic order in the interferometer,

Figure 8 - 1 1 . Apparatus for the study of displacement by frictional tangential traction. After Courtney-Pratt and Eisner [ l o ] .

Figure 8 - 1 2 shows some typical results for platinum against platinum for steel against steel. The tangential traction coefficient = T / N , where T is the tangential tractive force and N is the normal loading force. The displacements at low values of T are almost entirely irreversible when T is relaxed and hence are due to the plastic shear of asperity junctions. The tangential traction coefficient approaches the coefficient of friction (as measured in the usual way) while the dis-

and

167

b ‘ r l r l l 5 10 15 20 250

3

1

2

3

Displacement, p m

-

Figure 8-12. Initiation of sliding by tangential traction. (a) Polished platinum. (b) Steel. 1: Unlubricated. 2 : Lauric acid in cetane. Normal 1/40th of static plastic deformation contact diameter load 9.02 N. of rider. Data by Courtney-Pratt and Eisner [lo].

placement is still small compared to the diameter of an artificial single contact region calculated from the relation

:[

d = 2

I”*

Displacements corresponding to sliding in the macroscopic sense are outside the range of the apparatus. Campbell and Aronstein [la] developed an apparatus for the measurement of friction at small displacements and slow speeds that takes the Figure 8-13 observations on the initiation of sliding a stage further. shows the behavior of lead sliding against gold in this apparatus. This is true macroscopic sliding; the total displacement is 2 . 5 times the diameter of the nominal contact area of the rider. For the first 38 pm of displacement the friction curve bears a close resemblance to the curves of Fig. 8-12, but beyond that the friction force is rather irregular. There is no uniquely identifiable transition to a value uk < u,; instead, allowing for the irregular character of the sustained sliding - which can be ascribed to the soft, ductile nature of the lead uk remains substantially equal to the value of the coefficient riderof friction at the initiation of sliding.

-

0

25

50

75

100

125

150

I75

Tangential Displacement , u m

Figure 8 - 1 3 . Initiation of sliding in a frictional system with stiff restraint. Lead on gold. Normal load 9.8 mN. Speed 1 vm/s. Data by Campbell and Aronstein [ l a ] .

168

The behavior described above can be reconciled with the large body of experimental observations that show a distinct differentiation between the coefficient of friction at the initiation of sliding and the coefficient of friction for steady-state sliding by the concept of asperity growth under tangential traction as a rate process. I f the tractive force is applied to a system at rest at a rate slow enough so that the new asperity junctions formed when the rider advances have time to grow to the same strength as the junctions broken on initiation of sliding, then the friction force for steady-state sliding will be equal to that of initial sliding: i.e. pk = uL6. But i f the velocity of sliding does not allow the new asperity junctions to grow to full strength, then uk < uL6. Other factors that affect what is overtly observed in a friction experiment of this nature are intimately linked with experimental parameters and conditions such as the apparatus with which the friction force is measured, the materials that are rubbed, the preparation and condition of the contacting surfaces, etc. These must be considered in conjunction with the basic mechanism of friction. Campbell and Aronstein [ l a ] observed no distinction between static and kinetic friction ( i . e . between friction at the initiation of sliding and the friction of sustained sliding) because the slow rate at which the tangential force was applied and at which the rider was transported ( 1 p/s) together with the extremely low compliance of the frictionsensing transducer (0.6 urn) made conditions at the start virtually the same as during the course of steady-state sliding. On the other hand, Morgan, Muskat and Reed 1191 observed typical stick-slip behavior at 0.025 cm/s-which they considered to be very slow-with an apparatus in which the friction force on the slider was monitored with a compliant elastic linkage. When analyzed by the model described in Section 8 . 3 , such behavior implies that static friction is distinctly different from kinetic friction, with p A > uk. But quite another interpretation emerges in terms of asperity junction interaction. If the driven surface is being translated at such a velocity that following the first microslip from the "stick" position-which does not occur instanteously but requires a finite time, however smallthe new asperity junctions cannot attain their full potential strength, then the excess energy stored up in the elastic deflection of the slider restraint must be dissipated by fast sliding against the direction of translation in a "slip." Figure 8 - 1 4 shows two of the charts obtained by Morgan, Muskat and Reed 1 1 9 1 using the resolution of a fast oscillographic recorder. Instead of an abrupt breakaway at the "static" friction level, there is a perceptible interval of sliding until the inertial lag of the rider is overcome by the restoring force of the deflected spring. With Woods metal sliding on babbit the difference between the coefficients of "static" and "kinetic" friction is large enough S O that the rider is pulled past its null position

169

0

5

10

15

0

5

10

Time. milliseconds

Figure 8-14. Slip traces in a frictional system with compliant restraint. (a) Woods metal on babbit. (b) Constantan on steel. Load 2.45 N. Tractive velocity 0.025 cm/s. Data by Morgan, Muskat and Reed [ 191.

and a new stick occurs on the return swing. With constantan on steel the coefficient of "static" friction is high enough so that the rider sticks again before reaching the null position. We see, then, that static and kinetic friction are not basic properties of the interface, either at rest or during sliding; instead, they are two modes of overt behavior. The behavior observed does in patt depend on certain basic properties of the sliding surfaces, such as the number, the distribution and the kind of asperities; but it also depends on such macroscopic details of experimentation as the mass of the rider, the compliance of its elastic restraint, the velocity at which the moving body is translated and the acuity with which the sliding system is observed. However, the absence of a theoretical basis for their differentiation does not necessarily require the abandonment of the traditional use of the designations otatic and k i n e t i c friction. It is a nomenclature that has meaning in the behavioristic sense and utility for practical purposes. The factor that is least controllable in the deduction of static and kinetic friction values from stick-slip experiments is the condition of the contacting surfaces. This explains why Brockley and Davis 1 2 0 1 in their study of the influence of the time of contact on pL6 were unable to obtain repeatable results, as shown in Fig. 8-15a. For each series of determinations made with a single placement of the rider on the track, the plot of u A against the time of quiescent contact shows satisfactory self-consistency. But when the experiment is repeated with a fresh placement of the rider on the track, a different curve is obtained, selfconsistent but not a duplicate of the previous experiment. This was traced to the variability of the surface with location on the rubbing track. Furthermore, it was demonstrated that a model of time-dependent junction growth could be made to yield the following expression:

u* - uk

=

ctY

(8-31)

170 1

I

I

I

1

(b)

0.15

A 0

10

20

30

40 Time t, seconds

50

Influence of the time of Figure 8-15. static friction. (a) Effect of rest time t on the coefficient of static friction steel. (b) Test of Eqn 8 - 3 1 over a range Data by Brockley and Davis [ 2 0 ] .

2.0 0-5

0

05 log t

1.0

1.5

contact on the coefficient of and replacement of the rider for Atlas Nutherm on annealed of experimental conditions.

where the conditions are set so that c and y may be regarded as empirical constants. Figure 8-15b shows how the experimental data over a range of conditions conform to Eqn 8-31. The reason is that the fundamental mechanism of junction growth does not change with fresh placement of the rider on the track. Kato e t aL. [ 2 1 ] found that the value of the coefficient of "static" friction depended on the duration of the stick portion of the cycle in lubricated stick-slip sliding of cast iron on cast iron according to the formula (8-32) where u b is the observed coefficient of friction at the termination of stick, t is the time of stick, c ' and y ' are constants which depend on the properties of the lubricant and the character of the rubbing surfaces, urn is the asymptotic value of u, as t approaches infinity and u ' , is the value of v, when t approaches zero. The data of Kato and his coworkers cover sliding velocities ranging from 0.000367 to 0.157 cm/s. With mineral oil as the lubricant the value of u, ranged from 0.25 for a contact time of 0.2 second to 0.56 at 1 0 0 0 seconds: with vegetable oil u, was 0.20 at 0.2 second and 0.40 at 20,000 seconds. Obviously when t = 0 , the distance the slider is transported during stick is also zero, in which case, according to Eqn 8-26, p, = pk: hence when t = 0, = uk. Turning now to the case of u, < ph, let us examine the diagram shown in Fig. 7-5b at the stage where the block retracts to a position of rest when the plate stops moving. This behavior is at odds with the previously enunciated postulate that the total junction strength in the putative rubbing surface increases under tangential traction. Retractive slip of the rider upon halting the translation of the countersurface is typical behavior in the presence of "boundary" lubricants such as long-chain fat-

171

ty acids and fatty esters. The lubricating action of these substances is related to their adsorption on the rubbing surfaces. An increase in the coefficient of friction is associated with a decrease in the adsorptive coverage of the rubbing surfaces by the lubricant substance. Let us consider the behavior depicted in Fig. 7-5b in terms of the asperity-junction mechanism for the boundary-lubricated case. The asperities actively in contact are classified into two categories: bare asperities, and asperities protected by a film of lubricant. The junction strength concept gives the expression below for the tangential tractive force required for sliding:

where ai and a . are the cross-sectional radii of the bare and the lubrij are the corresponding shear cated asperities respectively, and 6 1 and strengths. For a well-lubricated surface J1 >> x; hence the behavior of the interface between the rubbing track and the rider will be dominated by the behavior of the lubricated asperities. As is seen in Fig. 8 - 1 2 , the displacement of surfaces lubricated with lauric acid in cetane goes over to sliding at levels of the coefficient of traction significantly lower than is observed for unlubricated surfaces. To explain why no stick is observed prior to macroscopic sliding in the boundary-lubricated case, it is postulated that shear of the lubricated asperity junctions occurs without the lag characteristic of junction growth of unlubricated asperities; i.e., in the case of adequate lubrication the contribution of the first term of Eqn 8 - 3 3 is insignificant. Hence there is no stickslip in boundary-lubricated sliding.

cs 0 .-

f : "

.-

'

0.14- Louric Acid 0.020 molol

ic Acid 0.0037 molol

60.04

1

1

1

1

1

1

1

1

1

.

Rubbing Speed, cm /s

Figure 8 - 1 6 . Effect of rubbing speed on friction of cast iron lubricated by fatty acids. Data by A . Dorinson, ASLE Trans., 1 3 ( 1 9 7 0 ) 2 1 5 - 2 2 4 .

Fig. 8 - 1 6 shows the effect of a moderate range of slow sliding speeds on the coefficient of friction for hardened alloy cast iron lubri-

cated with solutions of lauric acid and stearic acid in white oil. Focusing on the interval between 0 and 0.0423 cm/s,* the behavior can be explained in terms of speed-controlled desorption of the lubricant during sliding, thereby exposing an increasing proportion of asperities to metallic contact and junction formation ( L . e . , increasing the contribution of the first term of Eqn 8-33 to the tangential tractive force). Now let us consider the reverse process when the forward motion of the rider is stopped. In reality the velocity of rubbing is never brought instantaneously to zero, which means that by the time macroscopic motion is judged to have ceased, the interface area that has moved under the slider is better covered with adsorbed lubricant than preceding portions of the track that participated in steady-state sliding. Therefore a relaxation of the elastic restraint on the rider will be observed and the friction signal will be interpreted to mean p A < u k . Resumption of macroscopic motion will restore the dynamic desorption process and the instrumentation will again indicate the force of kinetic friction a s greater than that of static friction. 8.6.

SLIDING SPEED AND FRICTION

In tnis section the interaction of sliding speed and friction, in particular the interpretation of the instrumental displays in the measurement of motion, will be examined more closely than it was in Sections 8.3 and 8.4. We are interested specifically in the reliable determination of pk with an apparatus that employs elastic coupling of the rider as the measuring device, Let us proceed from the known experimental fact that when the speed of the driven surface is great enough, smooth sliding is observed, in the sense that the rider maintains a steady equilibrium deflection from the null position. ** We wish to examine the evaluation of kinetic friction in terms of the extended theory of stick-slip sliding. According to the simple theory, smooth sliding results when yo-y, in Eqn 8-26 is equal to zero:

Since

M,

g and

K

are not zero, it follows that

pA

is

indistinguishable

*The behavior over the entire range of speeds shown in Fig. 8-16 is discussed in Chapter 9.

** In

actual practice, except for the most carefully constructed devices, the picture is complicated by extraneous vibrations introduced by the driving mechanism. In most cases these can be evaluated and acI t is assumed, therefore, that in this discussion we are counted for. dealing with uncomplicated smooth sliding.

173

from u k ; in other words, only one coefficient of friction is found by experiment under these circumstances. To find how the critical velocity at which the driven surface is translated affects the transition from intermittent to smooth sliding requires that the theory of stick-slip be extended to include the empirical fact that the magnitude of the coefficient of kinetic friction is a funcof the velocity with which the rider rubs against the tion countersurface. Using the approach of Brockley, Cameron and Potter [ 1 5 ] , the expression for the coefficient of kinetic friction is written as (8-34)

where pm is the empirically determined minimum value of the coefficient of friction. The equation of motion for a slip Cch, Eqn 8-18] then becomes d2Y

'dt2

+

dY 1-

dt

+ KY

[

= ffl5 urn +

&

(. -31

(8-35)

Details of the solution of this equation are given by Brockley, Cameron and Potter. A usably adequate approximation for the amplitude of vibration is

where K is a quantity computed from the damping factor and p L b is a tion of the amplitude of vibration such that

func-

(8-36b) m

being the maximum amplitude of vibration.

It can be shown that

VAY

(8-37

where v is a constant derived from the behavior of the static friction function. The critical translational velocity at which b y approaches zero is given by vc = u(Ay),,,

In Fig. 8-17 the comparison of the results Cameron and Potter [ 1 5 ] from Eqn 8-37 for three with the data they obtained experimentally critical velocity concept in stick-slip sliding

(8-38)

calculated by Brockley, different sliding systems shows the behavior of the and its confirmation by

174

0.08

1

1

I

I

0.04

005 0.10 0.15 0.20 0.25 T r a c t i v e V e l o c i t y v,cm/s

0

Figure 8-17. Tractive velocity and the amplitude of stick-slip vibration. Data by Brockley, Cameron and Potter / 1 5 ] . experiment. For details of the theoretical treatment the reader can consult the publications by Singh [ 1 4 ] and by Brockley, Cameron and Potter [153.

Detailed direct experimental evidence for the frictional behavior during the slip part of a stick-slip cycle is found in the work reported by KO and Brockley [171. The rider and its elastic coupling were fitted with the following transducer devices: (a) a strain gage to measure the displacement of the rider from its null position; (b) an electromagnetic transducer to measure the velocity of the rider during vibration or transport; and (c) an accelerometer to measure the acceleration of the rider. The data obtained with this instrumentation were used in the equation for stick-slip ( c d . Eqn 8-18): +

+

KY

=

F

With appropriate circuitry an oscillocope can be made to display rn? + K Y as a function of j , which is equivalent to a plot of F - X i against j . With a spring of adequate stiffness, 1; is negligible with respect to F in a single cycle, and hence the display reduces to a plot of F against i . The sliding velocity in the slip part of the cycle is not v , the velocity at which the countersurface is translated by the driving motor, but v - j , the velocity with which the rider moves relative to the countersurface. The numerical sign of j is in the sense opposite to the motion of the translated surface. For a constant value of v there is no difficulty in interpreting the oscilloscope display as the rider goes through an excursion from the initiation of stick to kinetic sliding and back to recurrence of stick. Typical results for a single slip are shown in Fig. 8-18, where the diagram on the right gives the motion of the rider. In the diagram for friction, the force decreases as the true sliding speed increases to its maximum value, which occurs at about half-way through the slip. But attains its maximum value, what is to all intents and purafter v poses a discontinuity appears in the response of friction to rubbing

175

0.08C

8-

0.06-

6-

c

c

c

5 4-

E 5- 0.04 -

;2-

%S 0.02 -

0.

E&

I

0

I

I

I

I

2

%?*

, D

0

0

4

2

4

Sliding Velocity v - j , cm/s

Figure 8-18. Friction force and displacement cycle. Data by KO and Brockley [171.

in

a

single

stick-slip

speed and further decrease in the coefficient of friction is very small. It is evident that neither averaging the amplitude of the excursions of the recorder nor taking the speed at which the moving surface is translated as the velocity of sliding is a correct method of dealing with friction data in stick-slip sliding. The results obtained by Kato and his co-workers [211 for the lubricated sliding of cast iron on cast iron, using a method in principle substantially that described above, are consistent with those of KO and Brockley [171. 8.7.

NON-ADHESIONAL MECHANISMS FOR FRICTION

There are mechanisms other than the adhesion of asperity contacts that can result in phenomenologically observable friction. The two most important, from an engineering viewpoint, are plowing and hysteresis loss.

F

&

-,

------- --- ----Figure 8-19.

The plowing mechanism in friction.

Only a brief presentation of the plowing mechanism is The reader is referred to the description by Bowden and Tabor fuller treatment. Let us consider a hard metal sphere pressed into a soft metal block by a load W (Fig. 8-19a). If projected area of contact and p is the yield pressure of the al, then

given here. 1221 for a of radius h A is the softer met-

176

W

A = P

This assumes that the surfaces are perfectly smooth so that the deformed area is identical with the contact area. Now let us cause the sphere to slide by applying the tangential force F. This force is comprised of two parts, one being the shear force

S

=

Ah

where A is the force per unit area, acting in the tangential direction, required to shear the adhesions between the two bodies. The second part of the force, P, is the force required to displace the softer metal in front of the slider. I t is equal to the cross-section of the grooved track, A p , multiplied by the mean pressure p' required to displace the metal. The area A is approximately given by 1 / 1 2 ( d 3 / h ) , where d i s the P track width. The total force of friction is the sum of the shearing term and the plowing term:

F

+-

= S +

d3

P' 12h

(8-39)

If the plowing is accomplished by sliding a thin lamina (Fig. 8-19b), then the first term of Eqn 8 - 3 9 becomes negligible and the tangential force is

F

=

p =

d3

- p' 12h

(8-40)

The plowing force, therefore, is proportional to the third power of the track width. Experiments with a steel spade plowing through indium have confirmed this relation [ 2 2 ] . The plowing mechanism can operate on a microscopic as well as on a macroscopic scale. Asperities in each surface can be distributed through a range of heights and sizes. I f the relative hardness of the materials in the two surfaces is of the right order, plowing by large, hard asperities can be of equal or greater significance than adhesion in the friction process. Such behavior is particularly to be expected of metals such as steel, with hard grains in their structure. The hysteresis loss mechanism of friction is based on the fact that in real life recovery of a material from elastic deformation on removal of the stressing load is never perfect. The energy lost by this effect can be treated as a frictional loss. The hysteresis loss mechanism is of major importance in explaining rolling friction. Details of the rolling friction process are complex; the second volume of the monograph by Bowden and Tabor [231 devotes an entire chapter to various aspects of rolling.

177

REFERENCES F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1950, Part I , p. 30. 2. R. Holm, Electric Contacts, Hugo Gebers Fijrlag, Stockholm, 1946, Section 15. 3. F. P. Bowden and D. Tabor, o p . cit., pp. 147-148. 4. F. P. Bowden and D. Tabor, o p . cit., Chapter V, pp. 98-99. 5. D. Tabor, Proc. Roy. SOC. London, A251 (1959) 378-393. 6. F. P. Bowden and J. E. Young, Nature, 164 11949) 1089. 7. R. A. Brown and R. D. Burton, J. Lubrication Tech. (Trans. ASME), 89F (1967) 425-432. 8. D. H. Buckley, Friction, Wear and Lubrication in Vacuum, NASA SP-277, Nationii Aeronautics and Space Administration, Washington, D. C., 1971, pp. 56-60. 9. J. S. McFariane and D. Tabor, Proc. Rov. SOC. London. A202 (1950) 244-253. 10. J. S. Courtney-Pratt and E. Eisner, Proc. Roy. SOC. London, A238 (1957) 529-550. D. H. Buckley, a p . c i t . , pp. 67-83. 11. Appl. Phys., 5 ( 972) 12. J. Skinner and N. Gane, J. Phys. D: 2087-2094. 13. N. Gane, P. F. Pfaelzer and D. Tabor, Proc. Roy. SOC. London, A340 (1974) 495-517. This work is discussed in detail in Chapter 12 14. B. R. Sinah. J. Ena. for Industrv (Trans. ASME). 82B (1960) 393 398. 15. C. A. BGockley, *R. Cameron 'and A. F. Potter, J. Lubrication Tech. (Trans. ASME), 89F (1967) 101-108. 16. C. A. Brockley and P. L. KO, J. Lubrication Tech. (Trans. ASME), 92F (1970) 550-566. 17. P. L. K O and C. A. Brockley, J. Lubrication Tech. (Trans. ASME), 92F (1970) 543-549. 18. W. E. Campbell and J. Aronstein, ASLE Trans., 16 (1973) 223-232. 19. F. Morgan, M. Muskat and D. W. Reed, J. Appl. Phys., 12 (1941) 743-752. 20. C. A. Brockley and H. R. Davis, J. Lubrication Tech. (Trans. ASME), 90F (1968) 35-41. 21. S. Kato, K. Yamaguchi, T. Matsubayashi and N. Sato, Men. Faculty Engng., Nagoya Univ., 27 (1975) No.1, 1-71. 22. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1950, Part I , Chapter V. 23. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1964, Part 1 1 , Chapter XV. 1.

178

Chapter 9 LUBRICATED FRICTION

The present chapter deals with frictional behavior when lubricated surfaces rub against each other. In Chapter 7 attention was called to the distinction between viscous loss in a fluid film separating two solid surfaces and the friction of the surfaces rubbing directly against one another. In this chapter we shall discuss the type of lubrication in which the rubbing surfaces that carry the lubricant participate intrinsically in the lubrication process rather than merely as the geometric boundaries of the fluid film. The treatment of lubricated friction here will be mainly descriptive: detailed analysis and discussion of theoretical models for lubricated frictional rubbing is reserved for subsequent chapters. Much of the lubricated rubbing we shall examine involves the surfaces that would constitute the boundaries of a fluid film i f it could exist; therefore the designation "boundary lubrication" is commonly used. However, this should not be regarded as a rigorously defined category, for many difficulties lie in the way of identifying boundary lubrication In this work we shall use the term precisely in behavioristic terms. "boundary lubrication" in its commonly accepted sense without imputation of exactitude. Boundary lubricated friction is not basically different from the friction of what are commonly regarded as unlubricated surfaces. Essentially a boundary lubricant affects frictional behavior by modifying the character of the surfaces and thereby modifying the character of contact during rubbing. An unlubricated surface is not necessarily a clean surface, and thus our starting point in the discussion of lubricated friction is an examination of the behavior of clean surfaces.

9.1.

THE CONTACT AND FRICTION OF CLEAN SURFACES

The fact that the surfaces of materials exposed to the ordinary atmosphere are not clean is well established. Water vapor and the fixed atmospheric gases are ubiquitously adsorbed physically on even nonreactive surfaces. As for the ordinary metals, almost all of these are chemically reactive, and after substantial exposure to the atmosphere their surfaces carry a layer of oxide. The adhesive theory of friction implies true contact of the putative material of composition at asperity

179

junctions. For metals, this presumes that the oxide films are ruptured and penetrated in some manner. It is of consequence, therefore, to describe and compare the contact behavior of clean metals and clean oxides. The idea that adhesion is responsible for metallic friction was advanced as far back as 1724 El], but the acquisition of evidence for the role of clean surfaces in the friction of metals had its systematic beginning in the work of F. P. Bowden and his collaborators. Bowden and Young 121, who studied the cleansing of nickel surfaces by heating under vacuum pumping at 133 WPa torr) and the subsequent frictional behavior i n vacuo at room temperature, were able to achieve such largescale seizure that the nominal "coefficient of friction" wa5 of the order of 100. Table 9-1 shows data by Buckley [3] for the friction and adhesion of copper sliding on copper in high vacuum (1.33 nPa, torr). The coefficients of friction and the adhesion coefficients are all much larger than unity and with one exception the adhesion coefficients after sliding are greater than the coefficients of friction. Table 9-2 lists some characteristic coefficients of friction for metals sliding in vacuum environments in which the average levels of pressure lie in the range 400-1330 nPa. But before deciding that surface cleanliness is the controlling influence in the friction of unlubricated metals, some consideration should be given to the data in Table 9-3 and to the behavior of single-crystal copper sliding on the ( 1 1 1 ) face (Table 9-1). I t is quite apparent that the frictional process for sliding met-

TABLE 9-1. FRICTION AND ADHESION OF CLEAN COPPER IN VACUUM Form and orientation

Adhesion coefficient before sliding

Coefficient of friction during sliding

Adhesion coefficient after sliding

Single-crystal, matched (100) planes

1.02

40

Single-crystal, matched (110) planes

0.61

40

50.0

Single-crystal, matched ( 1 1 1 ) planes

0.30

21.0

10.5

Polycrystalline

1 .oo

40

130

100

Load: 0.5 N. Sliding velocity: 0.001 cm/s. Single pass of 0.735 cm. torr). Data by Temperature: 293 K (20 C). Pressure: 1.33 nPa D. H. Buckley 131.

180

TABLE 9-2.

COEFFICIENTS OF FRICTION IN VACUUM

Rider

Platen or disk

Iron (a)

Iron

2.2

-_---

Nickel (b)

Nickel

0.5-4

1.33 x

Platinum (b)

Plat i num

0.6-4

1.33 x

Silver (b)

Silver

0.4-3.5

1.33 x

Copper (c)

Copper

3.0

Copper (c)

Copper

4.0-5

Copper (c)

Copper

Copper (d)

Nickel

4.0

1.33

Copper (d)

Cobalt

2.00

1.33

Copper (d)

Tungsten

1.40

1.33

Cobalt (d)

Cobalt

0.35

1.33

Co-50/Fe alloy (e)

Co-50/Fe

1.2-1.3

1.33

Co-25/Mo-lO/Cr

Co-25/Mo-lO/Cr

0.25

1.33

(e)

Coefficient of friction

15

Vacuum, Pa

399 665-1330 x lo-’ 795-1330 x

lo-’

IO-’

(a) D. H. Buckley, NASA TN D-4775 (1968). (b) F, P. Bowden and G. W. Rowe, Proc. Roy. SOC. London, A233(1956) 429-442. (c) R. A . Brown and R. D. Burton, J. Lubrication Tech. (Trans ASME), 89F (1967) 425-432. (d) I?. H. Buckley 131. (el P. M. Vedarnanikam and D. V, Keller, ASLE Trans., 16 (1973) 73-81.

als is complex. The role of junction growth is shown in Table 9-1 by the large difference between the adhesion coefficients before and after sliding. I t can also be seen that crystal structure and face matching play an important part in initial adhesion and in sliding friction. This is probably the reason that copper gives only moderately high coefficients of friction sliding against nickel, cobalt or tungsten in a hard vacuum of 1.33 nPa. Some metals are intrinsically non-adhesive: clean singlecrystal cobalt sliding against itself on the basal hexagonal plane shows a coefficient of friction of 0.35 and an adhesion coefficient of < 0.05 both before and after sliding 141. The foregoing data demonstrate that clean metals are not necessarily prone to strong adhesion, high friction and extensive seizure, even when sliding. I t depends on the characteristics of the metal and the details of the interfacial contact. The frictional behavior of elemental metals can be related to those aspects of their atomic structure which are responsible for their metal-

181

TABLE 9-3. ADHESION AND FRICTION FOR SINGLE-CRYSTAL METALS IN HIGH VACUUM Metal pairs and orientation

Adhesion coefficient before sliding

Coefficient of friction during sliding

Adhesion coefficient after sliding

Copper (111) on copper (111)

0.30

21 .o

10.5

Copper (111) [ ? l o 1 on nickel (111) [1101

0.25

4.0

2.0

Copper (111) [1101 on cobalt (0001) [11201

0.10

2.0

0.5

Copper (111) [1101 on tungsten (110) [1111


1.40

0.5

Load: 0.5 N. Sliding velocity: 0.001 cm/s. Single pass of 0.735 cm. torr). Data by D. H. Buckley, Friction, Wear Pressure: 1.33 nPa and Lubrication in Vacuum, NASA SP-277, p. 63.

lic characteristics. In contrast, the frictional behavior of clean diamond is of interest because it is a one-element crystal, with a spatial arrangement analogous to that of metals and yet with much different properties. The difference lies in the nature of the carbon-carbon bonds of the diamond structure. Bowden and Hanwell 151 studied the friction of clean diamond at 6.65 pPa ( 5 x 10-l' torr) by reiterated reciprocation over a track a few millimeters in length at a frequency of about 2 cycles per second. Because diamond transforms to amorphous carbon when heated Bowabove 973 K (700 C), the maximum outgassing temperature was 723 K. den and Hanwell viewed the initial state of the diamond surface as contaminated by a tenaciously adherent layer of adsorbed gas and hence they regarded the initial friction ( v = 0.1) as not characteristic of a clean diamond surface. After 500 cycles of rubbing in a continuously pumped system, the friction began to fluctuate violently and rose to a value of 11 = 0.9, at which level it remained steady for 7000 cycles of rubbing. The wear track generated on the stationary specimen was characterized by much cracking and fragmentation. Bowden and Hanwell ascribed the change in frictional behavior to the cleansing of residual adsorbed gas from the contacting surfaces by rubbing, thereby allowing full scope to the adhesive mechanism. If the rider was lifted and exposed to the gases remaining in the vacuum chamber for 20 minutes and then put back in sliding contact, the coefficient of friction decreased to 0.1 but rose again to 0.9 after 10-20 cycles. Diamond can be slid against diamond in air with a low coefficient of friction and with no surface damage apparent at a magnification of 220 times.

182

Bowden and Hanwell [ 5 ] obtained an initial value of u = 0.6 for single-crystal sapphire (e-Al2O3) in contact on the (1070) plane, with a steady-state value of u = 0.7 after repeated cycles of sliding. Buckley [ 6 ] observed values of u for single-crystal sapphire ranging from 0.5 to 1.5, depending on the crystal orientation and the load. Polycrystalline aluminum oxide (A1203) showed coefficients of friction ranging from 0.5 to 0.15, depending on the load. For single-crystal magnesium oxide (MgO) Bowden and Hanwell [5] observed a rise in the coefficient of friction from an initial value of M = 0.33 to a steady-state value of u = 0.8 after 100 cycles of sliding. The track on the stationary specimen was extensively worn and cracked, and pronounced subsurface flow was observed in the material underneath the track. Quartz behaved much like magnesium oxide, with considerable damage to the track and a coefficient of friction which increased from an initial value of u = 0.33 to a stable value of = 0.7. Buckley 1 6 1 studied the friction of clean metals sliding against clean sapphire. A copper rider sliding against a stationary sapphire surface gives a coefficient of friction of about 0.2; the copper adheres to the sapphire and the shear occurs in the sapphire. I f a sapphire rider slides on copper, the coefficient of friction is 1.5, but in this case the major contribution to the friction is the plowing of the softer copper by the sapphire rider. A coefficient of friction of approximately 0.2 was found to be characteristic of the following metals sliding on single-crystal sapphire: copper, nickel, rhenium, cobalt and beryllium; = 0.1. Metal riders sliding against for silver o r gold on sapphire, polycrystalline aluminum oxide gave the coefficients of friction listed in Table 9-4. The behavior of plastics in contact with clean metals in exemplified by the findings of Brainard and Buckley I 7 1 for polytetrafluoroethylene (PTFE). Transfer of PTFE to clean aluminum, nickel, tungsten, copper, iron, tantalum, gold and silver was detected by the Auger electron emis-

u A1 umi num Iron Niobium Tungsten Copper Ti tan ium

1.35 1.1

1.05 0.9 0.85 1.35

Load: 9.8 N. Speed: 0.013 cm/s. Data by D. H. Buckley [ 6 1 .

?J

Zirconium Beryllium Cobalt Rhen i um Lanthanum

Pressure: 13.3 nPa

0.5 0.45 0.35 0.2 0.2

torr).

183

sion of carbon and fluorine. Transfer of PTFE was also observed on a deposited "clean" layer of aluminum oxide. Sliding of PTFE on a clean tungsten surface was essentially sliding of bulk PTFE on a transfer film of PTFE laid down on the track; the coefficient of friction was 1! = 0.06. Sliding of PTFE on a rotating aluminum disk is illustrated by Fig. 9 - 1 .

0 60 I20 180 240 300 370 60 120 Angular PosiCon of Dlsk

L 2-1

Figure 9-1. Friction of PTFE against clean aluminum in vacuum. revolution of the disk. 2 : Second revolution. Load: 2 . 4 8 N. velocity: 0.07 cm/s. Data by Brainard and Buckley [ 7 ] .

First Sliding

1:

Sliding starts out with )I = 0 . 0 8 , characteristic of PTFE against a transferred film of itself, but the PTFE rider a l s o pulls particles of aluminum out of the track and by the time the second revolution of the disk has begun the track is being scored by these particles and the coefficient of friction has risen to u = 0.5. The frictional behavior we have examined is sufficient to demonstrate that there are no easy generalizations about the sliding of clean surfaces, be they metal against metal, oxide against oxide, metal against oxide, or plastic against metal. In particular there is no foundation in fact that the behavior of clean metals in sliding contact is always strong seizure with very high values for the coefficient of fricI t depends on the specific metals and the circumstances. Nor is tion. the coefficient of friction for oxide sliding against oxide always low; typical values are of the order of several tenths and cases where p > 1 have been observed. 9.2.

THE INFLUENCE OF SURFACE OXIDES ON THE FRICTION OF METALS

When a clean metallic surface is exposed to ordinary ambient air, it acquires a contaminating film. Every common metal, with the exception of gold, reacts with the oxygen of the air to form an epitaxial film of oxide. In addition, there is a physically adsorbed film, comprised of oxygen, carbon dioxide, water vapor and other atmospheric constituents, that lies on top of the oxide layer. Consequently the process of "cleaning" surfaces for friction studies by abrasion, polishing, water-washing

184

and solvent-washing always leaves residual films of one kind or another. The effect of deliberately contaminating a metal surface that has been outgassed i n vacua by permitting a trace of oxygen to leak in was demonstrated by Bowden and ilughes [ a ] , who observed that the coefficient of friction for nickel against tungsten and copper against copper fell from u = 4.5-5.7 to u = 1.5-2.5 in a matter of 2 minutes. Longer contact with oxygen reduced to 0.5-0.8. The reverse effect of removing oxide by vacuum treatment as reported by Buckley [ 9 1 is illustrated in Fig. 9-2 for the sliding of ordinary oxide-covered A I S I 5 2 1 0 0 steel against itself. From the value of p = 0 . 4 5 observed for the initial rubbing there is a slow rise in the coefficient of friction with continued rubbing as the oxide coating is worn away and the behavior of the oxide-denuded portion of the surface becomes increasingly prominent. Eventually a pronounced change in frictional behavior occurs: the coefficient of friction rises sharply with further sliding and the pieces seize by welding.

0.5

I

.-E 5

I

I

t 0.4.t u-

-

0.3

0

+

5 0.2-

.-

.-0 u-

E

”

0.1 -

-

0

0

“r“

r

c

“ I 4

I

1

1

Figure 9-2. in vacuum. Buckley [ 9 1 Simple observation of sliding behavior in ordinary air cannot tell us whether the friction is governed by the contact of metallic or of oxide surfaces. Each individual case must be examined carefully for the influence of the experimental parameters. Figure 9-3 illustrates three different modes for the frictional behavior of oxidizable metals. Figure 9-3a shows the influence of load on the coefficient of friction for soft metals such as indium or tin. The surficial oxide is extensively disintegrated by the deformation of the underlying metal, even at the very lightest loads, and the frictional behavior is governed predominantly by metal-to-metal contact, as indicated by the electrical conductance. The coefficient of friction stays at substantially the same level over the entire load range; for a readily self-adherent metal such as indium the in ambient air may be as high a s 10. The behavior typified by value of

185

z

E 8

20'

(c)

15-

V

10-

-

050

I

I

I

I

I

Fig. 9-3b is characteristic of hard metals with robust films of surface oxide, such as chromium or steel; contact is oxide against oxide, as shown by the high values for electrical resistance. At the very lightest loads the asperities are deformed elastically; the true area of contact and hence the friction force is proportional to the two-thirds power of the load. The coefficient of friction is therefore inversely proportional to the cube root of the load. But when the load increases sufficiently, deformation of the asperities becomes plastic, the friction force is then directly proportional to the load, and the coefficient of friction assumes a constant value. Figure 9-3c illustrates the behavior of copper. At the lowest loads oxide slides on oxide, but copper is soft enough so that the friction is governed by the plastic deformation of the asperities and the coefficient of friction is constant up to the critical load level at which the oxide film begins to break down. This is marked by a transitional increase in friction to the terminal phase in which the contact is substantially metal-to-metal and the coefficient of friction becomes constant at a higher value. Detailed descriptions of the frictional behavior of various metals can be found in the monographs by Bowden and Tabor [ l o ] . 9.3.

LUBRICATED FRICTION: THE BEHAVIORISTIC VIEW

The simplest pragmatic criterion by which we become aware of the process of lubrication is a reduction in the friction and wear of a rub-

186

bing system. This, of course, implies that we have established what the unlubricated state of the system is. Suppose we define it as the uncontaminated surface and apply this definition to a metal; then if the metal acquires a surface film of oxide by exposure to the air, the friction between the oxide-coated surfaces could be regarded as lubricated friction. However, from a practical point of view, we could choose as well to regard the oxide-coated surface carrying an adsorbed film of atmospheric constituents as the unlubricated state and to consider lubricated rubbing as the process that occurs in the presence of a film of material deliberately introduced to function as a lubricant. Introduction of the special lubricant film brings about a substantial reduction in the friction between oxide-coated surfaces, which to begin with for most ordinary metals is less than that of meticulously clean surfaces. The criteria for the unlubricated state are therefore not fixed rigorously by theory; for the most part they evolve empirically and it is generally understood from context what they are. Consider the behavior illustrated in Fig. 9-4, which is typical of the slow-speed sliding of many metals in ambient air. When the lubricant is a highly refined mineral oil, the friction trace indicates stick-slip sliding. Addition of a small amount of long-chain fatty acid ( e . g . lauric acid) to the lubricant almost immediately results in a change to Since smooth sliding with a coefficient of friction less than 0.1. stick-slip behavior involves the characteristics of the friction-sensing device as well as what goes on at the asperity junctions (see Chapter 8 , Section 3 ) , the obvious conclusion is that under the conditions of load and speed employed the mineral oil does not form an effective lubricating film. The obvious corollary is that fatty acid added to the mineral o i l does form such a film. Rabinowicz and Tabor [ l l ] assessed the extent of contact in slowspeed friction experiments by the transfer of metal from a radioactive

.- 0.6 c .-0

t

0.4

0

Time v Figure 9-4. Frictional behavior of lubricated cadmium. Lubricant is refined paraffin oil. At A a drop of lauric acid is added to the oil. After Bowden and Tabor, The Friction and Lubrication of Solids, Part I, Chapter IX.

187

slider to an inert plate. Their data for cadmium on cadmium are shown in Table 9-5. The strongly irregular friction of the unlubricated reference state is associated with a high degree of transfer from the slider to the plate. On introducing the straight-chain hydrocarbon cetane as the lubricant, the amount of transfer decreases a hundred-fold and the coefficient of friction decreases from 0.8 to 0.66; the mode of sliding is stick-slip. With cetyl alcohol as the lubricant transfer, although reduced still further, remains appreciable, the coefficient of friction is still quite high, and the sliding is still stick-slip. With palmitic acid as the lubricant, transfer is reduced to almost negligible levels, the coefficient of friction is less than 0.1, and the sliding is smooth. TABLE 9-5. CONTACT AND TRANSFER: CADMIUM ON CADMIUM Transfer, nanograms per cm

Lubricant

P

None Cetane Cetyl alcohol Palmitic acid Copper palmitate

0.8 0.66 0.43 0.07

Load: 19.6 N.

0.05

Speed: 0.01 cm/s.

50,000 500 100 0.07 0.05

Friction Very irregular Stick-slip Stick-slip Smooth Smooth

Data by Rabinowicz and Tabor [ll].

TABLE 9-6. FRICTION WITH MONOMOLECULAR FILMS OF LONG-CHAIN COMPOUNDS DEPOSITED ON PLATES Coefficient of friction, uk

C atoms in chain

NO.

8 10 12 13 14 16 17

18 20 22 26 32

Fatty acids

Fatty amines

Fatty alcohols

Glass

Stainless steel

Glass

Glass

0.17 0.13 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.04

0.24 0.13 0.10

----

0.il

Stainless steel

Stainless steel

0.19 0.16 0.13

----

0.10 0.09 0.07 0.08 ----

0.08 ----

0.07

Stainless steel ball against glass plate: M~ = 7 . 1 ; against stainless steel; pk = 0.6. Loads: 0.01-5.88 N (57-482 MPa). Speed: 0.01 cm/s. Temperature: 298 K. From data by Levine and Zisman [12] and Cottington, Shafrin and Zisman I t 3 1 .

188

A similar state of affairs holds with copper palmitate as the lubricant. Data such as these provide evidence for the association of the filmforming properties of fatty acids with inhibition of direct asperity contact, low coefficients of friction and smooth sliding. This is the type of behavior to which the term baundahy tubhication is generally understood to apply. It can be demonstrated that long-chain aliphatic compounds form compact monomolecular films on suitable substrates (see Chapter 10). Table 9-6 shows results obtained by Levine and Zisman El21 and by Cottington, Shafrin and Zisman 1131 for the slow-speed sliding of a stainless-steel ball 1.27 cm in diameter against films of straight-chain fatty compounds deposited on flat plates of glass or stainless steel. Coefficients of friction less than 0.10 are indicative of effective boundary lubrication. Specific experimental parameters that influence the values of uh are the chemical structure of the lubricant substance, its chain length, and the nature of the substrate material. The fundamental aspects of the lubricating action of long-chain aliphatic compounds is discussed in detail in Chapter 10.

TABLE 9-7.

LUBRICATION OF COPPER BY PALMITIC ACID ~

Fresh None Cetane 0.001% Palmitic acid (3 x

M)

0.01% Palmitic acid (3 x

1% Palmitic acid ( 3 x Palmitic acid, saturated Palmitic acid, solid film

~~

Coefficient of friction

Lubricant

0.1% Palmitic acid (3 x

~~

M)

M)

M)

Oxidized

2.5 0.7

0.3 0.12

0.53

0.12

0.16

0.09

0.14

0.09

0.12 0.085 0.055

0.075 0.055

0.08

Copper pin on copper disk, 2.35 N load, sliding speed 1 cm/s. Solutions of palmitic acid in cetane. From data by Tamai and Rightmire I141. Data on the lubrication of copper by palmitic acid obtained by Tamai and Rightmire 1141 are given in Table 9-7. The copper specimens were polished, heated for 3 minutes at a temperature of 973 K (700 C) and a pressure of 6.6 Pa (0.05 torr), cooled, and then introduced into the friction apparatus as soon as they had come to room temperature. These are the specimens identified as "fresh" surfaces in Table 9-7. The

189

oxidized specimens were prepared from the fresh specimens by heating in air to produce an oxide layer estimated to be 100 nm thick; the oxide film on the fresh surfaces was estimated to be less than 5 nm thick. Thus, for the lubricated friction data in Table 9-7 there are two The reference states: one with p = 2.5 and the other with u = 0.3. "fresh" surface is substantially no more difficult to lubricate than the oxidized surface when the film of palmitic acid is deposited directly from the melt or from a saturated solution in cetane; but with solutions molar as well as with unof palmitic acid in the range 0.03 to 3 x compounded cetane, the coefficients of friction are significantly higher for the "fresh" surfaces. The influence of fatty acid concentration and chain length on the friction of hardened alloy cast iron over a range of slow rubbing speeds is shown in the data of Table 9-8 1151. Friction with the uncompounded carrier oil over the speed range 0.017-0.423 cm/s is strongly stick-slip, u h being 0.18-0.22. With stearic or lauric acid compounded into the lubricant, sliding is smooth and the friction is affected more by the chain length and the concentration of the fatty acid than by the sliding speed. TABLE 9-8.

FATTY ACIDS IN OIL

Speea, cm/s

AS

LUBRICANTS

Coefficient of friction Stearic acid, moles/1000 grams 2

0.017 0.034 0.051 0.085 0.169 0.254

I O - ~ 3.72 0.126 0.131 0.132 0.133 0.135

----

0.078 0.085 0.088 0.091 0.094 0.095

Pin on disk, hardened alloy cast ron. MPa). From data by A. Dorinson [ 51.

Lauric acid, moles/1000 grams 2

2

2

----

----

----

0.141 0.145

0.116 0.123 0.126 0.130

0.109 0.115 0.120 0.126

----------

Loads:

---4.9-9.8

N

----

(16.6-33.1

Metallic soaps of fatty ac ds are boundary lubricants: copper laurate, copper stearate, zinc laurate, magnesium laurate, cadmium steara.te and sodium stearate as f i ms on metals such as copper, zinc, magnesium, steel and platinum are associated with coefficients of fric= 0.04-0.12. Details of the action of metallic soaps tion in the range are given by Bowden and Tabor [161. Figure 9-5, which summarizes some findings by Bowden, Gregory and Tabor [17], shows the influence of temperature on the friction of sur-

190

I 0.5

-

I

I

I

.-0 .-50.4-

1

-

t

0.3

OO

100

200

300 400

Temperature, deg. C

Figure 9-5. Influence of temperature on lubrication by long-chain compounds. 1 : Docosane on platinum. 2 : Stearic acid on platinum. 3: Copper 5: laurate on platinum. 4: 1% lauric acid in paraffin oil on copper. Sodium stearate on steel. Data by Bowden, Gregory and Tabor 1 1 7 1 . Adapted by permission from Natuhe, Vol. 156, No. 3952, pp. 99. Copyright 1945, Macmillian Journals Ltd. faces lubricated by long-chain substances of various types. Friction with docosane (m.p. 43 C) or stearic acid (m.p. 69 C) on platinum increases sharply at temperatures close to the melting points of the lubricating substances. Copper laurate (softening point 110 C) on platinum and a 1% solution of lauric acid in paraffin oil on copper show closely parallel frictional behavior. A film of sodium stearate (softening point 290 C) on steel has a frictional transition at c a . 300 C. These facts led Bowden and his co-workers 1 1 7 1 to associate the temperature-governed transition in the coefficient of friction with the melting or the disordering of the lubricant film. The film on the surface of a non-reactive metal such as platinum is the fatty acid p e f i h e : on a reactive surface, e . g . copper, the film is the metallic soap of the fatty acid. However this view of the situation is oversimplified; treatment in detail is given in Chapter 10. far the discussion of lubricated friction has been concentrated on long-chain aliphatic substances which have strong propensity to form close-packed films on adsorbing surfaces. The experiments b y , which the lubricating properties of such substances are studied are usually carried out at slow sliding speeds, thus excluding or minimizing the hydrodynamic action of fluid films and emphasizing the influence of the close-packed adsorbed films on the coefficient of friction. But other types of substances that are added t o carrier oils to modify or improve their effect on friction, wear or scuffing are known not to form close-packed adsorbed films on the rubbing surfaces and a p h i C J h i would not be expected to do s o on the basis of their chemical structures. Lubricants containing such substances are usually tested under high applied loads and fast rubbing speeds. The designation “extreme-pressure’’lubricant is usually applied t o such compositions because the emphasis is on their antiscuffing effecSo

191

tiveness under heavy loading. Analysis of the frictional behavior observed with these lubricants runs into a number of complications, one of the more obvious being quasihydrodynamic action. Thus, in Fig. 9-6, which is based on the data by Sakurai e t a t . I181, the convergence of the curves for the lubricants consisting of solutions of dibenzyl disulfide and diphenyl disulfide in cetane, as well as the downward trend in the curve for dissolved sulfur, might be attributed to fluid film effects. The coefficients of friction observed at the lower speeds (5-10 cm/s), however, indicate a specific additive effect rather than a fluid film contribution.

".-" I

-," .0)

.c

1

OlOIp\

e

2

I

0.05

m

s

1.8% Dibenzyl Disulfide

-0.5%

4

Sulfur

I

01

0

I

I

I

I

I

400

200 300 100 Rubbing Speed, cm/s

Figure 9-6. Friction with sulfur-containing additives in the lubricant. Steel on steel. Load: 29.9 N. From data by Sakurai, Okabe and Takahashi [ 181.

TABLE 9-9. EFFECT OF DIISOPROPYL DITHIOPHOSPHATES ON WEAR AND FRICTION Additive

Wear and friction at 93 C Steel pin Wear,

Copper pin ?J

cm3 per centimeter Cupric salt Zinc salt Cadmium salt Lead salt Silver salt (isoC3H70)2P(S).SH [(

isoC3H70)2P(S) a s ]

Cetane (carrier)

u

Wear, cm3 per centimeter

3.1 1.8 0.63 0.43 0.15

0.36 0.43 0.27 0.36 0.35

2.2

0.50

10.0

0.40

1.2

16.0

0.28

----

2500

-_--

5.3 3.8 2.4 0.83 0.75 7.7

Additives at 0.047 wt-% P in cetane. Load: 73.6 N. Five hours cm/s. Data by Roue and Dickert [191.

0.47 0.26 0.31 0.15 0.28 0.39

at

10

192

Table 9 - 9 , from Rowe and Dickert's investigation of solutions of diisopropyl dithiophosphates in n-hexadecane [ 1 9 ] , lists the rates of wear in parallel with the coefficients of friction for steel against steel and copper against steel. A strong effect from the presence of dithiophosphate is seen for steel on steel in the sharp decrease in both the wear rates and the coeff cients of friction relative to that with uncompounded hexadecane as the lubricant. For copper against steel, the wear rate decreases signif cantly, particularly with the metal salts of diisopropyl dithiophosphate, but the coefficient of friction is not altered systematically. Tab e 9 - 1 0 shows the frictional behavior of hardened alloy cast iron in the presence of decalin solutions of triphenyl phosphate and diphenyl phosphate [ 1 5 1 . The mechanisms governing the action of phosphates and dithiophosphates are discussed in Chapter 1 1 . TABLE 9 - 1 0 .

FRICTION WITH TRIPHENYL AND DIPHENYL PHOSPHATE IN DECALIN

Rubbing speed, cm/s

Coefficient of friction Triphenyl phosphate, moles/1000 grams

0.017 0.034 0.051 0.085 0.169 0.254

Diphenyl phosphate, moles/1000 grams

0.020

0.002

0.020

0.002

0.188 0.192 0.194 0.194 0.194 0.195

0.205 0.210 0.213 0.216 0.218 0.219

0.212 0.224 0.231 0.235 0.240 0.241

0.214 0.221 0.228 0.223 0.237 0.237

Pin o n disk: hardened alloy cast iron.

Data by

A.

Dorinson [ 1 5 1 .

TABLE 9 - 1 1 . COMPARISON OF FRICTION WITH UNCOMPOUNDED WHITE OIL AND WITH 1 % DIBENZYL DISULFIDE AT SLOW SPEED ~~

Temperature, deg. K

Coefficient of friction White oil

298 313 363 373 398 418 443 458

0.07 0.07

---0.15 0.15 0.16 0.17 0.18

1%

Dibenzyl disulfide 0.07 0.075 0.17

---0.14 0.12 0.11 0.11

Load: 2 5 8 N ( 1 . 3 4 GPa). Speed: 0 . 0 7 cm/s. Stainless steel peg against hardened AISI 5 2 1 0 0 steel ball. Data by Bailey and Cameron r201.

193

Table 5-11 shows the data obtained by Bailey and Cameron [20] comparing the effect of temperature on friction in the presence of uncompounded white oil and a 1 % solution of dibenzyl disulfide in white oil. The difference in the trend of the data for the two lubricants is significant; the downward trend of friction with increasing temperature of the solution of dibenzyl disulfide is indicative of chemical reaction at the rubbing surface, as discussed in Chapter 1 1 . 9.4.

A THEORETICAL VIEW OF LUBRICATED FRICTION

In looking at the basic mechanisms of lubricated sliding friction, the major emphasis falls on the adhesive process because a p h i 0 h . i it is the one most likely to be influenced by the presence of the lubricant at the rubbing interface. The mechanisms to be considered here in particular are those that make their effect felt in thin film or boundary lubrication. The action of macroscopic liquid films, generated hydrodynamically or otherwise, are not included in this treatment because the surfaces are completely separated from each other; the meaning of friction in such cases is discussed in Chapter 2. A mechanism for the effect of boundary lubrication on friction can Chapter 8 ) , which be deduced from the relation d i = ko, ( c d . Eqn 8 - 1 4 , states that the effective shear strength of a contact, A ~ ,is some fracof the bulk material of the rubbing tion k of the full shear strength body; the lubricant film functions by reducing the average shear strength of the contact relative to the shear strength of the unlubricated contact. More detailed insight is afforded by the concept that the total friction force is the sum of all the tangential forces involved in the deformation and rupture of the asperity junctions, for which we write the generalized expression

(9-1)

where a . is the average radius and A . is the shear strength of each kind L A. of asperity junction. This expression may be satisfactory from a logical point of view, but it is not very useful in a realistic sense because of the practical difficulties of identifying each kind of asperity junction and determining its properties. A workable expedient is to assume that there are only two kinds of asperity junctions-bare metal and boundarylubricated-in which case we write

(9-2)

where F m is the force required to shear the metallic junctions and F b is the force required to shear the boundary-lubricated junctions; all the

194

junctions are assigned the same radius. This model has the merit that the properties of the metallic junctions can be evaluated independently I f in addition the properties of the juncby direct experimentation. tions protected by an oxide film can be determined separately, the expression for friction force can be extended by the contribution F c from such junctions:

(9-3)

Going back to the system represented by Eqn 9-2, of contact is nr' A =

1

nu2

+

nb 2

nu 2 (9-4)

1

1

the total real area

and the friction force can be expressed as (9-5)

,@,

where + O b = 1 gives the fraction of the total junction area in each I f the real area of metallic contact can be evaluated category. separately (for instance, by electrical conductivity), Eqn 9-4 can be used and the problem becomes tractable. Few experiments yielding data that can be applied to the quantitative demonstration of the mechanism of lubricated friction are on record in the literature. In the work of Rabinowicz and Tabor [ll], radioactive transfer is used to evaluate metal-to-metal contact and adhesion in the sliding of copper against copper. The transfer data shown in Table 9-12 a s nanograms of copper per cm of sliding distance are assigned a relative volume rating y, from which the relative area of the asperity junctions is computed a s follows: a = y2 / 3

(9-6)

Using the results for dry rubbing as the base reference, the data are applied to the relation

u

= (Prn llrn

+

(1 -

om)

?.lL

(9-7)

where u is the experimentally observed coefficient of friction, urn is the coefficient of friction for the dry rubbing of metal against metal, and uL is the coefficient of friction for completely lubricated rubbing. Equation 9-7 is obtained from the expression below [17],

by dividing it through by the load W .

TABLE 9-12. PARTITION OF CONTACT AREA BETWEEN METALLIC JUNCTIONS AND BOUNDARY LUBRICATION FOR COPPER Lubricant

Transfer, nanograms Cu per cm sliding

y

1 0.05 0.0015 0.00015

(a) p = pm (bare metal). (b) Qpm = a p m . Rabinowicz and Tabor [ll]. TABLE 9-13.

(b)

Q q v

1 0.136 0.0131 0.0014

Load: 19.6 N.

1.3 (a) 0.61 0.15 0.065

1.3 0.18 0.017 0.0018

Speed: 0.01 cm/s.

1.00 0.295 0.113 0.028

From data by

PROPERTIES OF BOUNDARY-LUBRICATED JUNCTIONS FOR COPPER

1.3 0.61 0.15 0.065

None Cetane Octadecanol Copper palmitate

4.61 2.33 1.13 1

1.000 0.269 0.053 0.006

(a) See Table 9-12. (b) Calculated from (A'/A)2 = 1

u

-

QmUm

=

@l

+

---0.731 0.947 0.994

2 12p

(e) A = W/pm; W = 19.6 N, p m = 863 MPa,

(d) Ql = 1 - 0m' (f) pl

Qllm

observed

20,000 1,000 30 1

None Cetane Octadecanol Copper palmitate

Ul

ct

*

.

A~

=

----

____

219 107 56

0.47 0.086 0.058

(c)

Qm

($

- @mbm)/~l.

=

4.61a*A/A'.

196

The last column of Table 9-12 shows the fraction of the total obin Eqn 9-7. In view served friction force contributed by the term #,ym can be taken of the uncertainties in the numerical computation, #,p,/u equal to zero for copper palmitate: i . e . for all practical purposes this effective boundary lubricant completely interdicts the junction area to metallic contact. In that case, the true area of contact for such a low level of the coefficient of friction can be evaluated by the simple relation A = W/p, and the shear strength of the lubricated junction can be 2

obtained easily. It comes out to be 56.2 MPa ( 5 . 7 5 kg/mm ) , which is 17 times the highest value found by R. W. Wilson [ 2 1 ] for the shear strength of bulk stearic acid. The calculations from the data in Table 9-12 can be refined and the conclusions can be carried a step further. Growth of the true area of contact under tangential traction is computed from the relation ( A * / A ) ’ = The value of Om, which is taken to 1 + 12u2, where A is given by W/p,. be CL in Table 9-12, is adjusted to fit the value of A ‘ and the values of oL, the shear strengths of the lubricated junctions, are calculated from Eqn 9-8, as shown in Table 9-13. All the values for oL in Table 9-13 are higher than anticipated from the intrinsic properties of the lubricant substances. In particular, the values of uL and be for the cetane-lubricated surface exclude the possibility of a liquid film, even with the viscosity enhanced by the pressure at the contact interface. The radioactive transfer technique underestimates the extent of metallic contact, since it does not detect transfer from the inactive surface to the radioactive body. The absolute magnitude of this error is large when protection by the lubricant is mediocre, as is the case with cetane. But even though the magnitude of the error is small with a good boundary lubricant such as stearic acid or copper palmitate, the relative influence of underestimating the extent of metallic contact is significant. Also, when the magnitude of adhesive effects becomes small as the effectiveness of the boundary lubricant becomes better, then non-adhesional mechanisms such as plowing become relatively more important in the friction process. The mechanisms for friction presented in Chapter 8 are accepted as both fundamentally sound and factually confirmed, and hence it seems manifestly reasonable that the mechanism for lubricated friction should be a modification of the general mechanism of friction. The experimental approach to the mechanism of lubricated friction represented by Tables 9-12 and and 9 - 1 3 is based on that premise. At the present writing the quantitative evidence supporting the theory of lubricated friction is extremely scanty and none of it is any better than the data in these tables. However, the deficiencies in the evidence appear to be matters of technique and interpretation rather than the incorrectness of the

197

basic model, and thus the way seems to lie open to improved t ion.

experimenta-

REFERENCES 1. 2.

J. T. Desaguiliers, Phil. Trans. Roy. SOC. Lcndon, 33 ( 1 7 2 4 ) 3 4 5 . F. P. Bowden and J. E. Young, Proc. Roy. SOC. London, A 2 0 8 ( 1 9 5 1 )

3.

D.

311.

H.

SP-277, 4. 5.

Buckley, Friction, Wear and National Aeronautics and Space

Lubrication in Vacuum, NASA Administration, Washington,

D. C., 1 9 7 1 , p . 5 8 . D. H. Buckley, a p . cit., p. 69. F. P. Bowden and A. E. Hanwell, Proc. Roy. SOC. London, A 2 4 5 ( 1 0 6 6 233-243.

6. 7. 8.

D. H. Buckley, ASLE Trans., 10 ( 1 9 6 7 ) 1 3 4 - 1 4 5 . W. A . Brainard and D. H. Buckley, Wear 2 6 ( 1 9 7 3 ) 75-93. F. P. Bowden and T. P. Hughes, Proc. Roy. SOC. London,

A172

(1939

263. 9.

Buckley, Friction, Wear and Lubrication in Vacuum, NASA National Aeronautics and Space Administration, Washington, D. C., 1 9 7 1 , p. 4 9 . F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford Universitv Press, 1 9 5 0 , 1964, Part I , Chauter VII. Part I1 Chapter 1 1 1 . E. Rabinowicz and D. Tabor, Proc. R o y . SOC. London, A 2 0 8 ( 1 9 5 1 )

D.

H.

SP-277,

10. 11. 12. 13.

455-475. 0. Levine

and W. A . Zisman, J. Phys. Chem., 6 1 ( 1 9 5 7 ) 1068'1077. R. L. Cottington, E. G. Shafrin and W. A. Zisman, J. Phys. Chem., 62 (1958) 513-518.

14.

Y. Tamai and B. G. Rightmire,

J.

Basic

Eng.

(Trans. ASME),

870

( 1 9 6 5 ) 735-740. 15. 16. 17. 18.

A. Dorinson, ASLE Trans., 13 ( 1 9 7 0 ) 2 1 5 - 2 2 4 . F. P. Eowden and D. Tabor, up. cit., Part I , Chapter X, pp. 2 0 3 - 2 0 7 . F. P. Bowden, J. N. Gregory and D. Tabor, Nature, 156 ( 1 9 4 5 ) 9 7 - 1 0 1 . T. Sakurai, H. Okabe and Y. Takahashi, ASLE Trans., 10 ( 1 9 6 7 )

19. 20. 21.

C. N. Rowe and J. J. Dickert, jr., ASLE Trans., 10 ( 1 9 6 7 ) 8 5 - 9 0 . M. W. Bailey and A. Cameron, ASLE Trans., 16 ( 1 9 7 3 ) 1 2 1 - 1 3 1 . R. W. Wilson, Proc. Phys. SOC. London, 68B ( 1 9 5 5 ) 6 2 5 - 6 4 1 .

91-101.

198

Chapter 10 LUBilICANT ADDITIVE ACTION.

10.1.

1.

BASIC CATEGORIES AND MECHANISMS

WHAT IS A LUBRICANT ADDITIVE?

No single description o r definition adequately covers all lubricants or lubrication processes. For example, we have seen that a fluid can function as a lubricant by virtue of its viscosity as a liquid. We have also seen that a monomolecular film of stearic acid deposited o n a metal surface acts as a lubricant and dramatically reduces the coefficient of friction. A polymeric substance such as polymethylmethacrylate when dissolved in an oil will increase its viscosity and improve its loadcarrying performance in the hydrodynamic lubrication process. Stearic acid dissolved in a carrier oil can effect a strong reduction in the coefficient of friction for metal rubbed against metal. We say that the polymethylmethacrylate o r the stearic acid is a lubricant additive. In each case the substance is added to a carrier oil which by itself functions as a lubricant. Thus, if to an oil which has a viscosity of 0.500 Pa-s at a pressure of 1 3 8 MPa and a shear rate of l o 4 s- 1 we add 4% of a polymethylmethacrylate, we raise its viscosity to 0.600 Pa-s ( i . e . by 2 0 % ) , thereby enhancing its hydrodynamic action. White oil of 0.20 Pa-s viscosity at room temperature is associated with a coefficient of friction of 0.2 for the slow speed sliding of cast iron against cast iron; addition of 0.001% of stearic acid to the white oil lowers the coefficient of friction to 0.06. In each case the lubricating action of the unmodified carrier oil is improved by the incorporation of the additive. Substances are added to carrier oils for purposes other than lowering friction or reducing wear during sliding. Such substances are also designated as additives for the lubricant. For instance, there are antioxidant additives to inhibit deleterious alteration of the oil by the action of the oxygen in the ambient air, particularly at elevated temperatures; there are antirust and anticorrosion additives; there are detergent additives that control the deposition of varnish and sludge on hot metal. I t would be easy to become enmeshed in the classification of additives by function: e . g . antifriction additives, antiwear agents, etc. But i f an antioxidant keeps the acid level of the oil low and reduces corrosion of the metal so that there is less corrosion product which is removable by rubbing, can we say that the antioxidant does not also function as an antiwear agent? Or i f an alkaline detergent neutral-

199

izes the acid generated by oxidation before i t can play a part in rubbing wear, do we regard it only as an antacid additive o r as an antiwear agent as well? These semantic entanglements can be avoided by bearing in mind the practical aspect of lubrication: keeping machinery in running condition, minimizing unnecessary expenditure of energy against friction, avoiding o r reducing wear, and eliminating those catastrophic aspects of wear that result in the destruction of the useful profiles of the contacting parts o r the stoppage of the machinery by seizure. We have already examined the evidence which demonstrates that liquid lubricants can maintain a hydrodynamic film to separate rubbing surfaces only under well-defined conditions which have an ultimate breakdown limit. But we have also seen that there are incontrovertible cases in which the hydrodynamic film has failed and yet none of the disastrous effects of lack of lubrication are observed. Now if it is not a hydrodynamically generated liquid film which is the functionality responsible for the lubrication process, then we must identify to what functionality lubrication should be attributed. At this stage of the discussion we shall not identify it any more precisely than to designate it as a non-hydrodynamic action. I f we can establish a connection between this functionality and the properties o r the structure of a particular substance, then an obvious expedient to improve lubrication would be to add this substance to the carrier oil. This is the concept of a lubricant additive at its simplest. Thus, by direct empirical observation o r by deduction from the theoretical model of an adsorbed film we might conclude that it would be desirable to add stearic acid to a But all carrier oil in order to reduce the friction of rubbing parts. lubricant additive effects are not as obvious as this. Sometimes only traces of a constituent are all that is required to bring about a pronounced antifriction or antiwear effect, and moreover the effective constituent may not have been introduced into the lubricant as such but may have been produced at the contact surfaces during the rubbing process. It is in this sense that we adopt the broad concept of a lubricant additive as any substance that aids in the Lubkication p k o c e d b at the rubbing interface by a functionality other than viscosity. Whether we put the additive in the carrier oil with the primary purpose of effecting such action o r whether the functionality is induced by interaction of the total lubricant with the rubbing interface does not have a fundamental bearing on what we regard as the real additive action. The participation of the rubbing interface in the lubrication process, however, is basic to our concept of lubricant additive action. On this basis viscosity improvers are excluded from consideration as lubricant additives in this discussion. I t is true that viscous shear is

200

one of the recognized processes in fluid film lubrication, and thus i f we add something to the oil which enhances this process, then we might: logically regard viscosity improvers as lubricant additives. The crux of the matter is that a viscosity improver modifies the bulk properties of the oil. The same result might have been achieved by blending oils of two different viscosities. The properties of the viscosity-modifying additive as such do not appear in the ultimate behavior of the oil as a lubricant.* 10.2.

CLASSIFICATION AND NOMENCLATURE

Having established how we propose to regard lubricant additives and additive action, let us examine some questions of classification and nomenclature. The reader of the current literature of lubrication cannot escape encounter with such terms as baundahy Lubaicatian, e x t h e m e phebbuhe additive, antiheizuhe additive, antiweah action, etc. The questions we shall consider are whether such nomenclature has meaning in a definitive sense and i f so whether the definitions are on a sound basis or are merely technological jargon.

Boundahy Lubhicatian is a familiar term in the vocabulary of the tribologist. In the general concept of the boundary lubricated condition, the lubricant film between the two surfaces is no longer a liquid layer; instead the surfaces are separated by films of only molecular dimensions. Friction is influenced by the nature of the underlying surface and by the chemical constitution of the lubricant films. This view of lubricating action at the solid surface was introduced by Sir W. B. Hardy [ 1 1 as an extension of Osborne Reynolds' concept that hydrodynamic action within the liquid film is a process treated by continuum methods which are not applicable at the discontinuity or "boundary" between liquid and solid. Since its first mention by Hardy, boundary lubrication has been defined and redefined from a number of different points of view. In one instance, the effective properties of the lubricant are regarded as being affected by the surfaces of the bounding solids as the lubricant film becomes very thin. I n another, severe loading and contact of surfaces are emphasized in the defining criteria, with the chemical properties of the lubricant rather than its viscosity playing the major role in the lubricating action. D . Godfrey, writing in the Standand tiandboak 06 *The physical chemist would disagree strongly with this concept of a viscosity improver. He would be able to show that it is the colloidal behavior of the viscosity improver which brings about the changed viscosity of the additive-fortified oil. In that sense he is correct, but in order to keep the discussion here within reasonable limits, we have excluded this extended point of view. Such exclusion does not seriously alter either our basic concept of a lubricant additive or the practical conclusions derived from it.

20 1

Lubhication Enyineeniny [ 2 ] , defines boundary lubrication as a condition "in which the friction between two surfaces in relative motion is determined by the properties of the surfaces and by the properties of the lubricant other than viscosity." In scope this definition encompasses most of lubrication, excluding only the sliding and seizing of absolutely clean surfaces and hydrodynamic lubrication. The weakness of the definition lies in its broadness and the wide range of cases which it covers. A s Godfrey himself shows 121, the mechanisms operative in boundary lubrication include physical adsorption, chemisorption, and chemical reaction. These mechanisms may be involved separately, sequentially, or in conjunction with one another. I t is quite obvious that i f the designation boundahy tubnication is to be used as more than a catch-all phrase, it must be analyzed in terms of explicit constituent mechanisms in the lubrication process. The history of the introduction of the term boundahy tubhication and the development of the concept shows the growth and the broadening of thought in the science of lubrication. It was not long after lubrication became a quantitative discipline that experimentation revealed behavior at variance with hydrodynamic theory. The emergence of surface chemistry and surface physics as specialized disciplines led to the next stage in thinking about the fundamentals of lubrication: namely, explanation of the effect of fatty compounds on the coefficient of friction in terms of films adsorbed on the sliding surfaces. This approach has come to dominate thinking about non-hydrodynamic lubrication as strongly as hydrodynamic theory dominated the early work on fluid film lubrication. In the authoritative monographs by Bowden and Tabor [ 3 1 , the strongest emphasis is given to explanations of additive action in terms of surface films. Modes of additive behavior that involve decomposition at the rubbing surface are treated rather sketchily. Like so many of the established practices of lubrication, the art of enhancing the performance of the lubricant by chemical action antedates its systematic development on an engineering and scientific basis. I t was an early empirical practice to save an overloaded bearing from destruction by adding elemental sulfur to the oil. The deliberate addition of chemically active substances to the lubricant became a recognized engineering practice with the advent of the hypoid gear in the automobile rear axle assembly. Sulfurized fats and lead naphthenates were found to prevent destructive scuffing of the hypoid gear. I t was found that the unit loading on the tooth surfaces was very high, and thus the designation "extreme-pressure" lubrication was applied to this type of service. Whereas the concepts and nomenclature of boundahy tubhication developed around the reduction of friction, the concepts and nomenclature of eXtheme-PheAbUhe IEP) eubhication developed around the prevention of scuffing, scoring, seizure and related types of surface damage that

destructively impair the functioning of contacting machine parts. But it is obvious that this distinction in nomenclature is based on the particular character of the rubbing phenomena under observation. Nothing in the nomenclature dictates u p h i o h i that a substance which functions as a boundary lubricant in one situation cannot function as an extremepressure lubricant in another. The same consideration applies to other annomenclature derived fr,om phenomenology: e . y . antiwear lubricant, tiscuff lubricant, antiseizure lubricant, etc. Unless it can be demonstrated that these distinctions in nomenclature have their source in basic tribology or in the intrinsic properties of the additives, they have no fundamental interpretation. This is not to deny the utility of such nomenclature. After all, if a lubricant significantly reduces wear at high contact pressures, its overt functionality is recognizably described by the designation U f l t i L u e U h Lublricunt. There is no necessity to reject the empirical nomenclature of the past completely, even though it does not legitimately carry all the implications ascribed to it. In the succeeding sections of this chapter and the next, we shall develop an understanding of lubricant additive action on a systematic and rational basis. The significance of the nomenclature of additive action a s encountered in the literature can then be correctly evaluated. Lubricant additive action can be divided into three broad classes, the first of which is designated i n this work as the interposed film category. The film that is formed on the bounding surfaces and interposes a barrier to their direct contact comes either directly from substances put in the lubricant o r else via secondary processes in the bulk lubricant. The three sub-categories in the interposed film classification are: (a) simple adsorbed films; (b) chemisorbed films; and (c) chemically deposited films. The second broad category of additive action is the formation of interaction films by chemical reaction of the additive with the material of the bounding surface to an extent that disrupts the molecular structure of the additive substance and generates a film containing moieties derived from both the additive and the surface material. At the appropriate place we shall examine the difference between this type of additive action and the formation of chemisorbed films. The third broad category of additive action is designated a s asperity junction-growth inhibition. The action occurs primarily in the vicinity of asperity contacts at the time they are being initiated. The interaction of the additive and the asperity material interrupts the growth of the junction so that i t does not form a scuffed or seized spot. This category of additive action and the interaction film category have some elements in common. The basic difference is the low level of reaction product necessary to be effective in the junction-inhibition mechanism.

203

INTERPOSED ADSORBED FILMS

10.3. 10.3.1.

Simple Adsorbed Films

It is taken for granted that it is broadly understood what an adsorbed film is. It might be said that simple adsorbed films are formed by the process of physical adsorption: however, as is frequently pointed out, there is no sharp dividing line between physical and chemical adsorption [41. For o u r purposes it is sufficient to state that the adsorbed species in simple adsorbed films is not permanently altered by residence on the adsorbing surface and can be recovered unchanged on desorption.

Furthermore, insofar as additive action is concerned, the films of interest are oriented films. Our particuiar interest is in such films formed on the adsorbing surface by the additive which is dissolved in the liquid carrier fluid of the lubricant. These are the films which are found in everyday technology, in contradistinction to Langmuir-Blodgett films which are deposited o n the solid surface by transfer of a preformed layer from the water surface of a film balance and which, despite their interesting properties, may be regarded as artifacts, as was pointed out by Zisman [ 5 ] in a review of the relation between wettability and the nature of adsorbed films. The nature of an oriented film of monomolecular thickness can be typically exemplified by the properties and behavior of stearic acid, one of the most thoroughly studied film-forming substances. Stearic acid (n-octadecanoic acid) in extended, rigid form has the molecular conThe total chain length is 2 . 4 4 2 nm (24.42 figuration seen in Fig. 10-1. 8 ) and the cross-sectional area is 1 8 . 4 x cm2 ( 1 8 . 4 R 2 ) . A regularly packed array of these molecules, with their hydrocarbon chains adlineated and their carboxylic heads located as shown in Fig. 1 0 - 1 , constitutes an oriented film of monomolecular thickness. The physical evidence for the existence and the nature of such films is well known and i s described in the standard texts on the chemistry and physics of surfaces 161. Adsorbed films cannot form without an adsorbent, and thus it is obvious that the properties of the adsorbing surface are also important. The adsorbent surfaces pertinent to practical lubrication are usually metallic, with a coating of oxide and probably carrying physically adsorbed atmospheric constituents such as oxygen, nitrogen, water, etc. Moreover these surfaces will usually be rough and of heterogeneous texture. So that our basic concepts about adsorbed films on solid substrates can be developed in a manner free from extraneous complications, our discussions here will for the most part deal with smooth surfaces of known composition and structure. The

best information about oriented monomolecular films is obtained

204

V

t 0- Carboxyl

m% -o-

-0-

e

0-

Alkyl Chain Methylene Methyl

Figure 1 0 - 1 . Schematic representation of an oriented, adlineated stearic acid monolayer.

pooo -

0

s c

I

I

I

1

I

3 (a) ------------- - 24 -------202 -I6

f

-I2

9'

0)

-8 -4 1

I

I

I

'0

Figure 1 0 - 2 . Adlineation of films of n-octadecylamine and n-hexadecane. (a) Adsorbed from nitromethane. (b) Adsorbed from n-hexadecane. (c) Proportion of n-hexadecane adlineated with n-octadecylamine. Data by Bewig and Zisman [ 9 1 .

by studies with the film balance, in which the supporting surface is water. This provides a smooth, uniform substrate surface of known properties. I n order to form compact, adlineated film structures such as shown in Fig. 1 0 - 1 , the film must be compressed by lateral restraints; otherwise the Brownian motion of the water molecules will tend to disperse the molecules of the substance on the surface of the water. Also,

205

in order in water.

to form solid condensed films, the substance must be insoluble

Compact, oriented monolayers can form spontaneously on the surfaces of metals, oxides and glass. I n their systematic study published in 1946, Bigelow, Pickett and Zisman [ 7 1 showed that when a piece of clean platinum foil was dipped into dilute solutions (0.1% by weight) of eicosanol-1, n-octadecylamine o r n-nonadecanoic acid in n-hexadecane and then withdrawn, the surface of the foil emerged dry and could not be wet by hexadecane. This oleophobic behavior was ascribed to a close-packed film of the solute with its molecules oriented vertically to the surface of the metal, the polar ends being attached to the solid interface and the methyl groups exposed in an ordered array to the atmosphere. The polar groups serve to anchor the film to the substrate, adlineation of the methylene chain locks the film up laterally, and the exposed surface of methyl groups has the property of not being wet by hexadecane. The monomolecular nature of the adsorbed film was demonstrated by the "multiple-dip" technique: platinum foil of known surface area was repeatedly immersed in and withdrawn from a soluxion containing a known amount of solute (n-octadecylamine) in dicyclohexyl, with intervening flame-cleaning until the solution was exhausted of solute when checked by the sensitive drop-spreading test on water. I t was calculated that the average area per molecule in the filrn formed on platinum was 30 8 2 This, however, is only an approximation to the area of 20.4 8 2 as determined by the film balance on an aqueous substrate.

.

Since 1946 a great deal of work has been reported amplifying, clarifying and to a certain extent correcting the information and models published by Bigelow, Pickett and Zisman [7]; but the essential validity of their original concept has not been seriously altered. The work of Timmons, Patterson and Lockhart [ 8 ] with C14-labeled stearic acid has firmly established that a monomolecular, oleophobic film is deposited on fire-polished smooth glass by retraction either from the molten liquid or from nitrobenzene solution. The area found per molecule, 18.9 E2, is very close to the minimum area of 18.5 R2 deduced for the carboxyl group from a Stuart-Briegleb ball model. The densest possible close-packing was spontaneously attained on glass. The contact angle for a drop of methylene iodide on the acid-covered surface was 70' t 1'. Contact potential measurements on adsorbed films of n-octadecylamine [91 and fatty acids [ l o ] demonstrated the orientation of the polar group toward the high-energy (metal) substrate surface. The contact angle of 70' observed for a drop of methylene iodide is a criterion for the existence of an oleophobic film whose top surface is composed of an array of methyl groups. However, observation of such a contact angle is not a demonstration that the film formed by retraction of an adsorbing surface from a solution of a polar long-chain compound is

206

composed only of solute molecules. I t must be established independently that the solvent does not become incorporated in the adsorbed film. This is the case when the shape of the solvent molecule is inconsistent with adlineation with a long-chain solute: e . g . when the solvent is nitromethane or nitrobenzene. But when the solvent is n-hexadecahe and the solute is a long-chain amine or fatty acid, it has been demonstrated that the adsorbed film is a mixture of solvent and solute molecules even though the contact angle of the test liquid indicates a fully oleophobic monolayer, as is illustrated by the results of Bewig and Zisman [91 shown in Fig. 10-2. Films of n-octadecylamine deposited on platinum by retraction from a 0.1% solution in nitromethane give the full surface potential for a complete layer of octadecylamine from the time the substrate is first retracted and show a contact angle of 68-69' for a drop of methylene iodide. Films adsorbed from a 1% solution in n-hexadecane are characterized by an initial value of 760 mV for the surface potential, which gradually increases to a maximum of 925 mV after 6 hours immersion in the solution and does not increase any further for immersion times as long as 24 hours. The proportion of n-hexadecane adlineated with the n-octadecylamine in the retracted film is about 2 2 mole-% for short immersion times (12 minutes) and drops to about 2 mole-% for 6 hours immersion. The methylene iodide contact angle, however, is 68-69' at all immersion times between 12 minutes and 24 hours because the upper surface of the adsorbed film is always an array of methyl groups. Doyle and Ellison 1 1 1 1 prepared mixtures of radioactive stearic acid l-C14 and n-octadecane-1,2-H3 at a concentration of 0.35 molar in stearic acid and studied the coadsorption of stearic acid and octadecane on polished surfaces of silver, platinum, copper and iron. The films were prepared by retraction from the melt at 40 C (at room temperature the mixture was solid). The proportion of n-octadecane in the film was assayed by differential extraction with cyclohexane. The results of the investigation adequately demonstrate that n-octadecane coadsorbs with stearic acid but not necessarily as a mixed oriented monolayer. Some of the data indicate that more than a single layer is present on the surface. Thus the structure of the long-chain material on the surface may be open to conjecture, but that each constituent adsorbs and in what relative amount is directly determined by radioactive assay. Adlineation is a basic part of the process by which long-chain polar compounds form condensed oriented films on substrate surfaces, and it is a reasonable expectation that the chain length of aliphatic adsorbates would be an important parameter in film stability. This was carefully investigated by Levine and Zisman [121 for a large number of polar aliphatic compounds, films of which were formed on glass by methods which insured that these films were free of coadsorbed contaminants. The surface properties of the films thus formed were explored by the contact

207

angle of a drop of methylene iodide. Figure 10-3 is a plot of the methylene iodide contact angle 0 against N, the total number of carbon atoms in the chain, for some straight-chain aliphatic carboxylic acids, For acids and amines with chain amines and alcohols in the range C 8 - C Z 6 . lengths N 2 14, 0 is 6 9 ” k 1’; for the alcohols the critical chain length For compounds of chain length shorter than the critical is N = 15. value, the magnitude of 8 decreases progressively with decreasing N. The critical value of N is thus a measure of the resistance of the adlineation of the chains in the film to disruption by the drop of test fluid. The strength of the adlineation is a function of the number of methylene groups per molecule bound to the methylene groups of neighboring molecules by van der Waals forces. The resistance of the film to disturbance by the test drop is not entirely a matter of adlineation; in exploring the wettability of the alcohol films it was necessary to use a solution of the appropriate alcohol in methylene iodide as the test fluid. I

I

I

I

I

I

I

I I

70

A Amines

z0

c

0

u

50

t

40k 6

I

U Alcohols

I

8

I

-On

glass

---On

stoiriless steel

i I1

I I 1 I I I 1 10 12 1 4 16 18 20 22 24 26 Number of Carbon Atoms, N

Figure 1 0 - 3 . Methylene iodide contact angles as a function of chain length for films of straight-chain aliphatic acids, amines and alcohols. From data by Levine and Zisman [ 1 2 ] and Cottington, Shafrin and Zisman I131.

Some parallel studies by Cottington, Shafrin and Zisman 1 1 3 1 using an adsorbing surface of polished stainless steel demonstrate the influence of change of substrate, as is also shown in Fig. 10-3. The major effect of changing the adsorbing surface from glass t o stainless steel is on tiie slope d0/dN below the critical chain length N. Above this critical value the angle e levels off to the same limiting value of 6 9 - 7 0 ” for either substrate. Contact potential difference is a valuable means of demonstrating the existence and nature of adsorbed monolayers on metal surfaces. Bewig and Zisman [ 1 4 ] investigated horizontal adlineation of n-alkanes on a

208

polished platinum surface by this technique. Table 10-1 shows the measured contact potential A V for the residual films of hydrocarbon left on polished platinum at 20 C and 50% relative humidity after vigorous rubbing. Even though the volatility of the adsorbates ranges from a boiling point of 68.7 C at atmospheric pressure for n-hexane to 286.7 C for n-hexadecane, A V stays substantially the same for all the hydrocarbons. This is taken as evidence for the adsorption of the hydrocarbons in the horizontal extended configuration, as illustrated in Fig. 10-4 for n-hexane. Bewig and Zisman [91 published data showing an increase in contact potential with chain length for aliphatic amines from c a . 710 mV for n-amylamine to ca. 945 mV for n-tetradecylamine. Timmons and Zisman [ l o ] observed analogous behavior for n-aliphatic acids from propionic to n-tetradecanoic. This was ascribed to the increasing extent of vertical adlineation with increasing chain length. The horizontal configuration of adsorbed n-alkanes can be inferred from their contrasting contact potential behavior.

TABLE 10-1.

NET CONTACT POTENTIAL OF n-ALKANES ON PLATINUM

Alkane

Boiling point, 'C (a)

A v , mV ( 2 100)

68.7 125.6 174.3 235.3 253.4 286.7

215 220 220 205 210 215

n-Hexane n-Oc tane n-Decane n-Dodecane n-Tetradecane n-Hexadecane -~

(a) At atmospheric pressure.

Data by Bewig and Zisman 1143.

I////// ////// ////////////////////// Figure 10-4.

Orientation of n-hexane adsorbed on a plane metal surface.

Table 10-2 shows data that Timmons and Zisman El51 associated with the formation of monolayers on platinum by substances which cannot adlineate because of the nature of tneir molecular structure. The absolute value of the contact potential difference, of course, depends on the na-

209

TABLE 10-2. SURFACE CONTACT POTENTIALS AND DROP CONTACT ANGLES FOR ADSORBED FILMS ON PLATINUM .

__ Substance

Tricresyl phosphate (a) Tri-p-tolyl phosphite Arochlor 1242 (b) Arochlor 1248 ( b ) Arochlor 1254 (b) Octanol- 1 n-Octanoic acid Methylene iodide

Contact potential, Drop contact angle, deg. A V , mV Water CH21 2 620 619 110 53 -20 140 120 120

25 21 24 15 9 31 45 23

62 62 68 67 69 68 75 73

(a) From mixed 0- and p-cresol. (b) Chlorinated biphenyls; the last two numbers of the code indicate the approximate percentage of chlorine. Temperature 20-25 C; 50% relative humidity. Data by Timmons and Zisman 1151.

ture and orientation of the polar group, but the fact that a substantial voltage was measured, is evidence for the presence of an adsorbed layer. The contact angles for methylene iodide and water show significantly high coverage of the metal surface. But the contact angles for methylene iodide indicate the lack of adlineation for the linear n-octanoic acid and octanol-1 as well as for non-compact molecules such as tricresyl phosphate, tricresyl phosphite and the Arochlors. Contact potentials of films adsorbed on chromium have been compared with the surface coverage assessed by ellipsometry of reflected light in an extensive study of numerous long-chain polar compounds of various types [16, 171. Some representative data are shown in Table 10-3. Film thickness as determined by ellipsometry is converted to surface coverage as monolayers calculated from the area assigned to the vertically oriented molecule. The contact potentials found in this study tended to be erratic, but i n general as the chain length increased the surface potential became fairly stable because adlineation held the polar heads of the molecules in fixed orientation. Data for the long-chain thiols are shown separately in Table 10-4. The longer members of this series apparently do not pack into films as closely as the related alcohols or ni t r iles. The effect of temperature on the oleophobic layers was studied by Bigelow, Glass and Zisman [l8]. Figure 10-5 summarizes some significant aspects of their observations. Figure 10-5a is a plot of the relation between C, the concentration of the solute, and ,T, the critical temperature above which the adsorbed layer is no longer autophobic to the solution on retraction. for solutions of n-octadecanol, n-octadecanoic acid,

210

TABLE 10-3.

PROPERTIES OF ADSORBED FILMS ON CHROMIUM

Chain length

Surface potential,

aV, mV

Film thickness, nm

Surface coverage, monolayers

Amines 4 14 18 22

220 5 6 5 f 30 560 f 30 734 31

0.47 1.37 1.85 2.41

0.69 0.72 0.76 0.81

0.27 1.03 1.46 2.77

1 .oo 0.76 0.60 0.79

0.40 0.44 1.11 1.91 2.31 2.69 3.71

0.74 0.41 0.50 0.78 0.85 0.90 1.05

0.59 1.84 2.84 3.72

0.55 0.75 0.80 0.91

0.34 0.60 1.34 1.91 2.74

0.63 0.55 0.70 0.88 1.12

Amides 2 10 18 26

178 453 398 656

f f f f

31 32 10 37

Alcohols 4 8 14 18 20 22 26

0 25 90 240 240 323 415

+ 5 t 10 k 10 f 15 f 30 f 31

Acids 8 18 26 30

47 270 290 260

f 7 f 10 2 10 f 10

Ni tr iles 4

a

14 16 18

0 105 264 349 483

50 33 9 29 c 54

f f k f

From selected data by Bornong and Martin [ 1 6 , 1 7 1 .

n-octadecylamine and n-octdecylamide (stearamide) in purified cetane. Figure 10-5b shows the effect of chain length by comparing the C18 alcohol and acid with the corresponding C 2 0 compounds. Figure 10-5c compares the infiuence of an adlineating solvent (cetane! with that of a non-adlineating solvent (dicyclohexyl). With the exception of stearamide in cetane, all of the solutes investigated exhibited a saturation effect whereby T, does not respond to further increase of C. The effect of

211

TABLE 10-4.

FILMS OF n-ALKYL THIOLS ADSORBED ON CHROMIUM

Chain length

Surface potential, A V , mV

60 103 147 110 96 213 170 203 15 155 234 30 410 348 288 287 210

0.30 0.37 0.52 0.24 0.46 0.37 0.52 0.76 0.25 0.73 1.03 0.14 1.12

f 53

f 42

*

-+ f ?

f f f f f f f f

Film thickness, nm

10 53 43 7 36 35 55 33 10 80 54 52 82

Surface coverage, monolayers 0.37 0.46 0.48 0.22 0.34 0.27 0.32 0.47 0.13 0.38 0.54 0.06 0.52 0.51 0.27 0.42 0.27

f 0.14

f f f f f f f

-+

t f f 1.11 f 0.65 f

1.03 -+ 0.66 f

0.15 0.05 0.1E 0.05 0.07 0.06 0.04 0.01 0.16 0.01 0.17 0.11 0.13 0.15 0.06

(a) Retracted from melt. (b) Rinsed with methanol because of incomplete retraction. (c) Retracted from nitromethane solution at 24 C. Data by Martin and Bornong [ 1 7 1 .

Y

440 V

f

420

Acid in dicyclohexyl

c

e

400

E

p380

F

.-

e

-

B

.-

' c

360 340 320

300 0

0.5

L.0

1.5 2.00

0.5

1.0

1.5

2.00

0.5

1.0

1.5

2.0

Concentration, wt-'10

Figure 10-5. Effect of concentration on critical wetting oleophobic films on platinum. (a) n-Octadecyl compounds n-Eiscosyl and n-octadecyl acids and alcohols in cetane. acid and alcohol in cetane and in dicyclohexyl. Data by and Zisman [l8].

temperature for in cetane. ( b ) (c) n-Octadecyl Bigelow, Glass

212

polar group, chain length and solvent are what we have about oriented adsorbed films would lead us to expect.

already

learned

Bigelow, Glass and Zisman advanced explanations for both the concentration-influenced and the concentration-constant portions of the curves shown in Fig. 1 0 - 5 . Their derivation of a model for the concentration-governed portion of the wetting curve can be simplified at the outset by treating the oriented monolayer as a solid phase in equilibrium with the solution. We can then write the following approximation:

(10-1)

where K is the equilibrium constant, R is the molar gas constant, T is the temperature in degrees Kelvin, and A l l is the difference in internal energy between the solution and the adsorbed state. A l l is so little different from the AH of the process that the substitution is allowable. When T = T,, the concentration of the solute molecules at the adsorbed surface is determined and hence their concentration in the solution can be used as a measure of K . I t follows therefore that en C vs. 1/T, should plot as a straight line.

-.---

2.3 24 2.5 2.6 27 28 2.9 3.0 31 3.23.3 3.4

Figure 1 0 - 6 . Logarithmic plots of equilibrium concentration vs. 1/'TM. From data by Bigelow, Glass and Zisman [ 1 8 ] for adsorption on platinum.

Figure 1 0 - 6 shows plots of the logarithm of the concentration (weight-percent) of n-eicosanoic acid in cetane and of n-octadecylamine in dicyclohexyl against 1/T, from data by Bigelow, Glass and Zisman [ l a ] . Each plot consists of a temperature-dependent and a temperature-

213

independent section. I f the thermodynamic reasoning behind Eqn 10-1 is valid, then the slope of the temperature-dependent portion of the plot can be used to calculate AH, the heat of adsorption of the solute as an oriented monolayer on the substrate. Bigelow, Glass and Zisman reported values of Atl of 42.3 kJ per mole (10.1 kcal per mole) for the adsorption of n-eicosanoic acid from cetane and 62.0 kJ mol-’ (14.8 kcal rno1-l) f o r n-octadecyiamine from dicyclohexyl. But, as is seen from both Fig, 10-5 and Fig. 10-6, this calculation cannot be applied to that portion of the observed behavior where T, is no longer affected by increase in the concentration of the solute. At first glance the above treatment of the temperature-governed behavior gives a reasonable picture of the oriented adsorbed monolayer, but on careful inspection it is seen that both the model and the thermodynamics are makeshift. One of the basic fallacies is the assumption that the critical temperature of wetting has an unequivocal relation to the state of the adsorbed film. Bartell and Ruch [191 demonstrated that monolayers of n-octadecylamine can be depleted as much as 50% by a strong solvent such as benzene and still exhibit oleophobic properties to a drop of n-hexadecane o r n-tetradecane because the advancing drop of alkane supplies material which adlineates and fills in the gaps left by leaching of the original monolayer. A l s o , from the observations of Bewig and Zisman 191, a non-wetting contact angle is not necessarily evidence for the existence of a one-component monolayer on the adsorbing surface. Thus the state of the adsorbed phase cannot be uniquely specified and the thermodynamic reasoning is therefore shaky. But experimental studies of the lubricant behavior of additive-fortified fluids - as discussed in Section 10.4.2 -show there is enough of an empirical parallel with the thermodynamic model to retain it for further examination. Direct study of the desorption of stearic acid from platinum and Their findings are from NiO was carried out by Timmons and Zisman [lo]. shown in Table 10-5. The methylene iodide contact angle and the surface potential measurements indicate that a stearic acid monolayer adsorbed on platinum can be removed completely by heating to 130 C o r by extraction with diethyl ether. But i f the adsorbent is nickel oxide, heating to 150 C o r extraction with diethyl ether fails to restore the original contact angle behavior or the surface potential of the adsorbent surface. Such behavior is consistent with what one would expect from the The chemical nature of the adsorbate and the adsorbent surfaces. platinum surface is unreactive and the behavior of the stearic acid film on it is typical of what is generally regarded as physical adsorption, while the NiO surface is reactive and the stearic acid is considered to be chemisorbed. I n Sectiort 10.3.2 below we shall examine the difference between physical adsorption and chemisorption in detail.

214

TABLE 10-5.

DESORPTION OF STEARIC ACID MONOLAYERS

Adsorbent

Surface potential,

CH212 contact angle,

dV, mV

degrees Bare platinum Stearic acid on Pt after heating to 130 C after ether extraction Bare nickel oxide Stearic acid on NiO after heating to 150 C after ether extraction

0 355 5 -15 0 210 180 165

23 5a

22 25 Spreads 71 61 51

Data by Timmons and Zisman [ l o ] .

10.3.2.

Chemisorbed Films

At a first approach we can take the feasibility of desorption as the distinguishing difference between physically adsorbed and chemisorbed films. Even though this criterion may break down both experimentally and semantically in certain cases, it is workable as an initial guideline and it keeps us from becoming enmeshed in exceptions and modifications before we are ready for them. Chemisorbed films can be put on the adsorbing surfaces by the same techniques as physically adsorbed films: retraction from the melt o r from the liquid, retraction from solution, vapor deposition, etc. Chemisorbed films i n b i t U respond to probes for the nature of the film-t.5. drop contact angle or surface potential-in the same way as physically adsorbed films. It is not until we attempt to desorb the film that we become aware of the difference between physical adsorption and chemisorption, as exemplified by the observations of Timmons and Zisman cited above [lo]. Timmons, Patterson and Lockhart [8] used radioactive stearic acid on iron in their study of desorption from a metal surface covered with a reactive oxide. Figure 10-7 shows the course of thermal desorption at About 35% of the 100 C and of solvent depletion by ether at 23 C. monolayer is desorbed very rapidly by ether and the next 27% at a progressively decreasing rate. A residue of c a . 38% of the original monolayer remains tenaciously on the iron. The results for thermal desorption are much the same except that initial depletion takes place at a slower rate. The easily desorbed portion of the film was regarded by Timmons, Patterson and Lockhart as the physically adsorbed fraction, the tenaciously retained 35-40% as the chemisorbed fraction. Also shown in Fig. 10-7 is the progress of exchange of the tagged film on the iron surface with inactive stearic acid in nitrobenzene. This curve closely parallels the thermal depletion curve. During the course of the exchange

215

a80 -

U

-

g

u) Q)

Time, minutes Figure 10-7. Desorption of stearic acid monolayer from iron. A: Depletion by diethyl ether. B: Thermal desorption at 373 K. C: Exchange with inactive stearic acid. Data by Timmons, Patterson and Lockhart [81.

the oriented monolayer persistently retains its close-packed character, as demonstrated by the contact angle of ? O D for a drop of rnethylene iodide. This means that the sites of physical adsorption on the surface of the adsorbent do not alter their properties in the process of exchange. Tinmons [201 carried out similar experiments with radioactive stearic acid on surfaces of chromium, nickel, 304 stainless steel and 4 1 6 stainless steel, in addition to iron. The films on nickel and chromium showed slightly less oleophobic behavior to a drop of methylene iodide The course of and also had a slightly less compact packing (Table 1 0 - 6 ) .

TABLE 10-6. SOME PROPERTIES OF STEARIC ACID MONOLAYERS ADSORBED ON METALS ~~

Metal

CH212 contact

Area per molecule, nm 2

angle, degrees Iron Nickel Chrom i urn Type 304 stainless steel Type 4 1 6 stainless steel Data by C. 0. Timmons [201.

71 69 67 70

70

0.22 0.23 0.24 0.22 0.22

216

depletion by carbon tetrachloride and the course of exchange with inactive stearic acid in nitrobenzene as seen in Fig. 10-8 reveals marked differences in the behavior of the adsorbing Surfaces, the strongly retained portion of the stearic acid ranging from 2 3 - 3 3 % for iron to 40-53% for chromium. 100

a

0" 60 c

40

40

20 0

0 20 40 60 80100 Desorption Time, min

0 20 40 60 80100 Exchange Ti me,mi n

Fi gure 10-8. Desorption of stearic acid monolayers. (a) Depletion by ca.rbon tetrachloride. (b) Exchange with inactive stear c acid. Data by C. 0. Timmons [ 2 0 ] . The most reasonable explanation for the pers stearic acid is chemisorption on the "metal" surface as mons and Zisman [ l o ] chose diethyl ether as the solvent of the monolayer adsorbed on nickel oxide because i t acid but not nickel stearate.

stently retained the soap. Timfor the depletion dissolves stearic

Exploration of the properties of the chemisorbed soap film formed by a fatty acid on a metal under ordinary ambient conditions calls for consideration of the nature of the "metal" surface. Most of the metal surfaces used i n the adsorption studies described in this and the preceding section were prepared by polishing with levigated alumina and water, followed by oven drying. The adsorption experiments were generally performed at ambient levels of relative humidity, but sometimes controlled at 50%. Under these circumstances the Surfaces of the "metals" unquestionably carried a layer of oxide and adsorbed water. The investigators were not naive about this; explicit recognition of the situation can be found in statements by Bewig and Zisman [141 and Timmons e t a L . [El. Nevertheless, surfaces prepared thus were designated as "metallic" without qualification. Such surfaces are commonly accepted as equivalent to the "metallic" surfaces of engineering practice in ordinary ambient environments. However, in a rigorous discussion of chemisorbed films and their A chemical role in lubricant additive action we must be more precise. reaction cannot be specified without specifying the reactants. In the case of metals in ordinary ambient surroundings, we must consider a s pos-

217

sible reactants the surface layer of oxide and the adsorbed water separately, and also both together. Metals that form surficial oxide films on exposure to atmospheric oxygen at room temperature can also adsorb a film of water on oxide-free portions of the surface which then reacts to generate oxide. In studying the wetting of scrupulously clean copper and silver by water in an oxygen-free environment, Schrader [21] detected the evolution of hydrogen by mass spectrometry and considered the possibility that the hydrogen was produced by the reduction of water at the activated clean metal surface. Some direct data o n the nature of the interaction between stearic acid and the surface of acid-cleaned, water-washed, air-dried copper are provided by the work of Dobry 1221, who weighed the amount of stearic acid adsorbed on the copper from a 0.1% solution in benzene. The stearic acid thus found ranged from an amount corresponding to 1.3 monolayers, which fits well with the roughness factor for rolled surfaces, to 4.5 monolayers, which fits the roughness of an abraded surface. When treated with hot benzene in a Soxhlet extractor, the adsorbed layer %as totally depleted. Hot benzene dissolves copper stearate as well as stearic acid; for every mole of stearic acid in the film on the copper surface, 0.35 gram-atom of copper was found in the hot benzene extract. This is a direct indication that part of the adsorbed stearic acid reacted with copper or copper oxide in the surface layer. No copper was found in the extract from the stearic acid film on a copper surface prepared by reduction with hydrogen at 723 K (450 C ) . This behavior is explained by the following thermodynamic calculation for AG, the Gibbs free energy of reaction: 1

C17H35CooH(sat'?

in benzene)

+

2 "(s)

__a 1

1

7 Cu(00C*C17H35)2(sat'd

in benzene)

1

C17H35CooH(sat'd 1

i n benzene) )

+

7 )s('"

2 Cu(00C*C17H35 2(sat'd in benzene)

+

7 H2(g) A

G

=

+32.94 ~ ~ kJ~

+ ' H O 2 2 (sat'd in benzene)

A

G

=

-26.08 ~ ~ kJ~

However, Smith and his co-workers [23, 24, 251 showed that fatty acids can react directly with metal surfaces, in apparent contradiction to the thermodynamic calculations of Dobry. The work of Smith e t n L . was carried out with freshly machined metals, whose surfaces were thereby more active than the standard state of the solid crystalline surface used

218

in the thermodynamic calculations. The tangible evidence for such activation is the emission of exo-electrons (the "Kramer effect" [ 2 6 1 ) : one electron-volt is equivalent to a free surface energy of 92.3 kJ/mole. The freshly cut surfaces were protected from the action of atmospheric oxygen by a flood of cyclohexane during and after machining and then were immersed in cyclohexane solutions of nonadecanoic acid radioactively tagged with C 1 4 . The following metals adsorbed a complete monolayer of nonadecanoic acid: Al, C o , Cu, In, Mg, Ni and Pb. Silver adsorbed 0.93 of a monolayer, Sn 0.48 (maximum), Au 0 . 6 1 (maximum) and Pt 0.38 of a monolayer (maximum). Desorption of the films on copper, lead and silver by cyclohexane demonstrated that they were chemisorbed: the amount of metal found in the desorbing solution corresponded to the amount of nonadecanoic acid that had adsorbed on the metal. Desorption from gold or platinum removed only unreacted nonadecanoic acid. The desorption behavior of fatty acid films on metals marized as follows:

can

be

sum-

1.

The effect of elevated temperatures or certain solvents is to remove only part of the film adsorbed on ordinary metal surfaces; the rest of the adsorbate is tenaciously retained. Desorption from noble metals such as platinum is total.

2.

Freshly machined surfaces of ordinary metals adsorb a complete monolayer of fatty acid. On desorption by an effective solvent, the entire layer is removed as metal soap. Gold and platinum adsorb less than a monolayer of fatty acid, and on solvent desorption the fatty acid is removed as such and not as metal soap.

On this basis we can develop concepts concerning simply adsorbed and chemisorbed films that have useful significance for lubricant additive action. The concept of a persistently retained chemisorbed portion of the film on the metal surface can explain why certain substances lower friction and shift scuffing and seizure to higher applied loads. That a fatty acid film adsorbed on freshly machined platinum yields no metallic ions when it is dissolved away by solvent is consistent with the concept of total desorption from an intrinsically unreactive surface. Therefore, i f an additive substance lubricates a non-noble metal under conditions consistent with formation of an adsorbed film and the lubricating action on that metal persists while analogous lubrication of platinum fails, we may infer the existence of a functional group in the structure of the additive that attaches it to the rubbing surface. We should also take note that the concept of a chemisorbed film excludes any deep-seated changes in the adsorbate molecule even though it may be altered on desorption. Thus, the formation of a soap when a fatty acid adsorbs on an active metal surface does not break up the fatty acid

219

chain or fundamentally interfere with the ability of a film to form by adlineation.* This should be distinguished from interactions with metal surfaces activated by drastic procedures i n v a c u o . In a vacuum of 133 nPa (lo-' torr) n-octadecane or n-decanoic acid is extensively decomposed with formation of hydrogen, methane and carbon monoxide when exposed to an evaporated film of iron [271. 10.4.

THE ADDITIVE ACTION OF ADSORBED FILMS

In this section we shall start with an examination of lubrication behavior under conditions in which the existence of an adsorbed film and the nature of its properties are known positively. The information s o obtained will then be applied to discussions of experiments carried out under less rigorous control. Among the carefully controlled investigations, those of Levine and Zisman [12, 281 are outstanding for the following reasons: (a) films were deposited on the substrate by methods known to form oriented monolayers (retraction from the melt, retraction from an appropriate solvent, vapor deposition); (b) the state of the adsorbed film was confirmed independently by the methylene iodide contact angle: (c) many homologues of each basic class of additives were investigated. The types of substances included n-alkyl amines and their salts, N-substituted amines and their salts, n-alkanoic acids, n-alkanols, fluorinated fatty acids, brominated fatty acids and acids with mixed halogens. Some of the data have already been examined in a non-critical manner (Chapter 9, Table 9-6) as examples of frictional behavior under lubricated conditions. 10.4.1.

Durability of Films

A revealing insight into the mechanism of additive action by adsorbed films is afforded by Levine and Zisman's studies of film durability on reiterated traverse [12, 281. The film was deposited o n a clean glass microscope slide over which a clean ball of 440C stainless steel 1.27 cm in diameter was slid under load at 0.01 cm/s for a distance Reiterated sliding consisted of successive unidirectional of 0.2 cm. traverses over the same path. The coefficient of friction recorded was the smooth, steady-state value of uk. Figure 10-9 shows the behavior of films of n-hexadecylamine hydrochloride and n-hexadecyltrimethylammonium bromide under various loads. n-Hexadecylamine hydrochloride forms a durable film under loads in the range 9.807-88.26 N (1-9 kg) as indicated by values of vk not greater than 0.05. n-Hexadecyltrimethylammonium

*There are some complicating factors, notably temperature. Stearic acid vapor reacts with activated aluminum oxide to form an aluminum stearate which is tenaciously retained by the adsorbent. On raising the temperature of the system, the desorbed material is not stearic acid. but decarboxylated, cracked olefinic hydrocarbons.

220

0 70 I

1

I

I

I

4

1

I

n-C,6H33NH3CI 88 2 6 N 0 6865 N V

0 60

981 N O /

f

050

c 0

040

4903 N

t 6 030

981 N

e

c

$- 0 2 0

u-

0

010

0 00

/4903 N

I

I

1

5

I

I

I

1

I

10 15 20 25 Number of Traverses

30

Figure 10-9. Durability of films to repeated traverses under load. by Levine and Zisman [281.

Data

bromide under a load of 9.607 N allows an increase in uk from 0.05 to 0.11 in 10 successive passes and a much faster increase to y k = 0.63 by the 21st pass. Under a load of 49.03 N n-hexadecyltrimethylammonium bromide gave steeply increasing ub from 0.07 to 0.40 in five passes. A believable explanation of the progressive rise in the coefficient of friction f o r n-hexadecyltrimethylammonium bromide is the disruption of the film by desorption during sliding, but the observed end result of the experiment cannot be used as proof of the mechanism which brought it about. The contact angle of 56-59" for methylene iodide as against the angle of 69-70" on a film of n-C,6H33NH3C1 is evidence for the looser packing of the n-C16H33N(CH3)3Br film. Even more convincing is the

03 a

3

C

9 +

2

LL +

02

0

c

c

m ;" 01

u-

a

0

0

oc 0

05

10

15

20

Distance Traversed, m m

Figure 10-10. Details of the course of a traverse over a film of n-hexadecyltrimethylammonium bromide under a load of of 9.81 N. Data by Levine and Zisman [281.

221

behavior illustrated in Fig. 10 10 for an adsorbed film of nC16H33N(CH3)3Br when the coefficient of friction is plotted as a function of the rubbing distance along the sl ding path. On the first pass, when the clean ball is traversed along the film-coated glass under a load of 9.807 N, the initial value of pk at 0 . 1 mm is 0.10 but falls to 0.05 at 0.3 mm and stays at that level for the remainder of the 2 mm sliding distance. The ball is then rotated in the holder to put a fresh portion of its surface in contact with the same track on the glass for the next traverse. The second traverse starts with initial p k = 0 . 1 2 and requires 0.4 mm of sliding to lower pk to 0.05. Succeeding repetitions of this procedure are characterized by progressively increasing values of initial uk and progressively longer distances of sliding to attain the steadystate value of p k . The fifth cycle starts with uk = 0 . 2 8 and the steadystate value of p k = 0.07 does not appear until 1.4 mm of track is traversed. Photomicrographs showed that the greatest surface damage to the glass substrate occurred at the beginning of each traverse and was least when pk attained its minimum value.* Frictional behavior during the course of a traverse over a condensed monolayer of n-hexadecylamine hydrochloride was similar to that for the quaternary ammonium bromide except, as expected from Fig. 10-9, the film of primary amine hydrochloride was more durable.

TABLE 10-7. DURABILITY OF FILMS RETRACTED FROM SOLUTIONS OF n-DOCOSYLAMINE IN n-HEXADECANE Pass number, N p

1

6 12

16 22

Coefficient of friction, pk 0.5 hr.

2 0 hrs.

0.06 0.08 0.10

0.06

0.19 0.37

0.06

---0.06 0.06

Load: 49.03 N. bpk/bNp changes from 0.0036 to 0.027 after the 12th pass over films formed by 0.5 hour immersion but is obviously zero for rubbing on films formed by 2 0 hours immersion. From data by Levine and Zisman 1 2 8 1 .

*The substrate does not remain totally undamaged even for the lowest values of u k . That unlubricated contact is always part of the rubbing process in boundary friction must be implicitly assumed unless there is direct evidence to the contrary. The specific significance for deductions from experimental behavior depends on the particular circumstances under consideration.

222

The behavior of films deposited by a solution of n-docosylamine in n-hexadecane is given by the data in Table 1 0 - 7 . If the glass plate was allowed to remain immersed in the solution for 20 hours before retraction, as many as 28 repeated traverses of the slider did not bring about any increase in p k over the initial value of 0.06. But i f immersion before retraction was only 30 minutes, an increase in vh to 0.08 was reliably detected on the sixth traverse and the rate of change with repeated traverses suddenly increased by a factor of 7.5 after the 12th traverse. Now it has been shown in Section 10.3.1 that n-alkyl hydrocarbon solvents of sufficient chain length coadsorb with polar n-alkyl solutes, the ratio of solvent to solute decreasing with adsorbent immerIt has also been shown that the adsorbed hydrocarbon is sion time. depleted from the adsorbent more readily than the polar adsorbate. I t is therefore obvious that depletion of the n-hexadecane from the mixed film during sliding uncovers areas of glass to direct interaction with the slider, giving a coefficient of friction higher than that for the fully covered surface. The changes in vk illustrated by Fig. 10-10 can now be explained in terms of film behavior. The initial sliding of the bare steel ball on the film-covered glass desorbs some of this film and the friction is dominated by the steel/glass contact, so that the initial pk is high. On further sliding, progressively increasing amounts of adsorbate are transferred from the glass to the ball and eventually the friction becomes that of film-covered steel sliding against film-covered glass. On the next traverse of the track by a fresh ball surface, the initial sliding is against that part of the surface already depleted by the previous traverse; hence it takes longer to achieve the condition of film-covered steel sliding on film-covered glass. The same factors that govern durability of adsorbed films in solvent or thermal depletion govern their durability in rubbing contact. Polar groups anchor the molecules of the film on the adsorbent: interchain forces adlineate the molecules in an oriented array. A bulky, substituted head-structure, such as occurs in n-hexadecyltrimethylammonium bromide, interferes with the close adlineation of the n-alkyl chains; this is a credible explanation of the difference between the frictional behavior of n-hexadecyltrimethylammonium bromide and n-hexadecylamine hydrochloride shown in Fig. 10-9, particularly in view of the other relations that have been demonstrated between the mechanical durability of adsorbed films and their physicochemical surface properties. Chain length, too, has an influence on the tightness of adlineation, as we have already seen in the relation shown in Fig. 10-3 for wetting by methylene iodide. A parallel relation for the coefficient of friction and the durability of adsorbed films is evident in the data of Table 10-8 for n-alkanoic acids from C8 to c20.

223

TABLE 10-8. Chain length

CHAIN LENGTH AND DURABILITY OF FATTY ACID FILMS Coefficient of friction, vk

CH21Z contact angle, degrees

First traverse 8 10 12 13 14

16 18 20

0.17 0.14 0.09 0.06 0.06 0.05 0.05 0.06(a)

Tenth traverse 0.80 0.46 0.18 0.07 0.05 0.05 0.05 0.06 (a)

Load: 9.807 N; (a) 49.03 N. Traverse: 0.2 cm. and Zisman [281.

57 58-59 62-63 66-67

68-69 69-70 70 71 From data by

Levine

The dynamic character of the formation and maintenance of an adsorbed film is demonstrated by the frictional behavior with a liquid layer of n-octanoic acid (m.p. 16.5 C) on the glass surface. The coefficient of friction remains unchanged at vk = 0.17 for 15 traverses of the slider. The data obtained by Cottington, Shafrin and Zisman [131 with stainless steel balls sliding against stainless steel plates carrying various adsorbed films has already been examined from two points of view. In Table 9-6, the coefficients of friction for adsorbed films of fatty acids and fatty alcohols on stainless steel were compared with analogous data for films adsorbed on glass. These were values for a single traverse of the track. Except for the lowest member of the homologous series (n-octanoic), the nature of the substrate carrying the film had only a barely detectable influence on the magnitude of uk. But in Fig. 10-3 we see a pronounced effect of the substrate on the methylene iodide contact angle for chain lengths in the range C6 to C14. If the value of the contact angle is an indication of the compactness of the adsorbed film, then what we see in Fig. 10-3 seems to be at variance with what is shown by Fig. 10-11 about the durability of films of fatty acid on stainless steel. n-Octanoic acid is much more durable on glass than on stainless steel, although the methylene iodide contact angle is 57O for the film on glass, 66' on stainless steel. For n-octadecanoic acid the contazt angle is 69-70D whether the film is on glass or on stainless steel. The value of vk on the first traverse is 0.05-0.06 for the film on glass, 0.08 for the film on stainless steel, a barely significant difference. But the film on stainless steel quickly loses it ability to control friction on repeated traverses. Hexatriacontanoic acid showed less durability on stainless steel than the shorter n-octadecanoic acid on glass. Similar behavior was observed with n-alkyl amines.

224

.c

0

0.3

0

s 0.0 I

I

I

I

I

5 10 15 Number of Traverses

20

Figure 1 0 - 1 1 . Durability of fatty acid monolayers on stainless steel and on glass. Data by Cottington, Shafrin and Zisman 1131. Cottington, Shafrin and Zisman [ 1 3 ] also examined the condition of the rubbing surfaces after repeated traverses. Photomicrographs of the wear scars on the film-coated steel surfaces revealed the existence of score marks, the number and severity of which increased with successive traverses. A s the coefficient of friction rose, the appearance of the wear scars became indistinguishable from that of scars generated by steel against unlubricated steel. This was due to the accumulation of adherent metal fragments on the ball. Twelve successive traverses with the same area of contact on the ball produced a badly torn scar and a terminal value of 0.4 for uk: twelve successive traverses in which a fresh area of contact was obtained by rotating the ball each time gave a relatively undamaged wear scar and a final value of 0.2 for uk. When the substrate carrying the film was glass, 6 5 successive traverses of the ball produced a wide, shallow, hardly damaged track. The existence of an adsorbed oriented monolayer under static conditions does not necessarily mean there is an absolute barrier to contact of rider and substrate during sliding. One obvious and important reason for this is displacement of some of the adsorbed film due to the input of energy by sliding: another is deformation of the substrate by the applied load. As a result there are localized microcontacts of rider material with substrate material. Once such a contact occurs, subsequent sliding behavior during the traverse is governed by the nature of the ridersubstrate combination. Transferred material from a self-adherent substance such as steel grows by accretion during the traverse and eventually the course of sliding is dominated by gross plowing and tearing. On the other hand, when steel slides against a fragile material such as glass, even though the substrate suffers visible damage, gross disruption of the adsorbed film is much slower i f growth of the initial microwelds by accretion is not self-accelerating. 10.4.2.

Influence of Temperature on Adsorbed Films and Friction

Increase of temperature in general favors desorption and

hence

the

225

1

1.0I c

.-0

c

0 ._

I

1

I

I

1'

strongly irregular-]

0.8

t .c

I

I

1

i

0

280 300 320 340 360 380 400 420 Temperature,deg. K

Figure 10-12. Influence of temperature on the behavior of various filmforming lubricants. (a) Paraffin oil on copper. (b) Octadecyl alcohol on copper. (c) Palmitic acid on cadmium. (d) Copper palmitate on cadmium. From data by Rabinowicz and Tabor [ 2 9 1 .

response of lubricated sliding behavior to temperature should be interpretable in terms of film stability. Figure 10-12, constructed from data by Rabinowicz and Tabor [ 2 9 ] , illustrates some broad categories of observed behavior. The experiments were carried out on the Bowden-Leben apparatus at very slow sliding speeds. Copper lubricated by paraffin oil showed controlled stick-slip sliding with a fairly high coefficient of up to the transition temperature of 3 7 8 K ( 1 0 5 friction ( u h = 0 . 4 - 0 . 8 ) C ) , where sliding became strongly irregular in character. A smear of solid octadecyl alcohol on copper gave sliding with pk = 0.1 up to a transition temperature of 3 2 6 - 3 3 3 K ( 5 3 - 6 0 C ) , above which the coefficient of friction rose sharply, with stick-slip. The transition to stick-slip sliding is explained by thermal disordering of the adsorbed film of octadecyl alcohol (m.p. 3 3 2 K ) so that the sliding surfaces no longer carry a condensed oriented array of adsorbed molecules. Paraffin oil, being a liquid at room temperature and of a molecular structure not conducive to close packing, permits stick-slip sliding throughout the temperature range investigated. By extension of this argument, with a smeared-on film of palmitic acid we would expect a frictional transition at its melting point of 3 3 7 K (64 C). However, for palmitic acid on cadmium the observed coefficient of friction remains low (uk = 0.05-0.07) up to 3 8 8 K ( 1 1 5 C), after which it rises until the friction becomes very irregular at ca. 408 K ( 1 3 5 C ) . Similar behavior is observed for a smear of copper palmitate on the surface of the cadmium except that the rise of the coefficient of friction with temperatures above the transition is less sharp. The transition temperature agrees satisfactorily with the softening temperature of cop-

226

per palmitate ( 3 8 8 K). Therefore it is concluded that the effective additive for palmitic acid on a cadmium surface is the metallic soap, cadmium palmitate. Fatty acids constitute a special class of long-chain film-forming additives because, as has been shown, they can react with the oxide on metal surfaces in moist ambient air to form soaps. The coefficient of friction observed under such circumstances and the effect of temperature on friction will then be governed by the presence of the soap film. An unreactive metal such as platinum will not form a soap and the observed transition temperature will be the melting point of the adsorbed acid. Bowden, Gregory and Tabor [ 3 0 1 observed a transition temperature of 4 3 C for lauric acid (m.p. 44 C) and 6 9 C for stearic acid (m.p. 6 9 C) on platinum. However, the relation between the fact that a metal carries a coating of oxide and the transition temperature is not always obvious, as Bowden e t n l . [ 3 0 ] explain this is evident from the data in Table 10-9. by ascribing different degrees of reactivity to the oxide coatings. TRANSITION TEMPERATURES FOR THE COEFFICIENTS TABLE 10-9. OF FRICTION WITH 1 % LAURIC ACID IN PARAFFIN OIL Metal

Zinc Cadmium Copper Magne s i um Iron Platinum Nickel A1 umi num Chrom i urn Silver

Coefficient of friction at 2 0 C

Transition temperature, degrees C

0.04 0.05 0.10 0.10 0.15-0.20 0.25 0.28 0.30 0.34 0.55

94 103 97 80 40-50 20 20 20 20 20

Type of sliding at 20 C

Smooth Smooth Smooth Smooth Irregular and smooth Stick-slip Stick-slip Stick-slip Stick-slip Stick-slip

Data by Bowden, Gregory and Tabor 1 3 0 1 . Adapted by permission from Natufie, Vol. 1 5 6 , No. 3 9 5 2 , p. 97. Copyright 1 9 4 5 , Macmillian Journals Ltd.. 10.4.3.

Thermodynamics of Adsorption and Lubrication

The critical temperature of lubricated friction has been related to the physical chemistry of adsorption by interpreting the transition from smooth sliding with a low coefficient of friction to high values of friction with scuffing as the critical depletion of the adsorbed lubricant film. The critical transition temperature is identified with the critical temperature of desorption. Frewing [ 3 1 1 developed the following relation for the stable existence of a film of adsorbed additive in equilibrium with its oil solution:

221

(10-2)

where K is the equilibrium constant, k, is the rate of adsorption, k d the is the fraction of the surface occupied by rate of desorption, molecules of the adsorbate and C is the concentration of the adsorbate in the oil. The variation of K with temperature is given by the van't Hoff isochore:

+

d Ln K AU -dT

RTI

The sign of AU/RT2 in Frewing's original derivation is negative, wh ch is not consistent with standard thermodynamic notation as given in Eqn 10-1. On integration we get

AU = - - +

K

i ~ t t 5 h a t i 0 nc ~ n n t a n l :

RT

10-3)

I f we assume that for a giver. system the transition to irregular sliding occurs when + takes on a critical value a which is not functionally affected by the temperature, then the concentration C is the variable that determines the transition temperature and from Eqn 10-3 we get

AU

a en

C(1

LPI

-

- _+ inteyhaxion c o n n t a n t a) RTt

Au

c

(10-4)

a

= -+

Ln - -

hltt5hatiOn

CCJnAtaMt

1 - a

RTt

(10-5)

is the critical transition temperature for scuffing in degrees

where Tt Kelvin.

From Eqn 10-5 we see that L o g l 0 C should be a linear function of Figure 10-13 is a plot of some of the results obtained by Frewing that shows the scope of the relation for various classes of additive compounds dissolved in white oil. The data were obtained o n a Bowden-Leben friction apparatus at a sliding speed of 0.005 cm/s and a load of 39.23 N (4 kg).

l/Tt.

The basic thermodynamics of additive action and scuffing were carried a step further by Askwith, Cameron and Crouch [321. The standard free energy of the adsorption process is

A G " = - RT

P_n K

where K is given by Eqn 10-2. A G O

=

AUD

-

TAS"

=

- RT Ln

K

By familiar thermodynamic relations (10-6)

228

2 .o

1.0 OB 1.6 1.4

c,

-

0.6-

0.0 -0.2 -0.4

-0.6 -0.8 -1

.o

2.8

3.0 103

3.2

34

i / r , K-1

Figure 10-13. Relation between critical temperature for scuffing and additive concentration for (a) stearic acid, (b) myristic acid, (c) capric acid, (d) oleic acid, (e) methyl stearate, (f) ethyl stearate, ( g ) n-butyl stearate, (h) n-hexyl stearate, (i) n-octadecyl stearate, ( j ) n-octadecyl acetate, ( k ) n-octadecyl chloride. Load: 3 9 . 2 3 N. Data by J. J. Frewing [ 3 1 1 .

lo3 1/T, K" Figure 10-14. Relation between critical temperature for scuffing and concentration for n-hexadecylamine. Load: (a) 5 5 N, ( b ) 3 3 N , fc) 2 2 N, (d) 1 3 . 5 N , (e) 4.4 N. Data by Grew and Cameron 1 3 3 1 .

229

(10-7)

I f on fixing the value of 4 at a, the critical surface coverage for scuffing, it is observed that plots of e n C vs. l / T t consistently give straight lines, then it may be inferred that ASO/R is to all intents and purposes constant and that the value of AHo can be evaluated from the slope of the plot. Grew and Cameron [331 obtained the predicted linear relation for solutions of lauric acid in various n-alkanes and for n-hexadecylamine in n-hexadecane (Fig. 10-14).

However, the treatment used by Cameron and his co-workers is physically incorrect. Equations 10-2 and 10-6 apply to a Langmuir-type adsorption equilibrium in which the solvent is merely the inert carrier for the solute and does not compete with it for the surface of the adsorbent. We have examined evidence in this chapter that demonstrates this is not always the case, particularly i f the solvent has the linear long-chain structure of the higher n-alkanes used by Cameron e t aL. The equilibria for the two-component adsorption are given by

(

10-8a)

(

10-8b)

where e l , and Q2 are the mole fractions of solvent and solute on the surface of the adsorbent and C, and C, their concentrations in solution I f 4 is defined as n $ / n b , the rstio of the number of sites on the [341. adsorbent occupied by molecules of solute to the total number of sites, then 1-$ is not the fraction of vacant sites as in Eqn 10-2 and 10-7; instead

where n ; is the number of sites on the adsorbent occupied by molecules of solvent and n t the number of vacant sites.

K2 =

~2c 1 .

Equations 10-8 then become

6 (1

-

6)

-

(nt/n*)

and the free-energy relations are

(10-9b)

230

enc, = - - -

+

RT

en

R

6

(10-lob)

No experimental evidence is available for the evaluation of the critical surface coverage fraction a . Askwith, Cameron and Crouch [321 advanced arguments to show that substantial deviations from a mean value of 0.5 for a had only a small influence on the magnitude of the intercept AS' - R e n [a/(l-a)]. But i f Eqn 10-7 is thrown into the form T

'

Aff

=

RI

en

c

- en

a/(l

-

a)]

+

AS")

it will be found that allowing a to range from 0.35 to 0.65 produces f 15-20 degrees in Tt when it has a mean range from deviations of 385-455 K. The fact that Cameron and his co-workers have obtained a substantial body of data in which the inverse of the critical scuffing temperature shows a good linear functionality with the logarithm of the additive concentration is a persuasive indication that for fixed materials and fixed experimental conditions the critical surface coverage adequate to protect against scuffing has a constant value. But what this means in terms of Eqns 10-10, the expressions applicable to solutions in long-chain alkane solvents, still remains unresolved. The response of scuffing to load can be treated as a temperature effect. Spikes and Cameron [35] showed that for steel rubbing at medium speed (1.34 cm/s) lubricated by palmitic acid in n-hexadecane a linear relation between 10510 C and l/Td is obtained when T' is calculated from the formula

where Ta is the ambient temperature and AT is the rise in surface temperature due to frictional heating: W is the applied load, p is the coefficient of friction and the factor 2 lumps together the physical parameters that enter into the computation of interfacial temperature from friction data. It may be reasonably inferred from these observations, although it is not rigorously demonstrated, that the mechanisms which disrupt the adsorbed film of additive are the same when the surface temperature is the consequence of frictional heating as when the temperature is raised by bulk heating of the rubbing specimens. Also suggestive is the relation between scuffing load and additive concentration shown in Fig. 10-15, which strongly resembles an adsorption isotherm. However

231

-

c

-

0

I I I 0 002 0.004 Palmitic Acid, Mold Concentration I

0

Figure 10-15. Effect of fatty acid concentration on scuffing load. by Askwith, Cameron and Crouch [ 3 2 ] .

Data

this, like other observations relating equilibria and thermodynamics with the adsorbed film mode of additive action, is an argument by analogy: no quantitative parallel experiments comparing adsorption and lubrication are found in the literature. For number of reasons, as discussed by Spikes and Cameron [ 3 5 ] , the bn C vs. 1/T relation is not obeyed at high rubbing speeds. 10.4.4.

Other Physicochemical Influences in Adsorbed Film Behavior

The reality of the adsorbed monomolecular layer and its relation to lubricant additive action is supported by the results of a number of investigations of the behavior of mica surfaces. Freshly cleaved mica furnishes surfaces which are smooth, flat and clean. Bailey and CourtneyPratt [ 3 6 1 worked with flakes of uniform thickness, molecularly flat on both sides over the entire area studied. The multiple-beam interferometric technique of Tolansky [ 3 7 ] was used to establish the flatness of the surfaces to within 0.2 nm ( 2 8 ) . The mica sheets were bent to form cylindrical surfaces, which were loaded against each other with their axes perpendicular. The dimensions of the contact area thus generated by elastic deformation were measured interferometrically. From the tangential force required to move one mica surface relative to the other and the area of the contact spot, a value of 98.07 MPa ( 1 0 0 0 kg/ cm2 ) was found for the shear strength of mica. The surfaces in contact were badly damaged by sliding. When a monolayer of calcium stearate was deposited on the mica surfaces by the Langmuir-Blodgett technique, the 2 shear strength for sliding was reduced to 0 . 2 4 5 MPa ( 2 . 5 0 kg/cm 1 and the contacting surfaces were practically undamaged. Bailey and Kay [ 3 8 1 measured the work required to cleave mica under The various circumstances. Some of their data are shown in Table 10-10. influence of exposure to air and moisture is clearly evident in the values seen there for interfacial energy; the surface energy computed from coulombic interactions i n vacua between freshly separated surfaces

232

TABLE 10-10. OBSERVED INTERFACIAL ENERGY OF CLEAVED MICA IN VARIOUS ENVIRONMENTS Environment

Interfacial energy, jo u l e s/m 2

Newly cleaved mica:

dry air (r.h. 1 % ) room air (r.h. 5 0 - 6 0 % ) water vapor (r.h. 90%) liquid water hexane vapor liquid hexane

0.308 0.220 0.183 0.107 0.271 0.255

Resealed mica:

dry air, matching sheets room air, non-matching sheets

0.250 0.120

Lauric acid monolayer: room air

0.037

From data by Bailey and Kay [ 3 8 1 .

Y?L

a

Figure 10-16. Interfacial model of mica surfaces covered monolayers of stearic acid.

with

adsorbed

is 2 . 8 7 5 J / m 2 [ 3 9 1 , while the value found by direct measurement i n uacuv is 5 . 0 0 0 J / m 2 [ 4 0 , 4 1 1 . The significant observation is the value 0 . 0 3 7 J/m2 for the separation of two sheets of mica, each coated with a monolayer of lauric acid by retraction from n-decane solution and resealed by contact and then re-separated. This value should be compared with the 0 . 0 2 4 J/m2 reported by Zisman [ 4 2 ] for monolayers whose exposed surfaces are comprised of methyl groups. Israelachvili and Tabor [ 4 3 ] investigated the van der Waals dispersion forces for mica surfaces exposed to the ambient atmosphere and thus carrying the ordinary contamination of adsorbed air and water vapor. They also investigated the van der Waals forces for mica surfaces covered

233

by an adsorbed oriented monomolecular film of calcium stearate. Figure 10-16 is a schematic representation of two mica surfaces carrying adsorbed layers of stearic acid separated by an air gap. The dispersion force for this system is given approximately by the relation

Fd =

1s”-

(2

+ X)3

+

( S + 2 1 ) 3J

=

6rrs3

(10-11)

where A . represents the Hamaker constant of the interaction between two .Ll k bodies L, and j separated by the medium k. Details of the way Eqn 10-11 is treated are given in the original communication by Israelachvili and Tabor [43]. Of significance here are the conclusions that at separations that , ( A = 2.5 nm, the chain length of stearic acid) A e d 6 = S < ! is, the van der Waals interactions are those of the combination monolayer-air-monolayer; but when S > X

that is, A e b d at large separation becomes the Hamaker constant for two layers of mica separated by air. I f we integrate the van der Waals forces thus computed over the area of the surfaces we get a value of about 0 . 0 3 0 J / m 2 for stearic acid against stearic acid, which is in reasonable agreement with the surface energy listed in Table 1 0 - 1 0 for mica carrying a monolayer of lauric acid. But for clean mica covered with an adsorbed 2 water film the calculated value for the surface energy is only 0.040 J/m whereas the observed values listed in Table 10-10 range from 0 . 1 2 0 to 0.308 J/m 2 Apparently at less than 2.0 nm separation ( i . e . ar: separations closely approaching contact) strong short range forces that are not dispersion forces come into play to dominate surface energy and adhesion.

.

Let us examine the quantitative comparison of lubricated sliding and the surface energy of close packed monomolecular films. A characteristic value of the coefficient of friction for the sliding of surfaces lubri2 cated with stearic acid is g k = 0.06. A rider with a real area of 1 cm sliding a distance of 1 cm under a load of 9 . 8 0 7 N ( 1 kg) expends 0.00588 joule of energy against this friction. I f the real area traversed by the slider is covered by a single close-packed film, there are 4.88 x 1014 molecules (8.11 x lo-’’ mole) of stearic acid in the monolayer, taking 2 0 . 2 0 5 nm as the cross-sectional area of a molecule of stearic acid. The question to consider is what physical processes can take place in the monolayer of stearic acid and how much energy will be consumed thereby. The rounded-off value of 0.038 J/m2 found experimentally f o r the energy of a surface covered by a film of fatty acid is only 0.065% of the frictional energy as calculated above for sliding. This assumes that new stearic acid is contacted by the sliding of the rider and that no energy

234

is regained in any way when the rider makes contact with the oncoming surface in its forward progress. A molecular model for the consumption of energy by sliding involves disorientation and disruption of the film. Disorientation of the close-packed array of aliphatic chains without disruption of the attachment of carboxyl groups to the substrate can be assigned a rounded-off value of 4 . 1 8 6 kJ per mole of -CH2- groups, a figure taken from calorimetric studies of the crystallization of fatty acids [44]. For a mole of stearic acid, disorientation would require 7 1 . 1 6 kJ, from which it is calculated that only 0 . 9 8 % of the observed input of frictional energy can be attributed to disorientation of close-packed aliphatic chains. I t is estimated that disruption of the carboxylic attachment to the substrate (desorption) would require 8 . 4 6 kJ per mole additional energy. Consequently, total desorption of the layer of stearic joule of acid adsorbed on 1 cm2 of surface would consume 6 4 . 5 7 x energy, which is only 1 . 1 % of the frictional work generated by sliding with uk = 0 . 0 6 . Thus, whether we use the measured surface energy of an adsorbed monolayer of fatty acid or the energy calculated from a model for the desorption of the monolayer, these values are a very small fraction of the energy computed directly from the observed coefficient of friction. This leads to the postulate that although the coverage of the rubbed s u r face by fatty acid may be very good, s o that only a few small subregions of the rubbing couple are exposed to contact, these contacting regions make the major contribution to the friction. Another concept that has been used freely and frequently in analyzing the coefficient of friction in lubricated sliding involves the dependence of the shear strength of a monomolecular film of fatty acid on the contact pressure, but n o detailed model has ever been advanced to show the relation between shear strength and the molecular structure of the film. Bowers and Zisman [ 4 5 1 wrote the following relation for the "bulk" coefficient of friction of stearic acid:

(10-12)

where So and P are the bulk shear strength and yield pressure for the o fatty acid. I f the stearic acid is present as a film o n a hard substrate of yield pressure p,, which becomes the effective yield pressure of the sliding system, then the coefficient of friction for the system becomes

(10-13)

The ratio of yield pressures can be replaced

by

the

ratio

of

Vickers

235

diamond pyramid hardness numbers:

=.();

(10-14)

Bowers and Zisman obtained an experimental value of 0 . 0 4 for the coefficient of friction of steel lubricated by a monomolecular film of stearic The acid, whereas the value calculated from Eqn 10-14 was 0,00006. relation

sis

u = -

P

(10-15)

was introduced to deal with this discrepancy, S being a function of the is applied normal pressure P. Although the actual handling of the data went somewhat deeper than a crude forcing of the numbers to make the magnitude of the coefficient of friction come out right, still there was a considerable degree of data fitting. The concept of the pressure-dependent shear strength of a thin lubricant film was used in a directly empirical fashion by Briscoe, Scruton and Willis [ 4 6 1 via the re ation F T = -

A

(10-16)

where T is the shear strength, F is the measured frict on force, and A is the area of contact calculated from elastic theory for the sliding pair (a glass sphere on a flat glass plate). The value of T was found to be approximately dependent on the value of the pressure W / A for a given normal load W . However, in view of the detailed knowledge about the constitution of adsorbed monomolecular films (their structure and the successful application of van der Waals dispersion forces to account for their properties), it seems reasonable to require that the pressure-dependent shear strength concept be treated with equivalent detail and precision. Otherwise the concept is essentially data-fitting and leaves the door open for another nameempirical explanation which is strongly supported by observation: ly, that in actual experimentation there are enough defects in the adsorbed film to permit significant contributions to the overall observed friction from microscopic regions not protected by the film. 10.5.

CHEMICALLY DEPOSITED FILMS

The films discussed in this section are derived from precursors in the carrier fluid, either deliberately added or naturally present, which react to form substances that deposit on the rubbing surfaces. The reaction may take place in the bulk of the carrier fluid or at the surfaces of the rubbing pieces when activated by contact. The essential feature -

236

that distinguishes these chemically deposited films from interaction films, which are discussed in Section 10.6, is the absence of deep-seated decomposition of the additive or the precursor. Instead, the material in the deposited film is a polymerizate or condensate of higher molecular weight than the original precursor substance. 10.5.1

Polymeric Condensation Films

A detailed exposition of the way these films form and function is given n a publication by Furey 1471. A typical reaction is the condensation of a glycol and a dicarboxylic acid to form a polyester film:

n HOOC-R-COOH + n HO-R'-OH

--+HO(OC-R-COOR'-O),H

+

2n-1 H ~ O

As an example, a paraffinic mineral oil was the solvent for 1% of equimolar mixture of the C36-dimer of linoleic acid and C16-glycol: H H HOOC (CH ) -C-~-C=CH ( C H) ~7~~~~

" /

an

H H R-cH~-C-C-CH~OH

y

\

HC-(CH~)~CH~

H2c\ / HC-C-(CH~)~CH~ H H C36-Dimer Acid

C16-Glycol

This oil blend was used as the crankcase lubricant in a running automotive engine equipped with radioactively tagged valve lifters so that the engine oil could be monitored for the amount of wear debris. The results are summarized in Table 10-11. The reduction in wear rate for the mixture of dimeric acid and glycol is substantially the same as that for zinc dialkyldithiophosphate, the standard type of antiwear additive in commercial compounding. The reduction in wear rate observed for the acid TABLE 10-11. INFLUENCE OF CHEMICALLY DEPOSITED POLYMERIC ESTER FILMS ON AUTOMOTIVE VALVE LIFTER WEAR Added to base oil

Nothing

Relative valve lifter wear rate 100

Beneficial carryover

---

1% Equimolar mixture of Cg6-dimer

12

Yes (a)

1% C36-dimer acid

42

No

1% cl6-glyc0l

30

No

1% Zinc dialkyldithiophosphate

10

No

acid and C16-glycol

(a) For 3-6 hours subsequent running with uncompounded base oil. M. J. Furey [471.

Data by

237

or the glycol separately is significantly poorer than that of the equimolar mixture. The beneficial carryover effect for 3 to 6 hours operation after the equimolar two-component blend was replaced by uncompounded base oil is an indication of the persistence of the chemically deposited film. This carryover effect was not observed with any of the other lubricants tested. Another type of reaction, ethenoid self-condensation, was studied with a 1% solution of vinyl acetate monomer in base oil. When this blend was tested in a ball-on-cylinder rubbing device, no evidence of additive action was observed: friction and wear were high, and the oscilloscopic signal for the time-averaged electrical conductivity across the rubbing interface indicated substantial metallic contact. But when the oil blend included a small proportion of the polymerization catalyst cumene hydroperoxide, the conductivity signal decreased by 80% and the friction by 40%. The film was extremely durable; its protective effect persisted for twelve hours of running after the blended lubricant was replaced by uncompounded base oil. When the steel rubbing pieces were treated with boiling benzene after being run in blended oil, the protective effect was destroyed. Two possibilities for the mechanism of additive action by chemically deposited films must be considered: (a) the effective polymer could form in the bulk of the lubricating fluid and then deposit on the rubbing surfaces; or (b) it could form on the contacting surfaces in the process of rubbing. The data in Table 10-12 are of interest in this respect. Precondensed esters of ethylene glycol and che dimer of linoleic acid were added to a carrier oil and the resulting blends were used in the radioactive valve lifter test. From the molecular weights cited in Table 10-12, the "monoester" and the "diester" can be regarded as being predominantly of the structures shown below: Monoester:

HOC2H400C-R-COOC2H40H

Diester:

HOOC-R-COOC2H400C-R-COOC2H40H

TABLE 10-12. PRECONDENSATION OF POLYMERIC ESTERS AND CHEMICAL DEPOSITION OF FILMS ON ALJTOMOTIVE VALVE LIFTERS Added to base oil

Nothing 1% "Monoester" 1 % "Dieste r " 1% "Tetraester"

Molecular weight (a)

Relative valve lifter wear rate

---

100

7 1 6 (609) 1264 ( 1 2 0 0 )

12

1975 (2367)

05

(a) Theoretical molecular weight in parentheses. [471.

8

Data

by

M.

J.

Furey

238

The "tetraester" might be the product of straightforward further polymerization of the "diester." The fact that the "monoester," which has no obvious route for further polymerization in bulk solution, is as effective an antiwear additive as the "diester" indicates the importance of the rubbing interface in the mechanism of additive action. The poor rating of the "tetraester" as an antiwear additive might be ascribed to greater solubility in oil so that it does not reside on the rubbing surface long enough to form a suitable reaction film, or else the proper spatial orientation is more difficult than it is for a shorter polymeric ester. 10.5.2.

Surface Resin ("Friction Polymer")

Still another form of additive action by chemically deposited films has its origin in the generation of "surface resin" or "friction polymer." Hermance and Egan [481 observed the visible accumulation of polymeric organic resin accompanied by a marked diminution in wear during the reciprocating sliding of palladium on palladium in an atmosphere saturated with benzene or limonene vapor. A wide range of other organic vapors was found to produce more or less resinous material under similar conditions. Campbell and Lee 1491 worked with the vapors of organic substances in a continuously sliding system and found that although vapors of such substances as limonene, diisobutylene and benzene produced polymeric resins, this was not necessarily accompanied by a decrease in wear. Fein and Kreuz 150, 511 studied the role of "friction polymer" in lubrication with the four-ball testing machine. This machine operates under very high contact pressures and the effects of a number of factors extraneous to the action of "friction polymer" must be taken into consideration. The most revealing demonstration of the formation and behavior of "friction polymer" was achieved with cyclohexane vapor in air or synthetic oxygenated atmospheres. In atmospheres of low oxygen concentration (5 ppm to 0.52%), rubbing in the presence of cyclohexane vapor was characterized by the absence of frictional seizure, very low wear, and the appearance of adherent organic material in the vicinity of the rubbing contact. Eventually enough of the "friction polymer" was deposited on the rubbing specimen so that it could be washed onto a sodium chloride plate and examined by infrared spectroscopy. Bands for >C=O, -COO-, -C-H and -CH2- were identified. When the parent hydrocarbon was benzene, the absorption bands at 3.25-3.3 pm characteristic of aromatic and olefinic structures were no longer seen in the polymer: i.e. deep-seated alterations of the original hydrocarbon structure had taken place. The molecular weight distribution of the polymer generated from cyclohexane depended on the duration of rubbing: two-hour runs generated polymer with fractions about one-third each in the molecular weight ranges 300-400, 400-850 and > 8 5 0 , whereas from 16hour runs o n l y half the material had molecular weights less than 850.

239

Further insight into the generation and nature of "friction polymer" o r "surface resin" is given by the results reported by Goldblatt The con1521 for mixtures of white oil and 1-methylnaphthalene. stitutional analysis of the low-viscosity white oil (0.0024 Pa-s at 298 K; 2.4 cp at 25 C ) showed it to be 85% isoparaffinic and 1 5 % naphthenic. The naphthenic rings can be regarded as analogues of the cyclohexane used by Fein and Kreuz 150, 5 1 1 . Mixtures of white oil and methylnaphthalene exhibited very good antiwear and antiscuffing behavior in all atmospheres (ranging from ordinary air to 0.1% oxygen in argon); white oil was a good lubricant in 0.1% oxygen but poor in ordinary air; methylnaphthalene was a very poor lubricant in 0.1% oxygen and fair in ordinary air. The composition of the solid debris recovered in these experiments is shown in Table 1 0 - 1 3 . Goldblatt proposed that the metal surface is activated by rubbing, which enables it to catalyze the formation of an aromatic radical anion: Metal* + Aromatic TABLE 10-13. Lubricant

MN MN MN/WO MN/WO

4 (Metal Cation)'

+

(Aromatic Radical Anion)-

ANALYSIS OF SOLID DEBRIS Atmosphere

0.1% Air

o2

0.1%

o2

Air

Weight-% C

H

N

Fe

50 45.2 71.9 59.2

4.3

-_

29

3.9

4

7.8 6.1

33 4

2

MN: 1-Methylnaphthalene. WO: White oil.

--

7.9

Data by I. L. Goldblatt [521.

The aromatic radical anion can react with metal or metal oxide to form lower-valent metal oxide or metal wear particles. "Surface resin" (as Goldblatt prefers to call it) is formed from the aliphatic or naphthenic constituents by the following process: Aromatic Radical Anion + White O i l j Adduct + Polymeric Resin Oxidation works on the aromatic radical anion and white oil as shown below: Aromatic Radical Anion + O2 +Aromatic

+Peroxides +Acids Aromatic Radical Anion +Acids

+

its

Hydrocarbon

+

combination

with

02

or Resins

White Oil + O2+Peroxides

(aliphatic)

(aliphatic) + Resins

In the presence of aliphatic or naphthenic material, surface resin is formed by the action of the aromatic radical anion in preference to

240

metal-containing wear debris; hence the low iron content of the MN/WO mixtures. Some iron soap may be formed from the organic acids. The mechanism of lubricant additive action by chemically deposited films, whether of the type described by Furey [471 or of the "friction polymer" type, is at present mostly conjectural. No direct demonstration of such film action by unequivocal identification of the film at the rubbing site has been reported. Figure 10-17a shows the scar on a stationary ball from an experiment by Fein and Kreuz 1501 with cyclohexane vapor lubrication; "friction polymer" can be seen at the leading edge of the scar and in copious amounts at the trailing edge, but none on the actual rubbed area. Fein and Kreuz reported interference colors indicative of a thin film on the contact region of the stationary ball after 9.23 revolutions of the top ball in the presence of cyclohexane vapor; presumably the film was disturbed by metallic wear on prolonged rubbing. Also, there was no conductance across the contact with a 10 ohm resistance in parallel and a current of 1.5 mA at 15 mV. The load was equivalent tc 2.45 GPa (25,000 kg/cm2) elastic deformation pressure and the rubbing speed was 0.35 cm/s; in the absence of a bulk liquid phase the possibility of hydrodynamic action was remote. Figure 10-175 snows the leading surface of a conically-ended rider which was immersed in a bath of liquid lubricant during a wear experiment;* a film of wear debris in a

a

C

0.500 mm

1.000 mm

U 10 urn

Figure 10-17. "Friction polymer" at rubbing surfaces. (a) Wear scar on stationary ball of four-ball test, leading edge at bottom; run in cyclohexane vapor. Fein and Kreuz [50]. ( b ) Wear scar on conically-ended pin, leading edge at bottom; run in white oil. Dorinson, unpublished work. (c) Wear debris in polymer matrix a s found in the lubricant. Dorinson, unpublished work.

*A. Dorinson, unpublished work.

241

matrix of "friction polymer" was deposited on the conical tip of the rider as the oil flowed around it. Figure 10-17c shows the nature of the debris found suspended in the oil; dense metallic or oxide particles are intermingled with the crumpled sheet of polymer. When a chemically deposited film of "friction polymer" or "surface resin" derived from precursors intrinsically part of a petroleum oil acts as an additive in the high-pressure lubricant behavior of that oil, then the function of the oil must be viewed in a two-fold light. That part of the oil which generates the surface film is in effect an additive. The rest of the o i l is the inert liquid carrier. 10.6.

INTERACTION FILMS

The concept of the interaction film in lubricant additive action is based on the postulate that material in the rubbing surface and the additive both contribute to the formation of the film by extensive chemical reaction with each other. The additives contain characteristic elements (e.y. sulfur, chlorine, phosphorus) in characteristic chemical structures. The material in the rubbing surface is usually metallic; iron is the metal most frequently encountered in technological practice. I n order to ascribe a given instance of lubricant behavior to the interaction film mechanism it is necessary to demonstrate the existence and the action of the film at the rubbing interface and also to show that the film was generated by deep-seated reactions between material in the rubbing surface and constituents in the lubricant. The interaction film need not necessarily have a precisely defined composition and structure. This is one of the fundamental differences between an interaction film and an oriented chemisorbed film, which has a definite structure that is directly related to the original molecular structure of the additive from which the film is derived. The other fundamental difference is that in the chemisorbed film the chemical forces which attach the polar group of the adsorbate to the substrate do not bring about any disruption of the essential structure of the adsorbate molecule. The generation of interaction films, on the other hand, is at the expense of extensive chemical decomposition of the additive substance when it reacts with material i n the rubbing surface.

The detection and evaluation of lubricant performance by interaction films usually hinges on wear rates, load or pressure dependence of wear, critical scuffing or seizure load, and the like. When these phenomena and criteria reflect the conditions of high loading and fast rubbing speeds under which the lubricant is often expected to function, they are designated as "extreme-pressure" conditions in the scientific as well a s the practical literature. In such cases the governing physical parameter is probably the high local temperature generated by the expenditure of rubbing energy. These are conditions under which we would expect exten-

242

sive chemical interaction between the material in the rubbing surface and constituents in the lubricant. Although i t is not a foregone conclusion that oriented physically or chemisorbed films would be severely disrupted by "extreme-pressure'' rubbing, it is doubtful that areas of significant magnitude would survive to affect friction data in the characteristic mode of such films. Because of the severity of the rubbing conditions and the complexity of the rubbing phenomena, there are no demonstrations of the performance of interaction films that are as elegant as the best demonstrations of the existence and functioning of oriented adsorbed films. Instead, much of the work on the mechanism of additive action by interaction films involves conjecture. Part of the conjecture requires knowledge of the reactive elements in the additive and the chemical structures in which they occur. The three most common reactive elements in the additives of commerce are sulfur, chlorine and phosphorus. Table 1 0 - 1 4 lists the most significant structural combinations in which these elements occur, as well as some other elements that have been found to participate in the formation of interaction films.

TABLE 10-14. IMPORTANT ELEMENTS AND CHEMICAL STRUCTURES IN THE FORMATION OF INTERACTION FILMS E 1ement

Structural types

Sulfur

Elemental, organic monosulfide, organic disulfide and higher polysulfides, sulfurized fats, sulfurized hydrocarbons, xanthates, dithiocarbonates

Chlorine

Alkyl and aryl chlorides, chlorinated fats, chlorinated silicones

Phosphorus

Organophosphates, organophosphites, organophosphonates, organophosphinates, organophosphorodithioates

Bromine, iodine, selenium, tin, lead, molybdenum, zinc, nickel, manganese

Various organic compounds and coordination complexes

The direct reaction of elemental sulfur with iron to form iron sulfides is well known and at first glance one would expect to see a systematic protective effect from elemental sulfur or polysulfides. Greenhill [53] found that the residual dry film deposited on steel by the action of ammonium polysulfide gave a coefficient of friction uk = 0.5 for slow-speed sliding in the Bowden-Leben apparatus compared to p k = 0.7-0.9 for bare steel. The thickness of the film was of the order of 100-200

243

nm. The lubricating action of white paraffin oil was enhanced by the However, the anpresence of the sulfided film, as shown in Table 10-15. tiwear action observed by Davey 1541 with white oil and sulfided balls in the four-ball testing machine is not so clear-cut, as seen in Table 10-16. TABLE 10-15. ENHANCEMENT OF LUBRICATING ACTION OF PARAFFIN OIL BY A PREDEPOSITED SULFIDE FILM ON STEEL Temperature, deg. C

Coefficient of friction Original steel

Sulfided steel

0.39 0.45 0.60

0.16 0.27 0.32

25 50 100 Data by E. B. Greenhill [531.

TABLE 10-16. INFLUENCE OF PREDEPOSITED SULFIDE FILM ON LUBRICATED WEAR OF STEEL -

Load, kg

70 85 102

Wear scar diameter, mm Original steel

Sulf ided steel

1.96 2.82 >3.5

1.92 2.33 2.43

Data by W. Davey [54]. When tested in the four-ball machine, solutions of sulfur in petroleum oils of moderate viscosity o r in white oil raise the critical load for the onset of severe, destructive wear, which is designated as "antiseizure" action in the technological idiom of the four-ball test. Davey [54] found a significant increase in the critical initial seizure load from 834 N (85 kg) for a petroleum base oil to 1275 N (130 kg) for elemental sulfur dissolved in the oil. Sakurai and Sat0 [551 observed a 3.2-fold increase in the load-wear index (mean Hertz load) for a 0 . 5 weight-percent solution of elemental sulfur relative to that of the uncompounded white oil. The load-wear index is a specialized result of the four-ball test that can be taken as indicative of the average antiseizure behavior of the lubricant. Mould, Silver and Syrett [561 reported a load-wear index ratio of 3.08 for 0.48% sulfur in white oil relative to that of the solvent oil, and also an increase in the initial seizure load from 441 N to 637 N (45 kg to 65 k g ) and in the 2.5-second seizure-delay load from 490 N to 833 N (50 kg to 90 kg).

244

The composition of predeposited films or of dynamically generated interaction films is not always predictable from the chemical composition of the additive. Simard, Russell and Nelson [57] by electron diffraction could see only a change of the original surface film of y-Fe203 to hydrated ferric oxide and y-FeO(OH) or Fe304 when steel was statically immersed in oil solutions of sulfur or run with this lubricant under low loading in the SAE lubricant tester; no iron sulfides were detected. Godfrey [581 examined films stripped from specimens run with oil solutions of sulfur in the SAE testing machine and also fragments of debris recovered from the used oil. Techniques employed were electron diffraction, X-ray diffraction and microchemical analysis for inorganic sulfide sulfur. The composition of the surface films was approximately 75% Fe304 and only 25% FeS. The ferrous sulfide was found in both the crystalline and the amorphous condition. Godfrey [581 also reported a set of experiments that offer some insight into the way interaction films might function. Rubbing specimens which had been given surface films of mixed Fe304-FeS by running in the SAE tester with oil solutions of sulfur were then run in the tester with plain mineral oil as the lubricant. The average load at failure by scuffing was 979 N (220 lb); untreated standard test pieces run with uncompounded mineral oil rarely survive scuff-free through break-in under an initial load of 66.7 N ( 1 5 lb). When the FeS was leached out of the interaction film with dilute acid, runs with plain mineral oil in the SAE machine scuffed at loads in the range 222-512 N (50-115 lb). Specimens with a chemically predeposited film of FeS formed by immersion in molten KSCN scuffed at loads less than 445 N ( 1 0 0 lb) when run with plain mineral oil. Godfrey concludes that an interaction film of FeS mixed with Fe304 is a better antiscuff lubricant than a single-component film of either FeS or Fe304. However, the mixed films were generated with considerable mechanical action, which may have affected their physical condition and their adhesion to the underlying substrate, whereas the chemically predeposited films could have been somewhat loose and friable.

I f the key element of an additive is made radioactive and this element reacts to form the interaction film, then radioactivity will be observed on the rubbing surfaces. To distinguish between a film of unreacted lubricant which merely wets the surface and the interaction film which is bonded to the surface, the rubbing parts are washed with a suitable solvent that removes the unreacted lubricant and leaves the interaction film. Borsoff and Wagner I591 used a mineral oil solution of dibenzyl disulfide tagged with S35 in a four-square gear-testing rig. The dynamic nature of the interaction is demonstrated by the following observations: (a) radioactivity on the working surfaces of the teeth increased with applied load for a given time of running; (b) more radioactivity was found on the addendum and the dedendum, the portions of the

245

tooth that experience the most rubbing, than in the vicinity of the pitch circle. Estimates of the number of layers in the interaction film by radioactive sulfur assay ranged from about 5 layers at low loads to 60-70 layers on the most active portions of the tooth profile at high loads. Sakurai, Ikeda and Okabe [60, 611 studied the effect of load, among other factors, on the thickness of the interaction films generated by the following substances tagged with S35: elemental sulfur, dibenzyl disulfide, diphenyl disulfide, n-dodecyl mercaptan. The eqdilibrium thickness of the interaction film generated by rubbing increased with applied load and was also governed by the chemical nature of the additive substance, as is discussed further in Chapter 14. Chloride interaction films were studied with the Bowden-Leben friction apparatus by Gregory [62]. Steel surfaces were treated with dry chlorine and then a slider was passed over the resulting film, either in the dry condition or lubricated with paraffin oil. Also, steel and platinum, coated with films of FeC13 evaporated from ether solution, were rubbed in the presence of paraffin oil. Figure 10-18 shows the behavior

:;I4, -1 ,

,

,

,

,

.1

0

.o

320 340 360 380 400 420 4 4 0 Temperature, deg. K

Figure 10-18. Effect of chloride films on friction. 1 : Steel treated with chlorine. 2: Steel treated with chlorine and lubricated with paraffin oil. 3: FeC13 on platinum, lubricated with paraffin oil. 4: FeC13 on steel, lubricated with paraffin oil. 5: Dry steel. From data by E. B. Greenhill [531 and J. N. Gregory 1621.

observed. Copper in the uncoated condition gave a coefficient of friction u k = 1.0: with a dry chloride film p k = 0.30, rising to 0.4 at 623 K (350 C); with a chloride film in the presence of paraffin oil p k = 0.2 over the whole temperature range. W. Davey 1631 treated steel balls with dry H C 1 and observed the antiwear effect shown in Fig. 10-19 on rubbing in the presence of mineral oil. P. Studt [641 examined steel chips from

246

I

E 4 E

I

I

1

I

1

untreated balls 0

0

treated with HCI

w o m

Figure 10-19. W. Davey [631.

? W

0 5 0 100 150 200 2 5 0 3 0 0

B

Applied L o a d , k g

Effect of chloride films on four-ball wear.

From data by

drilling tests with various organochlorine compounds as cutting-fluid additives and found significant amounts of chloride not removed by prolonged extraction with pentane but extractable with boiling water, which was interpreted as showing the reaction of the additive with the metal surface during drilling. Interaction films from phosphate esters were investigated by Barcroft and Daniel [ 6 5 ] , who tagged triphenyl phosphate with radioactive P32 and used it as the antiwear additive in the crankcase lubricant of an automotive engine. On examining the valve lifters for evidence of an interaction film, radioactivity not removable by solvent treatment was found on their working faces. The top layer of the lifter surface was dissolved in acid and the solution was searched for the following constituents: phosphides (volatile and acid-soluble); organophosphates (benzene-soluble); inorganic phosphates (acid-soluble). Table 1 0 - 1 7 summarizes the findings. The high proportion of organic phosphate on the chromium and the hardenable cast iron surfaces is attributed to their TABLE 10-17. SUMMARY OF SURFACE FILM CONSTITUENTS FROM ACTION OF TRIPHENYL PHOSPHATE ON AUTOMOTIVE VALVE LIFTERS Lifter material

Constituent, % of film Organic phosphate

Inorganic phosphate

Phosphide

~~~

Chromium-plated Hardenable cast iron (a) Chilled cast iron Case-hardened steel

71

23

41

27

31 73

74

26

(a) Ca. 3 0 % of the phosphorus was not removed from the lifter treatment with acid. From data by Barcroft and Daniel 1651.

by

247

porous texture; however, all four of the metals retained significant amounts of organic phosphate. This was probably in the form of phenyl acid phosphates, which adsorb on iron, as shown by Klaus and Bieber [661. Even though the triphenyl phosphate was of high purity originally, it would have hydrolyzed to some extent in the crankcase of a running engine. The fact that the rest of the phosphorus in the surface film is inorganic phosphate agrees with the work of Godfrey 1671, who found the product generated from tricresyl phosphate by rubbing steel surfaces to be a mixture of FeP04 and FeP04-2H20. The theory of Beeck, Givens and Williams 1681 that the interaction film formed from tricresyl phosphate and a metal surface is the metal phosphide, which for a time was frequently cited, has been effectively disproved. Loeser, Wiquist and Twiss carried out investigations of the interaction films formed by zinc dialkyldithiophosphate tagged with P32 1691 and The results obtained with a dynamically operating camwith S35 1701. tappet rig are instructive. Figure 10-20 shows the bound phosphorus and sulfur found by radioactive assay on the contacting surface of the tappet run in a mineral oil containing 1% of the zinc dialkyldithiophosphate additive. Figure 10-20a shows the build-up of the interaction film with progressive rubbing at an initial load of 1008 N (225 lb) and the increase in the rate at which film builds up when the load is increased. The interaction film contains a greater proportion of phosphorus than sulfur, although in the original zinc dialkyldithiophosphate there are two atoms of sulfur for each atom of phosphorus. The treated tappets carried a coating of manganese phosphate, which probably did not survive the initial phase of rubbing but made the surface somewhat porous: this

0,

KTreated,

0

50

100

150

200 0

50

100

,Untreated

150

200

Running Time, hours

Figure 10-20. Phosphorus (I) and sulfur ( 1 1 ) in an interaction film on hardened cast iron under dynamic conditions. (a) Effect of load and running time: 1% zinc dialkyldithiophosphate in SAE 10 base oil. ( 5 ) Effect of change from compounded oil to base oil. Treated parts furnished with surface coating of manganese phosphate. Data by Loesser, Wiquist and Twiss 1701.

248

is the most likely reason for the significantly higher levels of phosphorus observed there. Figure 1 0 - 2 0 b shows how quickly replacement of the compounded oil by uncompounded base oil brings about a reduction in the phosphorus and sulfur on the tappet face. The fact that the level of the additive elements in the surface was not reduced to zero can be linked to penetration of the additive below the depth reached by wear. Hoock and Kleinholz 1 7 1 1 ran an automotive engine with an oil

containing nickel dialkyldithiophosphate tagged with and examined the working surfaces of the valve lifters by removing successive layers of the surface region and assaying them for radioactive nickel. The data shown in Table 10-18 indicate that approximately 80% of the nickel is concentrated in the upper 2 5 % of the interaction layer.

TABLE 10-18.

DEPTH OF INTERACTION LAYER ON AUTOMOTIVE VALVE LIFTERS Radioactive Ni 6 3 count s/mi n

Depth, pm

0 (surface) 12 25 39 50 62 68 73

134.6 26.1 12.6 5.8 2.4 2.7 2.7 2.4

Lubricant: nickel dialkyldithiophosphate in automotive engine oil. by Hoock and Kleinholz 1 7 1 1 .

Data

277 hrs. Load:1008- 1846 N.

I

Ramp

I

Nose

1

Ramp

I

Cam Circumference

Figure 1 0 - 2 1 . Distribution of sulfur on the working areas of an automotive cam. Lubricant: 1% zinc dialkyldithiophosphate in SAE 10 base oil. Data by Loesser, Wiquist and Twiss [ 7 0 1 .

249

The dynamic aspect of interaction film formation is illustrated by Fig. 10-21, which shows the distribution of radioactive sulfur on an The heaviest radioacautomotive cam in relation to the running time. tivity is on the nose of the cam, which is the region of the highest contact pressure and the most active interaction of additive with the rubbing surface. The association of an element with interaction film formation is not necessarily an indication that a particular compound containing that element will function as an additive by the interaction film mechanism. The element must be present in a reactive structure and the tribological conditions must be suitable for additive action. Greenhill 1531 observed no reduction of friction with the following sulfur compounds: cetyl methyl sulfide, di-n-hexadecyl sulfide, dibenzyl disulfide, B:B'-dichlorocetyl sulfide. n-Dodecyl mercaptan and n-hexadecyl mercaptan did not promote smooth sliding of steel on steel at room temperature. That the longchain adlineation of alkyl thiols may not be as strong as that of other long-chain compounds is indicated by the data of Martin and Bornong 1171 shown in Table 10-4. The supposedly reactive thiol structure seems to be without influence in this case. The situation appears to be different for copper. Transition temperatures of 413-423 K (140-150 C ) observed for dodecyl and hexadecyl mercaptan are probably indicative of the strong anchoring of an oriented film via the mercaptide linkage. Substances such as dithioheptadecanoic acid and a-mercaptopalmitic acid,

inhibit the frictional transition on steel at temperatures of 373 and 503 anchoring action of the carboxylate structure and its thio-analogue to give a chemisorbed oriented film on the steel surface rather than to a deepseated chemical reaction of the sulfur with the metal.

K (100 and 230 C), but this behavior is ascribable to the

J. N. Gregory [621 found that long-chain alkyl halides such as n-octadecyl chloride, n-hexadecyl bromide and n-hexdecyl iodide at temperatures above their melting points gave stick-slip sliding on steel, which is to be expected of the chemically unreactive type of halogen in these compounds. Compounds such as R

\

/cl Se

R /, lC'

250

where R is phenyl or 2-chlorophenyl, are acid chlorides and function by way of the very reactive chlorine bound directly to the selenium; their solutions in paraffin oil give very low friction (vLb = 0.06) with steel over the temperature range 3 4 3 - 5 7 3 K ( 7 0 - 3 0 0 C). n-Octadecanoyl chloride behaves similarly. 10.7.

ASPERITY JUNCTION-GROWTH INHIBITION

There are circumstances under which n o firm evidence, either direct or indirect, can be found for the formation or existence of an additive interaction film and yet the behavioral signs of additive action are unmistakable. Such situations generally involve short times of contact with drastic surface changes and severe wear. A characteristic and important example is metal cutting, as illustrated by Fig. 10-22 which shows the basic geometry of orthogonal cutting. A s the tool advances in the direction shown, the force exerted by the cutting edge shears the metal of the work piece along the plane SS' and the chip flows up the face of the tool as indicated. Unlubricated, the formation of a wear scar on the face of the tool and eventual destruction of the cutting edge is very rapid. Additives blended into a cutting oil have a strong influence in decreasing the rate of wear and prolonging the working life of the tool.

Chip

Figure 10-22. Orthogonal cutting and access of cutting fluid to the chip-tool rubbing interface; shaded area shows formation of the wear scar. Direction of tool travel: t - t'. Direction of chip flow: c - c ' . Flow of cutting fluid: 61 - 61'. I t has been demonstrated ( 7 2 , 7 3 ) that access of cutting fluid to the chip-tool rubbing interface is via the clearance gap at the flank of the tool and then past the cutting edge. Only minute quantities of cutting fluid can get to the rubbing zone by this route. Furthermore, the contact time of the chip with the tool face is very short; at a cutting speed of 0.508 m/s ( 1 0 0 ft/min) an element of chip surface traverses the contact zone in 30 microseconds. Moreover, the chip never returns to rub the face of the tool; therefore any reaction of the free chip surface

251

contributes nothing to the lubrication of the chip-tool interface. It would take a strained interpretation of the interaction film mechanism to f i t it to the action of additives under these circumstances. To explain the pronounced effect of additives on tool wear in metal cutting, Dorinson [741 developed a theory of the inhibition of junction growth at contacting asperities based on the concept of dynamic competition between asperity adhesion and the quenching of such adhesion by additive reaction. The adhesion mechanism involves the following sequence: migration of metal on the chip side of the contact interface to the tool side,

and formation of a junction with the tool material, MI

+

M

where tion. MI

+

d MR

T

MR represents the intermetallic reaction that results i n the juncCompeting with this reaction is the action of the additive X:

X +MIX

The transfer MII+ MI occurs at a constant rate k,. The rate constant for the formation of MR is b,, and for the formation of MIX it is k3. The net rate of change in the concentration of MI is given by

P I1

d --

- b , - rnk2 [MI] - Ck3 [MI]

dt

(10- 7 )

where rn is a coefficient characteristic of the tool material MT and c is the additive concentration. The net rate of change of MR is given by

From Eqns 10-17 and 10-18 we get

rnk k2 CMR1

=

rnk k2

t +

rnk,

+

Ck3

(rnk,

+

Ck3)2

e x p 1- (mk2

+

Ck3)tl

(10-19) it is assumed that k3 >> k, >> k l , then the last two terms of Eqn 10-19 can be dropped altogether and the term rnk, can be omitted from the denominator of the first term; E o n 10-19 can then be shortened to the approximation below: If

(10-20)

252

I f now we introduce the postulate that the wear rate is proportional to d M /dt, we can write RI

t

( 10-21

where Wo is the rate for lubricated wear and 4 is a proportionality constant that expresses the lump removal factor for the formation of a wear particle from MR. In the absence of lubricant, k 2 and k 3 disappear from the wear expression and the unlubricated wear rate is given by Wo = k l q

(10-22)

Comparison of Eqn 10-21 and 10-22 shows that since k2/k3 << 1 , WA < Wo. Furthermore, additive action should become more effective in decreasing the lubricated wear rate with increasing concentration of additive. The concept 3f asperity junction-growth inhibition was specifically developed to explain the performance of metal-cutting oils, but its significance goes far beyond that. It can elucidate the improvement of load-limited scuffing in the presence of an appropriate additive by postulating that the mechanism of scuffing is the catastrophic increase of the lump removal factor 4 at a critical wear rate Wc. At this critical load catastrophe occurs in a very short time. Any influence that makes From Eqn 10-21 we see that increasing the W; < wc will prevent scuffing concentration of the additive or increasing its activ ty via the reaction rate constant k 3 are two poss ble means of inhibiting scuffing. REFERENCES 1.

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A177 ( 1 9 4 0 ) 1 0 3 - 1 1 8 . 69.

70. 71. 72. 73. 74.

H. Loeser, R. C . Wiquist and S. B. Twiss, ASLE Trans., 1 ( 1 9 5 8 ) 329-335. E. H . Loeser, R. C. Wiquist and S. B. Twiss, ASLE Trans., 2 ( 1 9 5 9 ) 199-207. W. S. Hoock and M. P. Kleinholz, 1961 SAE International Congress and Exposition of Automotive Engineering, Jan. 9 - 1 3 , Paper 3 0 0 B . W. E. Lauterbach and E. A. Ratzel, Lubrication Eng., 7 ( 1 9 5 1 ) 1 5 - 1 9 . W. E. Lauterbach, Lubrication Eng., 8 ( 1 9 5 2 ) 1 3 5 - 1 3 6 . A. Dorinson, ASLE Trans., 1 ( 1 9 5 8 ) 1 3 1 - 1 3 8 . E.

255

Chapter 1 1 LUBRICANT ADDITIVE ACTION. 1 1 . CHEMICAL REACTIVITY AND ADDITIVE FUNCTIONALITY

The incorporation of a chemically active substance into a lubricant to improve its performance by the formstion of a chemical interaction film, as described in Chapter 10, Section 6 , implies that we should find evidence for the interaction on the rubbing surfaces. ?he specific nature of the reactions that should bring this about, however, was not discussed. In this chapter we shall look closely at the structures of the various types of chemically reactive additives and examine in some detail how interaction with the material in the rubbing surfaces functions to reduce wear and inhibit catastrophically destructive processes such as scuffing and seizure. Since metals are technologically the most important materials to be preserved from the unfavorable consequences of rubbing, our main concern will be with them. We shall see that chemical action of "extreme-pressure" additives with rubbing surfaces is particularly important in enabling them to withstand high contact pressures and elevated local temperatures without scuffing or seizing.

1 I.

:. A BASIC VIEW OF REACTIONS BETWEEN ADDITIVZS

AND METAL SURFACES

Two basic factors should be considered in assessing the role of chemical reactivity in additive action: (a) the nature of the additivei . e . its structure and the reactive elements therein; (b) the reactivity of the rubbing surfaces, which includes their state of activation as well as the intrinsic reactivity of the constituent materials. In tribological processes, additive reactions occur at surfaces that are being rubbed o r have just been rubbed. For the most part the sequence of events is so complex that the reactivity of the surfaces cannot even be estimated, let alcne be specified precisely. Nevertheless it is valuable background to know how surfaces of known composition and properties react generally with chemical groups typical of additive substances a s well as with specific substances of established utility. Films of metal in a highly reactive condition can be prepared by flash evaporation in vacuum from a hot filament onto a receiving surface. The gaseous substance whose reaction is to be studied is then leaked into the system at low pressures. Morecrof: [ l ] , on admitting n-octadecane at 0 . 1 Pa (7.5 x torr) to a film of evaporated iron at room temperature, recovered methane, hydrogen and carbon monoxide in Ehe ratio

256

54:33:13 volume-percent. The same type of experiment carried out with nbutane in the ratio of one mole of C4H10 to one gram-atom of Fe showed complete decomposition of the butane to methane, hydrogen and carbon monoxide. The oxygen necessary for the formation of CC probably came from the walls of the reaction vessel. The decomposition of n-decanoic acid was more complex, yielding fragments ascribable to scission of the terminal methyl group in addition to fragments with the carboxylic acid giouping. Wright, Ashmore and Kemball [21 found that the dissociative adsorption of methane and ethane, with the evolution of hydrogen, depended on the metal and the temperature. Tungsten was active in the range 273-316 K (0-43 C); nickel did not adsorb o r decompose methane below 413 K (140 C ) but was reactive toward ethane at 273-318 K. Iron was much less reactive, requiring a temperature of 443 K (170 C) to decompose methane and 350 K (77 C) to decompose ethane. A dehydrogenated (n' < n + 2 of the original residue with the empirical formula CH,, hydrocarbon) remained tenaciously bound to the metal surface. Dissociative chemisorption of hydrogen sulfide by metal films depends on the nature of the metal. Saleh, Kemball and Roberts [31 observed evidence for the dissociation of hydrogen sulfide by adsorption o n films of nickel or tungsten at 193 K ( - 8 0 C), the gaseous product of the dissociation being hydrogen. The extent of dissociation increased on warming to 273 K and the stoichiometry of the desorbed gases was fitted to a reaction scheme in which the sulfur is bound to the metal. The adsorption of H2S on silver is predominantly reversible at temperatures below 423 K (150 C). The adsorption of H2S on films of lead is also substantially reversible at 193 K , but at 398 K (125 C) dissociation of the H2S and retention of the sulfur by reaction with the lead is extensive 141. If the film of lead is exposed to oxygen before the admission of H2S, then the stoichiometry of the dissociative reaction is altered drastically; formation of surface species such as -OH and -S=O is postulated. The dissociative adsorption of H2S on iron between 273 and C ) conforms to the reaction scheme below [5]: x Ce(s)

f

E2S(g)

FexS(s!

+

433 K

(0-160

H2(g)

where the stoichiometry of FexS is not uniquely determined. Saleh, Roberts and. Kemball [ 6 1 interpreted the interaction between methyl mercaptan and an evaporated film of nickel in the following terms. At temperatures in the range 193 to 293 K (-80 to + 20 C) the formation of methane was oscribed to the reaztion: CH3SH

+

Ni

NiS + CH4

The formation of hydrogen at 313 K ( 4 0 C) and higher was written as 2 CH3SH Tungsten

+

Ni --? NiS holds

+

methyl

CH3SCH3

+

H2

mercaptan

tenaciously; in the temperature range

257

313-363 K (40-90 C) carbon-hydrogen bonds are broken with the evolution of hydrogen and the average composition of the chemisorbed surface phase left behind is C0.62H1.25S. The effect of active elements in an additive substance on a clean massive metal surface was investigated by Buckley [ 7 , 8 1 , using Auger analysis of secondary electrons ejected from the surface by the impact of a primary beam. This is a sensitive technique for detecting elements present in the uppermost surface region of a solid substance; in fact, the response is so sensitive that elaborate and severe cleansing of the specimens must be carried out in vacuum to eliminate interference by elements such a s oxygen, carbon and sulfur which ordinarily contaminate metal surfaces. In working with iron, for instance, the specimen was bombarded with ionized argon at 2.67 Pa (0.02 torr) until only the peaks characteristic of iron were seen in the Auger electron spectra. The effect of minute quantities of reactive substance is readily detected: e . g . one Langmuir of oxygen (one Langmuir is equal to one second of exposure at 1.333 mPa). The diameter of the primary beam used by Buckley was 0.1 mm; hence the surface could be examined selectively. For example, the effect of sliding on surface interaction could be followed by focussing the beam on a moving track just behind its contact with a rider. For oxygen the Auger intensity was proportional to the logarithm of exposure over the range from 0.1 to 10,000 Langmuirs, with no difference in the oxygen found on the track for static exposure and exposure during sliding. On static exposure to hydrogen sulfide the Auger intensity is also 1ir.early proportional to the logarithm of exposure, as seen in Fig. 11-la. But when the rider moves over the track at 0.5 cm/s, the hydrogen sulfide coverage at the higher exposure levels decreases significantly. Methyl nercaptan has a discontinuous surface coverage behavior, both under static and under sliding conditions, a s shown in Fig. 11-lb.

IO-'~10

lo2 lo3 1 0 ~ 1 0''0~1

1

10

lo2 lo3 id

Exposure, Longmuirs Figure 1 1 - 1 . Adsorptive interaction of sulfur compounds with iron surfaces. Detection of sulfur retained adsorptively on iron surfaces by Auger spectroscopy. The sliding friction experiments were run at 0.5 cm/s, 0 . 9 8 1 N, 2 9 6 K. ( a ) Hydrogen sulfide. ( b ) Methyl mercaptan. From data by D. H. Buckley [ E l .

258

The Auger electron spectra are indicators of the interaction of chemically reactive substances such as oxygen, hydrogen sulfide and alkyl nercaptans with activated iron surfaces. We can also apply the known facts about the dissociative adsorption of H2S and CH3SH on activated netal films to inferences that aid in understanding some of the fundamental modes of action of reactive organosulfur groups. Thus, Buckley's observation [8] that prolonged heating at 523 K (250 C ) after exposure to H2S did not diminish the amount of sulfur in the iron surface i s an indication of a chemical Fe-S linkage rather than the adsorption of the H2S a s such. Buckley also reported that no evidence of the presence of carbon was found after exposure of the iron surface to CH3SH, another indication of the course taken by the dissociative reaction. The direct reaction of additive type-substances and additives with metal surfaces in various physical states has been carried out at elevated temperatures by techniques that range over a broad spectrum of elegance and sophistication. For example, Balandin, Kukina and Malakhova [91 investigated the reaction of di-n-butyl sulfide and of n-butyl mercaptan with bulk iron powder at 613-688 K (340-415 C). The volatile products were saturated hydrocarbons, unsaturated hydrocarbons and hydrogen; the products on the surface of the iron were identified a s FeS and FeS( 1 + x) ( x < 1). Fukuda 1101 demonstrated the following reaction for diethyl sulfide on tungsten powder at 523-573 K (250-300 C): C2H5SC2H5 --) 2 C2H4

+

H2

+

S(fixed)

The fixed sulfur is bound to the tungsten a s a surface layer with the average composition W8S. Secondary reactions subsequently produce ethyl mercaptan, ethane and H2S, and the average composition of the solid surface changes to W4S. No direct data for the decomposition of alkyl halides by clean, active metal surfaces seem to be available. Campbell and Kemball [lll, in their study of the hydrogenolysis of ethyl chloride, cite evidence for the dehydrochlorination reaction CZH5C1

C2H4 + HC1

on evaporated films of iron or nickel at 473-573 K (200-300 C). analogous reaction with t-butyl chloride (CH3)3C*C1

+ (CH3)2C=CH2

+

The

HC1

is fast and occurs easily on nickel at 273 K, but the reverse reaction is also fast and the equilibrium constant at low temperatures favors t-butyl chloride [12]. Auger spectroscopy was used by Buckley to study the interaction of the following chlorine compounds with sputter-cleaned iron surfaces: methyl chloride, ethyl chlcride, vinyl chloride and benzyl chloride [7, 131. With the exception of benzyl chloride, these halogen compounds left

259

carbon as well as chlorine on the iron. Table 1 1 - 1 summarizes the obserin each case the intensity of the Auger vations reported by Buckley. peak for carbon is taken as unity and the corresponding chlorine intensity is adjusted accordingly. In the case of benzyl chloride n o carbon peaks were observed and the chlorine intensity for vinyl chloride is taken as unity for these comparisons. COMPARATIVE AUGER PEAK INTENSITIES FOR THE TABLE 1 1 - 1 . INTERACTION OF ORGANIC CHLORIDES WITH IRON Chlorine compound

Relative Auger peak intensity for 10,000 Langmuirs exposure Static

Sliding

C Methyl chloride Ethyl chloride Vinyl chloride Benzyl chloride

c1 6.00 2.75

1 1 1 -

0.53 12.5(a)

C

c1

1 1 1 -

7.68 2.68

4.40 3.20fa)

Computed from original data by Buckley [ 7 , 131. The carbon intensities are arbitrarily adjusted to unity and the corresponding comparative chlorine intensities are computed with respect to this base. (a) Computed with the original corresponding intensity for vinyl chloride as unity. a)

Vinyl Chloride 0 Ethyl Chloridea

c

I 1

0

I

10

lo2 lo3 104105 Exposure, Langmuirs

Figure 11-2. Adsorptive interaction of organic chlorides with iron surfaces. Detection of chlorine retained adsorptively on iron surfaces by Auger spectroscopy. The sliding friction experiments were run at 0.5 cm/s, 0.981 N , 296 K. From data by D. H. Buckley [ 7 , 131.

Figure 11-2 shows how these organochlorides with surface by sliding and chloride, which also shows is in line with what would electrophilic phenyl group

exposure and sliding affect the interaction of iron. The difference in chlorine bound to the by static adsorption is smallest for benzyl the highest overall level of adsorption. This be expected of the activating influence of the on the benzyl-type carbon-chlorine linkage.

260

Ethyl chloride shows the same kind of linear response to static exposure but at a much lower level. Under static conditions vinyl chloride is adThe two-stage sorbed more readily on the metal than is ethyl chloride. interaction seen with vinyl chloride under sliding conditions may indicate its polymerization on the surface when the exposure factor is high enough. Sputter-cleaned surfaces and evaporated metal films cannot be regarded as characteristic of ordinary rubbing interfaces, and hence the pertinence of the behavior described above to additive action in technological context might be questioned. However, it should be kept in mind that lubrication under practical conditions is a complex mix of phenoaena and therefore clues frcm controlled experimentation should not be discounted in exploring mechanisms and explanations. The general concept of the activation of metals by rubbing is a credible postulate; f o r example, Schrader, Grund and Tetzner [ 1 4 ] increased the catalytic activity of nickel powder f o r the hydrogenation of benzene to cyclohexane by vibratory milling, the increased activity being ascribed to augmentation of the surface activity of the nickel rather than to augmentation of the surface area. The simple compounds whose interactions with activated metal surfaces have been described in the foregoing paragraphs can be regarded a s "type-examples" of the chemical structures encountered in additives, and the interactions observed can be extended to the elucidation of more complex substances under conditions less strictly controlied. The intrinsic complexity of additive/metal interactions under dynamic rubbing conditions probably means that the description and analysis of additive action even in fairly simple tribological situations The difficulties in the will not be entirely free of conjecture. elucidation of additive/metal interaction are illustrated by the work of Buckley [ 7 , 8, 131; for no matter how elegantly the presence of the active element (sulfur, chlorine, carbon) in the surface of the metal is demonstrated, it does not reveal the path by which that element got there from the additive substance as originally put into the system. The appropriateness of a conjecture o r an experimental investigation can be tested by questions such as the following: How is the initial encounter of the additive molecule with the metal surface treated? What is known about the interaction immediately subsequent to the initial encounter? How is the interaction affected by the duration of contact and by the local temperature? I s there further interaction, of the additive and secondary products or of secondary products directly, with the metal surface? In the section immediately following we shall try to establish a reasonable background for conjecture about additive mechanisms by examining the relation of chemical structures of type-substances and the interaction with metals.

261 11.2.

CHEMICAL STRUCTURES IN ADDITIVES AND MECHANISMS OF ADDITIVE ACTION

The predominant majority of lubricant additives are organic compounds, having in their structural constitution the elements carbon and hydrogen, a characteristic they share with the petroleum hydrocarbon oils that usually are the carrier fluids for the additives. But in addition to carbon and hydrogen, the additives that enhance the lubrication functionality contain key elements such as sulfur, chlorine, phosphorus, nitrogen, etc. Although these key elements are a convenient basis for formal classification of additive type-substances, this alone is not adequate for the systematic study of additive action. The structural relations within the additive compound must also be considered. It is with this in mind that we begin with an examination of compounds containing sulfur, the key element most frequently encountered in commercial lubricant additives. 11.2.1.

Sulfur Compounds:

Chemical Reactions

Table 1 1 - 2 shows the more important sulfur type-structures occurring in sulfur-containing additives.* The table does not include all the TABLE 1 1 - 2 .

STRUCTURES IN ORGANOSULFUR ADDITIVE TYPE-COMPOUNDS

Structure type

Structure type

Structure

s-s

Elemental sulfur ( S 8 )

/

\

S

s

\

s-s

/

Structure

Thioacid

s

-C

s

\.

SH S

I/

Mercaptan (thiol)

RSH

Monosulfide

RSR

Disulf ide

RSSR

Polysulfide

RSSxSR

x

= 1,

-C

I/ 2,

\

Thioketone

OH

>c=s

3...

various sulfur structures that have been proposed for lubricant enhancement; only those that are widely used commercially o r significant from a fundamental point of view are shown. Elemental sulfur, which finds fairly extensive use when dissolved in mineral oil, is not a simple substance, as its octatomic molecular formula shows. Mercaptans are among *Only structures in which sulfur is the sole additive key element Additive structures with more than a single key are shown in Table 1 1 - 2 . element are discussed later in this chapter.

262

the simplest of the organosulfur structures but are not used commercially because of their odor and their oxidative instability. The structure most important for additive action is the organic sulfide, R S n R (n = 1 , 2 , 3...), which i s found among the products of the reaction between elemental sulfur and organic substrates such as olefinic hydrocarbons, olefinic acids and olefinic esters [ 1 5 1 . The thioacid structures, although mentioned in the older discussions of the sulfurization reaction, are currently regarded as having little significance in either the theory of sulfurization or the practice of lubrication. The thioketone structure has been identified in the products of the sulfurization of certain olefinic hydrocarbons which have been proposed as extreme-pressure additives [ 1 6 , 171. The influence of the organic moiety R on the additive activity can be explored by examining some specific types of organic sulfide. Let us look first at the simple monosulfides. When R is a simple aliphatic group, there are three types of carbon-sulfur bonds possible, as shown below for the isomeric butyl sulfides: H

I

H

1

C3H7*C-S-C.C3H7

I

I

H

H

(primary)

$"3

7H3

HC-S-CH

y 3

y 3

CH3.C-S-C.CH3

I

I

I

'ZH5 'ZH5 (secondary)

CH3

I

CH3

(tertiary)

R may also be an aryl group such as phenyl, or an alkyl-aryl group, e . 5 . benzyl :

(diphenyl sulfide) A

(dibenzyl sulfide)

saturated cyclic structure such as thiacyclohexane

\ CH \2 CH

CH

/s

is easily recognized as a variant of the secondary alkyl structure. Thiophene is an example of heterocyclic sulfur compounds that behave as aromatics: HC-CH

II

II

CH

HC

\ / S

Let us compare the structures of a dialkyl monosulfide and its responding disulfide: RCHZSCH2R

RCH2S*SCHZR

cor-

263

Assuming that the most active sites in these molecules are in the immediate vicinity of the sulfur atoms, it is apparent the two carbonsulfur bonds plus the sulfur-sulfur bond of the disulfide constitutes an advantage over the two carbon-sulfur bonds of the monosulfide. T h u s the disulfide has one more mode of reaction available per molecular encounter with a metal surface. The extension of this reasoning to the polysulfide RS-Sx.SR is obvious. Ke must also consider the relative reactivities of the bonds. In the absence of direct data, we can compare bond dissociation energies as a measure of relative reactivity. Table 11-3 shows some pertinent data collected from various sources [la, 19, 20, 211. The carbon-sulfur dissociation energies for n-alkyl monosulfides and n-alkyl mercaptans lie within a narrow range. Whether the other sulfur linkage is to carbon, as in n-alkyl monosulfides, o r to the hydrogen of a mercaptan has no major influence. There is a small but perceptible trend toward weaker bonding with secondary carbon (isopropyl) and with rertiary carbon (t-butyl) in the unsymmetrical methyl aryl monosulfides, a trend that is not firmly evident in the in the corresponding alkyl mercaptans. The vinyl-sulfur TABLE 11-3.

BOND DISSOCIATION ENERGIES IN VARIOUS ORGANOSULFUR COMPOUNDS

Bond

Structural type

Dissociation energy, k J/mo 1e

s,- s

Elemental sulfur

117-147

RSS-SSR

Dimethyl tetrasulfide

151

RS-SR

Disulfides

280-289

R-SR

Alkyl monosulfides

293-306

iso-C3H7-SCH3

sec-Alkyl monosulfides

280

t- C4Hg- SCH

t-Alkyl monosulfides

272

vinyl methyl sulfides

218

Phenyl methyl sulfide

25i

C6H5CH2S-CH3

Benzyl methyl sulfide

213

R-SH

Alkyl mercaptans

289-310

iso-C3H 7-SH

sec-Alkyl mercaptans

297

t-C4H9-SH

t-Alkyl mercaptans

289

CH3CH=CH-SH

vinyl mercaptans

218

Phenyl methyl sulfide

335

Benzyl ethyl sulfide

222

Ss/

CH3CH=CH-SCH 3 C6H5S-CH3

C6H5CH2-SC2H5

264

linkage, R-CH=CH-S-, is much weaker than the saturated alkyl-sulfur bonding. I n the unsymmetrical methyl aryl monosulfides R-S-CH3, R being phenyl or benzyl, the S-CH3 bond is weaker than it is in the unsymmetrical dialkyl monosulfides. The dissociation energy of the phenyl-sulfur bond is 333 kJ/mole ( 8 0 kcal/mole), whereas that of the RCH2-S bond in benzyl ethyl sulfide is only 222 kJ/rnole (53 kcal/mole). There is a distinct difference between the S-S bond in disulfides, with a bond dissociation energy of 280-290 kJ/mole (67-69 kcal/mole) and the S - S bond of higher polysulfides with a dissociation energy of 151 kJ/ mole (36 kcal/mole), as in di-n-butyl tetrasulfide, for example. The value of 117-147 kJ/mole shown in Table 11-3 for elemental sulfur is postulated as the dissociation energy required to break an S-S bond and transform the cyclic molecule S 8 into the linear biradical a s 8 . The interior sulfur atoms of the polysulfide RS-Sx-SR show chemical reactivity similar to that of elemental sulfur: c . 9 . blackening of a copper strip. Di-n-octadecyl tetrasulfide, which has been isolated a s a crystalline solid with a melting point of 45.3 C and a sulfur content of 20.07% di-n-octadecyl (theoretical 20.15%), was quantitatively converted to disulfide, melting point 62.4 C , by reaction with copper powder at 100 c [221. The di-n-octadecyl disulfide was not decomposed further by copper even at 150 C. The abstraction of the internally linked sulfur from the higher polysulfides by copper is the basis of the “active” sulfur determination. I t is usually postulated a s a heterogeneous reaction at the surface of the metal; however Kende, Pickering and Tobolsky [I91 showed that homogeneous thermal decomposition of dimethyl tetrasulfide occurred at temperatures as low as 325 K (52 C). Trivecte and Coran [231 studied the exchange reaction C2H5S3C2H5

+

C3H7S3C3H7-

2 C 2H 5S 3C 3H 7

at 405-421 K (132-148 C ) under conditions such that the mechanism proceeded via purely thermal dissociation to thiyl radicals. But it has been observed that sulfur is removed from di-n-octadecyl tetrasulfide less rapidly by iron powder than by copper powder 1221, which indicates that the nature of the metal also has a noticeable influence. Most of the studies of the interaction between metallic iron and organic monosulfides or disulfides are based on the premise that the rate of formation of iron sulfides (FeS, FeS2) is a valid measure of additive reactivity. This was the premise used by Dorinson and Broman [24] in their comparison of the reactivities of di-t-octyl disulfide and di-noctyl disulfide with iron powder. The kinetic data for 25% of additive in white oil fitted the following equations: 10,853 Loglo k

=

16.684 -

[di-t-octyl disulfide]

~

T

(1

1-la)

265

10,454

-!oY~~

k = 12.694

-

-

[di-n-octyl disulfide

T

(11-lb)

where the units of the reaction rate constant k are gram-atoms of sulfur per cm' of iron surface per minute of reaction t me and T is the reaction temperature in degrees Kelvin. The reaction with di-t-octyl disulfide was carried out in the temperature range 4 3 3 - 4 5 3 K , with di-n-octyi disulfide at 4 8 3 - 5 2 3 K. At these temperatures the reaction of di-t-octyl disulfide i s 1 1 0 0 to 1 5 0 0 times faster than that of di-n-octyl disulfide. This result cannot be predicted from the carbon-sulfur and sulfur-sulfur Although this type of bond dissociation energies shown in Table 11-3. invescigation does not directly answer the question of whether i t is encounter r?nd adsorption of additive at the metal surface or subsequent deep-seated bond rupture that is the rate-controlling process, the fact that for a lubricant formulation containing 2 5 5 additive the kinetics of formation of iron sulfide are pseudo-zero-order supports the conjecture that adsorption is the fast step and that it is the slower C-S bond rupture which governs the observed reaction rate.

Sulfide

%

-

Di-n-butyl disulfide Diphenyl disulfide Di-t-butyl disulfide

Reacted

8.5 8,5 37.5

Sulfide Dibenzyl disulfide Di-t-nonyl polysulfide Elemental sulfur

% Reacted

37.5 77.1 63.0

Additive furnishes 0 . 4 8 wt-% sulfur to the solution. Reaction: 3 hours at 4 7 3 K ( 2 0 0 C ) . Data by Mould, Silver and Syrett [ 2 5 1 . Table 11-4 shows some reactivity data for disulfide solutions in white oil heated with steel filings for three hours at 4 7 3 K [ 2 5 1 . The postulated reaction is R S ~ Rj 2 R'

+

n

-s-

with the free-radical sulfur eventually going to form iron sulfide, which is determined analytically at the end of the reaction. There are discrepancies between the extent of reaction listed in Table 11-4 and the comparative bond dissociation energies shown in Table 1 1 - 3 , particularly for di-t-butyl disulfide and dibenzyl disulfide. According to Table 11-3, dibenzyl disulfide should be more reactive than di-t-butyl disulfide, but evidently the computed bond dissociation energies are only rough indicators of high-temperature chemical reactivity at a metal surface. The bond energies correctly identify the sluggishly reactive sulfides ( e . 5 . di-n-butyl disulfide, diphenyl disulfide) but do not differentiate well among the moderately active and quite active sulfides. Very active additives such a s the di-t-nonyl polysulfide and dissolved

266

TABLE 11-5.

REACTION OF ORGANIC SULFIDES WITH ACTIVATED STEEL PCWDER

Sulfide

Temperature , deg. K

Products

Dibenzyl disulfide

403 423

Dibenzyl monosulfide Dibenzyl monosulfide, toluene, (Fe-S) (a)

Dibenzyl monosulfide

423 443

Toluene, (Fe-S) Toluene, bibenzyl, (Fe-S)

Di-t-butyl disulfide

423

Di-n-butyl disulfide

423

Isobutene, isobutane, t-butyl mercaptan (Fees) n-Butyl mercaptan C4 hydrocarbons, Pe-S)

443

D i - n - bu t y 1 mono su fide, n-butyl mercaptan C4 hydrocarbons, Fe-S)

Di-n-octyl disulfide

423, 443

n-Octyl mercaptan n-octane, (Fe-S)

Diphenyl disulfide

403, 423

Thiophenol

(a) FeS o r FeS2 or a mixture.

From data by Forbes and Reid [261.

elemental sulfur correlate well with conjectures based bond energies shown in Table 11-3.

on

the

relative

Forbes and Reid [26] studied the reaction of tetradecane solutions of various monosulfides and disulfides with iron powder that had been activated by prolonged grinding under pentane. Table 11-5 summarizes the most significant results. The organic decomposition products were isolated and identified by gas-liquid chromatography. Mostly they are what e . 5 . dibenzyl monosulfide from an experienced chemist would expect: dibenzyl disulfide, bibenzyl from dibenzyl monosulfide, t-butyl mercaptan and isobutene from di-t-butyl disulfide, and thiophenol from diphenyl disulfide. Hydrocarbons such as toluene from the dibenzyl sulfides and isobutane from di-t-butyl disulfide obtain their hydrogen from the catalytic decomposition of the pentane adsorbed by t h e iron during g r nding or from the dehydrogenation of the tetradecane carrier fluid. Su fur bound firmly to the iron was determined by combustion; hence the ron sulfides could not be uniquely identified a s FeS o r FeS 2' The mechanism proposed by Forbes and ileid [ 2 6 1 is plausible but not rigorously demonstrated. The initial step is adsorption: R

I

SI

Fe

R

I

?I

Fe

267

The S - S link is not broken and the disulfide is held on the iron surface by coordinate bonding. However, this must be something else than straightforward chemisorption; Forbes and Reid reported no retention of either dibenzyl disulfide or diphenyl disulfide by the iron surface at 323 K (50 C ) . At 373 K ( 1 0 0 C ) the iron held more than a monolayer of organosulfide without evolution of decomposition products. At a suitable temperature the S-S linkage of the adsorbed disulfide undergoes homolytic scission : R

R

I

I s

?

Fe

Fe

I

I

What follows depends on the nature of the radicals held by the metal surface and on the environment. If the R-S bond is weak, the R' radical will leave the surface. If i t encounters a source of hydrogen, it can be converted to the hydrocarbon RH. Or two radicals may disproportionate to form RH and the corresponding olefin. Radical dimerization may occur to give R-R. The sulfur is left combined with the iron a s an inorganic iron sulfide. But if the R-S bond is strong enough and a source of hydrogen is available, the mercaptan RSH will leave the surface of the metal and enter the carrier fluid. The valence bond R-S-Fe may also be formed and the adsorbed radical will then become a mercaptide.

Time, minutes

Fiyure 11-3. Reaction kinetics of sulfur compounds by the hot-wire tech2: Didodecyl nique. 1 : 0.75% Elemental sulfur in white oil, 763 K. 3: Uncompounded white disulfide, 1 % S; diphenyl disulfide, 1% S; 763 K . 4: 0.75% Elemental sulfur in white oil, 703 K. 5: 0.75% oil, 763 K. Elemental sulfur in white oil, 633 K. From data by Sakurai and Sat0 1281.

268

Sakurai and co-workers [ 2 7 , 2 8 1 , using Barcroft's hot-wire technique [291, observed pseudo-zero-order kinetics for the reaction of organosulA wire of known diameter and resistivity is fur compounds with iron. heated to the desired temperature by passing an appropriately calibrated electric current through it. If a layer of high resistance reaction product forms on the surface, the effective conducting cross-section of the wire is reduced and a higher voltage will be required to maintain the current. The area of the reacted cross-section can be calculated from the changed resistance and thereby the thickness of the reaction layer can be computed. I f the sample of lubricant is large enough so that the additive concentration is not depleted sensibly by the reaction, then for pseudo-zerc-order reaction kinetics the square of the thickness of the reaction layer will be a linear function of reaction time, a relation which follows directly from the geometry of a circular annulus. Examples in which such a relation holds are seen in Fig. 11-3. However, uncompounded white oil also forms a reaction layer on the heated wire, which obscures any quantitative inferences about the mechanism of the reaction of organosulfur compounds that might be drawn from the results of a hotwire experiment. 11.2.2.

Sulfur Compounds:

Lubricant Additive Action

The connection between the influence of additive structure on additive/metal interaction and the functionality of the additive in the lubrication process has not been developed to the extent that would be anticipated, considering the wide-spread use of extreme-pressure additives in commercial practice. Most of :he comparisons are based on empirical correlations with results from standard lubricant bench-test machines silch as the four-ball machine, the Timken machine, the Falex machine, etc. One of the deficiencies in such data is the inability to maintain a constant contact pressure between the rubbing specimens during the course of the test. Another disadvantage is the arbitrary character of the evaluative criteria. Dorinson and Broman [ 2 4 ] investigated the additive efficacy of di-t-octyl disulfide and di-n-octyl disulfide by a pin-and-disk procedure in which the contact pressure could be maintained and the course of wear could be plotted via progressive multipoint measurements, so that reliable wear rates with basic significance could be computed. Table 11-16 shows some of the data they obtained. Di-toctyl disulfide is consistently the more effective antiwear additive. However, the ratio of the wear rates with the two disulfides i s much smaller than the ratio of 1100-1500 to 1 found for their relative reaction rates with iron powder (see Eqns 11-la and 11-lb). A rational explanation for this can be extracted from the asperity junction-inhibition theory discussed in Chapter 10, Section 7 by taking only the first term of E q n 10-19

269

TABLE 11-6. EFFECT OF DISULFIDE P.DDITIVES ON WEAR RATE Lubricant

Contact pressure, MPa

Wear rate, nm/s

Wear rate ratio

AISI 1141 steel, rubbing speed 25.4 cm/s 9% Di-t-octyl disulfide 9% Di-n-octyl disulfide White oil

896 896 896

223 607 678

1 .oo 2.70 3.02

Hardened AISI 1095 steel, rubbing speed 65.0 cm/s 23% 23% 23% 23%

Di-t-octyl Di-n-octyl Di-t-octyl Di-n-octyl

disulfide disulfide disulfide disulfide

2861 2861 2586 2586

483 9195 406 8128

1 .o 19.1 1 .o 20.0

Wear is measured by the increase in the radius of the scar on the end of a conically-tipped pin. From data by Dorinson and Broman [241.

["R]

=

mk1k2 mk2 + Ck3

6

( 1 1-2)

from which we obtain kl;

=

4

mk1k2 mk2 + Ck3

( 1 1-3)

Since m and k , are constsnt for fixed rubbing conditions (fixed pairs, fixed contact pressure, fixed rubbing speed), we can write

w;

metal

k2 =

( 1 1-3b!

Kw mk2 + Ck3

The value of Ck3 for di-t-octyl disulfide and for di-n-octyl disulfide at a given temperature can be computed from Eqns 11-la and 11-lb. Because these equations were fitted to data f o r 25% additive in white oil, adjustment for concentration uses the fact that the rate of a pseudo-zero-order reaction is a linear function of concentration. Let us select 498 K (225 C ) a s the temperature; the computed values of Ck3 are and 4.72 x lo-' gram-atom of sulfur per cm2 p e r minute for a 7.35 x 23% solution of di-t-octyl disulfide and di-n-octyl disulfide respectively. Let us utilize these values in the analysis of the relative wear rates for hardened AISI 1095 steel at 2586 MPa shown in Table 11-6. From Eqn 11-3b we get

=

20

where the subscripts t and n refer to the tertiary and the normal

disul-

270

fides respectively and it is assumed that K, is the disulfides. Also ( C k 3 ) * = 1 5 5 0 ( C k 3 ) , and therefore nk2

=

for

same

the

two

80.5(Ck3),

The influence of the comparative reactivity of the two disulfides is apparent from the following relation: 80.5(Ck3),

+

1550(Ck3)n I

80.5(Ck3)n

+

20

(Ck3),

The term (Ck3), has hardly any effect on the magnitude of the denominator, whereas in the numerator the value of 1 5 5 0 ( C k 3 ) , swamps the term 8 0 . 5 ( C k 3 ) , . The part that relative chemical reactivity plays in additive action can be explored in still another way. Let us take a value of 0 . 0 0 0 4 3 3 second a s the time required for the full circumference of the track on the disk to pass under the contact area of the rider; this corresponds to a circumference of 1 0 . 1 6 cm rotating at 6 5 cm per second. I n that time 1 . 9 1 x l o - ' gram-atom of sulfur from di-t-octyl disulfide will have reacted per cm2 of surface at a temperature of 4 9 8 K. The lattice constant of iron is 0 . 2 8 6 nm ( 2 . 8 6 8 ) ; hence there are 1 . 2 2 x 1 0 1 5 reaction sites per cm 2 , Thus the track can acquire a film of FeS 9 layers deep. Calculated in similar fashion, di-n-octyl disulfide reacts with 7 . 4 5 x 1 0 l 2 sites per cm2, which is only 0 . 0 6 % of the sites availzJle. In contrast to the foregoing treatment of the additive action of disulfides by an explicit physical and chemical model, the usual approach to interpreting results from lubricant bench testing is to look for empirical correlations. Table 1 1 - 7 shows some data obtained by Mould, Silver and Syrett 1 2 5 1 from experiments with organosulfur additives in the four-ball test. The additives are listed in order of inTABLE 1 1 - 7 .

FOUR-BALL TEST DATA FOR ORGANOSULTUR COMPOUNDS

Additive None Di-n-butyl disulfide Diphenyl disulfide Di-t-butyl disulfide Dibenzyl disulfide Di-t-nonyl polysulfide Elemental Sulfur

Wear/load index, kg (a)

Wear scar diameter, mm (b)

14.4 21.4 24.2 31.2 40.6 41.7 56.4

0.77 0.79 0.59 0.61 0.34 0.75 0.90

(a) 1 5 0 0 rpm; 60 seconds at each load in the procedure. (b) 1500 rpm; one hour at 1 5 kg load. Additive furnishes 0 . 4 8 % sulfur to the lubricant. Data by Mould, Silver and Syrett [ 2 5 1 .

271

creasing effectiveness according to the wear/load index (mean Hertz load). Comparison of Table 1 1 - 7 with Table 1 1 - 4 shows no systematic relation between the relative chemical activity of the additives and their performance in four-ball testing. There is an overall trend for the wear/load index to increase with increasing reactivity of the additive but the 15-kg wear test does not show a parallel correlation. An elaborate system of differentiation has been built around two different techniques with the four-ball tester [ 3 0 , 3 1 , 321. The series of 60-second runs with progressively increasing loads is designated as a load-carrying or extreme-pressure test because differentiation in the efficacy of additives is seen in the highly loaded portion of the test procedure. The prolonged test under 1 5 kg load is identified as a wear test.* The relative ranking of the load-carrying or EP performance of some organosulfides, obtained from the location of the curves in the These rankings wear/load diagram of Fig. 1 1 - 4 , is listed in Table 1 1 - 8 . correlate well with the bond dissociation energies shown in Table 11-3 and they f i t satisfactorily with the mechanism of deep-seated chemical decomposition by reaction at the surface, as postulated by Forbes and 3.2 3.0

2 -8 2.6 2.4

f 2.2

g 2.0

c

18 . 0

$ 1.6

p

1.4

-

1.2 1.o 40

120

I I 200

I I 280

-

I > 360

Load, kg Figure

Load-carrying action of organosulfides in the four-ball Additives test. "Extreme-pressure" procedure: 60 seconds at 1 5 0 0 rpn. furnished 1 . 1 9 % s u l f u r to the lubricant. a: Base oil. 1 : Di-n-butyl 4: Dibenzyl sulfide. 2: Diphenyl disulfide. 3 : Di-n-butyl disulfide. 5: Di-t-butyl disulfide. 6: Dibenzyl disulfide. 7: Diallyl sulfide. disulfide. From daEa by E. S. Forbes [ 3 2 ! . 11-4.

*Obviously both types of test are wear tests. Unless it can be demonstrated on fundamental grounds that there is a basic difference in kind rather than degree between the two, the classification is an arbitrary one.

272

TABLE 11-8. COMPARISON OF FOUR-BALL TESTS OF ORGANIC SULFIDES Sulfide

Relative ranking, EP test (a)

Wear test scar diameter, mm (b)

~

0.623 0.560

Diallyl disulfide Dibenzyl disulfide Di-t-butyl disulfide Dibenzyl monosulfide Di-n-butyl disulfide Diphenyl disulfide Di-n-butyl monosulfide (a) c ( j . Fig. 11-4.

0.865 0.509

__--_

(b) From data by ?.1lum and Forbes [31].

Reid [26]. But the low-load one-hour wear data, also listed in Table 11-8, are not in the same relative rank order as the EP data. Because of the empirical and arbitrary character of the four-ball test, it is probable that the contact and rubbing parameters have not been identified precisely enough for a quantitative formulation of the mechanism of additive action. 11.2.3.

Chlorine Compounds:

Chemical Reactions

Chlorine compounds are well established in the lexicon of extremepressure additives. A wide range of chemical structures has been investigated by bench testing: alkyl chlorides, aryl chlorides, chloroolefins, chlorine-substituted fatty acids, acid chlorides, chlorinesubstituted heterocycles, etc. However, investigations of the fundamental modes by which chlorinated additive substances function are scanty. Mostly, therefore, we must resort to conjectures from limited and highly specialized studies such as the work of Buckley [131 described in Section 11.1. The technologically important types of chlorinated additives are alkyl and aryl chlorides of fairly simple structure, and conjectures from their basic chemistry can be reasonable and useful. Simple alkyl chlorides decompose smoothly over a suitable catalyst to an equilibrium mixture of olefinic hydrocarbon and hydrogen chloride: for instance, isobutene in equilibrium with t-butyl chloride [33], propylene with isopropyl chloride and ethylene with ethyl chloride [341. Catalysts were glass wool and a mixture of nickel, cobalt and cadmium chlorides. When a metal is substituted for the chloride catalyst and the equilibrium is disturbed by removal of the olefin, the net result observed is reaction of the HC1 with the metal. Mould, Silver and Syrett [351 heated solutions of organochlorine compounds for 6 hours at 473 K in the presence of steel filings which were then washed free of oil and analyzed for inorganic chloride; the reactivities thus found are shown in Table 11-9. The order of reactivity is what an organic chemist would expect from reactions involving the elimination of HC1. The thermodynami-

273

TABLE 11-9.

REACTIVITY OF OIL SOLUTIONS OF ORGANIC CHLORIDES WITH STEEL

Compound(a)

X Reaction

Benzyl chloride t-Butyl chloride t-Pentyl chloride Cyclohexyl choride Chlorinated paraffin ( 5 1 % C 1 ) sec-Butyl chloride Carbon tetrachloride n-Butyl chloride n-Hexyl chloride Chlorobenzene

C-C1 bond dissociation energy, kJ/mole

51 49 47 30 25 23 15 15 9

--_

0

37 1

29 1 329

-__ 335

-__ 334 306 339

(a) 0 . 0 1 5 gram-atcn of chlcrine per 1 0 0 grams of oil solution. by Mould, Silver and Syrett [ 3 5 1 .

Data

cally calculated C-Cl bond strengths do not sensitively indicate the relative reactivities: for instance, the difference between the carbonchlorine bond strengths for benzyl chloride and t-butyl chloride is greater than the difference between the reactivities would lead one to suspect, and the relative reactivities of the secondary chlorides with respect to the primary chlorides show greater spreads than do the C-C1 bond energies. But in general the C-C1 bond energies parallel the reactivity toward iron, as a comparison of the chemically inert chlorcbenzene with the reactive benzyl chloride demonstrates. Prutton, Turnbull and Dlouhy 1 3 6 1 studied the chlorine balance in the thermal decomposition of oil solutions of chlorinated additives in the presence and the absence of iron powder. A summary of their results is shown in Table 1 1 - 1 0 . The effect of iron in promoting the l o s s of chlorine from chlorinated paraffin wax is evident at both 4 7 3 K and 5 2 3 K, the reaction being more pronounced at 5 2 3 K. On the other hand, iron has no influence on the decomposition of chlorine tightly bound to the TABLE 1 ! - 1 0 .

REACTION AND THERMAL DECOMPOSITION OF

O I L SOLUTIONS ‘3F GRGANIC CHLORIDES

Additive

Chlorinated paraffin wax Chlorinated paraffin wax Chlorinated diphenyl ether

Temperature, % of C1 in additive dedeg. K composed to HC1 i n absence of Fe 473 523 523

0.5 2.4 0.2

% of C1 in additive decomposed in the presence of Fe

to HC1

to iron total chloride

---

-__

4.3 0.04

6.4 0.02

2.5 10.7 0.06

3% Chlorine in the oil solution; heated at the temperature indicated for 1 5 minutes. From data by Prutton, Turnbull and Dlouhy [ 3 6 1 .

214

0

10

20

Time, minutes

Figure 11-5. Reaction kinetics of chlorine compounds by the hot-wire technique. 1, 3: 1% Benzyl chloride. 2: 1 % Hexachloroethane. 4: 1 % Chlorinated paraffin. 5: 1 % Pentachlorodiphenyl. a: Carrier oil without additive. From data by Sakurai, Sat0 and Yamamoto [ 3 7 1 . aromatic nucleus of chlorinated diphenyl ether. Figure 11-5 shows some data obtained by Sakurai, Sat0 and Yamamoto [ 3 7 1 that illustrate the influence of the nature of the carbon-chlorine bond on the reactivity of the chlorinated additive in the hot-wire I t is evident the reactivity of the chlorine bound directly procedure. to an aromatic ring-carbon in pentachlorodiphenyl is less than the reactivity cf the chlorine bound to non-ring carbon in hexachloroethane or benzyl chloride. 11.2.4.

Chlorine Compounds:

Lubricant Additive Action

Systematic data on the relation between chemical structure or reactivity of chlorine compounds and lubricant additive performance are sparse. Table 1 1 - 1 1 gives some four-ball test data obtained by Mould, Silver and Syrett [351, with the additives listed in order of increasing effectiveness in terms of tne wear/load index. The results show numerous departures from expectations based on chemical structure. For example, there is practically as much difference between the wear/load indices for the two primary chlorides, n-hexadecyl (16.2 kg) and n-hexyl (30.4 kg), A large difas f o r n-hexyl chloride and t-butyl chloride (46.1 kg). ference would be expected on the basis of chemical reactivity between the additive effectiveness of primary and tertiary alkyl chlorides, but only a small difference for the two primary aliphatic chlorides. The overall trends are what would be expected: in general, primary and aromatic chlorides are less efficacious than secondary chlorides, which in turn

275 TASLE 1 1 - 1 1 .

FOUR-BALL TZST DATA FOR ORGANOCHLORINE COMPOUNDS

Additive

Wear/load index, kg (a)

Wear scar diameter, m m (b)

14.4 16.2 17.8 22.5 25.8 29.9 30.4 31.5 31.6 34,4 35.9 37.8 46.1 46.6 52.8

0.77 0.64 0.70 0.73 0.74 0.65 0.75 0.73 0.74 0.69 0.73 0.60 0.74 0.66 0.70

None n-Hexadecyl chloride n-Butyl chloride Chlorobenzene 1,4-Dichlorobenzene Carbon tetrachloride n-Hexyl chloride 1,4-Dichlorobutane sec-Octyl chloride Cyclohexyl chloride sec-Butyl chloride Chlorinated paraffin (51% C 1 ) t-Butyl chloride Benzyl chloride t-Pentyl chloride

1500 rpm; 60 seconds at each load step in the procedure. (b) 1500 rpm; one hour at 15 kg load. Additive furnishes 0.53% chlorine to the lubricant. Data by Mould, Silver and Syrett 1351. (a)

are not as good as tertiary alkyl chlorides and benzyl chloride. However, the relation between chemical reactivity and structure of organic chlorides found in Table 11-9 is more sharply delineated than the No sigrelation between structure and wearjload index in Table 1 1 - 1 1 . nificant relationship can be seen in Tables 11-9 and 1 1 - 1 1 between the one-hour wear test at 15 kg load and the chemical structure o r the chemical reactivity of organic chlorides. Some of the factors which complicate the interpretation of the fourI

I

I

2.5

-

2.0

-

-

t 1.5 -

-

&

E

x

8 cn

1.0

-

0.5 0

_____----I

I

I

Figure 11-6. Behavior of octyl chlorides in the four-ball test. 8.52% t-Octyl chloride: 2 seconds - A . 10 seconds - . - * 8.48% n-Octyl chloride: 2 seconds - 0 . 10 seconds - - - Both chlorides: 2 seconds -0. Both chlorides: 2 seconds and 10 seconds Data by Doririson

.

1381.

.

.....

276

ball test were studied by Dorinson [38], using white oil solutions of noctyl chloride and the tertiary octyl chloride 4 - m e t h y l - 4 - c h l o r o h e p t a n e . The influence of applied load was investiga ed for rubbing times of 2 seconds and 10 seconds. The results, as shown n Fig. 11-6, fall in line with the postulate that the more chemically act ve t-octyl chloride is a better extreme-pressure additive than n-octyl chloride. There is no difference in the antiwear action at the lower loadings, which explains the 15 kg wear results of Table 11-11, but when the applied load becomes sufficiently severe, the inadequacy of the primary chloride as an additive is manifest by the sharp increase i n the magnitude of the wear scar. I n crease of the rubbing time from 2 seconds to 10 seconds shifts the overall wear transition to a lower load. I n summary, the significant aspect of the four-ball "extreme-pressure" lubricant test is not the value of the wear/load index by the set testing procedure but rather the load and the rubbing time at which transition to a regime of high wear occurs. 11.2.5.

Phosphorus Compounds:

Chemical Reactions and Additive Action

Compounds with phosphorus as the key element that have been investigated for extreme-pressure additive activity add up to arr impressively long list. But only a few of them have turned out to be of practical utility and these are predominantly esters o f phosphoric acid o r derivatives of thiophosphoric acid. I n this section we shall be concerned only with those compounds in which phosphorus i n combination with oxygen constitutes the key structure; dithiophosphates and related derivatives are The four main types of phosphorus oxyacid discussed in Section 11.2.6. esters treated in the present section are shown i n Table 11-12. Phosphoric and phosphorous acids are trifunctional; hence there are three o r ganophosphorus structures to be considered: the neutral triester, the monoacidic diester and the diacidic monoester. I n Section 10.6 of the preceding chapter it was shown that tricresyl phosphate, a widely used organophosphorus additive, left an interaction In film of ferrous phosphate on the steel surface that i t iubricated. terms of a mechanism generally applicable to the esters of phosphorus oxyacids, two reaction paths immediately suggest themselves. One is the thermal decomposition of the ester linkage, catalyzed by the activated metal interface:

RO-PO*(OR)2

+

Fe /Fe-OPO*(OR)2

+

R + , R', etc.

The other is a hydrolytic mechanism involving water vapor in the atmosphere: RO-PO*(OR)2

+

H20+HO-PO*(OR)2

ambient

+ ROH

The acid phosphate diester then reacts with the iron surface. fate

In principle the two mechanisms can be differentiated by tracing the of the organic moieties. The thermal reaction would eventually

277

TABLE 11-12.

TYPE STRUCTURES FOR PHOSPHORUS OXYACID DERIVATIVES

Phosphate esters

P=O,

( RO )

( RO )

P-OH , RO-P ( OH ) I1 0

0

Phosphite esters

0

II

ll (R0)3P, (R0)2P-H, RO-P-H \

OH 0 OR

Phosphonate esters

\\ / R-P \

R-P

\

R Phosphinate esters

0 OR

\\ / OR

O

R

\ If

/

/

R

OH

\

OH

O

\ I/

P-OR

0 OH \\ / R-P

P-OH

R

R is used as a generalized symbol for an organic group; generalized structure may be different.

each

R

in

the

produce an olefin from the carbonium-ion intermediate R+ o r a dimer R - R The product of the hydrolytic mechanism is the from the free radical R'. hydroxylic derivative ROH. However, lubrication tests are not ordinarily carried out in a fashion that allows neat identification of additive decomposition products , and therefore the evidence to firmly establish the mechanisms in the additive action of organophosphorus compounds is generally full of gaps. A n indirect approach to the role of thermal decomposition in the action of aryl phosphates is based on the theoretically easier scission of the PO-R linkage when R is an alkyl group. Gamrath, Hatton and Weesner 1391 cite data for the thermal decomposition of 2-ethylhexyl diphenyl phosphate into 2-ethyl-1-hexene and diphenyl phosphate. Triphenyl phosphate, when heated in vacuum with iron powder, volatilizes unchanged at about 473 K (200 C); i f a thermal decomposition had taken place, the expected volatile product would be biphenyl. On this basis, i f the additive action of a neutral phosphate ester proceeds by a thermal decomposition mechanism, alkyl phosphates should be more efficacious than aryl phosphates. The difficulty of utilizing this rationale lies in a finding test of additive efficacy that is basic rather than empirical and arbitrary. Un-

278

fortunately, most of the usable comparisons of the additive action of organophosphates and related compoands recorded i n r;he literature have been carried out with the four-ball lubricant tester and are vulnerable to criticism; this drawback extends to much of the data discussed in the subsequent paragraphs of this section. TABLE 11-13.

FOUR-BALL EVALUATION OF ALKYL AND ARYL PHOSPHATES

Ester

Tri-n-butyl phosphate Tricresyl phosphate Di-n-butyl phosphate Base oil

Wea r/load Initial Wear scar diameter, mm (b) index, kg (a) seizure load, kg 30 min. 45 min. 60 min. 13.8 14.1 ---10.4

40 40

--

30

0.39 0.25 0.37 0.25(c)

0.42 0.27 0.39 ----

.

0.47 0.28 0.43 0.76

P in white oil (16.21 cs/37.8 C ) . (a) 60 second runs at 1500 rpm. (b) 15 kg load at 1500 rpm. (c) 20 minutes. Data by Forbes and Silver 1401.

0.124%

Forbes and Silver [40] published data directly comparing the alkyl ester tri-n-butyl phosphate and the aryl ester tricresyl phosphate. Table 11-13 shows the details of this comparison as well a s wear data for the acid ester di-n-butyl phosphate. The wear/load index and the initial seizure load show substantially no discrimination between tributyl phosphate and tricresyl phosphate and very little advantage of the compounded oil over the base oil. The low-load wear test distinctly shows better performance with tricresyl phosphate. The data for di-n-butyl phosphate are at variance with the hypothesis that hydrolytic degradation to the acid ester is the first step in the antiwear action of neutral phosphate esters. On the other hand, Bieber, Klaus and Tewksbury 1411 separated acidic constituents from commercial tricresyl phosphate by preparative chromatography, and on blending these constituents back into the original tricresyl phosphate at various concentrations they observed enhancement of antiwear action in the four-ball test, a s shown in Fig. 11-7. It should be noted that Bieber e t a L . worked with only 0.051% phosphorus in the lubricant, which may explain the sensitivity they observed to acid impurities. The tricresyl phosphate of commerce is not a pure substance, being in part made up of the mixed cresyl-phenyl esters. Also, Bieber, Klaus ar,d Tewksbury [411 showed that in addition to about 0.3 weight-percent of diaryl acid phosphate, the impurity contributed about 0.3 weight-percent of diaryl chlorophosphate to the additive. The possibility that the chlorine in the acid impurities of commercial tricresyl phosphate was in[411 cannot be disvolved in the effect observed by Bieber e t a[. regarded. Sanin, Shepeleva, Ulyanova and Kleimenov [421 reported that

279

-

Mineral Oil

-------

, , -

-/----

0.4 cn

Reference

L

/

0

4” 0.2

-

/

/-.

0.1

1 /--v 1

2

I

4

/-

Hertz Diameter I 6 8 10 20 Load, kg

I l l

I I l l 40 60 80

Figure 1 1 - 7 . Influence of acidic constituents on the additive activity of tricresyl phosphate. Four-ball wear test: 1 hour at 620 rpm. Reference lubricant: 0.065% tricresyl phosphate in rust-inhibited nineral oil. <0.02 Mole-% acidic constituent i n tricresyl phosphate 0.1% Mole-% acidic constituent in tricresyl phosphate 0. 0.3 Mole-% acidic constituent in tricresyl phosphate A . From data by Bieber, Klaus and Tewksbury [ 4 1 1 .

..

organic compounds containing both phosphorus and chlorine reduced wear at heavy loads in tne four-ball “extreme-pressure” test. For example, the initial seizure load was found to be 40 kg higher with diethyl (trichloromethy1)phosphonate than with :he unchlorinated ester. An even stronger effect would be expected with an acid chloride such as dicresyl chlorophosphate. Goldblatt and Appeldoorn [431 prepared neutral tricresyl phosphate free of acidic contaminants by percolation through silica gel and compared its adsorption on iron powder with that of an acid phosphate. The phosphorus ccncentration i n the carrier fluids was at the extremely low level of 15-30 ppm and the amount of iron powder was sufficient to remove 50% of the phosphorus in the solution i f a monolayer of additive were adTABLE 11-14. COMPARISON OF UNTREATED AND DE-ACIDIFIED TRICRESYL PHOSPHATE IN THE FOUR-BALL TEST %

Additive in white oil

Wear scar diameter, mm i 0 kg

1% Untreated TCP 1 % Dc-acidified TCP 0.1% untreated TCP 0.1% De-acidified TCP 0.01% Untreated TCP 0.01% De-acidified TCP

0.20 0.21 0.25 0.25 Scuff Scuff

i 5 kg

____

____ 0.30 0.28

_-__ _-_-

20 kg

25 kg

0.32 0.33

Scuff Scuff

Scuff Scuff

Test run for 15 minutes at 1 2 0 0 rpm in an atmosphere of dry argon. From data by Untreated TCP: 0.038 mole-% dicresyl phosphate. Goldblatt and Appeldoorn [431.

280

sorbed. Neutral tricresyl phosphate was not removed from the solution, whereas two-thirds of the acid phosphate was transferred to the iron. In another experiment, the additive action of silica-gel-treated tricresyl phosphate in light white oil was compared with that of untreated tricresyl phosphate; the results are shown in Table 11-14. The tests were run in an atmosphere of dry argon to eliminate the influence of oxygen and water vapor. Deacidified tricresyl phosphate cannot be differentiated from untreated tricresyl phosphate at any of the concentrations and loads used. The overall response to concentration shows that there is an additive effect. From these results one would conclude that direct reaction with the rubbing surface rather than prior adsorption of acidic decomposition product is the mechanism by which organophosphate esters function as additives in the four-ball test. In

terms

of initial contact pressure, the four-ball test even at a

load of 10 kg is carried out under severe conditions. Dorinson [44] used slow-speed friction in a pin-and-disk test as the method of interpreting the additive action of neutral and acid phosphate esters under mild conditions, triphenyl phosphate and diphenyl phosphate being the compounds studied. Both are solids, readily purified by recrystallization and uniquely identifiable by melting point, phosphorus content and acidimetry. With a white oil solution 0.002 molal in triphenyl phosphate a s the lubricant, stick-slip friction was observed consistently at rubbing speeds up to 0.423 cm/s when the rider was in contact with a virgin disk surface, i.e. with a contact track that had not been subjected to rubbing at high speeds. Diphenyl phosphate in white oil at the same concentration started with stick-slip friction on a virgin track, but after a very short sliding distance the friction became smooth with a steady value of ulZ = 0.221-0.246 in the speed range 0.017-0.212 cm/s. The discrepancy between these results and four-ball wear and scuffing behavior can in part be attributed to the sensitivity of the frictional response to the transition from stick-slip to smooth sliding. When the rider lubricated by the solution of triphenyl phosphate that gave stick-slip friction at slow speeds on a virgin track was run f o r 3 0 minutes at 30.48 cm/s, friction during subsequent sliding in the speed range 0.017-0.212 cm/s was entirely steady and free from stick-slip. These experiments were carried out in ambient air of 25-35% relative humidity at 22-24 C. The slow-speed frictional behavior described above is consistent with the intrinsic chemical inactivity of the neutral phosphate esters relative to the acid esters. The change in the behavior with triphenyl phosphate after rubbing at 30.48 cm/s can be ascribed to either direct reaction of the triphenyl phosphate with the metal surface or its hydrolysis by the water vapor in the ambient air. The positive effect observed by Bieber, Klaus and Tewksbury [411 for the enhancement of the additive activity of tricresyl phosphate by its acidic impurities in con-

281

trast to Goldblatt and Appeldoorn's report of no enhancement [431 could be due to the difference in acid level: u p to 0.3 mole-% a s dicresyl phosphate in the additive used by Bieber 2 t a t . but only 0.038 mole-% in the experiments of Goldblatt and Appeldoorn. However, Bieber e t n e . report lubrication enhancement for as little as 0.02% mole-% acid impurity. We turn now to the comparison of phosphate esters with esters of other phosphorus oxyacids, namely phosphites, phosphonates and phosphinates. Phosphites are distinguished from phosphates by a lower formal valence number ( i . e . by a basically different bonding structure), whereas in phosphonates and phosphinates the Fhosphorus is formally pentavalent, as in phosphates. Phosphonates and phosphinates have direct carbonphosphorus bonding, while the linkage of the organic groups in the phosphate esters is all of the carbon-oxygen-phosphorus type. A direct comparison of the sdditive behavior of neutral phosphates and phosphites in the four-ball test under relatively mild conditions is reported in the work of Goldblatt and Appeldoorn 1431. The data shown in Table 11-15 are their findings for 3% of the additive dissolved in a heavy white oil and run in the four-ball machine for 15 minutes at 1200 rpm. In wet air all the phosphates show about the same wear improvement under a 10 kg load over wear with the base oil; in dry argon there is no significant improvement. Tributyl phosphite functions consistently poorer in the wear test than either triallyl or triphenyl phosphite, whose behavior is not significantly different from that of the c'orresponding phosphates. All the additives improve the performance of the

TABLE 11-15. COMPARISON OF ADDITIVE ACTIVITY PHOSPHATE AND PHOSPHITE TRIESTERS

0'7

Additive

%

P

Wear scar diameter, mm

Scuff load, kg

Wet air

Wet air

Dry argon

Dry argon

None

0

0.49

0.32

30

30

Phosphates Ally1 Butyl Phenyl Cresyl

0.43 0.35 0.39 0.25

0.38 0.34 0.35 0.36

0.33 0.33 0.30 0.29

60

70 50 50 60

Phosphites Allyi Butyl Phenyl

0.47 0.38 0.31

0.30 0.41 0.35

0.32 0.42 0.28

60 60 70

60

60

60 60

45 45

3% Additive in white oil (35.8 c p at 25 C). Four-ball test: 15 minutes at 1200 rpm; wear test with 10 kg load. Data by Goldblatt and Appeldoorn [431

282

3.0

kl

c

01

6 2.0

6

B

sI B

1.0

s! 01

I 1

I

I

I

2

3

4

1

5

% Additive

Figure 11-8. Comparison of phosphate and phosphite triesters as addiAdditives in solvent-refined mineral oil. Four-ball test: 60 t ives. seconds at 1500 rpm. 1: Tributyl phosphate, 120 kg. 2: Tricresyl phosphate, 120 kg. 3 : Tricresyl phosphate, 100 kg. 4: Tributyl phosphate, 100 kg. 5: Trixylenyl phosphate, 120 kg. 6: Trixylenyl phosphate, 1 0 0 kg. 7 : Tr ibuty 1 phosphite, 140 kg. 8: Tributyl phosphite, 120 kg. 9: Tributyl phosphi te, 100 kg. Data by W . Davey [451. base oil in the scuffing test; there is no overall significant pattern except for the smaller improvement with tributyl and triphenyl phosphites in dry argon. No overall conclusions can be drawn about the influence of the organic group or the valence state of the phosphorus. Also, the comparison is somewhat obscured by the differences in the phosphorus content of the various test oils. On the other hand, Davey [451 found a distinct difference in the additive action of neutral phosphate and phosphite esters in severely loaded testing with the four-ball machine, as shown in Fig. 11-8. At the loads used, the wear scars for the phosphate esters were large and the wear behavior was of the seizure type, irrespective of the additive concentration or the nature of the ester group. But with tributyl phosphite as the additive, wear dropped steeply with increasing additive concentration to a relatively low level at 1.0-1.5% additive and then remained almost unaffected by further increase of concentration up t o 5%. Forbes and Battersby [46] found that dialkyl phosphites were consistently better antiseizure agents than the corresponding dialkyl phosphates (see Table 11-16). At the antiseizure load limit in the four-ball test there is a transition from smooth wear with a relatively small scar diameter to wear that produces a large, rough scar. There is a parallel in the findings of Forbes and Battersby for the effect of acidic dialkyl phosphates and phosphites on the initial seizure load and the high-load results of Davey f451 for the nuetral triesters. But in the 60-minute low-load wear tests of Forbes and Battersby [461, the shorter chain dialkyl phosphites allow larger wear scars than do the dialkyl phosphates, a difference that substantially vanishes for the dilauryl esters.

283

TABLE 1 1 - 1 6 . COMPARISON OF ANTISEIZURE AND ANTIWEAR ACTION OF DIALKYL PHOSPHITES AND DIALKYL PHOSPHATES ~~

Additive Diethyl phosphite Diethyl phosphate Dibutyl phosphite Dibutyl phosphate Di(2-ethylhexyl) phosphite Di(2-ethylhexyl) phosphate Dilauryl phosphite Dilauryl phosphate

~~

Initial seizure load, kg (a)

Wear scar diameter, mm (b)

225 160 135 55

0.70 0.43 0.64

0.42

125

0.36

80 130

0.29 0.32

80

0.32

Lubricant blends: 0 . 0 4 mole P per 100 grams of white oil. (a) Fourball test: 6 0 seconds at 150C rpm from each load step. (b) Four-ball test: 60 minutes at 15 kg load, 1 5 0 0 rpm. Data by Forbes and Battersby [461.

TABLE 11-17.

ADDITIVE ACTION OF DIALKYL PHOSPHITES

Phosphite ester

Molal Wear/load Initial seizure Wear scar, mm ( b ) concentration index, kg (a) load, k g (a)

Base oil

C

10.4

30

3.72

ili ethyl

0.001 0.010 0.040

16.0 24.6 79.0

45 70

225

0.52 0.57 0.70

0.001 0.010 0.040

13.5 23.8

50.2

40 70 155

0.43 0.44 0.64

0.001 0.010 0.040

11.6 19.7 40.3

35 55

0.67 0.40 0.36

0.001 0.010 0.040

13.5 33.3 46.5

40 100 730

0.32

Distearyl

0.001 0.010 0.040

13.4 27.8 51.9

40 80 145

0.73 0.35 0.29

Dicyclohexyl

0.01 0.010 C. 0 4 0

14. i 18.1 33.4

40

Dibutyl

Di(2-ethylhexyl)

Di lauryl

125

0.69 0.32

50 95

(a) Four-ball test: 60 seconds at 1 5 0 0 rp!n for each load step. (b) Four-ball test: 60 minutes at 15 kg load, 1 5 0 0 rpm. Data by Forbes and Battersby [ 4 6 1 .

284

The work of Forbes and Battersby [46] is an integrated studp of the relations among the chemical structures of the dialkyl phosphites, their adsorption o n and reaction with iron, and their behavior in four-ball bench testing of lubricant additive effectiveness. The four-ball data in Table 11-17 for solutions of additive in white oil show that both the wear/load index (mean Hertz load) and the initial seizure load are critically responsive to concentration, with a strong effect when the concentration increases from 0.01 to 0.04 molal (0.031% to 0.124% P). The initial seizure load is an uncomplicated criterion with a straightforward interpretation, whereas the wear/load index is contrived, both in concept and performance. The low-load 60 minute wear data show inconsistencies i n the influence of additives that have not been explained. Contact of one cm3 of a 0.025 molar solution of dialkyl phosphite in tetradecane at 403 K (130 C ) with one gram of i r o n powder which had been ball milled under pentane resulted in depletion of the phosphorus in solution, a s shown in Fig. 11-5. Reaction as well a s adsorption took place, for soluble iron was found in the soiutions of di(Z-ethylhexyi), dilauryl and distearyl phosphites. Chromatography of the solutions after contact revealed large quantities of alcohol; dibutyl phosphite and di(2ethylhexyl) phosphite yielded 52-97% of the theoretical amount of alcohol after 24 hours. Hydrolysis of the phosphite esters was ascribed to w a t e r adsorbed on the walls of the reaction tube and on the iron powder. Forbes and Battersby [ 4 6 1 postulated that hydrolysis is an important aspect of the mechanism of the additive action of phosphite esters. Oxidation to phosphate by the oxygen of the ambient air is deemed minor; maximum augmentation of the oxygen uptake by a 6.5% solution of dibutyl phosphite over that of the tetradecane carrier fluid in the presence of iron was 20%. The easy hydrolysis of phosphites is well known. Partial

100

I

I

I

I

I

4

8 12 16 20 Test Durotion.hrr

I

80 .c

: a

.-

60

c

2 s

40

c

20

8 '0

24

Figure 11-5. Course of the reactive adsorption of dialkyl phosphites on ground iron. From data by Forbes and Battersby 1 4 6 1 .

285

hydrolysis is postulated as producing an adsorbed film of the type RO

G

\ // P

/ \ O H Fe and complete hydrolysis results in H

\

?

H0

P

/ \

I

Fe

? ,

Fe

Forbes and Battersby heated diethyl phosphite with ground iron powder at 453 K (180 C ) to produce a flammable gas which may have been hydrogen and a solid whose composition and other properties was compatible with the formula

Longer chain dialkyl phosphites reacted more slowly and products were isolated.

no

identifiable

Data on the additive action of phosphonate and phosphinate esters that can be used f o r comparative purposes or for conjectures on the mechanism of action are scarce. Sanin, Shepeleva, Ulyanova and K1eimeno.i [421 reported four-ball test data that demonstrate the antiseizure action of some organophosphonates; the initial seizure load of 69 kg observed with the base oil is raised to 108-110 kg by the incorporation of 0.06 moles of dibutyl methylphosphonate or dibutyl butylphosphonate into 100 grams of lubricant. Lozovoi, Shepeleva and Sanin [ 4 7 1 reported an augmentation of the initial seizure load from 84 kg to 120-125 k g by the addition of 0.06 moles per 100 grams of diethyl phenylphosphonate or diethyl tolylphosphonate. Forbes and Silver [ 4 0 1 made a systematic comparison of organic phosphonates, phosphates and phosphinates based on the results of the 6 0 minute four-ball wear test under a 15 k g load at 1500 rpm. On plotting the wear data for n-butyl di-n-octylphosphinate, di-n-butyl nhexylphosphonate, di-n-butyl phenylphosphonate, diethyl benzylphosphosphate phonate, diethyl o - n i t r o p h e n y l p h o s p h o n a t e and tri-n-butyl against the ionization constants of the corresponding parent acids (exThis led pressed as pK,), the solid curve of Fig. 11-10 was obtained. them to the hypothesis that the involvement of carbon-phosphorus bonding

286

pK,, o f Parent Acid

Figure 11-10. Comparison of organic phosphates, phosphonates and phosphinates as lubricant additives. Four-ball test: 60 minutes, 15 kg load, 1500 rpm. 4 mmoles of additive per 100 gm of white oil solution. Neutral esters 0 . Acids or acid esters A . 1: n-Butyl di-n-butylphosphinate. 1': Di-n-hexylphosphinic acid. la: Di-n-octylphosphinic acid. 2: Di-n-butyl n-hexylphosphonate. 3 : Di-n-butyl phenylphosphonate. 4: Tri-n-butyl phosphate. 4': Di-n-butyl phosphate. 5: Diethyl benzylphosphonate. 6: Diethyl o - n i t r o p h e n y l p h o s p h o n a t e . 7': Di(2-ethylhexyl) phosphate. 8': Dilauryl phosphate. 9: Tricresyl phosphate. From data by Forbes and Silver [401 and by Forbes and Battersby [46].

of phosphonates and phosphinates in additive action is not on the basis of ease of bond cleavage but through the influence o n the ionization constant of the organophosphorus acid. Data for di-n-octylphosphinic acid, di-n-hexylphosphinic acid and di-n-butyl phosphate fall reasonably close to the curve for neutral esters. The dibasic organophosphonic acids could not be tested because of their insolubility in oil. Diethyl benzylphosphonate lies significantly off the curve. Tricresyl phosphate, di(2-ethylhexyl) phosphate and dilauryl phosphate do not give data near the curve at all. 11.2.6. Phosphorus and phorodithioates), etc.

Other

Key

Elements:

Dithiophosphates

(Phos-

In this section we discuss compounds with key elements other than oxygen linked directly to phosphorus. Of these elements, the most important is sulfur, and of the phosphorusjsulfur compounds the most important are the metal salts of diesters of dithiophosphoric acid (phosphorodithioates), which are used extensively in commercial practice. These have the general formula S

OR

It / M-S-P\ OR

which in the systematic chemical nomenclature is designated as a metal salt of an 0,C-diester of phosphorodithioic acid. The two sulfur atoms are linked to the phosphorus by bonds of different character: the thiolo-

287

sulfur has an acidic function and thus is linked free acid S

I/ /

with

the

metal.

The

OR

HS-P\

OR is unstable at elevated temperatures; hence for lubrication the phosphorodithioate ester is used in the form of its metal salt. The zinc salt is the type of additive most widely used in commercial practice. The empirical formula ZnP2S404R4 can be written in the following structural format: RO

S

\J\ P

RO

/ \ / S

OR

S

Zn

/ \ /

\4\ S

P

OR

The steric configuration of lead 0,O-diisopropyl dithiophosphate [481 is consistent with this structure for the divalent salt.* Zinc phosphorodithioate esters were originally incorporated in automobile engine oils as antioxidants, and their usefulness a s antiwear For and antiscuffing additives was discovered by experience in service. anEioxidant service it was found that dialkyl esters of chain length in the range C 4 - C 6 were the most useful, and practical experience with antiwear performance has accumulated around zinc dialkyl dithiophosphates of this general type. Most of the fundamental knowledge about metal diester phosphorodithioates as antiwear additives has also been developed with zinc dialkyl dithiophosphates. For instance, Gallopoulos 1491 concluded that zinc dialkyl dithiophosphates in organic hydrocarbon solvents are covalent rather than ionic in character. Another important finding, reported by Heilweil [ 5 0 ] , is the association of metal derivatives of dialkyl dirhiophosphates in organic solvents. Osmometry of benzene solutions show trimers of zinc dialkyl dithiophosphates in equilibrium with dimers and monomers. Barium di-n-dodecyl dithiophosphate in cyclohexane forms micelles large enough to be measured by light scattering. The metal salts of the phosphorodithioate esters are among the most intensively studied of the lubricant additives. But the reader should be aware that in purity the preparations used have ranged from carefully synthesized, single-component, crystalline substances of known identity to heterogeneous commercial mixtures prepared in a mineral oil medium from which they were never separated. In the commercial process the diester of phosphorodithioic acid is prepared by treating the appropriate

*The outer electron shells of zinc and lead are similar this comparison to be valid.

enough

for

288

hydroxylic component (an alcohol or a phenol) dissolved in mineral oil with the so-called phosphorus pentasulfide (actually P4Slo). The zinc salt is made by the reaction of powdered zinc oxide with the crude ester. In the laboratory preparation of pure salts of phosphorodithioic esters, each intermediate is isolated purified and identified. and the hydroxylic compound to The reaction between P4S phosphorodithioic diester can be written formally as RO 8 ROH

+

P4Slo 3 4

\ RO

OS

P

/ \

form

the

2 H2S

SH

I n fact, however, some triester (R0)2P(S).SR and probably some polymeric product is also formed. I n careful synthetic work, the esterification is carried out by slowly adding the theoretical amount of P4Sl0 to the hydroxylic compound ROH. I f the hydroxylic reactant is a liquid, it acts as its own solvent for the reaction; otherwise an appropriate inert solvent is used. I n preparing pure phosphorodithioic esters, useful intermediates are the ammonium salts, which are well defined solids formed by the action of dry gaseous ammonia on the crude initial esterification product. These salts can be purified by recrystallization from a solvent such a s benzene. The metallic salt is prepared by metathesis in aqueous solution at carefully controlled pH; for example:

RO

S

\ 2

// P

+

ZnC12

-+ Zn[SP(S)(OR)2]2

+

2

NH4C1

In the case of zinc salts prepared in an aqueous medium, it is probably impossible to keep the product free from the basic zinc salt I f the neutral zinc phosphorodithioate ester is a Zn2[SP(S)(OR)2]30H. solid, crystallization from an appropriate solvent usually suffices to separate i t from the basic compound. In some instances--e.y. zinc di-nbutyl phozphorodithioate-it is difficult to get the preparation to crystallize. The basic zinc dibutyl dithiophosphate can be selectively precipitated by the addition of methanol. In comzerciai preparation, where the neutralizing reactant is powdered zinc oxide and the stoichiometry of the acid reaction mixture is not known accurately, the basic zinc salt is unquestionably a constituent of the final product. Investigations of the thermal decomposition of zinc dialkyl dithiophosphates of high purity were carried out by Luther and Sinha [ 5 1 1 and by Dickert and Rowe [521. I n general the findings of these two investigations are in agreement. Table 11-18 shows the volatile products isolated and identified during the homogeneous thermal decomposition of

289

TABLE 1 1 - 1 9 . PRODUCTS OF THERMAL DECOMPOSITION OF DI-n-BUTYL AND DIISOBUTYL ZINC PHOSPHORODITHIOATES

3

Di-n-butyl

Diisobutyl

Di-n-butyl sulfide n-Butyl mercaptan Butene- 1 Butene-2 Hydrogen sulfide Non-volatile residue

Diisobutyl sulfide Di-t-butyl sulfide t-Butyl isobutyl sulfide isoButyl mercaptan isoButene Hydrogen sulfide Non-volatile residue

hours heating at 4 5 3 - 5 2 3 K.

Data by Luther and Sinha [ 5 1 ] .

-n-

0

80 ;j

0.50

450 475 500 525 450 475 500 525 Temperature,degrees Kelvin Figure 1 1 - 1 1 . Thermal decomposition of di-n-butyl and diisobutyl zinc dithiophosphates. (a) Zinc di-n-butyl dithiophosphate. (b) Zinc diisobutyl dithiophosphate. Three hours reaction at temperature indicated. 1 : Di-n-butyl sulfide. 2 : n-Butyl mercaptan. 3: Butene. 4: Hydrogen sulfide. 5: isoButyl mercaptan. 6: Dibutyl sulfide. 7: Residue. Data by Luther and Sinha [ 5 1 1 .

zinc di-n-butyl phosphorodithioate and zinc diisobutyl phosphorodithioate in the temperature range 4 5 3 - 5 2 3 K ( 1 8 0 - 2 5 0 C ) . Figure 1 1 - 1 1 shows the quantitative distribution of the products; the influence of structure is definitely apparent. However, the level of the non-volatile residue seems to be little affected by whether the ester group is n-butyl o r isobutyl. Luther and Sinha 1 5 1 1 reported empirical formulas of the type ZnPaSbOcCdHe for the non-volatile residues, with the following ranges: b, 1 . 7 - 2 . 6 ; c , 2 . 6 - 4 . 6 ; d, 3.2-10; e, 5.5-15.6. Higher a, 1 . 9 - 2 . 4 ; temperatures promote loss of sulfur, carbon and hydrogen from the residue. Dickert and Rowe [ 5 2 ] , from results with zinc diisopropyl phosphorodithioate at 4 2 8 K ( 1 5 5 C ) , cite evidence for assigning the core structure

290

:

CH3

\CHI

I

0

I

-0-P-S-Zn-S-P-

CH3

CH3 ‘CH’

I 1

0

‘I

I1

S

S

L

to the solid residue. The chemical mechanism of che decomposition of metal salts of dialkyl phosphorodithioates is discussed in some detail by Luther and Sinha [51] and by Dickert and Rowe [521. The aspect of the chemistry of the o r g a n o p h o s p h o r o d i t h i o a t e salts most meaningful for their additive action involves their reaction with metals. Luther and Sinha [ 5 1 ] did not find any significant influence of the substrate metals on the thermal decomposition of isomeric zinc On the other hand, dibutyl phosphorodithioates over iron or silver. careful studies by Baumgarten [53] demonstrate the chemisorption of d i a l k y l p h o s p h o r o d i t h i o a t e salts on netal, either powder or a s evaporated film. Of particular interest are the findings for zinc diisopropyl phosphorodithioate triply tagged with the radioactive elements Zn65, P32 and S35. Within the limits of measurement precision P 3 2 and S 3 5 are adsorbed in a ratio which corresponds to the dithiophosphate: i.e. two atoms of sulfur per atom of phosphorus. But the ratio of Zn65 on the adsorbing surface was found to b e as much as four times that required for equivalence with the phosphorus and sulfur, depending on the individual characteristics of the metal specimen. Baumgarten ascribed this to ionic exchange between metal in the surficial layer of the adsorbent and the zinc of the adsorbate, which might be credible for surfaces contaminated with oxide and water vapor but which seems unlikely for surfaces that were cleaned, dried and carefully protected. Surface reactions in adsorbed films can concentrate species that are present in only traces in the bulk phase of the adsorbate. Francis and Ellison [54] found that ZnO was strongly concentrated in the adsorbed film deposited by basic zinc diisopropyl dithiophosphate on polished surfaces of silver or steel. Neutral zinc diisopropyl dithiophosphate in white oil heated to 393-423 K (120-150 C f gave films on polished metal which contained ZnS04-6H20 and an unidentified decomposition product in addition to the dithiophosphate. Rubbing in the presence of zinc dithiophosphate ester also put an unidentified constituent on polished metal. Investigations of the behavior of metal salts of phosphorodithioate esters along chemical lines have given rise to a number of proposed mechanisms for the action of these substances a s lubricant additives. The views of Baumgarten [ 5 3 ] are quite explicit: a chemisorbed monomolecular film of zinc dialkyl dithiophosphate is quickly e s -

291

tablished, from which an interchange between zinc and metal in the surface takes place by ionic diffusion; during the course of rubbing the adsorbed dithiophosphate is decomposed thermally a s well as by the mechaniThis last cally activated rubbing surface to form a protective layer. aspect of the mechanisn is similar to the scheme of Feng, Perilstein and Adams [551, in which the additive action is ascribed to a deposited layer formed by pyrolytic reactions of the additive in the bulk phase. However, Francis and Ellison [ 5 4 1 expressed doubt that the additive action is really understood. I t is tacitly assumed that the sulfur in phosphorodithioic esters makes an individualistic contribution to the additive action. But direct comparison of the antiwear action of zinc din-butyl dithiophosphate with that of zinc di-n-butyl phosphate in pinand-disk tests over a pressure range from 414 to 1034 Mpa (60,000 to 150,000 lb/in2) revealed no significant difference in the effectiveness of the two lubricants [ 5 6 1 . It would appear from this that sulfur is not an indispensable element in the lubricant additive action of zinc salts of thiophosphate esters, but it remains unresolved whether zinc is essential o r whether the phosphate-thiophosphate structures alone are sufficient to impart antiwear functionality. It is known from practical experience that in general metal salts of phosphorodithioic diesters, particularly the zinc dialkyl dithiophosphates, are effective antiwear and antiscuff additives, but systematic data relating chemical structure with additive performance are rather TABLE 11-19.

FOUR-BALL TESTING OF ZINC PHOSPHORODITHIOATE ESTERS

Ester group B a s e oil n- Pr opy 1 n-Butyl i soButyl isoButyl/pentyl ( b ) n-Oc t y 1 2-Ethylhexyl 2,2,4-Trirnethylpentyl (c) i sopropy1 sec-Butyl 1,3-Dimethylbutyl ( c ) 1-Methylheptyl (c) isoPropyl/l-methylheptyl ( b ) 2-Ethylhexyl/cresyl (b) C6-Cl0 paraffinic/cresyl ( b )

.isoPropyl/p-octylphenyl (b) 2-Ethylhexyl/p-octylphenyl (b) p-Octylphenyl

Initial seizure load, kg (a)

Wear scar at 70 k g , mm

55 90 70 75 75 65 65 55 105 80 70 65 85 70 85

2.26 0.38 1.83

75 70 75

---_ 0.38 1.71 2.07 1.80

----

0.38 2.08 1.90 0.37 1.78 0.37 0.40 1.85 0.40

(a) 1 minute at Blends in mineral oil made up to contain 0.056% P. each load step. (b) Mixed ester groups. (c) Secondary alcohols. F r o m data by Jayne and Elliott [ 5 7 1 .

292

sparse, especially as regards field performance. Systematized studies for the most part have been carried out in the laboratory with standard bench testers. Table 1 1 - 1 9 shows some data obtained by Jayne and Elliott [ 5 7 1 with the four-ball machine. The initial seizure load locates the transition from low wear to high wear; the values for 70 kg load give an idea of the relative magnitude of the wear in these two regimes. No systematic relation is apparent between the character of the ester group and the wear behavior. The amount of phosphorus in these blends is at the extreme lower level of effectiveness for engine oil service, but the additive effect relative to the carrier oil is apparent.

0 80 0.75

0251

I

I

30

45

h

L

6C

Rubbing Time,minutes

Figure 1 1 - 1 2 . Influence of the metal ion on the additive action of dialkyl dithi ophosphates. Four-ball wear test at 15 kg load, 1500 rpm. Additive furni shes 4 mmoles P per 1 0 0 gms white oil solution. a: Bi(II1). b: Sn(I1). c: Sb(II1). d: Pb(I1). e: Ag(1). f: Fe(II1). g: Ni(I1). h: Cd( 11). k: Zn(I1). Data by Allum and Forbes [ 5 8 1 . The influence of the metal ion is seen in Fig. 1 1 - 1 2 , which shows low-load four-ball wear data by Allum and Forbes 1 5 8 1 . The results fall ++ into three broad groups: low wear levels associated with the ions Zn , ++ Cd", Ni", Fe+++ and Ag+; intermediate wear with Pb , Sn", and Sb+++; +++ Where direct comparison for the effect of alkyl high wear with Bi groups are available, they show the ester of the secondary alcohol 4methylpentanol-2 has a stronger antiwear function than the ester of nhexanol, except for the nickel salts. No consistent trend on which to base an acceptable explanation for the additive action of these phosphorodithioates was observed i n the data for the wear/load index (mean Hertz load).

.

Rowe

and Dickert 1 5 9 1 ascribed the antiwear function of metal salts

293

of O,@-dialkyldithiophosphates to their thermal decomposition and presented wear rate data from pin-and-disk experiments in support. The thermal stability data, taken from a separate study by Dickert and Rowe [521, were obtained from the rate of formation of H2S for a series of zinc dialkyl dithiophosphates or from the rate of formation of propylene or H2S for a series of metal diisopropyl dithiophosphate salts. Plots of wear rate against decomposition rate are shown in Fig. 11-13; the log-log plots minimize the scatter of the data. With the exception of the silver salt, there seems to be a systematic relation of the nature of the metal in the diisopropyl dithiophosphates to the rate of formation of H2S or propylene and to the wear rate of the rider, as seen in Figs. 11-13(2) and 11-13(3). Rowe and Dickert [ 5 9 1 found that when the wear rate was plotted against the ionic radius of the cation in log-log coordinates, the lower wear rates were associated with the larger cations. Figures 71-1312) and 11-13(3) include data for the free diisopropyl dithiophosphoric acid i-C3H70\,;SH ,p\

i-C3H70

S

and the corresponding disulfide i-C H 0 3 7 \

0 - i-C3H,

/ P-s-s-P

x 2.5

10-6 10-5 10-4 10-3 10-2

H2S Formation, moles/mole/ min

10-410~ lo-' 1 Propylene or H2S, moks/mole/min

10-410-3 10-2 10-l I Propylene or H$, moles/mole/rnin

Figure 11-i3. Relation between wear testing and thermal stability of metal dialkyl dithiophosphates. (1) Wear of copper pin against steel disk: distance-dependent volume-rate, 8 kg load, 10 cm/s, 366 K , 5 hours. Additives: zinc dialkyl dithiophosphates in n-hexadecane, 0.04% P. a: Z,2-Dimethylpiopyl. b: n-Propyl. c: Ethyl. d: 1,2,2-Trimethylpropyl. e: 1,3-Dimethylbutyl. f: isoPropy1. (2) Wear of copper pin against steel disk: distance-dependent volume-rate. Metal salts of diisobutyl dithiophosphate. g: Pb. h: Ag. k: Cd. m: Cu. n: Zn. p: Free diisobutyl dithiophosphoric acid. r: Corresponding disulfide. (3) Wear of steel pin against steel disk: distance-dependent volume-rate. Metal salts of diisobutyl dithiophosphate. Data by Rowe and Dickert [ 5 9 j .

TABLE 11-20.

RO

THERMAL DECOMPOSITION OF METAL SALTS OF DIALKYLDITHIOPHOSPHATES

S-(M)

RO

S-(M)

\ / HC-0

RO

-a

S-(M) P

--

S

I

CH3

H-:-H

CH3

H

I

1 B

2 (CH3)2CH-SH d

i

I CH3

(CH3)2CH-S-CH(CH3)2 + HZS

-

N

(4 D

295

Dickert and Rowe [521 proposed the reaction scheme shown in Table 11-20 for the thermal decomposition of metal salts of dialkyl dithiophosphates. The influence of the cation on the decomposition rate can be explained by the coordination characteristics of the ligand bonding. The influence of the alkyl group Stems partly from the space orientation of the bonds and partly from the number of hydrogens located on a B-carbon atom relative to the hydroxyl, the latter accounting for the differentiation between secondary and primary alkyl esters. However, the mechanism of thermal decomposition does not specifically identify the components that function in the antiwear mechanism. The formation of the mixed sulfur/oxygen pyrophosphate analogue requires exact equivalence between the rates at which olefin and mercaptan are formed. But H2S is formed at rates between 10 and 100 times as rapidly a s olefin-see Figs. 11-13(2) and ll-l3(3)-and furthermore the generation of H2S from mercaptan by a thermal pathway is not in the main stream of the reaction mechanism shown in Table 11-20. It is doubtful that the correlations between the wear rates and the formation of H2S are other than empirical. It is more likely that the species involved in the antiwear action are the ionic intermediates o r a mixture of polymeric thiophosphate derivatives whose composition depends on the relative rates of the steps which generate olefin and mercaptan. The effect of systematically replacing the oxygen in the structure of esters derived from phosphorus oxyacids by sulfur was investigated by Sanin, Shepeleva, Ulyanova and Kleimenov [42] for a series of butyl esters. Solutions of the additives in oil at a concentration of 0.06 mole per 100 grams were evaluated in the four-ball "extreme-pressure" test run at 600 rpm. Table 11-21 shows the action of the esters studied in terms of the critical load of transition to high-wear seizure behavior. Phosphites do not appear to differ greatly from thiophosphites in additive action. The change from the fully oxygenated tributyl phosphate to tributyl thiophosphate, however, is marked by a 33% decrease in the seizure transition load. 11.3.

THE ACTION OF MULTICOMPONENT ADDITIVES

The simplest concept of a multicomponent additive is a straightforward mixture of individual additives each of which contains a single key active element, and in fact many multicomponent additives are just that. But since it is logically possible to have more than one type of key functional group in the same molecule, this is another kind of multicomponent additive to consider. There is a fundamental difference between a multifunctional additive compound of this kind and the additive structure with more than one key element but only a single functional group, such as is found in the zinc dialkyl dithiophosphates Zn[SP(S).(OR),], or the dithiophosphate esters of the type R S - P ( S ) O ( O R ) ~ .

296

TABLE 11-21. INFLUENCE OF SULFUR IN STRUCTURE OF THIOPHOSPHITE AND THIOPHOSPHATE ESTERS ON THEIR ADDITIVE ACTION Ester (C4Hg0)3P (C4HgS)2POC4Hg (C4HgS)3P

Seizure transition, kg 90

108 93

(C4H90)3P=0

102

(C4Hg0)3P=S

82

c~H~sP=s.(oc~H~)~

78

(C4HgS)2P=S*OC4Hg

72

(C4H9S)3P=S

68

Base oil

68

Additives: 0.006 mole in 100 grams base oil. Four-ball test at 600 rpm. From data by Sanin, Shepeleva, Ulyanova and Kleimenov [421.

11.3.1.

Multicomponenr Additives with Sulfur and Chlorine

The work of Prutton, Turnbull and Dlouhy [361 with a full-scale automotive hypoid gear in a shock-loading test is an illustration of the way mixtures of simple compounds of sulfur and chlorine are characteristically employed as multicomponent additives in technological practice. A passing test was obtained with a lubricant containing 3% chlorine as chlorinated paraffin wax and 0.50% sulfur as dibenzyl disulfide, whereas failure was observed with lubricants containing either 0.50% sulfur from dibenzyl disulfide or 3% chlorine from chlorinated wax as singlecomponents additives. i f the 3% chlorine in the multicomponent additive was furnished by chlorinated diphenyl ether, the compounded lubricant did not pass the shock-loading test. It may reasonably be conjectured that the functionality of the chlorinated component of the multicomponent additive is governed by the normal expectations of reactivity indicated by chemical structure. Figure 11-14 shows data obtained by Dorinson I381 in 'an investigation of the cooperative action of di-t-octyl disulfide and t-octyl chloride, two independently effective lubricant additives. The criteria for evaluation are the initial seizure load in the 10-second ASTM fourball test and the magnitude and course of the post-seizure wear. With either 2% sulfur or 2% chlorine as the single active additive element in the lubricant, the post-seizure transition occurs in the load interval 80-100 kg, and the degree of seizure, as judged by the extent of wear, is not severe. With a combination of 1% sulfur and 1 % chlorine in the

297

E 2.5 E

,.

-4

kl 2.0

c

0)

a b

0 v)

1.5 1.0

05 01

1 I 1 I J 100 200 300 400 500 Applied Load, kg

Figure 11-14. Cooperative additive action of t-octyl chloride and di-toctyl disulfide. Four-ball test: 10 seconds at 1750 rpm. Additives in white oil and wear/load index: A. 9.1% Di-t-octyl disulfide, 2.06% S ; 48.0 kg. B. 8.52% t-Octyl chloride, 2.05% C1; 51.9 k g . C. 4.55% Di-toctyl disulfide + 4.53% t-octyl chloride, 1.06% S , 1.00% C1; 81.0 k g . il. 9.1% Di-t-octyl disulfide + 8.52% t-octyl chloride, 2.1% S, 2.0% C1: 112.1 kg. Data by A . Dorinson [361. lubricant, the initial seizure load is raised to 130 kg and the posttransition wear is significantly ameliorated, with concomitant improvement of the wear/load index. The mixed additive exhibits a cooperative or synergistic function beyond what would be predicted from the sum of the individual components. A mixture with 2% sulfur plus 2 % chlorine allows no initial seizure phenomena at all up to 500 kg applied load. Similar experiments were run by Mould, Silver and Syrett [ 6 0 1 using the one-minute four-ball test (see Table 11-22). The initial seizure index shows moderate to loads tend to be ambiguous but the wear/load strong synergistic effects for the combination of dibenzyl disulfide and chlorinated paraffin. The chemical reactivity of the additives was investigated by reaction witn steel filings at 473 K (200 C ) for 6 hours, after which the solvent-washed filings were analyzed for inorganic sulfur and chlorine. Table 11-23 shows the behavior of the additives in terms of the amount of sulfur o r chlorine they contributed to the compounded lubricant that reacted with the steel. For the mixed additives, either chlorinated wax or benzyl chloride prociotes the reaction of di-t-nonyl polysulfide with steel but leaves the reactivity of aibenzyl discllfide unaffected. The effect of di-t-nonyl polysulfide on the reactivity of either of the chlorine compounds is small. The chemical reactivity data of Table 11-23 exhibit a persuasive parallelism with the four-ball test data of Table 11-22, but the synergistic behavior seen in Fig. 11-14 is much stronger than that shown by the results of Mould, Silver and Syrett [GO]. A

simple

question that follows directly from the additive behavior of mixtures of organochlorine and organosulfur compounds is whether

298

TASLE 11-22. FOUR-BALL TESTING OF MIXED ORGANOSULFUR AND ORGANOCHLORINE ADDITIVES Additive (c0nc.S o r C1) (a)

Wear/load index, kg

Intitial seizure load, kg

Di-t-nonyl polysulfide (0.030)

52.0

75

Dibenzyl disulfide (0.030)

48.8

70

Benzyl chloride (0.030)

56.7

65

Chlorinated paraffin (b) (0.030)

47.7

85

Di-t-nonyl polysulfide (0.015) + benzyl chloride (0.015)

78.3

80

Di-t-nonyl polysulfide (0.015) + chlorinated paraffin (0.015)

56.3

85

Dibenzyl disulfide (0.015) + beilzyl chloride (0.015)

64.8

80

Dibenzyl disulfide (0.015) + chlorinated paraffin (0.015)

45.3

80

(a) Gram-atoms per 100 grams of white oil solution. From data by Mould, Silver and Syrett [ 6 0 ] .

(b) 51%

chlorine.

TABLE 11-23. CHEMICAL REACTIVITY OF ORGANOSULFUR AND ORGANOCHLORINE COMPOUNDS TOWARD STEEL --

Additive (conc. S o r C1) ( a )

%

of Element reacted ~-

Sulfur

Chlorine

Benzyl chloride ( 0 . 0 1 5 )

__

51

Chlorinated paraffin ( b ) (0.015)

--

25

Di-t-nonyl polysulfide (0.015)

31

--

Dibenzyl disulfide (0.015)

17

__

Di-t-nonyl polysulfide (0.015) + benzyl chloride (0.015)

44

62

Di-t-nonyl polysulfide (0.015) + chlorinated paraffin ( 0 . 0 : 5 !

69

28

Dibenzyl disulfide (0.015) + benzyl chloride (0.015)

17

51

Dibenzyl disulfide (0.015) + chlorinated paraffin (0.015)

25

23

(a) Gran-atoms per 1 O C grams of white oil solution. From data by Mould, Silver and Syrett 1601.

( b ) 51%

chlorine.

299

the behavior of compounds in which the chlorine and the sulfur are carried by the same molecule would be the same a s or different from the equivalent binary mixture. I n part such questions can be answered by inspection of the chemical structures involved. Thus a structure such as CH3(CH2)n-S-(CH2)mC1 on basic chemical grounds could be expected to function a s the equivalent mixture

But the structure RCH2 SC 1

is a sulfinyl chloride and the chemical activity to be expected of it is o f a kind altogether different from that of a mixture of an alkyl sulfide and an alkyl chloride. Similarly the trichlorothioacetals of structure H SR C13C-C \ SR I

/

prepared and examined by Davey [ 6 1 1 cannot be compared with a mixture of alkyl sulfide and alkyl chloride of the same overall composition because of the basic difference in the type of sulfur bonding. 11.3.2.

Multicomponent Additives with Phosphorus and Chlorine

A considerable body of data has been obtained for the effect of chlorine in phosphorus-containing additives. The structures involved are typically illustrated by the formula of the phosphate ester below

0C2H5 which was cne of a number studied by Sanin, Shepeleva, Mannik and Kleimenov [62]. The chlorine is not part of the phosphate structure; instead it is found at the end of the long alkyl group of the ester structure or on the alkyl g r o u p linked to the phosphorus in phosphonates. Evaluation of the additive acticn was by means of four-ball "extremepressure" tests run at 600 rpm, with the sharp transition to seizure-type wear taken a s the criterion of failure. The data are shown in Table 11-24. The range of structural types included phosphate esters, thiophosphate esters (thiolic and thionic sulfur) and phosphonates; the chlorine linkage was exclusively of %he type -CC13. With the exception of O,O-diethyl-S-(w-trichloroamyl)phosphorodithioate, the presence of chlorine in the structure of the ester groups enhances the additive activity over that of the corresponding unsubstituted esters. Lozovoi, Shepeleva and Sanin [47], by a direct comparison of the phosphonate

300

TABLE 11-24. STRUCTURAL INFLUENCE OF CHLORINE ON ADDITIVE ACTION OF PHOSPHORUS ESTERS ~~

Additive formula

Seizure transition, kg

Additive formula

Phosphate esters

Seizure transition, k g

Phosphonate esters

(cH,),CH(CH,),OPO~(OC~H~)~

150

CH3PO*(OC2H5)2

138

C13CCH20P0.(OC2H5)2

20G

CH3PO-(OC5H11)2

130

C13CCH20PO-(OC4H9)2

225

C13CPO*(OC2H5)2

190

C13C(CH2)40PO*(OC2H5)2

230

CH3P0.(OCH2CC13)2

---(a)

C13C(CH2),0PO*(OC4Hg)2

225

CH3P0.(O(CH2)4CC13)2

190-300 (b)

C13CPO*(OCH2CC13)2

140-300 (b)

Thiophosphate esters (thiolic) C5H,1SPO*(OC2H5)2

150

Thiolo-thionic ester C1,C(CH2)4SPS*(OC2H5)2

130

Base oil

80

c ~ H ~ ~ s P o - ( o c ~ H ~ ) ~1 4 0

c ~ ~ c ( c H ~ ) , s P o * ( o c ~ H ~ )zoo ~

c~,c(cH,),sPo.(oc,H~)~

210

C ~ ~ C ( C H , ) , S P O ~ ( O C H ( C H ~ z)o~o) ~

Thiophosphate esters (thionic) C2H50PS*(OC2H5)2

140

C4HgOPS.(OC2H5)2

120

C13CCH20PS*(OC2H5)2

200

c~~c(cH~)~oPs.(oc~H~ 170 )~ (a) No seizure transition up to 300 kg. (b) No seizure transition; gradual increase of wear in load range shown. Additive: 0.06 mole per 100 grams oil. Four-ball test at 600 rpm. Data by Sanin, Shepeleva, Mannik and Kleimenov 1621.

301

esters showed as the load; C6H5P0

11.3.3.

C6H5P0.(OC2H5)2, C6H5P0.(OCH2CC13)2 and C6H5P0.(OCH2CH2C1)2, that the terminal monochlorinated structure -CH2C1 is as effective trichlorinated structure -CC13 in raising the seizure transition a specific effect in decreasing post-transition wear was seen with *(OC2H5)(0CH2CH2Cl).

Sulfur and Fatty Esters in Multicomponent Additives

The work of Dorinson [63] on the relation between the basic chemistry and the additive action of sulfurized fatty materials deals with one of the most widely used multicomponent lubricant additives in industry. There are two aspects to the multicomponent nature of products of the sulfurization of ethenoid fatty esters. One is the consequence of the complexity of the sulfurization reaction, so that even i f the starting material is a pure fatty ester, the ultimate sulfurized product is a mixture of several species. But the most important aspect of the structure of the sulfurized fatty product is the fact that even were it a single-component substance, it would still be intrinsically rnultifunctional. For instance, Dorinson [631 reported that the product of the sulfurization of methyl w-undecenoate can be shown to contain at least 5 0 % of the following compounds: TH3 iH3 CH,OOC(CH,)~-C-S~-C(CH~)~COOCH~

I

H

t

H

where n is either 1 or 2 . The multifunctionality of the structure above, be it a monosulfide or disulfide, arises from (a) its long-chain ( i . e . fatty) character, (b) the carboxylic moieties, and (c) the organosulfide structure. The long-chain structure by itself, as exemplified by n-aliphatic hydrocarbons, shows no extreme-pressure lubricant functionality. Evidently the additive action is connected with the carboxylate ester and the sulfide structures. To demonstrate this, Dorinson isolated an ester/ sulfide cpmponent from sulfurized metnyl undecylenate, identified its structure, synthesized an organosulfide-ester with this structure, and showed that the lubricant additive activity was the same for the fraction separated from sulfurized methyl undecylenate and for the synthetic material. The data, summarized in Fig. 11-15, were obtained by pin-anddisk wear tests with hardened steel rubbing specimens and show the effect of contact pressure on the depth-rate of wear, The significant feature is the change from a low rate of wear, relatively insensitive to increase of pressure in the range 0 . 2 7 6 - 1 . 7 2 4 GPa ( 4 0 , 0 0 0 - 2 5 0 , 0 0 0 lb/in2), pressure-sensitive increase of wear rate at 1 . 7 2 4 GPa and higher.

to

302

Contact Pressure, GPa

Figure 11-15. Sulfurized fatty esters as extreme-pressure additives. Pin and disk wear test at 85.65 cm/s with hardened steel. I: Sulfurized methyl undecylenate, 1.22% S in lubricant. 1 1 : Sulfurized methyl undecylenate fraction, 1.00% S in lubricant. 111: Synthetic 1,ZOdicarbomethoxy-9,12-dimethyl-lO,ll-dithiaeicosane, 1.13% S in lubricant. Data by A . Dorinson [ 6 3 1 .

Contact Pressure, GPa Figure 11-16. Interaction of organosulfides and fatty esters a s extremepressure additives. Pin and disk wear test at 65.65 cm/s with hardened steel. I: Di-sec-octyl disulfide, 1.17% S in lubricant. 1 1 : Methyl laurate, 8.8% in lubricant. 111: Di-sec-octyl disulfide (17 mmoles/lOOgm) + methyl laurate ( 3 3 mmoles/100 gm), 1.06% S + 7.2% ester in lubricant. IV: Base oil. V: Synthetic 1,20-dicarbomethoxy-9,lZ-dimethyl-lO,ll-dithiaeicosane (18 mmoles/100 gm). Data by A . Dorinson [ 6 3 1 .

The separate action of the organosulfur component and the ester component in the organosulfide-ester structure was studied with di-sec-octyl disulfide and methyl laurate respectively. The results are given by the curves I and I 1 of Fig. 11-16. Up to the liinit of the load capacity of the apparatus, the solution of di-sec-octyl disulfide shows no aneliorating effect relative to the course of wear with uncompounded base oil. Methyl laurate has an inhibitory effect on the wear rate up to a contact pressure of 1.379 GPa (200,000 lb/in2), after which the wear rate increases drasticaliy on further loading and the test terminates with

303

severe scuffing of the rider. But when di-sec-octyl disulfide and metnyl laurate are combined in the ratio of one gram-atom of sulfur for each mole of ester, synergistic interaction lowers the level of wear in the low-pressure domain and increases the transition load so that the behavior of the mixture is substantially the same a s that of the bifunctional synthetic ester-disulfide. Although the information obtained by Dorinson I 6 3 1 is by and large behavioristic, the investigation was oriented toward elucidating the mechanism by which sulfurized fatty esters function as extreme-pressure additives. The rubbing speed and contact pressures were not chosen arbitrarily but were selected to correlate with conditions in other types of testing. As the initial step, the behavior of a sulfurized fatty oil of proven performance in commercial service was observed in the SAE bench tester and the critical contact pressure for failure as well a s the rubbing speed was calculated by a basic analysis. Then the behavioristic response of the sulfurized additive to pressure was studied wit.h the pinand-disk apparatus and the essential parallelism with the behavior in the SAE test was established. Thus the multicomponent nature of the action of sulfurized fatty esters is interpretable in terms of basic parameters such as pressure and rubbing speed which are not tied to the set characteristics of an arbitrary bench test. But how these parameters interact with the chemistry of the additives remains open for investigation. Forbes, Allum, diester-disulfides

Neustadter

and

Reid

I641

prepared

a

series of

ROOC(CH2)n-S.S-(CH2)nCOOR

and related compounds, the additive action of which was investigated by the four-ball test. Figure 11-17 shows the results obtained with the

0.9 r

;0.8 -c 0

0.7

f 0.60.50.4-

rn 0.3L

0

0”

0.2 0.1

-

0-

Figure 11-17. Four-ball wear tests of ester-disulfide additives. Wear Additives: 18.52 mmoles/100 test: 30 minutes at 15 kg load, 1500 rpm. ams. A: C2H500C(CH2)nSS(CH2)nCOOC2H5. 0: Base oil. B: Diethyl sebacate. C : Diethyl disulfide. D: Di-n-butyl disulfide. E: Di-n-octyl disulfide. From data by Forbes, Allum, Neustadter and Reid [ 6 4 ] .

304

ethyl esters at a concentration of 0 , 1 8 5 2 rnolal in white oil, i.e. 1.19% S. Comparing the effect of the ester 1,22-dicarboethoxy-l1,12dithiadocosane with the action of the ester 1,20-dicarbomethoxy-9,12dimethyl-l0,ll-dithiaeicosane studied by Dorinson [631, we see a smaller effect of the additive OP the wear in the four-ball test than in the pinand-disk test. The unsulfurized dibasic ester diethyl sebacate increases the wear relative to that of the carrier oil. The effect of dialkyl sulfides seems to be the same in both the work of Dorinson [631 and Forbes e t aL. [641. 11.3.4.

Interference Effects with Multicomponent Additives

Cooperative enhancement is not the only possibility in the tion of multicomponent additive mixtures. Interference with the or antiscuff action of a lubricant additive by another component the compounded oil as a detergent or ap. anticorrosion agent is unusual experience in the commercial practice of lubrication. cf the experience is empirical; good basic studies of inhibition tiwear or antisruff functionality are rare.

interacantiwear added to not an The bulk of an-

The usual explanation for additive inhibition is the interdiction of the rubbing surface to the antiwear additive by another additive which is more strongly adsorbed. Spikes and Cameron [651 have presented some persuasive evidence to that effect. Curve I of Fig. 11-18a shows the adsorption of dibenzyl disulfide tagged with S35 from solution in nhexadecane ontc a plate of stainless steel. At a temperature of 383 K (I10 C ) there is a transition involving a chemical reaction with an activation energy of approximately 40 kJ/mole. Curve I 1 of Fig. 11-l8a shows the adsorption of dibenzyl disulfide from a solution which carries 0.036 mole of n-octadecylamine and 0.0033 mole of the disulfide per 100 grams. The adsorption of the disulfide is strongly suppressed at lower

N

E

0100

e'$0.075 .fg 0050 3 u)

$

0.025

0

c

0.2

.-EaJ .-u r r

a 0.1 0

0

0 280

-

.-0 0.3 t r

Q

s *-

C

.Q c

320 360 400

280 320360 400 440480

Temperature, degrees K

Figure 11-18. Interference in the additive action of dibenzyl dislulfide. (a) Adsorption on stainless steel. (b) Friction of stainless steel. I: Dibenzyl disulfide only in n-hexadecane. 1 1 : Dibenzyl disulfide plus noctadecylamine. 111: Dibenzpl disulfide plus calcium salt of petroleum sulfonate. Data by Spikes and Cameron [651.

305

temperatures, but above the transition temperature the relative effect of the amine falls off. This is in line with the adsorption of long-chain arnines as discussed in Chapter 10. The calcium salt of petroleum sulfonate, at a concentration o f 4.5 wt-% in conjunction with 0.8 wt-% of dibenzyl disulfide, strongly suppresses the adsorption of the disulfide throughout the temperature range 293-433 K (20-160 C). In parallel with these adsorpticn experiments are the slow-speed friction experiments, the results of which are shown in Fig. 11-18b. Curve I shows the response of friction to the temperature of the system wnen dibenzyl disulfide is the only additive in the lubricant. The sharp downward trend of the coefficient of friction in the temperature range 403-473 Y. (130-200 C) is ascribed to the growth of the chemically reacted sulfide film. The strong decrease in the coefficient of friction below 333 K (50 C) when either octadecylamine o r calcium petroleum sulfonate is the second member of a two-component additive system must be attributed to the antifriction effect of adsorbed amine or sulfonate. A s the Eemperature rises the amine is desorbed, and i f the temperature has not reached the level at which the sulfide reaction film can grow to adequate thickness, the friction rises, only to fall with increasing temperature as the film thickens. The calcium sulfonate, however, apparently desorbs enough t o permit an increase in friction but not enough to allow the sulfi5e reaction film to grow when the temperature increases beyond the critical transition value. But since commercial petroleum sulfonates are not pure substances, the effect observed here is complicated by the multicomponent nature of the sulfonate.

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527-530.

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65.

H. A. Spikes and A. Cameron, ASLE Trans.,

15 ( 1 9 7 0 ) 341-352. 17 ( 1 9 7 4 ) 2 8 3 - 2 8 9 .

308

Chapter 12 CONTACT OF SOLID BODIES

In the preceding chapters of this book it has been taken for granted that whenever contact was mentioned the meaning was apparent, either from the context of the discussion or from familiar experience with the behavior under consideration. Many details and implications of fundamental significance were thereby glossed over. In the present chapter we shall treat the question of contact more throroughly, both as to phenomenology and basic principles. A s it relates to friction, wear and lubrication, contact can be examined from two points of view. One of these, which can be designated as the topography and mechanics of contact, covers those aspects amenable to analysis by engineering mechanics. From the other point of view, which is the way the physicist or the physical chemist looks at it, contact is ultimately resolvable into interatomic or intermolecular action. Except in rare cases, surfaces are neither smooth nor clean. Thus, the contact of surfaces is a complex phenomenon, and even the most sophisticated models are idealized to some extent. The simplest example of the contact of three-dimensional bodies is the tangential contact of two spheres. The contact of two flat planar surfaces is often idealized as being complete over their common area. A geometrical treatment applicable as a first approximation is the case of a nominally flat surface carrying a set of peaks brought into contact with a rigid, flat, planar surface. Given that one surface is free to accommodate itself, then by simple geometry stable contact is established when three points on the uneven surface are coplanar with the rigid, flat surface. Real materials deform under load, and hence the simple geometric cases described above bring no meaning to a discussion of the fine-scale aspects of the mechanics of contact. For instance, in the case of threepoint contact against a plane, on further application of load the topmost asperities will yield, first elastically and then plastically, thus bringing the lower-lying asperities into contact. The number of asperities which come into contact and the manner in which they do so will depend on the applied load, the properties of the material and the small-scale topography of the surfaces.

309

12.1.

SURFACES AND SURFACE ROUGHNESS

From the materials point of view the surface of a solid can in a simple way be defined as a discontinuity in a lattice pattern. More precisely, a discontinuity in a lattice pattern is an interface. For example, the surface of a metal in a vacuum should be called the solid/ vacuum interface. The inner surface of a glass fish bowl filled with water should be called the glass/water interface. When we designate the interface simply as the surface of the solid we usually presume that what exists on the other side of the interfacial boundary has no effect on the solid at the interface. Sometimes this assumption is valid insofar as can be detected: at other times the "environment" does affect the properties of the solid side of the interface. No real surface is geometrically smooth, even when the atoms are ideally fixed in a crystallographically perfect lattice. The force fields which describe the structure of the atoms constitute a contoured envelope. However, such a surface is regarded as atomically smooth because its structure is determined by the regularity of the atomic centers in the lattice array. In real life, this criterion of atomic smoothness does not hold for large areas: but average atomic surfaces functionally equivalent to empirically smooth surfaces with Miller indices [loo], ill01 or E l l 1 1 can be made up of many small patches of smooth facets joined by planes of more complex orientation. Such structures have been observed by field ion microscopy. Mechanical cleavage of ionic crystals, particularly those with layer-lattice structure, produces fairly large areas which are atomically smooth and lie at levels separated by steps of only a few atoms in height. I t is a far cry from the surfaces described above, for which sensitive means such as field ion microscopy or multiple reflection light interferometry must be used to detect irregularities of a few nanometers in dimension, to the surfaces encountered in technological tribology. The structural irregularities of a highly reflective ground surface can

be as large as 126 nm (1260 8 ) . Even a mirror-finished surface lapped on a metallographic wheel can have long waviness of the order of 25 nm in amplitude. Surfaces with structural features averaging 2540 nm (100 mlcroinctes) are common in industrial practice. To understand how the roughness or smoothness of a surface can affect its behavior in contact and rubbing, it will be helpful to examine some simple aspects of surface topography. 12.1.1.

Descriptive Surface Topography

The most direct way of visualizing a surface profile is to cut an object in a plane perpendicular to the average surface o surface envelope of interest and after having prepared the cut surface for metallographic examination to examine i t at a suitable magnificat on, the mag-

310

nitude of which is governed by the dimensions of the profile roughness and the desired size of the field of observation. If the cut is made at an angle of 1 . 4 7 0 4 rad ( 8 4 . 2 5 ' ) from the perpendicular, vertical dimensions will be exaggerated by a factor of 10 relative to the horizontal scale. Figure 1 2 - 1 shows two such taper sections of a linearly ground surface of an average surface roughness in the range 2 5 4 - 5 0 8 nm ( 1 0 - 2 0 microinches). I n the optical photomicrographs the profile structure appears to consist of an irregular sequence of sharp peaks and steep valleys. But when profile diagrams are constructed in true proportion, a s shown in Fig. 1 2 - 2 , it is seen that the surface trace has a gently undulating contour.

300 y m Figure 1 2 - 1 . Taper sections of ground steel surfaces, metallographically etched. Vertical magnification 10 times horizontal magnification.

U 20 Micrometers Figure 1 2 - 2 . Profile diagrams of the surface of Fig. 1 2 - 1 in true proportion. The reference lines are arbitrarily placed for comparison of asperity contours.

311

Another technique for investigating the texture of a surface i s by means of a stylus probe instrument. The probe, usually a diamond-tipped Stylus with a radius of curvature of 2 5 . 4 pm (0.001 in) and an included angle of 1 . 8 3 2 6 rad ( 1 0 5 " ) , is mounted in such a fashion that it follows the fine details of the surface structure while its mounting follows the average envelope of the surface. This feature of the stylus-probe techThe stylus is part of a nique is discussed further in Section 1 2 . 1 . 2 . variably coupled inductance which generates a voltage proportional to the excursions of the probe. This voltage is amplified by appropriate means, and the signal is either displayed on an averaging meter to give a single number for the surface finish value or else it drives a recorder to generate a trace of the surface structure. Figure 1 2 - 3 shows two recorde r traces of profiles taken orthogonally across a linearly ground surface. The vertical magnification is 1 0 0 times the horizontal magnification. At this ratio the traces of most industrial ground sufaces are very rugged and serrated, and at first glance it appears that either the included angle o r the radius of the stylus is too large to permit the probe to follow the surface profile correctly. But the surfaces most frequently encountered in technological tribology have true structures like that seen in Fig. 1 2 - 2 , and it is obvious that such fears need not be considered seriously. Because of the very small radius, the contact stresses at the tip of the stylus are large even for very light loads and a detectable track is left o n the surface after traversal by the probe, but it has been demonstrated that for materials of the hardness generally found in machine parts such deformation is too small to effectively distort the picture of the surface structure.

I

( 0 )

(b)

Figure 12-3. Recorder traces from a Talysurf stylus probe of a linearly ground surface. (a) Mildly undulating surface. (b) Deeply pitted surface. Surface profiles can be visualized directly by optical interference i f the surface is reflective enough. Figure 12-4 shows an interferogram of a 7 5 - 1 2 5 nm ground surface and some diagrammatic representations of the profiles 111. The diagrammatic profiles are drawn with the vertical magnification 120 times the horizontal magnification. By far the great majority of surfaces encountered in engineering practice are structured, and for the most part such surfaces are finished

312

Figure 1 2 - 4 . Optical interferogram and profile diagrams of a linearly ground surface. (a) Interferogram. (b) Surface profile diagrams. Data by A . Dorinson [ l ] . by linear grinding. Profiles of these surfaces by the techniques described above (sectioning, stylus tracing, interferometry) are with few exceptions taken in a direction perpendicular to the orientation of the grind marks. Traverses of the surfaces parallel with the grind marks yield little useful information. If it is desired to eliminate the influence of oriented structure, data from bead-blasted surfaces are used. Such surfaces can be modeled a s an array of spheres of random height and spatial distribution. 12.1.2.

The Metrics of Surface Roughness

Profile traces are revealing representations of two-dimensional surface topography, but in ordinary industrial practice the demand is for a single number by which the surface roughness may be expressed quantitatively. The two most commonly encountered numerical systems of reporting surface roughness are the centerline average value ( C L A ) and the rootmean-square value (RMS). These are straightforward statistical concepts. the For a surface profile of length L , as illustrated in Fig. 1 2 - 5 ,

Ae - - - - - - L . '

L 2

hCL A =

Figure 1 2 - 5 .

+hL/Y/dl

hRMs=(i/o

11.2

Y dl)

Center-line average and root-mean-square surface roughness.

cenrer-line average peak height is given by

(12-1)

which is simply the average deviation of the peak heights from the reference line over the sampling distance L . The root-mean-square peak height, given by

313

(12-2)

is the standard deviation over the distance L.

of the peak heights from the reference line

Figure 1 2 - 5 is schematic: real surface profiles do not have the regular periodicity shown there, n o r is the position of the reference line automatically determined. The CLA or the RMS surface roughness is a statistically calculated quantity, to obtain which raw data must be suitably processed. Figure 12-6 shows schematically (with a surface profile of unrealistic ruggedness f o r convenience in illustrating the point) the kind of problem encountered with a stylus probe instrument.

Arm

Figure 12-6.

Basic scheme of a stylus probe trace of a surface contour.

The reference line x x ' is established by the skid as it slides along supported by the crests of the peaks; meanwhile the profile of the surface is generated by the vertical excursions of the stylus, y y ' , in conjunction with the horizontal movement in the x-direction. To convert these raw data into a statistical average with a symmetrically distributed deviation, the reference line x x ' must be translated so that the area bounded by the profile curve over the lenath L is equally distributed on both sides of the line, iis in Fig. 1 2 - 5 . Statistical treatments of surface profile data are discussed at length in Sections 12.3 and 1 2 . 4 . Table 1 2 - 1 various types of TABLE 1 2 - 1 . ~~~~

shows some characteristic surface roughness data for finish encountered in technological practice. The

CHARACTERISTIC ROUGHNESS VALUES OF VARIOUS SURFACES ~~

~

Nanometers Atomic sreps Polished, finely ground Commercial grinding, transverse to grind marks Sand-cast

0.25

angstroms 2.5

25-250

250-2500

750-2500

7500-25,000

2500-12,500

25,000-125,000

Microns

Microinches

0.00025

0.01

0.025-0.25

1-10

0.75-2.5

30-100

2.5-12.5

100-500

314

values are given in nanometers, gngstroms, microns and microinches. Table 12-1 is applicable to either the CLA or the RMS system; RMS values are 10-20% greater than CLA values for the same profile, depending on the specific shape of the individual profile. Our ultimate interest in the topography of surfaces is in relation to contact over an area. Cut sections and stylus probes yield only linear diagrams. Interferograms, where as many as 10 fringes can be observed ( c d . Fig. 12-4), yield information on the surface structure of a band approximately 0.25 mm wide.

12.2.

CONTACT AND ADHESION

The meaning of contact seems obvious from experience, until it becomes necessary to define it accurately. To establish that contact has occurred in a mechanical device, the investigator invokes one of two principles. Either contact is said to be achieved when a critically minimal resisting force is first sensed as two bodies are moved toward each other; or else contact is defined as the elimination of space between the two bodies. The latter definition suffers from an intrinsic ambiguity because of the difficulty in establishing the actual location of a real surface in the first place. On a molecular or atomic scale the approach of two solid bodies is seen quite differently than in the macroscopic sense. Let us consider two parallel plane surfaces in normal approach, each surface being regarded as an ordered, close-packed array of spherical atoms. On this scale the interactions of approach are a complex set of attractions and repulsions among the nuclei and the outer-shell electrons which can be expressed as inverse power functions of the separation distance. At close approach the repulsions have the major effect, so that there is a potential minimum at a distance closer than which the force required to bring the constituent atoms in the surface together increases sharply. This might be designated as the limiting condition for contact on an atomic scale. This concept does not have the sense of immediate reality that the model on a macroscopic scale does, and also it is much too complicated to put into a form which can be applied to real bodies.* Real contact on a macroscopic scale occurs over an area. As was shown in the discussion of friction, we must distinguish between the apparent and the true area of contact. The structural aspect of real surfaces has put the word "asperity" into the working vocabulary of surface

*For a detailed treatment of surface energy in terms of atomic interactions the interested reader is referred to pp. 9 4 1 66. of P h y s i c a l C h e m i b t h y by E. A. Moelwyn-Hughes, Pergamon Press, New York, London, Paris, 1957.

315

topography and contact. Etymologically and physically an asperity signifies a topographic feature which distinguishes a rough surface from a smooth one. The nature of the asperities and their distribution in the surface are what make up the quantitative description of the roughness of the surface. Good measurements of contact are difficult to carry out and even more difficult to interpret because of the individualistic character of a given surface. Therefore the tendency has been to f i t experimental results to behavior inferred from models. In one of the early simple models, a surface is viewed as an assembly of spherical asperities, and one of the basic schemes of contact is the mechanical interaction between a deformable plane surface and a spherical asperity. I f the deformation of the sphere is elastic the deformed area o n the sphere is a circle, and the relation between the load pressing the flat against the sphere and the radius of the circle is given by the familiar formula of elastic theory

f 12-3)

where a is the radius of the deformed area, W is the load, R2 the radius of curvature of the spherical asperity, v is Poisson's ratio, E is Young's modulus, and the subscripts 1 and 2 refer to the plane and the If both the plane and the sphere are of the same sphere respectively. material, such as steel, for which v = 0.3, then [21

(12-4)

The maximum pressure 4, on the area of deformation is at the center. Equation 12-4 then yields

(12-5)

The stresses are a compression uz

acting

normally

on

the

surface

of

deformation, radial stress cik and angular stress o e . The latter two stresses are symmetrical with respect to the axis of compression and obey the relation 1 + 2v Oh =

ue

=

~

2

OZ

(12-6)

Transition to plast c deformat on will occur when the maximum shear For the stress satisfies both the Tresca and the Huber-Mises criteria.

316

particular geometry discussed here plastic deformation is first detected on the z-axis at a depth of 0.5a below the common plane of deformation [2]. The following relations hold: uz

- ut

0.47

S,

= 0.31

4,

(12-7)

= 0.31

qo = 0.5 TY

(12-8)

where S, is the shear stress for the initiation of plastic flow and T is Y the limit of elastic stress in tension. Plastic deformation begins when S, = 1.1 T Y'

With continued loading of the ball, the small plastically deformed region grows and the mean pressure increases as well. Experimentally the mean pressure has been found to approach the limit 2.8 T as the load W Y increases. (For work hardening metals the value of T is taken as that Y at the edge of the indentation at any instant.) With the onset of plasheory no longer tic flow the elliptic stress distribution of Hertzian holds over the circular area of deformation. Ishlinsky [31 has published the approximate stress distribution shown in Fig. 2-7 for the ideal plastic case.

Figure 1 2 - 7 . plasticity. 12.2.1.

Radial Distance Stress distribution over the area of deformation f o r ideal

Simple Deformation Models of Contact

The significance of the theory of elastic deformation and plastic yielding for contact models is illustrated by a simplified version of a treatment published by Archard 141. If we think of a deformable surface

317

composed of spherical asperities situated at different levels a distance of h apart pressed against a flat non-deformable surface by a load W, then for the relation between the load and the total area of a large number of asperities we get

I

A = - I

(12-9)

where B and J are lumped constants derived from the analysis of Fig. 12-8 in terms of the elastic or plastic yielding of the asperities E41. The evaluation of 8 , J and A for various cases is shown in Table 12-2. For elastic deformation the true contact area is proportional to the fourfifths power of the load, for plastic deformation to the first power.

i

Deformable Surface

///N////////////~~ Non-deformable Surface

Figure 12-8. Simple model of deformable spherical asperities a non-deformable flat surface. After J. F. Archard 1 4 1 . TABLE 12-2. ____

contacting

SPHERICAL ASPERITY MODEL IN ELASTIC AND PLP.STIC DEFORMATION ~

8

J

3

4.25

z

A

ER1l2 I_

Plastic Deformation 1

In a subsequent analysis [51 Archard developed a model of contact by elastic deformation of asperities of several superimposed scales of magnitude. Figure 12-9 illustrates the model, and the main conclusions of the analysis are presented in Table 12-3. The effect of load on the deformation of a single spherical asperity and of an array of smooth spherical asperities has been examined by many investigators with respect to the transition from elastic to plastic deformation. Table 12-3 shows that as the structure of surfaces comprised of several superimposed or-

318

Figure 12-9. Models of contact with asperities of multiple order. (a) Single sphere with one suborder of spheres. (b) Single sphere with two suborders of spheres. (c) Array of spheres with one suborder of spheres. (d) Array of spheres with two suborders of spheres. After J. F. Archard [51.

TABLE 12-3. AREA OF CONTACT AND LOAD: MULTIPLEORDER ASPERITY MODEL FOR ELASTIC DEFORMATION ~~

~

Area is proportional to:

Nature of surface Single smooth sphere

w2/3

Single sphere with one suborder of spheres (a)*

w8/9

Single sphere with two suborders of spheres (b)* Array cf Smooth spheres

u26/27

Array of spheres with one suborder of spheres (c)*

w14/15

Array of spheres with two suborders of spheres (d)*

w44/45

w4/5

*See Figure 1 2 - 9 . ders of asperities increases in complexity, the relation between area of contact and load for elastic deformation rapidly approaches linearity. Therefore a linear dependence of coefficient of friction o r rate of wear on load is not necessarily a consequence of contact by plastic deformation of asperities. Corroborative observations must be available to establish fully the type of contact involved. Archard's two

treatments

of

contact

and

surface

structure

are

319

derived from an analytically specific model of the surface topography. Later in this chapter we shall examine models based on statistical inputs, which are better descriptors of the real surface topography. Nevertheless, the Archard models are often useful as simplified approximations and in many cases the results obtained from them do not differ greatly from the results of more refined treatments. 12.2.2.

Adhesion and Separation

Two atoms can be thought of as adhering i f the conditions for the formation of bonding orbitals are satisfied when the atoms are brought together. The behavior of multiatomic macroscopic bodies on progressive approximation is complex because the bounding surfaces are generally nonconforming over a wide range of magnitude. Adhesive phenomena for such bodies are governed by deformation of asperities as well as gross deformation. I f two bodies are pressed together by a load W and it requires a load W" in the reverse direction to separate them after W is removed, then the ratio W " / W may be designated as the degree or the coefficient of adhesion. Both the atomic and the operational concepts of adhesion enunciated above run into some obvious conflicts with experience. There are numerous instances on record where bodies have been put in contact under light normal load and on relaxation of the load no adhesive force could be measured when the bodies were separated. Yet on inspection of the surface after separation, unmistakable evidence of adhesion was found. I n such cases the major deformation is elastic, and o n release of the loading force relaxation of the elastic stress is the net behavior observed. Let us examine a specific case. Consider the elastic deformation of a sphere pressed against a flat plate to give a circular contact area of radius a . Now suppose that in the loaded state the two surfaces adhere over the contact area. Releasing the load is like applying a reverse load W ' , which is equivalent to pressing a rigid, sharp-edged circular cylinder against a flat plate. This produces a pressure distribution according to the relation below [ 6 1 : p' =

w'

2(1 2 na

>) 2

-1/2

(12-10)

By this formula the tensile stress at the periphery of the deformation area is infinite; i . e . o n unloading, the released elastic stresses peel the contacting surfaces apart. This analysis tells us that it is possible for weakly adherent surfaces to separate spontaneously on removal of the contact load. But it is not necessarily valid for strong adhesions. Otherwise we would never observe persistent adhesion after contact of bodies under load.

320

Another factor which complicates the matching of theoretical deductions with observed behavior in the study of contact adhesion is the influence of surface films. The effect on friction of adsorbed gas films, metal oxide films and additive reaction films has been discussed in detail in Chapters 9 and i 0 . Since the major frictional mode is adhesive, it follows that the factors which influence lubricated friction in such instances ultimately resolve back to their influence on adhesion. The interactions among surface films, surface topography, contact and adhesion are discussed in detail in Section 1 2 . 6 . 12.3.

CHARACTERIZATION OF SURFACES FROM PROFILE DATA

The surface models illustrated by Figs. 1 2 - 5 , 1 2 - 8 and 1 2 - 9 were deliberately simplified for easy treatment and therefore are more o r l e s s artificial. Stylus probe profilometric traces, taper section traces and interferograms satisfy the eye but require arduous workup to yield quantitative information. Greenwood and Williamson ( 7 , 8 , 9 ) have developed methods f o r the application of linear stylus profilometry to surface topography and contact which shift the burden of data treatment to instrumental techniques. Bead-blasted surfaces were selected for invesIntigation s o that the direction of tracing could be taken at random. stead of manipulating the statistics of surface roughness into a single number representing the deviation of peaks from a reference line, the analysis was concerned with finding a probability distribution function for the peak heights with respect to the reference line. The continuous signal of the conventional profilometric trace was chopped into a set of discrete digitized data which sampled the surface at intervals much smaller than the horizontal peak-to-peak separation. The details of the technique and the statistical treatment are beyond the scope of the discussion here and can be found in the oringinal sources. Overall, the distribution of peak heights thus obtained was Gaussian. Figure 1 2 - 1 0 is the cumulative distribution plot of peak heights found for a bead-blasted aluminum surface, the conventional profilometric trace of which is shown at the top of the diagram. The arithmetic probability coordinates used for the plot give a straight line i f the distribution obeys the Gaussian relation. In Fig. 1 2 - 1 0 a satisfactory straight line is given by the peaks lying in the cumulative range 1% (below which no peaks were detected) to 99%, above which the peak heights truncate. The values for the peak heights shown on the abscissa of Fig. 1 2 - 1 0 are with respect to an arbitrary datum, which from the scale of the prof lometric trace is obviously well below the deepest valley seen in I t is also obvious, from the direction in which the scale the trace. runs that the ordinate shows in inverse fashion the cumulative per-

321

6 3 n

99.9-m%

! !!:/

250 N m

6 $50. u)c I -

'g

200 = 2 50

0

0.0 1n & .E V 0.1 -

0

2

4

6

8

Height above datum, Mum

Figure 12-10. Cumulative distribution of peak heights for bead-blasted aluminum surface for which the profilometric trace is shown at the top. The peak heights are with respect to an arbitrary datum below the surface: the distribution is with respect to an envelope representing the top of the surface. Scale shows the surface roughness of the profilometric trace. Data by Greenwood and Williamson [ 7 1 .

cencage of peaks which would be cut by a plane descending towards the datum. Thus, on going from 8.5 pm to 8.0 pm above the reference datum, the percentage of peaks lying below the plane would decrease from 99% to 97.5%: i.e. at 8.0 pm the descending plane would cut through 2 . 5 % of the total number of peaks. This is on the assumption that the distribution is Gaussian throughout the entire range of heights. But in fact no peaks lying more than 8.5 pm above the datum were detected. Greenwood and Williamson 1 7 1 suggest that in the upper range of peak heights the distribution is better described by the exponential function

N

= yAe - h

(12-11)

A is the nominal area, y the surface density of the peaks and h = being the separation of the movable plane from the datum and u the standard deviation of the height distribution.

where


Note that Fig. 12-10 illustrates only a way of counting the number of peaks that would be encountered in descending toward the datum. It is not a physical description of contact. However, as we shall see subsequently, the cumulative distribution of peak heights is an important element in a model of physical contact. Therefore, i f the distribution of peak heights in the upper portion of the surface i s represented better by an exponential relation than by the Gaussian function, this will have important consequences for the mechanics of contact at light loads. Whitehouse and Archard 1101 used a more generalized statistical formulation and applied it to the ground surface whose profilometric trace

322

Figure 1 2 - 1 1 . Profilometric trace of a ground surface perpendicular to the direction of the grind marks. The standard deviation of the ordinate height distribution is u = 0.5 urn. The correlation distance p* = 6.5 urn. Data by Whitehouse and Archard [ l o ] . is shown in Fig. 12-11. The datum line is selected so that the ideal distribution of ordinate heights is Gaussian with a standard deviation of 6. The signal from the tracing instrument is digitally sampled at intervals of 1 0 0 0 nm. Peaks are located by use of the correlation distance When B = 2.38* the auto-correlation function b*. C(B)

=

e x p (-B/b*)

(12-12)

has declined to l o % , and this is taken as the limit of resolution of two Figure 12-12 shows the adjacent structures in the scrface profile. probability density function for the peak heights, normalized by the relation h

=

'5

(12-13)

of the surface profile trace seen in Fig. 1 2 - 1 1 . For a sampling interval L = 2 . 3 8 * the distribution curve actually found is skewed rather than

0.4

-

-

0.3 ZI

= v)

30.2

-

w. r: c

1

0.1

-

h

01 - 3 - 2 4

0 1 Normalized Height,y

I

2

3

Figure 12-12. Probability density curves for Gaussian distribution of peak heights and ordinate heights. A: Probability density of an ordinate being a peak at height g, where y = h/a and the sampling interval L = 2.3 b*. B: Probability density curve for the Gaussian distribution of ordinates where y = h/a. Data by Whitehouse and Archard [ l o ] .

323

being symmetrical as required by the ideal Gaussian relation. The distribution of all the ordinate heights is more nearly Gaussian (Curve B). The numerical data obtained by sampling the profile shown in Fig. 12-11 are given in Table 12-4 as the cumulative distributions of the The distribution of the orordinate heights h and the peak heights h P' dinate heights is symmetrical with respect to the central datum line of the profile between 5% and 9 5 % , but from 5% to 0 . 1 % the distribution becomes progressively skewed toward more negative values for the ordinates. The peak heights are positive with respect to the datum line in the range 1 2 . 2 % to 9 9 . 9 % of all the peaks; i.e. more peaks are found above the datum line than below it. It should be realized that the peak height

values

shown

in

Table

12-4 are not peak dimensions (heights from the base of an asperity to its

summit). The peak height values found in Table 12-4 were obtained by applying Gaussian statistics to the probability that an ordinate rises a given height above the datum line and that this ordinate is a peak. Therefore the cumulative distribution tells us how many peaks a flat planar surface would encounter as it descends towards the datum line but it does not tell us where the bases of these peaks are located. Nor does it tell us anything about the shapes of the asperities.

CUMULATIVE DISTRIBUTION OF ORDINATE HEIGHTS AND TABLE 12-4. PEAK HEIGHTS OF THE PROFILE SHOWN IN FIGURE 12-11. Cumulative percentage

99.9 99.0 95.0 91 . o 84.0 75.0 60.5 55.5 52.5 50.0 23.0 17.5 14.0 12.2 8.3 5.5 5.0 1.3 1 .o

0.1 0.05

Ordinate height, h

Peak height,

Micrometers

Micrometers

+5.80

+4.40 +3.20

+2.54 +1.80 +1.27 +0.51 + O . 25 +O. 13 0.0 -1.40 -1.76 -2.00 -2.24 -2.60 -4.02 -3.20 -5.10 -5.40 -7.95

Microinches +230 +173 +125 +loo + 71 + 50 + 20 + 10 + 5 0 - 55 - 69 - 79 - 88 -103 -159 -125 -20 1 -213 -313

From data by Whitehouse and Archard 1 1 0 1 .

+5.20

+4.20 +3.30 +3.00 +2.56 +2.20

+1.66 +1.50 +1.56 +1.40 +0.51 + O . 25 +o. 13 0.0 -0.25 -0.51 -0.58 -1.27 -1.38 -2.48 -2.54

crP

Microinches +205 +165 +130 +118 +lo1 + 87 + 66 + 59 .+ 62 + 55 + 20 + 10 + 5 0 - 10 - 20 - 23 - 50 - 54 - 98 -100

324 A description of the topography of a surface adequate for contact mechanics requires data for the radii of curvature of the asperities as well as their height distribution. Let us examine in simplified fashion the task which confronts us in extracting knowledge about the radius of curvature of an asperity, the peak of which has been located by profilometric analysis. The usual expedient in the statistical treatment is to postulate a geometrical configuration for the asperity. Whitehouse and Archard [lo] assumed that the asperity outline is parabolic: Greenwood and Williamson (7, 8, 9 ) examined cases for spherical as well as parabolic asperity contours. The asperity contour being either known or assumed, we ask what the probability is that an ordinate found by digital profile analysis is a peak of curvature C. The second derivative of the contour curve is taken as an adequate approximation of the curvature. The sampling interval L by implication defines the chord of the curve of which the ordinate is the peak. In the interval L there should be three successive ordinates which have the relation y, < y 2 > y3.

The probability density function of the curvature for a given surface profile is strongly influenced by the sampling interval. Figure 12-13 shows the dependence on the sampling interval found by Whitehouse

lo4

f

c 0

0

-

E

I 10

-

1,

I 1111I I I 1 I

15 10

5

11

2 0.5

Sampling Interval, ,urn

Figure 12-13. Mean curvature of the peaks of a ground surface as a function of the interval at which the profilometric trace is sampled. The full line is calculated from a theoretical equation. The experimental points are derived from digital analysis of the profile shown in Fig. 12-11. Data by Whitehouse and Archard [ l o ] . and Archard [lo] for the mean curvature of the peaks in the surface trace of Fig. 12-11. For an interval of 15 pm the mean radius of curvature of an asperity peak is 0.168 mm; when the sampling interval is shortened to 6.5 pm (equal t o the correlation distance B*), the asperity radius

325

decreases to 0 . 0 3 0 2 mm; and for an interval of 1 pm the radius is 0 . 0 0 2 8 7 mm. Overall the decrease is almost two orders of magnitude. Such sensitivity is not directly obvious from the behavior of the probability density function of the asperity heights, where a change in the sampling interval from 1 5 p m to 1 pm changes the most probable height from 0 . 7 5 pm to 0.5 p m and decreases the probability density from 0 . 1 7 to 0.11. Whether this strong difference between the response of the asperity height distribution function and the asperity curvature function to sampling interval is a computational effect o r a true phenomenological effect remains to be investigated. Interferograms and taper section profiles also can be analyzed for asperity structure. Table 12-5 gives a survey of the characteristics of the asperities in the surface whose interferogram and profile diagrams Approximately 2 5 - 3 0 asperities were examined in are shown in Fig. 12-4. TABLE 12-5. ASPERITY CHARACTERISTICS OF A GROUND SURFACE FROM INTERFEROMETRIC DATA Height range, pm

0.025-0.150 0.076-0.127 0.025-0.127 0.230-0.250

(a)

Range of widths at base, pm 7.6-12.7 12.7-20.3 5.0-17.8 30-35 ( a )

(a) Representati.ve of the coarsest asperities.

Radius of curvature, mm 0.134-0.296 0.264-0.405 0.125-0.311 0.490-0.615

From data by

Dorinson

Ill.

each 0.5-0.6 mm of surface profile. The radius of curvature was calculated from the base width UI and the asperity height h on the assumption that the profile of the asperity was a circular arc; the radius of curvature is then approximately given by

2h

(12-14)

The average values calculated from all the data listed in Table 1 2 - 5 are: 0 . 1 3 3 pm for asperity height, 2 0 pm for asperity width at the base and 0.374 mm for radius of curvature. These values are compatible with an average surface roughness of 0 . 1 3 3 pm ( 5 . 2 4 microinches). The surfaces shown in Fig. 12-1, although reflective, are too rough for the interferogram to be analyzable. However, the taper sections and the profiles constructed from them (Fig. 1 2 - 2 ) can be scaled to yield workable data from which radii of curvature can be calculated. The range of values thus found for the radii of curvature is 0,008 to 0.040 mm.

For bead-blasted surfaces, such as were studied by Greenwood and Williamson [ 7 , 81, the asperities have substantially spherical symmetry and a distribution such that no matter what direction the stylus travels in probing the surface profile, statistically the traces will all be the same. Linearly ground surfaces, such as were examined by Dorinson 111 and by Whitehouse and Archard [ l o ] , have widely different characteristics perpendicular and parallel to the grind marks. But any probe or examination perpendicular to the sense of the grind marks will be a statistically reproducible random sampling of the surface in that sense provided the sampling distance is long enough. Small departures from orthogonality do not significantly affect the characteristics of the trace. Let us consider the case where asperities of spherical contour are uniformly distributed over the nominal area of a base plane with a Gaussian distribution of summit heights. A stylus probe taken along a line in any direction will show a Gaussian distribution of peak heights. But these will not necessarily be summit heights; only if the stylus traverses the surface of the asperity along a great circle will a peak height be a summit height. If the peak is not a summit, then the radius of curvature of the profile trace will not be the radius of curvature of the asperity. Therefore, even though the peak heights and the radii of curvature in the profilometric trace follow Gaussian statistics, the analysis must be carried still further to extract the correct evaluation for summit heights and radii of curvature. Williamson [ 9 1 carried out a tedious three-dimensional mapping of a bead-blasted surface and found I t should that the summit heights do have a Gaussian distribution. therefore be possible to work out the correlation between the statistics of trace peaks and asperity summits to validly characterize the summits. Linear profilometry of straight-ground surfaces yields data which obey Gaussian statistics, as we have seen. There are also some individual characteristics of such surfaces which should be noted. Dorinson [ I ] described the finely-ground surface he examined by optical microscopy and white light interferometry thus: "the characteristic can be visualized as an elongated ridge 20 to 5 0 times as long asperity as it is wide and 5 0 to 100 times as wide as it is high." The ridges were estimated to be 0 . 2 5 - 0 . 5 0 mm long, which gives a range of 2 - 2 5 urn for their widths and 0 . 0 2 - 0 . 5 pm for their heights. A credible ideaJization of the geometry of this kind of asperity is an ellipsoid of revolution with a large ratio for the major axis relative to the minor axis. Only a small portion of the surface of the ellipsoid would stand proud of the datum plane of the nominal surface and be detected as an asperity.

...

Because of the extremely elongated shape of such an asperity the probability that a random orthogonal trace will cross a summit is even less than it is for a spherical asperity. But for most of the length of the ellipsoidal asperity its width changes very little and hence the

327

radius of curvature of the transverse profile remains very nearly coninto evaluating the stant. The simplification thus introduced profilometric data is obvious. '

SURFACE TOPOGRAPHY AND THE MECHANICS OF ASPERITY CONTACT

12.4.

Let us take a surface, nominally flat on a macroscopic scale but actually comprised of asperity structures on the microscopic scale, and let U S press a smooth rigid plane normally against the surface. The topographical analyses of Section 12.3 have shown how to sum up the number of asperity encounters on a geometrical basis. But each asperity encounter also involves the mechanics of deformation subsequent to initial contact. Greenwood and Tripp [ll] have pointed out how to go from deformation of asperities in microcontacts to the macroscopic deformation of the contacting bodies. The behavior of bodies in macroscopic contact is described in terms of engineering quantities such as average contact pressure or load per apparent unit area. The transformation of such macroscopic parameters into the behavior of deformed asperities in microcontacts gives us an insight into the basic origin of friction and wear. A statistical approach to the mechanics of asperity contact is that of Greenwood and Williamson [7], which may not be exact in all respects but does present a readily apprehensible physical model. Figure 12-14 is a diagram of the encounter of the smooth surface with the rough profile.

Smooth surface

\Reference

plane in rough surface

Figure 12-14. Contact of a rough surface. The load is supported by those asperities (shaded) whose heights are greater than the separation 5 between the reference planes. The deformation of an individual asperity is assumed to the Hertzian relations:

R1/2u1/2

nl

=

A1

= nRw

w

=

1

governed

by

(12-15) (12-16)

4 EtR1/2w2/3

5

-=-+E'

be

1-v:

1 - v2

El

E2

(12-17)

(12-18)

328

where h l is the radius of the asperity contact area, R is the radius of curvature of the asperity, A , is the asperity contact area, W 1 is the load on the asperity, E, and E2 are the Young's moduli for the two materials, and v 1 and u 2 are their Poisson's ratios. The compliance w is the distance by which points outside the deformed zone have approached each other normally after the deformation. Let the two planes Then the probability of making contact at be separated by a distance c . * any given asperity of height z is

(12-19)

where +(z) is the probability that the height of the asperity lies between z and z + dz. The total number of contacts is 03

N' = N

j 4fz)dz (12-20)

5

where N is the total number of asperities. nRw, the mean contact area is

Also,

since w = z-5 and A 1

=

LD

j nR(z - c)+(z)dz 5

and the total area of contact is

c

(12-21)

The total load carried by all the contacts is

(12-22)

To make Eqns 12-19 through 12-22 useful for the treatment of profilometric data we introduce the standardized separation h = < / 6 , where cr is the standard deviation 3f the height distribution, and we write N = y/A where y is the surface density of the asperities and A is the nominal macroscopic contact area. Then

N' A

= yAFo(h) =

nyARdF,(h)

(12-23) (12-24) (12-25)

*Equations 12-15 through 12-18 are the Hertzian compliance relations for a sphere pressed against a sphere. Figure 12-14 depicts the contact of a flat surface with a surface whose asperity summits are spheres. Later it will be shown that the contact of two rough surfaces can be reduced to a combination of their individual contacts with a rigid plane.

329

where the function Fn(h) is given by the relation m

F,(h)

J

=

(A

- h)'$*(b)dA

5

The standardized height distribution , $ * ( A ) is the height distribution scaled to make its standard deviation unity. A l l this is conventional statistics. The next part of the problem is to find explicit expressions for the functions FYL(h). If the distribution of peak heights is exponential, then $ * ( A ) = e x p ( - b ) and Flz(h) = l z ! e x p ( - h ) . !2-23, 12-24 and 12-25 become respectively N'

=

On

substituting,

yAe-h

Eqns

(12-26)

A = oyRoAe-h

(12-27)

W = n1/2yRoE' (o/R) 1/2Ae-h

(12-28)

Eliminating A e x p ( - k ) gives the following relations between N ' , A and W :

(12-29)

rr% A =

E' (G/R) 'I2

(12-30)

i . e . the number of contacts and the total area of contact are linear functions of the load i f the surface density of asperities, the surface roughness ( 0 ) and the asperity radius of curvature are constants. For a Gaussian distribution of asperity heights

(12-32)

Explicit evaluations of Fo(hI, F l [ h I and F3,,21h) in Eqn 12-32 are not available f o r general substitution into Eqns 12-23 through 12-25. Greenwood and Williamson [ 7 1 described the method by which they developed numerical solutions for the following case: .f

= 300

per mm 2

RG =

mm2

E'(a/R)'12

= 2 4 5 MPa

From these solutions they computed the functional dependence of the dimensionless separation
330

v) v)

2 1-

.-c0

E

lo-'

1

10

lo2 lo3

I 104

Loading Pressure P. kPa

Figure 12-15. Relation between the loading pressure and the dimensionless separation between reference planes for a rough surface. Data by Greenwood and Williamson [ 7 1 . apparent area of contact, as shown in Fig. 12-15. Under the more heavily-loaded contact conditions, a hundred-fold change in P from 10 kPa to 1000 kPa reduces the separation from 2.6 6 to 1.0 6. A t the other end of the load scale, a change in P from 0.1 kPa to 10 kPa reduces the separation from 3.8 6 to 2.6 6. In this latter range the separation This can closely approximates a linear function of the logarithm of P. be shown to be the equivalent of an exponential distribution of peak heights and to hold for the uppermost 25% of the asperities in most surfaces. Thus, even though overall the distribution of asperity heights is Gaussian, under lightly loaded conditions the assumption of an exponential distribution may be justified, in which case the solutions can be obtained in closed form.

If friction force F is written as A . f ( n ) , then from Eqn 12-30 we get the following expression for the coefficient of friction:

w

E'

F

Ti

- --

(C/R)

'1' -

'j2f( 6 )

COnAtaflt

f(A)

(12-33)

We arrive at this result from a model involving the elastic yielding of asperities rather than plastic yielding. This suggests that in the broadest sense the laws of friction stem from the statistics of surface roughness rather than only the ideal plastic flow of individual contact spots. Of course the model used here is a highly specialized one which is applicable to only the very lightest contact of the highest asperity peaks, but it does demonstrate clearly the scope of the results obtainable from the statistical approach to surface contact. The statistical model must cover plastic as well as elastic deformation of asperities. A s the load increases and the asperity peaks lying in the upper levels of the surface contour are progressively deformed more severely, the extent of deformation must pass from the elastic into

331

the plastic region. From the theory of ball indentation hardness Greenwood and Williamson 171 proposed the following expression for the asperity displacement required for plastic flow: w

P

=

R(H/E')2

(12-34)

where H is the hardness, expressed in units probability of a plastic contact is given by

consistent

with

E'.

The

m

(12-35)

Transformation of + ( z ) to + * ( A ) gives the expression below total area of the contacts which deform plastically:

Ap,

for

the

m

12-36b)

(

where w;

= w P /d

=

Ecr (

h) 2

(12-37)

The limit of elastic contact is defined to be when the area of plastic contact becomes some specified fraction of the total asperity contact However, a* is somewhat unsatisfactory as a surface area, e . g . 0.02. P roughness parameter, since it decreases winh increasing 6 , and therefore a quantity (I, designated as the peanticity i n d e x , is introduced: (12-38)

Table 12-6 shows values computed for the dimensionless critical separation h c = < / d and the critical nominal pressure P n o m corresponding to values of the plasticity index in the range 0.6 to 1.0, the ratio A /A

P

TABLE 12-6. VARIATION OF SEPARATION AND CRITICAL NOMINAL PRESSURE WITH PLASTICITY INDEX

tJ hc

Pn0,,

kPa

.o

0.6

0.7

0.8

0.9

1

0.11

1.34

2.57

3.80

5.08

4215

368

12

0.10

0.0002

Data by Greenwood and Williamson [ 7 1 .

332

being 0.02. The greater the plasticity index the less the load required and the larger the critical separation for the initiation of plastic yielding of the contacting asperities. Statistically, 99% of the asperities above the reference plane fall within the span 30. Hence very light loads suffice to deform the uppermost asperities plastically. At a separation equal to 6, 33% of the asperities above the reference plane are deformed plastically; this is relatively heavy contact. A plasticity index of 0.6, which corresponds to a
f,(x,y)

(12-39)

z2 = f2(x,q)

(12-40)

=

then the equivalent surface is given by z,

=

z1

+

z2

=

f,(x,y)

+

f2(X’Y)

I f z 1 and z 2 are Gaussian, then z , is also Gaussian. I f z 1 and z2 are uncorrelated, the power spectral density of z, will be the sum of the

power spectral densities of z 1 and z 2 , and ae2 = u , 2 + u2 2 dimensionless separation for the composite surface will be

.

Then the

Although the explicit development of the statistics is complicated, it leads to refinement rather than replacement of the conclusions arrived at by the simpler treatments we have already examined in detail. Two assumptions have been implicit in the foregoing discussions: (a) that the apparent pressures (W/A) are relatively low, and (b) that an individual asperity deforms independently of its neighbors in response to true contact pressure. But if the nominal contact pressures are high, the second assumption will not be valid. The investigation of Pullen and Williamson E l 4 1 affords considerable insight into the overall deformation of structured surfaces by loaded contact. The experimental technique consisted of inserting a cylindrical rod into a close-fitting cylindrical cavity and applying a load to a smooth, rigid ram in contact with the upper surface of the rod. This was the surface which carried the asperities. The walls of the cylindrical cavity restrained all movement of the rod except that of the structured upper surface. A profilometric

333

q-

(u

250 Am Figure 12-16. Profiles showing progressive deformation of asperities on an aluminum surface as loading pressure is increased. From top to bottom: virgin surface under zero load, 12 MPa, 62 MPa, 235 MPa and 372 MPa nominal pressure. From data by Pullen and Williamson [141.

trace of the surface was made after each load increment by using the relocation procedure of Williamson and Hunt [15]. Figure 12-16 shows the progressive flattening of the asperities on the end of a bar of aluminum as load was applied in stages up to an apparent p r e s s u r e of 372 MPa (54,000 lb/in2). Statistical analysis of the profilometric traces revealed that as the asperity peaks moved downward with respect t.o the reference plane, the valley floors moved upward. I f P, is the mean real pressure over the real contact area A and the work done when the ram descends a distance dz is equated to the work done on the contacting asperities, then Wdz = PhAdz

(12-42)

I f the dimensionless load is defined as

w*

= -

w hA

it is seen that

(12-43) where a is the degree of contact. The behavior of the rising portion of the surface can be fitted to a uniform rise model. On postulating that volume is conserved, the following relation holds for the rise du of the non-contacting part of the surf ace : du =

1 - a

dz

Since the work expended on the surface must be the sum of

(

that

12-44)

required

334

to deform the asperities and to raise the non-contacting portion, Wdz = P,A(dz

+ du)

(12-45)

But in order to conserve volume, it follows that

w*

=

c ( 1 - a

(12-46)

Equation 1 2 - 4 3 is an expression for a on the assumption that the asperities do not interact during the deformation, whereas Eqn 1 2 - 4 6 takes into account both the deformation of the asperities and the rise of the non-contacting material of the surface. For the non-interacting case, a can be evaluated from the profilometric data by Eqn 1 2 - 2 4 or Eqn 1 2 - 2 7 , depending on whether we use a Gaussian or an exponential distribution of asperity heights. The evaluation of Eqn 1 2 - 4 6 is then obvious. Figure 1 2 - 1 7 shows a plot of a vs. W y for the aluminum specimens studied The dashed line corresponds to a as calby Pullen and Williamson [ 1 4 ] . culated by the statistics of non-interacting asperity deformation with W* as given by Eqn 1 2 - 4 3 . The full line represents ci as calculated by Eqn 12-46. Analysis of Fig. 1 2 - 1 7 indicates that the contact behavior is essentially that of non-interacting asperities until about 30% of the apparent area is in contact; after that there i s a transition to the behavior of interacting asperities, which goes on until about 50% of the apparent area is in contact. Thus, even though the non-contacting part of the surface begins to rise toward the reference plane under very light loading, this does not significantly affect the contact relations until

1

0

I

2

I

I

4

Dimensionless Load, W'

Figure 1 2 - 1 7 . The observed dependence of degree of contact on load for the rough surface of a constrained deformable specimen against a rigid smooth flat, compared with the relations obtained by (a) assuming noninteraction of asperities (broken line) and (b) the asperity interaction model (solid line). Data by Pullen and Williamson [ 1 4 1 .

335

more than half of the asperities originally above the reference plane are in contact. Other findings of significance f o r the plastic deformation of asperities were reported by Williamson and Hunt 1 1 6 1 , who pressed polished steel balls into flats of rough aluminum under various loads and measured the area of the flattened asperities. Their results are summarized in Fig. 12-18. For solids with homogeneous surface characteristics, such as work-hardened aluminum, fully annealed aluminum, fully annealed gold and work-hardened copper, the ratio of the real area of contact to the nominal area of the indentation was 0.506 k 0.007. Solids with a hardened surface layer on softer underlying material gave ratios in the range 0.25 to 0.35.

q

s

c c

0

0

0

2

4

8

6

Nominal Area of Contact, lo-' m2

Figure 12-18. Degree of contact f o r a hard spherical indenter pressed into the flat, rough surface of an unconstrained deformable body. The drawn rc3 aluminum, data divide into two classes. Homogeneous solids: bead blasted; A cold rolled aluminum, bead blasted; 0 cold rolled aluminum, bead blasted and then annealed; V gold, bead blasted and then annealed; work-hardened turned copper. Cegree of contact: 0.508 k 0.007. Solids with hardened surface layers: 0 and A annealed aluminum, bead blasted. Degree of contact ranged from 0.25 to 0.35. Data by Williamson and Hunt 1 1 6 1 .

+

The experiments of Pullen and Williamson [141 were ingeniously carried out in a manner which left only the rough surface free to respond to the applied load. There are special consequences implicit in such an If the uniform rise model is applicable throughout the arrangement. loading process and the surface geometry is perfectly symmetrical with respect to the reference plane, then the depression of the material which lies above the reference plane should be matched by the rise of the material lying below it until the structure of the original surface is totally obliterated. On the other hand, the indentation experiments of Williamson and Hunt [I61 were carried o u t on a loaded area f o r which the only constraints o n the periphery were those imposed by the surrounding unloaded bulk material. Figure 12-19 shows the impression left by the

336

200 urn Figure 12-19. Static impression left on the ground surface of a disk by a rider under a nominal pressure of 1068 MPa. After A . Dorinson 1 1 1 .

static contact of a flat-ended hardened steel rider on the ground surface of a hardened steel disk (both 50 Rockwell C) under an average nominal contact pressure of 1068 MPa (10,899 kg/cm 2 ) . Calculated a s the plastic yielding of the highest ridges according to the simple relation A = W/p,,,, 20% of the apparent area would be involved in true contact. . A value of 20% for the real area of contact is equivalent to a value of 0.25 for the ratio a/(l-cr) as given by Eqn 12-46. When the pressure on the true contact area is calculated by both the simple model and the uniform rise model, it is found that the extent of plastic deformation is consistent with either model. This is what we would expect according to Fig. 12-17. Our ultimate interest in the mechanics of the contact of structured surfaces is to understand the relations which connect the number of contacts and the real area of contact with the measurable phenomena of wear and friction. At first glance it would seem that a disproportionate amount of effort has gone to the study of the contact and deformation of unrubbed surfaces, whereas from the tribological point of view the behavior of rubbed surfaces is of greater significance. For example, i f the rider which made the impression seen in Fig. 12-19 were traversed on the disk in a direction orthogonal to the grind marks, it would sweep out a contact track whose width would be the diameter of the circle of static On a second traverse the rider would encounter the topography contact. of the deformed surface of the track. Archard 151, as well a s Greenwood and Williamson [71, has emphasized that repeated traverses of the same track eventually stabilize contact to the case of elastic deformation. Thus, the elastic deformation of tribologically altered surfaces is obviously an important subject. But on the other hand, with hardened materials rubbed under the loads for which they were designed, alteration of surface topography by contact does not occur to the extent observed in the soft, ductile materials usually selected to emphasize plastic defor-

337

Figure 1 2 - 2 0 . Alteration of a hard ground surface by rubbing contact. (a) Interferometric fringes showing the characteristics of the original surface, roughness 7 5 - 1 2 7 um. (b) Fringes showing the characteristics of the rubbed track. mation in laboratory investigations. ferometric fringes of an unrubbed

Figure 1 2 - 2 0 shows the interground surface of hardened steel,

average surface roughness 100 urn, compared with the fringes on a track generated by five passes of a rider under a pressure of 1068 MPa with paraffinic white oil as a lubricant. Direct inspection of the photomicrograph with the naked eye serves to identify the rubbed track. The interferogram shows that most of the rubbing took place on the a r e a s created by the runc cation of the higher ridges of the grind marks. The contact of unrubbed surfaces becomes significant in the study of lubrication under heavy loading. In such cases surfaces in their original ground condition are prone to scuff or seize and rubbing damage is likely to be severe. Hence the contact behavior of unrubbed ground surfaces is an important aspect of the study of break-in and how to control i t by lubrication.

12.5.

EXPERIMENTAL STUDIES OF CONTACT AND ADHESION

The previously enunciated basic concept of adhesion a s atomic bonding (Section 1 2 . 2 . 2 ) is intellectually credible but rather remote in the overtly behavioristic sense. There are very few experiments which directly demonstrate the relation between adhesion of surfaces on contact Extraneous complications and interatomic o r intermolecular forces. introduced by the manipulations intrinsically connected with the exis perimentation obscure the results. The work of Bailey and Kay [ 1 7 ] especially noteworthy. Using a double cantilever technique, they partially split a thin sheet of mica. The specific surface energy of the process was calculated from the force required to pull the split portion

of the sheet apart and the amount of area exposed. They then relaxed the separating force, whereupon the deflected laminae rejoined each other. When the separation process was repeated, the force necessary to acccmplish this, although perceptibly less than the force of the first separation, was still of significant magnitude. No extraneous forces were required to reseal the first split. The "jump" technique, used by Tabor e t a e . [lE,19], measures the adhesion ascribable to van der Waals forces when two thin cylindrical sheets of mica oriented at right angles approach each other. Approach is controlled by a piezoelectric transducer and the separation of the two sheets is measured by interferometric fringes of equal chromatic order. The specimen not driven by the piezoeletric transducer is held in position by a sensitive cantilever spring. At some critical distance of approach the attractive van der Waals dispersion forces increase faster than the counterforce of the deflected spring and the two specimens flick into contact, a process which is monitored by the interferometric fringes. No external forces are applied to establish contact. In adhesion experiments where external forces are used to achieve interfacial contact, no matter how small they may be or how carefully applied, the process is always accompanied by macroscopic alterations in the contacting bodies (even the smallest asperity is macroscopic compared to an atom). Let us examine some findings of an investigation by Gane, Pfaelzer and Tabor [ 2 0 ] which took into account macroscopic deformation of the contacting bodies. They studied the contact and adhesion of two orthogonally crossed cylinders. The upper cylinder was held by an arm mounted in a pivot and counterweighted so that the net force on the conjunction of the two specimens was small (on the order of 100 mN). Fastened to the holder of the movable specimen and counteracting the moment of the downward acting force was a sensitive calibrated spring, enabling the net loading force to be adjusted at will and the "pull-off" force necessary to separate the two specimens after contact to be applied. Sensitive displacement transducers indicated the extension of the spring and the movement of the top specimen. The entire apparatus was put in an enclosure which was evacuated to pressures between 66.7 and 6.67 nFa ( 5 ~ 1 0 - ~ ' - 5 x torr). The specimens were polished to the best finish obtainable and were outgassed and ion-bombarded with argon in a vacuum. Thus the experiments were carried out with surfaces which were clean intially and which did not become contaminated during subsequent manipulation. The nature of the contact was followed by means of the electrical resistance. I f the contact area has a radius h , then to a close approximation the formula for contact resistance R is given by (12-47)

339

where p is the electrical resistivity of the material. The observed relations between the contact resistance and the loading or unloading forces can be used to interpret the deformation of the contacting surfaces and the nature of the contact. Curve 1 in Fig. 1 2 - 2 1 shows the behavior of the contact resistance when the deformation is reversibly elastic. Curve 2 shows the course of the contact resistance when adhesion occurs. The loading curve is similar to Curve 1. But i f the adhesive junction formed behaves in a ductile, plastic fashion on unloading, the contact resistance remains at the value Ro during the unloading and also during the "pull-off'' until sufficient tensile force is applied to rupture the junction, whereupon the contact resistance suddenly goes to inf inity. Contact Resistance, R 4

Loading Unloading Pullioff Force, W Figure 12-21. Diagram of conEact resistance behavior for contact without adhesion ( 1 ) and with adhesion ( 2 ) . After Gane, Pfaelzer and Tabor [ 2 0 1 .

The tensile "pull-off'' force T for clean polycrystalline copper was found to be proportional to the two-thirds power of the normal load in the range 0 . 5 to 50 mN (12-48)

the value of T ranging from 10 to 2 5 0 mN. of deformation is

From elastic theory the area

(12-49)

and hence T = KA

( 12-50)

This means that f o r a clean ductile metal with a smooth surface, the area of adhesive contact is substantially equal to the area of elastic deforIn accord with this, the dependence of Ro on the "pull-off'' mation. force was found to be (12-51)

340

a relation which can be obtained from Eqns 12-47 and 12-50. For rough surfaces, where the true area of contact is governed by the statistics of asperity encounter, we would expect a first-power relation between the "pull-off'' force and the normal load ( c 6 . E q n s 1 2 - 2 4 , 12-25,

12-29,

12-30).

Cobalt, a metal less ductile than copper, was much less selfadhesive, with "pull-off'' forces in the range 5-8 mN for loads in the range 5-15 mN. Hard materials such as titanium carbide, glass, sapphire, diamond and germanium showed little or no self-adhesion. The role of ductility in the adhesion process was demonstrated by the influence of temperature on the hardness and self-adhesion of germanium. Between 7 7 3 and 8 7 3 K (500-600 C ) , where the hardness of germanium begins to level off to a value of about 15% of the magnitude at room temperature, selfadhesion under normal loading becomes appreciable. But adhesive bonds formed at 973 K ( 7 0 0 C ) do not persist after cooling to 3 7 3 K under compressive loading and then unloading; i . e . , unless ductility is retained, adhesion is lost. Another demonstration of the influence of ductility is seen in the adhesive behavior of copper against titanium carbide. Under a load of 50 mN the "pull-off'' fcrce was only 20% of the value for copper against copper. Scanning electron micrographs of the fractured junction showed copper adhering to the titanium carbide but no damage to the TiC surface. Hence the rupture of the junction occured entirely within the copper. A study of the contact and adhesion of surfaces under compressive A small stress in ambient air was carried out by 0. L. Anderson "211. specimen of gold was fashioned by melting the end of a fine wire; the ball thus formed was shaped into a sphere by the surface tension forces. The ball was cooled and subsequently manipulated in air; therefore its surface carried the ordinary adsorbed films of atmospheric gases and water vapor. Since gold does not form an oxide by direct reaction with atmospheric oxygen, the film was not of the chemisorbed type and hence was easily removable. When the ball is loaded against a hard, smooth flat surface with sufficient normal stress, it will be deformed, both elastically and plastically, and the apparent area of contact will be A . But though the surface of the ball and the flat may seem macroscopically smooth ( e . 5 . to at least 10 nm), on the microscopic scale only asperities will actually be in contact. Moreover, if the adsorbed film of atmospheric constituents is not displaced from the surface, the area of true contact will be even smaller than that predicted from asperity contact.

In Anderson's experiments the resistance across the common interface of the gold ball and the opposing flat metallic surface was used to evaluate contact.

When izne ball! was

pressed

against

the

flat

under

341

static load, the contact resistance obeyed the following relation: R = .-

C

hm

(12-52)

where c and rn are empirical constants. For gold against a copper flat m was found to be - 2 . 5 , as shown at the top of Fig. 1 2 - 2 2 . (The size of the contact scar is plotted as diameter, but this does not affect the slope of the log-log plot.) The resistance of true metallic contact across an area generated by compressive deformation is given by the constrictive resistance formula (Eqn 12-47) and is inversely proportional to the first powe of the radius of the area. But i f the deformed area is covered with a poorly conducting film of adsorbed vapor or oxide, the electrical res stance across the area will be given by 2P' 2 fi

R = -

(12-53)

where p ' is the resistivity of the film. Thus it would seem that the resistance behavior seen at the top of Fig. 1 2 - 2 2 is of the film type.* If, without altering the load, the ball is twisted half a revolution and back again, the resistance drops by almost an order of magnitude. When subsequently the load is increased statically, thereby increasing the area of the macroscopic contact circle, the electrical resistance varies inversely with the first power of the radius of this area (Fig. 1 2 - 2 2 ) ; i.e. the resistance behavior has changed from the film type to the constrictive type. Such change in the nature of the contact resistance behavior does not necessarily mean that the entire true contact area becomes denuded of adsorbed film components. Electrical conduction is so much easier through the metallic junctions than through the adsorbed film that the film conductance is substantially overwhelmed. Further tangential twisting progressively increases the proportion of metallic contact, as the lower part of Fig. 1 2 - 2 2 shows. The magnitude of the contact resistance drops abruptly each time a shear strain is imposed by twisting, but on intervening increase of static loading the slope of the resistance function is still - 1 . Adhesion was confirmed by direct observation. I f the ball was twisted under load and the subsequent resistance behavior showed a slope of - 1 , attempts to separate the ball from the other contacting surface either broke the attachment of the ball to the wire from which it was formed or else left large chunks of the ball stuck fast to the other sur-

*In fact m (Eqn 1 2 - 5 2 ) is greater than 2.5. Anderson (Reference 2 1 ) ascribes this to work hardening of the metal by plastic deformation.

342

I

Twists

0.3 0.40.5 0.6 0.8 1.0 Contact Diameter, m m Figure 12-22. Behavior of contact resistance a s shear strains are imposed on a gold sphere in contact with a smooth flat surface in air. The slope of the contact resistance against the diameter of the nominal contact area changes from - 2 . 5 for static contact to - 1 on seizure; the drop in the contact resistance is too large to be ascribed to the increase in contact area. After 0. L. Anderson [211.

face. Adhesion required twisting under compressive load. The electrical resistance of two gold balls in contact under static load could be lowered one order of magnitude by the small vibrations of a tuning fork, but the linear log-log plot of subsequent resistance vs. deformation area had a slope of -2.7 and there was no gross adhesion after unloading. Thus we see that severe surface deformation during contact in an ambient air environment is required to bring about adhesion in the engineering sense even for ductile metals. I f we define a coefficient of adhesion E by the relation W" & = -

w

(12-54)

where W is the normal compressive force used to put the two surfaces into contact and W " is the reverse tractive force required to separate them, then the uncertainties in W " will govern the uncertainties in E . Anderson I 2 2 1 examined the results of 1 2 0 0 replicate tests of the adhesion of copper rods 6.35 mm in diameter twisted under a compressive load of 2 2 . 2 N; the technique and the apparatus were described elsewhere [231. The dispersion of E ranged from 0.24 to 4; the distribution was Gaussian with a median value of 0.96. In another study, where the normal load ranged from 1 1 . 1 to 111 N ( 2 . 5 - 2 5 l b ) , 90% of the values of E fell in the

range 0.6-2.5 with a median value of 0.9. The significance of this statistical aspect of adhesion in understanding the influence of contact on tribological processes will be discussed in the following section of this chapter. The inherent sensitivity of adhesion to the severity of true contact intrudes on even the most carefully conducted experimentation when the compressive load is applied by external means. In many of these studies much emphasis is put on the elaborate steps taken to insure surface cleanliness and on the delicacy with which small specimens and light loads can be manipulated. However, it does not seem to be generally recognized that small specimens with small radii of curvature inherently invclve high contact stresses and that the precision rather than the sensitivity of the loading is the governing parameter. Consequently the self-consistency of the adhesion data obtained in such studies is often little betEer than that obtained in larger scale experiments.

12.6.

THE TRIBOLGGICAL SIGNIFICANCE OF CONTACT AND ADHESION

The treatments of contact and adhesion in the foregoing sections of this chapter were based on the normal approach and loading of the two participating surfaces. Rubbing motion, however, is tangential. It remains, therefore, to demonstrate the relevance of analyses and experimental investigations of the normal approach and contact of surfaces to the tribological problems arising from tangential motion. Unfortunately this aspect of tribology has not been studied with the detail and intensity accorded normal contact. Nevertheless it is instructive to examine an analysis such as that of A. P. Green [ 2 4 1 for the junction model of friction. Green pointed out the inadequacy of Bowden and Tabor's simple formula for the coefficient of friction

where Sm is the mean shear stress for plastic flow of the softer material and p , is its yield stress, For most soft, ductile metals this ratio is about 0.17, giving a value of which is obviously at odds with the values greater than unity actually observed for "clean" metals sliding in air. In Green's model it is assumed that when the sliding has attained a steady-state condition the number and the size of the junctions remain constant on the average. All motion f s tangential; there is no normal movenent of one surface relative to the other. A s the surfaces move past each other, asperities engage to form new junctions as fast as old ones are ruptured, so that the load W i s continuously supported and the tan-

344

gentiai force F remains substantially constant. Each junction goes through a life cycle of formation, deformation and rupture, but the steady-state picture of the contacting interface a s a whole is one of numerous junctions, each in its particular instantaneous phase of the life cycle. At any instant the coefficient of friction between the surfaces is

F i = - = -

w

mi

(12-55)

where the bar denotes that the observed quantities for the whole interface are the averaged values of the individual quantities for all the junctions. Instead of this, we may examine the life cycle of the statistically typical junction, such that

(12-56a)

jWidx

8x. = Idx

(

12-56b)

where the integrations are taken over the distance from the initiation to the rupture of the junction.

Direction of sliding

Figure 12-23.

Diagram of a strong junction in steady sliding.

Figure 12-23 is a generalized representat on of a typical strong junction during steady sliding. The mean stresses pi and Si normal and tangential to the direction of sliding depend on the shape of the junction as governed by the angles 8 , 8 ' and 6. As sl ding progresses, the junction deforms. Figure 12-24 shows the plane strain deformation experienced by an asperity pair during encounter and sliding as illustrated by the behavior of a representational model made from plastic compound. It is evident that progressive deformation of the junction after encounter results in an increase in e and a decrease in 6. The detailed plane-strain/plane-stress solutions for this behavior have been published

345

Figure 12-24. Encounter (a), deformation (b), adhesion (c), and fracture (d) of a model asperity junction. After A. P. Green [241.

by Green 1251; they are too lengthy and complicated to present in detail here and the reader is referred to the original source. As an example, let us consider an asperity for which on initial encounter 6 is 0.175 rad (10') and 0 is also 0.175 rad. The computed ratio p i / S i equals 1.75. As the junction progresses along its life interval, both 6 and 8 decrease and the ratio p i / S .1 increases until pL. reaches it maximum, after which pL. decreases sharply. On further deformation of the junction 6 approaches zero (ti. Fig. 12-24c); the magnitude of pi also approaches zero while Thus the magnitude of ui = S i / the magnitude of S. changes very little. L pi is increasing rapidly. This state of affairs continues while p i goes through zero and becomes negative: i . e the junction is under tensile rather than compressive stress. Finally the junction ruptures and its life cycle is terminated. In physical terms, the behavior of a strong junction is governed by the dominant influence of the tensile phase of junction rupture. A weak junction is one in which translational motion of one asperity relative to the other can occur by sliding while the junction is still under compresIn analytical terms, Si remains at a lower level and the sive stress. peak of the curve for pi is broader than is found for a strongly adhesive junction. For either a strong o r a weak junction, substitution of the results of the stress/strain analysis into Eqns 12-56a and 12-56b gives a steady-state, non-fluctuating value for the coefficient of friction. Green's treatment has been criticized on the grounds that the planestrain model of asperity deformation is an oversimplified postulate and that the bald averaging of surface interaction is not in accord with the fluctuations actually observed in strip-chart records of friction experiments. What seems not to be recognized is the power which this general methodology lends to the analysis of rubbina: a physical model of asperity junction interaction is combined with the statistics of surface structure. In view of evidence like that of Anderson [22] for the dispersion of adhesion data, an improved analysis would result by putting tangential junction interaction into the differential format and intro-

346

ducing a statistical distribution expression instead of averaging in the integrated form for a steady-state value as in Eqns 12-56a and 12-5633. In functioning machinery the contacting parts repeatedly rub one anorher many times. The interaction of two surfaces on reiterated concact will i n part depend on the condition in which the previous iteration left them. Under ordinary circumstances, with the machinery operating satisfactorily, each iteration is much like the one before and an analysis of steady-state wear or friction can be made on the basis of one cycle of surface interaction. Generally in such cases, but not necessarily always, asperity deformation is elastic rather than plastic. Whether an adhesive junction forms depends on the condition of the asperity surface. If the materials p e t b e are easily adhesive but the surfaces are covered by a film which inhibits adhesion, then to initiate adhesion obviously the film must first be removed, broken up o r penetrated. The subsequent course of adhesive contact will then be governed by such factors a s the size of the contact, the shape of the asperity, the impressed load, the strength of the material, etc., in accordance with the fundamental modes of behavior. The interplay of those influences which inhibit adhesion and those which promote it must be recognized in interpreting two commonly encountered aspects of rubbing contact: smooth, regular, controlled wear on the one hand, and destructive, self-accelerating catastrophe on the other. Figure 12-25 shows the appearance of two locations on a disk of hardened steel used in a pin-and-disk wear experiment at a contact pressure of 1069 MPa (10,900 kg/cm 2 ) and a rubbing speed of 0.508 m/s with

b

Figure 12-25. Alteration of a ground surface by rubbinq contact. (a) Plastic deformation of grind marks. (b) Adhesive transfer from the slider. Unpublished work, A. Dorinson.

347

paraffinic white oil as a lubricant. The total rubbing time was one second, and in that time each location on the contact track was subjected to 5 passes of the rider. These rubbing condtions are quite severe, and the average depth-wear rate of the rider was 6 um/s. Figure 12-25a is a location on the track typical of smooth, controlled wear; the only signs of contact are the plastic deformation furrows in the grind marks. But in Fig. 12-25b there is recognizable evidence for the transfer of metal from the pin to the disk by adhesion. I f the purpose of lubrication were ideally achieved and the surfaces of machine elements transmitted force without any mutual contact of the materials of which they were made, there would be no problems of adhesive damage. I f this cannot be accomplished, then the next best thing is to eliminate the catastrophic aspects of adhesive contact (scuffing,

seizure, etc.) and keep the wear smooth, orderly and at an acceptably low rate. An extreme-pressure lubricant fulfills this function at contact pressures and rubbing speeds incompatible with the maintenance of a hydrodynamic film. Smooth, acceptable wear in the presence of an extreme-pressure additive means that on the one hand there are enough asperities in contact so that removal of material occurs at a detectable rate but on the other hand this rate stays at a tolerable level without any self-acceleration. Proper analysis of the functioning of additivecompounded lubricants requires knowledge of the basic contact condtions. Thus we see how study of asperity interaction in surface contact furthers insight into the nature of friction and wear and of their control by lubricants, both uncompounded and compounded.

REFERENCES 1. 2. 2

u.

4. 5. 6. 7.

A. Dorinson, ASLE Trans., 8 ( 1 9 6 5 ) 1 0 0 - 1 0 8 . S . Timoshenko and J. N. Goodier, Theory of Elasticity, 2 n d Ed., McGraw-Hill, New York, 1 9 5 1 , pp. 351 66. A. I . Ishlinsky, J. Appl. Math. Mech. USSR, 8 ( 1 9 4 4 ) 2 2 3 . J. F . Archard, J. Appl. Phys., 24 ( 1 9 5 3 ) 9 8 1 - 9 8 8 . J . F . Archard, Proc. Roy. SOC. London, A243 ( 1 9 5 7 / 1 9 5 8 ) 1 9 0 - 2 0 5 . K . L . Johnson, Brit. J. Appl. Phys., 9 ( 1 9 5 8 ) 199-200. J. A. Greenwood and J. B. P. Williamson, P r o c . Roy. SOC. London, A295 ( 1 9 6 6 ) 3 0 0 - 3 1 9 .

8.

J . A.

Greenwood, J. Lubrication

Tech.

(Trans.. ASME),

89F

(1967)

81-91.

10.

J . B . P . Williamson, Topography of Solid Surfaces, in Interdisciplinary Approach to Friction and Wear, NASA S P - 1 8 1 , National Aeronautics and Space Administration, Washington, D. C., 1 9 6 8 , pp. 8 5 - 1 4 2 . D. J. Whitehouse and J. F. Archard, Proc. Roy. SOC. London, A 3 1 6

11.

J . A. Greenwood and J. H. Tripp, J. Appl. Mechanics

12. 13. 14.

89E ( 1 9 6 7 ) 1 5 3 - 1 5 9 . Y. Kimura, Wear, 1 5 ( 1 9 7 0 ) 4 7 - 5 5 . P. R. Nayak, Wear, 26 ( 1 9 7 3 ) 3 0 5 - 3 3 3 . J. Pullen and 3 . B. P. Williamson, Proc. Roy. SOC. London, A327 ( 1 9 7 2 ) . 159-173.

9.

( 1 9 7 0 ) 97-121.

(Trans.

ASME),

348 15. 16.

J. B. P. Williamson and R. T. Hunt, J. Sci.

Instr. (J. Phys. E), Series 2, 1 ( 1 9 6 8 ) 7 4 9 - 7 5 2 . J. B. P. Williamson and R. T. Hunt, Proc. Roy. SOC. London, A327

17.

( 1 9 7 2 ) 147-157. A. I. Bailey and S. M. Kay, Proc. 47-56.

18.

D. Tabor and R. H. S. Winterton, Proc. Roy. SOC. London, A312 ( 1 9 6 9 )

19.

J.

Roy.

SOC.

London,

A301

(1964)

435-450.

N.

Israelachvili

and

D.

Tabor,

Proc. Roy. SOC. London, A331

( 1 9 7 2 ) 19-38. 20. 21. 22. 23.

N. Gane, P. F. Pfaelzer and D. Tabor, Proc. Roy. SOC.

London,

P.

Andreatch

and

0. L.

Anderson,

Rev.

Sci.

Instr., 30 ( 1 9 5 9 )

498-499. 24. 25.

A340

( 1 9 7 4 ) 495-517. 0. L. Anderson, Wear, 3 ( 1 9 6 0 ) 2 5 3 - 2 7 3 . 0. L. Anderson, J. A p p l . Phys., 30 ( 1 9 5 4 ) 5 9 3 - 5 9 4 . ?. Green, Proc. R o y . SOC. London, A228 ( 1 9 5 5 ) 1 9 1 - 2 0 4 . A. P. Green, J. Mechanics Phys. Solids, 2 ( 1 9 5 4 ) 1 9 7 - 2 1 1 . A,

349

Chapter 13 WEAR:

BASIC PRINCIPLES AND GENERAL BEHAVIOR

13.1.

A BASIC DEFINITION OF WEAR

At first glance wear seems to be a commonplace and obvious phenomenon that can be taken for granted without elaborate inquiry into its nature, but in fact it is so complex that it has not even been defined satisfactorily. The everyday meaning of the English word "wear" in its sense of impairment or deterioration or of loss of material seems to be derived from an older meaning signifying the deterioration of clothing by being wonn as body covering. In the vocabulary of ordinary mechanical engineering practice, the meaning is generally taken to signify a t t n i X i v e wear: i . e . wear by rubbing. As the first step toward the development of a fundamental outlook on the subject, let us establish in descriptive terms basically what is meant by wear. Since we are interested here in wear from a conventional engineering point of view, we can restrict our scrutiny to the behavior of solid bodies. The overt behavior designated as wear in the working language of engineering as well as in the everyday language of common experience is loss of material from and change of shape in a solid body by mechanical action. The mode of mechanical action encountered most frequently is rubbing, but other modes-impact, for example-can also bring about wear. It can be deduced from empirical evidence that the mechanical wear of solid bodies requires the simultaneous presence of these four physical conditions: ( A ) there must be at least two separate and distinct bodies, each with its own bounding surface; ( b ) these bodies must be in mutual contact over some portion of their surfaces; ( c ) the bodies must be loaded together by a force; ( d ) there must be motion of one contacting surface relative to the other. If these conditions are fulfilled and an irreversible change is observed in the size o r the shape of either or both of the bodies, then we conclude that the one or the both of the bodies has suffered wear. It is essentially This is our definition of mechanical wear. phenomenological, and in contrast to a purely conceptual model based on a phiahi assumptions and inexorable logical reasoning, the governing conditions and conclusions of this definition are in terms of observable behavior. Nevertheless the definition is fundamental enough to fit all

350

cases of wear that are significant in the theory and practice of lubrication. And because of its phenomenological origin the definition is free of the restrictions, psychological and otherwise, inherent in such stateo d o ~ ,u n d e n i h e d change of dimension i n ~ e h v i c e ments as "wear is resulting from pressure and sliding exerted by some other body."*

...

Our definition does not explicitly specify wear to be d o b n of material, which seems to contradict familiar experience. However, loss of material implies a corresponding decrease in the size of the specimen, a fact which is frequently used in the experimental study of wear, where sensitive measurements of changes in size are translated into loss of mass, and vice versa. Change of shape without necessarily o r explicitly including change of size is incorporated into o u r generalized definition of wear because in certain instances part of the total process may involve loss of material and formation of loose debris and part may be displacement of material from one location to another by mechanisms such as adhesive transfer or plastic deformation. The changes may be quite subtle: e.g. piling up of dislocations which require careful observation to detect leads to formation of overtly seen cracks after many reiterated cycles of contact. Since the same four input conditions may bring about loss of material and change of shape side by side, we have elected to make the definition of wear include them both. The definition does not require that the change of size or shape be slow, smooth o r orderly. Catastrophic wear fulfills the requirements of the definition; it differs from smooth wear in degree rather than in kind. By removing the restriction that all the participating bodies must be solid the scope of the definition can be extended to include cases such as the removal of material by impingement of a liquid, either as a stream or in discrete drops. Some semantic disagreements arise between this extended sense of the definition of wear and traditional points of view, but these do not affect the application of the definition to the behavior of solid bodies. 13.2.

PHENOMENOLOGICAL WEAR

By phenomenological wear we mean wear as it is actually observed and measured. The behavior encountered ranges from the crude qualitative observations of ordinary experience to the highly sensitive measurements of rigorously controlled laboratory experiments. Since our major interest in this discussion is in the fundamental and scientific aspects of wear, the treatment will be focused on quantitative behavior.

*It makes no essential difference, as far as the basic behavior is concerned, whether the change is fast o r slow, desired o r undesired, connected with a service function or unconnected.

351

TABLE 1 3 - 1 .

TYPES OF MOTION IN INTERACTING SURFACES

Type of motion

Engineering example

Laboratory example

Pure sliding

Journal in bearing Piston/cylinder Cam/fixed follower

Pin on disk Pin on ring Block on ring

Sliding/rolling

Involute gear teeth Cam/tappet (tappet rotat ing)

Ring on ring (differential speeds of rotation; differential tangential speed vectors)

Pure rolling

Wheel on rail Cam on rolling follower

Ring on ring (same diameters)

Impinging motion

Stream of abrasive particles Rolling contact (normal component)

Striker against plate

Table 1 3 - 1 shows a classificatory approach to phenomenological wear based on four types of motion that can be identified in the mechanical interaction of contacting surfaces. In pure sliding the region of contact remains fixed on the stationary body and travels along the rubbing path on the moving body. A familiar example of this kind of contact is found in a stationary pin rubbing on a rotating disk o r ring. I n mixed sliding and roiling the region of contact travels along the rubbing path on both bodies, typical examples being the action of involute gear teeth o r of differentially rotating rings. Pure rolling is exemplified by a wheel on a rail or by two synchronously rotating rings, provided there is no elastic deformation under load.* A simple example of normal o r impinging contact is the hammering action of a striker on a plate. A more complicated example is the periphery of a disk rolling on a flat surface, where there is an impinging component normal to the flat. Looking at wear in terms of these four types of motion does not constitute a f u n damental system of classification but it does provide a convenient empirical approach to the examination of phenomenological wear. 13.2.1.

Wear in Pure Sliding

In pure sliding a fixed area on one body is in continual contact with the other body along a path determined by the geometric configura-

*This restriction may be relieved i f the two rotating rings are of the same material and the same diameter. In such a case the contact region between the two rings is a flat plane and the changing radii when entering the contact region region produces the same strain in both bodies simultaneously.

352

tion of the system. The body with the fixed contact area is not necessarily the stationary body with respect to the overall mechanical system, as there are configurations in which the fixed area is on the body that moves in the absolute sense. The character of the sliding is determined by the geometry of the path and the relative motion. Pure sliding is probably the most widely utilized arrangement in laboratory studies of wear because of the ease with which experimental conditions can be controlled. Nevertheless, reproducibility of results is not always of the highest order, even for careful work. A l s o , there are so many different kinds of apparatus based on the pure sliding principle that reliable comparison of the primary data is often complicated by the individualistic details of the construction and operation of the In 1967 the OECD reported on a group study of wear various devices. during sliding [ l ] in which the specimen materials and experimental conditions such as load and rubbing speed were rigorously standardized but the choice of apparatus was left to the individual participants, of whom there were eighteen. The results obtained by the various participants were S O badly scattered that the report was concerned mainly with explaining the disagreements. A more encouraging attitude emerges when some of the careful work found in the literature is examined with close attention to the details of the experimental data. One of the pioneering investigations of modern w a r research is that of Burwell and Strang 121, who worked with steel sliding against steel in a pin and disk apparatus. Figure 1 3 - 1 shows the results for cylindrically-ended pins rubbing at 2 0 cm/s with hexadecane as the lubricant. Volumetric wear is linearly proportional T,O sliding

lo

t

1 -

3601 MPa

40.0MPa

-

/pa

0

0.2 0.4

0.6

0.8

1.0

1.2

Distance Rubbed, km

Figure 13-1. Course of wear: SAE 1095 steel pins, BHN 223, on SAE steel disks, BHN 55. Contact pressures in MPa as shown; speed 2 0 cm/s; hexadecane as lubricant. From data by Burwell and Strang 121.

353

distance and all the plotted lines pass through the origin; i.e. the wear rate for each loading pressure remains constant from the start of the run. similar investigation was carried out by Dorinson and Broman 131 with conically-ended pins of hardened A I S I 1045 steel rubbing at 50.8 cm per second in the presence of white oil. Figure 13-2 shows the average course of wear for six replicate experiments at a contact pressure of 1069 MPa (10,898 kg/cm2) and five experiments at 482.7 MPa (4922 kg/cm2). At either pressure there is an initial phase with a high rate of wear, followed by a transition to a low-rate plateau, which then goes over to a terminal phase with a substantially steady higher rate. A l s o shown in Fig. 13-2 is a comparison with some results by Burwell and Strang 121 using conically-ended pins. A

Rubbing Distance, km Figure 13-2. Wear of hardened steel; comparison of the results of Dorinson and Broman [3] with the results of Burwell and Strang [21. Burwell and Strang: (a) wear rate 0.057 c m / k m at 951.3 MPa contact pressure; (b) 0.0144 cm/km at 622.7 MPa. Dorinson and Broman: (c) wear rate 0.00830 cm/km at 1069 MPa; (d) 0.00201 cm/km at 482.7 MPa.

There is more resemblance between the results of the two investigations than the forced linearization of Burwell and Strang's data would lead one to believe. When the experimental data are examined closely, a s i n the curve for wear at 6 2 2 . 1 MPa, a small but definite inflection is observed, similar to the short plateau in Dorinson and Broman's results for wear at 1069 MPa. The manipulative difficulties notwithstanding, careful wear experiments do yield reasonably self-consistent results;

354

Dorinson and Broman [ 3 , 4, 51 have published data for many replicate experiments which demonstrate that the structured curves seen in Fig. 13-2 are reliable patterns of behavior and not artifacts due to imprecise and unreproducible experimental results. The three-stage curve can be regarded as characteristic behavior for wear in the presence of noncompounded petroleum oils under moderately severe pressure conditions. At extremely high contact pressures it is difficult to discern such structured behavior in the course of the wear process because of the dispersion and the poor reproducibility of the data: at very low pressures the structure of the curve shows only the transition from the initial rate to a stable phase with a much lower rate and the final transition to a higher rate does not appear at all. Burwell and Strang [ 2 ] observed the following relations between wear rate and loading pressure. Below a critical pressure which depended on the hardness of the rubbing specimen, the depth-rate of wear for conically-ended pins was a linear function of the pressure,

Ah

- -

L

-

kD

(13-1)

where Ah is the net depth of wear, L is the rubbing distance, p is the loading pressure and k is a constant. Figure 1 3 - 3 shows the wear behavior of A I S I 1095 steel at two levels of hardness, 4 3 0 Brine11 ( 4 5

z

\ N

25

-

5

OD

0

4," 200

600

1000 400 Pressure, MPa

1200

2000

Figure 1 3 - 3 . Influence of contact pressure on wear. Slider: 120' cone of SAE 1 0 9 5 steel. Rubbing speed: 20 cm/s. Lubricant: purified hexadecane. Hardness of slider: (a) 2 2 3 BHN; (5) 4 3 0 S H N . From data by Burwell and Strang [ 2 ] .

Rockwell C ) and 2 3 3 Brine11 ( 2 1 Rc). Equation 13-1 was found to be valid f o r pressures ranging from 1 3 0 to 1400 MPa, depending on the hardness of the rubbing specimen. The limiting pressure for the harder pieces was 1 4 0 0 MPa and the value of k was 1 . 5 3 x m2/N; for the softer pieces m2/N respectively. At pressures the values were 720 MPa and 1 . 2 8 x

355

above the critical value the wear rate increased very rapidly, suggesting a change in mechanism. Table 1 3 - 2 shows some wear results at higher For example, B u r pressures which do not obey the relation of Eqn 1 3 - 1 . well and Strang [ Z ] found that the wear rate, A h / L , divided by the pressure p was some 1.8 times greater at 9 5 6 . 3 MPa than at 6 2 2 . 7 MPa. Dorinson and Broman [ 3 ] observed analogous behavior in the comparison of wear at 1 9 6 9 MPa and at 4 8 2 . 7 MPa. TABLE 1 3 - 2 . Pressure, p MPa 951.3 622.7 1069 482.7

FAILURE TO OBEY EQN 1 3 - 1 AT HIGHER CONTACT PRESSURES

Wear rate, A h / L , cm/km 0.0500 0.0181 0.0126 0.00346

AH/Lp, 10-16

2

Speed, cm/s

Investigator

m /N

5.26 2.91 1.81 0.717

20 20 50.8 50.8

(a) (a) (b) (b)

(a) Burwell and Strang 1 2 1 . (b) Dorinson and Broman [ 3 1 . Hirst and Lancaster [ 6 1 , using a pin-on-ring apparatus, found that the course of volumetric wear showed three different modes of behavior, The behavior exhibited by an aluriinum pin as illustrated in Fig. 1 3 - 4 . rubbing on a Stellite ring as seen in Fig. 1 3 - 4 a is characterized by an initially steep rate. The steepness of the initial part of the curve and the slope of the steady-state terminal portion of this type of wear behavior may vary greatly, depending on the specimen materials and on rubbing conditions such as load, speed, etc. In the opinion of Hirst and Lancaster, the wear debris generated in the initial stage of this type of process with metal specimens is substantially metallic, whereas the debris from the steady-state stage is largely oxidized. The course of

3

0

100 200 300

0 100 200 300

0 1000 2000 3000

Time, seconds Figure 1 3 - 4 . Types of wear behavior for pins against Stellite rings; rubbing speed: 6 8 . 5 cm/s; lubricant: hexadecane. (a) A.luminum pin, load 9.6 N. (b) 6 0 / 4 0 Brass pin, load 7 . 3 5 N. (c) Bronze pin, load 1 2 . 2 5 N. Data by Hirst and Lancaster [ 6 1 .

356

wear exemplified by brass rubbing on Stellite (Fig. 13-4b) is linear from the start. The loose debris consists of relatively large fragments of metallic character and there is a smeared metallic transfer film on the moving specimen. The third kind of wear behavior (cd. Fig. 13-4c for bronze against Stellite) is characterized by a transition from a low initial rate to a high-rate steady-state phase which generates predominantly me tall ic debris. Hirst and Lancaster’s experiments for the most part were carried o u t with pins of soft metals such as brass, bronze o r aluminum rubbing against rings of Stellite in the presence of cetane as a lubricant. The primary experimental measurement was the depth of the wear scar on the pin, which was converted to volume of material worn away. Table 13-3, which is assembled from the results of a study of dry wear by Archard and Hirst [71, includes examples of hard materials rubbing against hard materials and lists the nature of the wear behavior in terms of the curves shown in Fig. 13-4. The kind of rubbing specimen is not the only factor that influences the course of wear: Fig. 13-5 shows some of the findings of Archard [81 f o r the effect of load o n the wear of both hard and soft pins. The type of wear behavior was inferred from the extrapolation of the steady-state wear line to zero time. The wear of Stellite rubbing on tool steel at lower loads can be represented by curves such as Fig. 13-4c, at higher loads by curves such as Fig. 3-4a, and at a load of 3.2 N by a straight line through the origin. The wear curves for brass against tool steel at higher loads are exemplif ed by

TABLE 13-3. WEAR BEHAVIOR OF VARIOUS MATERIALS IN PIN-ONRING APPARATUS CLASSIFIED ACCORDING TO FIGURE 13-4 Pin

Ring

Steel Brass, 70/30 Stainless steel Stellite Tool steel Teflon Brass, 40/60 Stainless steel Beryllium copper Stellite Tungsten carbide Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel

Steel Brass, 70/30 Stainless steel Stellite Tool steel Tool steel Tool steel Tungsten carbide Tool steel Tool steel Steel Tool steel Tool steel Tool steel Tool steel Tool steel Tool steel

Load, N 0.490 0.785 2.451 24.517 3.923 1.471 1.177 11.768 9.807 7.355 9.807 19.614 14.710 9.120 5.688 3.236 0.788

Wear behavior, Fig. 13-4 C C

a a b b b b b b b b a a a b b

From data by Archard and Hirst [7] for unlubricated wear at 180 cm/s.

357

40

30

20 10

0 10 20 30 40 50 Time,103 seconds

Figure 13-5. cated rubbing Stellite pin Data by J. F.

0 0

5 10 15 20 25 Time,lO* seconds

Influence of load on the type of wear behavior; unlubriat 186 cm/s; load in newtons as indicated on diagrams. (a) on tool steel ring; (b) 60/40 brass pin on tool steel ring. Archard [a].

Fig. 13-4a and at lower loads by Fig. 13-4b. Archard plotted the wear rates obtained from the slopes of the steady-state portions of the graphs in Fig. 13-5 against the loads on a For the most part the slope of the double-logarithmic log-log scale [ E l . plot was unity, which is compatible with a relation of the form

0

=

k,W

(13-2)

where 0 = AV/AL is the volumetric distance-dependent rate of wear, W is the load, and k, is the wear rate for some reference load, most conveniently set at W = 1. When the slope of the double-logarithmic wearrate/load plot differs from unity,

0

=

k,Wm

(13-3)

For m > 1, the wear-rate as a function of load plotted in Cartesian coordinates is concave upward; for m < 1 , concave downward. Abrupt transitions from m = 1 to m > 1, as shown in Fig. 13-6, indicate a critical change in the nature of the wear process in response to the magnitude of the load. A three-stage structured wear curve, such as is seen for Dorinson and Broman's data in Fig. 13-2, might be thought of as a combination of a curve such as Fig. 13-4a followed by a curve of the type of Fig. 13-4c. The fact that the wear is plotted in terms of volume in Fig. 13-4 whereas Dorinson and Broman's curves are for depth-wear does not introduce any real complications, for Dorinson and Broman showed that when their depthwear plots were converted to volume-wear, their resulting curves retained the three-stage structure [ 2 , 31. There is no demonstrable basis for regarding the curves of Fig. 13-4 as basic modes of wear behavior and

358

Load, newtons Figure 1 3 - 6 . Wear rate transitions and load. o Stainless steel on high speed steel, 180, cm/s. 0 70/30 Brass on hardened tool steel, 180 cm/s. Data by Archard and Hirst [ 7 ] .

therefore they cannot be viewed as more fundamental o r less behavioristic than those of Fig. 13-2. 13.2.2.

Mixed Sliding and Rolling

Rubbing action in mixed sliding and rolling is most easily visualized by the case of two rings of the same radius rotating at different angular velocities. The net sliding velocity is given by v2

-

v 1 = (w,

-

wl)R

where R is the radius of the rings and w, and velocities. I f the rings have different radii,

v2 - v 1 = I q 2

-

W,Rll

(13-4a) w2

are

the

angular

(13-4b)

the magnitude of the sliding speed being determined by the positive value of the difference between the peripheral velocities. Queener, Smith and Mitchell 191 published data for the wear of both the fast and the slow ring in a two-ring apparatus. Figure 13-7 shows some of their results recalculated to put them on a basis suitable for direct comparison; since one ring is larger than the other, wear is expressed in milligrams of metal lost per centimeter of periphery. Surface roughness has a strong influence on the rate of the initial "break-in" phase of the wear behavior, which diminishes when the course of wear changes to a constant-rate, steady-state phase. Both the initial breakin wear and the terminal steady-state wear rate are greater for the disk with the slower moving surface. In general the wear of a sliding/rolling configuration follows a basic course resembling that of pure sliding.

359

u

n r

E

Y

0

E.

Sliding Distonce , krn

Figure 13-7. Wear of two rings in sliding/rolling contact: AISI 4 3 4 0 steel: sliding speed 3 . 9 8 cm/s. (a) Slow ring 9 . 1 4 4 cm diameter, 1 1 4 3 nm surface roughness: (a') fast ring 6 . 0 9 6 cm diameter, 1 1 4 3 nm surface roughness. (b) Slow ring 9 . 1 4 4 cm diameter, 2 2 9 nm surface roughness; (b') fast ring 6 . 0 9 6 cm diameter, 2 2 9 nm surface roughness. From data by Queener, Smith and Mitchell [ 9 ] .

Numerous machine elements in engineering practice involve mixed sliding and rolling. The meshing action of involute gear teeth is a familiar example: another is the contact of the rolling elements against the inner and outer races of a rolling element bearing. The cam/tappet combination i n an automotive internal combustion engine operates with mixed sliding and rolling: the cam is offset from the axis of the tappet so that when the slanted cam nose contacts the crowned tappet it applies a rotational moment to the latter. Sliding occurs because there is enough friction between the tappet and its guide so that the motion of the tappet lags behind that of the cam. 13.2.3.

Pure Rolling

In pure rolling the surface velocities of the two contacting bodies are numerically equal and in the same direction. Idealized examples are a rotating wheel on a flat rail or a roller follower against a cam, provided that in general the contacting surfaces are not deflected, elastically or otherwise, by the imposition of a load.* The contact action in a rolling element bearing is pure rolling only in exceptional cases, even in the absence of load. As can be seen in Fig. 13-8, pure rolling

*For special circumstances, see the footnote on page 3 5 1 .

360

+

I

Figure 13-8.

Contact action in a rolling element bearing

.

requires that the inner and outer races rotate so that their peripheral velocities match that of the rolling element according to the relation

(13-5)

where nh is the number of revolutions of the rolling element about its own axis per unit time, M , the Iylmber of revolutions of the inner race and n 2 the number of revolutions of the outer race per unit time. In ordinary engineering practice both races of a rolling element bearing do not rotate simultaneously; one race is usually stationary. The net rubbing velocities at the contacting interfaces of a rolling element are the consequence of the interaction of a complex of tractive i f the bearing is lubricated-which introduces cage forces-particularly movement into the picture (see Fig. 1 3 - 8 ) . Thus the usual characteristic motion of the practical rolling element bearing is not pure rolling. Nevertheless the typical mode of surface damage in rolling element bearing action is fatigue, which is manifest by the appearance of cracks in the material and eventually by pitting and spalling. Since fatigue is associated with cyclical loading rather than continuous rubbing, the sliding component does not seem to be the crucial influence in the deterioration of a rolling element bearing, even though the ratio of sliding to rolling motion may be relatively large. The strong association of fatigue failure with rolling motion is exemplified by the behavior of involute gears: scuffing damage is found principally in the root and tip regions, where sliding is predominant, whereas pitting and spalling occur at the pitch line, where the motion is substantially rolling.

361

13.2.4.

Impinging Contact

The impingement of one body on another is characterized by the short duration of the contact. However, even a single such contact can result in detectable removal of material, as described by Bowden and Tabor [lo] for a hard metal hammer striking orthogonally a single time against a softer nail. The wear process in such case involves adhesive transfer of metal during contact. The gross wear observed on repeated impacts of a striker against a plate is a combination of permanent deformation by plastic flow and detachment of wear debris by fatigue failure. I f the striker and the plate are both materials of comparable hardness and not difficult to deform plastically, both bodies will experience comparable wear. But i f one of the bodies is substantially harder than the other-the striker, for example-then the preponderant fraction of the total wear will be found in the softer body. This type of wear process was reported in detail by Wellinger and Breckel [ll]. A n energy analysis of experiments with a hard alloy striker impacting on a mild steel plate showed that it required only 50 cycles of impact to achieve 95% of the flow deformation observed in a test lasting 500,000 cycles. Detached wear particles were found after 100 cycles, some of which were gray and some, obviously oxidized, of a red-brown color. The wear (measured as weight l o s s and converted to volume) for a test duration of 500,000 cycles ranged from a high of c u . 20 m m 3 to a low of 0.6 mm 3 , depending on the hardness of the struck body and the particular combination of the mass of the striker and its speed at impact. The model of Engel, Lyons and Siroco [12] treats impact wear as a two-stage fatigue process: an initial phase of accumulating subsurface damage with substantially no loss of material, followed by overt, measurable wear. Engel and Siroco [13] studied the experimentally observed course of wear of a cylindrically faced hammer striking a flat plate as a function of the number of impacts and found the following relation to hold for purely orthogonal impingement,

KI:(

hz h1 =

(13-6)

where si is the number of cycles required to produce wear to the depth Theoretically the lower limiting value of 5 A. should be c 0 , the numhi. ber of impacts at which detectable wear first appears. For dry wear 5 0 was usually an order of magnitude less than calculated; for lubricated wear 5 , was greater than calculated, sometimes by as much a s two orders of magnitude. The value of the exponent K ranged from 0.126 to 0.211 for dry wear, from 0.171 to 0.357 for lubricated wear. The range of 5 was from 104 to 109 cycles.

362

Another mode of impingement is that of a free particle borne by a stream of gas or liquid. The wear resulting from this type of impact is usually designated as erosion. Since an individual particle has a small mass relative to that of the impacted body, the damage to the latter is a consequence of the high velocity of the impacting particle and the large number of particles that impinge on the target. An important parameter in the wear is the angle of impingement. Bitter [141 distinguished between two basic phenomena in the overall wear: (a) embrittlement by strain hardening and subsequent spalling, and (b) cutting action as the impinging particle plows the target body. 13.2.5.

Dry and Lubricated Wear

?he distinction between dry and lubricated wear is often taken to imply that dry wear is a basic mode of behavior to be used as a standard of reference for lubricated wear. But it should be recognized that there is no generally accepted fixed standard f o r the dry surface condition. I n fact, each individual surface is influenced by the way in which i t was prepared, and furthermore the ambient surroundings in which it is placed also exert their influence even before the rubbing process proper begins. The usually accepted basic standard for dry wear in clean conditions is based on carefully cleaned surfaces in the cleanest vacuum obtainable, but the questions of technique thus brought up also involve questions about the rigor of the standard. I t follows that in terms of such a reference, surfaces in equilibrium with the oxygen and moisture of ordinary air could be considered as lubricated by a film of oxide and adsorbed water vapor: from the everyday practical point of view the difference between dry and lubricated wear is usually taken to be the behavior of rubbing surfaces with only this adventitious film and their behavior in the presence of deliberately introduced lubricant substances. ?he effect of such operating parameters as load and rubbing speed on the quantitative relation of dry and lubricated wear is neither simple nor obvious. Table 13-4 shows two direct comparisons: one of data from the work of Kerridge and Lancaster I 1 5 1 and the other of unpublished data TABLE 13-4. COMPARISON OF DRY AND LUBRICATED WEAR Load, Speed, Wear rate, N m’s 1 0 - 4 cm3N-lm-1 Brass on t o o l steel (a)

Dry 49 Lubricated (c) 221 Bronze on mild steel (b) Dry 19.6 Lubricated (d) 19.6

0.04 0.04 1.0 1.0

0.00967 0.000222 102,500 4.9 t 1.0

(a) Kerridge and Lancaster [151. (b) A . Dorinson, unpublished work. (c) Hexadecane. (d) 0.5% Stearic acid in white oil.

363

by A. Dorinson. The volumetric wear rates are given as cm3 of wear per meter of sliding distance per newton of loading force. The dry wear rate of bronze rubbing on mild steel is c a . lo7 times the dry rate of brass rubbing on tool steel. The analogous ratio for lubricated wear is only ca. 2.2 x lo4, a difference of some 450-fold. Lubricated wear is 2.3% of dry wear for brass on tool steel, 0.0048% for bronze on mild steel.

13.2.6.

Wear of Non-metals

The wear behavior of metals in a technological context is familiar because they are the traditional materials of construction of many critical and expensive machine components. The wear behavior of non-metals by and large has been studied less systematically than that of metals and is often regarded as belonging in an entirely different category. With only a mention of the fundamental differences between metals and non-metalswhich includes such items as electronic structure, solid-state bonding and chemical properties-we note that the most obvious properties which characterize metals from an engineering point of view are their high mechanical strength and their good ductility. Ceramic materials usually have good strength and high hardness but are generally brittle. Organic plastics, though they may be very ductile, for the most part show low reI t is to the numerical values of sistance to mechanical deformation. physical properties such as these that we look for the differentiation in the wear behavior of non-metals and metals. As anticipated, the wear rate of a hard ceramic is very low. E. J. D w e l l 1161 reported values for single-crystal rutile sliding at 30.5 cm per second, lubricated with water, that ranged from 1.02 x to 35.7 x ~ m ~ N - l ,m - depending ~ on the orientation of the crystal with respect to the direction of sliding. Analogous values for single-crystal to 51 x 10-l’ ~ m ~ N - ’ m - ~In . conMgA104 spinel ranged from 2.04 x trast, the lowest wear rate seen in Table 13-4 for brass against steel at a much lower rubbing speed is 2300 as great as the highest rate quoted for the MgA104 ceramic. Because of their low wear rates and their refractory characteristlcs, ceramics and jewels are frequently used as materials of construction for surfaces that rub at high speeds. AS pointed out by w. A. Glaeser [17], the heat generated at the highly stressed asperity contacts becomes significant in the wear Process; steep thermal gradients occur at these hot spots because of the low thermal diffusivity of the ceramic material and the resulting stresses can lead to fracture of surface layers, which becomes macroscopically evident a s cracking and flaking [la]. The behavior of weak, brittle non-metallic materials is exemplified by the wear of “hard” carbon such as is used in electrical brushes. Figure 13-9 shows some typical data [ 1 9 1 . Besides

straightforward observations of overt behavior, the wear of

364

Tool steel

-

Mild steel

Time,seconds

Figure 13-9. Wear of carbon riders against metal speed, 14.2 m / s . Data by J. K. Lancaster 1191.

rings:

load,

10 N;

12

g10 %I3 c

g6

84 92

S O 0

5

10

15 20 25

Distance,104cm

Sliding Speed,cm/s

Figure 13-10. Wear of polytetrafluoroethylene against glass. (a) Course of wear at 50 C , 9.81 N load. (b) Influence of sliding speed on wear rate. Data by Tanaka, Uchiyama and Toyooka 1201.

organic plastics is often studied in relation to the molecular structure of the material. In their investigation of the wear of polytetrafluoroethylene against glass, Tanaka, Uchiyama and Toyooka [20] found that the two modes of response to rubbing speed seen in Fig. 13-10a are particularized manifestations of a far-reaching systematic relation between wear rate and sliding speed as shown in Fig. 13-lob. The maxima seen in Fig. 13-lob can be related to the influence of chemical and cyrstalline structures in the polymeric solid. The wear behavior of ultrahigh-molecular-weight polyethylene against a special titanium alloy as observed by Miller e t al. [21] followed the low-speed pattern shown by PTFE 1201 but at a steady-state rate of wear Only 0.015 to 0.1 as great.

365

MECHANISTIC PROCESSES IN PHENOMENOLOGICAL WEAR

13.3.

As defined in Section 1 3 . 1 the wear of a solid body is the consequence of loading and motion at the contacting interface of two surfaces. In the present section we propose to inquire into the nature of the basic mechanistic phenomena that can take place at the interface in such circumstances. The occurrence of certain processes is easily visualized: adhesion at the interface, rupture of adhesions, displacement of material by plowing or shearing, detachment of displaced material, fatigue and cracking, oxidation, etc.; and in fact all of these processes have been observed and identified, either singly or in combination, in cases of wear as it actually occurs. We

speak

here

of

mechanistic

processes

in

wear

rather

than

mechanihmh 06 toean. The basic mechanisms of interaction between surfaces in contact under load and motion-e.g. plastic deformation, adhesion, fatigue cracking, chemical interaction-can be rigorously defined and analyzed; but although the mechanisms may be recognized individually, the overall observations in cases of real wear may involve their interdependent operation, either sequentially or simultaneously, so that classification of wear behavior in terms of simple mechanisms is futile. However, much of the overt phenomenology of wear consists of orderly and predictable combinations and sequences of the basic mechanisms; and it is in this sense that we use the designation mechanistic weah PnOCeAh. Because these processes are orderly and predictable, we can classify them and assign nomenclature. 13.3.1.

Adhesion and Transfer

The concept of adhesive interaction of contacting surfaces is already familiar to us from previous discussion of the adhesive mechanism of friction (Chapters 8 and 1 2 ) . I f the two bodies participating in the adhesive junction are in motion relative to each other, in particular tangential motion, the junction is ruptured shortly after it is established. Rupture of the junction at a location other than the original interface results in transfer of material from one body to the other. According to the broad definition of wear of Section 1 3 . 1 , each body has been worn-one by loss of material, the other by gain-but there has been no net loss or gain in the system a s a whole. We accept the existence of the adhesive junction as a phenomenological fact and restrain our curiosity about the basic mechanism of its formation in terms of the atomic, molecular or crystallographic structure of the contacting bodies. With regard to the transfer of material from one body to the other, we claim the ability, in our thinking at least, to distinguish the origin of the transferred material even though the interfaces between the microregions in the two asperities were obliterated by the formation of the junction. This is an important assumption in inves-

366

tigating junctions where both bodies are of the same material. We also claim the ability to distinguish between true and nominal contact of structured surfaces. Adhesive interaction during asperity encounter from the point of view of wear refers to the fate of the material in the interacting bodies rather than to the forces at the junction, as would be the case if the interaction was being considered with respect to friction. With respect to wear, it makes a difference on which side of the original interface the junction ruptures and whether it ruptures in one place or more than one. A single rupture by itself can result only in transfer of material from one body to the other. This is what one would expect as most likely and this is what was observed by A. P. Green [ 2 2 ] in his study of asperity interaction using large-scale models. Formation of a loose wear particle at an adhesive junction would require rupture in two places. This may actually occur in cases of severe wear, as was demonstrated by Brockley and Fleming [ 2 3 1 with large-scale model junctions of copper. The adhesive transfer of organic plastics has some special features of it own. Makinson and Tabor [ 2 4 1 observed that polytetrafluoroethylene sliding on glass left transferred material on the counter surface in the form of lumps, ribbons, sheets or very thin films, depending on the rubbing conditions. Pooley and Tabor [ 2 5 ] , who studied the transfer'process more intensively, also reported the behavior of other polymers such as fluorocarbon copolymers, polyethylene, polypropylene, polystyrene, polymethylmethacrylate and polyvinyl chloride. Descriptions of transfer in relation to wear were reported for PTFE by Tanaka e t a t . [20] and for polyethylene by Miller e t a t . [ 2 1 ] 13.3.2.

Plastic Deformation Processes

Given a load of sufficient magnitude and depending on the geometry and the relative hardness, the contact of two bodies will produce a change in the shape of one o r both of them. This in itself can be However, regarded a s wear according to the definition of Section 13.1. the significant role of plastic deformation as one of the mechanistic processes i n phenomenological wear is subtler than just grossly observable changes of shape. Plowing, shearing and cutting on a microscale during asperity contact are wear processes important by themselves and also in their interaction with other basic mechanistic processes, even though the interaction may be too intricate and the scale too small for all the details involved to be directly identifiable by simple inspect ion. Whether there is loss of material from the system of contacting bodies as the direct result of plastic deformation processes depends on specific conditions such as the geometry of the contacting surfaces, the properties of the materials, the magnitude of the applied load, etc.

367

Shallow gross plowing leaves only a plastically deformed track, with the displaced material not detached as loose debris: extensive data on this kind of behavior can be found in the work of M. Ronay [261 with a spherical ruby slider 0.1984 mm in radius on flat platens of copper under loads ranging from 0.049 to 4.90 N (5-500 grams). But if the geometry is suitable, the material displaced from the track will be separated as a chip, as was observed by Gane and Bowden [ 2 7 1 with a spherically tipped rider of titanium carbide 50 nm in radius sliding on a gold flat under a load of 0 . 9 8 1 V N gram). 13.3.3.

Fatigue Mechanisms

Fatigue involves the cyclically repeated imposition of stress on the contact region until permanent damage occurs. Spalling failures of rolling element bearings or of the working faces of gear teeth are the most familiar examples of wear by fatigue processes encountered in practice. I t is usually assumed that since the internal structure of ordinary materials is not perfect, grain boundaries, inclusions, voids and the like can act as stress concentrators to initiate formation of cracks which propagate with repeated stressing until a spalled particle detaches from the body of the material. But even i f the substance is nearly perfect crystallographically, it is theoretically still possible for dislocations to appear when the material deforms under the first stressing and then to grow under subsequent cycles of stress. The slip-lines seen on the surfaces of carefully prepared single-crystal specimens of metals and minerals after traverse by a loaded slider are evidence of this.

In contradistinction to adhesion and plastic deformation, which in principle at least are processes that are governed by regular laws of behavior, fatigue is a process with an element of accidental character. No general relations of practical use have as yet been found to predict the initial generation of dislocations and cracks and their growth to dimensions which result in spalling of material. The relations that are available are empirical and highly specific. 13.3.4.

Chemical Reaction Processes

Real wear takes place in an ambient environment; by ambient environment we mean that portion of the system which is not an intrinsic part of the contacting surfaces. The ordinary ambient environment is the surrounding atmosphere with its oxygen and moisture; to this might be added the lubricant, if any, and its additives, i f compounded.* AS a conse-

*Theoretically ever. the hardest man-made vacuum constitutes an ambient environment in comparison with the ideal absolute vacuum as the absence of an ambient environment. Whether the difference between the experimentally realizable high vacuum and the ideal vacuum is significant for the interpretation of wear results obtained " i n V U C U O " must be decided individually for the case under examination.

368

quence of contact and motion, material in the surface region of the rubbing specimens may react chemically with the ambient environment. The reaction may occur during contact or it may take place on an exposed free surface that has just cleared contact and has thereby been left in an activated condition. This latter type of behavior is exemplified by the work of Smith and McGill 1 2 8 1 with freshly cut metals and solutions of radioactive nonadecanoic acid. We must distinguish between the purely chemical and the thibochemic a t aspects of the chemical reaction process. In the purely chemical case the material of the surface is capable of reacting directly with the constituents in the ambient environment under the ordinarily.prevailing ambient conditions; but for tribochemical action the surface must be activated by rubbing for reaction to occur. The one type of action does not necessarily exclude the other for a given pair of rubbing surfaces, as the effect o n the overall course of wear is different for the two types of chemical action. The access of reactive constituent to the rubbing surface of a fixed rider is restricted compared to its access to the track on the moving countersurface, but the surface of the rider, being in a condition of sustained tribological activity, has the capability of faster reaction. At the same time the surface of the rider is subjected to sustained rubbing action which tends to remove the reaction product. The track on the countersurface, although less activated once it moves out of contact with the rider, has better access to the constituents of the ambient environment but experiences less overall rubbing contact time per unit area. We can therefore draw a distinction between the case of the tribologically activated surface reaction competing directly with the tribological removal of the reaction product and the case of ordinary chemical reaction with environmental constituents followed by a separate rubbing process that removes the reaction product. 13.3.5.

Combinations of Mechanistic Processes

Most instances of phenomenological wear involve the interaction of two o r more of the mechanistic processes described above, sometimes in orderly sequence, sometimes in competition. Although the quantitative outcome of a particular instance of wear is strongly influenced by the individualistic features of that particular case, nevertheless a number of useful generalities can be formulated. A s pointed out in Section 1 3 . 3 . 1 , the generation of a loose wear particle by the adhesive transfer process requires the simultaneous rupture of the junction in two places, which is an unlikely event. Obviously, then, the widespread and frequent occurrence of instances of wear in which evidence of the transfer process is unmistakable must involve its coupling with one or more of the other basic wear processes. A study of great significance in the literature of wear is that of M. Kerridge [291,

369

which demonstrates the interaction of adhesive transfer and oxidation in the formation and detachment of wear debris. The experiments were carried out with radioactive annealed steel pins rubbin'g on inactive hardened steel rings. Transfer of material from the pins was monitored by the radioactivity o n the ring, the time-dependent course of which is shown by Curve A of Fig. 13-11. Transfer is rapid in the initial stages of the wear process, but the amount of transferred material on the ring reaches an equilibrium value and stays at that level throughout the rest of the experiment. Wear of the pin, as measured directly by weight loss, proceeds at the same rate as the initial transfer of the pin material to the ring and maintains that rate throughout the duration of the run (Curve B )

.

-

A: Tronsfer

I

I

Time, seconds

Figure 13-1 1. Transfer i n the adhesive wear process; annealed steel against har,dened steel; load 9.8 N; speed 180 cm/s. From data by M. Kerridge [ 2 9 1 .

The material first transferred to the ring is a thin gray layer which later acquires patches of brown powder. The detached wear debris is a fine brown powder, either hematite (a-Fe203) or hydrohematite ( a Fe2O3.nH20). The overall wear process is postulated as follows: ( i ) transfer of material from the pin to the ring; (ii) oxidation of the transferred layer; (iii) removal of the oxide as detached debris. The role o f oxidation in the production of loose wear debris is substantiated by the strong decrease in wear rate on lowering the ambient atmospheric pressure to 0.133 Pa torr). The buildup of an equilibrium transferred layer is evidence for the formation of loose wear debris by the oxidation of the transferred material and its subsequent detachment. The possibility that debris is formed via direct oxidative reaction with the rubbing surface of the pin was eliminated from consideration by replacing the radioactive pin with an inert one, whereupon there was a gradual decrease in the activity of both the transferred layer on the ring and

the loose wear particles. The nature of the attachment of the oxidized material to the underlying transferred layer was not established and hence there is no information on how the wear particles were detached. Kerridge and Lancaster [15] found that adhesive transfer was the initiating process in the wear of 60/40 brass pins rubbing on tool steel or Stellite rings. The relation of the loss of material from the pin to the equilibrium transfer of brass to the ring followed a course similar to that observed by Kerridge for steel against steel [291. However, under the conditions of load and speed employed by Kerridge and Lancaster [151, the loose wear debris was metallic and not oxidic in character. The primary particles transferred from the pin to the ring in the early stages of rubbing were on the average only about 5% of the size of the particles in the transferred layer at equilibrium and in the loose wear debris. The detached wear particles were somewhat larger than the particles in the equilibrium transferred layer. The mechanistic processes best consistent with these observations are ( i )adhesive transfer from the pin to ) and agglomeration of the transthe ring, followed by (iicompression ferred particles by plastic deformation and adhesion, and finally (iii) detachment of free particles by a fatigue process as the pin repetitively rubs each element of contact area on the ring. Abrupt transitions of the wear of brass riders against hard steel from a domain of relatively low rate to one of substantially higher rate were observed by Archard and Hirst [71 in response to load, by Hirst and Lancaster [301 in response to rubbing speed and by Lancaster 1311 in response to ambient temperature. The regime of low wear rate was associated with evidence for the participation of surface films of oxide in the wear process, whereas the debris produced at high wear rates was predominantly metallic. The relation between these two kinds of wear behavior in terms of variables such as load, speed and temperature is quite complex [32]. Adhesive transfer and subsequent detachment of the transferred material is the characteristic process by which many plastics wear. Tanaka, Uchiyama and Toyooka [ZO] attributed the high wear of PTFE against glass to the easy detachment of the transferred film, which was only 30 nm thick. Briscoe, Pogosian and Tabor [331 reported that modifying high density polyethylene to improve its adhesion to steel reduced the wear rate. Observations on the nature of the transferred films of polymeric plastics 120, 24, 251 suggest that release of locked-in stress or of stress imposed by subsequent rubbing is responsible for detachment. If the polymer slides on a film that adheres to the countersurface, wear is low. However, Rhee and Ludema [341 found that under severe rubbing conditions the wear rate of the plastic sliding against an adherent transfer film can be high due to thermal softening induced by friction.

371

A mechanistic combination that has received considerable attention, particularly in the dry wear of steel, is oxidation at the rubbing interface followed by denudation of the oxide as loose wear debris. A s postulated by T. F. J. Quinn [35], the process involves oxidation during repeated encounters at asperities until a critical thickness of oxide is attained, whereupon an oxide wear particle of this critical thickness is detached. Qualitatively the picture is credible; however, no details are given for the manner in which contact pressure and tangential tractive force interact in the detachment process. Examination of rubbed surfaces by the electron microscopy of replicas and by scanning electron microscopy [ 3 6 , 3 7 , 381 indicated that the oxide on the surface was in patches of relatively large extent and that the detached flakes were greater in area than the average asperity contact calculated by analysis of the wear data [391. Earles and Powell [40] found that below a critical value for the load/velocity parameter, W1/2v, dry wear of steel proceeded smoothly but at higher values of this parameter the course of wear was marked by sudden stepwise jumps accompanied by concomitant increases in friction and bulk surface temperature [ 4 1 , 4 2 , 431. Tenwick and Earles [441 pointed out that the oxides of many metals are less dense than the parent metal and that formation of an adherent layer of oxide is accompanied by inherent stresses as well as stresses imposed by temperature gradients and by frictional traction. Thus it is to be expected that the more severe the rubbing conditions the less likely it is that the oxidation/ denudation will proceed as an orderly process. Although it has not been established by systematic study, the operating parameter that determines whether the wear process is adhesive transfer and oxidation or oxidation and denudation is most likely rubbing speed, which in the ultimate analysis means interfacial temperature. If the temperature is high enough, both the rider and the track will acquire a coherent film of oxide which will effectively block adhesive transfer of metal from the rider to the track. Below some critical temperature only the more activated sites will be oxidized, which affords an opportunity for transfer of metal from unoxidized sites on the rider to the track: oxidation of the transferred metal on the track is probably a consequence of its activated condition there. There is no clear-cut behavioristic demarcation between metallic transfer and the oxidation/ denudation process in the loss of material from the rider. Observers have frequently reported that wear experiments whose steady state proceeds by oxidation/denudation at a moderate rate may have as the initial stage severe wear with metallic debris ( e . g . [ 3 9 , 411). The manner in which material is detached to produce loose wear particles has been the subject of much speculation, but there is a paucity of directly supporting evidence, and for a good reason: the experimental

312

difficulties are great. At ordinary operating speeds an asperity contact lasts only a brief time, and thus isolation of the resulting wear fragment at the moment it is detached is a feat of major magnitude. Therefore most of the mechanistic models for the formation of loose wear debris lean heavily on inference, For example, it can be reasonably inferred that in the transfer/oxidation process studied by Kerridge 1291 the bond between the oxide and the underlying layer of transferred metal is so weak that the oxide cannot withstand the rubbing traction and the wear particle detaches immediately when oxidation occurs or very soon thereafter. We would expect such wear particles to be small. Particles produced by gross interference between two asperities on encounter would be expected to be larger. The weaker asperity would be sheared by the stronger to produce a free particle, the details of the process depending on the specific geometrical configuration of the asperities and the properties of the materials involved. Production of loose particles is often attributed to the fatigue mechanism, the process being differentiated from macroscopic spalling in scale but not in kind. As cited previously [151, metallic particles transferred to the countersurface from the rider by the adhesive mechanism can be detached by the fatigue mechanism on subsequent reiterated rubbing; Kerridge and Lancaster 1151, and Hirst and Lancaster 1301. have also ascribed the formation of transferable particles to fatigue as a primary mechanism.

Figure 13-12. Surface energy effects in the detachment of wear particles. (a) Adherent particle is compressed between two surfaces. (b) Elastic compression strain has been relaxed but volume tensile strain has been locked in by adhesion. (c) Direct detachment of wear particle by influence of surface pressure on zone of potential detachment (dashed line). E. Rabinowicz has proposed a surface energy criterion for the size Figure 13-12a and 13-12b ilof detached wear particles 1 4 5 , 461. lustrates the situation when a rider passes over a fragment adhering to In Fig. 13-12b the elastic compressive strain zmaX the countersurface. has been relaxed, but the horizontal tensile strain V E remains locked m4 y in by adhesion at the interface, so that the particle has elastic volume energy E,: (13-7)

373

where Y is Young's modulus and v is Poisson's ratio. at the adhesive interface is €,

=

Wab

The surface

energy

d"

*

"a-

(13-8)

where Wab is the energy of adhesion. come free is

The condition for a particle to be-

(13-9)

On inserting the values from Eqns 13-7 and 13-8, 6Wab

d = v2

Eiax

Y

(13-10)

By substituting the following values into Eqn 13-10, v = 0.1

= 0.003

Emax

Y = H/3

Rabinowicz obtained 'a6

d

60,000

H

( 13-1 1 )

as the formula for the diameter of loose wear particles. Figure 13-13 shows the comparison of experimental results with Eqn 13-11, where the is used instead of the interfacial cohesive energy of the material,, , W, energy Wab in the ratio of the surface energy to hardness. The approximation is very crude; the general trend of the relation is preserved but the double-logarithmic scale conceals the extent of deviation for large particles.

01

1 10 100 Surface Energy/Hardness, 10-8

cm

Figure 13-13. Test of the surface energy mechanism for the detachment of wear particles (Equation 13-11). Load: 19.6 N; speed: 1 1 cm/s. Data by E. Rabinowicz 1451.

374

The application of the surface energy criterion to the direct Since the detachment of a wear particle is illustrated in Fig. 13-12c. strains are within the body of the material, the volume energy is (13-12) and the surface energy is

En

=

2y,

*

Ti

d2 7

(13-13)

On applying Egn 13-9 to the contact area as shown in Fig. 13-12c and making the appropriate numerical substitutions, Y,

d

2

24,000 H

(13-14)

The delamination theory of N . P. Suh [ 4 7 1 is essentially a low-cycle process in which dislocations generated by plastic deformation propagate voids which in turn propagate cracks in a zone below the rubbing surface whose depth depends on the structure of the material and also on operating parameters such as load. When a crack grows to a critical length in the direction of rubbing, the material shears transversely as well a s longitudinally, releasing a sheet-like fragment which may be broken up into smaller particles by further rubbing. The wear equation proposed by Suh was questioned by Bates and Ludema [ 4 8 l , who pointed out that the validity of many of the key quantities should have been tested experimentally, since their significance and their pertinence were not clearly apparent. The bulk of the evidence offered in support of the delamination theory consists of qualitative observations of the condition of the specimens after rubbing ( c 6 . [ 4 7 , 4 9 , ' 5 0 ] ) . A plastic-flow process f o r the generation of loose wear particles proposed by Bates, Ludema and Brainard [ 5 1 1 is illustrated in Fig. 1 3 - 1 4 for the case of a hard cylindrical slider on a flat plate. The bulge of deformed substance that forms ahead of the slider eventually cracks away from the underlying material. The angles JI and 8 are material-specific, but the angle 4 is n/4 radian as required by plane shear theory. The

(a) Figure 1 3 - 1 4 . Generation of a primary wear particle by plastic shear. ( a ) A bulge forms ahead of the slider. (b) A crack propagates from the surface into the plastically deformed material. (c) The "chip" is ejected ahead of the slider. After Bates, Ludema and Brainard 1 5 1 1 .

375

situation resembles machining with a negative rake angle but with a large nose radius instead of a sharp cutting edge. It is to be expected that under these circumstances the primary particles will be small but that they might aggregate as they crowd one another in flowing away from the advancing slider. Transferred material and detached particles can introduce the abrasive process into the course of wear. Either transfer o r detachment may bring about work hardening, and any material so affected that stands proud of the general level of the contact interface can plow through the opposing surface. The result may be a ridge of displaced material which can interact further in the rubbing process o r else it may be the detachment of material directly by "micromachining." Loose wear particles may remain trapped between the two rubbing surfaces for a while to participate in "three-body'' abrasion before they become free. The type of sliding is of great significance for the course of wear A stationary body sliding on a and the production of loose debris. moving body is subjected to sustained contact so that its nominal area is never free of encounters with the countersurface, while each corresponding portion of the track area on the countersurface experiences reiterated interrupted contact. In the case of two differentially rotating rings, both surfaces experience reiterated interrupted contact. Descriptions and discussions of wear in the overt behavioristic sense must take cognizance of which surface is in sustained contact and which experiences interrupted contact. These two aspects of contact are even more significant when wear is analyzed in terms of asperity interactions, since each asperity, whether in the stationary or in the moving surface, generally requires multiple encounters before it contributes a loose particle to the course of wear. Even after being freed from the spot where i t originated, a particle can be subjected to further encounters before it becomes free of either the rider o r the track as loose debris. 13.4.

NOMENCLATURE

The nomenclature of wear is perhaps its most controversial aspect. Much of the difficulty lies in the mechanistic implications of the terminology, even when it is supposed to be only descriptive. Too often the description of the end result of a wear process comes from an inadequate examination; the implicit disadvantage of an incorrect characterization o r definition of the type of wear is that it leads to erroneous projections of how to modify it, whether by lubrication, change of material o r redesign of machinery. The complex and dynamic nature of the wear process makes it difficult, if not impossible, to keep the phenomenological terminology single-valued in meaning. Much of the current nomenclature should be regarded as descriptive rather than definitive. Some of the more important items of current terminology are listed in the

376

paragraphs below, with discussions of their characteristics and complications. Adhesive Wear: A typical definition of adhesive wear reads as fOllows: "Wear by transference of material from one surface to another during relative motion, due L O a process of solid-phase welding" [ 5 2 1 . The complications inherent in the adhesion/transfer process have been discussed in Section 1 3 . 3 . 1 ; it is quite apparent that purely adhesive wear is rare and that therefore the indiscriminate application of this definition to observed instances of wear is to be questioned. This is more than a matter of nicety in terminology: erroneous deductions from a definition incorrectly applied can lead to misinterpretations and incorrect predictions. In a practical sense the designation adheoive LOech is used to characterize cases of wear in which adhesive transfer is the important or controlling mechanism. In general, the limitations associated with this nomenclature being understood, the terminology is useful for practical description and characterization. Abrasive Wear; Abrasion: This category of wear is commonly associated with the action of abrasive papers and grinding wheels, where the mechanistic process has been identified as a variant of the kind of chip formation seen in machining-L.e. plastic deformation and shear. The OECD Research Group defines abrasive wear as "the displacement of material by the presence of hard protuberances, or by the presence of hard particles either between the surfaces or embedded in one of them" [521. Abrasive wear is basically plastic deformation that produces wear debris in the form of microchips; therefore on diagnostic examination, the external appearance of the loose wear particles should be compatible with this process as their origin.

...

Chemical Wear; Corrosive Wear: The relation of chemical reaction to tribological processes was discussed in Section 13.3.4. To be classified as chemical wear the production of wear debris must involve both the chemical reaction and the removal of the reaction product as the consequence of rubbing. Oxidative wech is a form of chemical wear in which the chemical reagent is oxygen, usually in the ambient atmosphere. C o h hanive weah usually has the pejorative implication of excessive wear; but chemical wear is not necessarily harmful or undesirable, for wear in the presence of a compounded lubricant is usually substitution of chemical wear at a low rate for some other mode of wear at a higher rate. The choice of whether to call the adhesive-transfer/oxidation process studied by Kerridge [ 2 9 1 adhesive wear or oxidative wear is a matter of which aspect it is desired to emphasize. Erosive Wear; Erosion: The OECD Research Group [ 5 2 1 defines erosive wear as " l o s s of material from a solid surface due to relative motion in contact with a fluid which contains solid particles." The ASTM Committee

G-2 designates its field of activity as ehObiOn and w e a h , thereby implying a distinction between the two. Erosion is subdivided into erosion by liquid impact, erosion by liquid cavitation, and erosion by a stream of particles carried by a liquid o r a gas. The basic mechanism behind the effect of liquid impact and liquid cavitation is probably fatigue under fluctuating stress; particle impingement causes wear by the kind of plastic deformation and chip separation characteristic of abrasion, although, as cited in Section 13.2.4., spalling as the result of repeated impact is also a possibility 1141. The OECD Research Group [521 defines two special categories: a b h a o i w e e h a o i a n , in which the trajectories of the solid particles are nearly parallel to the target surface, and i m p i n g e m e n t e h V o i a n , in which the trajectories are nearly perpendicular to the target. Fatigue Wear: The principles of fatigue as a basic wear mechanism are described in Section 1 3 . 3 . 3 . The designation datigue w e a h is usually reserved for instances in which loss of material by spalling is of major proportion and other mechanisms are insignificant. This type of wear is characteristic of rolling motion rather than sliding: e . g . in rolling element bearings and in involute gear teeth at the pitch line. Fretting; Frettinq Corrosion: Fretting wear occurs between two surA typical faces with oscillatory relative motion of small amplitude. case is damage to a loaded ball bearing subjected to vibration during storaoe, even though the load is light. Detachment of small particles proceeds by the fatigue mechanism. When these particles are oxidized in the ambient air and the resulting product is hard and abrasive, further interaction with the contacting surfaces produces the severe wear known as fretting corrosion. This is a particularly unfortunate designation, since it misplaces the role of corrosion in the wear process. Galling: This term is sometimes used to designate severe damage of adhesive character. It is descriptive rather than definitive and has no precise meaning. Mild Wear; Severe Wear: This terminology was introduced in the definitive rather than the descriptive sense by Archard and Hirst [ 7 , 531 and by Kerridge and Lancaster 1153. MiLd wean is associated with low wear rates and smooth surfaces [ 7 , 531, but the defining characteristic is that the wear debris consists of oxide. The rates for bewehe w e a h are high, the surfaces are extensively disturbed and the debris is metallic f 7 , 151. This definition has been criticized as resting on an arbitrary basis [541. The difficulty with the designations miLd and newehe in this sense is the implication that all oxidative wear occurs at a low rate and all metallic wear at a high rate. Also, the definition is tailored to dry wear o r to wear in the presence of uncompounded lubricants. From a broader point of view, mild wear can be differentiated from severe wear on two counts:

whether the course of wear is slow o r rapid

and

whether

378

is orderly or not. But more often than not there is an element of judgment involved which makes the distinction between mild and severe wear more in the nature of a description than a definition. it

Plowing: The OECD definition reads: "plastic deformation of the softer component of a rubbing pair" 1521. Presumably what is meant is displacement of material without separation, since the basic mechanism of abrasion is also plastic deformation. The utility and the wide acceptance of the term &cudding Scuffing: has given rise to the general impression that it has been defined precisely. However, the exact definition is still a matter of active debate. The OECD Research Group gives us "localized damage caused by the occurrence of solid-phase welding between sliding surfaces without local This definition emphasizes what is generally surface melting" [ 5 2 ] . recognized: that the dominant basic mechanism in scuffing is adhesion. But wear phenomena that include abrasive as well as adhesive effects are or also designated as scuffing without any serious disputes misunderstandings. Scuffing is a term characteristically used to indiIn cate the breakdown of lubrication, whether fluid-film or boundary. such cases the scuffing behavior can be very mild, below the limits of measurement and detectable only by a sudden rise in the coefficient of friction o r by microscopic examination of the rubbing surfaces for damage; but it can also be indistinguishable from severe wear as Since smooth wear at a very described by Kerridge and Lancaster [ 1 5 ] . low, controlled rate is sometimes accepted as effective extreme-pressure lubrication, scuffing in such cases means transition to wear at a higher rate accompanied by augmented surface damage. In spite of the semantic difficulties, scuffing remains a viable item of terminology because of its usefulness as a descriptor and because of the general recognition of the adhesive mechanism as the most prominent mechanistic process in the phenomena to which the term is applied. Scoring: The best way to define scoring is to go back to the classical sense of the word as given in the dictionary: the formation of grooves or scratches. The traces that abrasion leaves in a surface would thus be designated as score lines. But the occurrence of scoring at a surface does not necessarily mean that material was detached; plowing by a small particle or an asperity could make a groove by displacing material without detaching it. Whether material is lost or not, the basic mechanism of scoring is plastic deformation. Sometimes fine scoring is termed h c h a t c h i n g , but as there is no set standard for the demarcation between scratching and other types of scoring, the designation is only qualitatively descriptive. Because scuffing damage is frequently encountered intermingled with scoring, the distinction between the two categories becomes lost and the designation hcohing is applied to what could with better reason be called scuffing. The mechanistic basis for

the best nomenclature in such cases is which process is either the primary or the most important one: adhesion or plastic deformation. In practice it may be difficult to find the evidence upon which to base a decision. However, small torn streaks due to local adhesion should not be termed scoring, as proposed by the OECD group on nomenclature [521. Spalling: The definition assigned by the OECD terminology is "separation of particles in the form of flakes" [ 5 2 ] . In rolling element bearings, where spalling is a characteristic manifestation of service failure, the basic mechanism is subsurface fatigue. But this is not the only mechanism that can lead to the spalling off of wear particles; the growth of a layer of oxide or other reaction product on a rubbing surface can result in stresses that will eventually cause flakes of material to break off under the pressure of the slider. Nor is the removal of the material, by either fatigue or fracture, limited to flake-like particles; smaller, less asymmetric particles can also be released. This would produce small cavities in the surface, giving it a pitted appearance. 13.5.

WEAR MODELS

A wear model is defined here as a systematic and quantitative analytical description of a wear process, in which the amount of wear o r wear rate is related functionally to parameters of the tribological system such as load, rubbing speed, properties of the materials, surface roughness, etc. No strict categorical distinction is drawn between a wear model and a wear mechanism o r a mechanistic wear process as formulated in Section 1 3 . 3 , but a wear model is always quantitative whereas a mechanistic process, because of the complex interrelation of the constituent basic mechanisms, may be amenable only to qualitative description. A wear process may be truly phenomenological, i.e. real in the physical sense, or it may be a mental construct such as might be devised to explain geometrical changes observed in the real wear of riders of given shapes. The ideal in modeling is to identify all the mechanistic processes which contribute to the course of wear and to connect them quantitatively with the physical parameters of the system. So far, this ideal has not been realized. But imperfect though present models may be, they have proved useful as steps toward systematizing phenomenological wear on a rational rather than a merely behavioristic basis.

13.5.1.

Wear Models and Asperity Contact

A first approach to the quantitative modeling of wear is the postulate that the governing parameter is the number of effective contacts as one surface- slides upon the other. In the modern realistic view these are asperity contacts, and hence the sizes and the distribution of the asperities are an essential part of the model. I f N is the total number of asperity contacts in a given sliding process and N, is the number of

contacts that expressed as

result in wear particles, the effectivity factor

Z can be

(13-15) I f total wear volume is V , we can write W

N,

=

;;;;5

(13-16)

where a is the average radius of the contact area that produces a wear particle, B is a constant of proportionality, and all the particles are assumed to be of the same size. Let us consider the rubbing face of a rider with a gross area L O N which is subdivided into individual elements of area A ~ each , of which is the site of an asperity contact area. The number of contact sites in the Let the rider travel a distance L over surface of the rider is LW/A 2 the countersurface, which has the same surface density of contact sites Each contact as the rider, uniformly distributed in the same manner. element in the surface of the rider will encounter L / b contact elements in the countersurface, and the total number of contacts will be

.

N = -

LWL b

3

(13-17)

On combining Eqns 13-17 and 13-16

(13-18) If the values of 1 , w, b and a remain fixed throughout the course of the wear process, Eqn 13-18 is equivalent to V = k,ZL

where k , represents a lumped wear constant. dV

-

=

(13-19) Differentiation gives

k,Z

dL

(13-20)

The distance-dependent rate of volume-wear dU/dL is constant, provided that the gross rubbing area of the rider, the surface density of asperities, the average radius of an individual asperity contact area, the particle-volume proportionality factor B and the effectivity factor 2 all remain constant. I f L-w does not stay fixed during the course of wear but varies functionally with the length of rubbing path ( e . g . i f the gross rubbing area of the rider enlarges by wear), then we write V = k2ZA'L

(13-21)

381

where A ’ = el(: and h 2 is a new constant. If the initial value the volume rate of wear becomes denoted by A,,

of

A‘

is

dV

- _ dl

(13-22)

and increases with progressive wear, since the total number of contacts increases even i f the ratio N,/N remains unchanged. 13.5.2.

Models for Constant Wear Rate

I t is an observed fact that a constant rate of volume-wear, unaffected by progressive change in the apparent area of contact during the course of wear, is one of the consistently characteristic types of wear behavior. For Eqn 1 3 - 2 1 to be a variant of Eqn 1 3 - 2 0 requires that the area factor remains constant. One way to realize this is by means of the plastic deformation model of the real contact area of asperities, in which case the expression equivalent to Eqn 1 3 - 2 1 is V =

k;ZAL

(13-23

where A , the heaL area of contact, stays constant. and Z with the aid of Eqns 1 3 - 1 7 and 1 3 - 1 8 gives

,

NuJBa3 = k 2

NuJ

Substituting for V

AL (13-24)

On inserting A ’ L / n 3 as the equivalent of N , we get

(13-25)

(13-26)

Since k;, h 3 and B are constant, d ( a 3 ) / d L must vary inversely as ( A ’ ) 2 with dA’/dL i f A is to remain fixed during the course of wear. For a fixed load W this is what would be expected by the plastic deformation postulate A = W/p,: as the apparent area A ‘ , and therefore the number of contacts N , increases, the real area of an individual contact must is to be maintained. Insertdecrease i f the constancy of the ratio N,/N ing W/p, in Eqn 1 3 - 2 3 ,

( 13-27)

Hence for a fixed load the volumetric wear rate dV/dL is constant. A physical model of wear has been derived from the purely geometric

382

analysis of asperity encounter by the use of the plastic deformation postulate. A simple physical approach to Eqn 13-27 was described by Archard The unit event that generates a wear particle is the contact of two asperities on opposing surfaces. The area of asperity contact is assumed to be a circle of radius a and the volume of the wear particle is taken as the hemisphere 2na3/3. The contact area and volume per wear particle are denoted by [55].

6 A = na

2

2 3 6 V = -ra 3

The wear particle is generated by sliding transit across 6 A , 6 1 = 2a

so that 6A 6V = -

3

61

(13-28)

On summing all the individual areas of asperity contact, the average wear ra e is

U

c6V

61

(13-29a) =

2

3

z

= - A

3

(

13-29b)

where the effectivity factor Z enters because the real area of contact A is the sum of all the individual asperity contact areas whereas the wear volume V is the sum of only the asperity volumes that are removed as wear particles. Equations 13-29 can be put in the form

(13-30)

where the hardness H is equated with the yield pressure p m . The derivation of Eqns 13-29 implies that we know how to sum up the total wear volume and the total contact area. The format of Eqn 13-30 stems from Archard’s analysis of the surface model described in Chapter 12, Section 12.2.1, where the relation between real area of contact and load as given by Eqn 12-9 reduces to A = W / p , for the case of plastic deformation of asperities. Other relations between real area of contact and load and other models for the formation of wear particles will give other expressions for wear, as discussed by Archard 181. The quantity Z, which we have termed the effectivity factor, is designated as a

383

probability factor by Archard and is given the symbol K in his notation.* This notation has been erroneously interpreted to imply that the Archard K has a constant characteristic value for a given material. That it very nearly does so in many instances is a fortunate circumstance; otherwise there would be no regularity or predictability at all in phenomenological wear. But the Archard K (or Z in o u r notation) is also responsive to conditions that may be difficult to control reproducibly before the pieces are put into rubbing contact-for instance, the topography o r the character of the surfaces-or which may change during the course of rubbing. The extent of such variability for a given class of material is one of the major problems to be resolved in the empirical study of wear. The influence of changing Z is dealt with in Section 13.5.3 below. In the foregoing treatments of wear in this section the implicit asIt sumption has been that wear is loss of material from the system. should be recognized, therefore, that in the light of the broad definition of wear given in Section 13.1, which includes deformation and surface damage, our modeling here is a restricted view of wear. What we have designated here as wear rates or wear coefficients should, in the strictest sense, be qualified as Weah L a b b h a t e b or weah L O A b c o e d d i c i e n t s . But since there does not seem to be a serious possibility of confusion, we shall adhere to the customary nomenclature and write simply Meah h a t e .

Another approach to surface contact and wear is statistical modeling, as exemplified by the treatment of Greenwood and Williamson [ 5 6 1 ( c d . Chapter 12, Section 12.4). For a rectangular rider of side 1 travelling a distance L the number of asperity encounters is given by

where x is the surface density of asperities and e-' is the explicit function for a surface model with an exponential distribution of asperity A Gaussian distribution would be more realistic, but the exheights. ponential distribution is a good enough approximation and gives a straightforward solution in closed form. The apparent area of contact is eliminated from Eqn 13-31 by using the relation (13-32)

where R is the average radius of asperity curvature, a is the standard deviation of the asperity height distribution and Y is Young's modulus. Then

*In this chapter, we use K as the symbol for a lumped constant in the wear equation: c6. Eqn 13-27.

384

W N =

. L(13-33)

Note that N is given entirely in terms of measurable physical quantities. These can be regarded as fixed for a specified surface, in which case we write Eqn 1 3 - 3 3 as

N

L

=

-

k3W

(13-34)

L

We denote the wear volume by W = N,q

( 13-35)

where q is the average volume per wear particle. and 1 3 - 3 5 ,

By combining Eqns 1 3 - 3 4

(13-36)

If the gross cross-sectional area of the slider, the load and the effectivity ratio Z stay constant for the duration of the sliding, then y and L will also remain constant and W - -- K'W L

(13-37)

The equation above is equivalent in format to Eqn 1 3 - 2 7 . But in general it cannot be expected that the slider will remain in a configuration which keeps L constant throughout the course of the wear process. Formal differentiation of Eqn 1 3 - 3 6 gives dt'

-=

k3ZW

dL

li

+ I I-

+

-I

I (13-38)

where the inclusion of q a s a function of L implies that the average conThe plastic tact area of an individual asperity is a function of L . deformation postulate requires that the true area of contact be constant: XA'C-'

*

na2 = c o n n t a n t

( 13-39)

where X A ' e - ' is the total number of asperity contacts in the area A ' and na2 is the area of an individual asperity contact with average radius a. For a fixed load the distribution function e-' is constant, and hence

(13-40)

This 13-38

relation has the same format as Eqn 1 3 - 2 6 . In combination with Eqn it gives the physical condition for d W / d L to be constant, i . e . the

385

condition for a steady-state distance-dependent wear rate. A simple model for abrasive wear is illustrated in Fig. 1 3 - 1 5 . An individual abrasive contact is represented by a non-deformable cone that plows material out of the counterbody. The loading force 6W acts over only the leading half of the cone as follows:

6W

Abrosive particle

Figure 13-15.

Simple model for abrasive wear.

(13-41)

L

The volume of material displaced in sliding a distance 6 L is 6V

=

nhGL =

h

2

cot 6 6L

Elimination of 6v

- =

h

gives

e

26w c o t

nn

61

(13-42)

(13-43)

Summing up over all the abrasive contacts in a distance L yields V

-

-2. c a t

=

L

ntl

e

W

(13-44)

where 2 is the effectivity factor. I f 6 is accepted as a mean value for all the abrasive asperities and is assumed to be constant, then the volume-rate of abrasive wear will be a linear function of the load W and inversely proportional to the hardness H: W

dV - =

dL

K

(13-45)

where Ka is a lumped constant for the other parameters. I f the apparent area of the two surfaces in gross contact increases with the sliding dis-

386

tance L , thereby increasing the number of abrasive asperities acting on it, then the depth of penetration decreases. But since h and h have a simple relation to each other (Eqns 13-41 and 13-42), the constancy of the wear rate according to Eqn 13-44 is unaffected by increase in the gross apparent area. The model derived above is an extremely simplistic one, but the basic approach outlined there can be used for more sophisticated developments. Mulhearn and Samuels [571 showed the following relation to hold between the load W and b , the width of the groove generated in the counterbody by an abrading asperity,

(&y2

=

(13-46)

where k is the proportionality factor between b 2 and the projected area 6 Let of the asperity indentation and P is the mean indentation pressure. 5 be the factor that expresses the relation between b and h for a single asperity and let the fraction of the asperities which produce grooves o r scratches of depth lying between h and h + A h be related to the corin other responding values of b by form factors between 5 and 5 + A < ; words the expression for b will be of the form F(h)AhG(C)Ac. Then W = J c m U x J h m a x Pkd(gh)'XA'F(h)GL~)dhdg 0

0

( 13-47

which eventually yields 2

2

Pk 6 iA'hhmhchmh

W =

( 13-48

where hhmo and cam, are the root-mean-square values of h and 5 respectively. I t was observed in practice that no serious error results if the respective mean values h m and 5, are used instead of the root-mean-square values. Hence

(13-49)

volume of metal displaced in a single pass of length L over the area groove times the number of grooves times the distance L . The cross-sectional area of an individual groove is given by
A'

=

k - w is the cross-sectional area of a

(13-50)

387

where 2, is the total number of groves. 13-48 and using the relation

2

9

Substituting for hhmb from Eqn

= A'LM

(13-51)

where A' is the surface density factor of the asperities grooves,

generating

the

The asperity surface density factor X used in the static loading calculation (Eqn 13-48) is different from the factor A' used in the groove volume calculation (Eqn 13-52a) because of overlapping locations of asperities in the rubbing path. Assuming that the grooves extend the entire length of the abraded specimen and that no serious error results if ( h m o is replaced by cm,

w

,it

9 = - * k6Acm

(13-52b)

But not all the material displaced by the generation of grooves separates as loose debris; only a fraction 6, of the asperity contacts detaches wear particles, so that

A'

W

k6Aem

=

(13-53)

gives the cross-sectional area of the material lost from the system. the total length of the rubbing contact is L , the wear volume is

w

If

X'

(13-54) except for a negligible end correction. If the group ( i j w / k 6 ( , , , ) ( A ' / X ) can be shown to be constant, then the result of differentiating Eqn 13-54 with respect to L is equivalent to Eqn 13-45, since the indentation pressure P is substantially the same as The ratio A'/A will be constant i f the the indentation hardness H. average tcpography of the abrading surface remains the same during the course of rubbing, and k , and 5, will be constant i f the average shape of the asperities is not altered by the wear process. The effectivity fraction 6, is largely a function of the attitude angle of the asperities and has been shown to remain substantially constant when the abrading surface has been stabilized or "run in."

The

major

interest in models of the abrasive wear process and most

388

of the data are tied in with the action of abrasive papers and grinding wheels. Departures of observed behavior from constant-rate models such as were presented above are due to specific aspects of the particular case under consideration; the reader can consult the publications by Mulhearn and Samuels [ 5 7 ] and by Goddard and Wilman 1 5 8 1 for examples. Wear with Variable Rate

13.5.3.

The geometry and statistics from which the wear models of Section were developed do not predict a p h i o h i that the volumetric distance-dependent wear rate will be constant for a given load and rubbing speed. The conjoint regulation of several physical parameters is required to make these models fit the observed course of wear with a constant volume-rate. It follows, then, that alteration of the influence of any single one of these parameters could be sufficient to bring about a departure from observed wear at constant volume-rate to wear with a variable rate. For instance, consider the simple wear expression Eqn 1 3 - 2 0 and its concealed constituent Eqn 1 3 - 1 8 . A change in the value of N, during the course of wear-for instance, a diminution in the average volume of a wear particle by oxidative inhibition of the size of the asperity adhesion--will change the value of dV/dL. Or, as another example, the ratio N,/N might be preserved but the value of a (see Eqn 13-26) might change due to alteration in the structure of the surface by wear so that dV/dL assumes a new value or even a series of new values. The study of steady-state wear is emphasized in published reports because though wear is undesirable in general, from the practical point of view wear with low and predictable rates is tolerated. But, considering relations such as Eqns 1 3 - 2 2 and 1 3 - 3 8 , it is surprising, and fortunate as well, that so much of the wear observed in industrial practice does proceed at substantially low and constant rates. 13.5.2

A s an example of how wear behavior with a changing rate can be treated, let us examine a model for the competition of metal removal from a slider by direct adhesive transfer and by combined oxidation and ablation of the oxide. The total rate of phenomenological wear is given by

dV

dVi

- = - + -

dL

dL

dVa dL

(13-55)

where dVx/dL is the volume-rate of wear by metal transfer and dVa/dL is the rate of ablation after oxidation. Let us consider a surface area containing N contact sites and for simplicity let us postulate that neither the apparent area of the slider nor N changes during the course of wear. Then

dN,

dN,

dNa

dL

dl

dL

( 13-56)

385

where N, is the number of wear-effective sites on the slider surface. The separate expressions for the transfer, oxidation and ablation rates are:

dN,

--

- N,)

- k,(N

(13-57a)

dL dNh

- = k,(N

- k,N,

- N,)

dL

(13-57b)

dN, - =

'UNh

dL

(

13-57c)

Equation 33-57b expresses the fact that oxidation occurs at a bare-metal site (which can also be the site of an adhesive transfer) and that the net change in oxidized sites on the slider surface is the difference between the rate of their formation and the rate of ablation. The symbols kt, k, and k, are the rate constants for transfer, oxidation and ablation respectively. Equation 13-571, is integrated to give

k,N (13-58) by which Eqns 13-57a and 13-57c become

klLk,

dN,

--

- k,N

-

N (1 - e x p

~

k,

dL

k,k,

dNU

N

-=-

dL

b,

+

[-

(k,

+

k,)Ll)

ku (1

(

-

~ x [p- (k,

+

k,)L1)

k,

+

13-59)

(13-60)

and their sum is

(13-61) The wear volume V is obtained by multiplying N, by the particle volume factor; integration of Eqn 13-61 thus gives us the solution for the amount of wear via

- k,)

kh(k,

N,

=

ktNL

k,

+

ku

- k,)

k,(k, NL

+

N

+

(k,

+

*

e x p [ - (k,

+

k,)Ll

ku)2

The physical interpretation of Eqn 13-62 is strongly influenced relative magnitude of the reaction rate constants ktt' k, and k,.

(13-62) by the For ex-

390

ample, if kt is about 6 or 7 times the magnitude of k a and k, is slightly larger than ha, plots of wear as a function of rubbing distance will look like those in Fig. 1 3 - 1 6 , which were computed by substituting arbitrary numerical values into Eqn 1 3 - 6 2 .

Distance, arbitrary units-

Figure

13-16.

Course

of

wear

by

competing mechanisms (c6. Equation

13-62).

A model for abrasive wear with variable rate ca: be derived from the experimental observation that the effectivity factor for abrasive papers Equation decreases with use as a negative exponential function [ 5 7 ] . 1 3 - 5 4 would then assume the form

(13-63)

where

6,

=

6,

,-jL

(13-64)

6, being the value of the effectivity factor at the beginning of the wear process. If the other factors stay constant, the expression for the wear rate would then be of the form (13-65) 13.5.4.

Geometrical Influences in Wear Models

The development of the models discussed in the preceding sections was based on wear expressed in terms of volume. Much of the wear data in the literature is volumetric wear, no doubt because the primary measurements as loss of weight were converted to volume from the density of the material. But in many cases the interest from an engineering point of

391

view lies in the depth to which the piece is worn or in the change in the gross area of the contact interface. It then becomes more pertinent to express wear in terms of the depth-rate or a s the rate of change of some linear dimension related to the area. Change of volume during wear can be written as

dV

=

clA'dx

(13-66)

where x is the variable linear dimension governing the nominal area of contact A ' . The depth of wear h is a function of the first power of x . Then it can be shown that

dV = cgA'dh

dh

dV - =

C2A'-

dL

dL

Taking the case where dV/dL

dh

KW

dL

c2A'

- = -

dh - =

dL

(13-67)

(13-68) =

KW

(

13-69)

K

- P c2

(13-70)

Strictly on the basis of geometry, if dV/dL is a linear function of the load W, then the depth-rate of wear dh/dL is a linear function of p , the loading pressure or load per unit of apparent contact area. Generally a linear dimension related to the apparent area is easier to measure with accuracy and convenience than the depth of wear. For instance, i f the slider is a truncated circular cone, the convenient dimension to measure is the diameter of the contact circle; the depth of wear is then Ah = Ah c a t 8 , where 8 is the half-angle of the cone and h is the The volume wear is then A V = n/3.cot8.Ah3, and interconversion radius. of depth wear and volume wear is simple. The relation between volume wear and the change in the radius of the wear scar on a stationary sphere rubbed by a rotating sphere is somewhat involved. This particular configuration is of interest because it is the basis of the widely used four-ball lubricant tester. Because of the high loading pressures and the special characteristics of the contact geometry, elastic deformation becomes an important consideration in computing the volume worn away. Two cases must be considered, as illustrated in Fig. 13-17: one in which the wear scar has a convex profile, the other in which the scar is concave. In either case the wear scar is bounded by the elastically recovered surface after the load has been removed. For the convex case the wear volume is the difference between the two spherical segments with the bounding surfaces as shown in Fig. 13-17a:

392

(b)

(a)

Figure 13-17. Cross-sectional geometry of wear scars on a spherical ball including the effects of elastic relaxation. (a) Convex scar. (b) Concave scar.

Th4

Tih

nh

lIh

6

(13-71i For wear scars of the magnitude encountered in the four-ball test the last two terms can be neglected and the value of R can be calculated from elastic theory as follows 1591: ROh3

R =

w

1.364 - Ro - n 3 Y

(13-72)

From Eqn 13-71 we then obtain 1.364 ROW

-

h3Y

(13-73)

h3Y

In similar fashion, for a concave scar (Fig. 13-17b): 4 nfi4 nh

u=-+-

4R

4R0

u==h4 4Ro

In

(

(

1.364 ROW 1 +

h3Y

-

h3Y

1

13-74a)

(13-74b)

converting from scar diameter to volume wear a large burden is thrown

on the precision of the scar measurements relative to the diameter of the ball, particularly in the early stages of the wear process. 13.5.5.

physical Parameters in Wear Models

Load is one of the basic physical quantities governing wear in engineering practice and thus, explicitly or implicitly, it is a parameter in any wear model. For instance, Eqns 13-30 and 13-37 are explicitly linear with respect to load and therefore plots of volumetric wear rate against load in log-log coordinates should have a slope of unity. Ar-

393

chard and Hirst [ 7 1 found this to be true for most of the combinations Brass rubbing on tool steel showed a they investigated ( c 6 . Eqn 1 3 - 2 ) . transition from "mild wear" to "severe wear" Cc6. Fig. 13-6); within each regime the wear rate was a satisfactorily linear function of the load, Tool steel but the repeatability of the transtition load was erratic. rubbing on tool steel showed a non-linear dependence of wear rate on load with a slope exponent rn < 1 (c6. Eqn 13-3). Several different physical models f i t this non-linear relation. Pressure is sometimes more revealing as a parameter than load, particularly in lubricated wear, where a progressive decrease in the woeurnethic h a t e during the course of wear under constant load might reasonably be attributed to the increasing effectiveness of quasihydrodynamic lubrication as the pressure decreases when the nominal area of contact enlarges. But a decrease in the depth-hute of wear under constant pressure signifies a change in the wear process other than intervention of quasihydrodynamic lubrication. This is illustrated by the work of Dorinson and Broman [ 4 1 with hardened steel lubricated by white oil. Figure 13-18a shows the course of voeumethic W L U h under a

60

0

Rubbing Distance, meters

500 700 900 1100 Contact Pressure, MPa

Figure 13-18. Influence of contact pressure on wear rate under constant load. Hardened steel lubricated by white oil at 23.2 N load, 50.8 cm/s rubbing speed. (a) Course of wear. (b) Wear rate as a function of contact pressure. Data by Dorinson and Broman [ 4 1 .

constant load. The curve h a s two distinct portions: (I) a moderate amount of wear with a rapidly decreasing rate; (11-111) a sudden change to wear at a higher rate. Data were taken in a manner that allowed calculation of the depth-hate and the contact pressure as wear progressed. I t is apparent (Fig. 13-18b) that the wear process is multiplex in nature and cannot be represented by a continuous functional relation between rate and pressure. The discontinuous jump in wear rate between regions I and I 1 is inconsistent with the onset of quasihydrodynamic action as pressure decreases, whereas the falling wear rate in region I11 may be indicative of such action.

394

Wear rates expressed in distance-dependent terms--e.g. dV/dL o r dh/ dL--have the advantage of keeping the results of experiments run at different speeds on an equivalent basis. Sometimes it is more instructive t o look at wear in time-dependent terms,

dV

-

1 dV

v dt

dL

(13-75)

where v is the rubbing speed. In that case rubbing speed enters the relation of distance-dependent wear rate to time-dependent rate by way of geometry: L = vt. But rubbing speed can have effects on the wear process other than geometrical, as discussed in general terms by Dorinson and Broman [ 5 1 . A possible relation for the influence of speed is

v

=

f(v)h,t

(13-76)

where f ( v ) is a physical function which might, among other things, express the influence of rubbing speed on such parameters as the average size of a wear particle, the yield strength of the surface layer, the oxidation of the surface layer, the surface temperature, etc. The timedependent wear rate will then be related to the distance-dependent rate by dW

- _

- k,f(v)

dt

=

dV v dL

( 13-77)

from which dV

dL

- k4 f ( v )

v

(13-78)

A somewhat more explicit example is found in the following expression obtained from C. N. Rowe's analysis of a model for lubricated wear 1 6 0 1 ,

( 13-79)

where c ' is a contact factor, W is the load, [ F l is a lumped factor for various molecular-scale parameters of the model and e x p [-E/RT] is a physicochemical energy of activation factor in which T is the absolute temperature of the surface film. Increase of rubbing speed can increase the surface temperature, which, as one of the effects, can lower the value of p,. When a slider repeatedly retraces a closed path on the countersurface, each reiterated pass will modify the surfaces. The s u r face of the slider, of course, is continuously modified by its continuous contact with the track; the surface of the track is modified by each cycle that the slider passes over it. In some instances this

395

modification will improve the load-bearing capacity of the surfaces over their original condition, whether by plastic deformation of surface structures such as grind marks and asperities or by some other mechanism of smooth alteration of asperities. In such cases the course of wear will exhibit an initial break-in phase followed by a phase governed by the equilibrium load-bearing capability of the contacting conjunction, so that the changes manifest as observable steady-state wear persist for thousands of retraces. Figure 73-4a is an illustration of this type of wear behavior. I t is likely that surfaces sliding in air are oxidized and perhaps chemically activated so that other species besides oxygen in the ambient environment can produce a direct reaction on the surface. The surface species may limit the shear stresses that can be imposed upon asperities and they may thereby strongly influence the nature of the plastic deformation of the asperities. Thus, on the one hand plastic flow may alter chemical activity, and on the other hand the result of chemical activity may be changes of plastic flow.

But i f the first traverse of the slider along its path on the countersurface does not improve the load-bearing capacity of the conjunction by plastic deformation o r some other smooth alteration of the asperities, then it would be expected that surface disturbances would be For instance, removal of material exacerbated on repeated traverses. from an asperity by adhesive transfer might activate the site S O that a stronger adhesion on the next iterative contact might generate a larger transferred particle. Or activation of the surface by rubbing might facilitate direct reaction with chemically active substances in the ambient environment, producing an easily removable surface layer. The course of wear under these circumstances would be represented by curves similar to Fig. 13-4c. The effect of reiterative feedback, therefore, is a major consideration in the construction of wear models that realistically take into account the influence of changing physical parameters on the course of In some cases these changes are the result of the course of wear wear. itself, such as the decrease of contact pressure as the conjunction area In other cases, the externally imposed enlarges under constant load. magnitude of a parameter such as load or rubbing speed will determine the influence that reiteration of contact will have on the course of wear. 13.6.

CATASTROPHIC WEAR DAMAGE

The distinction between the extent or the kind of wear that can o r cannot be tolerated is a well-established concept in the thinking of practical engineering. The difficulty comes in deciding how much or what kind of wear is catastrophically damaging. The correct analysis of

catastrophic wear damage and the assignment of a generally accepted nomenclature is more than mere logical tidiness. In order to control catastrophic wear it helps to understand it, and in order to understand it one must penetrate past external appearances and identify the fundamentals. There is no quantitative fundamental standard for catastrophic damage. One type of machinery or usage might be able to tolerate an amount of wear and a degree of damage entirely unacceptable for another type of machinery or service. Therefore, the general concept of catastrophic wear is basically qualitative and descriptive rather than definitive; it includes drastic, measurable increases in the amount of material lost, but it also includes unacceptable immeasurable changes in the condition of the rubbing surfaces. Let us, then, examine the interpretation of some of the terminology discussed in Section 13.4 from this point of view. Scudding is perhaps the most widely used descriptive term in the nomenclature of catastrophic wear. The OECD definition has been examined in Section 13.4. A definition attributed to the Institution of Mechanical Engineers (London) has been quoted as "gross damage characterized by the formation of local welds between sliding surfaces" [611. The basic role of the adhesive mechanism is common to both the OECD and the British definition; the latter, however, specifically states that the nature of the damage is grossly apparent. But where the criteria of acceptable operation are those of hydrodynamic or elastohydrodynamic lubrication, even smooth wear is regarded as a serious failure and minor roughening of the surface is considered to be catastrophic. On the other hand, from the point of view of boundary or extreme-pressure lubrication, a limited amount of smooth wear is tolerable and the designation scuffing is not applied until the wear becomes rapid and the rubbing surfaces quite rough. Beerbower [62], in systematizing the relations between wear rate and load, looked upon scuffing as a sudden increase in rate from mild wear to severe wear. However, it is widely recognized that quantitative wear data are not required to establish the fact that certain kinds of visually perceptible, localized surface damage can be justifiably designated as scuffing. And given that the basic mechanistic processes involved can be identified, elimination or control of scuffing damagewhether by amelioration of operating condition, improvement of material properties or more effective lubrication-must operate by modification of these mechanisms.

The meaning of Atahing and the side-by-side occurrence of scuffing and scoring was discussed in Section 13.4, as were the interpretations of ApaLLing and p i t t i n g . These four appellations are the most important items of terminology for describing and understanding catastrophic wear.

397

Refinement and fragmentation of the nomenclature with numerous subis not likely to be of significant value, given the categories variability and the uncertain reproducibility of catastrophic wear as we understand it currently.

a

U 100 JI

b

U 2 0 0 JI

Figure 13-19. Initiation of a scuff. Corresponding views of a massive adhesion on the rider (a) and on the countersurface (b). Arrows show direction of rubbing. The role of reiterative feedback is particularly germane t o the way in which catastrophic wear damage originates and propagates. I n all probability most cases of extensive wear damage initiate at a single On further rubbing, the scuffed locale, as illustrated in Fig. 13-19. slider can damage other sites on the countersurface, and by reiterated contact the disturbance of both surfaces can be exacerbated. The initiation of surface damage, the interaction of the basic mechanistic wear processes and the growth of damage in the course of reirerated traverses are described and discussed by Dorinson [ 6 3 1 .

REFERENCES 1.

2. 3. 4. 5. 6. 7.

Organization for Economic Cooperation and Development, Group on Wear of Engineering Materials, Near during Sliding: Comparison of Test Methods, Technical Secretariat c/o Metal Research Institute TNO, Delft, The Netherlands, 1967. J. T. Burwell and C. D. Strang, J. Appl. Phys., 23 ( 1 9 5 2 ) 1 8 - 2 8 . A . Dorinson and V. E. Broman, Wear, 4 ( 1 9 6 1 ) 93-110. A. Dorinson and V. E. Broman, ASLE Trans., 3 ( 1 9 6 0 ) 165-175. A . Dorinson and V. E. Broman, ASLE Trans., 3 ( 1 9 6 0 ) 176-183. W. Hirst and J. K. Lancaster, J. Appl. Phys., 27 ( 1 9 5 6 ) 1057-1065. J. F. Archard and W. Hirst, Proc. Roy. SOC. London, A236 ( 1 9 5 6 1 397-4 10.

8. J. F. Archard, J. Appl. Phys., 24 ( 1 9 5 3 ) 981-988.

398

9.

C.

A.

Queener,

T.

C.

Smith

and

W. L. Mitchell, Wear, 8 ( 1 9 6 5 )

391-400. 11. 12. 13. 14. 15.

F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part 1 1 , Oxford University Press, 1964, Chapter VI. K. Wellinger and H. Breckel, Wear, 13 ( 1 9 6 9 ) 2 5 7 - 2 8 1 . P. A. Engel, T. H. Lyons and J. L, Siroco, Wear, 2 3 ( 1 9 7 3 ) 1 8 5 - 2 0 1 . P. A. Engel and J. L. Siroco, ASLE Trans., 18 ( 1 9 7 5 ) 2 7 9 - 2 8 9 . J. G. A. Bitter, Wear, 6 ( 1 9 6 3 ) 1 6 9 - 1 9 0 . M. Kerridge and J. K. Lancaster, Proc. Roy. SOC. London, A 2 3 6 ( 1 9 5 6 )

16. 17. 18. 19.

E. J. Duwell, ASLE Trans., ! 2 ( 1 9 6 9 ) 3 4 - 3 5 . W. A. Glaeser, Wear, 6 ( 1 9 6 3 ) 9 3 - 1 0 5 . L. B. Sibley and C . M. Allen, Wear, 5 ( 1 9 6 2 ) 3 1 2 - 3 2 9 . J. K. Lancaster, J. Lubrication Tech. (Trans. ASME), 97F ( 1 9 7 5 )

20. 21.

K. Tanaka, Y. Uchiyama and S. Toyooka, Wear, 2 3 ( 1 9 7 3 ) 1 5 3 - 1 7 2 . D. A. Miller, R. D. Ainsworth, J. H. Dumbleton, D. Page, E. H. Miller and Chi Shen, Wear, 28 ( 1 9 7 4 ) 2 0 7 - 2 1 6 . A . P. Green, Proc. Roy. SOC. London, A 2 2 8 ( 1 9 5 5 ) 1 9 1 - 2 0 4 . C . A. Brockley and G. K. Fleming, Wear, 8 ( 1 9 6 5 ) 3 7 4 - 3 8 0 . K. R. Makinson and D. Tabor, Proc. Roy. SOC. London, A 2 8 1 ( 1 9 6 4 )

10.

250-264.

187-194.

22. 23. 24. 25,

49-61. C. M. Pooley 251-274.

26. 27. 28. 29. 30.

M. N. H. M. W.

31. 32. 33. 34. 35. 36.

J. K. Lancaster, Proc. Phys. S O C . London, 70B ( 1 9 5 7 ) 112-118. J. K. Lancaster, Proc. Roy. SOC. London, A 2 7 3 ( 1 9 6 3 ) 4 6 6 - 4 8 3 . B. J. Briscoe, A. K. Pogosian and D. Tabor, Wear, 2 7 ( 1 9 7 4 ) 1 9 - 3 4 . S . H. Rhee and K. C. Ludema, Wear, 4 6 ( 1 9 7 7 ) 2 3 1 - 2 4 0 . T. F. J. Quinn, Wear, 18 ( 1 9 7 1 ) 4 1 3 - 4 1 9 . T. F. J. Quinn and J. L. Woolley, Lubrication Eng., 2 6 ( 1 9 7 0 )

37 *

T.

and D. Tabor,

Proc.

Roy.

Soc.

London,

A329

(1972)

Ronay, Wear, 18 ( 1 9 7 1 ) 187-205. Gane and F. P. Bowden, J. Appl. Phys., 3 9 ( 1 9 6 8 ) 1 4 3 2 - 1 4 3 5 . A. Smith and R. M. McGill, J. Phys. Chem., 6 1 ( 1 9 5 7 ) 1 0 2 5 - 1 0 3 6 . Kerridge, Proc. Phys. SOC. London, 6 8 B ( 1 9 5 5 ) 4 0 0 - 4 0 7 . Hirst and J. K. Lancaster, Proc. Roy. SOC. London, A 2 5 9 ( 1 9 6 0 )

228-242.

3 12-321.

F.

J. Quinn, Proc. Inst. Mech. Engrs., 182 ( 1 9 6 7 / 1 9 6 8 ) Part 3N,

201-213.

50.

T. F. J. Quinn, J. Microscopy, 9 4 ( 1 9 7 8 ) Part 2, 1 2 5 - 1 3 7 . T. F. J. Quinn, ASLE Trans., 2 1 ( 1 9 7 8 ) 78-86. S . W. E. Earles and D. G. Powell, Proc. Inst. Mech. Engrs., 181 ( 1 9 6 6 / 6 7 ) Part 3 0 , 1 6 - 2 4 . D. G. Powell and S. W. E. Earles, ASLE Trans., 1 1 ( 1 9 6 8 ) 101-108. S. W. E. Earles and D, G. Powell, ASLE Trans., 11 ( 1 9 6 8 ) 109-120. S. W. E. Earles and D. G. Powell, Proc. Inst. Mech. Engrs., 182 ( 1 9 6 7 / 1 9 6 8 ) Part 3N, 1 6 7 - 1 7 4 . N. Tenwick and S. W. E. Earles, Wear, 18 ( 1 9 7 1 ) 3 8 1 - 3 9 1 . E. Rabinowicz, J. Appl. Phys., 3 2 ( 1 9 6 1 ) 1 4 4 0 - 1 4 4 4 . E. Rabinowicz, Wear, 7 ( 1 9 6 4 ) 9 - 2 2 . N. P. Suh, Wear, 2 5 ( 1 9 7 3 ) 1 1 1 - 1 2 4 . T. R. Bates, j r . and K. C. Ludema, Wear, 2 8 ( 1 9 7 4 ) 1 4 1 - 1 4 2 . N. P. Suh, S. Jahanmir, E. P. Abrahamson I 1 and A. P. L. Turner J. Lubrication Tech. (Trans. ASME), 96F ( 1 9 7 4 ) 6 3 1 - 6 3 7 . S. Jahanmir, N. P. Suh and E. P. Abrahamson 11, Wear, 2 8 ( 1 9 7 4

51.

T. R. Bates, jr., K. C. Ludema and W. A. Brainard, Wear,

38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

235-249. 30

(1974

365-375. 52. 53 *

Organization for Economic Cooperation and Development, Research Group on Wear of Engineering Materials, Friction, Wear and Lubrication: Terms and Definitions, February 1 9 6 8 . J. F. Archard and W. Hirst, Proc. Roy. SOC. London, A238 ( 1 9 5 6 ) 5 15-528.

54.

J. F. Archard, in Interdisciplinary Approach to Friction and Wear, NASA SP-181, National Aeronautics and Space Administration, Washington, D. C., 1968, p . 2 7 0 .

399 55. 56.

J. F. Archard, op. r i t . Reference 5 4 , p. 2 8 2 . J. A. Greenwood and J. B. P. Williamson, Proc.

Roy.

SOC.

London,

A295 ( 1 9 6 6 ) 300-319. 57. 58. 59. 60. 61. 62. 63.

T. 0. Mulhearn and L. E. Samuels, Wear, 5 ( 1 9 6 2 ) 4 7 8 - 4 9 8 . J. Goddard and H. Wilman, Wear, 5 ( 1 9 6 2 ) 1 1 4 - 1 3 5 . S. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd Edition, McGraw-Hill, New York, 1 9 5 1 , Chapter 13, p. 375. C. N. Rowe, ASLE Trans., 9 ( 1 9 6 6 ) 100-111. A. Dyson, Tribology International, 8 ( 1 9 7 5 ) 7 7 - 8 7 . A. Beerbower, ASLE Trans., 14 ( 1 9 7 1 ) 90-104. A. Dorinson, Wear, 11 ( 1 9 6 8 ) 2 9 - 4 0 .

400

Chapter 14 ASPECTS OF LUBRICATED WEAR

The preceding chapter was devoted to the development of the fundamental concepts of mechanical wear and to the examination of generalized wear phenomenology in relation to these concepts. The same basic mechanistic processes govern both unlubricated and lubricated wear. The role of the lubricant in lubricated wear is essentially to ameliorate wear by modifying the extent and the rates of those basic processes that exert the critical influences in whatever particular case is under examination. Unlubricated wear is not necessarily simpler or more elementary than lubricated wear; in fact, unlubricated wear is more likely to be so destructive under severe conditions that it may be effectively impossible to specify what occurred at a given stage of the wear process. I n the discussions of Chapter 13 there was no categorical separation of unlubricated and lubricated wear. Given the existence of an unbroken film of liquid lubricant between two surfaces, it is generally expected that no wear will occur. This is not always so; transmission of hydrostatic pressure through the film can plastically deform the bodies which i t separates, and tangential tractive forces in the film can do the same. These are wear phenomena as defined in Chapter 13, and since they occur in the presence of lubricant they can be formally classified as lubricated wear. However, in this chapter we shall not concern ourselves with these particular aspects of lubricated wear. We shall be concerned instead with the course of wear in situations where the behavior of the lubricant does not conform fully with the laws of hydrodynamics o r elastohydrodynamics. The inference, of course, is that the lubricant at the rubbing surfaces is not there as an unbroken film.

Such being the case, further inferences about the nature of the wear process follow. A disrupted fluid film allows localized contacts at the rubbing surfaces, and it is the mechanistic processes at these contacts that determine the course of lubricated wear. When the wear process is abrasive, it is most likely influenced directly by fluid film thickness and surface roughness, whereas processes such as adhesion, transfer, oxidation, additive reaction and the like are responsive to surface conditions at the contacts as well as to the number of contacts. These are the aspects of lubricated wear that are emphasized ir. this chapter, from the viewpoint of phenomenology, mechanisms a n d modeling.

401

LUBRICATED WEAR BY PENETRATION OF THE FLUID FILM

14.1.

The problem of wear when the fluid film lubricant is no longer intact is associated with the asperity contact of structured surfaces. The contact behavior of such surfaces was discussed in Chapter 12; wear models governed by asperity contact were described in Chapter 13. Theoretically the laws controlling fluid film thickness can be coupled with asperity contact models to yield quantitative descriptions of the course of wear. I n this section we shall deal with those cases in which the function of the lubricant is only to provide a fluid film separating the two rubbing bodies, and the events at the contact, once it is established, are determined by the interaction of mechanical parameters such as load and rubbing speed with the properties of the contacting interface. 14.1.1.

Wear and Partial Elastohydrodynamic Lubrication

The term pahtial elantahydhadynamic Lubnication is used here in the same sense that it appears in the communications by Tallian and his coworkers [ l , 21, without any implication of a definition. The thickness of the fluid film is calculated by the usual techniques of elascohydrodynamics on the assumption that the surfaces of the rubbing bodies are smooth. The criterion of whether the fluid film i s thick enough to prevent metal-to-metal contact at the real rubbing interface is the quantity

lcol

hO

=

‘h

(14-1)

where ho is the average film thickness and dh is the composite root-meansquare surface roughness. It is obvious that since the usual picture of surface structure implies a distribution of asperity summits above and 2 1) is not the below the average datum level, ho 2 d h ( i . e . (<,I criterion f o r no-contact. Theoretically there is no upper limit f o r the value of h m , the tallest asperity summit; practically tne upper limit of h m is determined by the separation at which wear is either undetectable or insignificant. Tallian e t aL. [2, 31 used two types of data in working with Eqn 14-1. Profilometric traces of the surface of balls from ball bearings obtained with a stylus instrument were processed to provide data for the analysis of peak and summit height distribution. Electrical conductance data from lubricated rolling four-ball experiments were used to determine the percentage of che rubbing time which resulted in metal-to-metal contacts. The film thickness along a path across the conjunction between two balls has a distribution function F(hlho,uh);the non-dimensional film thickness corresponding to this distribution i s

402

.7

=

h - ho (14-2)

h'

with a mean value = 0 and a standard deviation 6 = 1. When h = 0, we 5 get Eqn 14-1. The distribution function F ( i i = O l h o , uh) corresponding to h = 0 is denoted by F ( c 0 ) . The no-contact fraction T/To is related to

F ( c o ) by 1 - (T1/T2)5,0 =

F(c0)

(14-3)

The postulate that the contact fraction is equal to the ratio of the true area of contact to the nominal area of the conjunction gives A

The expression Arc hard model,

for

wear is developed from what is essentially the

e

Q = - =

L

Kl",

(14-5)

where $ is the wear rate, 2 the mass of material lost by wear, L the length of the rubbing path and Wn is the load carried by the contacting asperities. I f the true area of metallic contact is proportional to the load carried by them (assuming either the piastic deformation concept or Archard's model of the elastic deformation of multiple orders of asperity sizes), I

W a = k,A

(14-6)

and Eqn 14-5 becomes @ =

K2A

(14-7)

Using the value of A given by Eqn 14-4, $ =

K2AoF(co)

For two bells pressed together by a total load area A, is given by an expression of the form A,

= k2W2l3

(14-8) W

the

Hertzian

contact

(14-9)

where the constant k 2 collects the various fixed parameters of the elastic deformation analysis. This changes Eqn 14-8 to Q =

K3W2/3F(c0)

(14-10)

Tallian and his co-workers [ 2 ] tested the validity of Eqn 14-10 by the following procedure. Wear was determined in rolling four-ball experiments by making the driving ball radioactive and measuring the radioactivity of the detached debris and of the material transferred to

403

the three freely rolling balls. The distribution function F ( c 0 ) was evaluated from the no-contact fraction obtained by electrical conductivity experiments. Since both 6 and A/Ao are directly related to F(<,) (Eqns 14-4 and 14-10}, @ = K3W2l3

A/Ao

( 14-1 1 )

and for a fixed load we can write Log K4 = L o g 6

- Lo5 (A/Ao)

(14-12)

The distribution function F ( c 0 ) is directly related to 5 , and hence both @ and A/A, can be plotted against 5 , . Tallian e t aL. [2] found that loglog plots of A/Ao against <, were straight lines and that log-log plots of @ against 5, were acceptably linear in most of the cases they studied. For the wear-rate constant K4 to obey Eqn 14-10 requires that log-log plots of @ and A/Ao be parallel straight lines.

---

P

--

-

0.7 1

2

KJ

3 4 5

0.51

2

5

I t0l

10

20

Figure 14-1. Wear and partial elastohydrodynamic lubrication. (a) Synthetic ester lubricant. (b) Mineral oil lubricant. Data by Tallian el: ae. [21. Tallian e t a L . [ 2 ] found this to be true for the two synthetic ester-type lubricants they tested, as exemplified by Fig. 14-la. B u t mineral oil lubricants showed the behavior illustrated by Fig. 14-lb; instead of remaining constant at K4, the wear-rate proportionality factor increases with increasing film thickness. This was attributed to the formation of a deposit o n the rubbing surfaces which acted gartly as an electrical insulator and also as a "solid" lubricant, the amount of deposit increasing as the fraction of asperity contact increases with decreasing film thickness. However, there may be doubt whether the experiments of Tallian el: aL. were a fair test of their own theory, working as they did with rolling element bearing balls whosa r.m.s. roughness was only 25-40 nm and with loads so large that in many cases the value of A,

404

the true contact area, was as high as 4 0 % of the Hertzian area A,. Under these circumstances small experimental errors have a large relative effect. The wear hypothesis used is one developed for sliding motion, whereas the experiments involved principally rolling, a small sliding component being contributed by the skewed spin of the balls. The depthwear rates are of the order of 500 nm/km or less and the average particle diameter of the loose wear debris is of the order of 1 6 0 0 nm, a relative value more consistent with the spalling of wear particles by fatigue than of smooth detachment by an adhesive wear process. On the other hand, there are the data for the influence of compounded antiwear additives in ester-type fluids, as shown in Table 14-1. These data show good conformity with the partial elastohydrodynamic wear model and the effect of compounded antiwear additives is what is anticipated in an adhesive wear process.

TABLE 14-:.

EFFECT OF ADDITIVES ON WEAR RATES WITH ESTER FLUIDS ~~

I

Type

15,

Diester, base fluid Diester, compounded Ester, base fluid Ester, compounded

1.97 1.97 1.95 1.95

Depth-wear rate, nm/km

Wear ratio, base/compounded

16.7 3.51 1.86 0.651

4.76

Rollin? four-ball apparatus, ball 12.7 cm load 8 1 0 N. Data by Tallian e t aL. 1 2 1 .

14.1.2.

~

diameter,

2.85

8.33

rps,

applied

Wear and Mixohydrodynamic Lubrication

M i x e d Lubaication and quadihydhodynamic Lubhication are two terms encountered in the literature of tribology f o r whose usage there is no inherently precise meaning. The implication is that the rubbing process involves patches of surface separated by fluid lubricant intermingled We shall adopt the designation with patches in direct contact. mixohydhodynamic Rubaication here instead of quasihydrodynamic lubrication; behavior in this type of lubricated wear is governed by a mixture of direct asperity contact and hydrodynamic action, whereas the term quasihydrodynamic lubrication implies behavior that seems to be hydrodynamic but in fact is not so rheologically. As will be pointed out, the behavioristic difference between mixohydrodynamic and partial elastohydrodynamic lubrication justifies the distinction in nomenclature, The kind of wear behavior characteristic of mixohydrodynamic The left-hand diagram shows the lubrication is shown in Fig. 1 4 - 2 . distance-dependent depth-rate of wear as a function of the contact pressure for a series of four rubbing speeds. The right-hand diagram shows

405

I

I

I

I

I

I

I

01

0

Pressure, MPo

I

10

I

15

I

20

I

25

I

30

I

35

1

I

40

45

I1 50

Rubbing Speed, ern /s

Figure 14-2. Wear behavior and mixohydrodynamic lubrication. (a) Pressure-dependent wear at various speeds. A: 5.08 cm/s; B: 10.16 cm/s; C: 25.4 cm/s; D: 50.8 cm/s. (b) Speed-dependent wear at various presn = sures and parameters of Eqn 14-14. 1: 827 MPa, k, = 37.08 x 0.4882; 2: 690 MPa, k, = 35.79 x n = 0.4959; 3: 552 MPa, k, = 30.39 x n = 0.4399; 4: 414 MPa, l~, = 43.59 x n = 0.5448. the same data plotted as a function of rubbing speed with contact pressure a s a parameter. The data are from unpublished work by A . Dorinson on the wear of hardened alloy cast iron lubricated by 1.43% of zinc dibutyl dithiophosphate in white oil. When rubbing speed is held constant the influence of contact pressure on the wear rate is given by the empirical relation

(14-13) where [dz/dLl, is the distance-dependent depth-wear rate at fixed rubbing speed, K p is the constant of proportionality, p is the contact pressure and p , is the intercept on the axis of the abscissa. Numerical analysis of the isobaric plots in Fig. 14-2b produces an expression for the distance-dependent wear rate as a function of rubbing speed of the form

(14-14) The convergence of the lines shown in Fig. 14-2a on a value of p , = 189 i 15.7 MPa cannot by itself be regarded as empirical justification for assuming that this is the critical contact pressure for the existence of a full fluid film of lubricant completely separating the two rubbing surfaces. The extrapolation to zero wear rate is not necessarily linear. However, it is reasonable to assume that the total load on the nominal area of the conjunction can be resolved into the load carried by the con-

406

tacting

asperities and the load carried by the

fluid film of lubricant. the conjunction is the sum of the average pressure on the contacting asperities and the average pressure on the fluid film: AS a simple postulate let u s assume that the total pressure on

P

=

P,

+

Pd

(14-15)

The depth-wear rate is governed by the pressure on the asperities,

E]"

=

Kppa (14-16)

and hence for that particular portion of the experimentally observed wear process as given by Eqn 14-13 the value of p, gives the average pressure carried by the fluid film of lubricant. The level of pressure that a fluid film of given thickness can carry is a function of its hydrodynamic behavior as governed by the relative speed of the bounding surfaces. Therefore the explanation for the ameliorating influence of increasing rubbing speed on the rate of wear as seen in Fig. 14-2 is straight-forward in principle, although the quantitative modeling is complicated. The function v - n in Eqn 1 4 - 1 4 was adopted by analogy with the empirical formulas of elastohydrodynamic lubrication derived by group dimensional analysis [ 4 1 . Sakurai, Okabe and Matsurnura [ 5 ] used a somewhat different approach to obtain an expression for the effect of contact pressure and rubbing speed on wear rate under conditions of mixohydrodynamic lubrication. Figure 14-3 shows the relation they observed between the volumetric distance-dependent wear rate and contact pressure with rubbing speed as

Contact Pressure, MPa

Figure 14-3. Influence of contact pressure on rate of lubricated wear at various rubbing speeds. Copper against steel, lubricated by white oil, 2 0 . 3 cs at 3 7 . 8 C. a: 2 1 . 1 cm/s; b: 41.8 cm/s; c: 6 3 . 5 cm/s; d: 11.7 cm/ s. From data by Sakurai, Okabe and Matsumura [ 5 ! .

407

the parameter. At each speed the wear-rate function can be extrapolated to a contact pressure at which its value is zero. This was taken as the critical contact pressure which permits a full fluid film at that speed, according to the following empirical equation,

(14-17) where p is the experimental contact pressure and p h is the limiting pressure for hydrodynamic action. When the values of k, and p h in Fig. 14-3 are plotted against sliding speed they can be fitted to relations of the following form, k,

=

k4 c x p (-k5w)

ph = ( p h ) ,

[l

-

(14-18)

e x p (-k6v)]

(14-19)

where ( p h l e 0 is the value that p h approaches asymptotically as w increases to a relatively large magnitude. Substitution into Egn 14-17 gives dV - =

k4 e x p ( - k 5 V ) i p - ( p h ) , [I - e x p ( - k 6 v ) ] 1

dL

(14-20)

5 ‘n

50

5 40

4

0 kx)

c

0

a

g 7al

-E 9

20 10

0 20 30

40

50

60

70

80

90

100

I 1 0

Rubbing Speed, cm/s

Figure 14-4. Influence of rubbing speed on rate of lubricated wear at various contact pressures. Copper against steel, lubricated by white oil, 2 0 . 3 cs at 3 1 . 8 C. a: 294.2 MPa; b: 245.2 MPa; c : 196.1 MPa; d: 137.3 MPa. From data by Sakurai, Okabe and Matsumura [ 5 1 . Figure 14-4 shows plots of Eqn 14-20 using the data of Sakurai, Okabe and Matsumura 1 5 1 for the wear of copper lubricated by white oil, from which the parameters listed in Table 14-2 are calculated. The curves in Fig. 14-4 exhibit acceptable parallelism with the curves in Fig. 14-2b, which were obtained from different data and by a different approach. The work of Sakurai e t aL. shown in Fig. 14-3, because it was carried out at lower contact pressures and higher rubbing speeds, reveals

408

TABLE 14-2.

PARAMETERS FOR PLOTTING EQUATION 14-20

k4 :

3.16 x

k5 :

0.0159 seconds/cm

k6 :

0.0252 seconds/cm

(PIZ)=:

201 MPa

cm2/MPa

From data by Sakurai, Okabe and Matsumura [51. the anticipated speed effect on the values of ph if they represent the critical pressures for a full fluid film. The apparent convergence seen in Fig. 14-2a may be an empirical effect due to the insensitivity of the wear measurements for the harder alloy cast iron in this particular range In that case the factor of contact pressures ar,d rubbing speeds. ( p - pee) in Eqn 14-4 can be regarded as an empirical variant of the factor { p - (ph),, [ l - e x p (-k6v)ll in Eqn 4-20 and the two equations can be viewed as two empirical expressions that yield the same numerical end result for a given set of data. The reader is cautioned against regard ng either of the foregoing empirical treatments as a general model for mixohydrodynamically lubricated wear. There is no rigorously defined concept of mixohydrodynamic lubrication nor is it precisely recognizable as a distinct mode of behavior. For the time being the term serves to designate an area of lubricated wear behavior which is easy to identify by its broad empirical characteristics but which is difficult to delimit. The particular examples examined above are relatively straightforward cases that are easiAn example of more complicated behavior is seen in ly treated. Fig. 14-5, which shows the wear observed with the uncompounded carrier oil of the lubricant used in the experiments of Fig. 14-2. With the carrier oil the depth-rate of wear is no longer linearly responsive to contact pressure. Since the properties that govern film thickness, such as viscosity and density and their pressure coefficients, are virtually identical for both the compounded and the uncompounded oils, the differences in behavior must be attributed to influences directly operative on the wear process, such as changes in the wear effectivity factor O K the wear particle volume. The basic idea of partitioning the load between the contacting asperities is retained, but the effectivity factor and the particle volume become functionally related to the contact pressure. The distinction between the partial elastohydrodynamic concept of Section 14.1.1 and the mixohydrodynamic concept of this section is one of

300

White Oil

i

5 250

f

150

0

100

0

0

I

20

I

40

Contact

I

60

I

80

I 100

Pressure, MPo

Figure 14-5. Influence of contact pressure at various rubbing speeds on the wear rate of hardened alloy cast iron lubricated with white oil. Unpublished data by A . Dorinson.

0

0

0.5 1.0

15 Rubbing Time,

20

2.5 3.0 3.5

lo3 seconds

Figure 14-6. Comparison of the wear of steel lubricated with compounded and uncompounded oil. Hardened AISI 1045 steel, 517.1 MPa, 50.8 cm/s. Unpublished data by A. Dorinson

Ip

0

m

410

point of view rather than something fundamental in the wear process. The wear observed by Tallian and his co-workers [ l , 2 , 31 was the consequence of asperity penetration through a fluid film whose thickness was governed by the laws of elastohydrodynamics applied to a conjunction with precisely defined boundaries. In mixohydrodynamic lubrication the conjunction area is thought of as being densely populated by true asperity contacts interspersed with channels in which the lubricating fluid flows hydrodynamically. Although not specified explicitly by Tallian e t aL. in their examination of the wear of rolling element parts under conditions of partial elastohydrodynamic lubrication, the sliding component of the relative motions of the two bodies must have been comparatively low; otherwise at the high nominal pressures applied to the conjunction surfaces the fluid film would have been profoundly disrupted, the wear would have been extensive and rapid, and the behavioristic basis for distinguishing partial elastohydrodynamic lubrication from mixohydrodynamic lubrication would have been lost. 14.2.

COMPOUNDED LUBRICANTS AND WEAR

In Chapters 10 and 1 1 the discussions of the behavior of lubricant additives emphasized their action at the rubbing interface without going into detail about wear processes and their overt results, In this section we shall examine the action of compounded lubricants in terms of

their effect on the course of wear, both as observed experimentally and as modeled theoretically. Figure 14-6 illustrates the effect that compounding an antiwear additive into a carrier oil can have on the course of wear. The wear of a conically-ended pin of hardened AISI 1 0 4 5 steel rubbing at 50.8 cm/s, 517.1 MPa contact pressure ( 1 0 0 ft/min, 75,000 psi) against a similarly hardened steel disk in the presence of white oil is compared with the wear in the presence of a lubricant of the same viscosity compounded with a commercial extreme-pressure additive [61. Disregarding the structured portions of the curves at the beginning of the course of wear, the main difference lies in the rates for the final portions, some 37 times grester with white oil as the lubricant than with the compounded oil. The experimental parameters of this particular study are easily amenable to analytical modeling. To develop a model it is necessary to identify the mechanistic process by which the additive influences the wear rate and to find a quantitative expression for this inf luence. The quantitative model for an individual case cannot be divorced from the nature of the particular additive used; however, the general principles of wear can be combined with those of additive action to give an acceptable treatment of wear in the presence of compounded lubricants. In Chapters 10 and 1 1 additive action was shown to fall into two broad categories: ( a ) an interposed film laid down by adsorption or deposition

411

from the fluid lubricant or by direct reaction with the rubbing surface; ( b ) quenching of the adhesion of asperities by additive reaction at contacting sites. Any film deposited on the surface will also be subject to wear and hence lubricated wear in such cases will be the dynamic resultant of the rates at which the film is laid down and removed. Static deposited films, e . g . monomolecular films deposited from solution by retraction techniques, do not p e h 6 e afford stable protection against wear, as is demonstrated by the work of Levine and Zisman [ 7 , 83 on the durability of such films ( c d . Chapter 10, Section 10.4.1). Modeling of stably effective antiwear lubrication by additive action obviously requires a reaction rate analysis. 14.2.1. Reaction-Rate Theories of Wear in Lubricants

the

Presence

of

Compounded

The modeling of lubricant antiwear action as a competition at the asperity junctions between metal-to-metal adhesion and additive reaction, as proposed by Dorinson [ 9 1 and by Dorinson and Broman [lo], was disThe cussed in Chapter 10, Section 10.7 and Chapter 11, Section 11.2.2. rate of wear depends on the surface concentration of asperity adhesions, denoted here by [ M A ] , the time-dependent relation for which is mkakb

[MA]

= m k b + Ck,

t ( 14-21 )

where m is a constant characteristic of the surface density of real contact sites, k, and k b are reaction rate constants for the formation of an asperity adhesion, k, is the reaction rate constant for additive reaction at the asperity juncti0r.s and C is the concentration of the additive at the rubbing surface, here considered proportional to its concentration in the bulk lubricant. On assigning an average particle removal factor q to I each adhesion, the wear rate Wo is written as

,

d[MA3

mkakb - 4

W o = T -

mkb

+

Ck,

(14-22a)

By collecting constants the effect of additive concentration on the wear rate can be expressed as

wo

=

mkb

+

Ck,

(14-22b)

So far there has been no determination of the separate values of m , or k, for a given experimental case, and thus there is no direct ha, kb verification of the validity of the above approach as a general model for lubricated wear. Dorinson demonstrated that the analysis gave an expres-

412

sion correctly assigning the concentration effect of cutting oil additives on the Taylor equation for tool wear in metal cutting [ 9 ] , and the work of Dorinson and Broman [lo] on the effect of additive reactivity was described in Chapter 11, Section 11.2.2, where it was shown that the ratio of che two wear rates,

(14-23)

could be made to yield the relation

(

14-24)

All the quantities on the right-hand side of the equation above are known o r measurable experimentally. A similar treatment can be used for two concentrations of the same additive, C,k, and C2k, being used instead 0 5 C(k,), and C(k,)*. Substitution of the values for mkb into Eqn 14-22a gives the value of hay. Sakurai and his co-workers [ l l , 12, 131 investigated the following sequence, exemplified by the additive action of sulfur dissolved in a lubricating fluid on metallic iron: Fe + S FeS

+ FeS

)

wear debris

The net rate of formation of PeS on the rubbing surface is d[FeS] ~- k, dt

[Fe] [ S ]

- b,

[FeS] (14-25)

where k, is the rate constant for the formation of FeS and k, is the rate constant for i t s removal by wear. The surface sites available for reaction at any time t are given by m-[FeS], and of these a fraction 9 U- are in adsorption equilibrium with the lubricant, so that from Eqn 14-25 we get dS

k,B,

- =

(m

- S) - k,S

(14-26)

dA where S represents [FeSl.

S

=

Sm i 1 - e x p

[ -(kh9,

+

Integration of Eqn 14-26 gives

k,)tll

where Sm is the value that S approaches asymptotically as infinity. All concentration are in moles per unit area. Sakurai

( 14-27)

t

approaches

e t at. used either a spherical ball loaded against the flat

413

surface of a rotating disk or a stationary cylindrical surface in contact with a raised circular land on the flat surface of a rotating disk a s the rubbing parts of their experimental apparatus. The additive substance was tagged with radioactive sulfur, and the behavior of the additive in the wear process was followed by assay of the radioactivity left on the rubbing track or on the raised land of the disk. Since Eqn 14-27 holds only for the rubbing interface, an implicit assumption is that the additive does not react with the surface of the track or the land when it is out of contact with the rider. Sakurai, Ikeda and Okabe [12] observed that So3 increased with increasing load, in conformity with this assumption; if Sm is governed by the total time the surface of the track is in contact with the lubricant, it should be insensitive to the magnitude of the load, while i f Sm is governed by the rate of wear, it should decrease with increasing load. Okabe, Nishio and Masuko I 1 4 1 eliminated the contact-free exposure complication by rubbing two circular lands against each other and found essentially the same type of behavior that was observed for a ball or a cylinder against a track or a land. When the compounded lubricant is replaced by the uncompounded carrier oil, then from Eqn 14-26 we get

s

=

so c x p [-h,(l:

- to,]

(14-28)

where So is the surface concentration of the reaction product at the time t = to that the substitution was made. The radioactivity of the track is given by the relation u

*

*

= Uo e x p [-c,(t

-

to)

1

(14-29)

* .is

where a. activity

the activity observed on the track at time t o and a* is the at time t. The radioactivity is proportional to the concentra-

tion of the reaction product, S ; hence by suitable calibration cw can be used to evaluate .b, The assumption here is that any direct metal-tometal contact does not perturb the wear of the reaction product. But if the radioactive compounded oil is replaced by its inert version theoretically the radioactivity is no longer directly proportional because it is progressively diluted by the formation of inert reacto s t ion product. At time t the composition of the reaction product on the rubb ng surface is given by (14-30) where S: is the surface concentration of radioactive product at time .to, AS; is the radioactive product worn away in the time interval t - Lo, AS, is the ir,ert reaction product generated in that time interval and ASw is :he inert reaction product worn away. If rubbing lubricated by radioac-

414

tive compounded oil had been allowed to continue to time .t, the activity of the surface would have been a: whereas because of the substitution by inert oil the observed activity is a*. Applying these facts to Eqn 14-30 gives the following expression for the amount of inert reaction product that dilutes the radioactive product generated up t o time to:

AS, - AS,

=

Sm$l -

E -(kaea

exp

+

k,)tIl

-

4) at

(14-31)

This being s o ,

s;

-

-

1

s; 1

-

e x p [-(k,B, exp

+

[-(k,e,

+

k,)t]

k,)Ro]

I

and it is theoretically incorrect to evaluate k,

(14-32)

from the ratio ,*/a;.

Rubbing Time, D3seconds

Figure 14-7. Radioactive monitoring of wear lubricated with a compounded oil. Contact pressure 0.991 MPa, rubbing speed 10.6 cm/s. Additive: * Replacement of tagged additive by dibenzyl disulfide, 13.2 mole/m 3 a:, inactive additive. Data by Okabe, Nishio and Masuko [141.

.

Figure 14-7 is an example of the course of lubricated wear as followed by surface radioactivity. The progressive accumulation of reaction product on the rubbing track in the presence of a tagged compounded lubricant is shown by the first part of the curve, and the fact that this is the net resultant of simultaneous reaction and wear processes is demonstrated by the shape of the final portion of the curve. Sakurai e t aL. [ l l , 12, 131 found such behavior to be characteristic of the following sulfur compounds, singly and in combination: sulfur, dibenzyl disulfide, diphenyl disulfide, dodecyl mercaptan; and also these sulfur compounds in combination with stearic acid, benzyl chloride, chlorobenzene or hexachloroethane. The qualitative observations are credible enough, but because of experimental difficulties and the complications noted

415

above in the application of the theory to the actual scheme of experimentation, the quantitative results, particularly the evaluation of the reaction-rate and the wear-rate constants, must be viewed with reservations. Sakurai, Ikeda and Okabe reported values of Sm equivalent to 30-50 layers of FeS [12], which makes the modeling of the reaction step via an absorption equilibrium somewhat strained. As an alternative, semiempirical approach we can adopt the parabolic rate hypothesis used in the oxidation of metals [151 and apply it to the formation of reaction product on the surface,

s,

=

k,t 1 /2 (14-33)

where S, is the surface concentration assigned to the reaction product and lz, is the overall reaction rate constant which includes surface condition and additive concentration effects. The expression below gives the net concentration of reaction product observed on the surface, (14-34) where ASu is the amount of reaction product worn away and k, and n are empirical constants that f i t the expression to the data. The expression for wear is ASu = K,S

= K,

kbtn

(14-35)

so that

S

=

k,C’/2 - K b k , t n

(14-36)

Table 14-3 gives the results of fitting Eqn 14-34 to the data obtained by Okabe, Nishio and Masuko 1141 which are shown in Fig. 14-8. There is considerable scatter in the values for k, and n , but n is consistently less than 0.5.

TABLE 14-3. PARABOLIC REACTION RATE HYPOTHESIS APPLIED TO ADDITVE ACTION OF DISENZYL DISULFXDE: s = k b t n Conc. DBDS, mo1/m3 26.4 13.2 6.6

k,

n

378

0.367 0.438 0.296

(a) Radioactive intensity per second of rubbing Okabe, Nishio and Masuko [141; see Fig. 14-8.

(a)

184 255 time.

From

data

by

416

c

.-r

E

\

c v)

4000

2 c %

.-c

x

0

.-

3000

0 0

a

0 0

5 10 15 Rubbing Time,103 seconds

Figure 14-8. Surface radioactivity and the overall course of wear lubricated with compounded oil. Copper against steel at 0.991 MPa, 2.75 cm/s, lubricated by tagged dibenzyl disulfide in white oil. Data by Okabe, Nishio and Masuko 1141.

14.2.2.

Reaction Rate Processes and Phenomenological Wear

The rate expressions of Section 14.2.1 are for the most part not particularly well suited for direct application to phenomenological wear and experimental require further treatment to adapt them to specific procedures for measuring wear. In the case of Eqn 14-22a, which was originally derived on the basis of unit apparent conjunction area [91, 4 is the volume of material removed per unit apparent area in unit time and has the dimension l/t. Wo therefore is the expression m k u k b i ( m k b + Ck,) the time-dependent volume-rate of wear d V / d t for unit apparent conjunction area. The distance-dependent rate of wear is given by dV

1

dV

dl

v

dt

- = - . -

(14-37)

v being the rubbing velocity.

dV

4

dL

v

- = _ .

Hence

mkukb mkb

+

Ck,

(14-38)

But as was shown, in Chapter 13, Section 13.5, dV - = K5Z

dL

(14-39)

where Z is the wear effectivity ratio of the asperity contacts as defined by Eqn 13-15. Thus we can write

417

mkb

+

Ck,

(14-40)

and any of the relations developed in Chapter 13 from Eqn 13-20 can be which evaluated the expressed in terms of the ratio m / z a k b / ( m k b + Ck,) lubricant additive in terms of its concentration and its reactivity. The specific influences of other experimental parameters-e.5. load or contact pressure, rubbing speed, specimen geometry, material propertieswere discussed in Chapter 13.

In examining the relation of distance-dependent wear rates to the corresponding time-dependent rates it is important not to lose track of I the units in which these rates are expressed. The units of Wo in Eqn 14-22a are volume per unit apparent area per unit time, which reduces to the dimensions LT-'. The units of dV/dL in Eqn 14-38 must therefore be volume per unit distance travelled per unit apparent area (which is dimensionless), if it is to be consistent with the right-hand side of the equation a s it was originally derived. The physical interpretation of Eqn 14-22a is not restricted to pounded lubricants. I f C = 3, the expression reduces to

wo

=

k,Y

(

com-

14-4 la)

The factor h a , which is a migration constant governing the establishment of asperity adhesions in dry contact, has a modified interpretation i f the surfaces carry an incomplete film of non-reactive lubricating fluid. The number of asperity contacts will be lower than in the case of a dry conjunction and we then write

wo

=

k,Y

(

14-4lb)

The additive effect relative to uncompounded lubricant is given by 1

(Wo)l

mkb

+

Ck, (14-42)

The model of Sakurai and his co-workers [ l l , 12, 13,] is essentially a quantitative description of a wear process via chemical reaction (corrosive wear). Its application to the customary techniques of direct of the volume wear of a rider rubbing against a measurement countersurface is neither straightforward nor easy. The area of the rider is in rubbing contact with the track during the full time of each revolution, whereas the time that the equivalent area on the track is in contact is given by the ratio of the area of the rider to the total area of the track; i . e . the rubbing time of the rider is greater than the rub-

418

bing time of the track. Therefore, if the data are obtained by scanning the track, they must be adjusted by the appropriate time factor in order to apply them to the rider. Having obtained the rate at which material is lost from the rider in time-dependent terms, the distance-dependent wear rate is

It can be shown by dimens onal analysis that dS

MAo _ = - . p dL

dV

(14-43)

dL

where p is the density of the wear debris and M is its molecular weight, both of which are constant for a given material. The apparent conjunction area A. is a determinable function of the rubbing distance L ; hence i f d S / d t for the rider can be evaluated experimentally, the conversion of distance-dependent volume-rate of wear in terms of directly measurable experimental parameters to surface concentration of reaction product (as evaluated by radioactivity, for example) is given by

(

14-44)

The model derived by Dorinson 1 9 1 for direct wear promoted by chemical action can be put into the form d8 - =

mq*

Ckh (14-45)

dt

where Q is the mass of material worn away per unit of apparent conjunction area and y * is the lump removal factor. This can be transformed to dV

mq*

Cb,

- = -

dL

pv

*

A,

(14-46)

The quantities m , 4 * , p and v are constant for fixed experimental conditions, and by stipulating a fixed area A, we get dV

- - - K6Ck, dL

(14-47)

as the relation between additive concentration and wear. This relation is at variance with the antiwear action of additives as given by Eqn 14-22. However, Eqn 14-22 pertains to the process by which additives inhibit adhesion at asperity junctions, whereas Eqn 14-47 is the model for direct wear of the additive reaction product. The overall wear rate is the sum of the two,

419 I

w = w0

+

wo

(14-48)

I

11

where Wo is the rate of wear for the adhesion inhibition process is the rate of wear for the directly formed reaction product.

and

Wo

Writing Eqn 14-48 as

"

I

Wo

+

mkb

Wo = cka

+

mkb

+

m q * Ck,

Ck,

(14-49)

we note that the effect of increasing the additive concentration C is to decrease the first term of the right-hand side of the equation and to increase the second term. Depending on the relative values of q and q * , it is conceivable that the second term could control the overall rate of the wear process; and in that case the wear rate would increase with increasing additive concentration. Such behavior was observed by Dorinson [161 for the wear of hardened AISI 1045 steel lubricated by di-t-octyl disulfide in white oil at 517.1 MPa and 50.8 cm/s rubbing speed, as shown in Table 14-4. The organic-free wear debris isolated from the wear experiment lubricated with the 22% solution of di-t-octyl disulfide was examined by electron-probe microanalysis and by X-ray fluorescence imaging The greater and was found to have the composition shown in Table 14-5. portion of the debris was a mixture of two iron sulfides, which points to the chemical reaction mechanism as the major process involved in the observed course of wear, but the presence of Fe304 and a-Fe indicates that TABLE 14-4.

CONCENTRATION OF DI-t-OCTYL DISULFIDE AND WEAR RATE

% Di-t-octyl disulf ide

Concentration ratio (a)

22 9.3 5.5 0 (c)

4.0 1.7 1.0

-

Depth-wear rate, cm/s

Wear-rate ratio (b)

0.00107 k 10 0.00048.4 0.00024.0

k

O.GC017.2

f 0.6

5.7

4.4 2.0 1 .o

-

(a) Ratio with respect to 5.5% di-t-octyl disulfide. (b) Wear rate with respect to rate for 5.5% di-t-octyl disulfide. (c) Uncompounded white oil. TABLE 14-5. COMPOSITION OF DETACHED DEBRIS FROM WEAR OF STEEL LUBRICATED BY DI-t-OCTYL DISULFIDE IN WHITE OIL CARRIER

...........

FeS 69.9% FeS2..........14.5 Fe304.........14.4 a-Fe.....

...... 1.2

420

some of the wear took place via the transfer/oxidation process. The lubricated wear described above is squarely at odds with the behavior illustrated in Fig. 14-6 and with the wear-reducing action of 22% di-t-octyl disulfide in white oil reported by Dorinson and Broman [lo] and shown in Table 11-6 (Chapter 1 1 , Section 11.2.1). If Eqn 14-49 is a correct representation of additive action, it should be valid for both the reduction and the increase of wear by such action. To reduce wear, the first term on the right-hand side of the equation must control the overail rate; and one way to do so is for the lump removal factor q to In that case, increase of C have a greater effect than the factor y * . decreases the value of m k b / ( m k b + Ck,) and the action of the additive is t o reduce the wear rate. B u t there is no physical necessity that y remains constant for all conditions of load, pressure, speed or state of lubrication. Since in physical terms the predominant effect of the lubricant is to inhibit the asperity adhesion process, it is not unanticipated that the average size of the transferred and detached particles as well as their number will be decreased by lubrication. I t is to this latter type of mechanistic process that we must look for an explanation of why such parameters as contact pressure, rubbing speed and material properties affect the balance between the inhibition or promotion of wear by additive action and the transition from smooth lubricated wear to catastrophically damaging wear behavior such as scuffing. 14.3.

THE CONTROL OF SCUFFING

An important aspect of the function of compounded lubricants is to increase the load that can be carried by machinery without catastrophic damage to the rubbing components. Since the typical antiwear additives affect the viscosity of the carrier oil very little, it is not a fluid film sffect that is responsible for the load-carrying augmentation. Examination of the various basic wear processes leads to the choice of the adhesive mechanism as the one most likely to respond to the action of boundary o r extreme-pressure additives. The type of macroscopically observed severe wear which has this mechanistic process as its primary cause is generally designated as scu66ing (c6. Chapter 13, Sections 13.4 and 13.6), and it is in this sense, as a description rather than a definition, that the term scuffing is used in the discussion to follow. Figure 14-9 is

a

relatively

uncomplicated

comparison

of

smooth

lubricated wear and scuffing as observed in a pin and disk experiment [17]. On the left is the scar on the end of a rider after rubbing at 2.069 GPa, 85.9 cm/s, lubricated by sulfurized sperm whale oil in a mincm per cm of ruberal oil carrier. The depth-wear rate was 3.09 x bing distance. The scar on the right was generated at a depth-wear rate of more than 25 x lo-' cm/cm in the presence of the uncompounded carrier

421

Figure 14-9. Examples of smooth lubricated wear and scuffing. (a) Smooth wear lubricated by sulfurized sperm whale oil in carrier fluid. (b) Scuffing: lubricant uncompounded carrier oil. Hardened A ISI 1045 steel pins rubbed at 85.9 cm/s, 2.069 GPa. Illustrations and data by A . Doriilson 1 1 7 1 . Imprint of

Figure 14-10. Genesis of scuffing on the rubbing face of a gear tooth. (a) View of regions rubbed at three progressively increased load steps in the Ryder test. (b) Shows the orientation of the imprint of the narrow tooth on the wide tooth of the test gear set. oil. In both cases the scar surface carries obvious score marks, which are more pronounced in the scar on the right; and in addition the trailing edge of the scar on tne right is characterized by a large area in which the metal has been subjected to gross adhesion and displacement. This is an overt, straightforward example of adhesive scuffing. An interesring example of the genesis and progress of scuffing on the rubThe bing surface of an involute a gear tooth is seen in Fig. 14-10. photomicrograph on the left shows the addendum region of a wide tooth of a test gear from the Ryder testing machine. I n this device for testing gears and gear lubrication, the narrow and the wide gears of the test sec mesh in a four-square power-return circuit [18]. The two slave gears in the power circuit have helical involute teeth and the test gears are loaded by forcing the slave gears to move axially relative to each other, which displaces the test gears as indicated by the diagram on the righthand side of Fig. 14-10. The surface of the wide gear uncovered by this

422

movement thus carries a record of the effect of rubbing contact at each load step of the test. We see three such regions on the surface of the tooth shown in Fig. 14-10a. At the lowest load, in the region marked I , the predominant effect is smooth wear of the crests of the grind marks; the large score marks are caused by trapped particles of dirt, which are practically impossible to eliminate from any large-scale test machine. The smaller score marks are probably the imprint of material transferred to the opposing surface via the adhesive mechanism. I n region I 1 we see the effects of the next loading step. Scuffing is evident at the tip of the tooth and the particles thus generated have produced fairly extensive scoring farther down on the face of the tooth. Region 111 is, characterized by large-scale scuffing as a consequence of increasing the load to the next higher stage. However, because of the interaction of geometric and mechanical factors, the behavior illustrated in Fig. 14-10 cannot be ascribed to the influence of load alone. I n the addendum portion of an involute gear tooth the rubbing velocity is highest at the tip, but because of the sharing of the load by two pairs of teeth in this part of the contact cycle, the pressure at the tip for this particular gear set is o n l y 73% of that when engagement shifts to single-pair contact, approximately onetenth of the way into the cycle. At each load stage the influence of the higher rubbing spPed at the tip outweighs that of the lower contact pressure there. The effect of increasing the gross load on the system is to extend the region of damage farther toward the pitch line. Failure in the Ryder test is deemed to have occurred when on the average scuffing extends over 2 2 . 5 % of the total tooth-face area.

I n view of the intricate interactions outlined above, the task of making a precise quantitative assessment of the critical combinations of contact pressure and rubbing speed that control failure in gear teeth seems very discouraging. A noteworthy contribution towards disentangling some of the difficulties is found in work reported by G. H. Benedict [19!. Figure 14-11 shows the comparison he observed between the scuffing loads* for the five lubricants A-E shown in Table 14-6, as obtained in the Ryder test and in the Caterpillar "roller" test described by Benedict Figure 14-llb shows a similar comparison for the and Kelly [ 2 0 ] . lubricants F-L with the British IAE gear test and the American SAE extieme-pressure test. These two sets of paired machines were selected for comparison principally o n the basis of matching rubbing speeds and

*Benedict uses the term scohiny in the same sense that the term is used here. The failure damage observed in "roller" test specimens ( c 6 . E. G. Jackson, C. F. Muench and E. H. Scott, ASLE Trans., 3 (1960) 69-82 and I?. 0. Bjerk, ASLE Trans., 16 (1973) 97-106) is compatible with what we term scuffing i n the present discussion. ncudtjing

423

fr a

:O

-

0

t 0

-1 1

2

3

4

5

Ryder Scuffing Lwd,103 N/cm

0

3

6

9

12

15 18

IAE Scuffing Load, 103N/cm

Figure 14-11. Correlation of scuffing load limits obtained on different test machines. See Table 14-6 for identity of lubricants and Table 14-7 for operating parameters of the test machines. From data by G. H. Benedict 1191.

TABLE 14-6.

LUBRICANTS USED IN SCUFFING COMPARISONS (See Figure 14-11)

Description

A:

Naphthenic refrigeration oil

B: Paraffinic residual, highly refined (MILL-6082 C Grade 1100)

Viscosity, Description Cs at 37.8 c H: Automatic transmission fluid

35.8

224

I: Oil H plus zinc dialkyl dithiophosphate

38.0

106

J: Oil H plus complex phosphorus-nitrogen additive

38.5

32.5

C: Marine turbine oil,

Grade 2190T-EP (MILL-17331 D ) D: Synthetic diester aircraft turbine oil (MIL-L-7808 C)

17.7

E: Thickened synthetic aircraft turbine oil

38.2

F: SAE 80 paraffinic

residual with small amount of .lead naphthenate soap

K: Industrial gear lubricant with sulfurized fat and lead naphthenate

173.7

L: MIL-L-2105 gear lubricant, SAE 90, with sulfur, chlorine, lead and fatty material

222.4

Synthetic aircraft turSine oil, Type 2

21.9

M:

75.1

G: SAE 90 paraffinic

residua1

Viscosity, Cs at 31.8 C

272

424

TABLE 14-7. OPERATING PARAMETERS OF TEST MACHINES USED FOR SCUFFING COMPARISONS (See Figure 14-11) Ryder gear Faster surface speed, cm/s Slower surface speed, cm/s Rubbing speed, cm/s Relative radius of curvature, cm Load step, N/cm Time at each load step, min Temperature at start, deg C Temperature rise per load step, deg C

Caterpillar roller

2083 1473 610 0.826

2146 1527 619 1.163

648 10 110 12.2

648 10 110 12.2

IAE gear

SAE-EP

475 259 224 0.818

495 259 236 1.188

534 5 110 3.9

51 1 5 110 3.7

load steps, as shown in Table 14-7. The relation of the scuffing loads as seen in Fig. 14-11 is satisfactorily linear; but i t should be realized that because of the geometry of specimen configuration and contact, the loading in newtons per cm of rubbing face width is not a straightforward equivalent of contact pressure and hence there is an element of empiricism in these comparisons. I t is not likely that fluid film thickness as governed by lubricant viscosity is the sole influence on the magnitude of the scuffing load. In Fig. 14-11a, lubricants B and E show substantially the same limiting scuff-free load although there is a difference of 206 centistokes in their viscosities at 37.8 C. I n Fig. 14-llb, oil J with a viscosity of 38.5 cs at 37.8 C shows a higher limiting scuff-free load than oil G with a viscosity of 272 c s at.37.8 C. Allowance for the effects of temperature and pressure on viscosity does not invalidate the reality of these observations. We are thus led to the conclusion that in addition to the fact that rubbing contact has occurred because of breakdown of the fluid film, the nature of such contact determines whether or not scuffing takes place. Benedict [19] postulated that scuffing was controllec! by the critical temperature 8, at the rubbing interface, 8 , being calculated by the formula

where e, is the bulk temperature of the lzbricant (assumed to be the same as the bulk temperature of the gears or the rubbing specimens), 1.1 the coefficient of friction, W ’ the load per unit width of contact face, i~~ and u 2 the velocities of the two rubbing surfaces, R the relative radius of curvature, and K 7 is a constant embodying among other parameters the properties of the lubricant and of the rubbing materials. This point of view contains two complications, one experimental, the other conceptual.

425

The experimental complication lies in the difficulty of obtaining data for the coefficient of friction at the exact onset of scuffing; results as good as those of Benedict and Kelley 1201, which deal with o ~ l y a limited number of uncompounded oils, are seldom encountered in the literature. The conceptual difficulty is even more troublesome, for friction cannot be basically separated from the rubbing process by which it originates, and hence we cannot say that a high value of friction (or its equivalent manifestation, high temperature) is pea ns the cause of scuffing. Instead we must look closely at the course of wear in terms of asperity contacts in order to evolve a picture of what distinguishes smooth wear from a catastrophe such as scuffing. For each wear-effective asperity contact there is a lump-removal factor y; smooEh wear is characterized by a relativeiy small magnitude for y and a relatively small dispersion about the average value. Scuffing, on the other hand, is characterized by a highly disperse distribution of the sizes of the wear particles, many of which are so large it is obvious that they were not generated by a single asperity encounter. Given the appropriate surface topography, the simplest source of a scuff would be a single, relatively massive adhesion. This is probably the origin of the deep pit observed by Dorinson 1211 on the track left by rubbing a hardened steel pin on a hardened steel disk (AISI 1045, 50 Rockwell C) lubricated by white oil at i070 MPa, 50.8 cm/s, as shown ir! Fig. id-12a. But in view of the reiterative nature of the rubbing path in the preponderant majority of cases, the typical examples of scuffing encountered in practical engineering or i n laboratory studies are the result of a cumulative sequence: a small localized adhesion transfers a particle to the opposing surface which in turn serves as the source of a largei s d h e r j j o n and tracsfer, a c d so on until a macroscopically massive scuff hecomes evident. Figures 14-12b and 14-12c show how a particle

Figure 14-12. Some individual features of scuffing damage. (a) Pit left by a single massive adhesion. (b, c) Two views of a localized adhesive transfer. Unpublished illustrations by A . Dorinson [211.

426

Figure 14-13. Combination of plowing and adhesion on the worn rubbing surface of a tooth from a Ryder test gear.

in the rubbing process can produce an adhesive scuff. it more susceptible to adhesion, as illustrated by Fig. 1 4 - 1 3 . generated

earlier

Also, non-adhesive plowing c a n disturb the rubbing surface and render

Detailed observations of the state of the rubbing surfaces during the course of wear in a pin and disk apparatus I 2 1 1 indicate that macroscopically evident scuffing is not the instantaneous result of the application of a critical load but rather the consequence of a cumulative sequence of small scale departures from smooth wear. The reason for the determinative effect of load is quite clear: the greater the load, the greater the number and the average size of the asperity contacts: the greater the extent of plastic deformation, the greater the heat generated within the asperity material and the higher the temperature of the contacting asperities. Within the framework of this kind of general behavior we find the influence of factors stemming from the topographical structure of the surfaces and the properties of the material which contribute to the particular behavior of individual cases. The role of the extreme-pressure or the boundary lubricant in relato the scuffing load also becomes clear. Basically there are three ways in which the additives that impart extreme-pressure or boundary characteristics to a lubricant can affect the scuffing load. ( i )The additive may deposit as an adsorbed film on the rubbing surfaces and thus prevent the metallic adhesion that gives rise to wear and scuffing; the tion

durability of this film will in part be governed by its response to thermal desorption arising from rubbing friction and in part by the extent of its disruption when the asperities are deformed. (ii) The additive may inhibit the formation of metallic adhesions by competitive chemical reaction at the asperity junctions; the influence of the additive on the scuffing load will depend on the effect that the temperature originating in load-governed deformation of asperities has on the competition between inhibition and adhesion. (Xii) The additive can react directly with the

421

material of the rubbing surface, thus substituting a surface which is not susceptible to metallic adhesion, so that we observe smooth wear instead of the self-accelerating wear that grows to the magnitude of a scuff. Even when such smooth wear takes place at an intolerably high rate it is not scuffing in the commonly accepted sense. Benedict [ I 9 1 reported that the SAE 90 gear lubricant containing sulfurized fat and lead naphthenate (Lubricant K in Fig. 14-llb) did not fail the I A E gear test or the SAE rig test by scuffing but by excessively high smooth wear. There is also the role of lubricated wear in "running-in'' to be considered. The localized pressures between asperities in the initial contact of machined surfaces of ordinary technological roughness are high enough to deform the asperities plastically, thereby reducing these localized pressures by increasing the true contact area. Other things being equal, the probability of scuffing should thereupon decrease in subsequent cycles of reiterated contact. The compounded lubricant functions by substituting inhibition or smooth wear for scuffing-type adhesions during the critical initial stages of the rubbing process, when contact conditions are severe, and then controlling the rate of wear when the contact conditions become less severe later in the course of rubbing. If Eqn 14-49 is used to model the action of the lubricant, the relative magnitudes of the two terms on the right-hand side change with changing contact conditions during the course of wear. Without the lubricant the beneficial effects anticipated from the increase in true contact area by running-in and the attendant decrease in true contact pressure might be overwhelmed by accumulation of adhesions on reiteration of the rubbing cycle. In principle at least, there is no impediment to putting scuffing and its amelioration by lubrication on a logical rather than an empirical basis. The factors that enter into the analysis of scuffing, such as rubbing speed, contact pressure, temperature, material properties, etc., are basically those found in the general analysis of wear. The main experimental difficulty is that scuffing has more of an element of casualty about i t than does smooth wear; therefore either great care must be exercised in running a test for scuffing limits or else a statistically significant number of replicates must be obtained. Generally the emphasis is on testing for engineering purposes, and thus even well-designed large-scale devices carry in them inherent complexities such as the complications that involute gear tooth contact imparts to the Ryder or the I A E test. The simpler geometry of the flat-faced ring of the S A E machine or the crowned ring of the Caterpillar tester makes the scuffing loads amenable to expression in terms of contact pressure, although the usual practice is to report the results as gross load or as load per unit width of specimen face. The work of Benedict [19] indicates that scuffing tests can be run on other than a blindly empirical basis. There are com-

428

pelling reasons to believe that the antiscuffing evaluation of lubricants can be carried out in terms of basic parameters which can be built into the functioning of simple test machines and that the results obtained thereby should replace the arbitrary tests which now dominate the scene. REFERENCES

5.

T. E. Tallian, Wear, 2 1 ( 1 9 7 2 ) 4 9 - 1 0 1 . T. E. Tallian, E. F. Brady, J. I. McCool and L. B. Sibley, ASLE Trans., 8 ( 1 9 6 5 ) 4 1 1 - 4 1 4 . T. E. Tallian, Y. P. Chiu, D. F. Huttenlocher, J. A. Kamenshine, L. B. Sibley and N. E. Sindlinger, ASLE Trans., 7 ( 1 9 6 4 ) 1 0 9 - 1 2 6 . D. Dowson and G. R. Higginson, Elasto-hydrodynamic Lubrication, Pergamon Press, Oxford, 1977, Chapter 7. T. Sakurai, H. Okabe and I. Matsumura, ASLE Trans., 14 ( 1 9 7 1 )

6. 7. 8. 9. 10. 11. 12. 13.

A. Dorinson, unpublished data. 0. Levine and W. A. Zisman, J. Phys. Chem., 6 1 ( 1 9 5 7 ) 1 0 6 8 - 1 0 7 7 . 0. Levine and W. A. Zisman, J. Phys. Chem., 6 1 ( 1 9 5 7 ) 1 1 8 8 - 1 1 9 6 . A. Dorinson, ASLE Trans., 1 ( 1 9 5 8 ) 131-138. A . Dorinson and V. E. Sroman, ASLE Trans., 5 ( : 9 6 2 ) 7 5 - 9 0 . T. Sakurai, S. Ikeda and H. Okabe, ASLE Trans., 5 ( 1 9 6 2 ) 6 7 - 7 4 . T. Sakurai, S. Ikeda and H. Okabe, ASLE Trans., 8 ( 1 9 6 5 ) 3 9 - 4 7 . T. Sakurai, H. Okabe and Y. Takahashi, ASLE Trans., 10 ( 1 9 6 7 )

14. 15.

H. Okabe, H. Nishio and M. Masuko, ASLE Trans., 22 ( 1 9 7 9 ) 6 5 - 7 0 . 0. Kubaschewski and B. E. Hopkins, Oxidation of Metals and ?.lloys, Butterworths, London, 1962, pp. 4 2 - 4 5 . A. Dorinson, unpublished work. A . Dorinson, ASLE Trans., 14 ( 1 9 7 1 ) 1 2 4 - 1 3 4 . E. A. Ryder, ASTM Bulletin, 184 ( 1 9 5 2 ) 5 9 1 - 5 9 6 . G. H. Benedict, Lubrication Eng., 2 4 ( 1 9 6 8 ) 5 9 1 - 5 9 6 . G. H. Benedict and B. W. Kelley, ASLE Trans., 4 ( 1 9 6 1 ) 5 9 - 7 0 . A. Dorinson, unpublished work.

1. 2. 3. 4.

22 1-225.

91-101.

16. 17. 18. 19. 20. 21.

429

Chapter 15 TEMPERATURE EFFECTS IN FRICTION, WEAR AND LUBRICATION

This chapter deals with temperature in friction, wear and lubrication: its origin and how it interacts with the tribological system. Sliding produces heat, and the disposal of this heat as it is being generated is part of the overall couise of the rubbing process. Among the effects of the temperature rise due to accumulation of heat in the system are alterations of the condition of the contacting surfaces, modifications of the physical properties of the lubricant, and activation of the chemical performance of additives. The effect of temperature on friction, wear and lubrication can be looked at from two points of view. I n one, temperature effects originate as a consequence of the rubbing process p e f i b e ; in the other, temperature is part of the ambient environment. This difference governs the way the influence of temperature is analyzed. In some instances temperature enters the analysis as an external experimental variable, the role of which is introduced by postulation. But in other cases temperature changes are an intrinsic part of the rubbing process, and refined experimental technique is required to obtain the data which must be combined with correct analysis to obtain valid results. 15.1.

INTERFACIAL TEMPERATURE AND RUBBING

The heat evolved by friction at the interface of two rubbing bodies passes by conduction into the material of both. The resulting interfacial temperature at equilibrium is a function of specific parameters such as the coefficient of friction, the loading force, the velocity of sliding, the dimensions of the interface, the properties of the materials, etc. The classical theory of heat conduction has been applied to the interfacial temperature problem with good to moderate success. The calculations are often so intricate that the physical picture is lost in the complexity; therefore our introductory consideration of interfacial temperature will be the simplified descriptive approach immediately following. 15.1.1.

A

Descriptive Model for Interfacial Temperature in Rubbing

From the viewpoint of the temperature problem the rubbing of a rider of bounded interfacial area G as it traces a track against the extended plane countersurface of an opposing body is regarded as equivalent to the

430

translation of a source of heat along the track.* Two separate analyses must be made in the calculation of the interfacial temperature. For the counterbody, all the heat generated in the interfacial area is treated as passing by conduction into the material of the counterbody taken a s a semi-infinite region; this is the solution for a moving heat source. For the rider, the heat is treated as being conducted entirely into it from the fixed area A ; this is the solution for a stationary heat source. The temperature of the interfacial area must satisfy both of these solutions simultaneously. To visualize the problem in simple descriptive terms, let us consider the situation for a rider of rectangular cross-section who*se area is A = 2 1 - 2 6 as shown i n Fig. 15-1. Let the rate at which heat is generated within the area A be q units per unit area per unit time. In the moving source problem the average temperature of A will be determined As by the rate at which heat flows into the semi-infinite counterbody. the source moves in the positive x-direction it encounters material in the track that has been warmed by the heat conducted there from locations of earlier contact. Eventually a state of equilibrium is reached in which the rate that heat is generated in the area of the source is The velocity with balanced by the rate that it is lost by conduction. which the source moves interacts with the rate at which heat flows out of it to influence the temperature distribution within the area of the source, since the rate at which heat is lost by conduction in both senses of the x - and y-axes from the sides of the source area and in the z direction into the counterbody are also governed by the velocity of translation. The other part of the temperature problem-namely source calculation-is much simpler, since it does velocity at which the source is translated.

the stationary not involve the

15.1.2. Calculation of Interfacial Temperature by Continuum Heat Conduction Theory

The basic differential equation for the conduction isotropic homogeneous solid is

a2e

a2e

a2e

1

ae

ay2

az2

K

at

- + - + - = - ax

2

of

heat

in

an

(15-1)

where K = K / p c , K being the thermal diffusivity, K the thermal conductivity, p the density and c the specific heat of the solid [ l ] . This equation is satisfied by the relation

*The geometric nominal area and the real area of taken to be identical.

contact

are

here

431

e =

QK

(x

-

x')

2

+

(y - y')2 + (z 4K

8 K ( i 7 K t ) 3/2

-

Z'J

t

21

(15-2)

which gives the temperature 6 at the points ( x , y , z ) at time t in an infinite solid initially at zero temperature,* due to a quantity of heat 2 liberated instantaneously at points ( X I , y ' , z ' ) at zero time [ 2 1 . The notation is different from but equivalent to that of Carslaw and Jaeger 1 1 1 , in which the quantity of heat is written as Qpc and Q is called the dthength of the source. For the semi-infinite solid bounded by the plane z = 0 the heat is distributed through only half as much material; hence

e =

QK 4K(i7Kt)3/2

(x -

+ (y

4K

y')* + (z - z') t

21

Figure 1 5 - 1 . Rider sliding on a countersurface as a source the interface.

(15-3)

of

heat

to

Consider

the case of the moving rectangular plane source of length as illustrated in Fig. 1 5 - 1 . The steady state is attained at time t = a; the center of the source at that time is chosen a s the origin of the coordinate system, At some given time previous, the center of the source was at the point (-Ut,0, O), U being the velocity of translation. To find the temperature at time t = a for a given point ( x , y , z ) in the area bounded by x = ?L and y = ?&, we must calculate the contributions of heat from every element of area d x ' d y ' within that area from t = 0 to t = a. Equation 1 5 - 3 becomes 2 L and width 2 b ,

*Or at some -fixed initial temperature, which is the case for practical physical and engineering problems.

432

qK(dx'dy')dt'

( x - x'

+

V t )

2

+

( y - y')2

+

@ =

4K

[ n K ( t-

t

i

4K(x -

)I 3/2

y being the rate at which heat is generated. the solution of the following relarion, QK

a =

4K(nK)3/'2

r

' O

e

dt'

m

J (2 -

t') The

problem

z2

1 then

(15-4) becomes

dx'

-[

tt')3/2

(15-5) where 8 is the steady-state remperature when t = m at the point ( x , y , z ) . The details of the solution are given by Jaeger 121. The expression for the steady state is obtained by integrating with respect to time in terms o f the dimensionless quantities below: vx

VY

2K

2K

x = - , Y = - ,

wz 2 = -

,

VL

L = -

,

Vb

B = -

2K

2K

21:

(15-6)

The expression for the temperature i s

where u = X - X ' and

M)

=

Y - Y'.

I t is apparent from th2 physics of the situation that the tempera= ture profile is maximized along the x-axis. Therefore on putting Y =

z

where K o ( l u l ) i s t h e modified Bessel function of the second kind of order zero. For large values of 8 the second term of Eqn 15-8b approaches zero and the result tends to that developed by Jaeger [ 2 ] for a band source of length 2L and infinite width. The evaluation of the band-source solution for specific cases and the evaluation of Eqn 15-8b for small values of L , X and 8 is discussed at length by Jaeger [ 2 ] .

433

I

I

I

I

0 t 2 x/l Figure 15-2. Surface temperature distribution at the interface of a source moving on a semi-infinite body, taken along the midline. Square source - Band source ---. Data by J. C. Jaeger [ 2 ] . -t

-2

The solution of Eqn 1 5 - 5 for the case of a square source is obtained by setting b = L . In Fig. 1 5 - 2 the plots of the quantity ( n K V / 2 4 ~ ) e against X/L = xlL compare the results of the computations for a square 1 and 2 . source and for a band source, with values of L equal to 0 . 2 , The broader the square or the band in the x-direction, the higher is the temperature peak: the maximum temperature lies to the rear of the center line. The larger the value of L , the smaller the proportional difference between the curves for the square and the band source. With a stationary square source generating heat at the rate q , the temperature at the surface of the plane z = 0 is given by

J (t - X t ) 3 ' 2

4K(i7K)3/2

e -e

dy'

exp

[

-

(x -

X ' ) *

Y

2Kn

J

e -L

dx'

J

e -e

dx'

-

+ (y - y')2

4K(f;

For the steady state, when t

e=-

e

dX'

It

Kq

e =

dy'

-

+

z

2')

(15-9)

= m

[(x - x') 2

The maximum temperature occurs at x

+

(Y

-

Y ' ) ~

+

z2]-li2 (15-10)

= y = z = 0:

(15-1 1 )

The average temperature over the area of the source is

434

Ln

(1

-

JT)

+

Kn

JS - 1 ~

3

1

= 0.946

-e4

K

(15-12)

For a circular source with radius a the maximum temperature is .e4

emax =

3

(15-13)

Jaeger [ 2 ] gives the following two formulas for the average temperature of a moving band source, depending on the value of L. I f L is large ( e . 5 . L > 51, -

8 y ~ L ~ ” 1.064

e=-=-

3KVn

(15-14)

K

I f L is small ( e . 5 .

L

< 0.11,

(15-15)

For a moving square source the average temperature when L is large is nearly the same as that given by Eqn 15-14 for a band source. If L is small,

(15-16)

For intermediate values of L ( 0 . 1 < L < 5 ) the formulas above do not hold and special calculations must be made, as discussed by Jaeger 1 2 1 , The problem of the temperature at a rubbing interface can be looked upon as the simultaneous satisfaction of the solution for a moving source and a stationary source over the common interfacial area. This requirement has the fundamental difficulty that the two theoretical temperature distributions are not the same. Nevertheless, as a workable postulate i t is assumed (a) that a fraction c1 of the heat generated in the source area passes into the moving body and the remainder 1 - c1 into the stationary body (the slider), and (b) that the average temperature over the interfacial area as calculated by the moving source theory equals the average temperature as calculated by the stationary s o u r c e theory-i.e. there is no temperature jump at the rubbing contact of the slider with the counterbody. I f the slider is a square protuberance on a semi-infinite body with no emissive losses to the anbient environment (Fig. 1 5 - 3 a ) , we have from Eqns 1 5 - 1 2 and 1 5 - 1 6 , when L = V e / 2 ~is small

(15-17)

435

W

W

Figure 15-3. Configuration of contacting bodies in rubbing. 1: Stationary body. 2: Moving body. (a) Protuberance on a semi-infinite nonemissive body. (b) Long emissive rod.

where the subscripts 1 and 2 refer to the moving counterbody and the stationary slider respectively. Obviously a = K1/(K1 + K2), and

6

Y.e

= 0.946

~

K1

+

(15-18)

K2

When L is large, Eqn 15-14 is used for the moving source:

i:

= 0.946

($)li2

(1

1.064 -

-

a)qL K2

(15-19)

K1(LV)"*

a = 1.125 K2"ji2 1.064

+

K 1 ( L V ) 'I2

(15-20)

~LK;'~

e = 1.125

K 2 ~ j l 2+

K1(LV)1/2

(15-21)

For intermediate values of L the average temperature g , must be obtained from Eqn 15-8 by a calculation using an appropriate algorithm. Then if we write

(15-22)

(15-23)

after solving for a the average interfacial temperature is given by

(15-24)

I f the slider is a square rod of cross-section 4L2, radiating heat with emissivity ci (see Fig. 15-3b), the average interfacial temperature is

436

s =

1/2

U(%)

( 15-25)

This value is equated with the temperature given by the moving source solution for the counterbody. The results for various ranges of L are shown in Table 15-1. TABLE 15-1. FORMULAS FOR THE INTERFACIAL TEMPERATURE OF A LONG, SQUARE ROD SLIDING ON A SEMI-INFINITE BODY

e

L 0.946 q l

<@. 1

K1

+

1.338 (LK,c~)’/~

0.707 ~ K ~ L ~ / ~ G

@.15 1.111

K,VL”2

+ K , ( K ~ c T ) /2G

Application of the formulas for interfacial temperature t o the frictional rubbing of a square rider is carried out by means o f the following relation:

( 15-26)

where W, the loading force on the rider, and I , the mechanical equivalent of heat, are both in units consistent with those of K and K. Insertion of Eqn 15-26 into Eqn 15-18 for the case where L is small ( L < 0.1) gives

e =

0.236~WV LJ(K1

+

K2)

(15-27)

Eqn 15-21 is used when L is large (L > 5 ) : -

0 . 2 6 6 ~j / ’ $ J V

e = 1.125K2~i/2 + Kl(LV)’/2] (15-28)

For values of L greater than 0.1 but less then 5, the calculation is made I f calculated by Eqn 15-27 (L small), with the aid of Eqn 15-24. temperatures are proportional to the first power of the sliding velocity;

437

calculated by Eqn 1 5 - 2 8 ( L large), they are proportional root of the velocity.

to

the

square

The physical interpretation of the influence of L is hidden by its nondimensionality and by restricting the value of z to zero in the evaluation of the equations for the isolated heat sources. In reality heat is being conducted into the material in the z-direction, for which J. F. Archard [ 3 ] presents the following treatment. Given the instantaneous release of a quantity of heat over the interfacial area at time t reach = 0, it will require some finite time ti f o r the maximum effect to the depth z. When z equals u , the radius of the contact area (assumed to be circular), 2

t

= _

2K

(75-29)

The time for the area of the source to move a distance a is

(15-30)

similar argument holds for a square source with sides 2L. For large values of L the time required for the heat to penetrate to a depth u or L is large compared with the time the heat source is applied to the area and thus the temperature at the surface is higher than in the interior of the material. The true physical parameter that governs this behavior is the velocity V , not the dimensionless quantity L. A

15.1.3. A Stochastic Model for Interfacial Temperature Generated at crete Sites

Dis-

The continuum theory of interfacial rubbing temperature described in the preceding section requires perfect contact of the two bodies over the entire nominal rubbing area: but we know that true contact of real surfaces is at the asperities. If the continuum treatment is to have any relevance for real rubbing temperatures, it must be an acceptable approximation to what actually occurs physically. One such possibility, advocated by Archard 131 as applicable for closely spaced asperities and slow sliding speeds, is to treat the aggregate true area of the asperity contacts as the equivalent area of a single contact. The generation of temperature by contact of individual asperities during sliding was examined by Ling and Pu [41 in the following manner, Consider the nominal area of contact, L x L , as the body 1 slides past body 2 under normal load W with velocity V (Fig. 15-4a). The area is

438

(b)

(a)

V

I

--X

Figure 15-4. Interface of a sliding surface with subdivided areas of true contact. (a) Cross-sectional view of the two-body contact; 1: stationary body, 2: moving body. (b) Plan view showing nominal and true contact area. also represented by the grid rn x m = t', in which only a fraction of the available sites are involved in real contact; Fig. 15-4b shows an example of one of the configurations possible. Given that the properties of the materials remain constant during sliding, the heat flux distribution depends on the history of the actual contacts. Let it be assumed that the real area of contact does not change with time but the number of contacts and their locations do. Let the distribution of these contacts be statistically random with respect to location in the area t 2 and to time; i.e. the distribution of the heat source in the nominal contact space and in time is modeled as a stochastic process. Another way of writing the temperature rise at a point in a semiinfinite solid is in the dimensionless format

where 13 is the dimensionless temperature and the following relations defined:

f(C',

$',

0, T') dC'd$'

5

are

2'/q0

2' is the strength of the heat source according to Carslaw and Jaeger [ l ] and qo is the heat flux per unit area. coordinates are defined as follows:

<:-

X

e

Z

g r -

e

The dimensionless space and time

439

If the total area of real contact is postulated as obeying the relation A W/p,, then qo = up,V. The total temperature change up to time T over the apparent area is

=

when the x - and y-axes are chosen as shown in Fig. 15-4b, the z-axis being oriented into the body of the material. Integration of Eqn 15-32 in the format of Eqn 15-33 by the tic treatment is written thus [41: fl-1

1

stochas-

1

(15-34)

where

M A T = T.

Upon integrating with respect to T'

(15-35)

Within a given time interval T' = kAT heat is evolved from a discrete number of sources of area AcA$, each of which is characterized by an identity of the form (15-36) (0 < , i s m -

1, 0 < j < m -

1)

The physical condi'tion which distinguishes the problem here from that of Section 15.1.2 and which governs the format of Eqn 15-34 is the fact that at any given time not every location ( c ' , $ ' , 0 ) is sending heat to the locations ( c , $, 5 ) and that over the total elapsed time M.AT the combinations of the individual areas iAg x ;A$ change with each time interval kAT. Hence the steady state is not represented by a straightforward integration to the limit T = m; instead the summation formulas of Eqns 15-34 and 15-35 are used. The treatment for a moving heat source is carried out n the same way except that h2 =

[< - 5 '

+

U(T

-

T')]'

+

(6

-

$ I ) '

+

5'

(15-37)

where U = Ve/4~. The manipulation of the equations and their utilization

440

r

400

1

a

0-

2 300

IL

200 100

0 0

0.1

0,3 0.5 0.7 0.1 0.3 0.5 0 7 0.2 0.4 0.6 0 0.2 0.4 0.6

Dimensionless Temperature,0 Figure 1 5 - 5 . Distribution of dimensionless temperature in a rubbing interface by stochastic modeling. Stationary body - Moving body Data by F. F. Ling [ 5 1 .

---.

in

computations

are

described in detail by Ling and Pu [ 4 1 and by Ling

[51.

Figure 1 5 - 5 shows some of the stochastic computations made by Ling [5] as frequency distribution histograms of the dimensionless temperatures when the ratio of real to nominal contact area is low, which is the equivalent of sliding under a very light load. These results are for values of the Peclet number V L / ~ Kequal to 1 and 1 0 respectively. At higher sliding speed the distribution peaks very strongly in the lowest temperature range and there is a significant difference there between the temperatures found in the stationary and the moving body. At the lower sliding speed the distribution peak broadens and the difference in the temperatures in the stationary and the moving body becomes smaller. Stochastic analysis was applied by Ling to data he obtained using a microminiature thermocouple capable of resolving temperature flashes of the order of 10 milliseconds in duration [ 5 1 . The temperature distributions so calculated showed strong similarity to those seen in Fig. 1 5 - 5 .

15.2.

EXPERIMENTAL OBSERVATIONS OF INTERFACIAL TEMPERATURE

Intricate a s the theoretical calculations described in the preceding sections are, still they only approximate the conditions in a real sliding system. Real contact interfaces are composed of asperities that are subjected to a great deal of plastic deformation with the generation of heat at highly localized sites. Ordinary metal surfaces carry films of oxides and adsorbed atmospheric gases, and even the very thinnest of lubricant boundary films introduces yet another complication into the heat transmission problem. The observer of experimentally measured interfacial temperatures is thus confronted with the task of evaluating

441

the significance of his data in terms of models which may have been idealized o r simplified to make them tractable. But also the theory and technique of the measurements themselves are beset with difficulties: for instance, the introduction of the measuring probe can itself perturb the events at the rubbing interface. It is with such considerations in mind that we proceed to the examination of experimental observation of interfacial temperature. Of the methods that have been utilized for measuring the temperature at a rubbing interface, the four regarded as important enough to be disthe dynamic thercussed here (by virtue of their wide use) are ( 1 ) mocouple, ( 2 ) the embedded thermocouple, ( 3 ) the strip thermistor and (4) the emission of infrared radiation.

15.2.1.

The Dynamic Thermocouple

The dynamic thermocouple, also known as the "Herbert-Gottwein" thermocouple, measures the temperature at the rubbing interface of two dissimilar metals by making it the hot junction of a thermoelectric circuit. The utilization of this principle for the measurement of the chip-tool rubbing temperature in metal cutting appeared on the scene in 1 9 2 5 / 1 9 2 6 [ 6 , 7 , 81 and for the measurement of temperature in ordinary rubbing about. 10 years later [ 9 1 . The techniques of making measurements with the dynamic thermocouple are relatively straightforward; the major difficulties associated with the method are theoretical and interpretive rather than manipulative. The usual assumption is that the signal of the potentiometric measuring instrument is equal to the average Seebeck e.m.f. over the nominal area of the thermocouple junction, i.e. proportional to the average temperature. Gaylord and his co-workers 1101 analyzed a thermocouple junction comprised of separate and distinct contacts, such a s might be representative of asperity contacts at a rubbing interface, and instead of the simple average of the individual e.m.f.'s they obtained the following weighted average:

(15-38)

where P ( m a ) is the experimentally measured potential, An is the area of an For individual asperity contact and En is the individual Seebeck e.m.f. a thermoelectric junction due to a temperature distribution over an extended continuous interfacial contact the weighting function is more complicated, being dependent o n the shape of the interfacial area [ll, 121. Another difficulty arises i f the slider transfers a film of metal to the countersurface, so that the rubbing interface is no longer identical with the thermoelectric junctior?.

442

Thus the interpretation of the signal from a dynamic thermocouple involves a two-fold problem: how to deduce the thermoelectric e.m.f. at the rubbing interface from the observed display of the potentiometric measuring instrument, and how to evaluate the significance of the e.m.f. data in terms of the interfacial temperature, given the possibility that the physical model cf the interface may have its own uncertainties. A s can be imagined, this problem has not been resolved satisfactorily. Figure 15-6 shows excellent agreement of the average chip-tool interfacial temperatures in metal cutting measured by Loewen and Shaw [13] using the dynamic thermocouple method with the average temperature calculated by a continuum contact model; the circumstances i n this case were

Cutting Speed, cm/s Figure 15-6. Comparison of observed and calculated temperatures for the chip-tool interface in metal cutting. From data by Loewen and Shaw [131 for sintered carbide cutting AISI B1113 steel.

unusually favorable. A typical example of the inconsistencies encountered in conventional frictional rubbing is found in the study by Sakurai, Okabe and Sethuramiah [14] of the interfacial temperature generated by r3 constantan rider on a steel disk, a s seen in Table 15-2. Experimental temperatures are compared with the results of two different calculations. Better agreement with measured data is shown by the calculations according to Jaeger's treatment of a square source ( s e e Section 15.1.2); in three out of the five experiments the deviation is of minor consequence. The other nethod of calculation is that described by Archard 131: 1

1

1

- = - = -

eo

ern

(15-39)

where is obtained from the stationary source theory and O m from the moving source theory, with due regard for the values of L ; these results deviate significantly from the temperatures measured experimentally.

TABLE 1 5 - 2 . COMPARISON OF MEASURED AND CALCULATED TEMPERATURES FOR CONSTANTAN RUBBING ON STEEL

q , c a l / s e c cm 2K 0.500 0.300 0.300

0.55 0.37 0.26 0.55 0.57

0.0059 0.0043 0.0040 0.0062 0.0086

( a ) C a l c u l a t e d by Eqn 1 5 - 3 9 . Sethuramiah 1 1 4 1 .

5.2 3.7 2.8

I

0.0051 0.0039 0.00314 0.00256 0.00183

l-

( b ) C a l c u l a t e d by Eqn 1 5 - 1 8 .

l-

8 , deg c, G , deg C, 8 , deg C, exptl. calc ( a ) calc ( b )

I

135

!: 2; 42

12 100

1

I

139 71 59 13

Data by S a k u r a i , Okabe

15

and

P k P w

444

3

u)

0

50 100 Sliding Velocity,cm/s

Figure 15-7. Comparison of calculated and experimentally observed temperatures in dry rubbing of constantan on steel. Load 19.6 N. Data by Nakayama and Sakurai [ 1 5 1 . TABLE 15-3. COMPARISON OF CALCULATED AND EXPERIMENTAL VALUES FOR SURFACE TEMPERATURE

6 16 27 63

18 65 25 1 446

13.96 55.84 111.7 223.4

44 109 335 578

13 23 52 73

25 99 195 385

14

48 71 90

Constantan on steel. Temperatures in degrees Centigrade, calculated by Eqn 15-39. From data by M. ;I. Furey 1 1 6 1 .

'

0

0

5 200

Sliding Speed, cm/s

Figure 15-8. Modification of calculated interface surface temperature by the junction growth adjustment. Adjusted calculations --Measured temperatures (Furey) -. From calculations by C. Dayson [ 1 7 1 ; measurement by M. J. Furey [ 1 6 ] .

.

445

Discrepancy between the experimentally observed interfacial temperature and the results calculated by the method of Archard 1 3 1 seems to be characteristic. Figure 1 5 - 7 shows a comparison of the temperature measured by Nakayama and Sakurai 1151 for constantan rubbing on steel in atmospheres of argon, air or oxygen with the calculated values. Table 1 5 - 3 shows a comparison of experimental and calculated results by 7urey [16]. In both investigations the measured temperatures were lcwer than the calculated values. Archard's computations are derived from the relation

Q

0 : -

4aK

(15-40)

which treats the heat flow through a circular area of radius u as the flow of a thermal current through a thermal resistance, by analogy with the electrical problem. To get Eqn 15-39 from Eqn 1 5 - 4 0 it is necessary to fix upon a partition of heat between the stationary and the moving body: the reader is referred to Archard's publication for the details [ 3 1 . The true area of interfacial contact enters through the relation u =

(x)

1 /2 ( 15-4 1 )

Dayson [ 1 7 1 applied the concept of junction growth by tangential traction to determine the effective value of a and adjusted the value of 6 as follows:

(15-42) A/A'

is given by ( 1 + k p ) ' / * Ccd. Egn 8 - 1 1 , Chapter 8 ) . Fi'gure 15-8 shows the effect of this adjustment and compares the results with some of the data of Furey 1161. The fit of the adjusted values when k is 1 2 with the experiinentally observed temperatures is very good; the influence of variations in k over the range 3 - 2 5 is relatively minor. Nakayama and Sakurai [ 1 5 1 also examined the effect of junction growth adjustment on their calculated values and found it necessary to set k equal to 2 5 in order to get agreement with experimentally measured temperatures. where

Physically the junction growth adjustment means that the interfacial temperature is lowered because the frictional heat is conducted into the body of the material through a larger contact area: i . e . the value of the heat rate factor q is decreased. In that respect the correction of the direction. calculated temperature is logical and in the expected However,it is also possible that the experimental measurement may be low. Consider the oscillographic record of the dynamic thermocouple signal ob-

446

!$ 200 'p

2

g 150

00 50

Figure 15-9. Oscilloscopic trace of temperature measurement by a dynamic thermocouple. Constantan against steel, 17.8 cm/s. (a) Starting temperature before rubbing. (b) Predominant temperature during rubbing. (c) Temperature spikes. Data by M. J. Furey [16].

tained by Furey [16] as shown in Fig. 15-9; there are numerous temperature spikes of about 0.2 millisecond duration c u . 90 degrees C above the predominant level of c u . 72 C. The spacing of these spikes corresponds to a rubbing interval about 90 um, which is a reasonable magnitude for the coarser asperities. The conventional potentiometric measuring apparatus may not respond to fluctuations of such short duration and thus the indicated temperature will be lower than the true average temperature. 15.2.2.

The Embedded Thermocouple

The use of a dynamic thermocouple is precluded in cases where the rubbing pieces are of the same metal, or are of a metallic pair that does not generate enough thermoelectric voltage to be distinguished from background noise, or are of non-metallic material, or are separated by a nonconducting oil film. An expedient often employed is to embed conventional bimetallic thermocouples in one or both of the rubbing pieces. The assumption that the temperature thus observed can be extrapolated back to the rubbing interface by heat conduction theory runs into a number of difficulties. With a moving source the steady-state temperature gradient perpendicularly into the body of the material is not linear, as the calculations by Jaeger "21 shown in Fig. 15-10 indicate. In instances with lower sliding velocities ( L < l), accurate placing of the thermocouple with respect to the location indicated by the knee of the temperature function is important; for the higher sliding velocities ( L > 4 ) , the thermocouple must be located precisely because of the magnitude of the temperatures as well as the steepness of the gradient. The temperature gradient with a stationary source is not linear either, as inspection of Eqn 15-10 indicates.

441

Dimensionless Distance Z

Figure 1 5 - 1 0 . Penetration of heat from the interfacial rubbing into the moving body as calculated from the temperature analysis. by J. C. Jaeger 1 2 1

area Data

M. Furey 1 1 6 1 carried out a direct experimental comparison of the temperatures measured by the dynamic thermocouple technique with the temperatures indicated by an embedded thermocouple located 0 . 0 2 5 cm from the rubbing interface of a constantan ball sliding on a rotating steel ring. The temperatures sensed by the dynamic thermocouple were higher than those of the embedded thermocouple; as the dynamically measured temperature increased, the proportionate lag in the temperature by the embedded thermocouple became greater. A. Cameron and his co-workers studied the use of embedded thermocouples in the determination of the temperature in an oil film between two disks rotating with different peripheral velocities. The theory of a moving heat source was adapted to the analysis of this particular problem [18]; the experimental work is described by O'Donoghue and Cameron 1 1 9 1 and by O'Donoghue, Manton and Cameron [ 2 0 ] . The problem is a difficult one and the degree of confidence in the results has considerable bearing on understanding the effect of temperature on fluid film failure in the lubrication of gears. The reader can consult the original work f o r deta i 1s.

15.2.3.

The Strip Thermistor

Strip thermistors are used to scan the temperature profile of an elastohydrodynamic contact in a fashion analogous to the scanning of a The early pressure profile as described in Chapter 3 , Section 3 . 5 . 4 . ones were adaptions of platinum resistance thermometers made by painting a thin, narrow strip of platinum powder suspended in a carrier across the width of a glass disk and then firing in a furnace to burn off the

448

vehicle. Characteristic dimensions are 35-37 pm wide and 0 . 1 vm thick [211. The thermistor, of course, requires an electrically insulated backing: hence the glass disk. Hamilton and Moore [22] used nickel a s the thermistor element. Kannel and Dow employed titanium on quartz and also described a method for sandwiching the thermistor between two insulating layers of silica or alumina for use on a steel disk 1231. A bisignal transducer on a steel disk for the simultaneous measurement of temperature and pressure is described by Kannel, Zugaro and Dow [24]. The signal issuing from the thermistor is amplified and displayed on an oscilloscope whose sweep time is synchronized with the passage of the strip through the conjunction between the disks. The results’ obtained by Kannel, Zugaro and Dow for the temperature profile with the bisignal transducer [ 2 4 1 show good parallelism with the pressure profile, the temperature peak being very close to the pressure peak. Cheng and Orcutt [21] reported that the temperature rise they observed was only about a third of the value calculated by elastohydrodynamic theory and that there were also differences between the shape of the experimental and the calculated temperature profile. In view of the work of Kannel e t u L . 1241, it seems likely that measurements with improved modern techniques will agree better with calculations from theory. However, the thickness and width of the thermistor relative to the thickness of the lubricant film and the dimensions of the conjunction constitute a fundamental uncertainty in the measuring system. 15.2.4.

Emission of Infrared Radiation

I t is a familiar fact that the radiation emitted by heated bodies characteristically lies in the infrared region of the spectrum. The ideal emissive behavior of a radiating source is that of the theoretical black body. By the Stefan-Boltzmann law the emissive power, i . e . the rate at which energy is radiated per unit area of radiating surface, is proportional to the fourth power of the absolute temperature of the radiating source. The emissive power of a real body is a constant fraction of the emissive power of the black body at the corresponding temperature, the constant of proportionality being characteristic of the particular substance. Details of the theory of the emission of infrared radiation can be found in the standard physics texts and in specialized monographs 125, 261.

If the infrared radiation from an emitting body can be captured and transduced into a usable signal, it can be made the basis for measuring the temperature of the emitting surface. Such a method is particularly attractive for the measurement of the temperature at a rubbing interface, since it does not require the insertion of a probe which might introduce a major perturbation into the system. However the method does require that the behavior of the system obeys the Stefan-Boltzmann relation

449

within the limits of experimental error, since calibration is carried out by comparison with an emitting surface at a known temperature. There are also ccmplications of technique, in particular knowledge of the cmissivity of every surface that contributes to the radiant energy received by the instrument and access of the instrument to the rubbing interface.

Photoconductive materials such a s lead sulfide, lead selenide or indium antimonide, which respond to incident infrared radiation by changing their electrical resistance, are used as the sensing elements in instrumentation for radiometric measurement of temperature. Bowden and Thomas [ 2 7 ] measured t h e temperature of "hot spots" in the sliding of a metal rider against a glass disk with a lead sulfide cell in the arrangeA glass disk was used because the ment illustrated in Fig. 15-17.

Figure 15-11. Measurement of "hot spot" temperatures at the rubbing surface with a lead sulfide photocell. A : Glass disk. B: Metal slider. C: PbS photocell. D: Brass shield. E: Chopper. After Bowden and Thomas [271.

countersurface must be transparent to the radiation generated at the interface. Caiibration is effected by means of a fixed filter; another technique is to use a chopper in conjunction with selectively placed filters. Bowden and Thomas studied the rubbing of sliders of steel, constantan and invar. Maximum hot spot t mperatures ranged from 773 to 1323 K (500-1050 C). The temperatures obse ved for a gold-aluminum alloy with a bulk melting point of 643 K (570 C did not exceed 873 K (600 C ) even at the highest loads and speeds, which was taken to be an indication of the reliability of the method. Some individualistic characteristics of the dry rubbing of metals on glass have been reported by Heighway and Taylor 1 2 8 1 . The temperature at the rubbing interface of two opaque solids can be measured by the use of a "peep hole" through which the detector sights on the rubbing surface. This technique was employed by Reichenbach [ 2 9 ] to measure the shear-plane temperature in orthogonal metal cutting (planing) and by Chao, Li and Trigger I301 for the flank temperature in orthogonal turning, using a lead sulfide detector. Deyber and Godet [31] described r h e measurement of the interfacial temperature generated by the lubri-

450

Running Time, minutes

Figure 15-12. Temperatures at the rubbing interface by infrared emission viewed through a peep hole. T : Contact temperature at interface by infrared emission. u: Coefficient of friction. Thermocouple temperatures: T B , block; T R , ring; T F , , oil film impinging on ring; T F 2 , oil film near conjunction; T F , bulk temperature of the oil stream. After Deyber and Godet 1 3 7 1 . cated rubbing of a block against a rotating ring with a lead sulfide cell which viewed the rubbing interface and a reference surface alternately through a peep hole in the ring. Figure 15-12 shows the results they obtained. The close parallelism between the coefficient of friction and the surface temperature indicates that the source of the temperature was the rubbing. Other temperatures, measured by thermocouples, were substantially lower and were much less sensitive indicators of the action of friction in generating temperature. The elegance and power of the infrared emission method is exemplified by the work of W. 0. Winer and his collaborators on surface temperatures in elastohydrodynamic lubrication. The techniques are described by Turchina, Sanborn and Winer [ 3 2 ] and Ausherman, Nagaraj, Sanborn and Winer 1331. The oil film was generated by rotating a steel ball under load against a flat, polished sapphire plate. The geometry of the interface and the oil film was monitored by optical interferometry essentially as described in Chapter 6, Section 6 . 2 . The radiation collected by the objective of the microscope viewing the interface was split between an eyepiece for the visible wavelengths sent to the interferometer and an indium antimonide detector cooled by liquid nitrogen for the infrared emission, thus enabling the temperature data to be oriented with respect to location in the interface. The infrared radiation comes from four sources: I,, the intensity due to reflected background radiation; I,, due to emission from the sapphire; 'I,,, due to emission from the ball; and 1 6 , due to emission from the lubricant film. Attenuation factors y reduce the intensity actually incident on the objective of the microscope, as shown in the diagram of Fig. 15-13. With suitable calibration and techniques the system can be

451

Figure 1 5 - 1 3 . Sources of infrared radiation emitted from a system posed of an oil film between a sapphire plate and a steel ball.

com-

0.20 E E- 0.15

tJ E 0.10

c

0 c

g

0.05

c

s 0.00 c

al

2

0.10

0 c

8

0.15

0.20

BALL OIL FILM Figure 1 5 - 1 4 . Temperature field on the ball surface and in the oil film as measured by the emitted infrared radiation. After Ausherman, Nagaraj, Sanborn and Winer 1 3 3 1 .

operated to yield separate data for the temperature of the oil film and the average temperature of the ball surface. Figure 1 5 - 1 4 shows typical plots of the temperature field on the ball surface and in the lubricant film. The isotherms for the ball surface are systematically spaced; those for the lubricant film are somewhat irregular and exhibit localized hot spots, particularly at locations where the optical interferograms indicate a thinning of the lubricant film. The resolving power of the detector is an area 38 um in diameter, as shown in the diagrams. Figure 1 5 - 1 5 shows the temperature profiles of the ball surface along the center line in the direction of sliding. The temperature in the film and on the ball surface is generated by the compression and the viscous shear of the lubricant as it passes through the conjunction gap. Ball surface temperatures were found to increase systematically with in-

452

180 160

@ I00 3

E 80

4-

60

I I

I-

.-E

I

40

LL

I )

0.2

0.1 0.0 0.1 Distance from Center,mm

0.2

Figure 1 5 - 1 5 . Temperature profiles on the ball surface and in the oil film along the center line in the direction of sliding by infrared emission. After Ausherman, Nagaraj, Sanborn and Winer [331.

2oo

f

I

I

k

0 Average -Calculated

I

1

I

I

I

I A

175

4 150 -

25 5 0 75 100 125 150 175 200 Calculated Temperature, degrees C Figure 1 5 - 1 6 . Comparison of calculated lubricant temperatures with experimental values obtained by infrared emission. Data by Nagaraj, Sanborn and Winer [ 3 4 1 .

453

crease of load or rubbing speed: a similar general trend was observed for Interfatemperatures in the lubricant film, with some irregularities. cial temperatures tended to rise with increased surface roughness, particularly i f some of the asperities penetrated the oil film and caused even the slightest wear [341. The interfacial temperatures were at a minimum for pure rolling of the ball against the sapphire plate and rose sharply with increasing ratio of sliding to rolling, with maxima for pure sliding [35]. The temperatures in the high-slip domain with the ball as the stationary surface were higher than those with the ball as the moving surface. The work of Winer e t aL. with smooth steel balls and sapphire flats is probably the best experimentation available to date for testing the applicability of continuum heat conduction theory to a tribological situation. The interface between the heat source in the lubricant film and the contact area on the ball is as close to an ideal interface as one can reasonably expect to achieve. Figure 15-16 shows the comparison Nagara), Sanborn and Winer 1341 made between experimentally measured temperatures and those calculated by Archard's adaption [ 3 1 of Jaeger's treatment [Z]. The agreement of the average measured temperatures with the average calculated temperature is quite good, especially at the higher pressures. Measured peak temperatures are higher than the, calculated ones. The use of the infrared emission method in the far from ideal circumstances prevailing in an operating spiral bevel gear set is described by Wymer and Macpherson 1361. The highest temperature rise of the tooth surface above that of the bulk oil ( 8 0 - 9 0 C) was found to be 50 C. 15.3.

AMBIENT TEMPERATURE EFFECTS

The implicit assumption in the tribological temperature calculations discussed in Section 15.1 is that the initial temperature of the rubbing interface is arbitrarily selected as zero. But in practice the rubbing interface has a real, finite value to which the tribologically generated temperature is added as an increment. Furthermore, there is an ambient environment with which the rubbing system interacts and temperature is one of the components of the environment that participates in the interaction. Therefore an examination of the mutual influences of the ambient environment and the rubbing interface is manifestly in order. I n controlled experimentation the temperature of the environment can be manipulated externally so that its influence dominates what is observed macroscopically. Thus in an experimental study of oil film thickness between two rolling/sliding bodies, the bulk oil temperature can be fixed by thermostatic means, and i f the bodies are immersed in the oil, their bulk temperature will be fixed also. The temperature field in the oil film as it passes through the conjunction and the surface temperature

454

of the disks will be the resultant of the various dynamic actions we have studied. To control a given experiment we could, for instance, establish an empirical relation between the minimum oil film thickness in the conjunction and the bulk temperature of the oil and vary that temperature to suit our requirements. This is the thinking that governs many of the experiments on the response of friction to temperature in the presence of "boundary" lubricants. Usually the slider is a body of small mass and restricted conjunction area, while the counterbody has a large mass and surface area. The lubricant layer is very thin, often only a monomolecular film, s o that effectively the temperature of the experiment is that of the counterbody. Cases arise in which the thermal contribution of the rubbing action to the bulk temperature of the ambient lubricant is significant. In many such instances temperature probes in the bulk oil or in the mass of the rubbing specimens indicate a steady-state condition when operating parameters such load or speed are held fixed. The macroscopic temperature behavior of the system is the balanced resultant of heat input from the rubbing interface and heat loss to the surrounding atmosphere and to the mass of those parts of the experimental device which, although not considered part of the ambient environment, are not part of the rubbing system either. An example of such a situation is the four-ball lubricant test, where the volume of oil is small relative to the mass of the four rubbing specimens. Such systems are very sensitive to thermal upset by scuffing, incipient seizure, or an increase of wear rate. Figure 15-17 illustrates diagrammatically the complexities of heat flow and temperature differences in a gear system as typically encountered in technological practice. The sources of heat that can raise the temperature of the bulk lubricant in the gear case are the following: ( A ) shear of the oil film at the gear tooth contact; ( B ) churning of the bulk oil in the gear case; ( C ) shearing and churning of the oil in the bearings; (D) heating of the oil film at the seals; ( E ) miscellaneous external sources. There are fifteen pathways by which heat can be transmitted from one part of the system to another. Not all of them may be operative in a particular case: there must be a temperature difference for heat to flow, and whether such a difference exists for two given locations depends on the individual circumstances. For example, i f the main source of heat to the bulk oil in the gear case comes from friction at tooth contacts, then part of the temperature rise in the bulk oil will be by pathway F (direct mass transport) and part by pathways G and H (conduction into the bulk of the gear, conduction out of the gear and mass transport by stirring of the oil). Whether a steady-state equilibrium is established in the bulk oil depends on the magnitude of the heat losses out of the oil and the gear case by the other pathways shown

455

Drive 4 R

C

I

dJ

4~

-

d S

Casing

Air and near-

by surfaces t

I

I1

l--l

0 Mounting

Figure 1 5 - 1 7 . Block diagram of the thermal flow in a lubricated gear and bearing system. Heat sources.-A: oil film at tooth contact; B: churning of bulk oil; C : oil film in bearings and bulk churning; D: oil film at seals; E: external sources. Heat transmission.-F: m; G: c; H: c , m; I: c; J: f; K: m; L: f; M: f; N: m; P: f; Q: c , f , r; R: c; S : n, f , r; T: c. c = conduction; f = forced convection; m = mass transport: n = natural convection; r = radiation. TABLE 15-4.

DISTRIBUTION OF HEAT LOSSES IN OPERATING GEAR UNITS

Type of gear unit

%

of heat generated

Tooth losses

Bearing losses

Seal

losses

Lubricant churning

Oil dip-lubricated, single-reduction worm gear, 1 5 0 0 rpm input

78

17

5

6

Oil dip-lubricated, double-reduction spur gear, 1 5 0 0 rpm input

29

13

0

50

Spray-lubricated, single-reduction helical gear (plain bearings), 1 5 0 0 rpm input

18

69

0

13

Spray-lubricated, single-reduction helical gear (tapered roller bearings, 1 5 0 0 rpm input

56

31

0

15

From data by Bathgate, Kendall and Moorhouse 1371.

in Fig. 15-17. Table 15-4 summarizes some estimates of the sources of heat flow For a into the bulk oil supply of operating reduction gear units [ 3 7 1 . worm gear unit the major contribution is from tooth rubbing, a s would be expected from the intrinsic nature of worm gear action, and hence in assessing sources of temperature which might influence lubrication failure, greater weight would be given to the direct action of heat generated at tooth contact than to the other contributions to the bulk temperature of the lubricant. But in the case of a spur gear unit, 71% of the heat input into the system comes from bearings, seals and churning. In a helical gear unit the major source of heat loss is shifted from the bearings to tooth contact by changing from plain bearings to rolling element bearings. It is not uncommon for external sources to furnish the major heat input to a lubricated system. For example, an oil sump may be exposed to the natural temperature of a hot environment such as a furnace room or the conducted heat of an internal combustion engine. I n the design of a lubricant system subjected to such influences, usually provision is made f o r forced cooling. But often the cooling facilities are limited by circumstances, and the lubricant perforce must function in a hightemperature environment. The study of lubrication in the ambient environment of high temperature may have as its direct objective whether o r not the lubricant will perform satisfactorily in this environment. However, the imposition of high-temperature environmental conditions is frequently used in bench testing to induce a transition from satisfactory performance to lubrication failure (scuffing, seizure, high wear, high friction, etc.). The critical imposed environmental temperature is reported a s the transition temperature for lubricant failure. The reader should be aware of potential complications in such an interpretation. The thermal influences of significance for lubricant failure operate at the rubbing interface, whereas temperature increases supplied externally are superposed grossly on the ambient temperature of the rubbing parts. Fast thermal feedback from the tribological events at the rubbing interface into the bulk of the lubricant will result in a different macroscopic temperature than i f the feedback is sluggish.

15.4.

EFFECTS OF TEMPERATURE ON FRICTION AND WEAR

A large proportion of the observations on the effect of temperature on friction and wear is empirical, and though the results may be of practical utility they afford n o insight into the basic reasons for this behavior. On the other hand, data such a s are seen in Fig. 15-18 [ 3 8 ] not only show observed behavior a s a response to temperature but have inter-

457

2.2

I

i

i

2 “0 1.8 1.6 C

2

1.4

0

5

1.2

0

E0, 1.0 .-

0

5 0.6

0”

0.6

0.4 0.2

0 300

400 500 600 Temperature, degrees K

Figure 15-18. Response of friction to ambient temperature. (a) Silver on silver, dry. (b) Silver on silver, lubricated by white o i l . (c) SAE 5 2 1 0 0 steel on SAE 4140 steel, dry. (d) SAE 5 2 1 0 0 steel on SAE 4 1 4 0 steel, lubricated by white oil. (el SAE 5 2 1 0 0 steel on silver, dry. (f) SAE 5 2 1 0 0 steel on silver, lubricated by white oil. From data by D. Godfrey 1381.

C

I-

Friction----

-------

r” 10-3

1.0

0

0.6 E 0.4 0.2 E 0.1

.Q

300 400 500 600 700 800 90C 000 Temperature, degrees K

Figure 1 5 - 1 9 . Effect of external ambient temperature friction of 6 0 / 4 0 brass sliding against tool steel. Lancaster [391.

a, 0

V

on the wear and From data by J. K.

458

pretations in terms of mechanisms as well. The strong upturn in the dry friction of silver against silver can be attributed to temperaturepromoted adhesion, and the strong thermal influence on lubricated friction can be ascribed to film breakdown. The much lower friction when hardened steel slides on silver is associated with a decrease in adhesion; the minimum at c a . 573 K (300 C) represents a balance between the The counteracting influence of temperature on plowing and on adhesion. influence of lubrication is not prominent in this case but becomes more pronounced when hard steel slides on hard steel. The sharp drop in the coefficient of friction for lubricated silver on silver and for lubricated steel on steel at the high-temperature end of the diagram could be the consequence of chemical action involving the lubricant. Chemical activity is the explanation for the wear and friction behavior shown in Fig. 15-19 [391. The data were obtained by the low-speed sliding of brass against tool steel ( 1 . 1 cm/s) so that the temperature of the rubbing interface was dominated by external ambient heating and the contribution from frictional heating was relatively minor. The wear rate of the brass rider decreased by two orders of magnitude a s the ambient temperature increased from 573 K (300 C) to 673 K (400 C); at 673 K the This behavior was coefficient of friction showed a sharp upward jump. correlated with the rate of oxidation of the film of brass.which was transferred to the tool steel ring in the wear process. If the rate of transfer is not inhibited by oxidation, then the wear particles are mostly metallic and the rate of wear is high. Oxidation of the transferred film changes the wear debris to small, unagglomerated particles of oxide and the wear rate decreases. The role of temperature in the process is obvious. However, when loads and rubbing speeds are high, the situation hecomes more complicated, although basically the effect of temperature on oxidation remains the same [401. The influence of temperature is especially significant in lubricaI n the tion, particularly i n the breakdown of lubricating action. descriptive literature the overt behavior associated with lubrication failure is usually designated as "scuffing." The difficulty of assigning a single-valued meaning to the term ACU66,inCj was discussed in Chapter 13, Sections 13.4 and 13.6, and this difficulty ccmplicates the study of temperature effects, which are strongly conditioned by the experimenter's criteria for scuffing. For example, H. Blok, a pioneer in the development of a quantitative temperature theory of lubricant failure [41], used the behavior of steel specimens in the I. A . E. spur gear rig a s the basis of his postulate Of a constant temperature of incipient scuffing [421. However, the concept is claimed to be valid only for lubrication by uncompounded mineral oils. The critical scuffing temperature was found to be responsive to the viscosity of the lubricant: 403-433 K (130-160 C ) for an oil of 7 cs at 60 C , 493-573 K (220-300 C) for an oil

459

of 1 5 0 cs at 60 C [ 4 2 1 . The basic mechanism of the critical temperature concept

is

simple.

Lubrication failure is envisioned a s occurring at the conjunction of the rubbing surfaces, and it is the critical temperature at this conjunction that controls the lubricating action. This temperature, T c , is made up of T,, the bulk temperature of the macroscopic rubbing specimens, and T 6' the added "flash" temperature generated by rubbing, which can be calculated by methods such as are presented in Section 1 5 . 1 . 2 ( e . g . Eqns 1 5 - 2 7 and 1 5 - 2 8 ) : Tc = T,

+ T6

(15-43)

Operating parameters such as load and rubbing speed, which according to theory systematically influence the frictionally generated flash temperaBut the ture, affect scuffing through the difference between T c and T,. analysis of real-life cases is more complex than this, and observed behavior is complicated further by the introduction of factors such as temperature-influenced changes in the properties of materials, surface contact conditions, etc. Hence, though the critical temperature concept seems valid in principle, a s of now it has not been tested enough to assess its practical utility thoroughly. Leach and Kelley 1 4 3 1 carried out an extensive test of the Blok hypothesis with an apparatus whose rubbing specimens were differentially rotating disks in contact on their cylindrical surfaces. The reading of a small thermocouple riding on the oil film at the inlet of the conjunction was taken as the value of T c ; the value of T d was calculated from the relation v;'5)

(15-44)

where u is the coefficient of friction at the conjunction, is the load in lbs force per inch of contact conjunction width, V 1 and V 2 are the peripheral velocities of the disks in inches per second, and 1 . 3 0 is a constant determined from the physical and thermal characteristics of the disk material and disk geometry. Scuffing (which Leach and Kelley called "scoring") was determined by the condition of the disks a s observed at the end of the test and by the sudden loss of electrical resistance across the conjunction. The latter observation leads to the conclusion that scuffing under these circumstances is the consequence of the breakdown of the oil film. Broadly, Leach and Kelley found the Blok critical temperature hypothesis to hold for three uncompounded mineral oils with viscosities ranging from 4.80 to 1 5 . 0 0 c p at 3 7 2 . 0 K ( 2 1 0 F ) and a compounded engine oil, 4 . 6 0 c p at 3 7 2 . 0 K; the average critical temperature for scuffing was 6 3 9 K ( 3 3 6 F), with an average deviation of 2 3 3 degrees K ( C 6 0 degrees F). This much deviation is a serious disadvantage for the

460

practicai utility of the critical temperature criterion, but it is not large enough to invalidate the differences Leach and Kelley found between Tc as calculated by Eqns 15-43 and 15-44 and and the measured values of T..) over the range of their experimental conditions. contradistinction to the viscosity effect reported by Blok [421, Leach and Kelley's critical temperature was not influenced by the viscosity of the lubricant; however, the range of viscosity for Leach and Kelley's oils was smaller than that of Blok's. A comparison of the two sets of results with respect to the range of experimental uncertainty is given in a discussion by Blok appended to Leach and Kelley's publication In

[431.

The constant critical scuffing temperature observed by Leach and Kelley may be the fortuitous consequence of a limited range of operating parameters in testing. Working with a similar two-disk machine, R. S . Fein [441 found the critical scuffing temperature to be affected by experimental details such as the break-in procedure, the magnitude of the load steps in the testing sequence, the spindle velocity of the machine, and the rubbing ratio of the specimens. Selected data are shown in Table 15-5 for squalane (2,6,10,15,19,23-hexamethyltetracosane), viscosity 4.19 cs at 2 1 0 F , and in Table 15-6 for a solvent-refined mineral oil, viscosity 5.09 cs at 2 1 0 F. Influences that prolong the duration of the test allow the base temperature of the disks to increase; among such influences are the break-in procedure, which conditions the surfaces of the disks, the load increments and the rubbing speed. The higher the scuffing load, the greater the frictional energy generated at lubricant failure and the greater the increment contributed to the conjunction temperature by the flash temperature. The conjunction temperature was computed by the formula (15-45)

where N is the spindle speed in rpm, W is the applied load in lbs force and v is the rubbing ratio of the two specimen disks. This is Blok's flash temperature equation adapted to these particular experimental conditions; the numerical coefficient 9.5 takes care of the material properties, geometry of the specimens, etc. Fein's evidence shows that the condition of the rubbing surfaces has a crucial effect on the scuffing load and the associated critical scuffing temperature, which accounts for the influence of the break-in procedure and the duration of the test proper. The observed cases of constant critical scuffing temperature for certain types of lubricants implies a rigorously standardized break-in and testing procedure. Niemann and Lechner 1451 investigated surface temperatures of gear teeth with respect to scuffing. This problem is complicated by the

461

T?.BLE 1 5 - 5 . CRITICAL SCUFFING TEMPERATURES FOR ROLLINGSLIDING STEEL DISKS LUBRICATED WITH SQUALANE Run-in Spindle Load Scuff Disk temperConjunction procedure speed in increment, load, lbs ature at scuff, temperature at test, rpm lbs deg. F scuff, deg. F A B None A B (a) A (b) B

425 425 850 850 850 850 1280 1280 1280

65 26 65 65 65 65 65 26 26

1080 2210 300 620 690 1210 360 600 880

129 182 92 114 109 163 102 114 103

402 590 313 320 323 552 307 372 37 1

Test r u n s : 2 minutes at each load increment. Bulk oil temperature held at 6 5 ? 5 F. Run-in procedure: rubbing ratio/rpm/minutes at l b s load. A: 1 . 5 0 / 8 5 0 / 1 0 @ 1 1 4 3 , 5 min 0 1 7 9 3 , 1 5 min 4 2 4 4 3 . B: 1 . 5 0 / 4 2 5 / 1 0 @ 1 1 4 3 , 5 min 4 1 7 9 3 , 1 5 min @ 2 4 4 3 ; then 2 . 6 0 / 4 2 5 / 5 @ 2 3 3 , 5 min @ 6 2 3 , 5 min @ 7 5 3 , 10 min 4 8 1 8 . (a) 1 . 5 0 / 4 2 5 / 1 0 @ 1143, 5 min @ 1 7 9 3 , 15 min 4 2 4 4 3 ; then 2 . 6 0 / 4 2 5 / 5 @ 2 2 3 , 5 min @ 4 9 3 , 5 min @ 6 2 3 , 5 min 4 7 5 3 , 4 0 min @ 818.

(b) 1 . 5 0 / 4 2 5 / 1 0 4 1 1 4 3 , 5 min 4 1 7 9 3 , 1 5 min 4 2 4 4 3 ; each 4 2 4 4 3 1 b s / 6 4 0 , - 8 8 0 , - 1 2 8 0 rpm. From data by R. S. Fein [ 4 4 1 .

then,

5 -min

TABLE 1 5 - 6 . CRITICAL SCUFFING TEMPERATURE FOR ROLLINGSLIDING STEEL DISKS LUBRICATED WITH MINERAL OIL Run-in Spindle Load Scuff procedure speed in increment, load, lbs test, rpm lbs C

425

65

B

425

65

B

425

26

C

1280

65

C

1280 1280 1280 1280

26 65 65 26

1210 1340 1530 1660 > 2 5 10

Conjunction Disk temperature at scuff, temperature at deg. F scuff, deg. F 114 136 151 153 >175

322 432 500 473 >499

67 89 102 94 170 >236

273 293 326 322 603 >776

(no scuff)

C' B B

230 360 360 430 1340 21420

( n o scuff) Test runs: 2 minutes at each load increment. Bulk oil temperature held at 6 5 ? 5 F . Run-in procedure: rubbing ratio/rpm/minutes at lbs load: 4 1 1 4 3 , 5 min 4 1 7 9 3 , 15 min @ 2 4 4 3 ; then B: 1 . 5 0 / 4 2 5 / 1 0 2.60/425/5/ 0 2 3 3 , 5 min 4 6 2 3 , 5 min 4 7 5 3 , 10 min 4 8 1 8 . C: 2 . 6 0 / 4 2 5 / 1 0 4 7 4 , 5 min 4 2 3 3 . C': 2 . 6 0 / 4 2 5 / 1 0 @ 7 4 , 20 min 4 2 3 3 . From data by R. S . Fein [ 4 4 ] .

462

functional relation of velocity to the location of contact on the tooth profile and by the division of contact between two adjacent pairs of teeth when the rubbing velocity at one pair is higher. Two material combinations of alloy steel lubricated with a formulated gear oil were Cr, VHN tested for scuffing. For one combination (1.25% Mn:1.15% 718-803, against 12% Cr:13% Ni, VHN 196) the measured surface temperature at incipient scuffing was 451 K (178 C ) as against 499 K (226 C) computed from flash temperature theory. With a harder combination (1.25% Mn:1.15% Cr against 1.1% Cr:4.5% Ni, VHN 5851, the measured critical surface calculated 718 K (445 C ) . Ishikawa, temperature was 623 K (350 C ) , Hayashi and Yokoyama 1461 carried out similar tests on spur gears of chrome-molybdenum steel, VHN 642-657, lubricated with uncompounded mineral oil. Scuffing temperatures were found to lie in the range 623-673 K (350-400 C). Using a slow-speed technique (0.04 cm/s) with the four-ball machine, Matveevsky [471 observed a critical seizure temperature of 423 K (150 C ) for the pure sliding of hardened alloy steel on hardened alloy steel. Due to the extremely slow sliding speed, the contribution from interfacial rubbing was negligible so that the effective temperature was that of the bulk oil. Hydrodynamic effects were eliminated from consideration at such slow sliding speed and the the onset of scuffing was governed principally by temperature. For softer metals, where plastic deformation can be an important influence on the true contact area, the critical temperature was found to fall off at higher loads. Bailey and Cameron [481, using the slow-speed technique with a modified four-ball apparatus and stainless steel specimens, observed a 423 K (150 C) scuffing temperature with white oil as the lubricant. With hardened AISI 52100 steel rubbing on stainless steel lubricated with white oil at the higher speed of 185 cm/s, a conjunction temperature of 453 (180 C) was observed at scuffing. On the other hand, Fein's [491 extensive study of transition temperatures and scuffing in pure sliding with the four-ball machine showed the same type of response to the velocity/load ratio that he found with the two-disk machine 1441. The sliding speeds ranged from 0.0002 to 68.6 cm/s, the loads from 19.6 to 88.2 N (2-90 kg). Two kinds of steel specimen sets were used: hardened A I S I 52100, diamond pyramid hardness 740, and heat-treated AISI 4140, hardness 270. There were 13 di.fferent lubricants, with the properties shown in Table 15-7. At low rubbing speeds the interfacial flash temperatures were negligible and the bulk temperatures of the lubricant were taken to be the transition temperatures. At speeds above 0.359 cm/s a particularized form of the flash temperature equation was used to calculate the contribution from interfacial rubbing to be added to the bulk temperature to obtain the transition temperature. A s shown in Fig. 15-20, the results cluster around a

straight

line

463

TABLE 15-7.

LUBRICANTS USED IN STUDY OF TRANSITION TEMPERATURES

Lubricant

Cetane Squalane Paraffin wax Dinonylnaphthalene Stearic acid, commercial Stearic acid, pure White oil Mineral oil Mineral oil Mineral oil Bright stock 0 . 4 3 % Pure stearic acid in cetane 0 . 4 3 % Pure stearic acid in squalane

Viscosity

Symbol (Fig. 1 5 - 2 0 )

Pa-s at 309.0 K

Pa-s at 372.1 K

0.00232 0.0165 0.0100 1.632 0.026

0.00087 0.00323 0.00289 0.0221 0.0051

0.0642 0.0186 0.0274 0.213 0.666 0.00232

0.00645 0.00354 0.00425 0.0154 0.0288 0.00087

0.0165

0.00323

on 5 2 1 0 0 steel

on 4 1 4 0 steel

it, d X

Data by R. S. Fein 1491.

Figure 15-20. Dependence of transition temperature on viscosity lubricant, rubbing speed and load. From data by R. S. Fein [ 4 9 1 .

of

464

representing the reciprocal of the transition temperature (in degrees Kelvin) as the inverse function of the parameter l o g ( q V / W ) . In some instances the fit of the data to this relation is excellent, as for example the case of 0 . 4 3 % stearic acid in cetane tested in a pin-on-disk machine with specimens of AISI 4 1 4 0 steel [ 5 0 1 and on a four-ball apparatus with Similar bespecimens of either AISI 5 2 1 0 0 or AISI 4 1 4 0 steel [ 5 0 , 5 1 1 . havior was observed with a light solvent-refined mineral oil. Rather than a simple response of the durability of the oil film to interfacial temperature, Fein sees the critical transition temperature as the result of competing influences such a s lubricant viscosity, true pressure at asperity contacts, duration of contact between asperities, chemical interactions at asperity contacts, etc. When chemical activity is minimal, the other influences affect the manner in which a thick film of lubricant (as distinguished from a monomolecular film) is trapped and squeezed out between interacting asperities. The critical transition temperature does not depend on the behavior of the lubricant alone. Fig. 1 5 - 2 1 shows the relations found by Fein, Rowe and Kreuz [ 5 0 1 between the critical temperature and the speed/load ratio for specimens of AISI 4 1 4 0 steel, copper and silver, lubricated by 0 . 4 3 % stearic acid in cetane.

Transition temperatures for various metals in pin and disk Figure 1 5 - 2 1 . experiments. Lubricant: 0 . 4 3 % stearic acid in cetane. From data by Fein, Rowe and Kreuz [ 5 0 ] .

15.5.

EFFECTS OF TEMPERATURE ON LUBRICATION AND LUBRICANTS

I n the discussions of the preceding section the breakdown of lubrication and the onset of scuffing at the critical temperature was accepted as an empirical fact, wirh little inquiry into the details of how and why temptrature should affecE the lubrication process. True, given

465

such parameters as the geometry of the rubbing interface, the speed of rubbing, the loading, the viscosity and other appropriate properties of the lubricant, one can calculate the temperature at which a hydrodynamic or elastohydrodynamic oil film will become so thin that it will not separate the rubbing surfaces effectively. But the interaction of temperature and lubricant goes beyond the stability of the fluid film. Consider the thermodynamic approach to the lubricating action of an adsorbed film of boundary lubricant ( c d . Chapter 10, Section 10.4.3) as given by the relation R

7

(15-46) where 4 is the fractional coverage of the rubbing surface by the boundary lubricant additive, C its concentration in the carrier oil, AH' and AS' are the standard heat and entropy of adsorption respectively, and R is the thermodynamic gas constant. The critical temperature, T c , is in degrees Kelvin. I f it is observed empirically that t n C is a linear function of l/Tc,

tn C

=

- KT/Tc

+

K'

(

15-47)

then. for Eqns 15-46 and 15-47 to be equivalent, + / ( l - 4 ) as well as AH' and AS" must be constants. Also, the carrier oil must not compete with the additive for adsorption sites on the surface. These are the formal requirements to be met i f the thermodynamic treatment of transition temperatures is to be strictly valid. I n practice, the variance in A H ' , AS' and @/(l - 4 ) that can be tolerated is determined by the limits of experimental precision. However, the real adsorption of boundary additives on metal surfaces frequently departs from the simple behavior to which Eqn 15-46 applies. For example, Spikes and Cameron [521 found that the adsorption of noctadeylamine from cetane onto stainless steel powder was not completely reversible, and they were therefore force to settle for the isosteric heat of adsorption, y h t , from the equation

(

15-48)

where the subscript r defines the extent of surface coverage by the adsorbate. Equation 15-48 therefore defines a family of straight lines for given surface coverages r . At low temperatures (<303 K) and less than 32% coverage, the isosteric heat of adsorption was less than 17.54 kJ/ mole (3.58 kcal/mole), changing to 63.7-102.9 kJ (13-21 kcal) per mole at Higher coverages (up to 40%) showed an temperatures above 303 K. Figure isosteric heat of adsorption of 117.6 kJ/mole (24 kcal/mole).

466

Temperature,degrees

370

350

330

310

K

290

-3

2.8

3.0

3.2

3.4

1000/Temperature (degrees K ) Figure 15-22. Effect of temperature on adsorption and scuffing, noctadecylamine in cetane on stainless steel. CiAdsorption at 21% surface coveraqe. o Scuffing. From data by Spikes and Cameron [52].

15-22 compares the e n C vs. 1/T relation for the adsorption of octadecylamine in cetane by stainless steel at 21% surface coverage and for the critical scuffing at slow speed (0.01 cm/s). The adsorption function is obviously not identical with the scuffing function. It seems unlikely that the consistent relation between e n C and l / T c observed f o r the scuffing and frictional transition is fortuitous, but on the other hand thermodynamic treatment of a non-equilibrium process such as scuffing cannot be theoretically sound. Much work remains to be done to resolve this problem. The typical parametrically governed plots of e n C against l/Tc are sets of parallel straight lines (see, for example, Fig. 10-14, Chapter 10). The parameters can be load, as reported by Grew and Cameron [ 5 3 ] for n-hexadecylamine in cetane, o r chain length, as reported by Frewing I f the plot is [541 for n-alkyl carboxylic acids in white oil. parametrically governed by load for a given lubricant, then over a not too extended temperature range Aff' and Aso are constant and therefore it is the critical value of + / ( 1 - + ) that responds to the magnitude of the load. But i f the governing parameter is determined by the nature of the lubricant, e . g . the chain length of a fatty acid additive o r its conmust stay concentration, then both AS and $ / ( l - + ) could vary. Aff' stant, of course, i f the lines are parallel. I f data f o r ASo are available from experimentation, then deductions can be drawn about the interaction of the critical value of +/(l

~ f f "

- $ ) and scuffing.

Two experimentally determined quantities are required to evaluate and AS". These are the integral heat of adsorption and the adsorp-

467

tion equilibrium constant Ke. The experimentation is not easy and the data S O obtained are often inconsistent. Very few data of sufficient scope are available to characterize the behavior of homologous series of F o r the alcohols from n-butanol to n-octadecanol additive substances. the integral heats of adsorption increase with chain length, albeit somewhat erratically, and the increase of ASo is even more erratic. The behavior of the n-alkanoic acids is similar. I t is reasonable to expect that the behavior of lubricant additives which function by chemical reactivity will respond to the influence of temperature in ways related to such activity. In general the experimental evidence bears this out, but few systematic relations to that effect are known. One such investigation is that of Nakayama and Sakurai [15] on the wear of copper rubbing on steel lubricated by elemental sulfur dissolved in n-hexadecane at concentrations ranging from 0;002% to 0.050%. Sliding speed was 47.1 cm/s and loads were 9.8, 19.6, 29.4 and 39.2 N. Bulk oil temperatures were 303, 3 3 3 , 3 5 3 and 3 6 3 K, to which the calculated flash temperatures were added to give the temperatures at the sliding surface. Figure 15-23a shows plots of the volume-rate of wear (in mm3 per mm of rubbing distance) of the copper slider vs. the surface temperature for the various concentrations of Sulfur. Increase of wear

1.5

10.025%

315 335 355 375 395 Surfoce Ternperature,degrees K

-5.5

2.5 3.0 1000/ T, (degrees K )

Figure 15-23. Effect of surface temperature on the additive action of dissolved sulfur in n-hexadecane, concentration as indicated, sliding speed 47.1 cm/s. Load: o 1 kg. 0 2kg. D3kg. 0 4 kg. Copper on steel. Data by Nakayama and Sakurai [ 1 5 1 .

rate with temperature is not unexpected, but the increase of wear rate with sulfur concentration and its strong augmentation with temperature for the higher concentrations indicate the complexity of the overall lubrication process. Nakayama and Sakurai postulated that the component which wears in the high-rate phase is a copper sulfide whose formation is promoted by increasing temperature. If the wear does indeed proceed in

468

this manner, then the plots of the logarithm of the wear rate vs. l/T, shown in Fig. 15-23b cannot be used as phima 6 a c i e data for the computation of the energy of activation for the reaction of the additive with the metal. Another instructive investigation of the effect of temperature on chemically reactive additives is that of Sethuramiah, Okabe and Sakurai [55] with the four-ball machine to determine the welding load by the oneminute procedure at 1440 rprn (54 cm/s). Two types of frictional behavior were observed at the welding load, as diagrammed schematically in Fig. 15-24. In one type (Fig. 15-24a), 1 indicates start-up when the driving motor is turned on, 2 indicates the rapid incipient seizure which goes over to the recovery plateau A with a drop in friction, and Tr-1 indicates the transition which almost immediately becomes a weld at 3. In r;ne other type (Fig. 15-24b), Tr-1 turns into a second plateau at B and

Time

c

Figure 15-24. Frictional behavior at the welding load with compounded lubricants in the four-ball test. After Sethuramiah, Okabe and Sakurai [551. TABLE 15-8. TRANSITION TEMPERATURES AT WELDING LOADS IN THE FOUR-BALL TEST ~

Additive

Diphenyl disulfide Diphenyl disulfide Diphenyl disulfide Dialkyl monosulfide Dibenzyl monosulfide Dibenzyl disulfide Sulfur Sulfur Hexachloroethane

~~

~~

x

Sulfur Welding Conjunction temperature, in lubricant load, N Tr-1 Tr-2 0.294 0.88 1.48 0.294 0.294 0.294 0.294 0.88 0.294% C1

1764 1960 2352 1960 1764 1960 2744 2940 1862

568 548 608 598 568 598 633 616 624

(635) (573) (636) (629) (635) (629) (671) (648 (644)

-

O K

-

1000 (1062) 1001 (1065)

- -

1000 (1062) 1083 (1173) 990 (1057)

- -

Figures in parentheses computed by alternative formula. Four-ball test: 60 seconds at 1440 rpm (54 cm/s). Carrier fluid for additives: white oil, 75.31 cs/311 K. From data by Sethuramiah, Okabe and Sakurai 1551.

469

welding occurs after a second transition Tr-2. Table 15-8 shows the calculated conjunction temperatures at transition for five sulfur additives and one chlorine compound. These temperatures are the sums of the temperatures calculated from the coefficients of friction plus the directly measured temperatures of the oil in the ball pot. The conjunction temperatures, which range from 568 K to 633 for Tr-1 and 990-1083 K for Tr-2, do not show any parallelism with the welding loads. The second plateau B, which seems to mark a chemical activation of the additive induced by rubbing, occurs for the two higher concentrations of diphenyl disulfide, for dibenzyl disulfide and for sulfur, but not for the less chemically active monosulfides. R. M. Matveevsky 1561 discussed the influence of temperature on lubricant additive action in terms of whether the additive functions by an adsorption/desorption mechanism o r by a chemical reaction mechanism. If the additive is a blend of two components, one of which acts via adsorption and the other by reaction, and if the critical temperature of desorption is lower than the temperature at which the rate of chemical reaction of the other additive will contribute substantially to the lubrication process, then the critical desorption temperature will control lubricant failure. Thus, if the load induces frictional heating at the rubbing interface so that the conjunction temperature exceeds the critical desorption temperature, this will be the critical failure load. But i f the surface exposed by desorption of the first additive reacts with the second additive at the temperature prevailing there, the failure load will be raised. Cameron and his co-workers [48, 571 used these concepts, although not as explicitly proposed by Matveevsky, to explain the behavior of multicomponent compounded lubricants containing dibenzyl disulfide and a commercial calcium petroleum sulfonate as the additives. The failure temperature characteristic of the calcium sulfonate as the sole additive was 468 K (195 C ) , whereas failure with dibenzyl disulfide With the two-component additive, inwas observed at 543 K (270 C). cipient failure began at ca. 473-493 K , which seems to mark a balance between desorption of the sulfonate and chemical reaction of the disulfide. A s the temperature increased above 493 K , the reactivity of the disulfide became more apparent and the coefficient of friction decreased, until at 543 K, the temperature observed for the failure of the disulfide alone, the rubbing pieces scuffed.

REFERENCES 1.

2.

in Solids, 2nd Edition, Oxford University Press, 1959, Chapters I , X . J. C. Jaeger, Proc. Roy. SOC. New S . Wales, 76 (1942) Part 3,

H . S . Carslaw and J. C. Jaeger, Conduction of Heat 203-224.

3. J. F. Archard, Wear, 2 (1958/1959) 438-455. 4, F. F. Ling and S. L. Pu, Wear, 7 (1964) 23-34. 5. F. F . Ling, J . Lubrication Tech. (Trans. ASME), 91F (1969) 397-405.

470 6. 7.

8. 9.

H. Shore, J . Washington Acad. Sci., 15 ( 1 9 2 5 ) 8 5 - 8 8 . K . Gottwein, Maschinenbau, 4 ( 1 9 2 5 ) 1 1 2 9 - 1 1 3 5 . E. G. Herbert, Proc. Inst. Mech. Engrs., 1 ( 1 9 2 6 ) 2 8 9 - 3 2 9 . F . P. Bowden and K. E. Ridler, Proc. Roy. SOC. London, A 1 5 1 640-656.

10. 11.

12. 13. 14. 15. 16. 17. 18.

(1936

__

ADD^ and F . F. Linq, Trans. ASME 80 (19581 307l310. W. F. Huqhes and E. W. Gaylord, J . Appl. _ _ Mech. (Trans. ASME), 82E ( 1 9 6 0 ) 259'262. H . H. H. Shu, E. W. Gaylord and W. F . Hughes, J . Basic Eng. (Trans. ASME), 86D ( 1 9 6 4 ) 4 1 7 - 4 2 2 . E. G. Loewen and M. C. Shaw, Trans. ASME, 7 6 ( 1 9 5 4 ) 2 1 7 - 2 3 1 . E. W. Gavlord. W. F . Huahes, F . C.

T. Sakurai, H. Okabe and A. Sethuramiah, Bull. Japan Petr. Institute, 13 ( 1 9 7 1 ) 8 9 - 9 6 . K . Nakayama and T. Sakurai, Wear, 2 9 ( 1 9 7 4 ) 3 7 3 - 3 8 9 . M. J . Furey, ASLE Trans., 7 ( 1 9 6 4 ) 1 3 3 - 1 4 6 . C. Dayson, ASLE Trans., 10 ( 1 9 6 7 ) 1 6 9 - 1 7 4 . A. Cameron, A. N. Gordon and G. T. Symm, Proc. Roy. SOC. London, A286 ( 1 9 6 5 ) 4 5 - 6 1 .

19. 20.

J. P. O'Donoahue and A. Cameron, ASLE Trans., 9 ( 1 9 6 6 ) 1 8 6 - 1 9 4 . J. P. O'Donoghue, S . M. Manton and A. Cameron, ASLE Trans., 10

21.

H. S . Chena

( 1 9 6 7 ) 175-182. 22.

and F . ( 1 9 6 5 / 1 9 6 6 1 Part 3B,

G.

M. Hamilton and

K.

Orcutt,

Proc.

Inst.

Mech.

Enqrs., .

180

158-168. S.

L. Moore, Proc. Roy. SOC. London, A322 ( 1 9 7 1 )

3 13-330. 23.

J.

W. Kannel and T. A. Dow, J . Lubrication Tech. (Trans. ASME),

96F

( 1 9 7 4 ) 611-616. 24. 25. 26. 27.

J. W. Kannel, F . F. Zugaro and T. A. Dow, J . Lubrication Tech. (Trans. ASME), 100F ( 1 9 7 8 ) 1 1 0 - 1 1 4 . N. H. Frank, Introduction to Electricity and Optics, 2nd Edition, McGraw-Hill, New York, Toronto, London, 1 9 5 0 , Chapter 2 0 . ' R. A. Smith, F. E. Jones and R. P. Chasmar, The Detection and Measurement of Infra-red Radiation. 2nd Edition. Oxford Universitv Press, 1968. F. P. Bowden and P. H.. Thomas, Proc. Roy. SOC. London, A223 ( 1 9 5 4 )

29-40.

35 *

R. J. Heighway and D. S. Taylor, Wear, 9 ( 1 9 6 6 ) 3 1 0 - 3 1 9 . G. S . Reichenbach, Trans. ASME, 8 0 ( 1 9 5 8 ) 5 2 5 - 5 4 0 . B. T. Chao, H. L. Li and K. J. Trigger, J. Eng. for Industry (Trans. ASME), 83B ( 1 9 6 1 ) 4 9 6 - 5 0 4 . P. Deyber and M. Godet, Tribology, 4 ( 1 9 7 1 ) 1 5 0 - 1 5 4 . V. Turchina, D. M. Sanborn and W. 0. Winer J. Lubrication Tech. (Trans. ASME), 9 6 F ( 1 9 7 4 ) 4 6 4 - 4 7 1 . V. K . Ausherman, H. S. Nagaraj, D. M. Sanborn and W. 0. Winer, J. Lubrication Tech. (Trafis. ASME), 98F ( 1 9 7 6 ) 2 3 6 - 2 4 3 . H. S . Nagaraj, D. M. Sanborn and W. 0. Winer, J. Lubiicati3n Tech. (Trans. ASME), 99F ( 1 9 7 7 ) 2 5 4 - 2 6 3 . H. S . Nagaraj, D. M. Sanborn and W. 0. Winer, ASLE Trans., 22 ( 1 9 7 9 )

36. 37.

D. G. Wymer and P. B. Macpherson, ASLE Trans., 18 ( 1 9 7 5 ) 2 2 9 - 2 3 8 . J . Bathgate, R. B . Kendall and P. Moorhouse, Wear, 15 ( 1 9 7 0 )

38.

D.

28. 29. 30. 31. 32. 33. 34.

277-285. 117-129. 39. 40. 41.

Godfrey, Proc. Fifth World Petroleum Congress, New York, June 1 9 5 9 , Section V I , pp. 3 4 5 - 3 6 2 . J. K. Lancaster, Proc. Phys. SOC. London, 7 0 B ( 1 9 5 7 ) 1 1 2 - 1 1 8 . J. K . Lancaster, Proc. Roy. SOC. London, A273 ( 1 9 6 3 ) 4 6 6 - 4 8 3 . H . Blok, Proc. Second World Petroleum Congress, Paris, 3 (1937)

42. 43. 44. 45.

H. Blok, Wear, 6 ( 1 9 6 3 ) 4 8 3 - 4 9 4 . E. F . Leach and B. W. Keliey, ASLE Trans., 8 ( 1 9 6 5 ) 2 7 1 - 2 8 5 . R. S . Fein, ASLE Trans., 10 ( 1 9 6 7 ) 3 7 3 - 3 8 5 . G. Niemann and G. Lechner, J. Basic Eng. (Trans. ASME), 87D ( 1 9 6 5 )

46.

64 1 - 6 5 4 . J . Ishikawa, K. Hayashi and M. Yokoyama, (Trans. ASME), 96B ( 1 9 7 4 ) 3 8 5 - 3 9 0 .

1-5,

47 1 - 4 8 6 .

J.

Eng.

for

Industry

471

47. 48. 49 * 50. 51. 52.

R . M . M a t v e e v s k y , Wear, 4 ( 1 9 6 1 ) 2 9 2 - 2 9 9 . M. W. B a i l e y a n d A . C a m e r o n , ASLE T r a n s . , 16 ( 1 9 7 3 ) 1 2 1 1 3 1 . R . S . F e i n , ASLE T r a n s . , 8 ( 1 9 6 5 ) 5 9 - 6 8 . 1959) 50-75. R . S. F e i n , C . N . R o w e a n d K . L. K r e u z , ASLE T r a n s . , 2 R . S . F e i n , ASLE T r a n s . , 3 ( 1 9 6 0 ) 3 4 - 3 9 . H. A. S D i k e s a n d A . C a m e r o n , P r o c . R o y . S O C . L o n d o n A336 ( 1 9 7 4 )

53.

W.

407-419. 54. 55. 56. 57.

London, A327 (1972) J . S . G re w a n d A . C a m e r o n , ? r o c . Xo y . SOC 47-59. 1943) 270-285. 2 . J . F r e w i n g , P r o c . Roy. S O C . L o n d o n , A183 A . S e t h u r a m i a h , H. O k a b e a n d T . S a k u r a i , Wea , 26 ( 1 9 7 3 ) 187-206. R . M. M a t v e e v s k y , T r i b o l o g y , 4 ( 1 9 7 1 ) 9 7 - 9 0 . X. A . S p i k e s a n d A . C a m e r o n , ASLE T r a n s . , 17 ( 1 9 7 4 ) 2 8 3 - 2 8 9 .

412

Chapter 1 6 PETROLEUM LUBRICATING OILS

I n the workaday world, reference to a lubricating oil usually

means petroleum oil and the common current practice of lubrication has been developed with such oils. The most important reason is the availability of petroleum and its cost advantage, but there are technologicai reasons as well. No other single source provides lubricant fluids with as wide a range of viscosity and other desirable properties such as low volatility. F o r the most part the lubrication engineer is familiar with petroleum oils a s fluids rather than as substances. He is keenly interested in t h o s e properties directly and obviously useful in the lubrication process, but because the lubricant comes to him already supplied, he tends to accept it a s it is, with only mild curiosity about its origin or its chemical composition. However, over the years the connection between useful properties and the chemical constitution of lubricating oils has become apparent and specifications to aid in procurement and utilization of iubricants have increasingly involved their chemical nature. But fixed specifications are static, while technology changes. New techniques of refining produce oils which do not meet the old physical and chemical specifications. Sources of supply are becoming l e s s dependable and deviations from established specifications must perforce be accepted. The lubrication engineer can prepare himself to deal with such contingencies adaptively by becoming acquainted with the constitution of petroleum oils and the processes by which lubricant fractions are obtained from the crude. By broadening his understanding of the significance of specifications he can reduce the amount of empirical testing which might be necessary to meet small changes in the character of the lubricant.

The material offered in this chapter is intended to provide some basic insight into the manner in which petroleum lubricants are prepared from crude oil and how the composition of a lubricating fluid thus obtained correlates with its properties. I t is only a summary of a subject which would require several volumes for adequate treatment. Particular emphasis will be put on the relations of chemical structures i n lubricating o i l s to classificatory properties and to performance in service. i6.1.

PROCESSING OF PETROLEUM LUBRICANTS Crude petroleum is a complex mixture of hundreds, possibly thousands of volatility and molecular

of individual compounds with a wide range

413

weight. The initial processing step is a straightforward distillation of the total crude, which separates it into broad fractions of progressively decreasing volatility. Table 1 6 - 1 , taken from a brief summary of the American Petroleum Institute's Research Project 6 on the constitution of illustrates the general character of such fractions. The petroleum [ I ] , atmospheric Doiling ranges for kerosine and heavier fractions are calculated from vapor pressure data. In actual processing the higher boiling fractions are distilled under reduced pressure to minimize thermal damage. SUMMARY OF THE BROAD FRACTIONS TABLE 1 6 - 1 . OBTAINED BY DISTILLATION OF PETROLEUM Fraction

Boiling range, ' C at 1 atm.

Gas

<40

Gasoline (a)

40-180

Kerosine (a)

180-230

Light gas oil Heavy gas o i l and light lubricating distillate

230-305

Lubricating oil

Range of C/mo 1ec ule

% of. orginal pet r oleum

'1-'5

4

'6-'10

33.2

c l l and c 1 2

13-'17

305-405

'18-'25

405-515

'26-'38

Residue (a) Straight-run distillate.

12.7 18.6 14.5

10.0 7

From data by F. D. Rossini 1 1 1 .

The information in Table 1 6 - 1 is a broad illustration of the nature of crude petroleum rather than a guide to its refining. I n technological practice the heavy gas oil is taken as a fraction separacely from the light lubricating distillate; the relative amounts of the two will vary depending on the demand for heating oil and gasoline cracking stock. Also, a s many as three fractions are taken during the distillation of the heavier lubricating oil. The specific details of this part of the fractionation are governed by the viscosities desired in the lubricating oil cuts. The raw lubricant distillates are not acceptable as such f o r modern lubricating practice. For one thing, they contain significant quantities For of dissolved wax, which crystallizes out when the oil is chilled. another, these distillates have enough aromatic rings in their constituent chemical structures to affect their temperature-governed viscosity behavior adversely. Also, many crudes give distillate fractions which are undesirably high in organic compounds of sulfur and nitrogen.

414

Therefore further treatment is into acceptable lubricating oils.

required to refine the raw distillates

For the removal of aromatics in particular and to some extent also for the removal of sulfur and nitrogen heterocycles, further treatments are dependent on the nature of the crude from which the raw distillates

are derived. A major difference is in the treatment required to reduce the aromatics. Aromatics can be removed from raw distillates which contain a sufficient proportion of paraffinic chains by a solvent extraction process, whereas distillates with a high proportion of naphthenic rings and too low a content of paraffinic chains do not respond to selective extraction by a solvent. The terms ahamatic and p a h a 6 6 i n . i ~ have precise meaning in organic chemistry. The designation n a p h t h e n i c no longer has a recognized place in chemical nomenclature but is understood by common consent to apply to ring structures with no unsaturated linkages. Petroleum oils o r fractions derived from them are identified as paraffinic, naphthenic or aromatic because a major or at least a substantial proportion of the constituent structures falls into one of these three chemical classifications. The nomenclature is a clue to the properties of the oil, since the properties of the oil are governed by its composition. The nomenclature system as applied to petroleum oils does not have the precision with which it can be used in the organic chemistry of pure hydrocarbons, and the significance and limitations of the type designation of lubricating oils will be discussed further in the following sections of this chapter. Figure 1 6 - 1 is a schematic diagram of the refining of a paraffinic lubricating oil. The total overhead take-off of the crude still, of course, includes all the cuts from the lightest naphtha to the heaviest lubricant distillate; Fig. 1 6 - 1 shows only the raw lubricant cuts, the number and nature of which depends on the way the particular refinery is being run. Each raw lubricating distillate is put through the solventrefining step, whereby selective extraction with a solvent system removes the aromatics and the sulfur and nitrogen heterocycles, leaving the treated oil behind as a separable phase. Most of the extraction processes in the U. s. operate with phenol as the solvent, but other solvent systems such as furfural o r nitrobenzene are used also. The waxy raffinate from the solvent-extraction process is mixed with methyl ethyl. ketone, chilled, and filtered to remove the precipitated wax, after which the ketone is distilled away from the dewaxed oil. The undistilled residue in the crude still can be made to yield a high-viscosity lubricant, used mostly in heavy-duty gear oils, by treating it with liquid propane under pressure to precipitate resins and asphalt and then putting the material recovered from the propane solution

475

[TI

Waxy raffinate to dewaxing

Heavy reduced crude bottoms

.-P c

Deasphalted propane extract

Heavy waxy raf f inate .

;E 0)

b C

-g0

Residual extract

cn

Resin ,asphalt ,etc.

-

Waxy raffinate __------

m p .5

! 8 20 + u a c

Z-O

P

I

.E

c u)

+ o

Dewaxed raffinate '

+

5 2

s

Refined lubricatq

,oil

b

through the phenol extraction and dewaxing procedures. Formerly the final step in the refining process was treatment with adsorbent clay and filtration. This had the double function of improving the color of the oil and removing the last traces of undesirable substances such as heterocyclic compounds, the residues of solvents, etc. Clay treatment is now largely replaced by hydrofinishing, which is light hydrogenation at moderate temperatures over a suitable catalyst. Solvent extraction is successful as a refining procedure only with stocks of paraffinic character. Raw stocks which have too much naphthenic character do not respond to solvent extraction. For some purposes the properties of naphthenic oils are desirable and there are procedures used specifically to obtain these special stocks from naphthenic crudes. Figure 16-2 is a schematic diagram of the refining of naphthenic oils. The final step in the modern process is hydrofinishing; the older process used a sulfuric acid treatment instead to reduce the content of aromatic compounds.

476

1

Refined lubricating

Figure 16-2.

Bottoms Typical refining scheme for naphthenic lubricating oils.

White oils are prepared by drastic further treatment of lubricant stocks. In the older process the appropriate stock was subjected to successive treatments with sulfuric acid until the refined oil met the desired specifications. Acid-treatment is still used to refine white oils because the other products of the process, mahogany petroleum sulfonic acids, are valuable and useful in their own right. The modern process for making white oils utilizes a severe double hydrogenation followed by clay bleaching. 16.2.

NOMENCLATURE AND CLASSIFICATION OF PETROLEUM O I L S

Classificatory designations and systems for petroleum oils have arisen in various ways and for various purposes. Some have developed in a grossly empirical fashion, such as the familiar SAE grades, which is a system of broad viscosity brackets principally for application to the lubrication of automotive engines and rear-axle gearing. Sometimes oils e.y., acid-treated, are designated by the way they were refined: hydrogenated, phenol-extracted, etc. A logical basis for the classifica-

tion of petroleum lubricants is according to chemical type: i.e., finic, naphthenic o r aromatic.

paraf-

In the nomenclature of petroleum oils, the designations panaddinic and ahamatic have the same standard meanings that they do in textbooks of organic chemistry. Paraffinic hydrocarbons are precisely defined by the generic formula CnH2n+2. n-Hexadecane (cetane) is an example of a straight-chain paraffinic hydrocarbon; 2,2,4,4,6,6,8-heptamethylnonane is an example of a highly branched hexadecane isomer. Aromatics are ring compounds characterized by a typical conformation of conjugated double bonds: e . g . , benzene, naphthalene, anthracene. Naphthenes are not so precisely definable; the terminology is used as a broad designation for various types of saturated rings which occur in petroleum fractions. One class of naphthenic structure is the polymethylene ring:

417

CH2

CH2

The term naphthene is also applied to fully hydrogenated condensed such as, for example, decahydronaphthalene

CH2

,p?? /CH2

CH2

and to saturated dicyclohexylethane

rings

/ CHZ-cH CH 2

\CH~-CH

linked

2

CH2

by a polymethylene bridge such as 1 ' 2 -

\

/ CH2-CH2

/ CH-CH2CH2-CH 2

rings

, \

CH2

\CH2-CH2

These are types of basic naphthenic ring structures; substitution of alkyl side chains in the ring is theoretically possible and in fact does occur. Petroleum oils are classified as paraffinic, naphthenic o r aromatic according to the preponderance of basic hydrocarbon structure in their composition. Table 1 6 - 2 gives some representative data for the lubricant stocks produced by a commercial refinery. For the oils classed as paraffinic, an average of 66% of the carbon atoms occur in the paraffinic chains, whether the product is a distillate or a residual oil. This does not necessarily mean that the paraffinic structures are all there as paraffinic hydrocarbons; some of these structures are undoubtedly to be found as side chains on the naphthenic o r aromatic rings. For the less thoroughly extracted oils of 85 viscosity index there is a perceptible gain in the percentage of aromatic carbon at the expense of both the paraffinic and the naphthenic carbon. The distillates obtained from naphthenic crude are substantially higher in both naphthenic and aromatic carbon and lower in paraffinic carbon than the 95 viscosity index paraffinic oils obtained by solvent extraction. I t is quite apparent that the classification of petroleum oils as paraffinic, naphthenic or aromatic has a sound basis in hydrocarbon chemistry. But because petroleum oils are mixtures of hydrocarbons of various types, structures and molecular weights, there are no sharp boundaries between the different classes. Classification of petroleum lubricating oils according ts the type of crude they come from o r the refining procedures used to obtain them is neither illogical nor grossly empirical. The physical and chemical properties of an oil depend on its composition, which in the last analysis is determined by the composition of the crude. Thus the nature

TABLE 16-2.

CARBON TYPE DISTRIBUTION IN LUBRICATING O I L S

9 5 VI paraffinic type distillate

Mean viscosity SUS/lOO F 60 80

110 ( a ) 130 160 200 200 ( a ) 500 600

Paraffinic type residuals

Paraffinic Naphthenic Aromatic carbon, % carbon, % carbon, 9 67 67 61 65 66 66 63 70 68

30 32 27

28

2 4

Avge. 6 6

30

4

34

31 31 29

28

3 1

12

Mean viscosity SVS/lOO F 2500 2700 6000

1 3 3 8

Paraffinic NaDhthenic Aromatic carbon, % ca;bon, % carbon, % 5

70 80

25 23

60

26

9 14

Avge. 6 6

25

9

Naphthenic type distillates 50 100 300 1200 2000 5000

( a ) Viscosity index 8 5

38 37 39 40 38 43

48 47 45 46 48 42

13 16 16 14 14 15

Avge. 3 9

46

15

-___

479

of the crude governs both the refining process by which it is treated and the product which results. For example, one would not expect to see a distillate fraction from a naphthenic crude treated by solvent extraction to produce a paraffinic oil. And designation of an oil in terms such as "a hydrofinished fraction from a Texas coastal crude," for instance, will have basic cocnotations beyond just ordinary empirical description. Whereas acid treatment removes aromatic compounds from the raw distillate, hydrogenation alters them chemically and leaves the altered material in the finished oil. Petroleum lubricating oils are sometimes characterized by their density. As will be seen when we come to the examination of chemical structures i n lubricating o i l s later in this chapter, density is associated with structural type. Paraffinic oils are lower in density than naphthenic or aromatic oils. Since paraffinic oils show more desirable viscosity-temperature behavior and better thermal stability than naphthenic oils, in the past density was widely used as an easily measured indicator of oil quality. With the development of additives to improve viscosity and thermal stability behavior, classification of oils by their density ratings has lost much of its former importance. Density is frequently referred to in the specialized literature of petroleum technology a s "gravity" and is reported in "degrees API." This is calculated from the specific gravity by the formula [2]: 141.5 API Gravity, degrees =

-

131.5

specific gravity ( 6 0 / 6 0 F ) Since the specific gravity of petroleum oil is less than unity, it is immediately apparent that its API gravity is greater than unity and that as specific gravity decreases, API gravity increases. The API gravity of a paraffinic oil is greater than that of the analogous naphthenic or aromatic oil. The API gravity system was originated to give a higher "quality number" to paraffinic oils. Lubricating oils are also classified by viscosity, chiefly to guide the blending of refinery stocks to furnish compounded oils of the required viscosity specifications. Oils are available directly from refinery streams in only a limited number of viscosities, covering a range from approximately 8.85 x m2/s at 4 1 1 K (55 Saybolt seconds at 100 F) for light distillate to 1079 x m2/s (5000 SIX) for the heaviest. Bright stocks and other fractions derived from still residues to 1295 x have viscosities which cover the interval from 539 x Viscosity by itself does not at 4 1 1 K (2500 to 6000 SUS at 100 F). m2/s necessarily have a direct relation to the constitution of an oil, but the temperature-dependent behavior of viscosity does. The usual paraffinic base oils of commerce, which are prepared by solvent extraction, have

480

values of the viscosity index ranging from 80 to 100. ,The viscosity index of naphthenic base oils lies generally in the range zero to 30. The implication of viscosity index values in terms of structure is obvious. 16.3.

STRUCTURES IN LUBRICATING OILS BY DIRECT TECHNIQUES

Except for a few untypical instances, such as the separation and identification of perylene and of 1-methylchrysene, no pure compounds have been isolated from fully refined lubricating oil fractions. Many of the properties which make cil desirable as a lubricant-viscosity behavior, low solidification temperature, poor crystaliinity of the solid phase-are the consequences of a complex mixture of compounds from which it is extremely difficult to separate identifiable single components. But all these difficulties notwithstanding, the study of chemical structures in petroleum lubricating oils has made remarkable progress. The underlying basis for this progress has been the interplay between the techniques of macroscopic separation of the oil into fractions and the investigation of these fractions by instrumental methods, particularly high-temperature mass spectrometry. An instrumental method of analysis in general responds indiscriminatsly to the physical or chemical function for which it is I f molecules of different chemical structure in a mixture calibrated. are associated with the same functional stimulus, then instrumental analysis may not tell anything about the composition of the mixture. Sometimes, with the aid of additional information about a given type of mixture, it is possible to establish empirical correlations that make instrumental determinations into useful methods of analysis. This we designate as the indirect technique. In contrast, direct techniques for determinin5 structures in lubricating oils involve considerable macroscopic separation to minimize the heterogeneity of the fractions and thus make it feasible to work from relatively straightforward analytical determinations. Instrumental methods become informative when applied to fractions obtained by macroscopic separation and purification procedures. We shall examine the results of some investigations based on techniques below. 16.3.1, Extraction, Spect rography

Chromatographic

direct

Adsorption, Distillation and Mass

Let us examine how structure types were assigned to one aromatic and six naphthenic-paraffinic fractions separated from the lubricating oil portion of the Midcontinent petroleum investigated in API Project 6. These fractions were prepared from the material which comprised the 83rd

to the 93rd percentile of the total petroleum (ranked by volatility), follows:

as

481

( c ) extraction of the raw lubricant distillate with liquid S O 2 ;

( 6 ) dewaxing of the raffinate with ethylene dichloride; ( c ) chromatographic

separation

of

the

dewaxed raffinate to yield a

water-white oil;

( d ) fractional distillation of the water-white oil; ( e ? reflux extraction of the water-white fractions with acetone;

(6)

fractional distillation of the extract soluble in

SO2;

! y ) reflux extraction of the S02-extract fract ons with acetonitrile.

Details of the actual process can be found in pub ished the work [ 5 , 6, 7, 83.

descriptions

of

The six fractions of the water-white oil (selected from a total of and the one of aromatic extract (out of a total of 170) are listed in Table 16-3, which gives their pertinent physical properties. The most informative single physical property of each fraction is the specific refractive dispersion. The characteristic value of this property for paraffinic and aromatic-free naphthenic ring hydrocarbons is 98. Aromatic and unsaturated hydrocarbons show an exaltation of specific dispersion over this value, the amount of which depends on the specific nature of the hydrocarbon. In Table 16-3 it is readily seen that Samples 1 - 6 of the water-white oil are paraffinic or naphthenic, whereas Sample 7 is obviously aromatic. This is shown also by the relatively higher refractive index and the higher density for its average molecular weight and by the large deficiency of hydrogen in the C/H ratio.* 204)

These seven samples were examined in 14 different laboratoties by infrared, ultraviolet and mass spectrography. The mass spectrographic results are the most revealing. Table 16-4 gives the distribution of molecular size i’n the various samples according to the number of carbon atoms in the molecule. These results were obtained from parent-peak data. The occurrence of pronounced maxima in the distributions shows resolution into fraction groups centered on four o r five adjacent molecular sizes. Parent-peak mass spectrography cannot densed polycyclic naphthene, e . ~ .

distinguish

between

a

con-

*Confusion of an aromatic deficiency in hydrogen with a polyolefinic deficiency is easily resolved by infrared or ultraviolet absorption spectrography.

TABLE 16-3.

PROPERTIES OF FRACTIONS FROM WATER-WHITE OIL

Sample No. Formula

1

2

3

4

& . 00 N

6

5

7

C27.8H55.6 C27.6H53.2 C 29.8H 57.6 C 34.4 H66.8

C

x in ‘nH2n+x (b)

0.0

-2.0

-2.0

-2.0

-4.0

-2.1

-11.2

Boiling pt., O c at 1 mm Refractive index, n D at 25 C Density, d , at 25 C , g/ml Kin. viscosity, cs at 100 F Kin. viscosity, cs at 210 F Viscosity index Specific refraction (c) Specific dispersion (d) n in ‘nH2n+x (e)

207

204

222

249

204

222

215

1.4607

1.4729

1.4713

1.4730

1.4836

1.4722

1.5180

0.832

0.861

0.860

0.860

0.878

0.862

0.9348

19.77

34.83

39.80

63.18

68.54

41.95

146

4.10

5.26

5.89

8.15

6.95

6.01

9.71

137 0.330

90 0.325

99 0.325

104 0.326

39 0.323

95 0.325

0 0,3242

99

99

99

99

99

99

132

27.4

27.2

29.6

33.7

27.4

29.0

-0.3

-2.2

-1.9

-2.2

-3.9

-1.9

x in ‘nH2n+x

H C H 27.7 51.4 29.8 57.5 C28.3H45.4S0.0400.08(a)

(e)

( b ) By direct elemental analysis. (c) Specific 4 (l/d)(ni - l)/(ni + 2). ( d ) Specific dispersion = 10 (n, - nC)/d. spectrography. From data published by Mair and Rossini [91. (a) Fraction from extract.

refraction

=

(e) From mass

483

TABLE 16-4. MOLECULAR SIZE DISTRIBUTION IN OIL FRACTIONS BY MASS SPECTROGRAPHY

No. of carbon atoms/mol ec ule

Volume-percent in sample (a) 1

22 23 24

25 26 27 28

29 30 31 32 33 34 35 36 37 38 39

3

2

5

4

1 2

1 2 1 4 2 9 4 17 6 19 8 19 14 9 26 4 1 5 1 1 2 7 3 1

2

4 7 14 26 24 12 7 3 1

4 9 1 19 5 23 a 18 14 13 21 8 2 0 3 1 4 10 5 2

6

1 3

4 9 14 17 17 13

7(b)

4 12 22 23 19 12 6 2 1

10

7 4 1

(a) For identity of samples see Table 16-3. (b) Fraction tract. From data published by Mair and Rossini 191.

from

ex-

/ y 2

I

I

C

CH2 \

/fi \cH2/ CH2 and its bridged, non-condensed isomer: \

CH7 -

/

/

\ CH*-CH~

CH2

/CH2-CHZ CH-CH2-CH

-

\ CH2-CH2

\ /

CH2

/

This problem can be resolved by the fragment-peak technique, which, however, suffers from the disadvantage that sometimes the naphthenic rings are altered by the impact energies required to fragment the side chains. Aromatic rings are stable in the fragment-peak analysis. Table 16-5 illustrates the information about the structure of an o i l that can be obtained by combining the two mass spectrographic techniques. Naphthenic ring compounds are the major constituents of the five fractions listed, the proportions ranging from 70 to 95 volume-percent. As the proportion of condensed dicyclic and tricyclic naphthenes increases, the proportion of paraffins decreases. Non-condensed cycloparaffins cluster in the range 39-49 volume-percent, dropping n o lower than 37 per-

484

TABLE 16-5. MOLECULAR TYPES IN FRACTIONS FROM WATER-WHITE OIL BY MASS SPECTROGRAPHY Type of hydrocarbon

Vo 1 ume-pe rc en t ~

Normal paraffins Branched paraffins Non-condensed cycloparaffins Condensed dicycloparaffins Condensed tricycloparaffins Condensed tetra- and higher cycloparaffins Aromatics

1

2

3

4

2 28 49 15 5

2 10 46 23 11

8 15 39 21

0 18 40 25 10

1

7 1

7 1

0

9

5

6 1 .

0 2 37 25 17 16 3

From data published by Mair and Rossini [9].

cent even in the fraction tetracyclic naphthenes.

with 33 percent of condensed tricyclic and

Mass spectrographic examination of the extract material of empirical composition C28.3H45,4S0.0400.08 (Sample 7 in Table 16-3) indicated that it is made up largely of molecules with one aromatic ring attached to from zero to four or more cycloparaffin rings (2.5 on the average) and to paraffin side and connecting groups [ 9 1 . Of the constituent molecules, 8 7 % contain a mononuclear aromatic ring, 6% are dinuclear aromatics and 7% are condensed multiring naphthenes with no aromatic components at all. 16.3.2. Distillation, Extraction, Diffusion and Mass Spectrography

Chromatographic

Adsorption,

Thermal

Melpolder, Brown, Washall, Doherty and Headington [lo] carried the findings of the direct techniques a step further by the use of improved separation and spectrographic methods. They started with a solventextracted, dewaxed distillate, molecular weight 540, viscosity 99.5 centistokes at 100 F , refractive index n D 1.4640 at 70 C ; and from this by a program of fractional distillation and solvent elution from silica gel they obtained a heart cut of molecular weight 474, viscosity 88.7 centistokes at 100 F, viscosity index 101, n D 1.4588 at 70 C and a pour point of 10 F. This heart cut was separated into 43 consecutive fractions by thermal diffusion, a process which segregates molecules by structural type but is relatively insensitive to molecular weight. Table 16-6 shows the properties of 16 key fractions out of the forty-three, and Table 16-7 shows the distribution of molecular types in these fractions, computed from mass spectrographic data. Melpolder and his co-workers found that the paraffins in all 43 fractions were branched-chain molecules. By comparison of Tables 16-6

TABLE 16-6.

PHYSICAL PROPERTIES OF KEY FRACTIONS OF THERMALLY DIFFUSED LUBRICATING OIL

Fraction Viscosity, c s Viscosity index 100 F 2 1 0 F

Density at 7 0 C

Refractive index, n D at 7 0 C

Pour Molecular wt. C/H ratio, point, by weight deg. F (a) (b)

~~

1 2 3 5 9

11 16 21 22 26 32 34 37 38 42 43

25.0 28.2 30.4

30.5 39.2 42.3 50.4 61.0 64.1 86.1 139 199 439 123

__ __

5.74 6.05 6.24 6.11 6.87 7.10 7.68 8.33

__

9.73 12.0

167 158 153 150 136 132 123 114

100 79

~

19.6 24.1 110 215

32.5 11

0.808 0.813 0.813 0.818 0.822 0.824 0.830 0.840 0.842 0.852 0.865 0.875 0.891 0.897 0.941 0.952

1.4402 1.4422 1.4437 1.4442 1.4461 1,4465 1.4486 1.4528 1.4536 1,4578 1.4632 1.4669 1.4735 1.4767 1.4947 1.4995

65 55 45 35 15 5 -15 -30 -30 -20 -10

0 20 35 95 115

482

-

5.87

461

~

413 478 480

-

5.82

_ .

__

6.01

476

487

6.28 6.32

491

-

6.59

490

-

475

488

_ .

-6.94

~~

( a ) Mass spectrographic.

( b ) Ebullioscopic.

From data by Melpolder e t a t .

[lo].

TABLE 16-7. MOLECULAR TYPES OF THERMALLY DIFFUSED KEY FRACTIONS OF LUBRICATING O I L BY MASS SPECTROGRAPHY % IsoFraction parafnumber, fin (a)

1 2 3 5

70.1 57.4 54.4 49.2 45.6 47.1 36.0 24.7 21.7 16.2 9.4 4.6 3.9 3.8

9 11 16 21 22 ,26 32 34 37 38 42 43 Composite (c) 25.8 Total oil (d) 26.3

% Monocycloparaf- Difin and noncondensed cycloparaffin

%

Condensed-ring naphthenes

%

Tri- Tetra- Penta- Hexa- Hepta- Octa-

24.4 36.1 38.2 40.8 33.8 32.8 37.6 42.2 40.2 40.2 37.7 37.8 33.3 34.1 23.2 25.9

3.8 5.2 6.3 8.7 18.8 18.2 23.1 26.1 29.5 29.1 31.4 27.2 23.5 20.9 18.9 16.1

36.37

21.7

7.5

36.9

19.8

7.0

0.1 0.2 - 0.2 0.1 0.2 0.4 0.1 0.4 0.2 0.9 0.9 2.6 0.4 0.9 3.1 1.0 9.0 14.4 2.1 16.5 6.1 20.1 7.9 18.7 10.1 22.8 11.1 9.7 21.9

0.2 -

-

- _ _

0.1 0.1 0.1 0.1 0.6 0.8 1.1 1.2 2.5 4.2 4.3 9.5 8.3

0.1 0.2 0.2 0.4 0.9 1.4 1.4 3.3 4.8

1.0 0.6

-

2.9

1.8

0.6

0.06

0.03

1.4

1.6

0.5

0.1

0.9

0.5 0.7

Phenyl % Indan % Naphthalene (b)

1.2 1.3 0.9 0.9 1.2 1.2 1.4 3.3 3.5 3.1 3.2 3.7 5.1 5.8 8.7 10.2

(a) Fraction number as in original reference: Melpolder e t aL. [lo]. spectroscopy. (c) Composite of all 43 thermal diffusion fractions. thermal diffusion.

___ -

I

__

0.5 0.2 0.5 0.3 1.0

0.1 0.1 0.1 0.2 0.4 0.4 0.7 0.8

2.96

0.12

0.14

4.9

0.5

0.1

0.1

(b) By ultraviolet (d) Total oil before

487

and 1 6 - 7 , it is seen that the isoparaffin content of the fractions listed there progressively decreases, while the viscosity increases and the viscosity index decreases. This behavior is characteristic of the entire series of 4 3 fractions described in the published report [ l o ] . A s in the work reported by Mair and Rossini [ 9 ] , pronounced progressive decrease in paraffinic molecules is counterbalanced by similarly pronounced increase in condensed polycyclic naphthenes, the content of monocycloparaffins and non-condensed cycloparaffins changing relatively much less from fraction to fraction. I n this respect the findings of Melpolder tt aL. [ l o ] parallel those published by Mair and Rossini 1 9 1 . The improved resolution of the mass spectrographic techniques employed by Melpolder e t at. shows the progressive increase in the proportion of polycyclic naphthenes as the content of isoparaffins decreases, and this can be correlated with the increase in viscosity. The changes in these important physical constants can be ascribed to the moiecular composition of the fractions, since, as is seen in Table 1 6 - 6 , the molecular weight remains relatively unchanged over the entire series of fractions. The relation between viscosity index and molecular constitution is somewhat obscured by the appreciable content of phenyl rings in even the most paraffinic of the fractions, but it is quite apparent that increase in the degree of condensation in the polycyclic rings influences the viscosity index adversely. 16.3.3.

Mass Spectrography of Refinery-Run Fractions

The investigations described above were carried out on fractions which had been separated with a great deal of rigor to insure that they were saturated hydrocarbons, i.e. that the constitutive groups were

TABLE 16-8.

PROPSRTIES OF REFINERY-RUN MEDIUM-VISCOSITY LUBRICANT STOCKS I

I1

111

IV

V

VI

VI I

Viscosity, SUS at 1 0 0 F at 2 1 0 F Viscosity index Pour point, deg F . Sulfur, % Mol. weight (a)

261.5 49.54 91 5

262.0 49.67 93 10

249.6 49.82 105 10

412.0 53.5 53 -25

548.0 55.9 29 -10

185 46.5 116 70

309 48.4 40 -30

0.06 418

0.14 433

0.11 432

0.28 410

0.53 358

0.03 332

0.15 332

Density, d':

0.8754

0.8736

0.8762

0.8960

0.9158

0.8705

0.9075

20 index, nD

1.4814

1.4829

1.4847

1.4897

1.5029

1.482

1.5010

Sp. dispersion

103

104

113

102

116

113

120

Refractive

(a) Ebullioscopic.

Data by Andrg and O'Naal [ l l ] .

488

either paraffinic or naphthenic and nothing else. This, of course, eases some of the difficulty in assigning structure from analytical data. In contrasr: is the study of Andrg and O'Neal [ 1 1 1 on the mass spectrographic analysis of seven refinery-run medium-viscosity lubricating stocks, characteristics of which are listed in Table 16-8. Oils I and 111 were obtained from Texas crudes, Oils IV and V from California crude, and Oil 11 from Oklanoma crude. Oil VI was a Pennsylvania stock oil and Oil VII was a Gulf Coast "naphthenic" stock. It is obvious from the specific refractive dispersion values that all the oils had appreciable proportions of aromatic constituents. The oils were separated into saturated and aromatic fractions, which were then analyzed by suitable mass spectrographic methods. Table 16-9 shows the composition of these fractions by molecular type. Since the original lubricant stocks had been refined by solvent extraction o r acid treatment, it is not unexpected that the bulk of the aromatics fall into the two-ring rather than the higher ring category. The sulfur compounds found in commercially extracted lubricant stocks become part of the aromatic fraction in an analytical separation by silica gel. 16.3.4. Nature of the Alkyl and Aromatic Structures I t is apparent from the data in Table 16-7 that the conde,nsed rings found in the thermally diffused oil whose analytical breakdown is given there must carry alkyl substituents. The entire input oil can be regarded as homogeneous in molecular weight; therefore, in a condensed bicycloparaffin of molecular weight 474, 24 methylene groups must be accounted for in the structural analysis. If the assumptions about the homogeneity of the molecular weight are valid, then the number of sub-

stituent side chains on the ring nucleus can be evaluated by analytical techniques which assay the number of methyl groups: for example, infrared absorpLicn spectroscopy or nuclear magnetic resonance spectroscopy. Lindeman [121 found NMR evidence that the substituents in complex ring molecules are numerous short-chain groups, e . y .

whereas monocyclic and condensed dicyclic structures have side chains the type

of

489

CH3

Hood, Clerc and O'Neal [ 1 3 ] have reviewed the evidence for the nature of side-chain substitution and favor one long chain and one or two short chains in condensed polycyclic structures with up to three rings. However, their physical evidence is for aromatics rather than naphthenes with cycloparaffinic rings. Hood, Clerc and O'Neal [ 1 3 1 also discussed the nature of the alkyl chains i n lubricating o i l fractions. Whereas petroluem waxes a r e mostly n-alkanes with some isoalkanes and substituted cycloalkanes, the alkanes TABLE 16-9.

STRUCTURAL TYPES IN REFINERY-RUN LUBRICANT STOCKS

Hydrocarbon type

I soparaf f i n s Cycloparaffins noncondensed condensed Total saturates

Volume percent IV

v

VI

VII

I

I1

I11

12.7

15.7

11.0

2.1

1.0

20.5

6.2

46.0 26.5 85.2

44.3 21.9 81.9

44.4 20.5 75.5

43.8 36.4 82.3

34.1 29.3 64.4

40.5 18.1 79.1

37.8 26.6 70.6

5.3

6.1

8.0

4.3

8.0

7.8

6.8

3.5

3.9

6.0

4.1

6.8

3.6

5.4

1.8

1.9

2.5

2.6

4.7

2.4

4.2

10.6

11.9

16.5

11.0

19.5

13.8

16.4

1.4

1.6

1.9

1.2

2.9

1.9

3.5

0.8

1.1

1.5

0.7

2.0

1.1

2.2

0.6

0.9

1.1

0.6

2.3

1.3

2.4

2.8

3.6

4.5

2.5

7.2

4.3

8.1

Monoaroma t ic s

c Total monoaromatics Diaromatics

Total diaromatics

490

TABLE 16-9 (continued) Hydrocarbon type

Volume percent

I

I1

I11

v

IV

VI

VII

Triaromat cs

0.37

0.55

1.0

0.44

1.1

1.0

1.3

0.05

0.06

0.25

0.02

0.51

0.26

0.34

0.4

0.6

1.2

0.5

1.6

1.3

1.6

0.05

0.12

0.53

0.06

0.40

0.56

0.48

0.02

0.04

0.12

0.00

0.12

0.20

0.12

Total tetraaromatics

0.07

0.16

0.65

0.06

0.52

0.76

0.60

Sulfur compounds

0.7

1.8

2.2

3.6

6.8

0.8

2.7

'

I

'

' -/..I A.i.,

+

Tota 1 t r la roma t ics Te t raaroma t ic s -

\'? -

;-\ \--

L-

,

I

+

?

\

*,

, I

\ L

>+'

Data by Andr6 and O'Neal [ l l ] .

in dewaxed lubricating oils are branched, with situated near the end of the pr ncipal chain.

the

branches

short

and

The aromatic constituents of raw lubricant distillate are of little direct interest to the lubricat on engineer except for that portion which is not removed from the iubricating oil by commercial extraction or other processing. The character of this material is shown in some detail in Table 16-9. Organosulfur, organonitrogen and oxygenated material tends to go with the aromatic fractions ( s e e Tables 16-3 and 16-9). Mair and Martingz-Picg [ 141 isolated and identified 4-methyldibenzothiophene, 4,6dimethyldibenzothiophene and benzo[b]naphtho[2,1-d]-thiophene. Mikhailov and co-workers [15] reported the presence of 1.5-2.7% of benzothiophenes in Russian 100 VI lubricating stocks of 0.85-0.92% sulfur content.

491

16.4. TYPE STRUCTURES IN LUBRICATING OILS BY CORRELATION PROPERTIES: INDIRECT METHODS

WITH

PHYSICAL

Macroscopic separation of a lubricat ng oil into fractions is tedious and laborious, and from the viewpoint of petroleun technology and lubrication engineering, characterization of an oil by methods which require such separations is not practical for ordinary purposes. Consequently, side by side with procedures directly based on fundamental data, there are also indirect methods of assaying petroleum lubricating oils for type structures via trends displayed by physical properties such as viscosity, density and refractive index. The development of the necessary correlations, involving a s it does a great deal of curve fitting and outright empiricism, will not be shown in detail here. There is no unified reference which treats all the significant correlation systems adequately, and the interested reader must therefore go to the individual sources. King, Kust and Kurtz 1161 list six different methods, the essentials of which are outlined in Table 16-10. ?he n-d-M method (n is refractive index, d is density and M is molecular weight), which is one of the methods most frequently cited, is described in detail in the book by van Nes and van Westen [ 1 7 1 . The equations of correlation f o r this method define total ring content, percentage of carbon in rings, aromatic ring content and percentage of carbon in aromatic rings; hence the naphthenic and paraffinic carbon content can be calculated by difference. The working equations are given in Table 16-11. For best accuracy the equation applicable to an oil with high content of aromatics is different from the equation for an oil of iow aromatic content. The calculations have been derived for values of

TABLE 16-10. PHYSICAL CORRELATION METHODS FOR CARBON TYPE ANALYSIS Designation

Physical properties utilized

n-d-M

Refractive index, density, molecular weight

Refractivity interceptkinetic viscositygravity constant

Refractive index, density, viscosity (in centistokes)

(hi-KVGC)

Refractivity interceptRefractive index, density, viscosity viscosity-gravity constant (in Saybolt seconds) ( hi-

VGC )

Refractivity interceptdensity (hi-density)

Refractive index, density, number of carbon atoms (from viscosity)

Boelhouwer-Waterman

Refractive index, density, viscosity

Cornelissen-Waterman

Refractive index, density, viscosity

ri-\

W

N

TABLE 16-11. Formula for

low range 0.44 + 0.080

RA % ‘A

‘A

R

high range

M

(2.51 An

-

Ad)

3660/M + 670 (2.51 An - Ad) 0.41

RA

%

FORMULAS OF THE n-d-M METHOD

+

0.080

M

(2.42 An - Ad)

3360/M + 720 (2.42 An - Ad) 1.33

+

0.180

M (Ad - 1.11 An)

0.44

+

3660/M

0.055

Temperature (a)

M

(2.51 An

0.41 + 0.055

M

(2.42 An - Ad)

410 (2.42 An - Ad)

c

20

c

70 C 70 C

+

1.33

0.146M

Ad - 1.11 An)

20

820

A d - 1.11 An)

20

+

10OOO/M

R

1.55 + 0 . 1 8 0 M (Ad - 1.11 An)

1.55 + 0.146M

Ad

% CR

12100/M + 1440(Ad

11500/M

Ad

1.11 An)

20

3660/M

10600/M + 1440(Ad - 1.11 An)

-

Ad)

430 (2.51 An - Ad)

+

% C

R

-

+

+

775

-

c c

1.11 An)

70 C

1.11 An)

70 C

(a) For refractive index and density data. R = total number of rings per molecule. RA = aromatic rings per molecule. % CR = percent of carbon in total rings. % CA = percent of carbon in aromatic rings. n = refractive index. d = density. M = molecular weight. Formulas by van Nes and van Westen [ 1 7 1 , p. 323.

493

the refractive index and density taken at either 2 0 C o r 7 0 C . The formulas for the n-d-M method

were

obtained

by

an

elaborate

scheme of empirical calibration based on the observed behavior of many different oil fractions. F o r a given fraction, the mean molecular weight and the density are determined, and the fraction is then hydrogenated completely; the number of aromatic rings can be computed from the It was shown by van Nes and van Westen [ 1 7 1 that the hydrogen uptake. number of rings in a particular structural category (aromatic, naphthenic or total rings) can be expressed by a relation of the form

R = a'

+

b'MAd

+

c'MAn

and the percentage of carbon occurring as the ring structure by

a %C =

-

+ bad + c A ~

M

where a, a ' , b , b ' , c , c ' are constants and Ad and An are the differences between the measured values of the density and the refractive index and the extrapolated values of these physical properties for the limiting paraffin, i . e . the hypothetical n-alkane of infinite chain length in the liquid state. Manipulation of the specific relations in the two formats given above yield the numerical equations shown in Table 1 6 - 1 1 . The h i - K V G C and the f i i - V G C methods do not require determination of the molecular weight. The refractivity intercept is calculated by the formula (16-1)

where n;' is the refractive index at 20 C and d i 0 is the density at 20 C in grams per cubic centimeter 1 1 8 1 . The viscosity-gravity constant is an oil characteristic recognized by ASTM I 1 9 1 and is computed from the relation l o g A p - 1 . 0 7 5 2 Log ( v n - 3 8 )

VGC

=

10 - Locj ( v *

-

38)

(16-2)

where g is the specific gravity at 6 0 / 6 0 F and v h is the viscosity in hlJ Saybolt seconds at 100 F. The kinematic viscosity-gravity constant is Its formula is described by Smith [ Z O ] .

KVGC =

d i O - 0.1384 Lay ( v

-

20)

- Log ( v

-

2011

0.1526

r7.14

+

0.579

(16-3)

where v is the kinematic viscosity in centistokes at 2 0 C. Within a limited but useful range of composition the viscosity-gravity constant (either VGC or K V G C ) and the refractivity intercept are linearly related

494

to the percentages of aromatic naphthenic and paraffinic carbon in an oil. By combining the two linear relations in a triangular composition diagram, Kurtz and co-workers [ 2 3 developed a method whereby determination of refractive index, density and viscosity could be used to assay the hydrocarbon types in an oil. The method, of course, required empirical calibration. A similar approach was used by Kurtz, King, Stout and Peterkin [22] to develop a correlation method for which the input data were density and refractivity intercept. The Boelhouwer-Waterman method [23] and the Cornelissen-Waterman method [241 depend on correlations similar to those used for the hi-KVGC method. The typical output of an indirect correlation analysis gives the rings, percentage of the total carbon distributed among aromatic naphthenic rings and paraffinic (alkyl) chains. There are a number of assumptions implicit in such results, depending on how the particular correlation method was calibrated. The usual assumption is that the percentage of carbon atoms in aromatic rings and the total number of rings are known exactly, since this part of the calibration depends on the direct data obtained from hydrogenation of the oil. Calculation of the number of aromatic ring and of the percentage of carbon in naphthenic rings assumes that the ring systems are built up of six-membered katacondensed rings. Percentage of paraffinic carbon is taken to be the Boelhouwer-Waterman and residual difference from 100%. The n - d - M , Cornelissen-Waterman methods use all these assumptions. The hi-VGC method and the hi-density method use the assumptions about aromatic carbon atoms and total rings but in addition have special calibrating assumptions about the size and the degree of condensation of rings which stem from analysis of properties of hydrocarbons of known structure. The h . - KVGC method is calibrated from experimental data obtained from A. aromatic-free petroleum oils and pure compounds. King, Kust and Kurtz [161 compared the results of the analysis of 44 different petroleum oils and oil fractions by the six correlation methods listed in Table 16-10. The deviations of the average results for all the oils by each method from the average "best analysis" for all the oils ranged from -0.2 to +1.8 for percent aromatic carbon ( % CA), -3.0 to + 0 . 5 for percent naphthenic carbon ( % C,) and -2.3 to +1.6 for percent paraffinic carbon ( % Cp). The magnitudes of the standard deviations from the "best analysis" were somewhat larger: 1.5 to 3.1 for % C A , 2.6 to 4.7 for The six methods were also applied to 154 % CN, and 2.1 to 4.6 for % Cp. pure hydrocarbons of known structure. The figures for the deviations of the average results from the correct analysis are: %CA, -2.1 to + 0 . 1 ; % CN, -0.7 to +5.2; % Cp, -4.7 to +0.7. The range of the standard deviations is somewhat broader: % CA, 3.4 to 11.0; % CN, 9.6 to 17.5; % Cp, 7.1 to 15.5. I t is not surprising that the six correlation methods work

495

as well as they do for petroleum oil, since these methods were calibrated with selected petroleum fractions. The less satisfactory results obtained for pure hydrocarbons indicate that cyclic hydrocarbons adequately characteristic of those found in petroleum lubricating oils have not yet been synthesized and tested. 16.5. TYPE LUBRICANTS

STRUCTURES

AND

THE

PERFORMANCE

OF

PETROLEUM

OILS

AS

For the lubrication technologist the significance of chemical structures in the composition of petroleum oils goes beyond mere classification of such oils as paraffinic, naphthenic or aromatic. Because their borderlines are not precisely distinguishable, these classification categories serve mostly as general indicators of what the lubrication engineer might anticipate about the behavior of the oil in use. The utility of classificatory designations can be extended by examining the details of the relations between the structural types upon which the classifications are based and the functioning of the oil as a lubricant.

50-1

I

I

I

I

I

I

I-

1, lp] I

(b)

0

40

80

120

160 0

40

80

120

160

Viscosity Index

Figure 16-3. Viscosity index and structural types in lubricating oil. (a) Commercial solvent-extracted lubricating stocks. (b) Aromatic-free fractions. 1: Non-condensed cycloalkanes. 2 : Condensed cycloalkanes. 3: Isoparaffins. 4: Aromatics. From data by Andr; and O'Neal [ 1 1 1 .

Viscosity index is a familiar item of technological interest in the physical properities of a lubricating oil. I t is by common experience that aromatics are associated with low values of the viscosity index; when the aromatic-rich extract is separated from raw lubricant distillate, the viscosity index of the extract is lower and that of the raffinate is higher than the original viscosity index of the raw distillate. The diagrams of Fig. 16-3 show the relations betveen viscosity index and structural types in refined oil. Figure 16-3a shows the summed-up contents of the various type categories in Table 16-9 plotted against the values of viscosity index a s given in Table 16-8. Figure 16-3b shows a related plot for the saturated portion of these oils after the aromatic hydrocarbons have been removed. Although the basis for computing volume-

496

percentage is different in Fig. 16-3a than in Fig. 16-3b, it is still obvious that the removal of aromatics from the oils raised the viscosity index. The linear relations depicted in Figs. 16-3a and 16-3b may be forced. The data from which these plots were constructed have some deficiencies in precision and self-consistency. Data of good precision are available from the work of Melpolder c: aL.[lO] on thermally diffused fractions of a petroleum oil, as listed in Tables 16-6 and 16-7;

180 160 140 120 100 % 5 80 8 60

g

-

5 40

20 [ i d , 0

,

,s ,i,1 I

10 20 30 40 50 60 70 Volume-Percent Component Figure 16-4. Viscosity index of fractions from thermally diffused lubricating oil. (a) Isoparaffins. (b) Condensed cycloalkanes. (c) Non-condensed cycloakanes. (d) Aromatics. From data by Melpolder e t

0

ae.

[lo].

Fig. 16-4 is a plot of viscosity index against molecular type made from these data. The relation of viscosity index to isoparaffin content is not linear until the VI attains a value of 100; below that value the viscosity index increases strongly with increasing concentration of isoparaffin and there is a pronounced transition to the linear terminal The relation between viscosity index and conportion of the graph. centration of condensed-ring naphthenes is inversely linear over much of the graph but shows a sharp drop in the VI range 20 to 8. Monocyclic and non-condensed cycloalkanes fluctuate somewhat with VI but lie within the concentration range 33% to 42% for viscosity index values between 10 and 160. The aromatic content drops sharply with increasing viscosity index, but i t should be noted that for this series of oil fractions the maximum level of aromatics is only 7% at a VI of 1 1 . Critical examination of the data plotted in Figs. 16-3 and 16-4 reveals that aromatic content is not the only constituent which influences the viscosity index. Table 16-12 shows data taken from these graphs for the structural type content of various oil fractions at three different levels of viscosity index. I t is obvious that the rise in the viscosity index from 100 to 140 for saturated oils as plotted in Fig. 16-3b cannot be ascribed to decrease in aromatic content. The decrease in the content of condensed-ring naphthenes from 34% to 18% and

497

TABLE 1 6 - 1 2 .

INFLUENCE OF MOLECULAR TYPES ON VISCOSITY INDEX

Molecular type

\'olume-% constituent 1 (a)

I1 (b)

I11 (c)

Viscosity index 3 0 Isoparaffins Aromatics Condensed naphthenes Non-condensed rings

3 29 34 34

3 6 58 33

Viscosity index 100 I soparaf f ins Aromatics Condensed naphthenes Non-condensed rings

13 20 20 45

15 -34 51

17 3.5 38.5 41

Viscosity index 1 4 0 I soparaff ins Aroma t i c s Condensed naphthenes Non-condensed rings

22 16 17 45

32

48

18 50

16 35

-_

1

(a) Commercially refined oils: see Fig. 16-3a. (b) Saturated fraction: see Fig. 1 6 - 3 b . (c) Thermally diffused fractions: see Fig. 1 6 - 4 .

the increase in isoparaffin content from 15% to 3 2 % are highly suggestive of two interrelated influences responsible for the rise in viscosity index. The content of monocyclic and non-condensed cycloalkanes remains virtually unchanged at 5 0 - 5 1 % . The data for the two oils of 30 VI indicate that aromatics and condensed-ring naphthenes are equivalent in their adverse effect on the viscosity index. The positive effect of isoparaffin content is strongest at the lower values of viscosity index: thus, in Fig. 1 6 - 4 we observe that an increase of viscosity index from 11 to 6 5 is characterized by a rise in isoparaffin content from 3% to 6 % (a two-fcld change), while the condensed-ring naphthenes decreased from 5 6 % to 5 2 % (a change of only 7 parts in a hundred) and the aromatics decreased from 7 % to 4% (a change of almost one and one-half times). But, as other evidence shows, the aramatics and condensed-ring naphthenes are equivalent in lowering the viscosity index; hence the observed rise in VI must be attributed directly to the strong positive influence of the modest increase in isoparaffin content rather than to the effect of the matching decrease in aromatics. The data in Tables 1 6 - 6 and 16-7 also show that the magnitude of the viscosity as well as the viscosity index changes systematically with the molecular composition of the oil. This effect must be ascribed to molecular structure rather than molecular size, given the substantially

uniform level of molecular weight of all the fracti0n.s listed tables.

in

these

If it is accepted that the viscous behavior of oils is reponsive to the proportions of rings and chains and their arrangement within the molecular structures, then the lubrication engineer with exacting requirements will be interested in how the oil was refined. Solvent extraction or acid treatment removes a portion of the cyclic components from the raw oil and thus affects the proportion of rings and chains in the raffinate. Strong hydrogenation converts aromatic rings to naphthenes; the type of rings is altered by this treatment but no portion of the cyclic compounds are removed from the raffinate. Thus, replacement of acid treatment by hydrogenation in the processing of naphthenic

oils has a noticeable influence on the properties of market.

such

oil

for

the

Another important area of technological utility influenced by the Two structure of petroleum lubricating oils is oxidation stability. modes of behavior must be considered. One is the resistance to the initiation of oxidation, ususlly defined by the period of induction before the uptake of oxygen proceeds at an appreciable rate. The other is the post-induction rate of oxidation and the kind of oxidation products formed thereby. There are no easy generalities about the relation of structure to these two aspects of oxidation. Such empirical relations as have been established are successful because the refining procedures produce oils of consistently stable properties in a broad sense. But changes in refining technique can result in unexpected alterations in the oxidation stability of the oil. For example, the light hydrotreating of paraffinic oils to improve color and color stability has as an undesirable side effect reduction of oxidation stability. Among the minor components of ordinary lubricant stocks strongly affected by light hydrotreating are the sulfur compounds which occur as polynuclear hererocycles. These are known to be oxidation inhibitors naturally occuring in the oil. Reduction of the sulfur level from 0.1-0.2% to 0.04-0.08% by hydrogenation has an adverse effect on the oxidation resistance of the treated oil Pour point is another lubricating oil characteristic of .technological interest. Although it has no specifically identified direct influence on the lubricating performance of the oil, there is an obvious disadvantage if the oil at rest in the sump cannot flow or be pumped to the sites where it is needed. Improvement of pour point is the reason for dewaxing oil. The insolubility and the crystallinity of paraffin waxes can be attributed to the straight-chain structure of their constituent alkane hydrocarbons, which promotes their removal in the dewaxing process. Branched-chain alkanes and long chains substituted on a

499

cycloparaffin ring are more likely to be found in the "microcrystalline" type of waxes, which are softer and more plastic than the higher-melting paraffin waxes. The high pour points of the first five fractions listed in Tables 16-6 and 16-7 can be attributed to the combination of isoparaffins and substituted monocyclic naphthenes. The minimum pour point, at Fraction 21, seems to be characterized by substantially equivalent levels of isoparaffins and bicyclic condensed naphthenes; then as the pour point progressively rises with the fraction number, the isoparaffins decrease and the polycyclic condensed cycloparaffins increase. From this it appears that in an oil of homogeneous molecular weight with a heterogeneous array of molecular constitutive types, the pour point minimum is governed by the smoothing of the distribution among the isoparaffins, the r?.onocyclicconstituents and the condensed polycyclic constituents, rather than the predominant influence of any one particular molecular type. REFERENCES 1.

2.

3. 4. 5. 6. 7. 8.

9. 10. 11.

12. 13. 14. 15. 16.

17. 18.

19.

F. D. Rossini, J. Chem. Ed., 37 (1960) 554-561. ASTM Method D 1298-67, Density, Specific Gravity o r API Gravity of Crude Petroleum o r Liquid Petroleum Products by Hydrometer Method, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. W. Carruthers and J. W. Cool, J. Chem. SOC. London, (1954) 20472052. R. J. Moore, R. E. Thorpe and C. L. Mahoney, J. Am. Chem. SOC., 75 (1953) 2259. B. J. Mair, S. T. Schicktanz and F. W. Rose, jr., J. Res. Natl. Bur. Standards, 15 (1935) 557-573. B. J. Mair and S. T. Schicktanz, J. Res. Natl. B u r . Standards, 17 (1936) 909-922. B . J. Mair and S. T. Schicktanz, Ind. Eng. Chem., 28 (1936) 14461451. F. D. Rossini, B. J. Mair and A. J. Streiff, Hydrocarbons from Petroleum, Reinhold Publishing Co., New York, 1953, Chapter 22. B. J. Mair and F. D. Rossini, Ind. Eng. Chem., 47 (1955) 1062-1068. F. W. Melpolder, R. A. Brown, T. A. Washall, W. Doherty and C. E. Headington, Anal, Chem., 28 (1956) 1936-1945. M. L. Andre' and M. J. O'Neal, jr., Anal. Chem., 31 (1959) 164-169. L. P. Lindeman. PreDrints. ACS Div. Petroleum Chemistry. _ . 14 (1969) No. 3, B186lB198. A. Hood, R. J. Clerc and M. J. O'Neal,. j- r . , J. Inst. Petroleum, 45 (1959) 168-173. B. J. Mair and J. L. Martingz-Pic;, Proc. Am. Petroleum Inst., 42 (1962) 1 1 1 , 173-185. I. A. Mikhailov, A. A. Polyakova, N. P. Izotova, E. S. Brodskii, M. M. Chern'isheva and I. M, Uvarova, Khim. Tekh. Topliv Masel, 17 (1972) No. 7, 13-17. R. W. King, M. A. Kust and S. S. Kurtz, j r . , Anal. Chem., 32 (1960) 738-745. K. van Nes and H. A. van Westen, Aspects of the Constitution of Mineral Oils, Elsevier Publishing Co., New York-Amsterdam-LondonBrussels, 1951. S. S. Kurtz, jr., in Chemistry of Petroleum Hydrocarbons, B. T. Brooks (Editor), Reinhold Publishing Co., New York, 1954, Vol. I , Chapter 1 1 . ASTM Method D 2501-66, Calculation of Viscosity-Gravity Constant ( V G C ) of Petroleum Oils, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia.

500

20. 21. 22. 23. 24.

E. E. Smith, Ohio State Univ. Eng. Exptl. Station Bulletin 152, May, 1953. S. S. Kurtz, j r . , R. W. King, W. J. Stout, D. G. Partikian and E. A. Skrabek, Anal. Chem., 28 (1956) 1928-1936. S. S. Kurtz, jr., R. W. King, W. J. Stout and M. E. Peterkin, Anal. Chem., 3 0 (1958) 1224-1236. C. Boelhouwer and H. I. Waterman, J. Inst. Petroleum, 4 0 (1954) 116121. J. Cornelissen and H. I. Waterman, J. Inst. Petroleum, 43 (1957) 48.

501

Chapter 17 NON-PETROLEUM LIQUIDS A S LVBRICANTS

A s pointed out in the preceding chapter, petroleum oils offer many advantages a s lubricants. In no other single class of liquids d o we find so many desirable attributes, such as versatility of performance, ready availability and economically bearable price. However, occasions arisewith increasing frequency a s the needs of modern machinery become more demanding-when the properties of petroleum oils are inadequate for the service required. These requirements, for the most part connected with higher service temperatures, include better viscosity behavior, better oxidative and thermal stability, and lower volatility. In particular, hydraulic fluids that must function at high pressures and elevated temperatures should have resistance to ignition without sacrifice of antiwear performance.

When the need for improved performance outweighs restrictions on price and desire for availability which ordinarily dominate the procurement of lubricants, then the purview expands to include fluids that can be made by synthetic chemistry. Even if we restrict ourselves to those fluids that promise reasonable potential for usefulness, there are as many a s 20 broad generic classes which can come under consideration, and within each class there may be 10 or more subclasses gradated according to some property such as viscosity or molecular weight. A comprehensive survey of all the synthetic fluids with potential for practical u s e would be a major undertaking. In this chapter, therefore, we shall restrict ourselves to the examination of those types of synthetic lubricants that have been tested well enough to establish their usefulness and their limitations. 17.1.

CHEMICAL TYPES AND STRUCTURES

In Table 17-1 are listed seven of the more important types of chemic a l structures according to which the non-petroieum liquids discussed in this

chapter may be classified. All of these lubricants are synthetic: ~ . e their . structures are the result of substantial chemical alteration of the starting material, in contradistinction to the refining of natural petroleum oils, which principally separates the crude oil into fractions and removes the unwanted portions thereof. Even though synthetic lubricants o f the hydrocarbon type may have had their origin in raw materials obtained from petroieum, they are the products of substantial

502

TABLE 17-1.

IMPORTANT CHEMICAL TYPES OF SYNTHETIC LUBRICANTS

Hydrocarbons Fluorocarbons and fluorohydrocarbons 3. Other hydrocarbon halides 4. Carboxylic esters 5 . Other esters 6. Ethers and glycols 7. Silicon derivatives 1.

2.

chemical alteration of the starting substances. Olefinic hydrocarbons of low molecular weight are among the byproducts of the cracking of petroleum stocks. Attempts to make synthetic lubricants by the polymerization of such olefins date back to but these efforts were not truly successful, either techthe 1 9 3 0 ' s , Polymers of butene and isobutene with nologically or economically. molecular weights of 100,000 and greater were developed, but such large molecules were found unsuitable as lubricant base stocks although they perform effectively as viscosity-improving additives. Similar polymers of ethylene and propylene are familiar and need no special mention. In order that olefin polymers be suitable for use a s lubricant fluids they must be u L i y u m e n . 5 : that is, they must be made up of relatively few basic repeating units so that the molecular weight of the polymer fluid lies within the range 300-500, which empirically has been found associated with desirable values of properties such as viscosity, pour point, volatility, etc. As the chain length and the branching of the parent olefin increases, the structural variations possible in the polymerized product proliferate. One of the ostensible objectives of synthesizing lubricants is better control over the structure and hence of the properties of the product, and such control starts at the beginning with the choice of the olefin to be polymerized. Olefins with terminal unsaturation are preferred: e . g . 1-alkenes, whether normal o r branched. In the examples below, the structure shown for the normal terminal olefin i s general, but that for the branched-chain terminal olefin is only one of several possible types. The values of x and y may both be zero, in which case the branched-chain olefin is isobutene (2-methylpropene-1):

R CH=CH2

R(CH2)xCH.(R')*(CH

)

2 Y

CH=CH2

CH 3 )C=CH2

CH3 Normal w-alkene

Iso-w-alkene

2-Methylpropene-1

Commercial olefin polymerizations are currently carried out in catalytic systems, and in many of them the course of reaction goes via a

503

Cha n

carbonium-ion mechanism. olef in proceeds

+

propagation

for

the

normal

terminal

+

R.C-CH3 + R.CH=CH2 H

I! + R-C-CH, C-CH3, etc. H

H

as the most likely course. Initiation of the chain requires that a hydrogen ion be furnished by the catalytic system: chain termination requires its removal. Control of the reaction to keep the molecular weight of the product in the desired range is a matter of specific technique. The ultimate oligomer has the general structure:

Isomers restilting f r o m wandering of the site of the electron deficiency and shifting of the double bond are not excluded. For a branched-chain structure, the reaction scheme outlined below for isobutene may be taken as representative:

Catalyzed free-radical mechanisms are also modes the chain is poiymerization. F o r the type olefin R.CH=CH, principally by the radical attack

R-C=CH2

+

R-CH=CH, j [H2C=C-;-;H R H

.

of olefin propagated

(b)

Configuration (a) is the favored one for the propagation giving the oligomeric product with the structure

of

the

chain,

H,C=CR.(CH2-CH);CH2-CH2R R

However, the structure H2C=CR*(CH-CH,);CH-CH3 R R generated from configuration (b) is not excluded.

All of the hydrocarbon oligomers whose structures have been drawn above are olefinic with one double bond per molecule. Hydrogenation to

504

produce a completely saturated hydrocarbon is the usual finishing step in the preparation of synthetic lubricant fluids from olefinic oligomers. The choice of synthetic hydrocarbons for lubricant use is not restricted to olefin oligomers. I t is entirely credible that among the thousands of hydrocarbons of various structures will be found many whose properties make them worthy of attention as possible lubricants. For example, Wilgus, Ettling and Pino [ l ] investigated the potential usefulness as high-temperature, radiation-resistant hydraulic fluids of a series of diarylalkanes of the general type

where X,, X2 and Y may be either H or an alkyl group. Schmidt-Collgrus, Krimmel and Bohner [ 2 ] reported on the properties of substituted bi- and terphenyls:

That so few of the synthetic hydrocarbons already known and synthesized have been investigated as possible lubricants is not only a matter of whether their properties are suitable; the overriding conditions are for the most part economics and availability. Halogen-substituted hydrocarbons in general do not show much promise as lubricant fluids. However, some of the properties reported for one class of hydrocarbon halides, namely the substituted w,w'-diphenylalkanes

where either x or y may be zero, make lubricants for special uses 131.

them

of

interest

as

synthetic

Fluorine heads the halogen group in the periodic table of the chemical elements, but fluorocarbons fall into a class distinct from other halogen-substituted hydrocarbons because of their distinctive properties. The carbon-fluorine bond in fluoroalkanes is among the strongest of alkyl bonds, and the fl'uoroalkane surface is among those with the lowest energy and the least wettability. In mixed fluorohydrocarbons, e . 9 . alkyl fluorides of empirical formula C H F (x+y=2n+2), the number of possible n x y structural combinations increases rapidly with increasing n. One general type is the terminally fluorinated chain: CH~(CH~)~CF~

505

Other types are illustrated by the structures shown below: CH, (CH2)n (CF2),CF3

and

CF3 (CF2),(CH2

)n ( C F 2 ),CF3

Ring-substituted fluoroaromatics and fluorocycloalkanes are tures to be considered.

also

struc-

Carboxylic esters today are mostly associated with the lubrication of jet turbine aircraft engines, but the practical use of an ester as a lubricar,t antedates the jet age. Castor oil, the iegendary h i g h viscosity crankcase oil for racing car engines, is a mixture of fatty esters whose principal constituent is triricinolein:

CH,OOC(CH,)~.CH=CH.CH~CH(OH).(CH~)~CH~

I I

CHOOC(CH2),*CH=CH.CH2CH(OH).(CH2)5CH3

CH200C(CH2)7-CH=CH.CH2CH(OH).(CH2)5CH3 But the requirements of jet engine lubrication call for properties quite different than those which governed the selection of castor oil as a crankcase lubricant, and it is these altered requirements that have their influence on the correlations between physical properties and chemical structures which determine the modern development of ester lubricant fluids. Of the numerous possibilities arising from the esterification of polycarboxylic acids by polyhydroxylic alcohols, fortunately only a few need be considered seriously from the viewpoint of utility as synthetic ester lubricants. Most of the esters that find application as lubricant fluids are products of the reaction of m,>nohydroxylic alcohols and dicarboxylic acids; for example, the simple type structure shown below:

ROOC.(CH2),*COOR Or, the reactants may be a monocarboxylic acid cohol :

and

a

dihydroxylic

al-

RCOO(CH2)m00CR Complex esters can be made by the interaction of a dihydroxylic alcohol and a dicarboxylic acid: for example, HO(CH2)~OOC~(CH2)n~COO~CH2)mOH which is then capped with a monocarboxylic acid to give RCOO(CH2)m00C* (CH2)n.COO(CH2)m00CR By blending diesters and complex esters, versatile control of the viscosity of the lubricant can be achieved. The illustrative formulas above were restricted to straight-chain w,w'-structures for both the dihydroxylic alcohol and the dicarboxylic acid, but there is no necessity for such a restriction, theoretically or practically. The combination of w,o'-straight-chain dicarboxylic acid and branched-chain monohydroxylic

506

alcohol is encountered more often than the reverse combination because Of the comparative availability of acid and alcohol. Among the non-carboxylic esters that have been investigated for lubricant service are tetra-alkyl orthosilicates, (R0)4Si; trialkyl orthophosphates, (RO)3P=O; phosphonates, (R0)2.PR'-O; phosphinates, RO*PR'.O. The phosphates, phosphonates and phosphinates were studied as lubricant liquids p e h n e and not as additives. Polyalkylene glycols of sufficient chain length can function acceptably a s lubricants. The simplest in structure are the polyethylene glycols: HO(CH2CH20);CH2CH20H Isobutylene epoxide gives polyoxyglycols with the structure

Polyoxyalkylene glycols have also been prepared from propylene epoxide and 1,2-epoxybutane. Structurally the polyoxyalkylene glycols are both ethers and glycols. The polyphenyl ethers constitute a class of oxygenated liquid lubricants without free hydroxyl or carbonyl groups. Some typical structures are shown below: c r 0 0 0 ~ 0 c >

bis(p-Phenoxyphenyl) Ether

m-Phenoxyphenyl p-Phenoxyphenyl Ether

Phenoxy-n-(m-phenoxy)benzene

n = 0,

1,

2

... etc.

In addition to the orthosilicates already mentioned, two other types of silicon derivatives have been studied as lubricants. The most familiar are the poly(diorganosi1oxanes); these are the well-known silicones: R R R-SiO (-iiO) -Si-R R R

The organic groups need not necessarily be all alike. are the tetraorganosilanes

In the other class

R R-Si-R R proposed as high-temperature lubricants by Baum and Tamborski 1 4 1 .

Here,

507

too, the organic groups are not necessarily alike. Since the polyoxyalkylene glycols are dihydroxylic alcohols as well as polyethers, they can be reacted with acids to give ester-type e . y . , carboxylates, phosphates, silicates, etc. lubricant fluids: Another type of chemical multifunctionality in synthetic lubricants is introduced by halogen substitution: for example, fluorine-substituted polyphenyl ethers; o r alkyl-aryl silicones with chlorine substituted for hydrogen on the aryl ring. 17.2.

CHEMICAL TYPES AND PROPERTIES OF SYNTHETIC LUBRICANTS

The criteria for the evaluation of a given synthetic liquid as a lubricant will depend upon the functional demands of the service required Some of these demands may not be directly connected with the of it. function as a lubricating fluid: for instance, odor, toxicity, o r attack on paints and'finishes. Those properties that are pertinently connected with lubricant service can be classified into the five categories listed below: 1.

FLaw Pnapehtien: Under this heading come the viscosity of the fluid and the effect of temperature on viscosity, The latter might be a theoretically derived function, or an arbitrary function such as the viscosity index, o r even a grossly empirical evaluation of the viscosity at two or more selected temperatures. Low temperature flow properties are frequently evaluated by the ASTM pour point determination [ 5 1 , but the inadequacies of this method of evaluation have led to the use of pumpability tests which have a better empirical relation to service conditions.

2.

H i y h Tempehatuhe Phopehtien: The high temperature domain may be arbitrarily taken to lie above 3 7 3 K ( 1 0 0 c ) . The chief properties of interest at such temperatures are resistance to thermal cracking, particularly in the presence of metals; absence o r low level of polymerized or carbonaceous residue; resistance to flammability; and low loss by volatilization.

3.

Oxidation Chahactehinticn: These characteristics include resistance to oxidation at ordinary and at high temperatures, the nature and the properties of the oxidation products, and response to oxidation inhibi tors.

4.

C o h n a n i o n Chahactehinticn: In general, rubbing parts to be lubricated are made of metal. The corrosiveness of the lubricant p e h n e and the corrosiveness of any degradation products resulting from oxidation, thermal decomposition or hydrolysis must be considered.

5.

Weak and S e i z u h e Chahactehinticn: The behavior o f the fluids themselves in various bench tests for antiwear or antiseizure performance

508

is of interest, as is also the behavior of antiwear and antiseizure additives when dissolved in the fluids. The criteria listed above are also used to judge petroleum oils; therefore evaluating synthetic lubricants by these criteria tests whether they perform better than petroleum oils under the conditions required by service. I n hydrodynamic lubrication considerable emphasis is placed on the temperature coefficient of viscosity. Figure 17-1 illustrates the extent of the control that can be exercised over this important parameter in the synthesis of hydrocarbon oligomers. Viscosity data are plotted o n the

10,000 5,000 2,000 1,000 B c 500 0

2 200

u)

s

n

ZI 0

g f 0

100

80 60

50 45 40 35 30 50 75 100 125 150 175 200

250 300

Temperoture,degrees Fahrenheit

Figure 17-1. Effect of temperature on the viscosity of mineral oils and hydrocarbon oligomers. 1: Mineral oil, VI 92. 2: Mineral oil, VI 92, 5: molecular weight 418. 3: White oil, VI 101. 4: Mineral oil, VI 29. Polybutene, VI 47. 6: Hydrogenated polyoctene, VI 113, molecular weight 420. 7: Hydrogenated polyoctene, VI 142, molecular weight 1100. 8: Hydrogenated polyoctene, VI 155, molecular weight 1300. From data by Duling, Griffith and Stearns [ 6 1 . viscosity-temperature scale for three of the hydrogenated oligomers The supeof octene-1 prepared by Duling, Griffith and Stearns [ 6 1 . riority of these synthetic hydrocarbons over the best of the solventrefined petroleum oils and over white oil is immediately evident from the slope of the temperature dependence function. Not so evident is the fact that the molecular weight of the synthetic hydrocarbon for a given viscosity at 372 K (210 Fj is higher than that of the corresponding naphthenic-paraffinic hydrocarbon; hence the synthetic oil has the better ASTM

volatility characteristics. The pour points for this series of synthetic hydrocarbons lie mostly at the level 211-214 K ( - 7 5 to -80 C ) . These values reflect the lack of

509

Figure 17-2. Viscosity-temperature behavior of various types of synthetic lubricants. 1: White oil, VI 101. 2: 4'-Undecyl-m-terphenyl. 5: Polyphenyl ether. 3: Fluoroalkane. 4: w,o'-Di(chloropheny1)pentane. 6 : Polyoxyalkylene glycol. 7: Di(2-ethylhexyl) sebacate. 8: Dimethyl silicone

.

crystallinity inherent in the molecular geometry of the polymerizates. Figure 17-2 shows the influence of temperature o n the viscosity of representative examples of synthetic fluids of various chemical types. Direzt comparisons can be made when individual fluids have the same viscosity at a given temperature: e . 5 . white oil and polyoxyalkylene glycol at 301 K (83 F). The viscosity of the glycol fluid at 372 K (210 F) i s 6 Saybolt seconds higher than that of white oil, which is a significant difference that immediately shows the better viscosity behavior of the synthetic fluid. In similar fashion, w,w'-di(chlorophenyl)pentane, di(2ethylhexyl) sebacate and a dimethyl silicone all have a viscosity of 120 Saybolt seconds at 340 K (153 F ) ; but at 372 K there is a spread of 15.7 Saybolt seconds in the viscosity behavior of these fluids. Table 17-2 shows some relations between structure and flow properties. The data for the substituted terphenyls are from the work of Schmidt-CollLrus, Krimmel and Bohner [ 2 ] ; those for the polyphenyl ethers are by Mahoney and his co-workers 171. For the substituted terphenyls the location of the alkyl group rather than the linkage of the aromatic r i n g s has the stronger influence on the viscosity behavior and the pour point. The viscosity at 310.8 K (100 F) for the n-heptylterphenyls substituted in the 2-position is 2.3 to 2.7 times that of the isomer substituted in another position, and the pour point for the 2-substituted isomer is also consistently higher. Unfortunately this trend in pour point is opposite to what is desired. The data for the polyphenyl ethers

510

TABLE 17-2. STRUCTURE AND PHYSICAL PROPERTY RELATIONS FOS n-HEPTYL-SUBSTITUTED TERPHENYLS AND POLYPHENYL ETHERS Pour point

Viscosity, cs

310 8 K(a) 372.0 K(b) 422.0 K(c) OK

O F

2-n-Heptyl-o-terphenyl 3-n-Heptyl-o-terphenyl 2-n-Heptyl-m-terphenyl 3-n-Heptyl-m-terphenyl 4-n-Heptyl-m-terphenyl

29 55.2 73 65 65

6.55 5.14 7.61 6.29 6.29

2.3 1.9 2.65 2.59 2.59

4'-n-Heptyl-m-terphenyl 2-n-Heptyl-p-terphenyl bis(m-Phenoxyphenyl) ether m-bis(m-Phenoxyphenoxy) benzene

64.9 110 60.9

6.18 7.03 5.98

2.5 2.65 2.45

264 15 -10 250 272 30 244 -20 liquid at room temperature 250 -10 278 40 261 10

3.85

278

12.7

332

40

From data (a) 100 F. (b) 210 F. (c) 300 F; extrapolated values. Schmidt-Collgrus, Krimmel and Bohner [2] and by Mahoney e t aL.[7].

by

-

u) 5

10 20

30 40 50 60 70 Degree of Polymerization

Figure 17--3. Structure and viscosity of silicones. 1: Polydimethylsiloxane. 2: Polyoctylmethylsiloxane. 3, 3': Polymethylphenylsiloxane. From data by Jakobsen, Sanborn and Winer [a].

show the strong influence of the number of rings in the structure. The viscosity behavior of the four-ring bis(m-phenoxyphenyl) ether is similar to that of the n-heptylterphenyls, whereas the five-ring m-bis(mphenoxyphen0xy)benzene is considerably more viscous.

Silicones have the least sensitive response of viscosity to temperature change of any of the synthetic fluids used as lubricants (see Fig. 17-2). The viscosity level depends on the nature of the organic groups linked to the silicon atom in each siloxane unit and on the number of organosiloxane units per molecule, as illustrated by Fig. 17-3 from

511

data by Jakobsen, Sanborn and Winer [81 for dimethylsiloxane, octylmethylsiloxane and methylphenylsiloxane polymers. The influence of the size of the organic substituent groups is so strong that 15 repeating units carrying one methyl and one octyl group per unit confers a higher viscosity than 70 units substituted with only methyl groups. The two curves for methylphenylsiloxane in Fig. 17-3 illustrate the difficulty of controlling the polymerization process to obtain uniform distribution of structural units in the product. Resistance to cracking, reactive condensation and oxidation, in conjunction with acceptable viscosity behavior, is a behavioristic property that often determines the choice of a given fluid as a high-temperature lubricant. A technique for evaluating thermal stability is to measure the temperature at which the gas pressure of an enclosed system rises at some given rate: e . g . 0.014 torr per second. McHugh and Stark [9] obtained the following rating by this method for various chemical classes: polyphenyls, 783 K (950 F); polyphenyl ethers 716-727 K (830-850 F); silicones, 655-661 K (720-730 F); aromatic ethers, 655 K (720 F): silicate esters, 616 K (650 F); super-refined mineral oil, 611 K (640 F); The diesters, 555 K uncatalyzed, 500 K metal-catalyzed (540 F, 440 F). individual members of the various classes were not specifically identified. Table 17-3 shows thermal stability data obtained by Brown, Aftergut and Blackington [ I 0 1 for three classes of aromatic compounds: unsubstituted polyphenyl hydrocarbons, polyphenyl ethers, and silanes sub-

TABLE 17-3.

THERMAL STABILITY OF VARIOUS AROMATIC COMPOUNDS Decomposition temperature for 0.014 torr per second

Polyphenyls p-Quaterphenyl m-Polyphenyls, mixed (a) Tetraarylsilanes p-Biphenylyltriphenylsilane o-Biphenylyl-p-biphenylyldiphenylsilane o-Biphenyloxytriphenylsilane o-Biphenylyl-m-phenoxyphenyldiphenylsilane bis(m-Phenoxypheny1)diphenylsilane Polyphenyl ethers bis(p-Phenoxyphenyl) ether m-Phenoxyphenyl-p-phenoxyphenyl ether [Phenoxytri(m-phenoxy1ene)lbenzene [Phenoxytetra(m-phenoxy1ene)lbenzene [Phenoxypenta(m-phenoxy1ene)lbenzene (a) Contains 2% halide by weight. ington [lo].

aeg. K

deg. F

714 663

826 734

699 727 708 707 679

799 850 815 814 763

713 71 i 717 703 716

824 82 7 832 806 830

Data by Brown, Aftergut and

Black-

512

stituted by phenyl, polyphenyl o r phenoxy groups. The high level of the decomposition temperatures can be ascribed to the absence of alkyl I n contrast, Baum and Tamborski [41 reported 586 K (595 F ) for groups. the decomposition temperature of tetra(n-dodecyl)silane, and SchmidtCollgrus e t aL. [2] recorded 5 4 6 K (523 F) for 4'-n-amyl-rn-terphenyl. Schiefer, Awe and Whipple [ 1 1 ] found decomposition temperatures of 705 and 677 K ( 8 1 0 , 760 F) for two different methylphenylsilicones. Mahoney and co-workers 171 compared di(2-ethylhexyl) sebacate, an aliphatic hydrocarbcn and the two aromatic ethers, bis(m-phenoxyphenyl) ether and m-bis(m-phenoxyphen0xy)benzene. They found the following temperatures for 1% decomposition per hour: ester, 583 K (590 F); hydrocarbon, 616 K (650 F); polyphenyl ethers, 739 K (671 F).

Heating for a given time at a fixed temperature is another technique for evaluating thermal stability. Duling, Griffith and Stearns [61 found that a sebacate diester fluid was significantly less stable at 644 K (700 F) than petroleum oil or synthetic alkanes from olefin oligomers. Wilgus, Ettling and Pino [ l ] observed that in a static heating test at 644 K for 20 hours a polyoxyalkylene glycol fluid was characterized by a large change i n viscosity and evolution of much gas; di(2-ethylhexyl) sebacate set to a solid; and a silicone fluid evolved more gas than naphthenic white oil, substituted biphenyl, substituted diphenyl ether or w,w'-diphenylalkane. Baum and Tamborski [41 on testing various teraalkylsilanes by a closed-tube static procedure for 9 hours at 644 K observed some loss of viscosity, but the extent of change was at an acceptable level. The effect of high-temperature oxidation on lubricant fluids is usually monitored by changes in viscosity and acidity, by the amount and Very nature of deposits and sludge, and by corrosive attack o n metals. few lubricants can withstand high-temperature oxidation without antioxidant additives. Hence in making comparisons it is the interaction of base fluid and additive which usually is being tested, and interpretation of the results is thereby complicated. The silicones are an outstanding exception, being resistant to oxidative degradation without the aid of an antioxidant additive. Murphy, Saunders and Smith [121 studied the oxidation of three methyl phenyl silicones and compared the results with those of a previous investigation of dimethyl silicone [ 1 3 1 . Their findings for uncatalyzed oxidation are summarized in Table 17-4 a s viscosity increase, loss of weight and evolution of formic acid and formaldehyde. Data for metal-catalyzed oxidation can be found in the original reference [ 1 2 ] . Baum and Tamborski [41 studied the oxidation of tetraalkyl silanes at 4 7 7 K (400 F) and reported that the oxidative resistance and antioxidant response of these substances were poor. Table 17-5 gives some comparisons of polyphenyl ethers with other synthetic lubricants in a 50 hour oxiaation-corrosion test [ 7 1 . A l l the

TABLE 17-4.

HIGH-TEMPERATURE OXIDATION OF SILICONES Temperature

Time, % Viscosity Wt. loss, Millimoles HCOOH hours increase at percent + H C H - 0 per gm 310.8 K(a) deg. C deg. K

Polydimethylsiloxane

200 225 P o l y m e t h y l p h e n y l s i l o x a n e s 200 225 250 250 250 275 300

c)

d) d) d)

473 498 473 498 523 523 523 548 573

168 168 168 168 168 168 168 168 168

48 gelled (b) (b) 85-124 165 34 137-209 336-577

2 2 (b) (b) 3.5 4 1 1.5 6

In air unless otherwise noted. (a) 100 F. (b) Unchanged. helium. From data by Murphy, Saunders and Smith [12]. TABLE 17-5.

(c)

1.7 0.003-0.015 0.015 0.004 0.002-0.006 0.007

In

oxygen.

% Viscosity

Acid number

(d)

In

OXIDATION TESTS: POLYPHENYL ETHERS AND OTHER FLUIDS Temperature deg. C

bis(m-Phenoxyphenyl) ether bis(p-Phenoxyphenyl) ether m-bis(m-Phenoxyphenoxy)benzene

m-bis(m-(m-Phenoxyphenoxy)phenoxy)benzene m-Terphenyl Methyl phenyl silicone Chlorophenyl silicone Diphenyldi-n-dodecylsilane Diester base oil (c) Mineral oil

589 589 589 589 589 589 533 533 505 477

increase, deg. F 372 K(a) 600 600 600 600 600 600 500 500 450 400

7 5.0(b) 29 84 8 1020 250 410 80 (d)

0.8 0.6 1.8 3.2 0.7 -

6.0 14 16

Deposits

None None None None None None None Heavy Very heavy Heavy and solidified

50 hour test; 200 cm3 air per hour; Cu, Mg, Fe, Ag, Al, Ti coupons immersed in fluid. (a) Data by 210 F. (b) At 421 K (300 F). (c) Formulated oil. (d) Oxidized oil is solid. Mahoney, Barnum, Kerlin and Sax [71.

514

fluids tested were unformulated except the diester, which was made up into a compounded jet aircraft engine oil. The influence of the aromatic structure of the polyphenyl ethers and of the m-terphenyl on oxidation resistance is shown by the low level of the acid numbers and the absence of deposits on metal coupons which were immersed in the fluids during the tests. Even the highest level of viscosity increase was not excessive. On the other hand, a petroleum oil oxidized at 477 K (400 F) set up to a solid, and the diester fluid (formulated with antioxidants) ran up a high acid number and left very heavy deposits. The instability of the tetrasubstituted silane is also apparent. The silicones survived the test with no deposits but with large increases in viscosity. AS long as the service conditions which the lubricant sees are compatible with the existence of a fluid film, there is no reason to believe that the characteristics which govern the behavior of a synthetic fluid in hydrodynamic or elastohydrodynamic lubrication are any different than those which hold for a petroleum oil: namely, viscosity, compressibility, and the temperature and pressure dependence thereof. But when failure of the fluid film is suspected and the possibility of metal-to-metal contact arises, the intrinsic antiwear and antiseizure behavior of the synthetic fluid becomes pertinent. Logically these problems should be studied by behavior under conditions related to service; in practice, as is mostly the case in the evaluation of conventional lubricants, they are dealt with usually in terms of the commonly used arbitrary bench tests.

Table 17-6 indicates that concern with the intrinsic influence of the specific lubricant on wear is valid. The fluids listed there are of low viscosity because they were investigated for low-temperature hydraulic service [141. However, the extent of wear shows no direct relation to viscosity; the silicate fluid, which permits the most wear, is not the least viscous of the fluids tested, and the silicone, which is the most viscous, is not the one which gives the best antiwear rating. Figure 17-4 shows intrinsic lubricant behavior in a different version of TABLE 17-6. FOUR-BALL WEAR WITH SOME SYNTHETIC LUBRICANT FLUIDS Viscosity, cs 310.8 K (a) Silicate ester Dimethyl silicone Fluorohydrocarbon Fluorinated polyether Hydraulic fluid (d)

1.66 12.09 2.38 0.99

-

Four-ball wear scar diam., mm (c) 372.0 K (b)

0.80 5.01 1. 14 0.43 -

1.06 0.56 0.44 0.39 0.28

(a) 100 F. (b) 210 F. (c) 10 kg load, 2 hours, I200 rpm, 348 K (167 F). (d) Fully formulated commercial fluid. From data by C. S. Armstrong [ i41.

515

10 5 E E

r30 40

10 20 Load, kg

5

Figure 17-4. Four-ball testing of various lubricant fluids. One hour at 2 4 0 0 rpm, 4 7 7 K ( 4 0 0 F). A: Di(2-ethylhexyl) sebacate. B: bis(p-Phenoxyphenyl) ether. Data by Mahoney e t aL. 1 7 1 . the four-ball wear test. While the consistent difference in the size of the wear scars obtained with di(2-ethylhexyl) sebacate and with polyphenyl ether might be ascribed to viscosity effects, such a reason cannot be advanced for the extremely high wear found with m-terphenyl. The behavior with white oil is probably indicative of a load-governed wear transition. The

data

in

Table

17-7,

taken from work by Klaus, Tewksbury and

Fenske [ 1 5 ] , compare the behavior of silicate ester and silicone fluids with that of dicarboxylate ester and mineral oil in four-ball antiwear testing. At 3 4 8 K ( 1 6 7 F ) under moderately heavy load of 1 0 kg the silicate ester and the silicone are comparable to the other two fluids in anTABLE 1 7 - 7 . ANTIWEAR PERFORMANCE OF SILICATE ESTER AND SILICONE FLUIDS IN THE FOUR-BALL TEST Temper at ur e deg. K Silicate ester Silicone Dicarboxylate ester Mineral oil

One hour at 6 2 0 rpm.

348 533 589 348 533 589 348 533 58 9 340 533 589

deg. F 167 500 600 167 500 600 167 500 600 167 500 600

Avge. wear scar diameter, mm 10 kg

4 0 kg

0.22 0.22

0.44 1.04 1.17 0.31 0.77 1.38 0.56 0.68 0.63

0.28 0.31 0.20

0.47 0.57

0.63 1.62 1.19 0.67 1.56 1.30 0.69 0.96 1.10 0.60 1.38 1.71

1

k9

0.21

0.72 0.78 0.18 0.39 0.29 0.34

0.42

From data by Klaus, Tewksbury and Fenske 1 1 5 1 .

516

tiwear action, but at 5 8 9 K ( 6 0 0 F) the silicate definitely inferior. Under 40 kg load the similarly.

and the silicone are fluids all behave quite

The relation between structural types in silicones and wear or friction control has been studied from several points of view. Brown 1 1 6 1 prepared a series of methyl alkyl polysiloxanes whose properties are shown in Table 1 7 - 8 . The results of their wear testing in the four-ball machine is seen in Fig. 17-5. The sharp drop in wear as the size of the

TABLE 17-8.

I

PROPERTIES OF METHYL ALKYL POLYSILOXANES c

YH3 CH -Si-0-

7

r 3

-Si-0-

1.7'3

I

3 1 CH 3

nCH3

Alkyl group, R

Ethyl n-Propyl n-Butyl n-Amy1 n-Hexyl n-Octyl n-Decyl n-Dodecyl n-Tetradecyl

3

-Si--CH

Viscosity, cs 310.8 K (a)

3 7 2 . 0 K (b)

67 67 82 98 99 147 195 246 298

22 21 27 29 29 37 44 51 58

(a) 100 F. (b) 210 F. Data by E. D. Brown, jr. [ 1 6 ] .

L

0.5 -

0

L - 4R,-Number- 8of -Carbon-Atoms 12 kin Side 7Chain

Figure 17-5. Effect of alkyl group size on antiwear action of methyl alkyl silicones in four-ball testing. One hour at 6 0 0 rpm, 5 0 kg load, 3 4 8 K ( 1 6 7 F). Data by E. D. Brown, jr. [ 1 6 ] .

517

alkyl group R increases from methyl to octyl and the levelling off for R > 8 is not likely to be a viscosity effect because the viscosity differences are greater for the higher temperature. Brown attributed the influence of the size of the alkyl chain to general bulkiness of the polymer molecule at the rubbing interface, a point of view for which Tabor and Willis [ 1 7 ] found some support on the basis of friction results. Halogen substitution on the phenyl group in methyl phenyl silicones can improve their antiwear function, but the character of such effects is governed by the test device as well as the test conditions. Descriptions of testing and experimental results are found in work reported by Gainer [ 1 8 ] and by Bowers, Cottington, Thomas and Zisman [191. Figure 1 7 - 6 from work reported by Schiefer [ 2 0 ] shows four-ball wear under various conditions with a methyl silicone copolymer that has dichlorophenyl groups in its structure. The abscissa, which is scaled in of chlorine content, is a measure of the proportion of terms dichlorophenyl groups in the makeup of the silicone. At 4 kg load and a temperature of 3 4 8 K ( 1 6 7 F), a chlorine content of C U . 6 - 7 % gives minimum wear, whereas at 4 7 7 K ( 4 0 0 F) wear increases steadily with chlorine content. With a load of 40 kg increase of chlorine content in the range 6 to 17 percent progressively reduces wear at both 3 4 8 and 4 7 7 K, but even at the lower temperature the smallest wear scar is still in the high-wear domain. Fluorine-substituted silicones do not behave like halophenyl methyl silicones. Figure 1 7 - 7 shows four-bali wear with ccpolymers containing 2.4 2.2

2 .o 1.8

E E, 1.6 c

& t E

.. .

p-

0'.

0

6

1.4

1.2

b 1.0 0

u,

p

0.8 0.6

0.4

-

0

0.2 0

0

4

8 12 Percent Chlorine

16

Figure 1 7 - 6 . Four-ball wear with methyl dichlorophenyl silicones. One hour at 1 2 0 0 rpm. From data by H. M. Schiefer [ 2 0 ] .

-

10 15 20 25 30 35 Percent Fluorine Figure 1 7 - 7 . Four-ball wear with methyl trifluoropropyl silicones. One hour at 1200 rpm. From data by H. M. Schiefer [ 2 0 1 .

0

5

518

methyl and triflouropropyl groups; 35% fluorine on the abscissa corresponds to a polymer with the siloxane chain completely filled with trifiuoropropyl groups. The absence of a sharp downward inflection in the curve for 40 kg load at 348 K probably indicates that fluorine, unlike chlorine in the chlorophenyl copolymers ( c d . Fig. 17-6), does not react chemically in the lubrication process. Tabor and Willis [17] found that trifluoropropyl silicones fell on functional curves for the behavior of methyl alkyl silicones in sliding friction and contact resistance as though the trifluoropropyl group were equivalent to an octyl group. 17.3.

APPLICATIONS OF SYNTHETIC LUBRICANTS

I n this section we shall examine some of the more important areas where synthetic non-petroleum liquids find utility as lubricants because One such area where the use of of their specialized properties. synthetic lubricants is particularly well-established is the lubrication of jet aircraft engines. The principal requirements for this service are good resistance to thermal and oxidative degradation, absence of hightemperature deposits, suitable viscosity throughout the range of service temperatures, solubility of additives, and availability. The parts to be lubricated are rolling element bearings and geared drives for auxiliary equipment such as pumps, etc. The synthetic fluid first widely used for this service was di(2-ethylhexyl) sebacate, and it is still accepted a s the typical fluid to which new developments are compared. I t has a wide range of satisfactory fluidity, with the viscosity lying in the range 1450 centistokes at 233 K (-40 F) to 3.350 centistokes at 310.8 K ( 2 1 0 F). I t dissolves complex esters and polymers which are used to augment its high-temperature viscosity. I t responds to oxidation inhibitors and antiwear additives. I t does not deposit excessive amounts of varnish or sludge and it does not thicken excessively after service at high temperatures. Experience with synthetic esters for jet engine iubrication has been so good that improvement has been concentrated on optimization of ester structures to push the durability of the base fluid into the higher temperature field as the demands of jet engine lubrication become more severe. The reader is referred to the patent literature and the open reports of various engineering laboratories for specific information about this highly specialized endeavor.

The intrinsic control possible with synthetic lubricants comes to the forefront in the formulation of nonflammable or fire-resistant hydraulic fluids. The lubricating function of the fluid must protect the pump which pressurizes the hydraulic system against wear. Some typical ranges of operating temperatures within which the fluid must function are: 220 to 505 K (-65 to 450 F); 233 to 561 K (-40 to 550 F); 255 to 644 K ( 0 to 700 F). In addition to acceptable viscosity, the fluid must have good thermal stability above 505 K, high autogenous ignition

519

temperature, and resistance to flame propagation. Blake and co-workers [ 3 1 reviewed the properties of 47 synthetic fluids with respect to these requirements; the following chemical types were represented: partially fluorinated hydrocarbons, fluorinated carboxylic esters, fluorosilicates, fluoroamines, halogenated tetrasubstituted silanes, fluoroaromatic ethers, halogenated w,w'-diphenylalkanes, and phosphorus esters (phosphates, phosphonates, phosphinates). I t turns out to be very difficult to optimize all the desired properties; low volatility and flame resistance are for the most part incompatible with the viscosity and pour point requirements. Phosphate esters, a much-recommended type of fire resistant hydraulic fluid, are not truly suited for high-temperature service because of excessive thermal decomposition at as low as 486 K ( 4 1 5 F). Surprisingly enough, although hydraulic pump tests are easy to carry out and probably thousands have been run routinely, few usable comTable parisons of synthetic fluids are recorded in the open literature. 17-9 shows the results of some comparative work carried out by W. H. Millett [ 2 1 ] with a vane pump. The polyglycol fluid gave the best allaround antiwear protection; however, fluids of this type have relatively low flash and fire points, of the order of 5 1 9 to 5 6 1 K ( 4 7 5 to 5 5 0 F). They show good antigumming behavior, a property which is very important for servov.alves with close clearances. The phosphate fluid had the poorest antiwear behavior of the three tested.

TABLE 17-9.

WEAR TESTING BY HYDRAULIC VANE PUMP (a) Petroleum oi 1

Phosphate ester fluid

Polyalkylene glycol fluid

Wear loss of pump part, mg Ring Rotor Vanes Bushings Total

400 20 460 30 910

540 260 130 110 1050

23 17 11

1 52

Viscosity, SLJS/lOO F 32 1

(a) 7 5 0 hours, 1000 psi, 1 2 0 0 rpm, 150 F. [211.

153

From data by

302

W.

H.

Millett

Service tests have not always confirmed the potential as hightemperature lubricant fluids one would expect from silicones on the basis of their properties and their behavior in laboratory investigations. As early a s 1 9 4 6 a study by Fitzsimmons, Pickett, Militz and Zisman [ 2 2 ]

520

reported. the poor durability of steel on steel and steel on cast iron in hydraulic pumps working with dimethyl silicone as the fluid. Some of the non-ferrous combinations, however, did not show this disadvantage. The benefits of the high-temperature stability of silicones may be illusory, for the small quantities of degradation products that do form may be wear-promoting o r may generate enough gel to clog filter elements. I n some instances synthetic fluids are proposed f o r lubricating service on the basis of their resistance to degradation in a radioactive environment. These are likely to be unsubstituted or short-chain substituted polyphenyls or polyphenyl ethers. Their radiation stability outweights their disadvantages in other respects, such a s high pou'r point and poor temperature coefficient of viscosity.

REFERENCES 1.

D. R. Wilgus, A. C. Ettling and M. A. Pino, J. Chem.

Eng.

Data,

6

( 1 9 6 1 ) 106-111.

2.

J.

3.

E n g . Data, 6 ( 1 9 6 1 ) 1 1 8 - 1 2 4 . E. S . Blake, G. A. Richardson, J. A. Webster and

4. 5.

6.

J.

Schmidt-CollGrus, J.

A. Krimmel and G. E. Bohner, J. Chem.

R. E. DeBrunner, ASLE Trans., 9 ( 1 9 6 6 ) 4 7 - 5 8 . G. Baum and C. Tamborski, J. Chem. Eng. Data., 6 ( 1 9 6 1 ) 1 4 2 - 1 4 5 . ASTM Method D 9 7 - 6 6 , Standard Method of Test for Pour Point, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. I. N. Duling, J. Q. Griffith and R. S. S t e a m s , ASLE Trans., 9 (1966)

1-12.

9. 10.

C. L. Mahoney, E. R. Barnum, W. W. Kerlin and K. J. Sax, ASLE Trans., 3 ( 1 9 6 0 ) 8 3 - 9 2 . J. Jakobsen, D. M. Sanborn and W. 0. Winer, J. Lubrication Tech. (Trans. ASME), 96F ( 1 9 7 4 ) 4 1 0 - 4 1 7 . K. L. McHugh and L. R. Stark, ASLE Trans., 9 ( 1 9 6 6 ) 1 3 - 2 3 . G. P. Brown, S. Aftergut and R. J , Blackington, J. Chem. Eng. Data,

11.

H.

12.

C. M. Murvhv. C. E. Saunders and D. C. Smith. Ind.

7.

8.

6 (1961)

M.

(1961)

125-127.

Schiefer, R. W. Awe and C. L. Whipple, J. Chem. Eng. Data, 6 155-160.

Enq.

Chem..

42

(1950) 24g2-2468. 13.

D.

C.

Atkins, C. M. Murphy and C. E. Saunders, I n d . Eng. Chem., 3 9

( 1 9 4 7 .) 1 .. 395-1401. 14. 15.

C. S. Armstrong, ASLE Trans., 9 ( 1 9 6 6 ) 5 9 - 6 6 . E. E. Klaus, E. J. Tewksbury and M. R. Fenske, J. Chem. Eng. Data, 6

16. 17. 18. 19.

E. D. Brown, jr., ASLE Trans., 9 ( 1 9 6 6 ) 3 1 - 3 5 . D. Tabor and R. F. Willis, Wear, 11 ( 1 9 6 8 ) 1 4 5 - 1 6 2 . G. C. Gainer, Ind. Eng. Chem., 4 6 ( 1 9 5 4 ) 2 3 5 5 - 2 3 6 2 . R. C. Bowers, R. L. Cottington, T. M. Thomas and W. A. Zisman, Ind. Eng. Chem., 4 8 ( 1 9 5 6 ) 9 4 3 - 9 5 0 . H. M. Schiefer, ASLE Trans., 9 ( 1 9 6 6 ) 3 6 - 4 6 . W. H. Millett, Ind. Eng. Chem., 4 2 ( 1 9 5 0 ) 2 4 3 6 - 2 4 4 1 . V. G. Fitzsimmons, D. L. Pickett, R. 0. Militz and W. A. Zisman, Trans. ASME, 68 ( 1 9 4 6 ) 3 6 1 - 3 6 9 .

( 1 9 6 1 ) 99-106.

20. 21. 22.

521

Chapter 18 LUBRICATING GREASE

In its general sense grease refers to a fatty solid, firm enough to hold its shape under its own weight but soft enough to flow under a low stress. These two characteristics determine what is known as the consistency of the grease. The consistency of a grease is the basis of its special utility as a lubricant and enables it to be applied to locations which cannot be supplied by a flow of liquid. In earlier times lubricating greases were actually solid fats, but modern greases are basically made up of a liquid oil and a solid thickener or gellant. The systematic study of the structure and the rheology of greases The falls mostly in the domain of colloid and physical chemistry. manufacture of greases is adequately treated in specialized books. A thorough treatment of greases in lubrication technology would require a None of these objectives can be specialized monograph of its own. achieved in the space of the single chapter t o follow, but the fundamental principles governing grease structure and the relations between structure and the utilization of greases are known well enough to be dealt with informatively. 18.1.

BASIC ASPECTS OF LUBRICATING GREASE STRUCTURE

The consistency of a grease is a complex of related properties, easily demonstrable empirically but difficult to define precisely. We can single out yield stress as a truly definable, pertinent property and then have a quantitative parameter in terms of which we can treat consistency. Criddle and Dreher [ l ] observed typical solid-body stress-strain behavior in greases, with an elastic region, a region of plastic deformation and an ultimate yield or rupture point. At rest grease behaves like a solid body; provided the specimen is not too big, i t will not flow under the force of gravity.* As stated above, a grease contains two basic components: an oil, which has the flow properties of a liquid; and a thickener o r gellant, which is a solid insoluble in the oil. I t will be shown later that the

*The behavior described above is idealized and simplified. In fact the yield point is affected by the rate of strain and there is slow creep at pressures within the nominal elastic range.

oil behaves as the continuous phase in this system. We must therefore explain the structure and the behavior of the system in which the continuous phase is a liquid and which responds to initial stress as an elastic solid. The structure and behavior is that of a gel. Following the reasoning of Hotten [ 2 ] , we shall call the solid component the g e e Lanf rather than the thickeneh. In this way we emphasize the fundamental structure of the grease as a gel and call attention to the difference between the action of a gellant and that of a polymeric viscosity improver, which functions by dissolving in the oil. Many different solids can be used to gel oils into greases. However, the gelling agents around which the standard technology of grease-making developed historically are the metallic soaps of fatty acids, and the bulk of the present-day output of greases consists of soap-gelled products. Therefore, when the nature of the grease is not explicitly specified otherwise, it will be understood that the gelling agent is fatty soap. The usual technique in making a soap-gelled grease is to form and disperse the soap in the oil at an appropriately elevated temperature and then to cool the mixture. The desired consistency in the finished product is achieved by a vigorous stirring and shearing process, known as milling. One of the forms in which soaps crystallize is a long-fiber phase. The structure of the soap phase in a grease is affected by the intrinsic nature of the fibers p e h b e , by the network which they form as they are generated and dispersed in the oil, and by the rearrangement of the fiber structure when the grease is milled. With the aid of electron microscopy, pictures showing soap fibers in great detail have become commonplace. Figure 18-1 shows some views of soap fibers separated from greases and converted to replicas by vacuum-shadowing with metals. The technique for making these replicas involves leaching the oil phase away from the soap with a volatile hydrocarbon solvent. While this treatment preserves the structure of the individual soap fibers adequately, it destroys the three-dimensional structure of the soap phase as a whole, upon which the characteristics of the grease depend. To preserve the structure of the soap network as it exists in the grease, the o i l phase must be displaced by a liquid that has the correct combination of critical temperature and critical pressure, so that i t can be evaporated from the oil-free soap without dissolving any of it and without forming a liquid film on the surface of the fibers which would disrupt their structure by surface tension forces. The soap skeleton resulting from this treatment is often termed an aerogel. Peterson and Bondi [31 described the sodium soap aerogel obtained from a grease by displacement of the oil with butylene as a chalky, pithy, rather brittle, opaque, white, porous

523

Figure 1 8 - 1 . Soap fibers from greases, photographs of replicas taken by electron microscopy. (a), ( b ) Lithium 12-hydroxystearate. ( c ) Lithium 1 nm oleate. ( d ) Calcium-sodium soap. Fiduciary marks:

524

solid which had maintained the bulk volume of the original grease to Determination of the surface area of the aerogel by nitrogen within 1%. adsorption and comparison with the area calculated from fiber diameter The grease which indicated the absence of pores in the fibers petr b e . was reconstituted by allowing the oil to permeate the aerogel in vacua experienced some shrinkage in gel volume. Key properties such as cone penetration value and durability of consistency in the roll test differed little for the original and the reconstituted grease. McClelland and Cortes [ 4 ] prepared aerogel specimens which could be examined directly in the electron microscope. These preparations were compared with soap specimens which had been prepared by the conventional solvent-washing techniques. All specimens prepared by the aerogel technique showed the typical closely interlocked network structure, whereas the soap structures resulting from solvent-washing were broken down, with dispersed fibers. Aerogels were also studied for non-soap gellants such as treated bentonite, purified attapulgite clay, esterified silicic acid and carbon black. I f structure is imparted by the gellant, what part does the oil play in the behavior of a grease? Let us think of an ideal grease as one with the fibers of the gellant interlocked to form a uniformly arranged system of passages filled with liquid oil as a continuous phase. Then let us consider a cubical element of this grease, restrained from gross motion as a whole but with the liquid phase free to move through the cube under the influence of the hydrostatic pressure p in the direction from face There will be an efABCD to face A'B'C'D', as illustrated in Fig. 18-2.

D

A,

61

Figure 18-2. Gel structure of a grease and the flow of the oil phase. The oil will nove through the pores of the gel structure under the pressure p.

525

flux of oil through the pores of the gellant structure and out of the cubical element at the face A ' B ' C ' D ' . As a simplified analogue of a passage in the gel structure of grease let us examine the behavior of a liquid in a straight capillary tube of circular cross-section. I f we start with the capillary filled with liquid and displace a volume V in the capillary to form a drop, as shown in Fig. 18-3, two general cases arise. I f the liquid wets the wall of the

Figure 18-3. a grease.

Capillary analogue of oil flow through the gel structure of

capillary but movement of the column a distance h leaves the exposed wall dry, then the work done by the moving liquid must be equal to the work of wetting plus the work of creating new surface in the exuded drop. The energy thus required is given by the general relation n t2p h = Z n t h E , + A A E ~ (18-1) where p is the hydrostatic pressure, t the radius of the capillary, A A the increase in the surface area due to the exuded drop, E l the energy of wetting per unit area and E2 the surface energy of the liquid per unit area. I f the movement of the liquid in the capillary does not de-wet the wall, then ntI2ph

=

(2nt'h

+

aA')E2

(18-2)

Zqn 1 8 - 2 probably represents the behavior actually encountered, as complete de-wetting by retraction of the liquid is unlikely.

The basic model of a grease, then, is that of a self-supporting structure of interlocked fibers or aggregates of gellant, within which liquid is held by capillary forces. This model is consistent with the two characteristics most typical of grease: resistance to change of

526

shape below the yield stress and relatively easy flow at higher stresses. However we shall find that the actual behavior of real greases has a number of nuances and complexities which require modification and sophistication of this basic model. 18.2.

THE MANUFACTURE OF LUBRICATING GREASE

In principle the manufacture of a grease comprises two simple operations: dispersion of the gelling agent in the oil, and mechanical working o r stirring of the gel to give the grease the desired consistency. In practice there are many technological complexities, as the reader can discover by consulting a specialized text on the subject [ 5 1 . Our interest in the influence of technological manipulations in the manufacturing process on the properties of the grease is motivated by our concern with the relations between the properties of greases and their function as lubricants. The most important greases are those gelled by metal soaps of fatty acids. Table 1 8 - 1 gives a schematic outline of the typical processes by which soap-gelled greases are manufactured. These processes can have TABLE 1 8 - 1 .

SCHEMATIC OUTLINE OF MANUFACTURE OF SOAP-GELLED GREASE

I. Soap formed in the oil A. Saponification of glyceride

fats or other fatty acid esters

B. Saponification of fatty acids

1 . Dehydration 2. Dissolution or tempering of soap in the o i l 3 . Cooling and crystallization of the soap 4. Milling for consistency 11. Preformed soap added to the oil

1. Dissolution o r tempering Cooling and crystallization 3. Milling 2.

direct influences on the properties of the greases which they produce. For example, the direct saponification of a glyceride fat in the oil which is to be gelled into a grease means that the water which participates in the saponification and the glycerol released from the fat must be removed from the mixture. How well this is done is a function of the time allotted and of the configuration of the equipment. Thus, a grease gelled by preformed dry soap could have properties different from one made with soap saponified in b i t U and not fully purged of small amounts of retained water o r glycerol. After the soap has been made and dehydrated, the reaction mixture

is

527

tempered thermally to obtain the desired gel structure. To economize on heat in the commercial manufacturing process, the dehydrated soap is not dissolved. in the oil and then crystallized o n cooling. Instead, a thermal soak which gives the desired crystal structure to the soap in the solid phase is employed. The phase transitions involved in the production of lithium soap greases were investigated by Suggit 161, who showed that soaps prepared below a critical temperature characteristic for each fatty acid anion species crystallize as platelets which are mediocre gellants for grease. I f held above this critical temperature, the platelets are transformed to the type of fiber structure seen in Fig. 18-1. Suggit found the critical temperature for lithium stearate to be 468 K (195 C). The phase diagram for lithium stearate and white oil (390-440 molecular weight) as determined by Cox 171 and shown in Fig. 18-4 has 458 K (185 C) as the temperature of transition from the field representing a mixture of lithium stearate crystal I and isotropic solution to the field representing a waxy phase. I

250

I

I

I

I

I

I

I

E

I

~

/

00 200-/cLD

1 \

0

v

\

150-

-II

B+E

3

Eg 100E

I-"

50, I

A+ E I I I

I

'

I

I

I

-

Mole-% Lithium Stearate

Figure 18-4. Phase diagram for the system lithium stearate-white oil. Crystalline lithium stearate I. B: Crystalline lithium stearate 11. C: Waxy phase. D: Liquid crystal phase. E: Isotropic solution. Data by D. B. Cox [71. A:

Both Suggit [6] and Cox [7] discussed those structural aspects of the waxy phase which would favor the formation of fibrous soap crystals. It is obvious that the fibrous soap structure desired in a grease at room temperature must be in a metastable, supercooled state. Cox commented'on the strong supercooling of the waxy phase 171. Vold, 3 z u and Bils 181 were able to demonstrate supercooling directly by comparison of heating and cooling curves in differential scanning calorimetry of the system lithium stearate in white oil. In modern greasemaking oil mixture is subjected to break up clumps of soap the grease. This stiffens

technology the to milling: i . and distribute the grease, a s

gel formed by cooling the soape . , passage through narrow gaps

the fibers uniformly throughout i s evidenced by decrease in the

cone penetration values; but even more important, it reduces gross leakage of oil out of the gel structure [91. Evidently reduction of the proportion of large passages in the free space of the soap structure is an important aspect of improving the utility of a grease. At least 90% of the grease produced in this country is gelled with soaps, and in these soaps the most prevelant cationic constituents are calcium, lithium and sodium. At the most, only 10% of the soaps have other cations, principally aluminum, barium, strontium, and perhaps lead. Glyceride fats are most likely to be tallow, animal grease,* hydrogenated lard oil, hydrogenated vegetable oils, liquid vegetable oils, or fish oils (liquid and hydrogenated). Mixed acids from fats and*oils are available commercially, as well as individual constituent acids such as stearic acid, palmitic acid, oleic acid, myristic acid, lauric acid, etc. fr fatty acid of particular importance is 12-hydroxystearic acid. Commercial grade fatty acids are usually contaminated by their nearest homologues. Commercial 12-hydroxystearic acid is likely to be the mixed hydrogenated acids from castor oil. It is thus apparent that one of the chief technological difficulties of making grease reproducibly is control of the quality of the starting materials. Non-soap gellants for grease add u p to a n impressive list, examples of which include the following: treated bentonite clays, treated attapulgite clays, terephthalamate salts, treated silica, aryl ureas, indanthrene, phthalocyanines, carbon blacks. The same general principles which govern soap-gelled grease structure hold for these non-soap gellants, but individual techniques for making the grease differ from one type of gellant to another. Another variation in grease formulation is the substitution of a synthetic organic liquid for the petroleum oil phase, particularly for use in severe environments. Silicones of various types-dimethyl, methyl phenyl, trifluoropropyl-have been incorporated into greases for such service. 18.3.

FURTHER CONSIDERATION OF GREASE STRUCTURE

Now that we have some idea about the composition of greases and how In they are made, let us inquire into their structure a little further. particular we wish to establish a basic connection between the structure of a grease and the reason it is used for lubrication service. 18.3.1.

Bleeding and Permeability

Booser and Wilcock 1101 viewed the function of grease in ball bearing lubrication as a controlled release of oil to the zone of contact of the balls with the races and the cage. Following this line of thought, A. E.

*A mixture of solid stearine and liquid olein; not the lubricating grease made by gelling liquid lubricating oil.

529

Baker [ 1 1 1 regarded test data on the bleeding of oil out of a grease a s a significant evaluation of its lubricating quality. The bleeding test employed to arrive at this conclusion is a simple one [121. Ten grams of grease are placed in a wire mesh cone hung in a closed vessel which catches the oil that bleeds from the grease. Temperature and time can be fixed to suit the experimenter's requirements. Obviously the test is grossly empirical, and moreover its significance is obscured by complications which will be discussed later in this section. As pointed out in Secrion 18.1, grease is composed of a network of solid gellant fibers that hold the continuous liquid phase by interfacial and surface forces. Spontaneous exudation of liquid from this structure requires the unbalancing of these forces. The method of Sisko and Brunstrum 1 1 3 1 for measuring the permeability of grease to the movement of oil depends on driving the exudation artificially; the apparatus is illustrated in Fig. 18-5. The sample of grease is filled into the volume bounded by the retaining ring and the screen-supported Millipore filter;

Burette-

n

a

Gaskets Retainingring

Screens and millipore filters

Grease'Sample Figure 18-5. Apparatus for the grease by oil

determination

of

the

permeability

of

the thickness and the cross-sectional area of the sample are then known. clamp fastens the sample to the adapter that carries the burette. The adapter and the burette are filled with oil, preferably the same oil from which the grease was made. Under these conditions, the only liquid surfaces and interfaces of any consequence are those at the bottom surface of the sample tisk, and even those can be reduced to negligible proportions by having the bottom of the sample holder in contact with a pool of oil in a receiver. Movement of the oil will be governed by the viscous resistance of the passages in the gel structure and Darcy's law for the flow of liquids through porous beds is taken to be applicable: A

530

where u is the velocity of oil flow through the sample, p is the pressure is the viscosity of the oil. The perdrop across the thickness a, and meability B has the dimensions of area, but it can also be interpreted as the volumetric flow rate of the liquid through the unit cube of porous material under unit pressure drop. The experimental determination of permeability by the method of Sisko and Brunstrum [13] is obtained from the rate of fall of the level of the oil in the burette. Then from Eqn 18-3 we get h2

dh

- - _ = -

K2 d t

Bpgh

(18-4)

qa

where n is the radius of the burette, R the radius of the grease sample, h the height of the oil column above the sam le, p the density of the oil and cj the acceleration of gravity. Equation 18-4 can be rearranged to

g = -

2.303 vanL d(Racj h )

5R2

dt

where v is the kinematic viscosity.

(18-5) Collect ng the constants gives us

d(toy h)

B = - k

dt

(18-6)

The validity of E q n 18-5 was tested experimentally by Ewbank and his co-workers 1141. They found that plots of h against t on semilogarithmic coordinates were consistently linear. The viscosity of the permeating 2 oil was varied over the range 0.00003-0.001 m / s (30-1000 cs), but fluctuations in the value of 8 stayed within the range 5-10% i f the oil was of the same general chemical type. Change in the type of oil sometimes gave deviations of up to 40% in the permeability. In some cases sensitivity to the thickness of the sample bed caused as much as 30% deviation, especially when the permeability of the qrease was intrinsically low * I t is a mistake, however, to ascribe deviations from the results expected by Darcy's law to weakness of the experimental technique. A more productive point of view is to assume that Darcy's law holds for the ideal gelled grease structure and to interpret deviations from predicted behavior as informative of the actual structure. For instance, Brown and Ewbank [15] proposed that permeation takes place predominantly through the larger pores of the grease structure and cited evidence that only about 25-50% of the oil held by a grease can be made to flow out of the structure. Persistent retention of the oil can be ascribed to physicochemical interaction with soap fibers, the effect of which is

531

relatively more pronounced in the narrower passages. Thus the strong effects of oil viscosity and oil type reported by Zakin and T u [ 1 6 1 can be given a rational explanation. Greases are often used to lubricate bearings at elevated temperatures, sometimes 4 7 8 K ( 2 0 5 C ) or higher. Therefore oil bleeding tests are frequently carried out at the anticipated working temperature of the grease. Two factors affect the influence of temperature on oil separation. One is the decrease in the viscosity of the oil as the temperature rises, thereby facilitating filtration of the separated oil away from the grease. The other factor is the phase state of the oil-soap system at from data by Hotten and Birdsall the test temperature. Figure 1 8 - 6 , [ 1 7 ] , shows the combined effect of these two influences on the bleeding of greases made with various lithium soaps in naphthenic oil. A l l the

I , , , , , , , ,

0 25 5 0 75 100 125 150 175 200

~

!5

Ternperature,deg . C

Figure 18-6. Eff ect of temperature on oil separation from greases made with lithium soaps: 1 2 % of the lithium soap in naphthenic oil: 3 hours vacuum filtration at the indicated temperature. Data by biotten and Birdsall [ ! 7 1 . greases exhibit an increase in the amount of oil separable by 3 hours vacuum filtration as the temperature rises to a critical value which depends on the soap. The maximum in the bleeding curve is followed by a decrease which is quite sharp for the greases made with oleate, stearate The grease or myristate soap but less so for the laurate soap grease. gelled with lithium 12-hydroxystearate shows the least sensitivity of bleeding to temperature and also has a high critical temperature. The sharp decrease in bleeding is probably associated with a transition to the waxy phase. I n Fig. 1 8 - 6 the dip in the oil separation curve is at

532

453 K ( 1 8 0 C); in Fig. 18-4 the transition for the system lithium stearate-white oil is at 463 K ( 1 9 0 C). The sharp rise in the bleeding of oil from the lithium 12-hydroxystearate grease is due to transformations to the liquid crystal and the isotropic liquid states. If controlled bleeding of oil is desired for the lubrication of bearings, then Fig. 1 8 - 6 illustrates the importance of the phase behavior of the soap component of grease with change of temperature. The reason for the superior utility of lithium hydroxystearate greases is apparent from the bleeding behavior. 18.3.2.

Consistency and Penetration

It has already been pointed out that the consistency of a grease is the characteristic most overtly connected with its functionality. In qualitative terms consistency can be thought of a s resistance to unwanted flow; in terms of performance it is manifest as antislumping behavior, the correct degree of channeling, resistance to ejection from a bearing by centrifugal force, etc. The physical test by which consistency is evaluated quantitatively is the ASTM cone penetration determination [ l a ] , which is illustrated schematically by Fig. 18-7. The cone and its attachments weigh 0.1500 kg. At the start of the test the cone and dial

I !

Figure 18-7.

initial position of the cone

Cone penetration of greases

assembly is adjusted so that the tip of the cone just touches the level, undisturbed surface of the grease sampie (AA') when the dial reads zero. The cone is then released and sinks into the grease. The distance A , read on the dial in tenths of millimeters, is the penetration value of the grease. The test is usually carried out at 298 K (25 C). The softer the grease the greater the penetration value. Table 18-2 gives the relation between the National Lubricating Grease Institute classification system and penetration values.

533

TABLE 18-2.

PENETRATION VALUES FOR NLGI GREASE GRADES

NLGI Grade NO. 000 00 0 1 2

3 4 5 6

Penetration at 2 9 8 K (a) 445-475 400-430 335-385 310-340 265-295 220-250 175-205 130- 1 6 0 85-115

(a) ASTM D 2 1 7 (worked 6 0 strokes). The ASTM penetration value is not a measure of yield stress. The theoretical difficulties in the determination of the true yield stress of a grease have been discussed by Evans, Xutton and Matthews [ 1 9 1 . Greases do not really have a sharp stress boundary between elastic and plastic deformation; there i s always some residual creep although the flow rate may be slow enough to be treated as zero for practical purposes. The apparent viscosity of grease is dependent on rate of shear, and slow lowering of.the penetrator at a uniform rate will give results different from those of the quick-release ASTM method. Also, the buoyancy due to the behavior of the grease a s a fluid must be taken into account. Evans e t al. developed a relation for a simple right circular 90' cone as an indenter:

w

Pb =

- W'

-

where on the in the ing as

A

(18-7)

pb is the bearing pressure which supports the cone, W is the load cone, W ' is the buoyancy force and A is the cross-sectional area plane of AA'. I f T~ denotes the yield stress of the grease behava plastic solid, then

where c is a constant of proportionality which in theory is obtainable Therefore p b is from the solution of the plastic deformation problem. fundamentally proportional to the yield stress of the grease, whereas the empirical ASTM penetration value is not. Nevertheless, it is the ASTM penetration numbers that are the generally accepted measure of the consistency of greases, and numerous investigations are on record where the penetration values are used to assess the influence of the type of gellant, the concentration of the gellant, the method of manufacture, the working of the grease (milling, shearing, flow), etc. The empirical character of such information has

534

TABLE 18-3.

EFFECT OF FIBER LENGTH ON GREASE CONSISTENCY ~~~

Nylon fibers

Soda soap grease

Axial ratio

Micropenetration, fiber diameter of

L/D

300/1 100/1 70/1 50/1 6/ 1

95

Axial ratio L/D

118 125 -

165 208 208 Fluid

Micropenetration

170/1 80/1

120 200

Data by Bondi e t a L . [ 2 0 ] . not seriously affected its utility for technological purposes. A direct demonstration that the geometry of the gellant fibers influences the penetration response of grease is found in the work of Bondi and his collaborators [20], who gelled a turbine oil into a grease by incorporating 10% of completely insoluble nylon fibers. The consistency of the resulting product depended on the ratio of length to diameter ( L / D ) of the suspended nylon particles, as shown by the data in Table 18-3. The same trend holds for a grease gelled by a soda soap. R. H. Leet [211 obtained the ratio of the average fiber length L to the average diameter V for nine greases of different composition, samples of which were worked i n various ways o r allcwed to harden by aging and then tested for penetration. The relations between ASTM penetration value and L / V are shown diagrammatically in Fig. 18-8. The influence of the individual nature of the grease is evident, but there is also a consistent linear

400

I

I

c

g e c C

fv)a a"

& \ \ \ 0 0 3 g

200

A ,

535

relation between ASTM penetration and L/D for each grease. Other data showing the influence of L / D on penetration for a grease gelled by 7% lithium 12-hydroxystearate have been reported by Borg and Leet [22]. All greases suffer a degradation in consistency when subjected to prolonged shearing action. One of the devices commonly used to shear greases in stability testing is the ASTM grease worker, a full description of which is given in the ASTM penetration Method D 217 [l8]. In essence the grease worker is a circular plate 2-15/16 inches in diameter with 41 1/4-inch holes. The plate is worked up and down with a stroke length of 2-5/8 inches through the grease sample in a cup 3.000 inches in diameter. The instructions f o r standard working call for 60 double strokes [18]. Prolonged working may amount to 100,000 strokes or more. Table 18-4 gives data by Woods and Trowbridge [231 showing the effect of prolonged working on penetration value for six different types of soapgelled greases. Another method of working greases is with the roll tester [241, which consists of a cylinder 3-35/64 inches i n diameter and 7-3/32 inches long, i n which are placed a 50-gram sample of grease and a solid roller 2-3/8 inches in diameter, 6-15/16 inches long, weighing 5 kg. The cylinder is driven o n a set of idlers at 165 rpm. The grease is sheared by the motion of the roller on the inner surface of the cylinder. Loss of consistency is monitored by a quarter-scale penetration test. Figure 18-9 shows some characteristic behavior. Comparison of Fig. 18-9 with Table 18-4 shows that the results of the roller test and the grease worker test do not rank the greases in the same relative order. 18.4.

THE FLOW OF GREASES

I n lubrication with a liquid, the rheology of the lubricant at the functioning site is the dominant behavior; transportation of the lubricant to that site, e . 5 . a bearing o r a gear, by piping or spray nozzle is on the whole a routine matter and rarely affects the selection

TABLE 18-4.

EFFECT OF WORKING ON PENETRATION OF SOAP-GELLED GREASES

Type of soap

ASTM penetration 60 strokes

100,000 strokes

277 295 282 270 269 268

286 335 354 358 370 380

Li 12-hydroxystearate Ca tallow Na tallow/stearate A 1 stearate Li stearate Na tallow Data by Woods and Trowbridge [231.

536

240

200

s s

E

160

W C

a

2

P 120 80

I0

I 24

I

t

48 72 Rolling Time, hours

96

Figure 18-9. Roll testing of grease consistency. Gellants: A . Lithium stearate. B. Lithium 12-hydroxystearate. C. Calcium tallow soap. D. Sodium tallow-stearate. E. Aluminum stearate. From data by Woods and Trowbridge [23].

of the lubricant. But when the lubricant is a grease, rheological problems associated with getting i t to the functioning site are often a s important as those directly connected with its primary lubricating action. These two aspects of grease behavior are frequently at variance with each other. For instance, in a bearing it is preferred that the grease remains packed in place and not be bodily moved around by stress, whereas for transportation in a piping system, gross flow is desired. Let us look at the behavior wanted of grease in a rolling element bearing. Some lubricant must get into the conjunction zone between the ball or the roller and the race, small though the quantity required may be. There are a number of reasonable models f o r how the lubricant gets into the conjunction zone. If we postulate that it is the total grease which flows into the conjunction and functions there as the lubricant

0

2.5

a Q 2.0

(u

< 1.5

1 E 3i 8

F First cycle

300 seconds

E--

Sleady stale after 1000 sec preshearmg

1.0

8 0.5

10

0.0

I 8

I

1

I

I 1

I

160 8 160 8 Rote of Sheor,.i, lo3 sec-'

I 16

Figure 18-10. Flow behavior for lithium stearate grease. Bauer, Finkelstein and Wiberly [261.

From

data

by

537

without segregating into oil and soap, then the principles of elastohydrodynamic lubrication can be applied. A detailed analysis is given by Kauzlarich and Greenwood [ 2 5 ] ; what interests us particularly in this work is the viscosity function used for the grease. An informative study of the flow behavior of soap-gelled grease is that of Bauer, Finkelstein and Wiberly [ 2 6 ] . Figure 1 8 - 1 0 shows the relation between the rate of shear and shear stress for a grease gelled with 12% lithium stearate. The three diagrams show the behavior for the first cycle of shearing, the second cycle, and the ultimate steady State. The first cycle is characterized by pronounced hysteresis as the rate of shear is increased from zero to the maximum of the viscometer and then decreased back to zero. In the second cycle the hysteresis loop is much smaller. A shearing time of 100 seconds at a shear rate of approximately 975 5-l removed the hysteresis loop from the flow curve having a cycle period of 300 seconds. With the hysteresis eliminated, the flow diagram clearly shows the existence of a yield stress. Bauer and his co-workers [ 2 6 ] proposed the following equation for the flow relation of greases: T

-

To

= Cli

+

-n C2y

where c l and c2 are constants and T~ is the yield stress. Greenwood [ 2 5 1 generalized the flow function to T

-

To =

f(i)n

(18-9)

Kauzlarich and

(18-10)

in order to facilitate manipulation of the elastohydrodynamic computations. The evaluation of f(:)n required for a specific problem can be obtained from experimental data by graphic or numerical methods. Usually it is assumed that hysteresis has been eliminated. But obviously it is incorrect to use steady-state grease rheology when measuring starting torque.after a long rest or evaluating flow resistance in slow reciprocation. The thixotropic properties of grease and the relation of structure to thixotropy, as exemplified by the work of Eyring and his collaborators C27, 2 8 1 , can be highly pertinent aspects of the flow of grease, although the details of an adequate treatment are too involved for the space available here. Just a s complex is the viscoelasticity of grease. The work of Forster and Kolfenbach [291 indicates a relation between viscoelastic behavior and structure. The flow of grease in piping or tubing brings up two questions of technological importance: (a) How much pressure drop is there along the run of pipe? (b) Given the driving pressure at the pump, what is the flow rate at any selected distance along the piping? Both of these questions can be treated adequately in terms of the general principles of

538

viscometry discussed in Chapter 4 and the flow relations for grease given above. The following expression (see Chapter 4, Eqn 4 - 1 4 ) can be used to obtain 2, the volumetric rate of flow through a tube:

where A p is the driving pressure, R the radius of the tube, L its length is a functional relation between the shear stress and the rate and T"/+ By one means of shear such as shown in the flow diagram of Fig. 1 8 - 1 0 . or another the steady-state flow diagram can be made to yield a value for A capillary flow determination such as ASTM Method D the exponent n'. 1092 I 3 0 1 yields values of 2 for preselected values of Ap, R and L . Furthermore, Eqn 4 - 1 of Chapter 4 gives the expression below for the shear stress at the wall of the tube o r piping through which the grease is flowing: ApR

T = -

2L Substitution into Eqn 1 8 - 1 0 gives APR T - T o = -

(18-12)

2L

The yield stress T~ can be obtained by the rotational viscometry technique as shown in Chapter 4. Thus from two sets of rheological determinations, one the capillary flow technique and the other rotational viscometry, enough information can be obtained to treat the problems associated with the flow of grease in pipes. A quantity cited fairly often in discussing the properties of greases is the apparent viscosity. This is the empirical ratio of measured shear stress to rate of shear: T

nappatlent =

Y

(18-13)

Apparent viscosity is useful as an evaluation of the difficulty of pumping a grease. Since greese moves by non-Newtonian flow, knowledge of the rate of shear and also of the yield stress required to initiate flow is necessary for apparent viscosity value to have any utility. 18.5.

GREASE AS A LUBRICANT IN SERVICE.

Greases are used as lubricants i n a wide range of service conditions, The lubricathe more important of which are summarized in Table 1 8 - 5 . tion of high-speed rolling-element bearings is probably the most familiar service use of grease, but other applications are the lubrication of

539

TABLE 18-5.

TYPES OF SERVICE FOR LUBRICATING GREASES ~

Motion and contact

Examples

Unidirectional Fast, continuous Slow, continuous Slow, intermittent

Rolling element bearings Bearings, cams Gears, cams

Oscillatory or reciprocating Slow to moderately fast

Suspensions, linkages, cams

slow-speed plain bearings a s well as of large, slow-acting gears which i t is impractical to enclose in a case that holds an oil lubricant. Automotive suspensions, which cannot be sealed adequately against oil leakage, are also advantageously lubricated with grease. Basically the lubrication of a high-speed rolling element bearing is no different with grease than with oil. Booser and Wilcock [ l o ] studied the running life of No. 306 ball bearings turning at 3600 rpm under a radial load of 7 1 1 . 7 N 1 1 6 0 lb) when lubricated with oil in submilligram quantities. With less than 0.35 mg of oil on the bearing, running life was gi’ven by the expression

t

=

0.66

w

2 being the life of the bearing in hours and

milligrams. given by

LU the quantity of oil in For quantities of oil greater than 0 . 3 5 mg, bearing life was

I t was calculated that 0 . 3 5 rng of oil would cover the balls, races and F o r bearings retainer pockets with a film 51 nm ( 2 rnicroinches) thick. of conventional precision (Grade ABEC-1) lubricated with one milligram of oil, a running time of 4 . 7 hours was observed, and with high-precision Grade ABEC-5 bearings the running time was 1 4 . 5 hours. With fully packed open bearings lubricated with grease the life times were 2000 and 4000 hours respectively. The grease is believed to function a s a source of oil by controlled bleedincj a s it is worked by the motion of the roIling elements in the bearing.

However, there are n o a phiahi grounds for excluding the possibility that the whole grease instead of just the exuded oil is the functioning lubricant. Dyson and Wilson I 3 1 1 and also S . Y. Poon [ 3 2 1 have published film thickness data for the elastohydrodynamic lubrication of rolling disks with grease. This may be regarded a s a close experimental approximation of a roller acting against a race in a bearing. Figure 18-11 is a diagram of typical results obtained. Curve A shows the ratio of

540

0

oc"=

1.0

ln ln 0,

c

1

0

._ E LL

0.0 0 10

20

30 40

50 90

Time, minutes

Figure 18-11. Elastohydrodynamic film ments. 10% Lithium 12-hydroxystearate sure; 335.3 cm/s surface velocity at base oil film thickness 2.201 Um. A : before experimental r u n . Data by Poon

behavior of grease in disk experigrease; 965.3 MPa contact pres800 rpm; temperature 308 K (35 C ) ; Original grease. B: Presheared [321.

measured film thicknesses for a grease gelled with 10% lithium 12hydroxystearate and for the base oil a s a function of the duration of running. At the beginning, the thickness of the grease film was 1.6 times that of the base oil, but after approximately 50 minutes running the ratio dropped to a steady 0.7. The part that degradation of gel structure by flow through the conjunction zone played was assessed by preshearing the grease in a gear mill before the disk experiment. The initial film thickness ratio for grease/oil decreased to 1.1 and a final ratio of 0.7 was attained in 30 minutes. The film thickness of the ungelled base oil was 2.201 urn ( e 7 microinches); hence a ratio of 0.7 c o r responds to 1.549 Urn ( 6 1 microinches) for the grease film. Even though the film of grease was thinner than that of the base oil, it was still thick enough to prevent contact of the bearing surfaces. Poon [321 explained the film behavior of grease in terms of viscoelastic behavior a s the lubricant passes through the conjunction zone. Kauzlarich and Greenwood [251 suggested that because of its gel structure grease heats u p by shear faster than oil and loses the heat by conduction more slowly. I n their estimation, a thermal rather than an isothermal treatment of the elastohydrodynamic problem is required. Elastohydrodynamic action of the total grease and selective bleeding of the oil are not mutually exclusive mechanisms in the lubrication of I n this respect grease i s a versatile rolling-element bearings. lubricant, for i f the flow of the grease a s a whole suffers a temporary interruption, then the residual oil coating the bearing can protect the system from damage for a while. Still another mechanism for lubrication by soap-gelled greases stems from the fact that soap is a "boundary" lubricating agent. Using a slow-

541

speed pin-on-disk type tribometer, Godfrey [33] showed that the friction with dry soaps such as calcium stearate or sodium stearate, as influenced by temperature in the range 373-473 K (100-200 C), resembled that of the greases made with these soaps and was quite distinct from that of the base oil. Simple dispersions of silica, bentonite o r calcium carbonate in the base oil showed maxima in the coefficient of friction at 473 K , whereas the soaps and the greases made with them gave minima at that temperature. Horth, Sproule and Pattenden [341 compared the frictional torque of a 120' journal bearing lubricated with greases against the torque obtained with the base oil; their results are summarized in Fig. 18-12. Speed-governed transitions to hydrodynamic action are apparent for the base oil and for the greases gelled with aluminum soap,

I

1

I

I

I

L

I

1

I

,

0.05 0.1 0.2 0.5 1.0 2.0 5.0 10 Journal Speed, cm/s Figure 18-12. Speed-dependent torque behavior of greases in a journal bearing, steel journal in bronze bearing: load 3718 N , temperature 311 K (37.8 C ) . A: Base oil 300 SUS at 37.8 C. B: Aluminum soap grease. C: Calcium soap grease. D: Sodium soap grease. E: Lithium soap grease. Data by Horth, Sproule and Pattenden [341.

calcium soap or sodium soap, but there seems to be no identifiable transition speed for the lithium soap grease. When the torque values are converted to coefficients of friction in the non-hydrodynamic region, there is a reliable difference between the friction with the base oil hnd the greases. Interpretation of these data would be even better i f flow curves of shear stress vs. rate of shear were available for the greases. Although elastohydrodynamic transport of grease through the conjunction between the rolling element and the race is the operative mode of flow for the basic lubrication process, the overall movement of the lubricant in a grease-packed rolling-element bearing is more complicated in than that. Consider the ball bearing shown diagrammatically Fig. 18-13a. The movement of the inner ring rotates the ball in the direction shown, but there is also partition of sliding so that the entire ball assembly held by the retainer will also rotate slowly. The

542

Grease within

Shield vent-

-&

Retainer Inner ring

Figure 18-13. Diagram of ball bearing. (a) View showing modes o f motion which interact with grease lubrication. (b) Cross-sectional view with shields mounted. grease packed into the bearing between the rings is subject to gross stirring by the following kinds of action: (a) There will be viscous shear, most probably turbulent, of the grease in the gap between the inner and the outer rings as the inner ring rotates. (b) There will be turbulent mixing of the grease as the ball and retainer assembly plows (c) Superimposed on the movement of the grease due to the through it. rotating of the bearing components around the axis of the shaft there will be movement due to the rotation of the balls around their individual axes. In addition to these large-scale movements of the grease there are two other modes of motion, which under favorable circumstances should proceed by streamline flow of grease through the conjunctions between the balls and the races, and flow of grease between the balls and the retainer. The gross flow of soap-gelled grease in rolling-element bearings was studied by O'Halloran, Kolfenbach and Leland [ 3 5 ] . They used a shielded ball bearing, a cross-sectional diagram of which is shown in Fig. 18-13b. A weighed sample of grease treated with two kinds of dye, one an'oilsoluble blue and the other a water-soluble sodium fluorescein which dissolved in the soap phase, was packed into the bearing proper, and a weighed portion of undyed grease was put on the shields. The mixing of the qrease was monitored by assaying the migration of the dye into the grease on the shields. The results showed that the grease moved as an entity; i.e. soap and oil moved at the same rate. Soft greases mixed readily, whereas with harder greases the moving components of the bearing tended to plow channels and leave portions of the grease unmixed.

543

0

10 20 30 40 50 Running Time, minutes

60

Figure 18-14. Grease consistency and the running temperature of a rolling element bearing. I: Grease with initial worked penetration 200. 11: Grease with initial worked penetration 260. Spindle speed 10,000 rpm. Data by Horth, Norton and Pattenden [361.

TABLE 18-6.

DISTRIBUTION OF GREASE IN SHIELDED BEARINGS Grease I (a)

Grease I 1 (a)

Total original packing

3.00 grams

3.00 grams

Total grease in bearing within cage outside cage

1.10 0.32 0.78

1.43 0.34 1.08

Total grease on shields on shield faces in shield cups

1.92 1.04 0.87

1.53 1.15 0.37

(a) One hour at 10,000 rpm. 1361.

Data by

Horth,

Norton

and

Pattenden

The extent cf mixing is reflected in the gross temperature behavior of the running bearing. Figure 18-14 shows the two extreme types of behavior as observed by Horth, Norton and Pattenden [361. In Curve i the temperature of the bearing quickly rises to a maximum and then gradually stabilizes at a level less than 2.9 K above ambient. The time interval t ' is often designated as the clearing time because i t is associated with the expulsion of the excess grease from locations where it can be churned by the moving components of the bearing and thus generate heat. In Curve I1 the clearing phenomenon is absent: the temperature of the bearing rises to a level 33 K above ambient. Horth e k a e . 1361 demonstrated that the distribution of grease in the disassembled bearings was consistent with this explanation of the temperature behavior (see Table 18-6). With Grease I , once the excess was displaced from the path of the moving ball/ retainer assembly, little back mixing took place, whereas Grease I 1 readily slumped back into the inter-ring annulus. This was demonstrated

544

by dye-partition experiments, which showed that there was only 33% back mixing of Grease I from the faces of the shields into the bearing in the course of an hour's running, but 100% back mixing of Grease 11. The worked penetration of Grease I when i t was packed into the bearing was 200, that of Grease I 1 260. However, Horth e t at. 1361 found that the penetration value was not sufficient by itself to predict the behavior of a grease in an operating bearing. Soap content is another important parameter which is related to the tendency of a grease to channel in the bearing and therefore to r u n cooler. Channeling greases are characterized by sharply defined yield stress, by shear hardening in the bearing and by short fibers. It is the entire complex of rheological properties which influences the functioning of a grease in service. SO far n o all-encompassing generalizations have been developed. In lieu of an overall rationale, there are numerous empirical tests for evaluating greases as lubricants for rolling-element bearings. A. Schilling [37] published descriptions of 14 different bearing tests with outlines of the failure criteria and diagrams of the operating principles of the testers. These tests are concerned with the ability of the grease to prevent bearing failure o r its ability to withstand prolonged shearing without intolerable loss of consistency o r both. Bearing failure may be signalized by increased power required to drive the test rig at the rated speed, o r a sharp increase in the temperature of the bearing after establishment of steady-state operation, o r persistent unusual noise. Other manifestations of failure are: scuffed locations on the races o r the rolling elements (balls or rollers), spalled races, spalled balls o r rollers, worn o r broken retainers, excessive wear of races o r rolling el emen t s

.

Breakdown of grease by prolonged shear to the point of excessive l o s s of the whole grease by leakage o r of the oil by bleeding is undesirable because of the danger of leaving the bearing inadequately lubricated and because of soiling or contamination of the surroundings by the leaking A standard test for this type of leakage is ASTM Method lubricant. D 1263 [38]. This test is a credible analogue of service in an automotive front wheel bearing assembly. Stokely and Calish [391 noted that shearing the grease in an ASTM worker o r the roll tester does not necessarily predict its behavior in an overpacked bearing. The ASTM leakage test is carried out with an overpacked assembly. In contradistinction to rolling-element bearings, the lubrication of automotive suspensions, which is the second major service area for greases, is characterized by lower contact pressures, lower rubbing speeds and intermittent o r oscillatory motion. In 1960 Brunstrum and Hayne [ 4 0 ] published the results of a road test with four different greases used on 15 different vehicles. Cumulative plots of the distribu-

545

tion of wear showed no consistent trend assignable to a particular grease or a particular vehicle. Wear was low, c a . 4 mg average l o s s per 1000 miles at the most sensitive locations in the suspension. Tests with these four greases in a laboratory oscillatory contact rig also showed no differentiation among the four greases, but in the same type of test a special lithium grease gave a cumulative distribution diagram with a significantly lower level of wear. Another point of view on the function of grease in automotive suspensions is found in the laboratory ball joint tests reported by Gilbert, Verdura and Rounds [ 4 1 1 . A convex surface is oscillated against a concave housing under load to simulate the ball joint action in an automotive front wheel suspension. The desired standard of performance is torque stability at a predetermined level: high, erratic torque is symptomatic of “ride harshness,” but torque at too low a level adversely affects the damping required in the suspension system. Results obtained with various commercial greases indicated significant differences in perf ormance. There are three ASTM extreme-pressure bench tests specifically applicable to greases [ 4 2 1 . Considerable empirical bench test data is to be found in the literature for greases compounded with extreme-pressure additives. A particularly interesting study along such lines was carried out by Silver and Stanley [ 4 3 1 . Greases were made u p from a base oil with various concentrations of lithium 12-hydroxystearate or a treated bentonite a s gellants and with the following substances as additives: dibenzyl disulfide, chlorinated wax, and tricresyl phosphate. A special set of greases was made up with 15% ground graphite a s the gellant. The behavior of these greases in the four-ball machine was tested by two procedures: a one-hour wear test under 15 kg load and the standard ASTM extreme-pressure test. Table 18-7 shows the results. The data in Table 1 8 - 7 do not permit a firm interpretation of additive action in a complex system such as grease but they do offer a number of suggestive hints. For the greases without additives there is no discernible relation between penetration or gellant concentration and the 15-kg wear scar. With the exception of graphite, which seems to have no influence whatsoever on the 15-kg wear, the type of gellant makes only minor differences in the wear results. But in the EP test graphite has the strongest influence, while the mean Hertz loads for the other two gellants group at substantially the same level. The basic behavior of additives in the ungelled oil is given by the following ranking of effecdibenzyl disulfide = tiveness in terms of the 15-kg wear test: chlorinated wax < tricresyl phosphate. Ranking in terms of the mean Hertz load is tricresyl phosphate < chlorinated wax < dibenzyl disulfide. Adsorption of the additive by the gellant was determined by filtering

546

TABLE 18-7.

FOUR BALL TESTING OF GREASES COKPOUNDED WITH E? ADDITIVES No additive

Gellant

Dibenzyl disulfide (a)

Chlorinated wax (b)

Tricresyl phosphate (c)

Wear scar, mm (d) None Bentonite (treated), 2.5% worked penetration >385 Bentonite (treated), 5.0% worked penetration 197 Bentonite (treated), 7.5% worked penetration 167 Li 12-hydroxystearate, 4% worked penetration >385 Li 12-hydroxystearate, 8% worked penetration 320 Li 12-hydroxystearate, 12% worked penetration 219 Graphite, 15% worked penetration >385

0.77 0.55

0.61 0.63

0.63 0.47

0.26 0.33

0.67

0.63

0.43

0.47

0.56

0.54

0.48

0.50

0.56

0.60

0.52

0.29

0.61

0.65

0.46

0.49

0.53

0.59

0.37

0.48

0.72

0.61

0.53

0.43

% Left ~

~~~

None Bentonite (treated), 2.5% 5.0% 7.5% Li 12-hydroxystearate, 4% 8% 12% Graphite, 15%

__ __ -_ -__ __ ---

in oil (e)

__

__

__

95 68 69 98 89 96 86

86 81 65 99 92 95 96

70 44 20 87 83 87 67

~~

Mean Hertz load, kg None Bentonite (treated). 2.5% 5.0% 7.5% Li 12-hydroxystearate, 4% t 8% I 12% Graphite, 15% 11

,I

16.6 22.3 22.8 23.7 20.3 21.4 21.0 27.4

41.4 30.7 34.0 41.1 28.9 36.4 33.3 55.1

37.7 34.0 27.0 31 .O 28.3 30.8 32.7 48.0

27.6 22.4 19.6 23.3 20.8 24.5 24.5 34.1

(a) 1 .7% in grease. ( b ) 51% C1, 1.7% in grease. (c) 1.7% in grease. (d) 1 hour, 15 kg load, 1500 rpm, 50 C. (e) At end of wear test, after' separation of oil from gellant by 0.45 pm Millipore filter. Data by Silver and Stanley [431.

off a known proportion of the oil and assaying it for additive content. The treated bentonite was the strongest adsorbent for all the additives. But close scrutiny of Table 18-7 reveals enough irregularity and anomaly to make the simple concept of reduction of the effective concentration of the EP additive by competitive adsorption on the gellant untenable. Each system seems to have its individual characteristics. For instance, the effect of interaction between gellant and dibenzyl disulfide seems to be

541

minor with respect to the 15-kg wear test and irregular with respect to the mean Hertz load. The antiwear action of tricresyl phosphate in the 15-kg test is noticeably inhibited when i t is compounded in a grease: the same holds true for the mean Hertz load except for the grease thickened with graphite. The reader will have noted that the emphasis in this chapter has been on basic modes of behavior and that specific discussion of grease of particular compositions and types has been limited. This is not for lack of available information. However, a great deal of such information is empirical and non-systematic. The fundamental aspects of a complex colloidal system such as grease are difficult to investigate; therefore it is not surprising that the major attention has been directed to studies with direct technological applications. The intent of the presentation in this chapter is to equip the reader with enough basic background so that he can examine the results published in the technical literature of grease composition, manufacture and use with the insight to appreciate a l l the implications he finds there. REFERENCES 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

D. W. Criddle and J. L. Dreher, NLGI Spokesman, 2 3 ( 1 9 5 9 ) 9 7 - 1 0 1 . B. W. Hotten, in Advances in Petroleum Chemistry and Refining, J. J. McKetta, Editor, Interscience, New York, 1 9 6 4 , Volume 9, Chapter 3. W. H. Peterson and A. Bondi, J. Phys. Chem., 57 ( 1 9 5 3 ) 3 0 - 3 5 . A . L. McClelland and 3. Cortes, jr., NLGI Spokesman, 2 0 ( 1 9 5 6 ) NO. 6 , 1 2 - 1 6 . C. J. Boner, Manufacture and Application of Lubricating Greases, Reinhold Publishing Co., New York, 1 9 5 4 . R. M. Suggit, NLGI Spokesman, 24 ( 1 9 6 0 ) 3 6 7 - 3 7 5 . D. B. Cox, J. Phys. Chem., 6 2 ( 1 9 5 8 ) 1 2 5 4 - 1 2 5 6 . M. J. Vold, Y. Uzu and R. F. Bils, NLGI Spokesman, 3 2 ( 1 9 6 9 ) 3 6 2 367. S. F.

E.

Calhoun, NLGI Spokesman, 2 9 ( 1 9 6 6 ) 3 2 8 - 3 3 2 . R. Booser and D. F. Wilcock, Lubrication Eng., 9 ( 1 9 5 3 ) 140-143,

156- 1 5 8 . A . E. Baker, NLGI Spokesman, 2 2 ( 1 9 5 8 ) 2 7 1 - 2 7 7 . A . E. Baker, E. G. Jackson and E. R. Booser, (1953) 249-253.

Lubrication

Eng.,

9

kT. Sisko and L. C. Brunstrum, NLGI Spokesman, 2 5 ( 1 9 6 1 ) 7 2 - 7 6 . W. J. Ewbank, J. Dye, J. Gargaro, K. Doke and J. Beattie, NLGI Spokesman, 2 7 ( 1 9 6 3 ) 7 5 - 8 2 . W. L. Brown and W. J. Ewbank, NLGI Spokesman, 2 9 ( 1 9 6 5 ) 7 7 - 8 3 . J. L. Zakin and E. H. Tu, NLGI Spokesman, 2 9 ( 1 9 6 6 ) 3 3 3 - 3 3 7 . B. W. Hotten and D. H. Birdsall, Ind. Eng. Chem., 4 7 ( 1 9 5 5 ) 4 4 7 - 4 5 1 . ASTM Method D 2 1 7 - 6 7 , Cone Penetration of Lubricating Grease, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. D. Evans, J. F. Hutton and J. B. Matthews, Lubrication Eng., 13 A.

( 1 9 5 7 ) 341-346. 20. 21. 22. 23.

A. Bondi, A. M. Cravath, R. J. Moore and W. H. Peterson, NLGI Spokesman, 13 ( 1 9 5 0 ) No. 12, 1 2 - 1 8 . R. H. Leet, NLGI Spokesman, 19 ( 1 9 5 5 ) No. 1, 2 0 - 2 3 . A . C. Borg and R. H. Leet, Lubrication Eng., 15 ( 1 9 5 9 ) 4 5 0 - 4 5 4 . H. A. Woods and H. M. Trowbridge, NLGI Spokesman, 19 ( 1 9 5 5 ) No. 5, 2 6 - 3 1.

548

24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

43.

ASTM Method D 1831-64, Roll Stability of Lubricating Grease, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. J. J. Kauzlarich and J. A. Greenwood, ASLE Trans., 15 (1972) 269277. W. H. Bauer, A. P. Finkelstein and S. E. Wiberly, ASLE Trans., 3 (1960) 215-224. S. J. Hahn. T. Ree and H. Evrins, NLGI SDokesman 23 (1956) 129-136. H. Utsugi; K. Kim, T. Ree-and-H. Eyring, NLGI Spokesman, 25 (1961) 125- 13 1. E. 0. Forster and J. J. Kolfenbach, ASLE Trans., 2 11959) 13-24. ASTM Method D 1092-62, Apparent Viscosity of Lubricating Greases, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. A. Dyson and A. R. Wilson, Proc. Inst. Mech. Eng., 184 (1969/1970), Part 3F, 1 - 1 1 . S. Y. Poon, J. Lubrication Tech. (Trans. ASME), 94F (1972) 27-34. D. Godfrey, ASLE Trans., 7 (1964) 24-31. A. C. Horth, L. W. Sproule and W. C. Pattenden, NLGI Spokesman, 32 (1968) 155-161. R. O'Halloran, J. J. Kolfenbach and H. L. Leland, Lubrication Eng., 14 (1958) 104-107, 117. A. C. Horth, J. H; Norton and W. C. Pattenden, Lubrication Eng., 27 (1971) 380-385. A. Schilling, NLGI Spokesman, 30 (1967) 388-400, 420-432. ASTM Method D 1263-61, Leakage Tendencies of Automotive Wheel Bearing Greases, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. J. M. Stokely and S. R. Calish, NLGI Spokesman, 19 (1955) No. 9, 1215. L. C. Brunstrum and W. L. Hayne, jr,, NLGI Spokesman, 23 (1960) 394400. A. W. Gilbert, T. M. Verdura and F. G. Rounds, NLGI Spokesman, 29 (1966) 356-365. (a) ASTM Method D 2266-67, Wear Preventive Characteristics of Lubricating Grease (Four Ball Method). (b) ASTM Method D 2509-66, Measurement of Extreme-Pressure Properties of Lubricating Grease (Timken Method). (c) ASTM Method D 2596-67, Measurement of Extreme-Pressure Properties of Lubricating Grease (Four Ball Method). ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. H. B. Silver and I. R. Stanley, Tribology Int., 7 (1974) 113-118.

549

Chapter 19 LUBRICATION BY SOLIDS

19.1.

CLASSIFICATION AND TERMINOLOGY

Lubrication by solids is a well-recognized branch of lubrication technology, and the experienced practitioner finds little difficulty with the meaning of this designation when he sees it. But careful scrutiny shows that the distinction between lubrication by solids and other aspects of lubrication is not one of fundamental principles. Instead, the term as it is generally understood is applied to a collection of techniques characterized by one common feature: the lubrication process is governed by the presence of a deliberately inserted solid substance in the rubbing interface. There are many nuances in this concept. Consider the definition of "...any solid used bea solid lubricant proposed by W. E. Campbell [ 1 1 : tween two surfaces to provide protection from damage during relative movement and/or to reduce friction or wear." As a definition it is straightforward and logical. Using it as a guideline, we would be able to recognize without doubt any instance of lubrication by a solid substance. But it turns out to be ambiguous in practice because it does not say anything about the original condition of the two surfaces to be lubricated. F o r example, i f the surfaces are steei exposed to ambient air and thus carrying the usual film of oxides and adsorbed moisture, are we to regard these surface constituents as lubricants with respect to oxide-free iron? And with respect to which initial surface condition, the oxide-free or the contaminated state, should the lubricating action of purposively introduced solid substances be evaluated? The theoretical ambiguities posed by these questions do not seriously affect actual practice. In situations of technological significance, the lubrication engineer usually h a s some knowledge of the initial surface condition of the unlubricated rubbing parts. His criterion of the effectiveness Of the solid lubricant is the improvement in tribologicai behavior with respect t o such initial condition. It is essentially from this point of view that lubrication by solids will be treated here. By and large, the initial conditions of the surfaces as encountered in practice will be taken as the reference state in assessing the behavior of lubricating solids in their interaction with these surfaces, both at rest and during rubbing.

550

As a specific example of some of the subtleties involved, consider an oriented condensed film of long-chain fatty acid formed on an ordinary oxide-covered steel surface by chemisorption from a compounded lubricating oil. This type of film has been discussed at length in the treatment of additive action and it has been demonstrated that such a film may be regarded as the two-dimensional analogue of a solid lattice laid down on the underlying surface. Thus it fits Campbell's definition of a solid lubricant [ I ] , and yet the experienced lubrication engineer is not disturbed by semantics when he excludes fatty acid films from his pragmatic category of solid lubricants. In a suspension of molybdenum disulfide in oil, the additive is overtly recognizable as a solid, while in a solution of stearic acid in oil, the additive is unquestionably not in the solid state. The use of solid lubricants is governed largely by practical considerations, and the need for them may be put in the following words: the engineer l o o k s to solid lubricants for "low and, above all, constant friction and increased durability of the lubricating film under extreme environmental conditions" [ 2 ] . Among the extreme environmental conditions are high temperature, high contact pressure, hard vacuum and corrosive atmospheres. At the low atmospheric pressure of the stratosphere o r the high vacuum of outer space, the most important function of the lubricant is to insure absence of seizure and to maintain reliable movement of rubbing parts. I t is apparent why solids are particularly suited as lubricating substances in these circumstances. Even though the technology of lubrication by solids is largely empirical, it is useful to systematize classification and terminology. Substances that are used as solid lubricants can be grouped into the six

TABLE 15-1.

TYPES OF SOLID LUBRICANTS Inorganic MoS2, graphite,

Layer-lattice

graphite fluoride Other inorganic solid compounds

CaF2, PbO

Soft metals

Pb, Ag, Au Organic ~~

Soaps, fats, waxes

Calcium stearate, dimethylstearamide

Polymeric plastics

Polytetrafluoroethylene, pol ymide

Layer-lattice solids

Phthalocyanines

551

general types shown in Table 19-1, witn examples to illustrate each type. The methods of lubricating with solids fall into three broad categories:

( i )pretreatments which put a film of solid lubricant parts before they are brought into rubbing contact:

on

(ii) systems which feed solid lubricant as such to parts during operation;

rubbing

the

the

(iii) systems which bring the solid lubricant to the rubbing parts suspended in a carrier oil o r in a gas stream. Pretreatment can be divided into two sub-categories. In the first, a protective film is formed by physical adhesion of the externally applied solid lubricant to the surfaces. Burnishing or rubbing may be used to develop the adhesicn of the applied solid, but as far as is known, the adhesion does not depend on chemical reactivity; deliberate intent to alter the surface by chemical reaction is not an intrinsic part of this method of applying the lubricant Silm. The second category of pretreatment, on the other hand, specifically involves the formation of solid lubricating films on surfaces by chemical treatments such as phosphatizing, suifidizing, anodizing, acid etching, etc. The question of when the coating thus formed is to be regarded as a lubricant and when as an initial condition of the rubbing surfaces cannot be answered unequivocally. For instance, carburizing might be viewed as a technique of solid lubrication, but it is usually considered to be a way of modifying the material properties of steel. The same viewpoint might be taken towards ion implantation. Midgley and Wilman [ 3 1 have shown that though the film put 01: mild steel by phosphatizing is worn away during initial rubbing, the surface is rendered more responsive to protection by oil on subsequent rubbing, an observation which makes it difficult to classify the action of the phosphate film in terms of formal nomenclature. The efficacy of a pre-applied, self-adherent solid film depends on its durability during rubbing. Deficiencies in durability can be overcome by supplying material for the maintenance of the film by methods (in) or (iii) listed above. For instance, material can be transferred to the lubricating film by a compact of the solid lubricant in rubbing contact with one of the surfaces o r by dropping powdered solid as needed. The film can also be maintained by using the solid lubricant as an additive in a carrier o i l or in a gas stream. 19.2.

LAYER-LATTICE INORGANIC SOLIDS AS LUBRICANTS

Many inorganic solids crystallize in layer-lattice structures; cadmium iodide is frequently cited as the type example. The cadmium ions are arranged hexagonally in sneets, each with a sheet of hexagonally arranged iodide ions above and below. The separation of adjacent sheets of

552

iodide ions is greater than the spacing between a sheet of iodide ions and its neighboring sheet of cadmium ions. Many of the inorganic substances which have layer-lattice crystalline structure can be cleaved into thin sheets and therefore are termed lamellar solids, but the ability to be cleaved into lamellae is not necessarily a property of all solids with layer-lattice crystalline structure. As pointed out by A. J. Haltner [41, the nature of the bonding between the sheets of ions whose separation defines the layer-lattice structure is what determines the cleavage behavior. Thus, the easily cleaved phlogophite and muscovite micas are characterized by the presence of K + ions, whereas in a brittle ++ mica such as margarite, Ca acts as an ionic cement. Haltner also stated that cleavage of a layer-lattice solid is more akin to a tensile Hence a solid which can be easily failure than it is to shearing. cleaved into lamellae is not necessarily a lubricating substance, particularly in the sense of reducing friction. The easily cleaved micas are riot really useful as lubricants. Lubrication is associated with low tangential force at the rubbing interface; therefore those lamellar solids that function a s lubricants are characterized by low interlamellar slip force. 19.2.1.

Molybdenum Disulfide as a Lubricating Lamellar Solid

Of the lamellar solids which do show lubricating action, the two most familiar tc the lubrication engineer are molybdenum disulfide (MoS2) and graphite. The lubricant-grade MoS2 of commerce is made by processing

TABLE 19-2. CHEMICAL ANALYSIS OF MOLYBDENUM DISULFIDE H20, Oil,

MoS2,

Fe,

Moo3,

%

%

m

x

0.12 0.059 0.072

0.03 0.014 0.025

0.00 0.047 0.035 0.024

Lubricant grade 98.04 Sample A 99.6 Sample B

%

- -

C,

Acid insoluble,

%

%

1.22 0.200

-

0.50 0.022 0.032

From data by Risdon, Maurer and Barry 151.

and purifying mined natural molybdenite. Table 19-2 compares the chemical analyses of lubricant grade MoS2 and two specimens which were purified further 151. Treatment of the commercial grade material reduces the silica (acid insoluble) and iron content, a s shown for Samples A and B. The presence of Moo3 is a characteristic feature of MoS2 surfaces which have been exposed to air; sulfuric acid is a concomitantly occurring contaminant [ 6 , 71. The oil and carbon content, which comes from the flotation agents used in processing mine-run lowered by milling and solvent extraction.

molybdenite,

can

be

553

Milled MoS2 is available in a wide range of particle sizes, from as small as 0.3 urn up to 100 urn and larger. Scanning electron microscopy of 50 Vrn powder at magnifications up to lOOOX by Holinski and Glnsheimer 18, 91 revealed that the grains are not single crystals and do not consist of flat platelets; also grains this size have flakes of more finely divided material adhering to their surfaces. A single traverse of a loaded steel ball across a plate sprinkled with powdered MoS2 was sufficient to flatten the grains into a compact aggregate of platelets. Platelets as thin as 15 nm ( 2 4 atomic layers of MoS2) were formed on prolonged running. The process by which the granules characteristic of milled MoS2 are transformed into platelets and the platelets are further compacted into adherent films was studied during the course of 1000 revolutions of the ring in a ring-on-block apparatus under a loading pressure of 1 . 1 1 kPa (1.1 kg/cm2). Provided that the initial supply is sufficient, burnishing by repeated traverses puts a compacted film of MoS2 on the substrate surface. This film may be several microns thick. Such behavior of MoS2 granules during rubbing under load is consistent with the layer-lattice structure shown in Fig. 19-1. On either side of each sheet of molybdenum atoms in a planar hexagonal arrangement is a The sheet of sulfur atoms, also in a planar hexagonal arrangement.

Figure 19-1. The unit cell of hexagonal sions in nanometers.

molybdenum

disulfide.

Dimen-

554

molybdenum-sulfur distances (0.241 nm) correspond to the atomic bonding radii, but the sulfur-sulfur distances in adjacent layers (0.349 nm) are greater than the combined atomic sulfur radii. These widely separated adjacent sheets of sulfur atoms are oriented parallel to the basal planes of the crystal, which are the planes of easiest shear characteristic of solids that crystallize in the hexagonal system. Evidence for the orientation of crystallites in rubbed films of MoS2 along their basal planes is seen in X-ray and electron diffraction spectra [lo, 11, 12, 13, 14, 151.

The full details of the formation of burnished films of MoS2 and their adhesion to substrates are not well understood. H. E. Sliney [161 observed the generation of a burnished film of MoS2 from 10 Um powder during the sliding of a tool steel ball on a glass plate. The MoS2 adhered to the rubbing surfaces of both the ball and the track on the plate. Y. Tsuya 1171 reported that the adherent MoS2 film on the rubbing tracks of metallic substrates could not be removed by the butylcellosolve transfer technique. The strong adhesion of burnished films of MoS2 to the underlying metal is at odds with the postulate of easy sliding on the basal planes of the crystal. Brudnyi and Karmadonov [15] presented evidence that the edge planes (1700, 1070, 0170) of MoS2 are harder and have a higher surface energy than the basal (0001) planes; Andrews, Groszek and Hairs 1181, on the basis of adsorptive behavior postulated that the edge planes are polar in nature and hence are high energy surfaces. According to Brudnyi and Karmadonov’s picture of the burnished film, strong attachment to the metallic substrate is via the suitably oriented (1700, 1070, 0170) faces of the crystallites in a randomly arranged layer directly on the metal surface; the basal planes of the crystallites on the surface of this layer become oriented in the direction of sliding during the course of rubbing. Chemical bonding via the reaction 2FeS + MO MoS2 + 2Fe has been suggested, but according to GHnsheimer and Holinski I141 this reaction does not take place below 700 C. Johnston and Moore [121 did not detect the presence of FeS at the junction of a surface which had been burnished with MoS2 at 300 C nor did Spengler and Peltzer 1191 find evidence of FeS or mixed crystals at the rubbing surface by X-ray diffraction. J. K. Lancaster [20] proposed mechanical embedding of MoS2 in the substrate as a mechanism of film attachment. The lubricating performance of MoS2 is evaluated by various criteria: magnitude of the coefficient of friction, rate of wear of the rubbing parts, durability of the antifriction or antiwear effect, magnitude of the scuffing load. Experimental studies and testing procedures are governed by the criterion adopted. Since MoS2 frequently comes under

555

consideration as a lubricant for severe conditions and hostile environments, such as high temperatures, vacuum or corrosive atmospheres, these conditions are often deliberately part of the experiment o r test, Because

of

the

usefulness of MoS2 in high vacuum (more precisely,

extremely low ambient pressure), the influence of the constituents of ordinary ambient air is an important factor to evaluate. Basically it resolves into identifying the intrinsic tribological behavior of MoS2 and distinguishing it from the rubbing behavior in a particular ambient environment. Rubbing in hard vacuum is the experimental approach used to study the basic behavior of MoS2 sliding against itself, the favored technique being to generate a transfer film from a pellet in contact with a moving countersurface, usually of metal. The generation of the oriented transfer film also orients the material in the surface of the pellet, so that the rubbing is along the basal planes of the MoS2 in each surface. Coefficients of friction ranging from 0.02 to 0.15 have been reported for such experiments [21, 22, 23, 241, as shown in Table 19-3. Results by Matsunaga, Hoshimoto and Uchiyama [251 and by Jamison and Weber 1261 for a metallic slider against a burnished film on a metallic substrate are shown for comparison. It might be thought that cleaning treatment such as washing with NH40H solution and refluxing with organic solvents, followed by conditioning in a hard vacuum environment, would give MoS2 a clean surface with stable tribological properties, but experimental results do not consistently substantiate this. Johnson and Vaughn [21] observed that on resumption of rubbing after quiescent standing in vacuum, the initial TABLE 19-3. COEFFICIENTS OF FRICTION OF MoS2 SLIDING ON MoS2 IN HARD VACUUM Reference source

uk

Pressure, torr

Speed, cm/s

Temperature, deg. C

Substrate

t211

0.07-0.09

1 Ow6

310

25-60

Stainless steel lapped with 600 mesh carborundum

[221

0.06-0.09

10-7-10-9

0.4-68

25

HCOF copper

[231

0.07

2

-

room

Copper

“241

0.03-0.12

5 x

lo-’

0.05a

room

Copper

t251

0.02-0.10

5 x lo-’

0.05a

room

Copper b

[261

0.07-0.10

1 f71 O-’

0. 042a

room

Copper

(a) Average speed, reciprocating Stainless steel slider.

motion.

(b)

Copper

slider.

(c)

556

0.04 0 0 1. 2

3 04

5

66 7

8

9 L

Running Time, min.

Figure 19-2. The effect of rest time I n vacuum on the friction of molybdenum disulfide. Rest time: I , 16 hrs.; 1 1 , 15 hrs.; 1 1 1 , 185 min.; IV, 134 min.; V, 90 min.; VI, 8 5 min. Data by Johnson and Vaughn 1211.

coefficient of friction was higher than the steady-state value characteristic of prolonged rubbing, as shown in Fig. 19-2. This kind of behavior was confirmed by Haltner [22] and in part by Matsunaga e t ae. [24, 251. Johnson and Vaughn [21] attributed the low steady-state coefficient of friction to the generation of a superficial coating of sulfur from the tribological decomposition of MoS2. The reaction 4MoS2

+ 2M02S3

+

S2 (9)

is known and has been studied [27], Johnson and Vaughn postulated that cessation of rubbing in vacuum allows the MoS2 surface to be denuded of the adsorbed sulfur by evaporation. Haltner [22], in view of the rate at which sulfur evaporates i n v a c u a , expressed doubts that sulfur generated by the tribological decomposition of MoS2 would remain on the surface long enough to influence the kinetic coefficient of friction. To complicate the picture further, Matsunaga and Nakagawa [28] claimed that the cleanest MoS2 surfaces were obtained from powder deposited electrophoretically from acetone suspension onto a copper substrate and baked for 4 hours at 280 C in a vacuum of lo-' torr; the steady-state coefficient of friction they observed for a run-in film so prepared was 0.15. Matsunaga and Nakagawa [281 found that hydrogen, nitrogen, argon o r helium could be put into the system at pressures ranging from to 100 torr and pumped away without at any time changing the coefficient of friction from its clean-surface value of 0.15, as measured by their reciprocating technique. Haltner [221 reported a steady-state value of uk = 0.081 f o r a pellet of compacted MoS2 rubbing against a transfer film

557

5 .' t .-

. I -

0.12

-

0.10

-

-

0.08 -

-

-

-

0.04 -

-

.I-

," 0.06 c

I

1

0, .-

2 8

.I-

0,

0.02 0,OO

6

-

o Admission

-

Evacmiion

I

I

I

I

I

I

on copper in an atmosphere of nitrogen at 175 C, almost the same value that was observed in hard vacuum. The effect of water vapor as observed by Matsunaga and Nakagawa [28] is shown in Fig. 19-3; an analogous minimum and hysteresis effect was seen f o r n-butanol. Admission of oxygen produced a sharp rise in friction at c a . 1 torr pressure, with a marked hysteresis effect on pumping off; ethane qave a sharp drop in friction with even stronger hysteresis in the pump-off. Interpretation of the tribological behavior of MoS2 in air is often complicated by uncertainty about its initial surface condition. Salomon, de Gee and Zaat [29] observed the sequential evolution of the following gases chromatographically when MoSZ powder was heated i n v a c u a : oxygen, nitrogen, carbon dioxide (above 300 C ) , methane (above 400 C ) , and hydrogen (from 450 C up). Commercial milling of MoS2 to particle sizes useful f o r lubrication permits oxidation of the surface and adsorption of water vapor from air. J. W. Midgley [301 equilibrated MoS2 of 1-3 um particle diameter with air of 60% relative humidity at room temperature and then heated it to 120 C. The MoS2 lost 1.1% of its equilibrium When moist, equilibrated MoS2 powder was used to lubricate the weight. humidity, the value of uk rubbing of steel i n air of 60% relative dropped from 0.2 to 0.05 in the course of three hours, during which time the temperature of the steel specimen piece near the rubbing surface rose from 2 2 C to 50 C. When the system was cooled to room temperature in dry air ( < 0 . 1 % relative hunidity) and then rubbii.9 was resumed, u k stayed at 0.05; but i f quiescent cooling and subsequent rubbing occurred at 60% relative humidity, uk rose to 0.15. This effect was attributed to the adsorption of water on the surface of the MoS2 crystallites. Haltner and Oliver [311 observed a strong influence of the relative humidity between 0 and 40% on the increase of the friction of a MoS2 compact rubbing against a transfer film on copper in an atmosphere of nitrogen.

558

0.6

0.5

0 ._ c

0.3 .c

0

,

0

.

0 0

K)

20 30 40 50 6070

% Relative Humidity at Specimen

Temperature

Figure 10-4. Effect of relative humidity on the static friction of molybdenum disulfide films. Data by Pritchard and Midgley 1321.

Pritchard and Midgley [321 found that the coefficient of static friction of steel lubricated by a burnished film of MoS2 was influenced by the relative humidity over a range of temperatures as shown in Fig. 19-4. Haltner and Oliver [31] observed a sharp rise of vk from 0.12 to 0.22 in the range 0-37% relative humidity for a MoS2 compact against a transfer film. Ballou and Ross [331 demonstrated hysteresis effects in the adsorption and desorption of water vapor on and from MoS2, depending on the past treatment of the surfaces; about 6 0 % of the adsorbed water vapor was retained when the relative pressure was reduced from 50% of saturaJohnston and Moore [71 observed that the adsorption equition to 5%. librium of atmospheric water vapor at 30 C with the surface of a sample of commercial MoS2 powder was reversible; however, if the powder was heated i n vacua to 350 C, the adsorption/desorption isotherms in air at 30 C showed a strong hysteresis effect o n the first cycle but subsequent adsorption/desorption cycles were reversible. I f the MoS2 is not heated higher that 800 C , decomposition to Mo2S3 and elemental sulfur does not occur. Heating in v a c u a at 350 C drives off any H2S04 contaminating the MoS2 surface hut leaves Moo3. Thus the second adsorption/desorption cycle in air (measured a s gain or loss of weight with a thermogravimetric balance system) starts with the base line established by chemisorption during the first cycle. It is thus seen that the interaction of molybdenum disulfide with its ambient surroundings in a tribological context involves complexities that have not been fully resolved. It has not been established why the friction of rubbed MoS2 should be adversely affected by adsorbed water vapor. Speculations range from the formation of intercalation structures

559

within the lattice [ 8 , 9 , 341 to reactions which alter the nature of surface, such as MoS2 + 2H20 + [O] -+Moo3

+

the

2H2S

the occurrence of which was demonstrated by Haltner and Oliver [31]. Atkinson and Swift [ 3 5 J observed decrease in sulfur and increase in oxygen by the X-ray photoelectron spectroscopy of MoS2 films rubbed in ambient air. Another unresolved aspect of the tribological behavior of MoS2 is whether the sliding occurs between the exposed basal-plane faces of one crystallite against another or whether it occurs by shear of the (0001) slip planes within the individual crystallites. The first alternative should be sensitive to the influence of ambient atmosphere because the basal planes are always exposed, whereas the internal slip along the ( 0 0 0 1 ) plane within a crystallite should be governed by the true shear strength of MoS2 in that direction. The two modes of behavior are not mutually exclusive. Furthermore, the observations of Sliney [16] indicate that under sufficient pressure individual crystallites of MoS2 can be compressed into larger single-body aggregates by plastic flow. In view of the complications connected with the intrinsic tribological behavior of MoS2 discussed above, interpretation of its overt response to experimental parameters such as load and rubbing speed and of its behavior in empirical testing is obviously not straightforward. F o r example, Fig. 19-5 shows the results by Haltner and Oliver 1361 for the effect of load and rubbing speed on the coefficient of friction for a steel ball rubbing against a burnished film of MoS2 on a chromium-plated steel disk. Because of the absence of a speed-dependent effect, Haltner and Oliver discounted the influence of release of adsorbed vapor and interpreted the load-dependent behavior in terms of Bowden and Tabor's mechanism f a r a thin, soft film of solid on a hard substrate [37] (see

(a)

(b)

0.2 -

:

D **em

0.00

I

I

I

I

0.0,

I

I

I

I

, *

I

.

560

Section 19.3). I n a detailed study by S. A . Karpe, [381 using a steel ball sliding with reciprocating motion at an average speed of 0.1 cm/s against burnished MoSZ on a steel plate in air of 30% relative humidity at 2 5 C, the effect of loading pressure on the coefficient of kinetic friction showed essentially the same pattern observed by Haltner and Oliver [36]: a strong decrease over the lower range of loading and a gradual transition to a much slower rate of decrease over the rest of the graph. This response of pk to contact pressure followed the course calculated for Bowden and Tabor's thin-film model. Akaoka and Nitanai [39] found similar effects of contact pressure in the continuous sliding of torr) at 16.7 steel against burnished MoS2 on steel in vacua (2 x cm/s. Haltner and Oliver's experiments on the effect of rubbing speed were carried out in an environment of nitrogen [361. Barry and Binkelman [ 4 0 ] observed a similar lack of rubbing-speed effect on friction in dry air and also insensitivity to applied load for the friction of films of MoS2 on metals such as steel, molybdenum, tungsten, copper, brass, bronze and silver. But in ambient air of 50% relative humidity at room temperature, the coefficient of friction decreased with increasing speed or load, to a greater or less extent, for films of MoS2 on various metals. J. GQ'nsheimer [13, 411 found the systematic effect of applied load and relative humidity to be that shown in Fig. 19-6: increasing the load stepwise lowers the coefficient of friction, decreasing the load raises it,

0.12

0.10

0.08 0.06 c

c

.-0

0.04

5

0.02

0)

F V

0.00

0

10

20

30

40

50

60

70

Time,minutes

Figure 19-6. Effect of relative humidity on the frictional behavior of molybdenum disulfide. 1:16.2% R.H.; 2:6.56% R.H.; 3:0.12% R.H.; 4: dry air. Data by J. Ghsheimer [13].

561

I

!

0.00I

I

I

1

I

1

133

1467 2801 1467 133 k ~ o a d4 -iw 0 a d m g - - + ( Load,newtons

Figure 1 9 - 7. Effect of vapors on the frictional behavior of molybd enum disulf i de (e) (a) n-Butanol. (b) Water. (c) Benzene. (d) Heptane. Dry a i r. Vapors at saturation pressure, 20 C. Data by J. Gznshe imer

.

[411.

0.3 Contact pressure ,MI 0

0.08

n 0.17 0

0.25

v 0.33 0 0.42

1

1

0.5

1.0

I

I

I

1.5

2.0

2.5

I

3.OxlC

Frictional Heat,uPV (J/m2d

Coefficient of friction of molybdenum disulfide as a funcFigure 19-8. tion of frictional heat. u = coefficient of friction; P = pressure; V = sliding speed. Data by Tanaka, Nakagawa and Matsunaga 1 4 2 1 .

562

and the effect is stronger at higher levels of relative humidity. In dry air change of load has a negligible effect. This lack of load effect is not altered by the presence of hydrocarbon vapors such as benzene o r heptane at saturation pressure in dry air, but the admission of the vapor of a hydroxylic compound such as butanol has an effect like that of water vapor, as shown in Fig. 19-7. Tanaka, Uchiyama, Nakagawa and Matsunaga [421 carried out experiments on the sliding of a MoS2 compact against its transfer film on steel in air of 50-60% relative humidity at 23-26 C with loads ranging from 10 to 50 N (8-420 kPa) and at speeds from 85 to 583 cmis. As shown in Fig. 19-8, the coefficient of friction decreases with increasing rate of heat input per unit area; i . e . friction decreases with increasing surface temperature. Thus there is a significant body of evidence which can be put together to show that influence of contact pressure and rubbing speed on the coefficient of friction observed with transfer films of MoS2 involves the effect of the surface temperature on the moisture content of the film. The antiwear and antiscuff action of MoS2 and the durability of its lubricating efficacy involves the behavior of the film interposed between the two rubbing bodies as well as the intrinsic tribology of MoS2 itself. I f each surface of the rubbing bodies carries an intact film of MoS2, neither body will suffer attritive wear and the friction observed will be that of MoS2 sliding on itself under the conditions prevailing. But i f any part of the film fails to adhere to either of the two rubbing bodies, then there will be a local occurrence of friction between the exposed substrate material and the MoS2 film on the other substrate and wear of the exposed material rubbed by the MoS2 as well as wear of MoS2. Local breakdown of the MoS2 film which results in contact between both substrate bodies results in metal-tometal wear at that site; i f the breakdown is extensive enough, the wear augments to scuffing. The lubricating effect of MoS2 on the wear of soft steel (English EN 2 A , equivalent to A I S I 1 0 2 0 ) as observed by J. K. Lancaster [43] is shown by the comparison of wear rates in Table 19-4. The film of Mo2 was maintained dynamically by rubbing a compact of MoS2 against the sliding track at a location diametrically opposite the contact of the steel rider with the rotating disk in the experimental apparatus. The easiest interpretation of these results is to assume that the MoS2 film blocked enough metal-to-metal contacts to reduce the wear rate by four or five orders of magnitude relative to that of unlubricated steel. But it cannot be assumed 'that there is no intrinsic wear of metal by MoS2 sliding against it. Lancaster rubbed riders of copper against compacts of MoS2 in a manner which minimized reiterated traversals of the sliding path on MoS2, thereby minimizing the abrasive effects of copper particles which might have transferred to the compact; nevertheless significant wear of the copper rider was observed [441. Using this technique for copper sliding

563

TABLE 19-4. EFFECT OF A DYNAMICALLY MAINTAINED FILM OF MOS2 ON THE WEAR OF STEEL Wear rate, cm3/Nm Load: 58.8 N

Load: 255 N

Unlubricated

0.561 x

0.561 x

MoS2 film

0.5404 x 10-l'

0.714 x

Rubbing speed: 0.60 m/s.

TABLE 19-5.

Data by J. K. Lancaster [431.

SCUFFING LOADS FOR A DYNAMICALLY MAINTAINED FILM OF MoS2

Speed, m/s

Steady-state

pk

Contact pressure at scuffing, MPa

0.10 0.60 3.00

0.1 0.1 0.1

139 126 51

0.60

0. 04a

126

(a) MoS2 on phosphated steel surface. From data by J. K. Lancaster [431.

against clean massive polytetrafluoroethylene, Lancaster reported a wear cm2/Nm, but with a film of MoS2 on rate for copper of less than 2 x the PTFE the wear of the copper was increased by more than 10-fold 1201. Table 19-5 shows the scuffing loads Lancaster observed for mild steel rubbing at various speeds in atmospheric air against a dynamically maintained film of MoS2 on mild steel [43]; load was applied in incrernental steps until the coefficient of friction increased drastically above the steady-state value. The effect of maintaining the film by transfer from a compact is seen in Fig. 19-9, where the scuffing pressure is compared with that for a preformed film which is not renewed by transfer. The role of the compact in maintaining the film is also shown by a decrease in the electrical contact resistance from 38 ohms to 10 ohms when the compact was lifted from the rubbing track for 400 seconds and restoration of the contact resistance to 38 ohms in 1400 seconds when the compact was replaced, the steel rider meanwhile rubbing against the track under a sub-scuffing load. The rate of transfer from the compact to the track decreases as the surface of the compact is conditioned by rubbing, and eventually the film becomes too thin to protect against scuffing under the particular load employed. Akaoka and Nitanai [391 observed a

564

G1o4-

I

I

4

c

f0

0 u)

with qac+\

without compact

p 3-

-

v)

0

8

-I

Sliding Distance to Scuffing ,km

Figure 19-9. Effect of a maintained film of scuffing. From data by J. K. Lancaster [ 4 3 1 .

molybdenum

disulfide

on

L

2 15c

1

0

% Relative Humidity at Rubbing Surface I

10

I

I

I

30 50 70 % Relative Humidity of Air

I

90

Figure 19-10. Influence of relative humidity on the friction coefficient and the durability of a molybaenum disulfide film. Load: 613 N. Speed: 100 cm/s. The humidity of the surrounding atmosphere (lower scale) is higher than that at the rubbing surface (upper scale) because the rubbing surface is warmer than the atmosphere. The friction coefficient (right-hand scale) increases with humidity and is higher at the beginning ( p i ) than the termination (p,) of the run. Data by Salomon, de Gee and Zaat [29!. sharp decrease in the endurance of preformed burnished films of MoS2 with high contact pressure for the lubrication of steel i n vacuo and attributed failure to fatigue of the film. Environmental conditions such as relative humidity and the composition of the ambient atmosphere influence the durability of the MoS2 film. Figure 19-10, from work by Salomon, de Gee and Zaat [29], shows the effect of relative humidity on the smooth-running life of steel rubbing

565

against steel lubricated by a burnished film of MoS2. No explanation is advanced for the strong beneficial effect of 7% relative humidity at the surface; it seems to coincide with the maximum value of the temperature of the ring. The rapid decrease in durability with increase of relative humidity beyond this level is attributed to tribologically catalyzed chemical reactions, such as the evolution of H2S reported by Haltner and Oliver [311; Salomon and his co-workers observed that large quantities of H2S were evolved when rubbing experiments were carried out at 90% relative humidity and 25 C in an atmosphere of argon o r nitrogen. Pritchard and Midgley [321 found a strong decrease in the durability of MoS2 films as the relative humidity rose from 7% to 20%. The effect of oxygen as observed by Salomon e t a L . [291 is shown in Table 19-6. They also obof large served g r o s s visual evidence of film failure-formation blisters-which seemed to be promoted by oxygen. Tanaka e X aL. 1421

TABLE 19-6.

INFLUENCE OF OXYGEN ON THE DiiRABILITY OF A MOS2 FILM

Atmosphere

Durability, hrs.

Oxygen Air Argon (0.05% 0 2 )

Steel specimens; 613 N; 1 m/s; Gee and Zaat [291.

measured the response of

wear

2-4 6-9 >150

dry atmospheres. From data by Salomon,

rate

of

steel

lubricated

by

Mo2

de

(in

reciprocating motion) to the influence of ambient atmosphere from to lo5 Pa (7.5 x lo-’ to 750 torr) and found a sharp increase at about 2 0 0 0 Pa (15 torr).

R. L. Fursaro [45] made a detailed study of the durability of burnished films of MoS2 on 440 C stainless steel disks of surface roughness (0.09 pml to 0.3 um by the sliding of ranging from polished hemispherically-ended pins (0.467 cm radius) with an applied thrust of 9.8 N at a rubbing speed of 2.6 m/s. Table 19-7 shows the results obtained in moist air (50% relative humidity at 25 C) and in dry argon. The initial wear rates for the first 1000 cycles of traverse are relatively high but the corresponding coefficients of friction were found to lie in the range 0.09-0.13. This portion of the wear process seems to be associated with the formation of transfer films of MoS2 on the rider and localized depletion of this film at the rubbing interface. The steadystate rubbing process appears to be controlled by MoS2 supplied from the rubbing track, particularly from pockets and grooves in the surfaces of

566

TABLE 19-7.

DURABILITY OF BURNISHED MOLYBDENUM DISULFIDE FILMS

Traverses, kilocycles

Rider wear rate, Sandblasted,

Abraded,

1.2

0.30

urn

urn

m3/m Polished, 0 . 0 9 ym

Moist air 0- 1 1-5

5-10 5-15 10-30 15-60 60-70 70- 100

8.80

2.00

1 .8

0.64

0.55

3.6*

0.07 0.11

1.60* 0.22

2.40* 0.49

-

-

Dry argon 0- 1 1-15 15-60 60-200 200-400 400-700 700-940 700- 1500 1500- 1 8 6 0 1500-2700 2700-3700 3700-4450

4.500 0.048 0.013 0.003 0.006

0.490 0.062 0.019 0.012 0.012 0.008

0.100 0.038 0.018 0.004 0.002 0.002

-

-

0.100*

0.010

0.011

-

0.018*

0.009

0.012 0.009 0.046*

*Failure: uh 2 0.30. Data by R. L. Fusaro [ 4 5 1 .

the abraded and the sandblasted disks. The lower durability of the films in moist air is ascribed to chemical degradation of MoS2 (probably to Moo3) with adverse effects on the ability of MoS2 to flow under pressure and maintain the film. 19.2.2.

Graphite as a Solid Lubricant

Graphite is a lamellar solid with the layer-lattice structure shown in Fig. 1 9 - 1 1 . The distance between neighboring carbon atoms in each layer is 0 . 1 4 2 nm, very close to the 0.140 nm for the C-C distance in benzene; the distance between layers is 0 . 3 3 5 nm. This long interlayer spacing was the basis of an early postulate [ 4 6 1 that the low friction observed for the rubbing of graphite against solid surfaces in ordinary ambient air could be ascribed to weak interatomic forces between the

561

Figure 19-11. nanometers.

Layer-lattice

structure

of

graphite.

Dimensions

in

parallel sheets of carbon atoms. R. H. Savage [ 4 7 1 demonstrated that the friction observed for graphite in air is strongly influenced by gases and vapors and that i n vucuu the friction of clean graphite rubbing against a copper surface can attain a value as high as pl: = 0.8. This brought about a radically altered view of the intrinsic nature of graphite and its frictional behavior. The electronic and orbital structure of graphitic carbon is such that TI bonds are formed between the unused p orbitals of adjacent carbon atoms in two neighboring layers [481. In MoS2, because of its different electronic and orbital structure, there is no interlayer sulfur-sulfur bonding; its lubricating properties are thus a direct consequenc9 of its intrinsically low interlamellar surface energy, even though the 0.299 nm sulfur-sulfur distance between layers is less than the 0.335 nm interlayer distance in graphite. Bryant, Gutshall and Taylor [ 4 9 1 , by cleaving flakes in vacuum, found a value of 1.750 J/m2 for the interlayer energy of graphite, and by using the quantum mechanical calculations of R. 0. Brennan [50] they computed a value of 2.500 J/m2. Girifalco and Lad [511 carried out interaction calculations with a Lennard-Jones 6-12 potential function and computed a value of 0.330 J/m2 for the surface energy, which Good, Girifalco and Kraus [521 claimed was confirmed by the average values of 0.234-0.260 J/m2 computed from heats of immersion. But there are doubts about applying heat of immersion data obtained in air to the calculation of the surface energy of clean graphite. Bryant e i d.[ 4 9 1 observed that admission of oxygen to a bifilar specimen of graphite cleaved in vacuum and maintained in strain by the original cleaving force caused further propagation of the cleavage crack because adsorption of the gas lowered the binding energy of the strained surfaces. The reader is also referred to the description of the cleavage of mica and the influence of atmosThe pheric gases on the surface energy (Chapter 10, Section 1 0 . 4 . 4 ) .

568

best interpretation of the evidence indicates that the intrinsic inter2 layer energy of graphite is of the order of 1.75-2.50 J / m

.

The influence of gases on the tribological behavior of graphite is described in detail by Savage [ 4 7 1 . The rate of rubbing wear i n vacuo against a copper disk at a speed of 1 3 7 0 cm/s under a contact pressure of 4 9 0 kPa was reduced by 5 0 % when water was admitted at an ambient vapor pressure of 0.5 torr. At an ambient pressure of 3 torr, the wear rate was very low mm/s) and the coefficient of friction was 0.18. Savage found that hydrogen, nitrogen or carbon monoxide did not change the wear of graphite from that observed i n v a c u o , that oxygen required an ambient pressure of 4 0 0 - 6 0 0 torr to equal the effectiveness of water vapor at 3 torr, and that easily condensable vapors such as ammonia, acetone, benzene, ethanol, diethyl ether, hexamethyldisiloxane or hexane

1.6-

cE 1.2 E

I 1

I

3

4

I

5

I

I

6 *

e

8

-

-

7

-

-

zO.8 al

-

a

b

g0.4-

-

-

.,

0.0. lo-*

to-'

I

10

Vapor Pressure, torr

Figure 1 9 - 1 2 . Bromopentane. tetrachloride. Schaefer 1531.

Effect of vapors on the wear of graphite. 1: 12: n-Heptane. 3: n-Propanol. 4 : n-Pentane. 5: Carbon 6: Methanol. 7: Propane. 8: Water. Data by Savage and

0.6

,g 0.5 0 E 04

-

f

O

03

i'D .- 0.2 r w-

8

0

0.1

0 0

0.1

0.2 0.3 0.4 05 Vapor Pressure, torr

0.6 0.7

Figure 19-13. Effect of vapors on the friction Nitrogen. 2: Hydrogen. 3: Water. 4: Dry air. 5: Heptane. 7: Oxygen. From data by G . W. Rowe 1 5 4 1 .

of graphite. Ethanol. 6:

1:

n-

569

were effective at pressures below 5 torr. Figure 19-12 shows the behavior observed by Savage and Schaefer I531 with the vapors of 1bromopentane, n-heptane, n-propanol, n-pentane, carbon tetrachloride, methanol, propane and water. G. W. Rowe [54], working with graphite sliding against graphite at low velocity, obtained the results shown in Fig. 19-13; under these conditions, both hydrogen and oxygen were effective in lowering friction at low ambient pressure. Savage found that the beneficial effect of water vapor at 3 torr for graphite sliding against itself held only at rubbing speeds below 200 cm/s; higher pressures were Although required at higher speeds: e . y . 6 to 7 torr at 800 cm/s 1471. the numbers vary somewhat with the specific experimental conditions, the general observation by various investigators is that the friction and wear of graphite are high i n wacuo and much lower in air. G. W. Rowe [541 found that the high friction of graphite i n vacuo (11 0.45) persisted up to temperatures of c a . 1123 K (850 C ) , above which it fell, dropping at a steady rate to )I = 0.32 at 1623 K (1350 C ) . This effect was attributed to the weakening of the TI bonding at the higher temperatures. A . P. Semenov 1551 observed a gradual decrease in the coefficient of friction of out-gassed graphite i n vucuo from u = 0.70 at room temperature to u = 0.65 at 675 K , followed by a sharper rate of decline t o u = 0.30 at 975 K and a slow, steady decrease to p = 0.15 at 2175 K . On cooling, the friction increased at this terminal rate to ca. p = 0.35 at 575 K and then at a faster rate to restore the value of p = 0.70 at room temperature. For the friction of a platinum rider against a rubbed layer of graphite on a platinum substrate in ordinary air Deacon and Goodman [ l l ] saw a substantially slow decrease in friction from u = 0.25 to u = 0.10 in the temperature range 298-623 K (25-350 C ) , followed = 0.4 with stick-slip over the by increase in friccion from u = 0 . 1 to Then there was a short interval of interval 623-823 K (350-550 C ) . smooth sliding at p = 0.25, and finally a sharp rise to p = 0.8 at 873 K which was related to the oxidation of graphite as shown by the course of thermogravimetric analysis. =

Savage and Brown [56] found that the dust generated by the wear of graphite i n vacuo consisted of laminar platelets, some thinner than 10 nm. Surfaces of rubbed polycrystalline graphite compacts abraded with fine emery paper show orientation along the (0001) direction of the hexagonal crystal structure, with about 10' tilt of the platelets against the direction of rubbing [57, 58, 591. Thus, although the basal planes are not intrinsically directions of easy slip within the body of a crystal or crystallite, once an exposed surface is generated on the basal plane, it becomes associated with easy sliding behavior in a favorable ambient environment. The properties of the basal-plane surface are different from those of the edge-plane surface, a s shown, for example, by the differential adsorption of n-dotriacontane and butanol from solution

570

in n-heptane 6 0 1 . A s an illustration of how ambient environment can influence the surface properties of graphite, material whose surface area was increased from 5 m 2 /g to 658 m 2 /g (as evaluated by BET adsorption of nitrogen) by milling in air showed an average value of 3.6 2 0.6 for the ratio of basal-plane to edge-plane surface; the same type of graphite milled under heptane increased its surface area to only 9 2 m 2 /g but the ratio of basal-plane to edge-plane surface was 51.8. Such a high ratio of basal-plane to edge-plane surface signifies preferential cleavage of crystallites along the ( 0 0 0 1 ) direction by the milling process. Judged by its frictional and wear behavior when rubbing against itself, graphite is not a lubricant intrinsically; its tribological action The is strongly influenced by constituents in the ambient atmosphere. lubrication of metals by graphite is governed by the formation of films on the substrate surfaces and by the behavior of these films in the rubbing process. Thus the study of graphite as a lubricant resolves itself into the study of the formation and properties of the films in relation to the basic behavior of graphite and the specific conditions of rubbing, which include, in addition to mechanical parameters such as load and speed, the condition of the substrate surfaces and the nature of the ambient atmosphere. Most of the information available is for films of graphite on copper because of the use of graphite brushes against copper commutators in electrical machinery. Savage [ 4 7 1 reported estimates of films 33 nm thick laid down by electrographitic compacts rubbing on copper. Electrographites are made by the thermal treatment of non-graphitic carbons such as petroleum coke or carbon black, and depending on the degree of graphitization, may consist of randomly oriented crystallites up to several hundred gngtroms in size, either interlocked among themselves or bonded by a non-graphitic carbon cement. The film transferred to copper by rubbing is strongly oriented in the direction of rubbing [61, 621. The equilibrium film generated by rubbing electrographite against copper (635 nm surface roughness) at 1800 cm/s rubbing speed. and 550 kPa pressure for 11,400 reiterations i n air was c a . 1000 nm thick [611 and was maintained in that condition by an average depth-wear rate of 3.6 nm per traverse of the graphite slider. The transfer process involved the formation of a soft surface layer ( 6 kg/mm2 VPN) on the relatively hard electrographic compact ( 1 0 0 0 kg/mm2 VPN), as was demonstrated by rubbing electrographite against itself. When an unrubbed compact of electrographite was run against fresh copper at 1800 cm/s, it required 80 reiterations to initiate transfer, whereas transfer from a previously rubbed compact to fresh copper occurred during the first traverse of the track 1 6 2 1 . The role of the transferred graphite film in the lubrication of steel was studied by Lancaster [ 4 3 1 , using the technique of dynamic maintenance described in Section 9 . 2 . 1 for MoS2. The wear at a rubbing speed

571

TABLE 19-8.

SCUFFING LOADS FOR A DYNAMICALLY MAINTAINED FILM OF GRAPHITE

I

Speed, m/s

Compact load, N

Steady-state

ph

Contact pressure at scuffing, MPa

Compacted natural graphite powder 0.10 0.60 0.60 0.60 3.00

-

9.8 0.98 2.94 9.8 9.8

100.95 16.10 16.10 28.49 16.10

0.18 0.12 0.15

Electrographite

0.60

9.8

0.25

16.10

Data by J. K. Lancaster [431.

to4

6

c

I o with

5

=*

0

compact without compocl

I0 n 0)

5

-

lo,-\

5

VJ

0

8

-I

lo*

I

of 0.6 m/s was reduced from an unlubricated rate of 0.561 x cm3/Nm cm3/Nm to 0.3059 x 10-l' cm3/Nm at a load of 58.8 N and to 0.2754 x at 255 N. Table 19-8 shows the influence of the dynamically maintained film on the scuffing behavior under various conditions. The load on the compact that maintains the film dynamically does not affect the scuffing load when the speed is held constant at 0.6 m / s , whereas there is a pronounced influence of rubbing speed on scuffing load for a constant compact load of 9.8 N, particularly at the lowest speed used, 0.1 cm/s. The durability of preformed films of graphite on steel in relation to the applied load on the rubbing specimens, as measured by the sliding distance to the onset of scuffing, is shown in Fig. 19-14. Once the transfer film is established, the presence of the compact has no effect on its durability under these conditions. Powdered natural graphite does not aggregate into coherent films on rubbing as easily as MoS2, according to the observations of Sliney 1161.

512

Nor does graphite adhere to

the substrate surface as well as MoS2: graphite films can be stripped from the rubbing track on a copper substrate by the usual techniques for making replicas for electron microscopy, whereas MoS2 films cannot [17]. A mechanism for the adhesion of carbon to metals in ordinary air proposed by Buckley and Johnson [631 involves chemisorptive formation of a carbonate-like metal-oxygen-carbon J. K. Lancaster [ 4 4 ] advocated the following mechanical linkage. process: direct embedding of the lubricating solid into a softer substrate, deposition of the solid into surface depressions generated by the abrasive action of the solid p e t b e , and deposition of the solid into surface depressions characteristic of the original surface finish of the substrate ( e . g . grind marks). Lancaster [43] suggested that the failure of the transferred film can be ascribed to desorption of water vapor and other protective adsorbed gases as the surface temperature increases during rubbing. When a steel rider was rubbed against a preformed film of graphite on a steel substrate, the coefficient of friction increased with temperature and scuffing failure occurred at 390 K (117 C) after 0.36 km of rubbing; under the same load (196 N ) at room temperature, the critical rubbing distance for scuffing was 10 km. It can be inferred from such behavior that the influence of protective vapors on the wear of a transferred film of graphite parallels their influence on the “dusting” wear of graphite in bulk. 19.2.3.

Graphite Fluoride as a Solid Lubricant

Graphite fluoride is the name applied to material with the generic formula (CFx!n resulting from the action of elemental fluorine on graphitic carbon. The value of x can range from 0.68 to 1.12; since (CFx),, is a giant macromolecule, the exact value of n is unknown but is very high. The preparation of graphite fluoride was first reported in 1934 by Ruff, Br.etschneider and Ebert [641, who obtained material with the empirical formula CF0.921 by the reaction of fluorine with graphite at 693 K. W. Rcdorff and G. RGdorff [651 prepared specimens with formulas ranging from CFo.676 to CF0.988, depending on the temperature (693823 K ) and the time of reaction (1-15 hours). Lagow., Badachhape, Wood and Margrave [661 found that material with the formula CF1.,* could be prepared consistently at reaction temperatures of 900 f 3 K by careful attention to the experimental details. Strictly speaking, the designation graphite fluoride is a misnomer, for the various materials with the formula (CFxIn do not have graphitic structures or graphitic properties; f o r example, they do not conduct electricity. The consensus of the available evidence [65, 66, 67, 68, 691 is for the structure shown in Fig. 19-15, in which the carbon

573

@ C a r b o n 0 Fluorine

Figure 19-15. Layer-lattice structure of graphite fluoride. in nanometers.

Dimensions

skeleton is that of a giant "hydroaromatic" molecule with a carbon-carbon bond distance of 0.154 nm and interlayer distances variously reported a s 0.60 nm [671, 0.66 nm [681, 0.58 nm [661 and 0.616 nm 1631. The carbon skeleton is usually assigned the cyclohexane "chair" configuration, probably on the basis of thermodynamic stability 1661; however, Ebert, Brauman and Huggins [691 suggest that nuclear magnetic resonance calculations favor the "boat" structure. According to Lagow e t uL. 1661, stacking of the layers is such that the locations of the carbon atoms are staggered. The carbon-fluorine bonds are covalent, which accounts for the high electrical resistivity of graphite fluoride. Infrared absorption spectra of samples with the empirical composition C F l a 1 2show stretching frequencies assignable to tertiary carbon linkages and to CF2 bonding [661. The CF2 bonding occurs with the carbon atoms located on the periphery of the polynuclear sheet. Heavy fluorination can open the polynuclear structure Light with the formation of volatile fluorocarbons CnFnc2 1651. fluorination would leave patches of graphite unreacted. The possibility that a particular preparation is a mixture of underfluorinated and superfluorinated structures must also be considered. T h u s , there is no particular merit in the designation poly(carbon monofluoride) [701 for substances with the empirical formula (CFxIn (n c u . 1). Graphite fluoride, whatever its shortcomings as a name in other respects, does not have any implications of precision as regards the composition or nature of the material and hence will be used here as the designation of materials with the composition (CFxIn.

574

Lagow e t n l . 1661 reported that preparations with the composition CF1.12 were stable in air up to a temperature of 873 K and decomposed at 1073 K. Under high vacuum graphite fluoride decomposes at 693-853 K to form a series of polyolefinic fluorocarbons 1711. Ruff e t a l . [64] found the fluorocarbons CF4, C2F4, C2F,-, etc. as the products of the thermal decomposition of their preparations. Depending on the particular method of preparation, RGdorff and RGdorff [651 reported critical temperatures of decomposition in the range 743-773 K. Gisser, Petronio and Shapiro f721 observed a change in (CF0.9)n at 678 K by differential thermal analysis.

8

0

100 200 300 400 500 600 Temperature, deg. C

Figure 19-16 Comparison of the effect of temperature on the durability and the frict on of films of graphite fluoride and molybdenum disulfide. 440 C stain ess steel riders against burnished films on 440 C stainless steel disks. Load: 4.6 N. Sliding speed: 1.6 m/s. Atmosphere: dry air. A: Friction f unlubricated metal. B: Onset of thermal decomposition of (CF1.12)n. Data by Fusaro and Sliney [731.

Although graphite fluoride has been known since 1934, its properties as a solid lubricant were not investigated until 35 years later. Fusaro and Sliney [731 studied the behavior of burnished films on stainless steel with a pin and disk apparatus. Figure 19-16 shows a comparison of the effect of temperature on the durability and the friction behavior of films of (CF1.12)n and MoS2 on 440 C stainless steel in dry air, the criterion of film failure being the strong increase of friction to that of the,unlubricated metal. Under these conditions (CFlVl2),, exhibits better durability than MoS2 up to the temperature at which thermal decomposition of graphite fluoride is appreciable. The relation between durability and temperature can be expressed as a linear function of temperature by

Log L

= bog

L o - he

(19-1)

TABLE 19-9.

Disk

440C 440C 440C 440C

BEHAVIOR OF GRAPHITE FLUORIDE A S A SOLID LUBRICANT

u

(a)

(CF1.12 ’n

Dry air

506

0.03-0,15

Dry air

99

0.02-0.04

Moist air (e)

__

0.06

1200

Moist air (e)

-

0.15

30

Dry air

200

MOS

(CF1.12)n MO 5

2

(CF1.12)n

310

Graphite

Dry air

310

M0S2

Dry air

310

h

Atmosphere

310

310

Lo, min.

Lubricant

(CF1.12)n

Graphite

Moist air (e) Moist air (e)

~

Dry argon

_ .

MoS2

Dry argon

310

~

(b)

450 70

250

Fa i lure(g)

~

Graphite

310

min.

Failure(g)

-

53

(CF1.12)n

0.02-0.07

I _

Dry argon

310

0. 004222(f

L,

0.002?71(h)

0.05

700’

0.09

350

0.02-0.04

50 <2 <2

440C Stainless steel rider o n 440C or 310 stainless steel disk. Load: 4.90 N. Speed: 1.16 m/s. ( a ) Average range in region of smooth sliding. ( b ) Experimental result. ( c ) Temperature range 0-400 C. (d) Temperature range 0-446 C. (e) 10,000 ppm HZO.

( f ) Temperature range 0-590 C. (9) High friction immediately. (h) Temperature range 0 636 C. From data by Fusaro and Sliney [731.

cn -4 cn

516

where L o is the durability at 0 C, e is the Centigrade temperature and k is the constant of proportionality. Table 19-9 shows this expression applied to the data of Fusaro and Sliney [731. Gisser e t at. [721 compared the effect of temperature on the behavior of burnished films of (CF0.9)n and of graphite on AISI 1020 steel rubbed by an AISI 52100 steel rider in air under a load of 2.45 N at 0.17 cm/s. The friction with graphite fluoride was maintained steadily at p = 0.10-0.12 in the range 300-617 K , whereas with graphite the coefficient of friction rose from 0.11 at 488 K to 0.48 at 533 K and 0.53 at 593 K. The effect of fluorine content o n the lubricating behavior of graphite fluoride preparations ranging in empirical formula from CF0.25 to C F l a lwas investigated by Fusaro [73, 741, using the experimental technique and conditions described above. In air (moist or dry), the durability of burnished films increased with increasing fluorine content: in dry argon, durability increased up to C F 0 . 6 7 and then leveled off. Minimum friction coefficients were not strongly influenced by the fluorine content: values of p = 0.03 in dry air or dry argon and p = 0.07 in moist air were observed over the entire range of compositions. R. Mecklenburg [751 found that a burnished film of (CF1.,8)n 508 roughness averaging 1.09 i 0.19 p m did not eliminate wear when rubbed by a M-10 K.

pin thick O E the surface of a disk of M-10 steel with a surface

steel ball 0.3175 cm in diameter under an initial loading pressure of 841 MPa at 1.57 m/s. A definite wear scar formed on the ball after only 7 traversals of the rubbing track, and the wear continued smoothly without scuffing at substantially constant volume-rate for 150,000 traversals.

TABLE 19-10. WEAR WITH GRAPHITE FLUORIDE AS THE LUBRICANT Traversals, k ilocvcles

0- 1 1-5 5-15 15-42 15-60 60-100 100-200 200-308 308-381 200-400 400-800 800-1200 1200- 1250

Rider wear rate,

10-15 3 m /m

Sandblasted 1.2 f 0.2 pm

Sanded 0.30 t 0.5 pm

polished 0.09 f 0.2 Vrn

3.3 2.0 1.2

1.6 0.43 0.03

0.59 0.45 0.53 1.4 Failure

-

-

0.13 0.12 0.06

0.04 0.11 0.12 0.45 2.2 Failure

-

0.20 0.52 c.95 2.9

Failure: coefficient of friction = 0.25.

Data by R. L. Fusaro [761.

511

Such behavior does not support the concept of a thick barrier film of graphite fluoride between the surfaces of the rider and the disk. A detailed study of the role of graphite fluoride in wear processes of this type was carried out by Fusaro [761 with burnished films of (CFo,84)n/(CFl.o)n on hardened 440 C stainless steel disks (60 Rc) rubbed by spherically-ended 440 C riders at a speed of 2.6 m/s in air of 50% relative humidity at 25 C; initial contact pressure was of the order of 1.38-1.77 GPa. The disks were finished to three different surface roughnesses: polished (0.09 ?r 0.02 um), sanded ( 0 . 3 0 ? 0.05 urn) and sandblasted ( 1 . 2 ?r 0.2 urn). Table 19-10 shows the wear rates at various stages during the course of wear. The initial wear is higher the rougher the surface finish but the duration of the lubricating action is greatest for the roughest surface. The stable coefficients of friction were 0.060.08 for the polished and the sanded surfaces, 0.10 for the sandblasted surface. Examination of the rubbing tracks and of the scars on the riders un2er t h c micrcsccpe i~dicntedthat the m2terit.l cf t h e criginally applied burnished layer on the disk was squeezed out laterally from under the rider as the rubbing progressed but tenacious films of the order of 0.7-0.4 nm thick remained on the high spots that participated in the real rubbing contact. Flcw behavior of graphite fluoride was Eound by Sliney in his observations of the rubbing process on a glass disk 1161. With stainless steel, the higher asperities of the rougher surEaces penetrate the original burnished film, which accounts for the higher initial wear. After adherent films of graphite fluoride have been formed on the areas of real contact, the wear rate moderates and the graphite fluoride trapped in the pockets and valleys act as reservoirs of supply to these areas, hence the longer duration of the lubricating accion with the rougher surfaces. The metallic v e a r d e b r i z fcr the ste~d;f-stateriibbing process, which consisted of very fine particles, some displaced from the rubbing zone to the side of the track and some intermingled with the graphite fluoride on the track and on the rider wear scar, did not seem to impair good lubrication as long as a sufficient supply of graphite fluoride was available. Atkinson, Waghorne and Swift 1771 examined the state of the graphite fluoride remaining on a steel rubbing track after failure (rise of friction to u = 0.2) by X-ray photoelectron spectroscopy. Decrease in the intensity of the covalently bonded F lb peak was associated with loss of volatile carbon-fluorine components via rhermal degradation by frictional heating, thereby disrupting the structure of the film. But the wear track showed the presence of icjnic fluoride, perhaps an irc!? fluoride. Thus, in addition to its film effect as a solid lubricant, graphite fluoride may also function as a chemically active additive.

19.2.4.

Boron Nitride as a Solid Lubricant is

Boron nitride (empirical formula B N )

a

microcrystalline

white

578

solid which by appropriate thermal treatment can be transformed into an ordered layer-lattice structure analogous to that of graphite. The layers are made up of sheets with the hexagonal arrangement shown below:

I

I

N

N

\ / \ / \ / B

B

I

l

N

B

l

N

N

I \ / \ / \ B

B

I

1

The boron-nitrogen bond length of 0.1446 nm (C-C in graphite 0.142 nm) is considerably less than the sum of the single-bond covalent radii of boron and nitrogen, 0.156 nm; the interlayer separation of 0.330 nm is close to that of graphite, 0.3345 nm 178, 791. The short carbon-nitrogen bond length might indicate a partial double-bond character; Silver and Bray 1601, on the basis of B1' nuclear magnetic resonance data deduced the existence of 45% double-bond contribution. But the low electrical conductivity of boron nitride is inconsistent with any appreciable degree of boron-nitrogen double bonding [79]. The preparation of boron nitride from orthoboric acid and urea is described by T. E. O'Connor [Sll. Special measures are required to remove the last traces of boric oxide: commercial preparations are likely to be significantly contaminated with B203 and water. Deacon and Goodman [ll] found a small loss of volatiles at 373-423 K from boron nitride subjected to thermogravimetric analysis in air and a large increase in weight at 1123-1173 K , which is the temperature range of the active oxidation of BN to B203. In view of its similarity to graphite in crystal structure and in the lamellar properties of the crystallites, it was expected that boron nitride would function effectively as a solid lubricant. However, it has been found that the friction of boron nitride is characteristically higher than that of graphite under the same circumstances. D. H. Buckley [821 observed a value of u = 1.0 for the friction of pyrolytic* boron nitride in high vacuum (lo-'' torr) at 296 K; G. W. Rowe [541 obtained p = 0.5 in a vacuum of 5 x torr at room temperature and = 0.37 at ca. 1073 K. Some characteristic values for the coefficient of friction I by Buckley of pyrolykic boron nitride sliding on metals i n V ~ C L L C measured I821 are: Au, '0.3; Ag, 0.4; Cu, 0.5; Pt, 0.65; Fe, 0.7; Al, 0.8; Ti, 1.0. Evidence of transfer of EN to the metallic surface was seen in the Auger

* This designation is applied to boron nitride which has been converted from the microcrystalline, turbostratic state to an ordered layerlattice, graphite-like structure by thermal treatment.

579

emission spectra. A. J. iialtner [4] reported that a thick transfer layer was formed when a compact of boron nitride was rubbed against copper i n W ~ C U O (lo-' torr) and noted a value of p = 0.70. For the friction in air, Haltner 141 found a value of p = 0.25 for boron nitride rubbed against copper; Buckley [821 reported p = 0.5 for boron nitride against iron; and Rabinowicz and Imai [831 found p = 0.170.22 for stainless steel against boron nitride. G. W. Rowe 1541 admitted gases and vapors to clean boron nitride sliding against itself and observed the following: heptane, ethanol or caproic acid gave a sharp drop from p = 0.50 to p = 0.17; water vapor, a gradual decrease with pressure to p = 0.20; oxygen or nitrogen, a drop to u = 0.45: hydrogen, a drop to p = 0.35. Rowe also compared the effect of temperature on the friction of stainless steel sliding against burnished films of boron nitride or graphite on stainless steel in air; at room temperature the values were essentially the same ( c a . u = 0.151, but with increase of temperature the friction for boron nitride rose to p = 0.25-0.28, while the friction for graphite decreased to p = 0.08 at 673 K. Graphite failed at 873 K with a sharp increase of friction to p = 0.5, whereas the friction of boron nitride remained unaltered at 973 K. 19.2.5.

Other Layer-Lattice Inorganic Solids as Lubricants

The parallelism in chemical composition and layer-lattice crystal structure between MoS2 and such Group VI transition metal dichalcogenides as MoSe2 and W S 2 suggests there also may be parallelism in their behavior as solid lubricants. Lavik, G r o s s and Vaughn [ 8 4 1 measured steady-state values of u = 0.05-0.07 f o r compacts of tungsten disulfide rubbing against transfer films i n v a c u u , with stop-time effects like those observed by Johnson and Vaughn for MoS2 [21]. Flom, Haltner and Gaulin [23] found u = 0.17 for WS2 in air, u = 0.15 in a baked-out vacuum system ( 8 x lo-' torr), and p = 0.06-0.07 in dry nitrogen; they were unable to explain why the friction ~n WGCUO was unexpectedly high. Lavik, Daniel and Abbott [ 8 5 1 reported a steady-state value of p = 0.108 k 0 . 0 0 4 with Spengler and stop-time effects for molybdenum diselenide i n V G C X O . Fischer [ 8 6 ] compared the durability of films burnished on the pins of the Almen-Wieland tester and found the following relative ranking: MoS2 1.00, WS2 0.82. WSe2 0.32, MoSe2 0.098. They also observed cooperative effects in mixtures; f o r instance 20% of MoS2 admixed with MoSe2 raised its relative durability to 0.72. Peterson and Johnson 1871 found that W S 2 and MoS2 gave closely parallel results for a segmented annulus of hardened steel rubbing on a full annulus: u k = 0.03-0.07, wear = 0.0109 lr

O.OOOI cm'.

Jamison and Cosgrove [881 studied the friction characteristics of disulfides and diselenides of the following transition metals of Groups IV-VII: Zr, Hf, Nb, Ta, Mo, W , Re. A film of the chalcogenide was bur-

580

nished on a brass disk and rubbed with a hardened 4 4 0 C stainless steel ball at 200 cm/s under a progressively increasing load up to 4.9 N. The chalcongenides that showed successful lubricating behavior with p k in the range 0.040-0.075 (MoS2, MoSe2, WSz, WSe2, NbSe2) all crystallized in the hexagonal system with the layer-lattice configuration characteristic of MoS2. A specimen of WSe2 that crystallized in the rhombohedra1 system did not form an adherent film on the brass disk, but when it was transformed into the hexagonal crystal habit by thermal treatment, it behaved as a lubricant with p = 0.037. But although NbS2, TaS2 and TaSeZ crystallize in the MoS2 configuration, they did not show lubricating

proper-

ties. The following solid solutions performed as lubricants: WSe2-TaSe2 with at least 72 mole-% of WSe2; WSe2-ReSe2 with at least 4 1 mole-% of We2. Table 1 9 - 1 1 shows the comparative friction data for transition metal disulfides, diselenides and ditellurides obtained by P. M. Magie [ 8 9 ] . Compacts of the dichalcogenides were rubbed against a 4 4 0 stainless steel plate at 25 cm/s in room air: i . e . against a transfer film. All the chalcongenides crystallized in the hexagonal system except WTe2 (orthorhombic), NbTe2 and TaTeZ (trigonal). The friction of graphite is shown for comparison. 19-12

A. J. Haltner [ 4 1 observed the frictional behavior shown in Table for compacts of Bi13, LiOH, Ni12, CdClZ, Cd12 and CdBr2 against

TABLE 19-11.

FRICTIONAL BEHAVIOR OF TRANSITION METAL CHALCOGENIDES

Chalcogenide

uk

Chalcogenide

pk

MoS

0.18

TaS2

0.05

MoSe2

0.17

0.08

MoTe2

0.19

TaSe2 TaTe2 (b)

0.53

0.17

TiS2

0.22

ws2 WSe2

0.09

TiSe2

0.17

WTe (a

0.49

TiTe2

0.33

NbS2

0.08

ZrS2

0.22

NbSe2 NbTe2 (b)

0.12

ZrSe2

0.18

0.53

ZKTe2

0.23

Graphite

0.20

(a) Orthorhombic.

(b) Trigonal.

lata by P. M. Magie [ 8 9 1 .

581

TABLE 19-12.

FRICTION DATA FOR LAYER-LATTICE SOLIDS

Air

Vacuum

Bismuth iodide, B13

0.34

0.39

Lithium hydroxide, LiOH

0.37

0.21

Nickel iodide, Ni12

0.48

0.44

Cadmium chloride, CdC12

0.35

0.16

Cadmium bromide, CdBr2

0.22

0.15

Cadmium iodide, Cd12

0.24

0.78

Graphi te

0.19

0.44

Molybdenum disul'fide, MoSZ

0.18

0.07

Data by

A.

J. Haltner [41.

transfer films on copper. These substances all have layer-lattice crystal structures. Baldwin and Rowe [901 prepared films of Ti12 on titanium and of CrC13 on chromium which were identified by X-ray diffraction. These gave coefficients of friction of c a . 0.23-0.25 up to temperatures of 673-923 K, which roughly correspond to the thermal decomposition temperatures of the films. However, none of these investigations went so far as to demonstrate real utility a s lubricants. 19.3.

LUBRICATION BY NON-LAMELLAR INORGANIC SOLIDS AND B Y SOFT METALS The intensive study of lamellar Solid5 a s lubricants stems from pos-

tulates about their low friction based on their crystal habit and crystal structure. But in order to meet the severest requirements of modern technology, such as extremes of temperature and high vacuum, properties in addition to low friction must be considered, and the literature of the past twenty-five years abounds with reports of investigations of a wide array Of solids as lubricants. Table 19-13 gives a representative listing of Some of the solids which have been seriously studied, but it is not complete by any means. A direct comparison of the behavior of lamellar and non-lamellar Solids is seen in the work of P. H. Bowen [911 with CaS04, PbCr04, PbS, Sb2S3, MoS2 and graphite in a block-on-ring apparatus run at 343 K (160 F ) in dry nitrogen with loading pressure in the range 690-2070 kPa and a rubbing speed of 113 cm/s. Coefficients of friction when the non-lamellar solids were fed as powder to the interface were significantly higher ( p k = 0.17-0.41) than for graphite and MoS2 ( p k =

582

TABLE 19-13.

SOME NON-LAMELLAR SOLIDS STUDIED AS LUBRICANTS

Oxides:

B203, PbO, ZnO, CdO, SrO, Cu20, CuO, Mn02, Co203, Moo3, W03, S n O , Ti02

Chalcogenides:

PbS, As2S3, Sb2S3, Bi2S3, Bi2Se3 CdS, CdSe, CdTe, Ag2S, HgS, Ag2Te, ZnTe, Cu2S, CoS, Ce2S3

Ha 1ides :

Pb12, CuC12, BiOC1, CaF2, BaF2, LiF, NaF

Phosphates:

Fe3(P04)2.hydrated, Zn3(P04)2-hydrated C ~ ~ ( P O ~ ) ~ - h y d r a tMn3(P04)2-4H20 ed,

Molybdates:

PbMo04, NiMo04, FeMo04, CaMo04 Cr2(Mo04)3, Ag2Mo04, K2Mo04

Tungstates:

PbW04, CuW04, NiW04, FeW04, Cr2(W04)3, CaW04, Na2W04

Metals:

Au, Ag, Pb, Bi, Ba, Al, Ag/Pd

0.02-0.04); wear was somewhat higher for the non-lamellar solids but not destructive, as evidenced by the polished condition of the wear scars.

Numerous investigations deal with the behavior of inorganic solids as lubricants for service at severe temperature conditions. Table 19-14 shows the results obtained by Peterson, Murray and Florek [92], who sprinkled powders on a platen rubbed with reciprocating motion at an average speed of 0 . 7 6 2 cm/s by a hemispherical rider under a load of 1 8 . 4 N. Of the oxides tested, PbO, Moo3, W03, Co203, ZnO, CdO, Cu20 and SnO agglomerated into continuous films which prevented surface damage even when the friction was relatively high; the ineffective oxides were brushed aside by the rider and did not protect the rubbing parts from damage. The protective action seemed to be related to the shear strength of the lubricating solid: when the temperature was lowered most of the effective solids n o longer protected the surfaces from damage, presumably because they did not shear easily enough. Experiments carried out by Cosgrove, Sibley and Allen [ 9 3 1 in air at 8 1 1 K (1000 F) with a four-ball test machine gave indications of the efficacy of PbO and Ag2S. Table 1915 shows data from the work of Orcutt, Krause and Allen [ 9 4 1 with a highspeed rolling/sliding disk machine. Two kinds of disk material were used: a Tic-Ni-Nb cermet for which the initial Hertzian contact pressure

Material

Temperature, deg. K

Coefficient of friction (a)

A9

1061

0.40

Au

1061

0.57

Pb( b,

300

0.24

PbO

977

MOO

Material

Temperature, deg. K

Coefficient of friction (a)

977

0.28

977

0.42

Ti02

977

0.41

0.12

PbMo04

97I

0.29

977

0.20

NiMo04

917

0.29

wo 3

977

0.55

Ag 2'004

977

0.28

ZnO

977

0.33

K2Mo04

977

0.20

CdO

977

0.48

PbW04

977

0.35

cu20

971

0.44

Na2W04

977

0.17

( a ) A t the end of 100 cycles of rubbing. Peterson, Murray and Florek 1 9 2 1 .

30Z' SnO

(b) Melting

point

600 K.

From

data

by

TABLE 19-15. BEHAVIOR OF SOLID LUBRICANTS IN ROLLING/ SLIDING DISK EXPERIMENTS AT ELEVATED TEMPERATURES Tic-Ni-Nb Disks: 481-589 K

699-811 K

Relative wear (a)

k' 922 K

H9S

B A

B A -

A A

Bi S 2 3 Bi Se 2 3

-

B

B

B

PbO

-

Co-Cr Alloy Disks: 481-589 K

1.75 0.60 0.90

699-811 K

Relative wear (a)

'k 922 K

C B B

C B -

A

2.30 1.00 0.30

B

B

A

0.80

B B

Ag2S

A

ACl2Te

B

c uo

B B

CUCl2

B B

B B

0.90 1.00

B C C

1.30

PbS CdO CdS Ce2S3 ZnSe MoS2

A

B

B

0.07

B

C

C C

2.60 0.60

Graphite

A

A

A

0.07

C

B

A

0.30

uk: A

-

=

<0.10

B = 0.10-0.14

C = >0.14.

1.30 1.50

Rolling

2.30

__

speed:

4.775

m/s.

Sliding

speed:

0.191 m/s.. Initial contact pressure: 662 MPa, Co-Cr alloy; 813 MPa, Tic-Ni-Nb. (a) Relative to Hertzian width of wear track. From data by Orcutt, Krause and Allen 1941.

TABLE 1 9 - 1 6 .

FRICTION AND WEAR L I F E FOR

Fluorides,

Thickness.

wt-% cm

FLUORIDE COATINGS ON N i - C r

Temperature,

Load, N

Wear life (a)

ALLOY

'k

Wear r a t e , 10-l' c m 3 / s

deg. K

I

80 C a F 2 / 2 0 BaF2

5.1

811

4.90

229(b)

0.16

1.42

38 CaF2/62

BaF2

3.8

297

4.90

229(b)

0.20

0.30

38 CaF2/62

BaF2

2.6

811

4.90

229(b)

0.16

0.30

3 8 C a F 2 / 6 2 BaF2

3.1

1089

4.90

180

0.15

0.30

3 8 C a F 2 / 6 2 BaF2

2.5

1089

4.90

80

0.20

-

3 8 CaF2/62

3.1

1089

9.81

120

0.20

-

77 CaF2/23 L i F

3.1

297

4.90

229(b)

0.16

0.84

77 CaF2/23 L i F

3.8

811

4.90

229

0.15

0.23

7 7 CaF2/Z3

LiF

3.1

811

9.81

80

0.18

-

7 7 C a F 2 / 2 3 LiF

3.1

922

9.81

48

0.15

-

77 CaF2/23 L i F

3.1

533

9.81 ( c )

10

0.24

-

77 CaF2/23 L i F

3.1

811

9 . 8 P

20

0.24

-

BaF2

cn m

TABLE 19-16. FRICTION AND WEAR LIFE FOR FLUORIDE COATINGS ON Ni-Cr ALLOY (continued) Fluorides, wt-%

100 LiF

3.3

811

4.90

229(b)

0.15

1.06

100 LiF

3.8

1089

4.90

229

0.10

0.42

81.4 CaF2/18.6 NaF

3.8

811

4.90

229 (b)

0.07

3.75

Uncoated

0

811

4.90

-

0.47

82.08

9.81

-

0.47

165.83

811

Wear life (a)

Wear rate,

cm

0

Load, N

’k

Temperature, deg. K

Uncoated

Thickness,

~o-’O

cm3/s

( a ) Thousands of reiteration cycles: failure by sharp rise in friction. (b) No failure at the end of run. (c) 508 cm/s. Sliding speed 1016 cm/s. Riders: hemispherically ended, 0.476 cm. From data by Sliney, Strom and Allen [951.

587

was 813 MPa under a load of 863 N, and a Co-Cr-base alloy for which the initial contact pressure was 662 MPa. The powdered lubricant was fed into the rubbing interface suspended in a stream of commercial nitrogen (2-4% oxygen). With the TiC cermet, although many of the solids gave the same general friction level and some were equivalent to graphite in this respect, none of the non-lamellar materials approached the effectiveness of McS2 or graphite in controlling wear, The softer cobalt-based alloy was more difficult to lubricate. The advantages of alkaline-earth and alkali fluorides as solids which would remain stable at high temperatures in aggressive environments was recognized on thermodynamic grounds. Their usefulness as solid lubricants is complicated by problems of adhesion to substrate surfaces. Sliney, Strom and Allen [ 9 5 J studied mixtures of CaF2/BaF2, CaF2/LiF, CaF2/NaF as well as LiF by itself: these solids were fused to the surfaces of Ni-Cr alloy disks and rubbed against a Ni-Cr hemispherically tipped rider. Table 19-16 shows the findings for temperatures up to 1088 K (1500 F) in an atmosphere of 10% hydrogen-90% nitrogen. A 272-fold decrease in the wear rate of the rider at 811 K and a 4.90 N load relative to the wear of unlubricated metal is seen with coatings of 38% CaF2/ 62% Ba F2 on the disk. However, effects such as the decrease in coating durability with lowered sliding speed and lower temperature for some of the runs with 77% CaF2/23% LiF point to the complexity of the tribological phenomena involved. The value of pk = 0.16-0.20 seems to be characteristic of fused coatings containing CaF2; B. Blampin [96] reported numerous instances of pk = 0.14-0.22 for CaF2 on special alloy annuli rubbing at 1.7 m/s in the temperature range 473-773 K under 535-4015 MPa pressure, although with some substrates p h rose to 0.25-0.35.

10.50.4

C

I

!i Load, newtons

1

1

1

1

I

. (b)

(a)

l 4

l

/-I

1

2L

00

2

4

6

Load, newtons

Figure 19-17. Friction of thin films of soft metals. (a) Indium on tool 1: Unlubricated tocl steel; 2: steel from data by Bowden and Tabor [97]. tool steel lubricated with mineral oil: 2 : film of indium 0.0004 cm thick on tool steel. (b) Lead on steel from data by Burton and Russell [98]. 4: Massive lead; 5: lead film on steel.

588

The frictional behavior of films of soft metals on hard substrates is described by Bowden and Tabor I971 and is illustrated in Fig. 19-17a for the effect of load on the coefficient of friction of a steel rider against a film of indium on a steel substrate. Whereas the friction for unlubricated steel or steel lubricated with mineral oil is independent of applied load in conformity with Amontons' law, for a film of indium on steel it decreases with increasing load. The frictional force is determined by the shear strength of the indium and the area of contact between the film and the rider, but this area is governed by the elastic deformation of the underlying steel substrate, which increases less than linearly with load. Burton and Russell [98] investigated the behavior of lead films on steel and demonstrated the following: ( 1 ) when the load was light so that substantially all of the deformation was by plastic yielding of the lead and plowing of a track in the film, the course of friction obeyed Amontons' law and the coefficient of friction was independent of load: ( 2 ) but when the load was heavy and the underlying steel was also deformed, the incremental increase in area as load increased was then determined by the elastic deformation of the steel platen by the spherical rider while the shear force at the interface was governed by the shear strength of the lead and consequently the increase of friction force was no longer linearly governed by load. Figure 19-17b shows these effects. The analysis above applies to counterformal, concentrated contacts. The behavior of a soft metal on a conforming interface was investigated by Tsuya and Takagi [991 for a film of lead between the flat annular surfaces of two copper rings at the extremely slow speed of 0.005 cm/s in the contact pressure range 0.04-9.8 MPa. The films of lead ranged in thickness from 0.130 mm down to 0.0001 mm. The general trend of behavior was the same for all film thicknesses: a sharp drop in the coefficient of friction as the loading pressure was increased from 0.04 to 0.53 MPa and a relatively minor decrease thereafter up to a loading pressure of 9.8 MPa. The analytical treatment of the course of friction best suited to this particular geometry is the basic adhesive theory presented in Chapter 8 (see Eqn 8 - 8 ) , from which we get an approximate value of uh = 0.5 for lead sliding on lead. The steady-state values observed by Tsuya and Takagi have approximately this magnitude for the thinner films, but for the 0.130 mm films the coefficient of friction was c a . 0.75. The applicability of the analysis for a plastically deformed solid film on an elastically deformed substrate is not restricted to films of soft metals. This effect applies also to burnished films of other kinds of solid substances which can act as lubricants. Some of the practical ways of utilizing solids as lubricants involve compounding them with a substance, often an organic plastic of low shear strength, which bonds them to the surface to be protected, and hence the mechanical properties

589

of the film of bonding agent enter into the overall picture of lubrication by solids. 19.4.

ORGANIC SOLIDS

AS

LUBRICANTS

Many organic solids can be coated on metals and other hard materials to form rubbing interfaces with low friction, but most of them do not meet the other criteria required of solid lubricants, such a s durability, resistance to high temperatures, and low volatility. Only a handful of organic substances have been given serious consideration as solid lubricants p e t b e , the behavior of which depends on the properties of macroscopic coatings as distinct from a d b a h b e d d d m b of fatty acids, soaps and related long-chain compounds, which act on a molecular scale. Macroscopic coatings of fats, soaps and waxes do function .as good lubricants in the sense of reducing friction and preventing adhesion, but because of poor durability their usefulness is restricted to a oncethrough basis, as in wire-drawing and related metal-forming processes, and therefore they will not be discussed further.

Figure 19-18. Chemical !b) Iron chelate.

structure of phthalocyanines.

(a) Metal-free.

By and large, the organic solids that have been found useful as lubricants are polymers. The outstanding exceptions are the phthalocyanines, which form lamellar crystals. The chemical structure of metal-free phthalocyanine is shown in Fig. 19-18a, the structure of a typical chelated compound with a metal in Fig. 19-18b. High-resolution electron microscopy by J. W. Menter [loo] indicates an interlamellar In air, spacing of 1.2 nm for a crystal of platinum phthalocyanine. metal-free phthalocyanine shows only a slight darkening after 4 hours at 7 2 7 K (850 F ) but decomposes at 811 K (1000 F ) with evolution of ammonia and nitrogen; in V U C U U , it sublimes at 7 8 3 K (950 F) without decomposition [loll. The work of Krause e t d .includes an excellent demonstration of the lubricating behavior of phthalocyanine: a stream of nitrogen carried the powder into the rubbing interface between a pair of rolling/ sliding disks ( 5 0 6 3 / 2 0 3 cm/s) under 689.5 MPa pressure (100,000 psi) at

590 9 2 2 K (1200 F). Coefficients of friction ranged from 0;03 to 0.08; MoS2 under the same conditions gave vh = 0.34. Salomon, Begelinger and de Gee [lo21 found vk = 0.3-0.4 and a durability of 4 hours for burnished films of phthalocyanine on steel at 1 m/s in dry air at room temperature; with MoS2 uk was 0.03 and the durability was 5-7 hours. Flom, Haltner and Gaulin [23] reported vk = 0.33-0.37 for compacts of phthalocyanine rubbing against copper, either in air or in v a c u a . Grattan and Lancaster [lo31 observed that phthalocycanine was about three times as effective as MoS2 in reducing the wear rate of copper sliding against sapphire although u h was substantially the same with either lubricant (0.11-0.12).

Phthalocyanine is synthesized from the sodium o r lithium derivatives, which are prepared by condensing phthalonitrile with the appropriate metal salt in isoamyl alcohol. Other metal derivatives can then be prepared directly by ion interchange. Coatings of metal derivatives can be prepared directly by reacting the bulk metal with phthalonitrile o r with metal-free phthalocyanine at elevated temperatures. Salomon e t aL. [lo21 investigated the behavior of commercial samples of the copper derivative and found them substantially equivalent in action to metal-free phthalocyanine. Krause e t a L . [loll tested the behavior of surface-treated components in oscillating bearing rigs. In addition, they carried out practical tests at elevated temperatures with metal-free phthalocyanine in liquid carriers such as polyisobutylene and polyglycol. Of the organic polymeric plastics, polytetrafluoroethylene (PTFE) was one of the earliest to be investigated as a solid lubricant because of its chemical inertness and its low surface energy. Kay and Tingle [I041 deposited films of PTFE on various metals and found the friction to be in the range uLIz= 0.07-0.20 from room temperature to 373 K. At the very slow sliding speed (0.1 cm/s) of the Bowden-Leben apparatus and a load of 39 N , films on copper gave uk = 0.04-0.06 at 573 K and withstood up to 2 0 0 iterations of the track by the rider. Speerschneider and Li [lo51 observed uLh= 0.04-0.08 for steel against massive PTFE in a fricticn pendulum and measured a steady-state decrease in film thickness of ca. 0 . 3 5 urn in 28,000 traverses at 1.1 MPa of a Steel slider over a PTFE coating on steel. Grattan and Lancaster 11031 rubbed phosphor-bronze balls against PTFE, Delrin (a polyacetal-type plastic) and nylon and found wear rates of the br,onze of <0.5 x 10-12cm3/cm-N. Aromatic polymides made by the condensation reaction of pyromellitic anhydride with aromatic diamines have attracted attention because of their high-temperature properties such as thernal stability (in air at 811 K, in inert atmosphere at 1005 K) and good mechanical strength, as well as resistance to radiation damage 1 1 0 6 , 1071. The generic structure conventionally assigned to these substances is that of a linear polyimide

591

CH

CH but

it is apparent from the tetrafunctionality of pyromellitic acid that

cross-linking to a thermosetting polymer is an obvious possibility and is probably the reason f o r sane of the high-temperature behavior. The nature and the properties of a particular specimen of pyromellitimide is determined by the starting materials from which it was prepared and the conditions under which the preparation was carried out. Devine and Kroll [lo71 observed pk = 0.08-0.15 f o r polished A I S I 1025 steel against massive polyimide at 424 cm/s and 207 kPa. Detailed and extensive data on the tribological behavior of polyimide films on hard substrates is reported in the work of R. L. Fusaro at the Lewis Research Center of NASA [108, 109, 110, 1 1 1 1 . These films were deposited on 440 C stainless steel disks (60 Rc) to thicknesses of 2-25 pm and cured for one hour at 573 K. The riders were uncoated hemisphericallyended specimens of 440 C stainless steel. Figure 19-19 shows typical friction and durability behavior in dry air, dry argon and moist air, durability being the number of rubbing reiterations the film withstood before the friction rose abruptly to uk = 0.30. The coefficient of friction at 298 K was uk = 0.22-0.29 in an atmosphere of dry argon or dry

10,000

t I.000

0.3

270370 470 570 670 770 070 Tempemture, deg. K

Figure 19-19. Effect of atmosphere and Lemperature on the durabilty and friction of polyimide films. 1: Dry argon. 2: D r y air. 3: Moist air (10,000 ppm H20j. Decomposition temperature of polyimide: A , in air; B, in argon. From data by Fusaro and Sliney [1081.

592

air, uLh= 0.12-0.15 in moist air. Friction dropped sharply with increasing temperature; in an environment of dry argon, a steady-state value of uLh= 0.03 was established within the temperature range 323-353 K and persisted up to a temperature of 823 K 11091. Air and moisture have an adverse effect on the temperature stability of the friction level. Durability improves with increasing temperature up to the maximum seen in Fig. 19-19 and then decreases.

10

I

-5

I

I

I

J

5lo6-

0

5 \

N

E " , 10 -I

-

I

B

g

lo4

-

lo? 270

I

I

I

320

370

420

I 470

Temperature, deg. K Figure 19-20. Effect of atmosphere and temperature on the wear rate of polyimide films. 1: Dry argon. 2: Dry air. 3: Moist air (10,000 ppm H20). From data by R. L. Fusaro [llo].

The effect of atmosphere and temperature on the wear rates of polyimide films is summarized in Fig. 19-20, from the work of Fusaro [110]. Wear is measured by the cross-sectional area of the rubbing track in the film. At 298 K , the wear rate is high and unresponsive to atmosphere; at higher temperatures, dry argon is the most favorable environment and moist air the poorest. Thermal aging of the film at 618 K embrittles it, causes it to wear rapidly at 298 K, and increases the coefficient of friction from uLh= 0.11 to vLh = 0.23 because the rider breaks through to contact the substrate material 1 1 1 1 1 . An important aspect of the behavior of organic plastic solid lubricants is their ability to form transfer films on the opposing surfaces as they wear. This is not so significant on its own merits, for the intrinsic durability of the transfer film is governed by the properties of the organic plastic and cannot be expected to exceed that of a pre-applied film on the other surface. But i f the organic plastic is made the carrier and bonding agent for an intrinsically more durable lubricant solid, such as MoS2 or (CFx),,, then the wear of the organic polymer is the means of maintaining the supply of the other lubricating material at the rubbing interface. The plastic can be used to bond a

593

pre-applied film to a substrate or it can be part of the composite material of a working part, such as the retainer of a ball bearing. Exanples of such applications are described in Section 19.5. Bowers, Clinton and Zisman [112] showed by electron diffraction that an oriented film of polymer was transferred from a rider of polyethylene or PTFE to a steel surface in a single pass. They also found the same steady-state coefficient of friction whether steel slid against polymer, polymer against steel or bulk plastic against bulk plastic for such polymers as polyethylene, PTFE, polyvinyl chloride or polyvinylidene chloride. The transfer of PTFE from a bulk slider t o a glass plate as films 10-40 nm thick was observed to occur at slow sliding speeds by Makinson and Tabor [113]; Pooley and Tabor [114] reported the transfer of films less than 10 nm thick. If the sliding speed is slow enough ( e . g . 1 mm/s), polymeric plastics of linear structure, such as PTFE or highdensity polyethylene, transfer as uniform films to an opposing glass surface and show low coefficients of friction of the order of vk = 0.06-0.08 [1141. Polymers with bulky side chains in their structure show relatively high coefficients of friction against glass and the transferred material consists of macroscopic fragments intermingled with thin-film regions. Many' of the laboratory investigations of the tribological behavior of polymeric plastics are carried out under conditions much different from those of practical use. K. C. Ludema [115], in discussing R . L. Fusaro's interpretation of the temperature-dependent friction behavior of polyimide plastics relative to their viscoelastic properties [log], pointed out the wide discrepancy in the magnitude of the strains and of the strain rates between sliding conditions and viscoelastic measurements. Analogous discrepancies in such parameters as sliding speed and loading pressure can be found between laboratory studies of friction and wear and technological practice. Rhee and Ludema [ 1 1 6 , 1171 investigated the friction and wear behavior of various polymeric plastics under loading pressures (up to 5.34 MPa) and sliding speeds (up to 231 c d s ) that They observed produced sensible rises in the interfacial temperature. such seeming anomalies as increase of friction and decrease of wear as the interfacial temperature increased with the duration of rubbing. This was ascribed to the softening of the polymeric plastic at the interface with the transferred film on the countersurface. However, if the temperature becomes high enough by frictional heating, the transfer film loses its stability and the polymer from the rider agglomerates into Anaglobules and ridges so that the wear of the rider becomes severe. lytical treatment of the friction and wear problems under these circumstances would have to include properties of the system materials, operating and environmental parameters, surface finish, geometry, etc. Unless it maintains a barrier that completely separates the two sub-

594

strate surfaces, the transfer film cannot be considered as functioning effectively, according to the strictest criteria of solid lubrication; the overt consequences of a defective solid film are wear of one or both of the rubbing parts. Fusaro demonstrated that there was no wear of a spherically-ended rider rubbing against a macroscopically intact film of polyimide-bonded graphite fluoride under a load of 9 . 0 N at 2.6 m/s 11181. But when the bonded film was worn through to the level of the substrate, a s shown by profilometric cross-sections of the rubbing track, measurable wear was observed on the rider, the rates ranging from a low of 0.018 x m 3 per meter of sliding up to 2.0-2.7 x m3/m on the verge of failure (pLh= 0.3). Interferometric colors indicated the presence of patches of film of the order of 0.4-0.7 nm thick on the rider and on the track. The action of these thin patches in modifying wear is probably analogous to "mixohydrodynamic lubrication" (see Chapter 14, Section 14.1.2). Fusaro and Sliney [ l o 8 1 showed that the wear of 440 C stainless steel riders which had slid for 60 kilocycles against disks coated with uncompounded films of polyimide was 1/400th that of the wear against uncoated disks. The protective effect of the simple bonded polyimide film was equivalent to that of burnished films of (CF,.l)n or MoS2; however, compounding of graphite fluoride o r MoS2 in the polyimide fila reduced rider wear by another order of magnitude. 19.5.

THE TECHNOLOGICAL UTILIZATION OF SOLID LUBRICANTS

To the practising lubrication engineer the technological utility of solid lubricants means how they work in service. The circumstances that prompt him to consider the use of soiid lubricants are varied and the conditions of service are often at odds with the optimum reduction of friction and wear. For instance, weight limitations in space vehicles rule out the accessory equipment such as supply tanks, pumps and lines necessary f o r lubrication by fluids and restrict the choice to lubricants which are applied to the rubbing site ahead of time. I n many cases, even when pre-applied oils, greases or plastics function for the time allotted, their volatility may result in the fogging of critical optical sensors, and hence non-volatile inorganic solids must be used. Requirements which have nothing to do with lubrication pea 4 e may dictate the selection of the solid: c . g . chemical stability to aggressive components of rocket fuel such a s liquid oxygen, nitrogen tetroxide, hydrazine, etc. F o r reasons such a s these, the technology of lubrication by solids is still highly empirical. I f the circumstances require the use of a pre-applied solid film, then in addition to the tribological properties of the film (i.e. its intrinsic: friction and wear and its interaction with the countersurface against which it r u b s ) the adhesion of the film to the substrate surface comes into consideration. An important aspect of practical lubrication

595

by solids is the formulation and application of mixtures which adhere well to the substrate surface and have the durability necessary to meet the demands of service. The study and testing of bonded films of solid lubricants in laboratory rigs is the customary prelude to confirming their utility in simulators o r in full-scale machinery, and therefore such procedures can be included in the purview of the technological application of solid lubricants. Much of the information on the behavior of bonded films of solid lubricants is in the form of results from laboratory testers. The lubrication engineer is frequently faced with the problem of extrapolating from such results to technological practice. For example, in developing a lubricant composed of a mixture of MoS2 and Sb203 in a phenolic resin binder, Benzing, Hopkins and Petronio [119] compared the results from a laboratory bearing simulator with those from the Falex bench tester and from a block-on-ring test machine. All three devices agreed in the relative rating of the optimum proportions of MoS2Sb203-binder i n terms of film durability, but there was no agreement on the relation between film thickness and durability, BINDERS FOR SOLID LUBRICANTS

TABLE 1 9 - 1 7 .

Lubricant solids MoS2; MoS2

+

Binders

graphite; MoS2

Inorganic: sodium silicate; sodium-

+ graphite + A u ; MoS2 + PbS; MoS2

potassium borosilicate; sodium sili-

+

SbZ03; graphite; AgC1; graphite

cate modified by oxides such as CaO,

+

AgC1; (CFxln; (CFx),,

CaF2; BaF2; CaF2 +

+

+

graphite; T1203, BeO, Ce203, NbO; B203; Fe304

BaF2; CaF2

LiF; PbO; As2S3; Sb2S3; AsAsS4;

AsSbS4; PTFE

+

Si02; COO; phosphon trilic chloride

polymers Organic: phenolic res ns; silicone resins; epoxy resins; vinyl butyral resins; polyimide resins

The combinations of solid lubricating substances and binders tnat been investigated are t o o numerous to treat in detail here. Table 19-17 is a generalized list of binders and the solid lubricants with which they have been combined. Inorganic binders naturally suggest themselves for severe conditions such as high temperatures and oxidative environments where organic substances would not be stable. Johnson and Sliney I1201 found that a film of PbO bonded to steel by a small admixture of S i 0 2 showed acceptable wear protection up to 950 K (1250 F) whereas the upper temperature limit for resin-bonded MoS2 was 589 K (600 have

596

F). Calcium fluoride and barium fluoride are stable in.air at elevated temperatures but have adhesion problems with Ni-Cr-Mo alloy substrates. When Sliney 11211 added 23% basic calcium silicate to correct this problem, he observed good adhesion and lowered friction up to 1366 K (2000 F); a coating 0.025 mm thick on a rotating disk lowered the wear rate of an uncoated rider 1000-fold from its wear rate against an uncoated disk in the temperature range 299-1088 K at a rubbing speed of 254 cm/s with a load of 9.8 N. Sliney, Strom and Allen [95] bonded CaF2 to the Ni-Cr-Mo alloy by the inclusion of COO to give acceptable wear rates up to a temperature of 950 K and values of uk ranging from 0.20 at 380 K (225 F) to 0.15 at 1088 K (150C F). Amato and Martinengo 11221 found that addition of 2 parts of metallic iron to 93-Pb0:5-Si02 in the bonded film significantly reduced the wear rate of an AISI 403 stainless steel rider in the temperature range 298-873 K relative to that with a 95PbO:5-Si02 film; also, a bonded film with the composition 45-CaF2:30BaF2:25-Ag afforded better wear protection than 60-CaF2:40-BaF2 in the temperature range 298-673 K.

Temperature, deg. K

Figure 19-21. Effect of temperature and load on the durability of bonded Data by Stupp and Wright with the Hohman tester MoS2-graphite films. [123]. Load: 1 , 321 N; 2, 943 N; 3, 1529 N; 4, 2756 N. Figure 19-21 shows the effect of temperature and load observed by Stupp and Wright [1231 on the durability of films of mixed MoS2 and graphite (4.44:l) bonded with 6.49% Na3P04. The important parameter is temperature; at higher temperatures the durability is so poor that the influence of load becomes minor except for the lightest load. The results obtained by R. H. McDaniel 11241 with the same kind of test machine, confirm the strong effect of temperature on durability, as summarized in Table 19-18. Table 19-19, from work by McConnell, Wieser and Mecklenburg [1251 shows the effects of vacuum as well as temperature on

597

the durability of films of MoS2 + PbS (2.13:l) bonded with 33% mixed sodium and potassium borosilicate modified by small amounts of A1203, Co203, CdO, LiN03 and Ca(N03)2. These films were prepared by spraying slurry on the substrate, drying, curing at 1060 K , depositing a second coating electrophoretically to fill the voids and curing. The best durability of a single-coat film at 588 K was 28.4 kilocycles of rubbing: mechanical densification improved this to 153 kilocycles.

TABLE 19-18. EFFECT OF TEMPERATURE ON THE DURABILITY OF BONDED FILMS OF SOLID LUBRICANTS Lubricant

Durability, cycles of rubbing 299 K

589 K

755 K

I (a)

160,355

19,451

-

2,701

11(a)

45,347

21,199

-

11,640

12,255

- -

III(b) Ida)

54,964

811 K

3,333

922 K

1088 K

7,069

6,142

10,979

___

I: PbS + MoS2 bonded with B203 on case-hardened AISI 4620 steel. 11: PbS + MoS2 bonded with B203 on case-hardened nickel-base alloy. 111: CaF2 on nickel-base alloy. IV: MoS2 + graphite bonded with sodium silicate on nickel-base alloy. Film thickness: (a) 0.0381 mm, (b) 0.0127 mm. Tests run on Hohman dual rub-shoe machine with tool steel blocks, 2373 N load, 65 cm/s. Data computed from the work of R. H. McDaniel [124]. TABLE 19-19. EFFECTS OF TEMPERATURE AND VACUUM ON THE DURABILITY OF BONDED MoS2/Pb5 FILMS Ring material Temperature, Ambient Coefficient of friction Durability, kilocycles pressure deg. K Start Finish AISI AISI AISI AISI AISI AISI M-10 M-10 M-10

4130 4130 4130 4130 4130 4130 steel steel steel

M-10 steel

Room Room Room 755 866 588 Room Room 588

A V V V V V

755

V

A

V A

0.09 0.04 0.05 0.09 0.06 0.08 0.085 0.02 0.0150.025 9.085

0.25 0.16 0.17 0.17 0.17 0.15 0.16

0.15 0.10 0.10

578 4,002 3,466 1,388 570 317(a) 758 1,783 55

278

A = atmospheric. V = vacuum (1.5-7.2 x torr). Tests r u n on the Hohman dual rub-shoe machine with blocks of nickel-base alloy, 539 N load, 110 cm/s. ( a ) Load, 532 N. Data by McConnel, Wieser and Mecklenburg 11251.

598

In certain cases inorganic binders are disadvantageous for various reasons--e.g. brittleness and high wear rates at lower temperatures or poor adhesion K O the substrate because of mismatch in thermal expansion-and therefore considerable attention has been given to the development and use of organic polymeric resins and binders for films of solid lubricants. The structures of these resins are not known precisely, and furthermore they are usually identified only in general terms such as phenolic resin, epoxy resin, etc. i n published investigations of bondedfilm solid lubricants. The literature of the subject is highly empirical and not systematized, and the interested reader is faced with a mass of papers and reports of developmental work and field tests.

4

! i

:105

* c 3

G

n

104

300 400

500

600 700

Temperature, deg. K

Figure 1 9 - 2 2 . Effect of temperature on the durability of bonded solid lubricant films. Data by Campbell and Hopkins [lo61 with the Hohman tester at 73.15 cm/s, 2158 N load. The curves are identified in the text.

An outstanding exception to this state of affairs is the study of aromatic polyimides as binders, althouqh for the most part they are identified only by the manufacturer's code designation. Mention has already Seen made of the thermal stability and the good mechanical strength of polyimides. Figure 19-22 shows the results of Campbell and Hopkins [ I 0 6 1 with the Hohman dual-block-on-ring tester of the durability of an optimized formulation of MoS2 + Sb203 and polyimide compared with other bonded solid lubricant films. The film m o s t durable in the temperature range 338-533 K (150-500 F ) contains MoS2, SbZ03 and polyimide in 1:l:l ratio (I). The other compositions are 3-MoS2:1-Sb203:1.07-polyimide

599

(II), 10-MoS2:l-graphite:5-Au:7-sodium silicate (III), and 10-MoS2:1At temperatures above 533 K , composition graphite:14-Bi:10-AlP04 (IV). IV has the best durability. Falex tests with 3566 N jaw load at 3.3 cm/s rate durability in the order I-11-111-IV in the temperature range 366-588 K (200-600 F). The durability of composition I at room temperature decreases by a factor of 6.7 for an increase in load from 2185 N to 6473 N, but its durability is approximately three times better than that of the other three formulas.

TABLE 19-20.

DURABILITY OF POLYIMIDE-BONDED FILMS

Lubricant film

PI-bonded (CF1.,) (a) PI-bonded M0S2 (b) Poly imide

Durability, kilocycles of rubbing

298 K

373 K

473 K

2950

2750

1400 8

573 K

673 K

773 K

1800

450

320

20

550

100

30

4

480

925

250

61

5

-

-

-

Sod,ium s i 1icatebonded MoS2/graphite

500

Burnished (CFl.l)n

230

180

00

80

40

60

31

16

8

5

Burnished (MoS?)

-

_.

(C)

16 (C)

(a) 3 parts (CF,.,)n/2 parts polyimide. (b) 3 parts MoS2/1 part polyimide. (c) Failed immediately, p = 0 30. Lubricant film on 440C stainless steel disk; uncoated stainless st el rider: films 0.010-0.020 mm thick. Dry air. Load, 9.8 N; speed, 2.6 m/s at i 0 0 0 rpm. Data by R. L. Fusaro tl081.

The behavior of polyimide as a bonding agent has been investigated extensively by R. L. Fusaro. Table 19-20 shows the durability of polyimide-bonded films of (CF,.,),, and MoS2 in comparison with burnished films, MoS2 + graphite bonded with sodium silicate, and unfilled Up to 673 K, the temperature at which polyimide decompolyimide [ 1 0 8 ] . poses, the durability of the bonded film of (CFl,l)n is significantly better than that of the burnished film; the superiority of the bonded Fusaro also exfilm of MoS2 over the burnished film is not as great. amined the effect of thermal soaking of polyimide-bonded films of graphite fluoride on the wear rates of uncoated riders [ l l l ] , as shown in Table 19-21. I t requires thermal soaking at 618 K to seriously affect the wear rate of the rider for rubbing at 298 K; raising the rubbing temperature to 586 K has a similarly serious effect on the wear rate of the rider against the unsoaked film on the disk.

m 0

TABLE 19-21. WEAR RATES OF 440C STAINLESS STEEL RIDERS AGAINST THERMALLY SOAKED POLYIMIDE-BONDED GRAPHITE FLUORIDE FILMS ON 440C STAINLESS STEEL DISKS Soak temperature, deg. K

None

588

618

643

673

Air environment

Moist Dry

Moist Dry

Moist Dry

Moist Dry

Moist Dry

Rider wear rate,

m3/m

Test temperature 298 K Sliding

0-15

(a)

0.47

(a)

- 0.86

-

0.55

(a) 0.62

interval, 15-60

0.047 0.017 0.049 0.014 0.29

0.16 0.29

kilo-

0.034 0.034 0.014 0.031 0.39

60-250

(a)

0.80

-

0.50

-

-

-

cycles Test temperature 588 K 0-63

I

Test temperature 628 K

0.33

~

-

0.33

~

-

0.38

- -

__

-

-

-

(b)

- __

__

__

__

(a) Transfer only, no wear. (b) Film failed after 30 kilocycles, wear rate 0.39 x 3 m /m. Soak time 100 hours. Moist air: 10,000 ppm H20. Dry air: <20 ppm H20. Load, 9.8 N; speed, 2.6 m / s . Data by R. L. Fusaro [1111.

601

500 urn

POLYIMIDE-BONDED GRAPHITE FLUORIDE FILM

wSANDBLASTED

HEMISPHERE

Figure 19-23. polyimide-bonded kc, (c) 5 0 0 kc, kc. After R. L.

METALLIC

1’

(e)

SUBSTRATE

0.95rnrn DIAMETER FLAT

Cross-sectional diagram of tracks worn in films of graphite fluoride. Amount of rubbing: (a) 1 kc, (b) 5 (d) 4 4 0 0 kc, (el 1 kc, (f) 5 0 0 kc, (g) 3 5 0 0 kc, (h) 8 5 0 0 Fusaro [ 1 1 8 ] .

The work of R. L. Fusaro with a pin and disk apparatus [ 1 1 8 , 1 2 6 1 is especially relevant to the extension of results obtained with bench testers to practical use, particularly as regards the phenomenological significance of the criteria in such tests. Figure 1 9 - 2 3 shows the cross-sectional profiles worn in films of polyimide-bonded graphite fluoride by two differently shaped sliders: one with a hemispherically ended tip 4 . 7 6 mm in radius, the other with a flat 0 . 9 5 mm in diameter on the hemisphere. The computed Hertzian pressures of the rider against the substrate which carries the film are c a . 6 7 0 MPa and 1 4 MPa respectively for an applied load of 9.8 N. It can reasonably be assumed that the substrate was elastically deformed at the higher pressure and that the bonded film was also deformed, conformally; but the surface profile after 1 0 0 0 reiterations of sliding showed no discernible wear or disruption. However, after 5 0 0 0 cycles of sliding the film was worn through to the substrate surface. When the test started with an initial contact pressure of 14 MPa, it took 3 5 0 0 kilocycles of rubbing to reach the substrate surface. From one point of view, this can be taken to be the durability of the film; Table 19-22 indicates that so long as there is a bonded film of graphite fluoride between the rider and the substrate, wear of the rider is nil. When the film has been worn down to the substrate, rider

602

TABLE 19-22. EFFECT OF BONDED GRAPHITE FLUORIDE FILM THICKNESS ON THE WEAR OF HZMISPHERICALLY TIPPED RIDERS

Sliding interval, kilocycles

Rider wear rate, 10

0-1 1-5 5-15 15-60 60-120 120-250 250-500 500-900 900-1800 1800-2800 2800-3800 3800-5000 5000-6000 6000-6250

None 0.60 1.19 0.13 0.12 0.14 0.51 0.75 2.7

(a)

m3/m

18 pm

45 pm

62 um

None None None 0.083 0.15 0.043 0.034 0.19

None None None 0.069 0.056 0.023 0.025 0.047 0.15

None

2.0

0.33 0.64 0.88

1 .o

(b)

(C)

None None 0.062 0.039 0.008 0.018 0.030 0.062 0.14 0.24 0.49 0.174 1.3

(a) Failure at 980 kilocycles. (b) Failure at 1845 kilocycles. (c) Failure at 4400 kilocycles, Bonded film on 440C stainless steel disk, no film on 440C stainless steel rider. Load, 9.8 N; speed, 2.6 cm/s on 2.5 cm track at 1000 rpm. Moist air (10,000 ppm H20). Temperature 298 K. Data by R. L. Fusaro [1181. wear becomes apparent, but the fact that it takes longer for the failure criterion of il. = 0.3 to appear when the original bonded film is thicker shows that the graphite fluoride continues to play a role in the lubrication process after the macroscopic film has been disrupted. Wear of the bonded film, as distinct from the wear of the rider, is a complex process. Figure 19-24 shows the results obtained by Fusaro 11261 with a pin and disk apparatus for the effect of contact pressure on the wear of bonded graphite fluoride films under 9.8 N load, the pressure being controlled by the area of a pre-worn contact flat on the rider. A bimodal expression was fitted to the primary data: (19-2)

where W is the wear of the film in m 3 , p is the contact pressure in MPa, A is the area of the flat on the pin in c m 2 and b is the sliding distance in meters. The mechanism assigned to the linear term is spalling of a very thin layer (*< 0.001 mm) at the surface of the film; the exponential term is associated with defects propagating in the bulk of the film and causing detachment of large wear particles (up to 0.006 mm thick). The work of Fusaro [108, 1 1 1 , 118, 1261, demonstrates that there is a distinction between the macroscopic durability of bonded multicomponent films, as shown by profilometric measurements for instance, and the dura-

603

'I 10

30 50 70 Contact Pressure, MPo

Figure 19-24. Wear of bonded graphite fluoride f i lms. Load: 9.0 N. Area of rider in cm 2 : 1, 0.0025; 2, 0.0071; 3, 0 . 0 1 4 5 ; 4, 0.0240. Wear 1 I O - ~ A ~ - ~ / rate algorithms: I, w1lh = 1.2 p; 1 1 , w2i6 ~ ( 1 . 3 ) ~ .Data by R

L. Fusaro 11261.

tion of the lubricating action as assessed by a frictional failure criterion. R. H. McDaniel's examination of the terminal condition of the rub blocks from his work with the Hohman tester [124] showed large variations in the size of the wear scars, depending on the test temperature, and yet the failure criterion was the same in all cases: u = 0.4. From the practical point of view, it is the ultimate lubricating performance of the film that counts, no matter by what process it is achieved; but as guidance in developmental work one should keep the complexities of bonded film behavior in mind, particularly when examining mechanisms of film wear and durability based on elastic deformation analysis of a bilayer surface region. Lubricating films can be generated on substrate surfaces by chemical processes such as phosphatizing or sulfidizing, but these films are not tightly bound and have little durability: their principal function i s to act as a sacrificial break-in adjuvant for oil lubrication, and hence they do not fall within our purview of solid lubrication. A notable exception is the process patented by Brophy and Ingraham [127] in which a film deposited electrolytically on 2 metal substrate from a molybdate bath is reacted with hydrogen sulfide. The electrodepositied film is not

604

metallic molybdenum [128], nor is the chemically reacted film MoS2. Xray diffraction of the freshly converted film 1128, 129, 1301 does not give any lines for MoS2, but Nishimura e t aL. 11301 cite a Mo:S ratio of 1:3 by electron probe microanalysis as evidence for MoS3. All investigators [128, 129, 1301 found X-ray diffraction lines corresponding to the interlamellar spacing of MoS2 after the film had been rubbed at least 10,000 times or heat treated in vacuo at 673 K. Nishimura e t aL. El301 observed durability up to 1.8 megacycles for films 0.004 mm thick generated on the disk of a pin-on-disk apparatus; films applied by burnishing were only 5% as durable. Di Sapio and Maloney 11281 reported that the i n n i t u generated film had twice the durability of a resinbonded film of MoS2 in a ring-on-block test. Tightly bound thin films of MoS2 can be deposited on a substrate by sputtering (cathodic bombardment) as described by T. Spalvins [131]: a gaseous plasma composed of energetic positive argon ions propels MoS2 from a target to a specimen surface at a temperature below the decomposition limit, so that the film formed on the specimen is substantially MoS2. Sputtered under the proper conditions, the films are composed of crystalline MoS2 [132, 1331. Coefficients of friction for the sputtered films of MoS2 are those characteristic of burnished films: lik, = 0.020.08 in dry air o r i n vacuo [ 130, 131, 1341. Spalvins [134] reported a durability of 580,000 cycles in vacuum (lo-’ torr) at room temperature for sputtered films 0.0002 mm thick on disks of 440 C stainless steel rubbed by a 440 C stainless steel rider at 16 cm/s under a loading pressure of 433 MPa (62,000 psi); at 675 MPa (98,000 psi) and 2 7 cm/s the durability fell to 38,000 cycles. Nishimura e t aL. 11301 obtained a durability of 376,000 cycles in dry air at room temperature for sputtered films O.OGO56 mm thick on 440 C stainless steel at 751 MPa (109,000 psi) and 1.5 m/s. Christy and Barnett [135] found that sputtered films of MoS2 70 nm thick on the balls, races and retainers of ball bearings intended f o r oscillating slow-speed, small-arc operations in space under a Hertzian stress of 606 MPa more than met the functional requirement of 88,000 cycles with torque not to exceed 0.8493 N-m ( 1 0 in-oz). Solid lubricating substances can be incorporated into composites used for machine components to be subjected to rubbing. Much attention has been given to the utilization of such composites for the retainers of rolling element bearings which must function in the vacuum of space or under severe temperature conditions. Not only are these materials selflubricating but they also act as sources of transfer films of the lubricant component to the balls and races of the bearing. P. H. Bowen [91] cited evidence of transfer of MoS2 and PTFE from a retainer made of bronze-PTFE-MoS2 to the balls and to the rubbing tracks on the races of a bearing which ran with no damage for the duration of a 100-hour test at

605

K in a vacuum of 3.3 x tors, and Hubbell, McConnell and Van Wyk [1361 found similar evidence of transfer from Ta-MoS2 retainers in 150hour bearing tests run at temperatures up to 588 K. Devine and Kroll [ l o 7 1 described experiments in the construction of ball bearings with polyimide-based composite retainers that showed formation of transfer films of the lubricating component. H. E. Sliney [1371 and M. N. Gardos 1 1 3 8 1 both demonstrated that the self-lubricating properties of porous metals impregnated with CaF2-BaF2 eutectic depends on maintaining a film of CaF2-BaF2 at the rubbing interface. 663

The principal wear problem in a rolling element bearing is the rubbing action of the retaining spacer on the rolling elements and on the shoulders of the races. Particular attention is given to the wear behavior of self-lubricating composites intended for such service. The semantic problem of whether it is the properties of a material of construction or the behavior of the lubricating component which is being tested cannot be unequivocally resolved a phiohi; but transfer of the lubricating component to the rubbing countersurface is supported by the bulk of the evidence and is the best explanation for the part that solid lubrication plays in the overall tribological process in these cases. Table 19-23 lists substances which have been studied seriously as The matrix materials concomponents of self-lubricating composites. tribute properties such as mechanical strength, resistance to corrosion, etc. The function of a polymeric plastic such as polytetrafluoroethylene

TABLE 19-23.

SELF-LUBRICATING COMPOSITE COMBINATIONS

Matrix substances

Lubricating components

Organic polymeric plastics:

MoS2, WS2, WSe2, graphite

Polyimides, epoxy resins, nylon, polytetrafluorethylene Metals and alloys: Ag, Cu, Fe, Ni, Pb, Sn, Ta, Ag-Co,

MoS2, WS2? WSe2, CaF2, CaF2-BaF2,

PbO-Si02, (CFx)n, graphite

Ag-Hg, Cu-Sn, Cu-Co-Ba, Fe-Ta Ga-In, Mo-Ta, Mo-Nb, Ni-Cr, stainless steel Mixed components: Ag-PTFE, Ag-Hg-PTFE, CU-PTFE, Aq-polyimide

MoS2, MoSe2, MoTe2, WS2, WSe2 NbSe2

606

in a mixed-component matrix may be two-fold: it can contribute to the lubricating action as well as to the mechanical properties of the composite, but it does not carry the major burden of the lubricating process. Boes and Bowen [139] found that adding MoSe2 to a CU-PTFE combination drastically lowered its wear rate against a polished stainless steel disk at high contact pressures and that a substantial ratio of MoSe2 to PTFE in a ternary Cu-PTFE-MoSe2 composite was required for maximum effectiveness at these pressures. The coefficient of friction measured by Devine and Kroll [lo71 for polished mild steel against polyimide at 424 cm/s and 207 kPa was low (uk = 0.08-0.15) and against a polyimide-graphite composite it was even'lower (uk = 0.05-0.08). They found that the performance life of 20-mm ball bearings with polyimide-graphite composite retainers run in air at 10,000 rpm and 505 K was extended by a factor of 3.07 over that for bearings with plain polyimide retainers. The service life of the composite retainers was lowered 51% when the temperature was increased to 5 8 9 K; at 644 K the service life of the bearings was lowered to 19%. MoS2 and WS2 were less effective than graphite at 589 K. or The incorporation of solid lubricants, particularly MoS2 graphite, in oils and greases for industrial use is an established practice founded on experience; however, hard comparative data in the open literature are sparse. Much of it is like the description by G. H. Kitchen f1401 of a well-simulated service test of small-motor bearings; he reported that a high concentration (not specified) of molybdenum disulfide powder in a mineral oil-lithium soap grease could increase service life from 2 0 , 0 0 0 hours to 100,000 hours. Unfavorable effects of MoS2 added to oils and greases have been reported also: e . 5 . J. P. Giltrow [1411 found that bearing tests and chain/sprocket tests with MoS2 dispersed in oil showed about 10 times the wear observed with uncompouned base oil. But the preponderance of the evidence from laboratory and bench testing indicates that solid lubricant adjuvants can impart additional antiwear and antifriction action to the carrier lubricant. Bartz and Oppelt 11421 found that 1 % of MoS2 dispersed in mineral oil of 42.9 c s at 37.8 C lowered the wear rate of the steel ball in a ball-oncylinder apparatus by as much as 56%; 3% MoS2, while proportionately no: as effective in lowering the wear rate, doubled the limiting antiseizure load. Significant improvements of the antiseizure behavior in the fourball test were also seen upon adding 1% MoS2 to the base oil. J. GBnsheimer [41] observed that addition of 1.25% of MoS2 to white oil raised the antiweld load in the Almen-Wieland test from 200 kg to the limit of 2000' kg and that 5% MoS2 reduced the wear in the Reichert block-on-ring test by a factor of 5. W. J. Bartz 11431 showed by means of the FZG gear tester that 1% suspensions of MoS2 in gear oil reduced the wear rate and raised the scuffing load.

607

The mechanism of the lubricating action of solid adjuvants to oils or greases is attributed, sometimes explicitly and sometimes by implication, to deposition of a film of the solid on the rubbing surface. Extension of what is known about the behavior of pre-applied solid films to solid lubricants suspended in a fluid carrier is basically reasonable but not necessarily straightforward. Cusano and Sliney 1 1 4 4 , 1451, using the optical technique for the study of dry films described in Section 19.2.1 [161, found that films did not form as easily from suspensions of graphite or MoS2 in oil on polished surfaces under pure sliding conditions at high contact pressures (400-630 MPa) a s they did with dry powders sprinkled on the surfaces. Part of the difficulty is ascribed to the pile-up of solid particles at the inlet of the elastohydrodynamic flow region, thereby blocking their transport into the rubbing zone where they could be compacted into a film by the loading pressure. I t is hypothesized that rough surfaces are better than smooth surfaces for the formation of adhered films because they furnish pockets and grooves that trap particles and thus act as reserviors. Ultimately the usefulness of solid lubricants is a matter of how they behave in service, and here the lubrication engineer becomes involved with fitting all that is known about various solid lubricants to the particular demands of the problem at hand. For example, Wisander and Johnson [1461 describe the development of a bonded solid film that would permit the operation of bearings and seals at high sliding velocities (up to 81.23 m/s) in liquid nitrogen (77.4 K). Commercial resin-bonded and fused PTFE films spalled from the substrate at this low temperature. Two alternative solutions to the problem were found: a mixture of PTFE, epoxy resin and lithium aluminum silicate which had a suitable coefficient of expansion and the required coefficient of friction and which exhibited the necessary durability; and a coating of fused PTFE which had to be built up layer by layer to the thickness which gave the required wear J. Przybyszewski [1471 discussed the durability without spalling. problem associated with the lubrication of sliding and rolling element electrical contacts, where minimization of both wear and electrical noise is required. Self-lubricating composites are used for sliding brush materials: e . 5. Ag-MoS2, Ag-Cu-MoS2, Ag-NbSe2. Thin films of soft metals are used in rolling element electrical contacts: e . 5. silver in rotating anode X-ray tubes [148]. Lewis, Murray, Peterson and Esten [149] used a modified rotating anode X-ray tube as a device to test the tribological durability of films on thrust-loaded bearings operating at 3000 rpm in a vacuum of lo-’ torr and obtained the best results with films of bismuth and with fused coatings of PTFE. Harris, Read, Thompson and Wilson [lSO], who used a similar technique to investigate a variety of solid-lubricated rolling element bearings, reported that the optimum results were 8000-15,000 hours of continuous running with films

608

of lead as the lubricant. Much attention has been given to the testing of solid lubricants under simulated space service conditions, which includes the manner in which the contacting parts rub against one another as well as the presence of high vacuum. The most demanding service is not necessarily high speed continual rotation. Table 19-24 shows the simulated service conditions investigated by Vest and Ward [151]. Bearings lubricated by PTFE-MoS2 retainers were in good condition after 10,000 hours of oscillatory testing. Continuous full circular motion at 100 rpm was more severe; an increase in rubbing torque was observed but the bearings were still in serviceable condition after 12,600 hours. Burnished MoS2 or plated gold were effective in controlling wear and electrical noise in Murray, Lewis and the brush-commutator contacts of the tachometer.

TABLE 19-24.

SERVICE TESTING FOR SPACE APPLICATION

Oscillatory bearing test Service use: in the support of scanning mirror Motion: oscillatory, 50'

at 0.333 rpm followed by 50'

return at 10 rpm

Radial load: 32.4 N Vacuum:

torr

Expected service life: 18 months Oscillatory tachometer test Service use: in the brush commutator contact and the support bearings

of the tachometer of a star tracker operating in an oscillatory mode Motion: through an arc of +80° at 0.25'/s, mode of 20 cycles/s through

f7O

Vacuum: 4 x 10-7-3.5

torr

x

Expected service life: more than

0.5'/s

or 4'/s

and a dither

year

Slaw speed bearing test Service use: in the drive unit of an observation package in the orbiting 'geophysical laboratory Motion: constant rotatory at 100 rpm Vacuum: 1 0 - ~ - 1 0 - ~ torr From data by Vest and Ward [151].

609

Babecki [1521 tested ball bearings at 30 rpm in a vacuum of 10-7-iO-8 torr and found that a bonded MoS2-graphite-sodium silicate film on all components was more durable than burnished MoS2 or evaporated metal films aided by MoS2 on the balls. The durability goal was 1000 hours of operation; failure was assessed by a two-fold rise in torque, which was traced to the accumulation of wear debris and jamming of the clearances. Operating life of bonded and burnished films was prolonged by a preliminary run-in followed by removal of the resulting debris by hand-applied suction. The silicate-bonded MoS2-graphite film was also the most durable in oscillatory tests at 2 and at 14.3 cycles/s through an arc of .'1 An example of high-speed rotation i n vacua is the work of Brown, Burton and Ku 11531, who carried out simulation tests of ball bearings rotating at 1800 rpm. The best result, 900 x 106 cycles of low-torque operation (420 days), was with a self-lubricating epoxy-MoS2 retainer; silicate-bonded cycles.

film

of MoS2 on retainer and races lasted only 36 x

a

lo6

McKannan and Demorest [154] described the solid film lubrication of a crossed-journal gimbal bearing used in the upper-stage propulsion system of a space satellite. The bearing carried a load of 10.825 MPa (15,700 psi) and was required to respond at a rate of 7.5'/s over an arc Two lubricants, one a film of 10-MoS2/5-Au/l-graphite bonded of +a". with sodium silicate and the other MoS2 burnished on a flame-sprayed coating of zirconium silicate, were found suitable for this service. Another solid lubrication problem connected with space vehicles involves the clamps on the hold-down arms of test towers and launching pads of space rockets. These must adjust to movement under a pressure of 1034 MPa (150,000 psi). Demorest and Whitaker [1551 evaluated solid lubricants by the magnitude of the coefficient of friction as a function of loading pressure during reciprocating motion at 0.028 cm/s. The best results were obtained with two bonded-film formulations: one consisting of MoS2/graphit.e and a zinc-based binder, the other of MoS2/graphite/ A1P04. The best of the resin-bonded films, MoS2 in a phenolic resin binder, was somewhat poorer in performance. L. C. Lipp e t a L . [156, 1571 reported on the role of solids in the lubrication of the supersonic transport airplane which is designed to cruise at Mach 2.7 at an altitude of 22.25 km, corresponding to an atmospheric pressure of 28.8 torr. Temperatures can range from 227 to 600 K (-50 to 620 F ) and contact pressure can be as high as 1379 MPa (200,000 psi). Areas where solid lubricant materials are needed include access doors, variable-geometry nose sections, bearing housings, faying wing pivot surfaces, wing control surfaces such as flaps, slats, spoilers, elevons and ailerons. Desired service life is 5000 flight hours. In one application, insertion of a rub strip made of a MoS2-Ta compact between

610

two titanium surfaces protected them from galling at 533 K for the required time. The effectiveness of bonded films depended on the contact pressure: at 1379 Pa (200 psi) and 505 K (450 F), a film of MoS2 bonded by polyimide resin was found to have twice the wear life of a ceramicbonded MoS2-Ag-graphite film, whereas at 68.95 kPa (10,000 psi) the wear life of the polyimide film was only 43% that of the ceramic-bonded lubricant. Molybdenum disulfide in a Nb-Mo matrix was found to be a useful self-lubricating compact for the liner of a sleeve bearing intended for reciprocating operation at 138 kPa (20,000 psi). The foregoing discussions have emphasized the utility of 501id lubricants in space and at high altitudes, where specialized requirements exclude the use of oils and greases. But it should be borne in mind that solid lubricants are used in many familiar industrial applications where experience has shown them to be advantageous in direct competition with oils and greases or as adjuvants to improve their performance. The experience is highly empirical and the details are for the most part not publicized in the open literature. However, the basic information which has been developed about the behavior of lubricating solids in response to various tribological parameters such as temperature, ambient atmosphere, rubbing speed, contact pressure, nature of the substrate surface, etc. can be used by the lubrication engineer to guide him in solving problems which occur in the more familiar circumstances of ordinary industrial practice, just a they can be used in the specialized problems of aviation and space. REFERENCES W. E. Campbell, in Boundary Lubrication, F. F. Ling, E. E. Klaus and R. S. Fein (Editors), American Society Of Mechanical Engineers, New York, 1969, Chapter 10, Solid Lubricants. 2. G. Salomon, TNO-Nieuws, 21, (1966) 39-48. 3. J. W. Midgley and H. Wilman, Proceedings of the General Discussion on Lubrication, Institution of Mechanical'Engineers, London, 1957, pp. 230-236. 4. A. J. Haltner, ASLE Trans., 8 (1966), 136-148. 5. T. J. Risdon, T. A. Maurer and H. F. Barry, Lubrication En ., 28 (1972) 168-172. 6. S. ROSS and A, Sussman. J. Phys. Chem., 5 9 (1955 , 889-892. 7. R. R. M. Johnston and A. J. W: Moore, i. Phys. Chem., 68 ( 964), 3339-3406. 8. R. Holinski, Proceedings of the International Conference on Solid Lubrication, American Society of Lubrication Engineers, 1971, pp. 41-58. 9. R. Holinski, and J . Gsnsheimer, Wear, 19 (1972), 329-342. 10. I-M.'Feng, .Lubrication Eng., 8 (1952) 285-288, 3 6-308. 1 1 . R. F. Deacon and J. F. Goodman, Proc. R o y . SOC. London, A243 (1958) 464-482. 12. R. R. M. Johnston and A. J. W. Moore, Wear, 7 (1964) 498-512. 13. J. Gznsheimer, Schmiertechnik, 1 1 (1964) 271-280. 14. J . Ggnsheimer and R. Holinski, Wear, 19 (1972) 439-449. 15. A. I. Brudnyi and A. F. Karmadonov, Wear, 33 (1975) 243-249. 16. H. E. Sliney, ASLE Trans., 21 (1978) 109-117. 17. Y. Tsuya, ASLE Trans., 15 (1972) 225-232. 1.

611

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.

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612

65. W. Riidorff and G. Rcdorff, 2 . anorg. Chem., 253 (1947) 281-296. 66. R. J. Lagow, R. B. Badachhape, J. L. Wood and J. L. Margrave, J. Chem. SOC. Dalton Trans.,(1974) 1268-1273. 67. D. E. Palin and K. D. Wadsworth, Nature, 162 (1948) 925-926. 68. w. RGdorff, Advances in Inorg. Chem. and Radiochem., 1 (1959) 223266. 69. L. B. Ebert, J. I. Brauman and R. A. Huggins, J. Am. Chem. SOC., 96 (1974) 7841-7842. 70. A. K. Kuriakose and J. L. Margrave, J. Phys. Chem., 69 (1965) 27722775. 71. A. K. Kuriakose and J. L. Margrave, Inorganic Chem., 4 (1965) 16391641. 72. H. Gisser, M. Petronio and A. Shapiro, Lubrication Eng., 28 (1972) 161-164. 73. R. L. Fusaro and H. E. Sliney, ASLE Trans., 13 (1970) 56-65. 74. R. L. Fusaro, ASLE Trans., 20 (1977) 15-24. 75. K. R. Mecklenburg, ASLE Trans., 17 (1974) 149-157. 76. R. L. Fusaro, Wear, 53 (1979) 303-323. 77. I. B, Atkinson, R. M. Waghorne and P. Swift, Wear, 37 (1976) 123128. 78. R. S. Pease, Acta Crystallogr., 5 (1952) 356-361. 79. K. Niedenzu and J. W. Dawson, in The Chemistry of Boron and Its Compounds, E. L. Muetterties (Editor), John Wiley and Sons, New York, London, Sydney, 1976, pp. 424-427. 80. A. H. Silver and P. J. Bray, J. Chem. Phys., 32 (1960) 288-292. 81. T. E. O'Connor, J. Am. Chem. SOC, 84 (1962) 1753-1754. 82. D. H. Buckley, ASLE Trans., 21 (1978) 118-124. 83. E. Rabinowicz and M. Imai, Wear, 7 (1964) 298-300. 84. M. T. Lavik, G. E. Gross and G. W. Vaughn, Lubrication Eng., 15 (1959) 246-249, 264. Phys., 32 85. M. T. Lavik, T. B. Daniel and A. N. Abbott, J. Appl. __ (1961) 1795. 86. G. Spengler and W. Fischer, Schmiertechnik u. Tribologie, 18 ( 971) 76-80. 87. M. B. Peterson and R. L. Johnson, Lubrication Eng., 1 1 (1955) 325330. 88. W. E. Jamison and S . L. Cosgrove, ASLE Trans., 14 (1971) 62-72. 89. P. M. Magie, Lubrication Eng., 22 (1966) 262-268. 90. D. J. Baldwin and G. W. Rowe, J. Basic Eng. (Trans ASME), 83D ( 961) 133-138. 91. P. H. Bowen, ASLE Trans., 5 (1962) 315-326. 92. M. B. Peterson, S. F. Murray and J. J. Florek, ASLE Trans., 2 (1959) 225-234. 93. S. L. Cosgrove, L. B. Sibley and C. M. Allen, ASLE Trans., 2 (1959) 2 17-224. 94. F. K. Orcutt, H. H. Krause and C. M. Allen, Wear, 5 (1962) 345-362. 95. H. E. Sliney, T. N. Strom and G. P. Allen, ASLE Trans., 8 (1965) 307-322. 96. B. Blampin, Wear, 1 1 (1968) 431-459. 97. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1950, Part I, Chapter V, pp.lll-121. 98. R. A. Burton and J. A. Russell, Lubrication Eng., 21 (1965) 227-233. 99. Y. Tsuva and R. Takaai. Wear, 7 (1964) 131-143. 100. J. W.-Menter, Proc.-Roy. S o c . London, A236 (1956) 119-135. 101. H. H. Krause, S. L. Cosgrove and C. M. Allen, J. Chem. Eng. Data, 6 (1961) 112-118. 102. G. Salomon, A. Begelinger and A. J. W. de Gee, Wear, 10 (1967) 382396. 103. P. A. Grattan and J. K. Lancaster, Wear, 10 (1967) 453-468. 104. E. Kay and E. D. Tingle, Brit. J. Appl. Phys., 9 (1958) 17-25. 105. C. J. Speerschneider and C. H. Li, Wear, 5 (1962) 392-399. 106. M. E. Campbell and V. Hopkins, Lubrication Eng., 23 (1967) 288-294. 107. M. J. Devine and A. E. Kroll, Lubrication Eng., 20 (1964) 225-230. 108. R. L. Fusaro and H. E. Sliney, ASLE Trans., 16 (1973) 189-196. 109. R. L. Fusaro, ASLE Trans., 20 (1977) 1-14.

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110. 111. 112.

R. L. Fusaro, ASLE Trans., 21 (1978) 125-133. R. L. Fusaro, Lubrication Eng., 36 (1980) 143-153. C Bowers, W. C. Clinton and W. A. Zisman, Lubrication Eng., 9 1953 204-208, 218-219. K. R. Makinson and D. Tabor, Proc. Roy. SOC. London, A281 (1964) 49-6 1 C. M. Pooley and D. Tabor, Proc. Roy. SOC. London, A329 (1972) 251274. K. C Ludema, discussion of paper by R. L. Fusaro, Reference [log]. S. H. Rhee and K. C Ludema, in The Wear of Non-Metallic Materials: Proceedings of the 3rd Leeds-Lyon Symposium on Tribology, D. Dowson, M. Godet and C. M. Taylor (Editors), Department of Mechanical Engineering, University of Leeds, September, 1976, pp. 11-17. S . H. Rhee and K. C Ludema, Wear, 46 (1977) 231-240. R. L. Fusaro, ASLE Trans.,'24 (1981) 191-204. R. J. Benzing, V. Hopkins and M. Petronio, Lubrication Eng r 28 (1972) 153-160. R. L, Johnson and H. E. Sliney, Lubrication Eng., 15 (1959 489491, 496. H. E. Sliney, ASLE Trans., 15 (1972) 177-183. I. Amato and P. Martinengo, ASLE Trans., 16 (1973) 42-49. B. C. Stupp and J. W. Wriqht, Lubrication Enq., 19 (1963) 463 469. R. H. McDaniel, Lubrication Eng., 21 (1965) 463-473. 3. D. McConnell, L. E. Wieser and K. R. Mecklenburg, Lubrication Eng., 24 (1968) 81-91. R. L. Fusaro, International Conference on Wear of Materials, San Francisco, Mar. 30-Apr. 2, 1981, American Society of Mechanical Engineers, New York, pp. 625-636. J. E. Brophy and R. W. Ingraham, U. S . Pat. 2,902,417, Sept. 1 , 1959. A. Di Sapio and J. Maloney, ASLE Trans., 1 1 (1968) 56-63. W. 0. Winer, Wear, 10 (1967) 447-448, citing a private communication from A. Kroll of the Dow Corning COrp. M. Nishimura, M, Nosaka, Y. Miyakawa and J. Sakomoto, J. Japan SOC. Lubr. Enqrs., International Ed., Issue No. 1 , November 1980, 119-126. T. Spalvins, ASLE Trans., 12 (1969) 36-43. M. T. Lavik and M. E. Campbell, ASLE Trans., 15 (1972) 233-234. T. Spalvins, ASLE Trans., 17 (1974) 1-7. T. Spalvins, ASLE Trans., 14 (1971) 267-274. R. I. Christy and G. C. Barnett, Lubrication Eng., 34 (1978) 43 443. R. D. Hubbell, B. D. McConnell and J. W. Van Wyk, Lubrication Eng 25 (1969) 31-39, H. E. Sliney, ASLE Trans., 9 (1966) 336-347. M. N. Gardos, ASLE Trans., 18 (1975) 175-186. D. J. Boes and P. H. Bowen, ASLE Trans., 6 (1963) 192-200. G. H. Kitchen, Lubrication Eng., 20 (1964) 311-315. J. P. Giltrow, Tribology International, 7 (1974) 161-168. W. J. Bartz and J. Oppelt, Lubrication Eng., 36 (1980) 579-585. W. J. Bartz, ASLE Trans., 15 (1972) 207-215. C. Cusano and H. E. Sliney, ASLE Trans., 25 (1982) 183-189. C. Cusano and H. E. Slinev, ASLE Trans., 25 (1982) 190-199. D. W. Wisander and R. L. johnson, ASLE Trans., 3 (1960) 225-231. J. Przybyszewski, Lubrication Eng., 24 (1968) 454-463. G. R. Kessler and G. R. Mahn, Lubrication Eng., 23 (1967) 372-379. P. Lewis, S. F. Murray, M. B. Peterson and H. Esten, ASLE Trans., 6 (1963) 67-79. C. L. Harris, J. E. Read, J. B. Thompson and C. I. Wilson, Lubrication Eng., 24 (1968) 131-138. C . E . Vest and B. W. Ward, Lubrication Eng., 24 (1968) 163-172. S. F. Murray, P. Lewis and A. J. Babecki, ASLE Trans., 9 (1966) 348-360. R. D. Brown, R. A. Burton and P. M. Ku, ASLE Trans., 7 (1964) 236248. R. (

113. 114. 115. 116.

117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135.

136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 49. 50. 51. 52. 53.

614 154.

E. C. McKannan and K. E. Demorest, Lubrication Eng., 20 ( 1 9 6 4 ) 134-

155. 156. 157.

K. E. Demorest and A. F. Whitaker, ASLE Trans., 9 ( 1 9 6 6 ) 160-170. L. C. Lipp, Lubrication Eng., 24 ( 1 9 6 8 ) 154-162. L. C. Lipp, J. W. Van Wyk and F. J. Williams, Lubrication Eng., 29

141.

( 1 9 7 3 ) 108-115.

615

AUTHOR INDEX

For each author this index shows the chapter in which the reference occurs, its number in the reference list, and the pages on which the reference is cited. For example, Baum, G.:

1 7 ( 4 ) , 506, 512

The reference is the fourth item in the reference list of Chapter 17 is cited on pages 5 0 6 and 5 1 2 .

and

Adam, N. K.: 1 0 ( 6 ) , 2 0 3 Adamson, A. W.: 1 0 ( 4 ) , 2 0 3 ; 1 0 ( 3 4 ) , 229

Akaoka, J.: 1 9 ( 3 9 ) , 5 6 0 , 5 6 3 Allen, C . M.: 6 ( 2 1 ) , 1 2 5 Allum, K. G . : 1 1 ( 3 0 ) , 1 1 ( 3 1 ) , 2 7 1 ; 1 1 ( 5 8 ) , 2 9 2 ; see also E. S. Forbes Amato, I.: 1 9 ( 1 2 2 ) , 5 9 6 American Society for Testing and Materials: see ASTM American Society of Lubrication Engineers: 7 ( 2 ) , 140 Andr;, M. L.: 1 6 ( 1 1 ) , 4 8 8 Andreatch, P.: 1 2 ( 2 3 ) , 3 4 2 Anderson, L. 0.: 1 2 ( 2 1 ) , 3 4 0 ; 1 2 ( 2 2 ) , 3 4 2 , 3 4 5 ; see also P. Andrea tch Andrews, G. I.: 1 9 ( 1 8 ) , 5 5 4 Archard, G . D . : 3 ( 1 9 ) , 4 9 Archard, J . F . : 3 ( 2 0 ) , 5 1 ; 6 ( 6 ) , 115, 1 1 7 ; 1 2 ( 4 ) , 3 1 6 ; 1 2 ( 5 ) , 3 1 7 , 336: 1 3 ( 7 ) . 356. 370. 377. 392:

Barcroft, F. T.: 1 0 ( 6 5 ) , 2 4 6 ; 1 1 ( 2 9 ) , 268

Barlow, A. J.: 4 ( 4 3 ) , 9 8 Barry, H . F.: 1 9 ( 4 0 ) , 5 6 0 ; see also T. J. Risdon Bartell, L. S.: 1 0 ( 1 9 ) , 2 1 3 aartz, W. J.: 1 9 ( 1 4 2 ) , 1 9 ( 1 4 3 ) , 606

Bates, T. R., jr.:

13(48), 13(51),

374

Bathgate, J . : 1 5 ( 3 7 ) , 4 5 6 Bauer, W. H.: 1 8 ( 2 6 ) , 5 3 7 Baum, G . : 1 7 ( 4 ) , 5 0 6 , 5 1 2 Baumgarten, E . : 1 1 ( 5 3 ) , 2 9 0 Bayer, R. G . : 7 ( 5 ) , 141 Beeck, 0.: 1 0 ( 6 8 ) , 2 4 7 Beerbower, A.: 1 3 ( 6 2 ) , 3 9 6 Bell, J . C: 6 ( 1 9 ) . 1 2 2 : see also 457;

1 4 ( 2 0 ) , 422, 425

4 4 5 , 4 5 3 ; see a1so.D. J; Whitehouse Armstronq, C. S.: 1 7 ( 1 4 ) . 5 1 4 Askwith,-T. C.: 6 ( 4 ) , 1 1 3 , 1 2 9 ;

Benzing, R. J.: 1 9 ( 1 1 9 ) , 5 9 5 Bewig, K . W.: 1 0 ( 9 ) , 2 0 5 , 2 0 8 ,

1 0 ( 3 2 ) , 2 2 7 , 230 ASTM: 4 ( 2 1 ) , 4 ( 2 4 ) , 7 9 ; 4 ( 2 6 ) , 8 3 ; 1 6 ( 2 ) , 479; 1 6 ( 1 9 ) , 493; 1 7 ( 5 ) , 5 0 7 ; 1 8 ( 1 8 ) , 532, 535; 1 8 ( 2 4 ) , 535; 1 8 ( 3 0 ) , 538; 1 8 ( 3 8 ) , 544; 1 8 ( 4 2 ) , 545 Atkins, D. C.: 1 7 ( 1 3 ) . 5 1 2 Atkinson, I. B.: 1 9 ( 3 5 ) , 5 5 9 ; 1 9 ( 7 7 ) , 577 Ausherman, V. K.: 1 5 ( 3 3 ) , 4 5 0 Ausman, J. S.: 5 ( 1 ) , 1 0 3

Bitter, J. G. A . : 1 3 ( 1 4 ) , 3 6 2 Bjerk, R. 0.: 4 2 2 (footnote) Blake, E. S.: 1 7 ( 3 ) , 5 0 4 , 5 1 9 Blampin, B.: 1 9 ( 9 6 ) , 5 8 7 Blok, H . : 1 5 ( 4 1 ) , 4 5 8 ; 1 5 ( 4 2 ) ,

Bailey, A. I.: 1 0 ( 3 6 ) , 10 231;12(17),

337

Bailey, M. W.: 9 ( 2 0 ) , 1 9 3 462, 469

213;

1 0 ( 1 4 ) , 207, 215, 216

Bieber, H. E.: 1 1 ( 4 1 ) , 2 7 8 , 2 8 0 Bigelow, W. C.: 1 0 ( 7 ) , 2 0 5 ; 1 0 ( 1 8 ) , 2 0 9 , 212

458, 460

Boelhouwer, C.: 1 6 ( 2 3 ) , 4 9 4 Boes, D. J . : 1 9 ( 1 3 9 ) , 6 0 6 Bondi, A.: 1 8 ( 2 0 ) , 5 3 4 ; see also W. H. Peterson Boner, C. J.: 1 8 ( 5 ) , 5 2 6 Booser, E. R . : 1 8 ( 1 0 ) , 5 2 8 , 5 3 9 ; , see also A. E. Baker

616

Booth, M. J.: 3!10), 41; 4(48), 99 Borg, A . C.: 18(22), 535 Bcrnong, B. J.: 10(16), 209; see a l s o P. Martin, jr. Borsoff, V. N.: lO(59). 244 151; 8(4), E(6), 152; 8 ( 2 2 ) , 175; 8(23), 176; 9 ( 2 ) , 179; 9(5:, 181, 182; 9(8), 184; 9(10), 185; 9(16), 9(17), 189; 10(3), 201; 10(30), 226; 13(10), 361; 15(Y), 441; 15(27), 449; 19(37), 559; 19(97). 588: see also N. Gane Bowen, P. H.: 9(91), 581, 604; see also D. J Boes Boxers, R. C.: lO(45) 234; 17(19), 517; 9(112) 593 Bradbury, D.: (20), 7, 83, 85 Bragg, W. L.: 9(46), 566 Brainard, .'h A : 9(7) 182 Brennan, R. 0. 19(50 , 567 Briscoe, B. J. lO(46 , 235; 13(33). 370 Brockley, C. A.: 8(15), 162, 174; 8(16), 162, 163, 164; 8(20), 169; 13(23), 366; see a l s o P. L. KO Brophy, J. E.: 19(127), 603 Brown, E. D . , jr.: 17(16), 516 Brown, G. P.: 17(10), 511 Brown, R. A . : 8(7), 152 Brown, R. D.: 19(153), 609 Brown, W. L.: 18(15), 530 Brudnyi, A. I.: 19(15), 554 Brunstrum, L. C.: 18(40), 544; see also A. W. Sisko BrGser, P.: 6(5), 115 Bryant, P. J.: 19(41), 232; 19(49), 567 Buckley, D. H.: 7(9), 144; 8(8), 152; 8(il), 157; 9(3), 179; 9(4), 180; 9(6), 182; 9(9), 184; 11(7), 257, 260; 11(8), 257, 258, 260; 11(13), 258, 260, 272; 19(63), 572; 19(82), 578, 579; see also W. A . Brainard Burton, R. A.: 19(98), 588; see also R. D. Brown aurwell, J. T.: 7(10), 144; 13(2), 352, 353, 354, 355, 357 Calhoun, S. F.: 18(9), 528 Cameron, A.: 3(26), 55; 6(13), 117; 15(18), 447; see also T. C. Askwith, M. W. Bailey, P. S. Y. Chu, C. A . Foord, R. Gohar, W. J. S. Grew, I. 0. MacConochie, J. P. O'Donoghue, C. Siripongse, H. A . Spikes, and L. D. Wedeven Campbell, J. S.: 1 1 ( 1 1 ) , 11(12), 258 Campbell, M. E.: 19(106), 590, 598; see a l s o M. T. Lavik Campbell, W. E.: 7(12), 146; 8(18), 167, 168; 10(49), 238; 19(1), 549

Carruthers, W : 16(3), 480 Carslaw, H. S : 15(1), 430, 438 Chao. B. T.: 5(30), 449 Cheng, H. S.: 3(12), 46; 3(13), 50: 3(21), 5 ; 15(21), 449 R. I : 19(135). 604 Christv. z . Chu, P. S. Y.: 6(23), 128 Clark, W. T.: 19(61), 19(62), 570 Coffin, L. F., jr.: 7(7), 142 Cohen, M. H.: 4(30), 8 8 Cornelissen, J.: 16(24), 494 Cosgrove, S. L.: 19(93), 582; see also W. E. Jamison, and H. H. Krause Cottington, R. L.: 9(13), 188; lO(13). 207, 223, 224: see also R. C . Bowers Couette, M.: 4(9), 72 Courtney-Pratt, 2 . S.: 8(10 I 153, 154, 156, 157: see a l s o A . I. Bailey Cox, D. B.: 18(7), 527 Criddle, D. K . : 18(1), 52 Crook, A. W.: 3(23), 54: 6( ) , 1 1 1 : 6(7). 116: 6(8). 116. 117; 6(9j, 116. Cusano, C.: 19(144), 19(145), 607

Cavey, W.: 10(54), 243; 10(63), 245; 11(45), 282; 11(61), 299 da Vinci, L.: 1(1), 2 Dayson, C.: 15(17), 445 Deacon, R. F.: 19(11), 554, 569, 573 Dean, E. W.: 4(25), 82 Demorest, K. E.: 19(155), 609; see also 2 . C. McKannan Besaguiliers, J. T.: 9(1), 179 Devine, M. J.: 19(107), 590, 591, 605, 606 Deyber, P.: 15(31), 449 Dickert, J. J., jr.: 11(52), 288, 289, 293, 295 Di S a p i o , A . : 19(128), 604 Dobry, A.: 10(22), 217 Doolittle, A . K.: 4(31), 4(32), 89 Dorinson, A . : 9(15), 187, 10(74), 251; 11(22), 264; 11(24), 264, 268; 11(38), 276, 296; 11(44), 280; 11(56), 291; 11(63), 301, 303, 304; 12(1), 311, 326; 13(3), 353, 355, 357: 13(4), 354, 393; 73(5), 354; 13(63), 397; 14(6), 410; 14(9), 411, 416, 418; 14(17), 420; 14(21), 425 Dow, R. B.: 4(12), 76 DowSOn, D.: 3(15), 48; 3(16), 3(17), 49; 14(4), 406; see also B. J. Hamrock Doyle, W. P.: 10(11), 206 Duling, I. N.: 17(6), 508, 512 Duwell, E. J.: 13(16), 363 Dyson, A . : 13(61), 396: 18(31), 539

617

E a r l e s , S. W. E . : 1 3 ( 4 0 ) , 1 3 ( 4 2 ) , 1 3 ( 4 3 ) , 3 7 1 ; see a l s o D. G . P o w e l l , a n d N. T e n w i c k E b e r t , L. B . : 1 9 ( 6 9 ) , 5 7 2 , 5 7 3 E i r i c h , F. R . : 4 ( 1 ) , 6 1 ; 4 ( 3 4 ) , 4 ( 3 5 ) , 92 E n g e l , P. A . : 1 3 ( 1 2 ) , 1 3 ( 1 3 ) , 3 6 1 E v a n s , D.: 1 8 ( 1 9 ) , 5 3 3 Ewbank, W. J . : 1 8 ( 1 4 ) , 5 3 0 ; see also W. L. Brown E y r i n g , H: 4 ( 2 8 ) , 87, 90; see a l s o S. J. Hahn, T. S. Ree, a n d H. Utsugi E e i n , R. S.: 4 ( 4 7 ) , 9 9 ; 1 0 ( 5 0 ) , 2 3 8 , 2 3 9 . 240: l O ( 5 1 ) . 239: 1 5 ( 4 4 ) , 460, 462; 1 5 ( 4 9 ) , 462; 1 5 ( 5 0 ) , 1 5 ( 5 1 ) , 464 F e n g , I-M.: 1 1 ( 5 5 ) , 2 9 1 ; 1 9 ( 1 0 ) , 554 F i t z s i m m o n s , V. G . : 1 7 ( 2 2 ) , 5 1 9 Floin, D . G . : 1 9 ( 2 3 ) , 555., 5 7 9 , 5 9 0 F l o w e r s , A . E.: 4 ( 1 6 ) , 76 Foord, C. A . : 6 ( 1 5 ) , 117 F o r b e s , 3 . S.: 1 1 ( 2 6 ) , 2 6 6 , 2 7 2 ; 1 ; ( 3 2 ) , 271: 1 1 ( 4 0 ) , 278, 285; 1 1 ( 4 6 ) , 282, 284; 1 1 ( 6 4 ) , 303, 3 0 4 ; s e e alss K . G . A l l u m F o r s t e r , E. 0.: 1 8 ( 2 9 ) , 537 F r a n c i s , S. A . : 1 1 ( 5 4 ) , 2 9 0 , 291 F r a n k , N . H..: 1 5 ( 2 5 ) , 448 F r a n k l i n , J . L.: 1 1 ( 1 8 ) , 2 6 3 F r e w i n g , J. J : 1 9 ( 3 1 ) , 2 2 6 ; 1 5 ( 5 4 ) , 466 Fukuda. K.: 1 ( l o ) , 258 6 ( 2 2 ) , 126; 1 0 ( 4 7 ) , F u r e y , M. J.: 2 3 6 , 2 4 0 ; 15 1 6 ) , 4 4 5 , 4 4 7 F u s a r o , R. L. 1 9 ( 4 5 ) , 5 6 5 ; 1 9 ( 7 3 ) , 574, 576; 1 9 ( 7 4 ) , 576; 1 3 1 7 6 1 , 577: 1 9 ( 1 0 8 ) , 5 9 1 , 5 9 4 , 5 9 9 , 6 0 2 ; 19 1 0 9 ) . 5 9 1 . 5 9 2 , 5 9 3 : 191I I O ) , 591; 1 9 ( 1 1 ) , ‘ 5 9 1 , . 5 9 2 , 599, 602; 1 9 ( 1 1 8 ) , 594, 601, 602; 1 9 ( 1 2 6 ) , 601, 602 G a i n e r , G . C . : 1 7 ( 1 8 ) , 517 G a i n e s , G . L . : 1 0 ( 3 9 ) , 232 G a l l o p o u l o s , N . : 1 1 ( 4 9 ) , 287 G a m r a t h , H . R . : 1 1 ( 3 9 ) , 277 Gane, N . : 8 ( 1 3 ) , 159; 1 2 ( 2 0 ) , 3 3 8 ; 1 3 ( 2 7 ) , 3 6 7 ; see a l s o J . S k i n n e r G a r d o s , M. N.: 1 9 ( 1 3 8 ) , 6 0 5 G a r n e r , W. E . : 1 0 ( 4 4 ) , 234 G s n s h e i m e r , J . : 1 9 ( 1 3 ) , 554, 560; 1 9 ( 1 4 ) , 554; 1 9 ( 4 1 ) , 560, 606; see a l s o R . H o l i n s k i G a y l o r d , E . W.: 1 5 ( 1 0 ) , 4 4 1 ; see a l s o w. F . H u g h e s , a n d H . H . H . Shu G e m a n t , A . : 7 ( 1 ) , 134 Gilbert, A . W.: 1 8 ( 4 1 ) , 545 G i l t r o w , J . P.: 1 9 ( 1 4 1 ) , 6 0 6 G i r i f a l c o , L . A . : 1 9 ( 5 1 ) , 5 6 7 ; see a l s o R. J. Good Gisser, H.: 19(72!, 574, 576 G l a e s e r , W . J..: 1 3 ( 1 7 ) , 3 6 3

G o d d a r d , J.: 1 3 ( 5 8 ) , 3 8 8 G o d f r e y , D.: 1 0 ( 2 ) , 2 0 0 ; 1 0 ( 5 8 ) , 244; 1 9 ( 6 7 ) , 247; 1 5 ( 3 8 ) , 456; 1 8 ( 3 3 ) , 541 G o h a r , R.: 3 ( 2 8 ) , 5 5 ; 6 ( 1 2 ) , 6 ( 1 4 ) , 1 1 7 ; s e e a l s o A . Cameron G o l d b l a t t , 1 . L.: 1 G ( 5 2 ) , 2 3 9 ; 1 1 ( 4 3 ) , 2 7 9 , 281 Good, R. J.: 1 9 1 5 2 ) , 5 6 7 1 5 ( 7 ! , 441 G o t t w e i n , K.: G r a t t a n , P . A . : 1 9 ( 1 0 3 ) , 590 Green, A . P.: 1 2 ( 2 4 ) , 343; 1 2 ( 2 5 ) , 345; 1 3 ( 2 2 ) , 366 G r e e n h i l l , E. B.: 1 0 ( 5 3 ) , 2 4 2 , 2 4 9 G r e e n w o o d , J. A , : 1 2 ( 7 ) , 3 2 0 , 3 2 4 , 326, 327, 329, 331; 1 2 ( 8 ) , 320, 324, 326; 1 2 ( 1 1 ) , 327; 1 3 ( 5 6 ) , 3 8 3 ; see a l s o J . J. K a u z l a r i c h G r e g o r y , J. N.: 1 0 ( 6 2 ) , 2 4 5 , 2 4 9 G r e w , W. J . S.: 1 0 ( 3 3 ) , 2 2 9 ; 1 5 ( 5 3 ) , 466 G r i e s t , E. M.: 4 ( 1 3 ) , 7 6 , 92 G r o s z e k , A . J . : 1 9 ( 6 0 ) . 5 7 0 ; see a l s o G . I. A n d r e w s G r u b i n , A . N.: 3 ( 1 1 ) , 4 3 H a h n , S . J . : 1 8 ( 2 7 ) , 537 H a l t n e r , A . J.: 1 9 ( 4 ) , 552 5 7 9 , 5 8 0 ; 1 9 ( 2 2 ) , 5 5 5 , 5 5 6 ; 19 3 1 ) , 5 5 7 , 558, 5 5 9 , 5 6 5 ; 1 9 ( 3 6 I 5 5 9 , 5 6 0 ; s e e a l s o D. G . Flom H a m i l t o n , G. M.: 3 ( 1 8 ) , 4 9 54 ; 6 ( 1 1 ) , 1 1 7 ; 1 5 ( 2 2 ) , 448 Hamrock, B . J . : 3 ( 2 2 ) , 51 H a r d y , W. B.: 1 0 ( 1 ) , 200 H a r r i s , C. L . : 1 9 ( 1 5 0 ) , 607 H a t s c h e k , E.: 4 ( 6 ) , 6 6 , 6 7 , 68 H e i g h w a y , R. J.: 1 5 ( 2 & ) , 4 4 9 H e i l w e i l , I . J . : 1 1 ( 5 0 ) , 287 H e r b e r t , E. G.: 15(81, 441 H e r m a n c e , H. W.: 10(48) 238 H e r s e y , M. D.: 4 ( 1 9 ) 7 6 ; 4 ( 2 7 ) , 83 H i r s t , W.: 1 3 ( 6 ) , 3 5 5 : 1 3 ( 3 0 ) , 3 7 0 , 3 7 2 ; see a l s o J . F . A r c h a r d , M. J. B o o t h , and W. T . C l a r k Hogenboom, D. L.: 4 ( 1 5 ) . 7 6 , 8 7 , 8 8 , 8 9 , 91 H o l i n s k i , R.: 1 9 ( R ) , 1 3 ( 9 ) , 553, 5 5 9 ; see a l s o J . G a K s h e i m e r Holm, R.: 1 ( 2 ) , 2; 8 ( 2 ) , 1 4 9 Hoock, W. S . : 1 0 ( 7 1 ) , 248 Hood, A . : 1 6 ( 1 3 ) , 4 8 9 H o p k i n s , V . : 4 ( 3 7 ) , 9 3 ; See a l s o M. E. C a m p b e l l , a n d R . J. B e n z i n g H o r t h , A. C.: 1 8 ( 3 4 ) , 5 4 1 ; 1 8 ( 3 6 ) , 5 4 3 , 544 H o t t e n , B . W.: 1 8 ( 2 ) , 5 2 2 ; 1 8 ( 1 7 ) , 53 1 H o w l e t t , K . E.: 1 1 ( 3 3 ! , 1 1 ( 3 4 ) , 272 H u b b a r d , R . M . : 4 ! 1 7 ) , 4 ( 1 8 ) , 76 H u b b e l , R. D.: 1 9 ( 1 3 6 ) , 6 0 5 H u g h e s , W. F.: 1 5 ( 1 1 ) , 4 4 1 ; see a l s o E. W. G a y l o r d , a n d H. H. H. Shu

618

Ishikawa, J.:. 15(46), 462 Ishlinsky, A . 1.: 12(3), 316 Israelachvili, J. N.: 10(43), 232; 12(19), 338 Jackson, E. G.: 422, (footnote) Jaeger, J. C.: 15(2), 431, 432, 434, 446, 453; see also H. S. Carslaw Jahanmir, S.: 13(50), 374; see also N. P. Suh Jakobsen, J.: 17(8), 511 Jamison, W. E.: 19(26), 555; 19(48), 567; 19(88), 579 Jayne, G. J. J.: 11(56), 292 Johnson, K. L.: 12(6), 319 Johnson, R. L.: 19(120), 595; see also D. H. Buckley, M. B. Peterson, and D. W. Wisander Johnson, V. R.: 19(21), 555, 579 Johnston, R. R. M.: 19(7), 552, 558; 19(12), 554 Karpe, S. A . : 19(38), 560 Kannel, J. W.: 3(24), 54; 6(18), 122; 15(23), 15(24), 448 see also J. C. Bell Kato, S.: 8(21), 171, 175 Kauzlarich, J. J.: 18(25) 537, 540 Kay, E.: 19(104). 590 Kekde, I.: 11(19j, 263 Kerridge, M.: 13(15), 362, 370, 372, 377, 378; 13(29), 368, 370 Kessler, G. R.: 19(148), 607 Kimura, Y.: 12(12), 332 K i n g , J. N.: 19(59), 569 King, R. W.: 16(16), 491, 494; see also S. S. Kurtz, jr. Kitchen, G. H.: 19(140), 606 Kittel, C.: 4(46), 98 Klhus, E. E.: 4(38), 93; 10(66), 247; 17(15), 515; see also H. E. Bieber KC, P. i.: 7(8), 142; 8(17), 162, ! 7 4 , 175; see also C. A . Brockley Kramer, J.: 10(26), 218 Krause, H. H.: 19(101 , 589, 590; see also F. K. Orcut Kubaschewski. 0.: 14( 5), 415 Kuriakose, A ; K.: 19( 0 1 , 573; 19(71), 574 Kurtz, S. S., j r . : 16 181, 493; 16(21), 16(22), 494; see also R. W. King

Lagow, R. J.: 19(66), 572, 573, 574 .~ Lamb, H.: 3(1). 27: 3(4). 33 Lancaster, J. K . : i3(19); 363; 13(31), 13(32), 370; 15(39), 15(40), 458; 19(20), 544, 563; 19(43), 562, 563, 570, 572; 19(44), 562, 572; see also W. T. Clark, P. A . Grattan, W. Hirst, and M. Kerridge

Lander, E. W.: 6(25), 29, 132 Laub, J. H.: 5 3), 105 Lauterbach, W. E.: 10( 21, 10(73), 250 Lavik, M. T.: 9(84), 9(85), 579; 19(132), 604 Lawton, S. L.: 1 1 (481, 287 Leach, E. F.: 15(43), 459, 460 Lee, D.: 3(30), 56 Leet, R. H.: 18(21), 534; See also A . C. Borg Levine, 0 . : 9(12), 188, 10(12), 206, 219; 10(28), 219; 14(7), 14(8), 411 Lewis, P.: 19(149), 607: see also S . F. Murray Lindeman, L. P.: 10(12), 488 Lindsay, R. B.: 4(45), 98 Ling, F. F.: 15(4), 437, 439, 440; 15(5), 440; see also E. W. Gaylord Lipp, L. C.: 19(156), 19(157), 609 Loeser, E. H.: 10(69), 10(70), 247 Loewen, E. G.: 15(13), 442 Lowitz, D. A . : 41141, 76 Lozovoi, Yu. A . : 11(47), 285, 299 Ludema, K. C: 19(115), 593; see also T. R. Bates, jr., and S. H. Rhee Luther, H.: 11(51), 2 8 8 , 289, 290 MacConochie, I . 0.: 6(3), 113 Mackle, H.: 11(20), 263 Magie, P. M.: 19(89), 580 Mahoney, C. L.: 17(7), 509, 512 Mair, B. J.: 16(5), 16(6), 16(7), 481; 16(9), 481, 482, 487; 16(14), 490; see also F. D. Rossini Makinson, K. R.: 13(24), 366, 370; 19(113), 593 Martin, P., Jr.: 10(17), 209, 249; see also B. J. Bornong Matheson, A . J.: 4(33), 90 Matsunaga, M.: 19(24), 19(25), 555, 556, 19(28), 556, 557; see also K. Tanaka Matveevsky, R. M.: 15(47), 462; 15(56), 869 McClelland, A . L.: 18(4), 524 McConnell, B. D.: 19(125), 596; see also R. D. Hubbell McDaniel, R. H.: 19(124), 506, 603 KcFarlane, J. S.: 8(9), 153 McHugh, K. L.: 17(9), 511 McKannan, E. C.: 19(154), 609 Mecklenburg, K. R.: 19(75), 576; see also B. D. McConnell Melpolder, F. W.: 16(10), 484, 487, 496 Menter, J. W.: 19(100), 589 Metzner, A . B.: 4(5), 64 Midgley, J. W.: 19(3), 551; i9(30), 557; 19(58), 569; see also C. Pritchard Mikhailov, I. A . : 16(15), 490

619

Miller, D. A . : 13(21), 364, 366 Millett, W. H.: 17(21), 519 Moelwyn-Hughes, E. A . : 314 (footnote) Moore, R. J.: 16(4), 480 Morecroft, D. W.: 10(27), 219; 11(1), 255 Morgan, F.: 7(6), 141; 8(19), 168 Mould, R. W.: 10(56), 243; 11(25), 265, 270: ll(35). 272. 274: ll(kO), 297 Mulhearn, T. 0.: 13(57), 386, 388. 390 Murphy, C. M.: 17(12), 512; see also D. C. Atkins Murray, S. F.: 19(152), 608, 609; see also P. Lewis, and M. B. Peter son Nagaraj, H. S.: 15(34), 15(35), 453; see also V. K. Ausherman Nakayama, K.: 15(15), 445, 467 Nayak, P. R.: 12(13), 332 Newton, I., 34 (footnote) Niedenzu, K.: 19(79), 578 Niemann, G.: 15(45), 460 Nishimura, M.: 19(130), 604 Novak, J. D.: 4(8), 69, 85 Obreimoff, J. W.: 10(40), 232 O'Connor, T. E.: 19(81), 578 O'Donoghue, J. P.: 15( 19), 15(20), 447 OECD: 13(1), 352; 13(52), 376, 377, 378. 379 O'Halloran, R.: 18!35), 542 Oka, S.: 4(4), 64, 74 Okabe, H.: 14(14), 413, 415; see also T. Sakurai, and A. Sethuramiah Organization for Economic Cooperation and Development: see OECD Orcutt, F. K.: 3(25), 54; 6(10), 116, 117; 19(94), 582; see also H. S. Cheng, and L. B. Sibley Palin, D. E.: 19(67), 572, 573 Partington, J. R.: 4(22), 79 Pease, R. S.: 19(78), 578 Peterson, M. B.: 19(87), 579; 19(92), 582; see also P. Lewis Peterson, W. H.: 18(3), 522; see also A. Bondi Philippoff, W.: 4(11), 74 Pinkus, 0.: 2(3), 19; 2(4), 23; 3(6), 37; 3(7), 39; 3(8), 41; 5(4), 106 Pooley, C. M.: 13(25), 366, 370; 19(114), 593 Poon, S. Y.: 18(32), 539, 540 Porgess, P. V. K.: 19(57), 569 Powell, D. G.: 13(41), 371; see also S. W. E. Earles Pritchard, C.: 19(32), 558, 565 Prutton, C. F.: 11(36), 273

Pryor, W. A.: 11(15), 262; 11(21), 263 Przybyszewski, J.: 19(147), 607 Pullen, J.: 12(14), 332, 332, 335 Queener, C. A.: 13(9), 358 Quinn, T. F. J.: 13(35 , 13 36), 13(37), 13(38), 13(39 , 37 Rabinowicz, E.: 9(11), 186, 194; 10(29), 225: 13(45), 3(46 , 372; 19(83), 579; see also J. T Burwell Ree, T. S.: 4(29), 88 Reichenbach, G. S ; : 15 29), 449 Reilly, J.: 4(7), 66, 7 Reiner. M.: 3(3). 31 Reynolds, 0.: 2(2), 10 Rhee, S. H.: 13(34), 370; 19(116), 19(117), 593 Risdon, T. J.: 19(5), 552 Roberts, M. W.: 11(5), 256 Ronay, M.: 13(26), 367 Ross, S.: 1916), 552; see also E. V. Ballou Rossini, F. D.: 16(1), 473; 16(8), 481; see also B. J. Mair Rowe, C. N.: 9(19), 192; 11(59), 292, 293; 13(60), 394; see also J. J. Dickert, jr.,and R. S. Fein Rowe, G. W.: 19(54), 569, 578, 579: see also D. J. Baldwin Rcdorff, W.: 19(65), 572, 573, 574; 19(68), 572, 573 Ruff, 0.: 19(64), 572, 574 Ryder, E. A.: 14(18), 421 Sakurai, T.: 10(55), 243; 10(60), 10(61), 245; 11(27), 11(28), 268; 11(37), 274; 14(5), 406, 407; ia(il), 412, 414, 417; 14(12), 412, 413, 414, 415, 417; 14(13), 4 1 2 , 414, 417; 15(14), 442; see also K. Nakayama, and A. Sethuramiah Saleh, J. M.: 11(3), 11(4), 11(6), 256 Salomon, G.: 19(2), 550; 19(29), 557, 564, 565; 19(102), 590 Sanborn, D. M.: 3(29), 55; 6(24), 125; see also V. K. Ausherman, 3 . Jakobsen, H. S. Nagaraj, and V. Turch i na Sanin, P. I.: 11(42), 278, 285, 295; 11(62), 299; see also Yu. A. Lozovoi Savage, R. H.: 19(47), 567, 568, 570; 19(53), 19(56), 569 Schiefer, H. M.: 17(11), 512; 17(20), 517 Schilling, A.: 18(37), 544 Schmidt-Coll&rus, J. J.: 17(2), 504, 509, 512 Schrader, M. E.: 19(21), 217 Schrader, R.: 11(14), 260

620

Semenov, A. P.: 19(55), 569 Sethuramiah, A.: 15(55), 468 see also T. Sakurai Shaw, M. C.: 3(9), 41; see a so E. G. Loewen Shore, H.: 15(6), 441 Shu, H. H. H.: 15(12), 441 Sibley, L, B.: 3(31), 57; 6(17), 121, 123; 13(18), 363; see also S. L. Cosgrove, and T. Tallian Silver, H. B.: 18(43), 545; 19(8@), 578; see also E. S. Forbes, and R. W. Mould Simard, G. L.: 10(57), 244 Simkins, T. E.: 7(11), 146 Singh, B. R.: 8(14), 161, 174 Siripongse, C.: 6(2), 112 Sisko, A. W.: 18(13). 529, 530 Skinner, J.: 8(12), i58 Slinev, H. E.: 19(i6), 554, 559 571. 577. 607: 19(95). 587. 606; 19( i21), '596;'19( 137); 605: ee also C. Cusano, R. L. Fusaro and R. L. Johnson Smith, E. E.: 16(20), 493 Smith, H. A.: 10(23), 10(24), l0(25), 217; 13(28), 368 Smith, R. A . : 15(26), 448 Spalvins, T.: 19(131), 19(133 19(134), 604 Speerschneider, C. J : 19(105), 590 Spengler, G. S.: 19( 9), 554; 19(86), 579 Spikes, H. A.: 19(35 , 230, 231; 11(65), 304; 15(52) 465; 15(57),

Tanaka, K.: 13(20), 364, 366, 370; 19(42), 562, 565 Tenwick, N.: 13(44), 371 Tichy, J. A.: 4(40), 94 Timmons, C. 0.: 10(8), 205, 214, 216; 10(10), 205, 208, 213, 214, 216: lO(15). 208: lO(20). 215 13(59), 392 Tolansky, S.: 6(16), 120; 10(37), 23 1 Tower, B.: 2(1), 9 Trivette, C. D., jr.: 11(23), 264 Tsuva. T.: 19(17). 554. 572: 19199), 588 Turchina, V.: 6(20), 122; 450

'

4.6_ 9 _

Sternlicht, B.: 5(2), 104 Stevens, D. R.: 11(16), 11(17), 262 Stokely, J. M.: 18(39), 544 Stubbles, J. R.: 19(27), 556 Studt, P.: 10(64), 245 Stupp, B. C.: 19(123), 596 Suggit, R. M.: 18(6), 527 S u h , N. P.: 13(47), 13(49), 374; see also S. Jahanmir Summers-Smith, D.: 19(34), 559 Tabor, D.: 8(5), 152, 153, 156; 12(18), 338; 17(17), 517, 518; see also F. P. Bowden, B. J. Briscoe, G. L. Gaines, N. Gane, J. N. Israelachvili, K. R. Makins o n , J. J. McFarlane, C. M. Pooley, and E. Rabinowicz, Tallian, T.: 6(26), 6(27), 130; 14(1), 401, 410; 14(2), 401, 402, 403, 410; 14(3), 401, 410 Tamai, Y.: 7(13), 147: 9 ( 1 4 ) , 18a

Utsilgi, H.: 18(28), 537 van Nes, K.: 16(17), 491, Van Wazer, J. R.: 4(2), 6 72, 76; 4(3), 61, 75 Vest, C. E.: 19(151), 608 Vold, M. J.: 18(8), 527 Walther, C.: 4(23), 79 Wedeven, L. D.: 3(14), 47 55 Wellincrer, K.: 13(11), 361 Whitehouse, D. J.: 12(10), 321, 324, 326 Wilaus. D. R.: 17(1). 504, 512 Wiliiamson, J. B. P.: 12(9), 32G, 324, 326: 12(15), 333; 12(16), 335; see also. J. A. Greenwood, and J. Pullen Wilson, R. W.: 9(21), 196 Winer, W. 0.: 19(129), 604; see also V. K. Ausherman, J. Jakobsen, D. Lee, H. S. Nagaraj, J. D. Novak, D. M. Sanborn, J. A. Tichy, and V. Turchina Wisander, D. W.: 19(146), 607 Woods, H. A.: 18(23), 535 Wostl, W. J.: 4(42), 98 Wright, K. H. R.: 1(4), 3 Wright, P. G.: 11(2), 256 Wright, W. A . : 4(39), 94 Wymer, D. G.: 15(36), 453 Yazgan, E.: 4(44), 98; see also A. J. Barlow Zakin, J. L,: 18(16), 531 Zisman, W. A.: 10(5), 203; 10(42), 232; see also K. W. Bewig, W. C. Bigelow, R. C. Bowers, R. L. Cottington, V. G. Fitzsimmons, 0. Levine, and C. 0. Timmons,

621

SUBJECT INDEX

Abrasion and the wear process, 375 and wear nomenclature, 376 Abrasive erosion, as wear nomenclature, 377 Abrasive wear as nomenclature, 376 modeling of, 365 variable rate model, 390 Acids: see Fatty acids Active sulfur, in polysulfides, 264 Additives: see Lubricant additives Adhesion and theory of friction, 151,152 and wear nomenclature, 376 and wear of plastics, 370 coefficient of, 342 in wear processes, 365, 368 of copper in vacuum, 179 OF gold, 340 of metals, 338 ff. of mica, 338 on ccntact, 319 tribological significance, 342 Adhesive junctions and friction behavior, 157, 168 and lubricated friction, 171 mechanism of friction, 151, 152 Adhesive wear, as nomenclature, 376 Adsorption, see also Chemisorption alkanes on metal, 207, 208 and temperature, 209 dibenzyl disulfide on stainless steel, 304 long-chain mixtures, 206 of additives by grease gellants, 545, 546 physical, 203 temperature and lubrication, 465, 466 Aerogels, and grease structure, 522 Alcohols: see Fatty alcohols Alkanes, orientation on metal surfaces, 207. 208 Alkyl chlorides, see also Organoch1orir.e compounds thermal decomposition, 272 Aluminum oxide, frictional behavior, 182 American Society for Testing and Materials: see ASTM Amides: see Fatty amides

Amines: see Fatty amines Ammonium polysulfide, lubricating films from, 242 Amontons' laws, 152 API gravity, definition, 479 Aromatics in petroleum lubricating oils, 474, 476 in lubricating oil fractions, 481, 488 and viscosity index, 495 Asperities and friction theory, 149, 152 and contact models, 314. 316. 327 and lubricated wear, 40j, 406, 410, 416 and models of rubbing, 437 deformation by contact, 332 elastic and plastic deformation, 317, 318 in surfaces, 2 junctions, tribological behavior, 343, 344 radius of curvature, 324 shape, in ground surfaces, 325 ASTM methods D 97, pour point, 507 D 217, cone penetration, grease, 532, 535 D 341, viscosity-temperature charts, 79 D 1092, apparent viscosity of grease, 538 D 1263, leakage of grease, 544 D 1298, density, specific gravity, API gravity, 479 D 1831, roll stability, grease, 535 D 2161, viscosity conversions, 79 D 2266, fcur-ball wear test, 545 3 2270, viscosity index, 83 D 2501, visccsity-gravity, 493 D 2504, Timken 'test, 543 D 2596, four-ball EP test, 545 Auger spectrometry of sulfur compounds on metals, 258 of chlorine compounds on metals, 259 Barium fluoride, as solid lubricant, 587 Bear i ngs action of grease in, 541 f f . energy losses in, 17 full journal, 19

622

gas lubricated, 103 grease lubricated, 5 3 6 , 5 3 7 , 5 3 9 journal, lubricant film failure, 125

pivoted slider, 18 plane slider, 1 4 rolling element, motion and wear, 355, 3 6 0 Beauchamp Tower, bearing experiment, 8 Benzyl chloride lubricant additive action, 2 7 4 on iron surface, Auger spectrometry, 2 5 9 reactivity toward iron, 2 7 4 Biphenyls, as synthetic lubricants, 5 0 4 bis(2-Ethylhexyl) sebacate lubricant action, 5 1 8 thermal stability, 5 1 2 viscosity characteristics, 5 0 9 viscosity, effect of pressure and temperature, 8 3 viscosity, high pressure, 7 0 Bleeding, of oil from grease, 5 2 8 ff. Boron nitride friction of, 5 7 8 , 5 7 9 preparation and properties, 5 7 7 Boundary lubrication and friction model, 193 and scuffing, 4 2 6 by adsorbed films, 219 by grease, 5 4 0 , 5 4 1 meaning of, 1 7 8 , 188 nature of, 5 nature of and definition, 2 0 0 Brass, wear mechanisms, 3 7 0 Bulk modulus adiabatic, isentropic, 9 7 isothermal, 52 n-Butane, dissociation on iron, 256 t-Butyl chloride dehydrochlorination, 258, 2 7 2 additive action, 2 7 4 n-Butyl mercaptan, reaction with iron, 2 5 8 Cadmium, transfer during sliding, 187

Calcium fluoride, as solid lubricant, 5 8 7 Calcium stearate, and lubrication of mica, 2 3 1 Capacitance, electrical: see Electri,cal capacitance Carbon, wear of, 3 6 3 Castor oil, as lubricant, 5 0 5 Ceramics, wear of, 3 6 3 Cetane, see also n-Hexadecane effect on adsorbed films, 2 1 0 lubricated friction of copper, 195

lubrication of cadmium, copper by, 187, 188

Cetyl alcohol, lubrication of cadmium, 1 8 7 Chalcogenides: see Dichalcogenides Chemical reaction and wear nomenclature, 3 7 6 in wear processes, 3 6 7 Chemical wear, as nomenclature, 376

Chemisorption and additive action, 2 1 8 nature of, 214 of stearic acid, 214 of stearic acid on copper, 2 1 7 of zinc dialkyl dithiophosphate on iron, 290 Chlorides, organic: see Organochlorine compounds Chlorinated paraffin additive in lubricating grease, 545,

546

in multicomponent additive, 2 9 6 reactivitv. _ . thermal decomDosition, 2 7 3 Chlorinated wax (Chlorowax): see Chlorinated paraffin Chlorine, lubricating films from, 245

Chlorobenzene, reactivity toward iron, 273 Chromium, friction behavior, 1 8 5 Cobalt, contact and adhesion, 3 4 0 Coefficient of friction and interfacial temperature, 4 3 6 , 450

and long-chain boundary lubricants, 1 8 8 and metal soaps, 1 8 9 basic expression for, 151, 1 5 3 contact model for, 3 3 0 lubricated, model for, 193 of metals against aluminum oxide, sapphire, 182 of metals, in vacuum, 1 7 9 kinetic, static, phenomenological definition, 138 Compressibility and lubrication, 9 9 and molecular structure, 9 4 of liquids, 92 Consistency, of lubricating grease, 5 3 2 ff. Contact and asperity deformation, 3 1 6 and friction, 1 4 9 , 1 5 7 end lubricated wear, 4 1 6 meaning of, 3 1 4 metallic, 1 2 6 metallic, and film thickness, 1 3 0 solid bodies, 3 0 8 surface asperities, 3 2 7 topography of surfaces and, 3 2 1 two rough surfaces, 3 3 2 Contact potential adsorbed films, 206, 2 0 7 , 209, 210

and orientation of films, 205

623

n-alkanes on platinum, 208 n-alkyl thiols, 211 non-adlineated films, 209 Contact pressure: see Pressure Copper contact and adhesion. 339 friction, adhesion i n vacuum, 179 frictional behavior, 185 lubrication, dithiophosphates, 191 lubrication, palmitic acid, 188 reaction with stearic acid, 217 Copper laurate, effect of temperature on friction, 190 Copper palmitate lubricated friction of cadmium, 187 lubricated friction of copper, 195 temperature and friction, 225 Corrosive wear, as nomenclature, 376 Cycloalkanes (Cycloparaffins): see Naphthenes Cyclohexane, surface resin from, 238 Damping of pendulum, measurement of friction, 147 n-Decanoic acid, dissociation on iron, 256 Deformation, see also Plastic deformation asperity junction, model of, 344, 345 contact of rough surfaces, 334 of asperities, elastic and plastic, 317, 318 of asperities on contact, 315, 332, 333 of asperities, plastic, 331 of rubbed surfaces, 337 Delamination. wear mechanism, 374 Density and lubricatinq oil structure, 491 liquids, elevated temperature and pressure, 93 petroleum lubricating oils, 481 Desorption fatty acids from metals, 218 from mixed films, and lubrication, 222 stearic acid from iron, 214 stearic acid from platinum, nickel oxide, 213 de Waele-Ostwald law, 64 Dewaxing, of petroleum lubricating oils, 414 Dialkyl dithiophosphates influence cf metal ion on additive action, 292 structure and nature of, 287 zinc salt, additive action, 247 zinc salt, additive mechanism, 290

zinc salt, preparation, 288 zinc salt, thermal decomposition, 288 Diamond, friction behavior, 181 Diary1 alkanes, as synthetic lubricants, 504 Dibenzyl disulfide additive action, 414, 415 additive in lubricating grease, 545, 546 frictional behavior, 191 in multicomponent additive, 296 interference effects on in multicomponent additive, 304 reactivity toward iron, 265, 266 temperature and friction, 192 Dibenzyl sulfide, reactivity toward iron, 266 1,22-Dicarboethoxy-11,12-dithiadocosane, lubricant additive, 302 1,20-Dicarbomethoxy-9,12-dimethyllO,ll-dithiaeicosane, lubricant additive, 302 Dichalcogenides, transition metal as solid lubricants, 579, 580 Dicyclohexyl effect on adsorbed films, 210 solvent for film forming substances, 205 Di(2-ethylhexyl) sebacate: see bis(2-Ethylhexyl) sebacate Diethyl sulfide, reaction with tungsten, 258 Diisopropyl dithiophosphates, thermal decomposition and additive action, 293 Di(4-methylphenyl) dithiophosphates, metal salts as lubricant additives, 292 Dimethyl tetrasulfide, thermal decomposition, 264 Di-n-butyl disulfide, reactivity toward iron, 265 Di-n-butyl phosphate, lubricant additive action, 278 Di-n-butyl sulfide, reaction with iron, 258 Di-n-butyl tetrasulfide, bond strength, 264 Di-n-hexyl dithiophosphetes, metal salts as lubricant additives, 292 Di-n-octadecyl disulfide, from din-octadecyl tetrasulfide, 264 Di-n-octadecyl tetrasulfide, abstraction of sulfur from, 264 Di-n-octyl disulfide additive action of, 268 reacKion with iron, kinetics, 264 Diphenyl alkanes halogenated, as lubricants, 504 halogenated, viscosity, 509 Diphenyl disulfide frictional behavior, 191 reactivity toward iron, 265, 266 Diphenyl ether chlorinated, reactivity and ther-

624

ma1 decomposition, 2 7 3 in multicomponent additive, 2 9 6 Diphenyl phosphate frictional behavior, 1 9 2 lubricant additive action, 2 8 0 Discharge voltage and fluid film thickness, 1 1 2 and scuffing, 128, 129 Di-sec-octyl disulfide, lubricant additive action, 3 0 2 Disulfides, metal: see Dichalcogen ides Disulfides, organic additive action o f , 2 6 8 bond strength, 264 reaction with iron, 2 6 4 , 2 6 5 Di-t-butyl disulfide, reactivity toward iron, 2 6 5 Dithioheptadecanoic acid, lubricant additive behavior, 249 Di-t-nonyl polysulfide, reactivity toward iron, 2 6 5 Di-t-octyl disulfide action in multicomponent additive, 296 and lubricated wear, 4 1 9 reaction with iron, kinetics, 2 6 4 Docosane, temperature and friction, 190 n-Docosylamine, durability of films, 2 2 1 , 2 2 2 Ductility, of metals and contact adhesion, 3 4 0 Elastic deflection, and measurement of frictior., 1 4 i Elastohydrodynamic lubrication by grease, 540 partial, and wear, 4 0 1 , 408, 4 0 9 theory of and behavior, 42 ff. Elastohydrodynamics computing techniques, 47 in lubrication, 42 "line" contact, 4 6 "point" contact, 5 1 theory, 4 3 thermal effects, 4 6 Electrical capacitance, and fluid film thickness, 1 1 4 Electrical resistance and film failure, 1 2 5 and fluid film thickness, 110 of contacting surfaces, 150 Erosion and wear nomenclature, 3 7 6 as mode of wear, 3 6 2 Erosive wear, as nomenclature, 3 7 6 Esters as hydraulic fluids, 5 1 9 carboxylic, as lubricants, 5 0 6 silicate, as lubricants, 5 0 6 Ethane, dissociation on metals, 256

Ethyl chloride dehydrochlorination, 2 5 8 , 2 7 2 on iron surface, Aucjer spectro-

metry, 2 5 9 2-Ethylhexyl diphenyl phosphate, thermal decomposition, 2 7 8 Extreme-pressure lubrication and scuffing, 4 2 6 by grease, testing, 5 4 5 , 5 4 6 by halogenated silicones, 5 1 7 by synthetic lubricants, 5 1 4 ff. chemical interaction films, 2 4 1 four-ball test for, 2 7 1 multicomponent sulfur/'chlorine additives, 296, 2 9 7 multicomponent thiophosphorus/ chlorine additives, 2 9 9 nature of, 5 nature of and definition, 2 0 1 organochlorine additives, 2 7 4 organophosphate additives, 2 7 8 organophosphate and organosphosphite additives, 2 8 1 sulfurized fat additives, 3 0 1 thiophosphate and thiophosphite additives, 2 9 5 , 2 9 6 zinc dialkyl dithiophohsphate additives, 2 9 1 Fat i gue and impingement wear, 3 6 1 and wear of rolling element bearings, 3 6 1 and l o o s e wear debris, 3 7 2 a s a wear mechanism, 3 6 8 in the wear process, 3 7 0 Fatigue wear, as nomenclature, 37; Fatty acids durability of films, 218, 2 2 3 effect on friction, 1 8 7 effect on scuffing load, 1 1 3 reaction with metals, 2 1 8 stability of monolayers, 2 0 6 Fatty alcohols effect on friction, 187 stability of monolayers, 2 0 6 temperature and adsorption, 2 0 9 , 210,

211

Fatty amides, temperature and adsorption, 209, 210, 2 1 1 Fatty amines effect on friction, 1 8 7 stability of monolayers, 2 0 6 temperature and adsorption, 2 0 9 , 210,

211

Ferric chloride, lubrication by films of, 2 4 5 Ferrous sulfide films and lubrication, 2 4 4 from additive a c t i m on metals, 258

Films, see also Monolayers additive, lubricated wear behavior, 4 1 0 , 4 1 1 adsorbed, 2 0 3 adsorbed, additive action, 2 1 9 chemical interaction, 2 4 1 chemically deposited, 2 3 5 chemisorbed, 214, 217

625

chernisorption and, 2 1 6 contact potential of, 2 0 5 , 2 0 6 , 207, 2 0 9 , 2 1 0 , 2 1 1

durability, 2 1 9 elastohydrodynamic, pressure distribution, 4 7 , 48, 50, 51, 5 3 , 54 fluid, and wear, 129 fluid, failure of, 113, 123 fluid, thickness, 1 1 0 fluid, thickness profiles, 47, 48,

53,

54,

55

graphite fluoride, lubricaticn by, 5 4 7 ff. hydrodynamic, pressure distribution in, 10, 16 indium on steel, friction, 5 8 8 lubricant, temperature and fai ure of, 5 4 8 ff. lubricant, temperatures in, 4 5 mixed, 2 0 6 , 2 1 3 mixed, iron oxide/iron sulfide 244

nixed, 12bricating behavior, 2 molybdenum disulfide, durabili 563 ff. non-adlinezted, 2 0 8 oleophobic, 2G5 penetration of. wear. 4 0 1 polymeric condensation, 2 3 6 solid lubricant, bonded, 5 9 5 ff. solid lubricant, generated by surface treatment, 6 0 3 ff. stability of, 2 0 6 surface energy of, 231, 2 3 2 thermodynamics and lubrication, 226

thickness and wear, 4 0 1 transfer, from composites, 6 0 4 transfer, graphite and lubrication, 5 7 0 ff. transfer, molybdenum disulfide and lubrication, 562, 5 6 3 transfer, organic plastics, 5 9 2 Flash temperature: see Tenperature Fluid classical, 2 7 continuity equation, 3 6 stress analysis, 2 7 viscous, 3 3

Fluorides inorganic, high-temperature solid lubricants, 5 8 7 bonded, practical application, 596

Fluorohydrocarbons, a s lubricants, 504

synthetic lubricants, 514, 5 1 5 , 517

Fretting corrosion: see Fretting wear Fretting wear, as nomenclature, 377

Fr ic t ion additive action and temperature, 468

additive interference and, 3 0 4 asperity junction model, 3 4 3 , 3 4 4 basic mechanism, 1 4 9 boron nitride, 5 7 8 , 5 7 9 coefficient of: see Coefficient of friction definitions, 134 diamond, 1 8 1 dichalcogenides, 5 7 9 ff. diphenyl phosphate, effect on, 288

EP additives and, 1 9 0 film failure and, 1 2 4 , 128 graphite, 5 6 8 ff. graphite fluoride, 5 7 4 ff. interfacial temperature and, 4 3 6 , 450

indium film on steel, 5 8 7 lubricated, 1 7 0 , 1 7 1 , 178, 1 8 5 lubricated, influence of temperature, t 90 lubricated, journal bearing, 2 1 lubricated, model for, 1 9 3 lubricated, surface damage, 2 2 4 measurement, 1 4 0 ff. measurement in vacuum, 1 4 2 , 1 4 4 metals, influence of oxides, 1 8 3 metals in vacuum, 1 7 9 metals, on aluminum oxide, 1 8 2 molybdenum disulfide, 5 5 5 molybdenum disulfide, effect of water vapor, relative humidity, 5 5 7 ff. negative load and, 158 non-adhesive mechanisms, 1 7 5 non-lamellar solids, 5 8 2 ff. phthalocyanine, 5 8 9 , 5 9 0 PTFE, 5 9 0 polyimides, 5 9 1, 6 0 6 polyimide/graphite composites, 606

sapphire, 1 8 2 scuffing and, 1 2 9 , 4 2 4 , 4 2 5 sliding speed and, 172 static and kinetic, nature of, 765,

167,

169

28 1

static and kinetic, behavioristic definitions, 137, 1 3 8 , 139 static, inclined plane, 1 3 7 , 1 4 6 stick-slip, 1 5 9 , 1 6 8 sulfur, effect on, 2 4 3 surface contact and, 2 3 0 temperature and, 4 5 6 tripheny? phosphate, effect on,

organosulfur additives, 2 7 0 sulfur in oil, 2 4 3

vibratory, 1 6 2

Four-ball test "extreme-pressure''method, 2 7 1 lubricating grease, 5 4 5 , 5 4 6 multicomponent sulfur/chlorine additives, 2 9 6 , 2 9 7 organochlorine additives, 2 7 4 organophosphate additives, 2 7 8 ,

288

626

Fricfion polymer: resin

see Surface

Galling, as wear nomenclature, 377 Gases lubrication by, 102 properties of and lubrication, 106 Gas law, ideal and lubrication by gases, 106 Gellants adsorption of additives by, 545, 546 and grease consistency, 534 non-soap, 528 of lubricating grease, 521, 522 Germanium, ductility and contact adhesion, 340 Glycols: see Polyoxyalkylene glycols Gold adhesion under load, 340 ff. friction against lead, 167 load and friction, 158 Graph i t e in mixed bonded films, 596 in oils and greases, 606 interlayer energy of, 567 lamellar solid lubricant, 566 ff. polyimide composite, friction and wear of. 606 wear and friction during rubbing, 568 ff. Graphite fluoride as solid lubricant, 574 ff. bonded films, durability, 599 ff. films o f , and wear, 574 ff. preparation and properties, 572, 573, 574 Gravity: see API gravity Grease: see Lubricating grease Hagen-Poiseuille law, 63 Heat conduction theory, calculation of interfacial temperature, 430 Hexachloroethane, reactivity toward iron, 274 n-Hexadecane, see also Cetane solvent for film-forming substances, 205 n-Hexadecyl chloride, lubricant additive action, 274 n-Hexyl chloride, lubricant additive action, 274 Huber-von Mises: see Tresca-Hubervon Mises Hydrocarbons, see also Alkanes, Olef ins orientation on metal surfaces, 207. 208 synthetic, as lubricants, 501, 502, 504, 508 ff. synthetic, viscosity and pour point, 508, 510

Hydrodynamic lubrication nature of, 5 theory and behavior, 8 ff. Hydrofinishing and oxidative stability, 498 of petroleum oils, 475 Hydrogen chloride, lubricating films from, 245 Hydrogen sulfide dissociation on metals, 256 on metal surfaces, 257 12-Hydroxystearic acid, and manufacture of grease, 528 Hysteresis, mechanism for friction, 176 Impingement, and wear behavior, 361 Impingement erosion, as wear nomenclature, 377 Indium films on steel, friction, 588 frictional behavior, 184 Infrared radiation, and measurement of interfacial temperature, 448 Interfacial temperature: see Tempera ture Interferometry: see Optical Interferometry Iron action of tricresyl phosphate on, 279 dissociation of organic compounds by, 255, 256 dissociative adsorption of hydrogen sulfide, 256 reaction with dibutyl sulfide, 258 reaction with disulfides, kinetics, 264, 266 reactive adsorption of dialkyl phosphites, 284 reactivity with organic sulfides, 265 Iron sulfides, see also Ferrous sulfide from additives on metal surfaces, 258 Isoparaff ins and pour point, 498, 499 and viscosity index, 497 in lubricating oil fractions, 487 Isopropyl chloride, dehydrochlorination, 272 Junctions, see also Adhesive junctions asperity, and interfacial temperature, 445 asperity, behavior of, 343, 344 Lauric acid friction, temperature effect, 1 9 0 lubricated friction, 171, 186,

627

189 scuffing load, effect on, 114 surface energy of monolayer, 232 Lead action on hydrogen sulfide, 256 friction against gold, 167 friction of, 587 load and friction, 158 Lead diisopropyl dithiophosphate, structure of, 287 Linoleic acid, dimer, additive film from, 236 Liquids and lubrication, 59 compressibility and bulk modulus, 92 molecular structure and viscosity. 87 Lithium fluoride, as solid lubricant, 587 Lithium 12-hydroxystearate, as grease gellant, 531 Lithium stearate, phase behavior in oil, 527 Load and dry/lubricated wear, 362 and oxidative wear of steel, 371 and wear behavior, 356, 357, 358 and wear rate, 370, 392 Long-chain compounds, as lubricants, 188 Lubricant additive action interference effects, 304 multicomponent, sulfur/chlorine, 296, 297 multicomponent, thiophosphorus/ chlorine, 299 organochlorine compounds, 274 organophosphates, 276 organophosphites, -phosphinates, -phosphinites, 281 organophosphorus compounds, 276 organosulfur compounds, 268 sulfurized fats, 301 thiophosphate esters, thiophosphite esters, 295, 296 tricresyl phosphate, 278, 279 zinc dialkyl dithiophosphates, 290, 291 Lubricant additives and wear behavior, 411 classification, 200, 202 dialkyl dithiophosphates, 286 EP in grease, 543, 546 films, chemical interaction, 241 films, chemically deposited, 235 films, nature of action, 218 films, sulfide interaction, 244 films, thermodynamics of, 226 interference effects, 304 junction growth inhibitors, 250 multicomponent, 295 monolayer, model of action, 233 nature of, 198 organochlorine compounds, 274 organophosphorus compounds, 268

organosulfur compounds, 276 pro-wear action, 418 radioactive, and wear behavior, 414 scuffing contr31, 420 sulfur compounds, 414 sulfurized fats, 301 Lubricants compounded, and lubricated wear, 410 compounded, control of scuffing, 420 compounded, pro-wear, 418 mineral oil, and lubricated wear, 403 synthetic esters, lubricated wear, 403 Lubricants, non-petroleum: see Synthetic lubricants Lubricants, solid: see Solid lubricants Lubricating grease basic nature, 521 bench testing, 545 bleeding, permeability, 528 ff. consistency, penetration, 532 ff. failure in bearings, 544 flow of, 535 gel structure, 522, 524 lubrication of bearings, 536, 537, 539, 541 ff. manufacture, 526 oil in, function, 524 viscometry, 537, 538 Lubricating oils, see also Mineral oils, Petroleum oils chemical structures, 480 ff., 488 classification, nomenclature, 476 fractionation of, 480, 481 ff. mass spectrography, 481, 484, 487 organonitrogen, organosulfur compounds in, 490 oxidation stability, 498 petroleum, refining, 472 ff. physical properties and structure, 491 ff. structure and lubricant behavior, 495 ff. thermal diffusion, 484 Lubrication, see also Boundary lubrication, Elastohydrodynamic lubrication, Extreme-pressure lubrication, Hydrodynamic lubrication, Quasihydrodynamic lubrication, Mixohydrodynamic lubrication adsorbed film, 2 1 9 adsorption thermodynamics of, 226 bearings, by grease, 536, 537, 539, 541 ff. chemically deposited films, 219 dichalcogenides, 579, 580, 581 dithiophosphates, 191 failure, and temperature, 458 failure, transition temperature, 462 ff.

628

fatty compounds and, 188, 189 fluorides, 587 graphite, 566 ff. graphite fluoride, 572 ff. in metal cutting, 250 molybdenum disulfide, 552 ff. non-lamellar solids, 581 ff. oil bleeding of grease, 528 organic solids, 589 ff. organosulfur compounds, 191 oxides, 582 soft metal films, 588 solids, methods of, 551 synthetic fluids, 514 ff. transfer from composites, 604, 605

Magnesium oxide, friction, 182 Margules equation, 73 Mass spectrography, of petroleum lubricating oils, 481, 484, 487 Mechanical wear, definition 349 Mercaptopalmitic acid, additive behavior, 249 Metal cutting lubricating action in, 250 interfacial temperature, 442 Metals activation by rubbing, 260 friction in vacuum, 179 friction on aluminum oxide, 182 reactions with organic compounds, 255, 256

soft films, lubrication by, 508 surface oxides and friction, 183 Methane, dissociation on metals,

Mixohydrodynamic lubrication behavior, 404 ff. meaning of, 404, 408 Molecular structure of liquids and compressibility, 94

of liquids and theories of viscosity, 07 Molecular weight, and lubricating oil structure, 491 Molybdenum diselenide, as solid lubricant, 579 Molybdenum disulfide crystal orientation and lubrication, 559 lamellar solid lubricant, 552 ff. layer-lattice structure, 553 in composites, 604 in mixed bonded films, 596 in oils and greases, 606 sputtered surface films, 604 surface species on, 557 temperature and friction, 574 transfer film and lubrication, 562

Monolayers, see also Films mixed, 206, 213 model of additive action, 233 of lauric acid, surface energy, 232 of long-chain compounds’, 205 of stearic acid, 203 on fresh metal surfaces, 218

shear strength under pressure, 234

stability of, 206

256

Methyl chloride, on iron surface, Auger spectrometry, 259 4-Methyl-4-chloroheptane: see t-Octyl chloride Methyl laurate, lubricant additive action, 302 Methyl mercaptan dissociation on metals, 256 reaction with metals and Auger spectrometry, 251 I-Methylnaphthalene, surface resin and lubricant behavior, 239 Methyl undecenoate, sulfurization and additive action, 301 Mica contact and adhesion, 331, 338 layer-lattice properties, 552 surface energy and lubrication, 23 1

Mild.wear, as nomenclature, 317 Milling, of lubricating grease, 521, 528

Mineral oil, see also Lubricating oils, Petroleum oils friction and lubrication, 186 hydraulic fluids, 519 lubricated wear, 403 oxidative stability, 514 viscosity characteristics, 508

Naphthenes and pour point, 499 and viscosity index, 496 in lubricating oil fractions, 481, 483. 401

in petroleum lubricating oils, 474, 476

Navier-Stokes equations, simplification, 35, 36 Newton, Sir Isaac, definition of viscosity, 34 Newtonian flow, 61, 62 in cone-and-plate viscometer, 75 i n Couette viscometer, 7 3 Nickel cleansing of, 179 dissociation of organic compounds o n , 256 Nickel dialkyl dithiophosphate, additive action of, 248 Nickelous oxide, desorption of stearic acid from, 213 Nitrobenzene, solvent for filmforming substances, 205 n-Nonadecanoic acid oleophobic monolayers, 205 direct reaction with metals, 218 Non-Newtonian flow, 64

629

function of shear rate and shear stress, 71, 7 5 in rotational viscometry, 7 5 n-Octadecane dissociation on iron, 2 5 5 in mixed monolayers, 2 0 6 Octadecanol lubricated friction of copper, 195

temperature and friction, 2 2 5 n-Octadecylamine additive interference effects, 304

oleophobic monolayers, 2 0 5 surface potential of films, 2 0 6 temperature and additive action, 465,

466

n-Octyl chloride, lubricant additive action, 2 7 4 t-Octyl chloride in multicomponent additive, 2 9 6 lubricant additive action, 2 7 4 Olefins, polymerized, synthetic lubricants, 5 0 2 Oligomers, olefinic, synthetic lubricants, 5 0 2 Optical interferometry and asperity structure, 3 2 5 and fluid film thickness, 5 4 , 117 and surface topography, 3 1 1 Organochlorine compounds alkvl chlorides. dehvdrochlorination, 2 7 2 as lubricant additives, 2 4 9 reactivity toward metals, 2 7 2 , 2 7 3 , 297

Organonitrogen compounds, in lubricating oil fractions, 4 9 0 Organophosphates as lubricant additives, 2 7 6 ff. comparison with organophosphites, 281,

282

Organophosphinates, as lubricant additives, 2 8 5 Organophosphites as lubricant additives, 281, 2 8 2 reaction with iron, 284 Organophosphonates, as lubricant additives, 2 8 5 Organophosphorus compounds, as lubricant additives, 2 7 6 ff. Organosilanes as lubricants, 5 0 6 oxidative stability, 5 1 2 , 5 1 3 thermal stability, 5 1 1 Organosulfur compounds, see also Disulfides, organic bond strengths, 263 in lubricating oil fractions, 4 9 0 reaction with iron, kinetics, 2 6 8 reactivity toward steel, 2 9 7 structural types and reactions, 26 1

Oxidation in the wear process, 3 6 9 , 3 7 1 ,

376,

377

of petroleum lubricating oils, 498

Oxidative stability, of synthet lubricants, 5 1 2 Oxidative wear, as nomenclature

C

376

Oxides and friction of metals, 183 high temperature lubrication, 5 8 2 Oxygen and friction of metals, 184 on metal surfaces, Auger spectrometry, 2 5 7 Palmitic acid lubrication of cadmium, 1 8 7 lubrication of copper, 1 8 8 temperature and friction, 2 2 5 Paraffin oil, see also Mineral oil, White oil temperature and friction, 2 2 5 Paraffins and pour point, 4 9 9 and viscosity index, 4 9 6 in lubricating oil fractions, 481,

484,

487

in petroleum lubricating oils, 474,

476

Peclet number, 4 4 0 Penetration, of lubricating grease: see Consistency Pentachlorodiphenyl, reactivity toward iron, 274 Permeability, of grease by oil, 5 2 8 ff. Petroleum, fractions from, 4 7 3 Petroleum oils, see also Lubricating oils, Mineral oil hydraulic fluids, 5 7 9 viscosity, influence of pressure and temperature, 8 3 , 8 5 Petroleum sulfonate, calcium salt, additive interference by, 3 0 5 Phosphate esters, as hydraulic fluids, 5 1 9 Phosphates, organic: see Organophosphates Phosphorodithioaces, dialkyl: see Dialkyl dithiophosphates Phosphorus compounds, organic: see Organophosphates, Organophosphinates, Organophosphites, Organophosphonates, Organophosphorus compounds Phthalocyanine, as solid lubricant, 5 8 9 Pitting as wear nomenclature, 3 7 9 behavioristic significance, 3 9 6 Plastic deformation, see also Deformation and loose wear particles, 3 7 4 in the wear process, 3 6 6 Plastic flow, and mechanism of friction, 1 4 9 , 153

630

Plastics, see also Polymers adhesion and transfer during wear, 3 6 6 lubrication by films of, 5 9 3 wear of, 363, 364 Plat i num adsorption of fatty acids on, 2 1 8 desorption of stearic acid from, 213

lubrication by fatty acids, 2 2 6 Plowing a s wear nomenclature, 3 7 8 a s wear process, -166 mechanism for friction, 1 7 5 Polyethylene, transfer films and lubrication, 5 9 3 Polyimides as binders, 5 9 8 , 5 9 9 a s solid lubricants, 5 9 1 ff. films of, wear, 5 9 4 preparation and properties, 5 9 0 , 59 1

Polymeric condensation, additive films by, 2 3 6 Polymers, see also Plastics lubrication by films of, 5 9 3 olefinic, as lubricants, 5 0 2 Polymethylmethacrylate, and viscosity of paraffinic oils, 8 5 Polyphenyl ethers a s lubricants, 5 0 6 oxidative stability, 512, 513 radiation resistance, 5 2 0 thernal stability, 5 1 1 viscosity and pour point, 5 0 9 Polyphenyls a s lubricants, 5 0 4 radiation resistance, 5 2 0 thermal stability, 5 1 1 Polyoxyalkylene glycols as hydraulic fluids, 5 1 9 as ldbricants, 5 0 6 thermal stability, 5 1 2 viscosity properties, 5 0 9 Polysulfides, bond strength, 2 6 4 Poly(t-butylstyrene), and viscosity of petroleum oils, 8 5 Polytetrafluoroethylene adhesion, transfer during wear, 366

as solid lubricant, 5 9 0 friction against metals, oxides, 182

transfe: films, lubrication, 5 9 3 wear of, 3 6 4 Polyvinyl chloride, transfer films and lubrication, 5 9 3 Polpviqylidene chloride, transfer films and lubrication, 5 9 3 Pour point of syntheti? lbbricants, 5 0 8 , ff. structures in lubricating oils and, 4 9 8 , 4 9 9 Pressure and lubricated wear, 4 0 5 ff. effect on viscosity, 8 0 , 8 3

effect on viscosity, theoretical models, 90 in elastohydrodynamic films, 47, 4 8 , 50, 5 1 , 5-1, 5 4 in fluid films, 10, 16 sliding and wear, influence on, 352,

353,

354

wear rate, influence on, 3 9 3 Profilometry by stylus probe, 3 1 1 statistical treatment, 3 2 0 ff. PTFE: see Polytetrafluoroethylene Quartz, frictional behavior, 182 Quasiharmonic vibration, frictional behavior and analysis, 162 Quasihydrodynamic lubrication, 4 0 4 Radioactive tagging adsorbates, 2 0 6 dibenzyl disulfide, 3 0 4 , 4 1 4 dithiophosphates, 2 4 7 , 2 9 0 stearic acid. 2 1 4 steel, 3 6 9 sulfur additives, 244, 2 4 5 . 4 1 3 triphenyl phosphate, 2 4 6 Reaction rate, chemical, and lubricated wear mechanism, 4 1 1 ff. Refractive index and lubricating oil structure, 49 1

of petroleum lubricating oil, 4 8 1 Relative humidity, and lubricating action of molybdenum disulfide, 558,

560,

564

Resistance, electrical: see Electrical resistance Reynolds equation and gas lubrication, 102 generalized, 3 7 two-dimensional, 10 Rolling sliding, and wear behavior, 3 5 8 wear behavior, 3 5 9 Rolling element bearings: see Bearings, rolling element Roll test, for consistency of lubricating grease, 5 3 5 Rubbing speed: see Speed SAE test, and sulfdr in oil. 244 Sapphire, friction behavior, 162 Scoring as wear nomenclature, 378 behavioristic significance, 3 9 6 Scratching, and wear nomenclature, 370

Scuffing additive concentration, 230, 2 3 1 additive desorption, 2 2 6 as wear nomenclature, 3 7 8 behavioristic significance, 3 9 6 control by compounded lubricants, 420

critical temperature for, 4 5 8

631

discharge voltage and, 128, 1 2 9 gear surface temperature, 4 6 0 genesis of, 4 2 5 film failure and, 113, 124 molybdenum disulfide films and, 563

temperature effects, 2 2 7 , 2 2 9 , 230

Seebeck e.m.f., 4 4 1 Seizure, of copper, nickel in vacuum, 1 7 9 Severe wear, as nomenclature, 3 7 Shearing, of greases, 5 3 5 Shear rate, effect on viscosity 71

Shear strsnqth and friction, 151, 153, 156 and model of lubricated friction, 193

of monolayers under pressure, 2 3 4 Shear stress, effect on viscosity, 71

Silanes: see Organosilanes Silicate esters as lubricants, 5 0 6 lubricating action, 5 1 4 Si 1 icones as lubricants, 5 0 9 in lubricating grease, 5 2 8 lubricating action, 5 1 6 oxidative stability, 5 1 2 , 5 1 3 structure and viscosity, 5 1 0 , 5 1 6 thermal stability, 512 viscosity behavior, 5 0 9 Silver, action on hydrogen sulfide, 2 5 6 Sliding and wear processes, 3 7 5 reiterated path, wear, 3 9 4 , 3 9 5 rolling, wear behavior, 3 5 8 wear behavior, 3 5 1 Sliding speed: see Speed Soaps boundary lubrication by, 5 4 0 , 5 4 1 coefficient of friction, 189 gellants for grease, 5 2 2 phase behavior in oil, 5 2 7 , 5 2 8 Sodium stearate, temperature and friction, 1 9 0 Solid lubricants bonded films, 5 9 5 ff. composites, 6 0 4 ff. dichalcogenides as, 5 7 9 friction behavior, 5 5 0 layer-lattice solids, 5 5 1 ff. nature of, and definition, 5 4 9 non-lamellar solids, 5 8 1 ff. technological utility, 5 9 4 ff. types of, 5 5 0 Solvent extraction, refining of petroleum lubricating oils, 4 7 4 Sommerfeld number, 2 3 Sommerfeld solution, jcurnal bearing, 2 1 Spa11i ng and wear nomenclature, 3 7 9

behavioristic significance, 3 9 6 Specific dispersion, of petroleum lubricating oils, 4 8 1 Specific refractive dispersion: see Specific dispersion Specific gravity: see Density Speed and friction, 172 and lubricated friction, 1 7 1 and lubricated wear, 4 0 4 ff. and lubricated wear rate mechanism, 4 1 6 , 4 1 7 and oxidative wear of steel, 3 7 1 effect on dry and lubricated wear, 4 0 4 ff. effect on wear rate, 3 7 0 , 3 9 4 Squeeze films, 4 0 in journal bearings, 40 between parallel plates, 4 1 Stearic acid chemisorption, 2 1 4 desorption, 2 1 4 effect on lubricated friction, 171,

189

effect on scuffing load, 114 in mixed films, 206 lubrication of platinum, 2 2 6 model of lubricating action, 2 3 3 monomolecular films, 203, 2 0 5 reaction with copper, 2 1 7 temperature and friction, 190 Steel frictional behavior, 185 mechanisms in wear of, 3 6 9 oxidative mechanism in wear, 3 7 1 oxide films and friction, 184 Stick-slip and lubrication, 1 8 6 and sliding speed, 1 7 2 analysis of, 1 6 0 frictional behavior, 1 5 9 Sulfides, organic, see also Disulfides, organic; Organosulfur compounds; Polysulfides behavior in lubricant additive tests, 2 4 9 , 2 7 0 bond strengths, 2 6 3 reaction with iron, 2 6 6 reactivity toward steel, 2 9 7 structural types and reactions, 262

Sulfonate: see Petroleum sulfonate Sulfur additive activity and temperature, 4 6 7 a s EP additive, 2 4 3 bond strength, reactivity with iron, 2 6 4 frictional behavior, 191 lubricant additive action, 4 1 2 Sulfurized esters, as lubricant additives, 3 0 1 Sulfurized fats, as lubricant additives, 3 0 1 Surface energy and lubrication of mica, 2 3 1

632

and wear mechanism, 3 7 2 in lubrication model, 2 3 3 Surface potential: see Contact pot en t ia 1 Surface resin, formation and lubricating action, 2 3 8 Surface roughness and fluid film behavior, 130 and fluid film thickness, 111 and friction, 3 3 0 asperity structure, 3 2 5 metrology, 3 1 2 of solid bodies, 3 0 9 statistical treatment, 3 2 0 ff. Surfaces clean, friction of, 178 cleansing of, 179 contact and friction, 1 6 9 lubricated friction damage, 2 2 4 mica, van der Waals forces, 2 3 2 nature of and adsorption, 2 0 3 rough, behavior in contact, 3 3 2 rubbed, appearance of, 3 4 6 rubbed, topography of, 3 3 6 , 3 3 7 solid bodies, nature of, 3 0 9 ff. Surface topography alteration by deformation, 3 3 2 , 333

and contact, 3 1 6 , 3 2 9 and rubbing, 3 3 7 of solid bodies, 3 0 9 statistical treatment, 3 2 0 ff. stylus probe profiles, 3 1 1 three-dimensional, 3 2 6 Synthetic lubricants and lubricated wear, 4 0 3 applications of, 5 1 8 in lubricating grease, 5 2 8 lubricating behavior, 5 1 4 non-petroleum liquids, 5 0 1 oxidative stability, 5 1 2 thermal stability, 5 1 1 types, properties of, 5 0 7 Tait equation, and compressibility of liquids, 94 Temperature ambient, tribological effects of, 453

and bonded solid lubricants, 5 9 6 ff. and dry wear of steel, 3 7 1 and friction of graphite, 5 6 9 and friction of solid lubricants, 582

211

effect on compressibility, 9 4 effect on electrical resistivity of oil, 122 effect on films and friction, 224,

190,

192

effect on lubrication, 4 6 4 ff. effect on viscosity, 7 9 , 8 3 frictional, calculstion, 4 3 6 flash, and lubrication failure, 549

gear scuffing, 4 6 0 , 4 6 1 in lubricant film, 4 5 0 , 4 5 1 in o i l films, 1 2 2 interfacial, and lubrication, 4 6 4 interfacial, and scuffing, 4 2 4 interfacial, calculation of, 4 3 0 interfacial, measured and theoretical, 4 4 1 , 4 4 2 interfacial, measurement, 4 4 0 interfacial, model for, 4 2 9 interfacial, stochastic model, 437

Terphenyls as synthetic lubricants, 5 0 4 oxidative stability, 5 1 2 , 5 1 3 viscosity and pour point, 5 0 9 Thermal diffusion, of petroleum lubricating oils, 4 8 4 Thermal stability, of synthetic lubricants, 5 1 i Thermistors, and measurement of interfacial temperature, 4 4 7 Thermocouple dynamic, and interfacial temperature, 4 4 1 embedded, and interfacial temper ature, 4 4 6 Thickeners, for grease: see Gellants Thiophosphate esters, structure and additive action, 2 9 5 , 2 9 6 Thiophosphite esters, structure and additive action, 2 9 5 , 2 9 6 Tin, frictional behavior, 184 Transfer and wear nomenclature, 3 7 6 and wear of plastics, 3 7 0 from composites, 6 0 4 graphite films, 5 7 0 ff. in wear processes, 3 6 5 , 3 6 8 , 3 6 9 molybdenum disulfide films, 5 6 2 , 563

of cadmium during sliding, 1 8 6 , 187

of copper in lubricated friction, 194

and infrared radiation, 4 4 8 and lubrication by graphite fluoride, 5 7 4 effect on additive action, 4 6 7 effect on adsorbed films, 209, 210,

effect on friction and wear, 4 5 6 effect on lubricated friction,

225

of PTFE to metals and oxides, 182 organic plastic films, 5 8 2 ff. Tribology, definition, 3 Tricresyl phosphate additive in lubricating grease, 545,

546

lubricant additive action, 2 4 7 , 278,

279

Tri-n-bucyl phosphate, lubricant additive action, 278 Triphenyl phosphate

633

frictional behavior, 192 high-temperature behavior, 2 7 7 lubricant additive action, 2 4 6 , 280

Tresca-Huber-von Mises relation and friction mechanism, 153 and plastic yielding, 3 1 5 Tungsten dissociation of organic compounds on, 2 5 6 reaction with diethyl sulfide, 258

Tungsten diselenide, as solid lubricant, 5 7 9 Tungsten disulfide, as solid lubricant, 5 7 9 van der Waals equation, and lubr cation by gases, 107 van der Waals forces and contact of mica, 3 3 8 of mica surfaces, 2 3 2 Vinyl chloride, on iron surfaces Auger spectrometry, 2 5 9 Viscometers Cannon-Fenske (capillary), 6 7 Couette (rotational), 7 2 Ferranti-Shirley (cone-anddate). 7 5 high-pressure, high-temperature, 69,

77

rolling ball, falling sinker, 7 6 Saybolt (orifice), 78 Viscometry capillary, 6 1 , 6 5 , 6 6 of lubricating grease, 5 3 7 , 5 3 8 rotational, 7 2 under pressure, 6 9 Viscosity ASTM temperature charts, 8 1 definition of, 6 0 dynamic, 6 7 effect of pressure on, 8 3 gases, ideal and real, 1G7 high-pressure, 6 9 in fluid mechanics, 34 kinematic, 67 of lubricating grease, apparent, 5 3 8 of petroleum lubricating oils, 479

of synthetic lubricants, 5 0 8 ff. structures in lubricating oils, 491,

497

Walther equation, 7 9 theories of, 8 7 ff. temperature effect on scuffing, 458

Viscosity index, 8 0 of petroleum lubricating oils, 480

structures in lubricating oil fractions and, 4 8 7 , 4 9 5 Viscosity modifiers, response to pressure and temperature, 8 5

Walther equation, 7 9 Water vapor and lubricating action of molybdenum disulfide, 5 5 7 and lubricating action of graphite, 5 6 8 Wax in lubricating oil, removal of, 474

petroleum, chemical structures in, 4 8 9 , 4 9 8 Wear adhesion and transfer, 3 6 5 and film failure, 1 2 4 and film thickness, 1 2 9 basic definition, 3 4 9 catastrophic, 3 9 5 chemical reaction and, 3 6 7 combined mechanisms, 3 6 8 debris, formation of, 3 7 1 delamination mechanism, 3 7 4 deposited polymeric films, effect of, 2 3 6 disulfides and rate of, 2 6 8 dithiophosphates, effect of, 1 9 1 dry and lubricated, 3 6 2 elastohydrodynamic lubrication and, 4 0 1 fatigue, 3 6 7 four-ball test, and chemical properties of dialkyl dithiophosphates, 2 9 2 , 2 9 3 four-ball test, organochlorides, 274

four-ball test, organophosphates, 278,

281

four-ball test, organophosphites, 28 1

four-ball test, organosulfides, 270

four-ball test, zinc dialkyl dithiophosphates, 2 9 1 graphite fluoride, bonded, 6 0 2 impingement, 3 6 1 lubricated, additive-promoted, 4 18

lubricated, behavior, 4 0 2 lubricated by graphite fluoride, 576,

577

lubricated, nature of, 4 0 0 lubricated, running-in, 4 2 7 mechanical, definition of, 3 4 9 modeling of, 3 7 9 ff. molybdenum disulfide, effect on, 562

nomenclature, 3 7 5 non-metals, 3 6 3 of graphite, 5 6 8 Of organic plastics, 3 7 0 , 5 9 3 of steel, dry, 3 7 1 , 3 7 4 plastic deformation, 3 6 6 rate, models and mechanisms, 3 8 1 , 384,

388,

390,

394

reiterated sliding, 3 9 4 , 3 9 5 rolling motion, 3 5 9

634

sliding, behavioristic, 3 5 1 ff. sliding, rolling motion, 3 5 8 solid lubricant films, 5 9 4 sulfur, effect on, 2 4 3 sulfurized fats and rate of, 3 0 1 surface energy mechanism, 3 7 2 temperature and, 4 5 6 ff. temperature and lubricated, 4 6 7 Wear debris, from di-t-octyl disulfide and steel, 4 1 9 Wear loss rate, 3 8 3 Wear rate Archard's K-value, 3 8 2 , 3 8 3 geometrical parameters, 3 9 0 lubricated, theory of, 411 modeling of, 3 8 0 , 3 8 1 nomenclature, 3 6 3 variable, modeling of, 3 8 8 White oil, see a l s o Paraffin oil refining of, 4 7 6 sulfur as additive in, 239, 2 4 3

surface resin from, 2 3 9 temperature and friction, 1 9 2 viscosity characteristics, 5 0 9 Working of grease, 5 3 5 X-rays, and fluid film thickness, 121

Zinc dialkyl dithiophosphates additive action of, 2 4 7 , 290 as lubricant additives, 267 chemisorption on metal, 2 9 0 Zinc diisobutyl dithiophosphate, thermal decomposition, 2 8 9 Zinc diisopropyl dithiophosphate, thermal decomposition, 2 8 9 Zinc di-n-butyl dithiophosphate lubricant additive action, 2 9 1 thermal decomposition, 2 8 9 Zinc di-n-butyl phosphate, lubricant additive action, 2 9 1