The Third Body Concept: Interpretation of Tribological Phenomena : Proceedings of the 22nd Leeds-Lyon Symposium on Tribology Held in the Laboratorie De Mecanique Des contacts (Tribology Series)

THE THIRD BODY CONCEPT INTERPRETATION OF TRIBOLOGICAL PHENOMENA

TRIBOLOGY SERIES, 31 EDITOR: D. DOWSON

THE THIRD BODY CONCEPT INTERPRETATION OF TR IBOLOGICAL PHENOMENA edited b y

D. DOWSON", C.M. TAYLOR, T.H.C. CHILDS, G. DALMAZ, Y. BERTHIER, L. FLAMAND, J.-M. GEORGES, A.A. LUBRECHT *Principal Editor

Proceedings of the 22nd Leeds-Lyon Symposium on Tribology held in the Laboratoire de Mecanique des Contacts, lnstitut National des Sciences Appliquees de Lyon, France 5th-8th September 1995

ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Tokyo 1996 For the Institute of Tribology, the University of Leeds and lnstitut National des Sciences Appliquees de Lyon

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN: 0 444 82502 9

0 1996 Elsevier Science B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521,1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Sience BV, unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book i s printed on acid-free paper. Printed in The Netherlands.

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Proceedings of the 22"dLeeds-Lyon Symposium on Tribology INTRODUCTION

The 22nd Leeds-Lyon Symposium on Tribology was held at the Institut National des Sciences Appliquees de Lyon from Tuesday 5th to Friday 8th September 1995. Its central theme was: "The Third Body Concept: Interpretation of Tribological Phenomena". A topic which was chosen to honour the work of Professor Maurice Godet. The symposium opened on Tuesday afternoon with two keynote lectures by Professor K. Ludema from the University of Michigan and by Dr. Y . Berthier. The first lecture centred around the scientific work and the numerous publications of Professor Maurice Godet whilst the second one gave an impression of the life and work of Maurice Godet as perceived by a close collaborator. The organisers were happy to welcome to Lyon 143 delegates from 23 countries and it was once again a pleasure to receive a large and active representation of our sister organisation from the University of Leeds. The Symposium Review board had examined and selected abstracts from more than 90 submitted papers. In view of the large number of interesting proposals it was decided to organize two sessions in parallel during the afternoon. Furthermore, a reviewing process during the conference or directly afterwards, was organised in order to obtain an independent opinion regarding the quality of the proposed papers. This has led to a number of interesting discussions resulting in revisions or extensions of the papers presented. The organisers think the experiment has proved to be a valuable addition to the conference and are counting on continuing and extending it. They would like to thank all those who took part in this reviewing process, a complete list appears in the proceedings. The traditional symposium banquet was held in the Tasino le Lyon Vert'l. The dinner was prepared by the young and promising chef Philippe Gauvreau. On Thursday, the delegates attended a cultural evening organised by Ms V. Gylbert and Professor N. Gelas from the "Universite de la Mode" entitled: "Lyon, Fibres and Fashion Designers". It allowed the scientists a double view of Lyon: that of the historic capital of the silk industry, home of the "canuts" (weavers), and the modern one, a dynamic, creative and flourishing fashion centre.

vi

The usual Friday barbecue party was organised by the laboratory staff. The Saturday tour took some of the delegates to the Lake of Annecy. In the nearby bell museum, a special bell with inscription "Leeds-Lyon Symposium" was offered to the members of the University of Leeds. The organisers would like to thank all the members of the L.M.C. for participating in the organisation and thereby contributing to the success of the Leeds-Lyon Symposium. They would like to thank in particular Mrs. A.-M. Colin for handling the entire administration. The organisers gratefully acknowledge the financial support received from the following companies : FAG Schweinfurt, Germany SHELL Thornton, U.K. SKF Nieuwegein, The Netherlands SNR Annecy, France TIMKEN Colmar, France The Leeds-Lyon Symposia have now covered a wide range of topics, as shown in the following list. The essential aim is to select each year a topic of current interest to tribologists and to contribute to the further advance of knowledge in selected fields. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15.

16. 17. 18. 19.

20. 21.

22.

Cavitation and Related Phenomena in Lubrication Superlaminar Flow in Bearings The Wear of Non-Metallic Materials Surface Roughness Effects in Lubrication Elastohydrodynamic Lubrication and Related Topics Thernial Effects in Tribology Friction and Traction The Running-In Process in Tribology The Tribology of Reciprocating Engines Numerical and Experimental Methods Applied to Tribology Mixed Lubrication and Lubricated Wear Global Studies of Mechanisms and Local Analyses of Surface Distress Phenomena Fluid Film Lubrication - Osbonie Reynolds Centenary Interface Dynamics Tribological Design of Machine Elements Mechanics of Coatings Vehicle Tribology Wear Particles: From the Cradle to the Grave Thin Films in Tribology Dissipative Processes in Tribology Lubricants and Lubrication The Third Body Concept: lntcrpretation of Tribological Phenomena

Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds

1974 i975 1976 1977 1978 1979 1980 198 1 1982 1983 1984

Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

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We look forward to the 23rd Leeds-Lyon Symposium in Leeds from Tuesday 10th to Friday 13th September 1996 under the title: "Elastohydrodynamics: Fundamentals and Applications in Lubrication and Traction".

Ton Lubrecht

Gerard Dalmaz

viii

22nd Leeds-Lyon Symposium on Tribology "The Third Body Concept : Interpretation of Tribological Phenomena" Names of the reviewers

Adams M. Armbruster M. Bayada G. Berthier Y. Briscoe B. Cann P. Chaomleffel J.-P. Childs T. Coy D. Dalmaz G. Dowson D. Elrod H.

Flamand L. FrGne J. Georges J.-M Greenwood J. Jacobson B. Kapsa P. Kennedy F. Lubrecht T. Martin J.-M. Mathia T. Meurisse M.-H. Morales-Espejel G.

Olver A. Raous M. Schipper D. Sidoroff F. Singer I. Spikes H. Taylor C. Torrance A. Vannes B. Vincent L. Williams J.

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CONTENTS Introduction Session I

Session II

V

Keynote Addresses

1

Third Bodies : Perspectives on Modeling in Lubricated Contacts, in Close Fitting Contacts, etc : Following on the Concepts of Dr. Maurice Godet. K.C. LUDEMA

3

Maurice Godet's Third Body Y. BERTHIER

21

Invited Lectures

31

Stress Waves in a Sliding Contact Part 1 : Experimental Study T. ZEGHLOUL and B. VILLECHAISE

33

Stress Waves in a Sliding Contact Part2 : Modelling M. RAOUS and S.BARBARIN

39

Third Body Effect in Fretting J. WEI, S.FOUVRY, Ph.KAPSA and L. VINCENT

45

-

SESSION 111

Elastic Plastic Microcontact Modelling Using Dislocations I.A. POLONSKY and L.M. KEER

55

Third Bodies

67

The Surface Plasticisation and Lubrication of Poly (ether ether Ketone) by Third Body Formation B.J. BRISCOE and B.H. STUART

69

Third Body Formation and Friction Reduction on MolSIc Sliding in Reactive Gasses I.L. SINGER, Th. le MOGNE, Ch. DONNET and J.M. MARTIN

79

From Phenomenology to the Concepts Which Flow from the Third Body. Application to Radial Face Seal Y. BERTHIER, P. JACQUEMARD and M.H. MEURISSE

91

Mechanisms of Third Body Formation with Polymers. Role of Mechanical and Adhesive Interactions in the Friction and Transfer of Polyethylene M. BRENDLE and S.LAMOURI

103

Elusive 'Third Bodies' L. ROZEANU and F.E. KENNEDY

115

X

125

SESSION IV Third Bodies in EHL Direct Obsewation of Particle Entry and Deformation in a Rolling EHD Contact P.M.E. CANN, J.C. HAMER, R.S. SAYLES, H.A. SPIKES and E. IOANNIDES

127

The Entrainment of Solid Particles into Rolling Elastohydrodynamic Contacts R.S. DWYER-JOYCE and J. HEYMER

135

Behaviour of PTFE Suspensions in RollinglSliding Contacts S. PALIOS, P.M. CANN, and H.A. SPIKES

141

-

SESSION V

SESSION VI

Third Bodies in Wet Friction Couples In-Situ-Measurementwith Electrical Impedance A. PAUSCHITZ, G. MIKOLASCH, F. FRANEK and G. ABRAHAM

153

A Ball-in-Socket Apparatus for the Test of Hip Joint Prosthesis. Influence of the Third Body on the Friction Behaviour F. BERNARD, C. ANNARELLI, J. BERT, J. DUPUY-PHILON and J. FORNAZERO

161

Nanotribology

171

Nanometer Scale Mechanical Properties of Tribochemical Films S. BEC and A. TONCK

173

In-Situ Measurement of the Visco-Elastic Properties of a Sliding Lubricated Contact A. TONCK, D. MAZUYER and J.-M. GEORGES

185

Nanorheological Behaviour of Confined Liquid Layers for Normal Contact F. AUSLENDER and F. SIDOROFF

195

How to Achieve Contact Recording with a Low Stiction Force L. TOSl and B. BOU-SAID

205

Starved EHL

21 1

Starvation Phenomena in EHL Point Contacts : Influence of Inlet Flow Distribution F. CHEVALIER, A.A. LUBRECHT, P.M.E. CANN, F. COLIN and G. DALMAZ

21 3

Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and VI-Improvers B.R. HOHN, K. MICHAELIS and V. MANN

225

Waviness Orientation in EHL Point Contact P. EHRET, D. DOWSON and C.M. TAYLOR

235

xi 245

SESSION VII Thermal Aspects Study on Heat Transfer and Temperature Field of Rotating Friction Interface M. SATO, T. WATARAI, K. MIYATA, T. INAGAKI and Y. OKAMOTO

247

Three-Body Contact Temperature Fretting Conditions J. PEZDIRNIK, B. PODGORNIK, J. VlZlNTlN, M.KALIN and F. VODOPIVEC

257

Infrared Technique for Measuring Temperature Distributions in EHD Contact Zone. Part One : Technique. Part Two : Experimental Results W.X. QIU, S.Z. WEN and A.K. TlEU

271

An Iterative Heat Balance Technique for Rapid Estimation of Engine Bearing Temperatures A.O. MlAN and G.J. JONES

291 299

SESSION Vlll Invited Lectures

SESSION IX

Friction Modelling for Internal Combustion Engines D.DOWSON, C.M. TAYLOR and L.S. YANG

301

Non-Laminar Flow in Hydrodynamic Lubrication J. FRGNE and V.N. CONSTANTINESCU

319

Third Body Formation in Soft Solid Processing M.J. ADAMS, B.J. BRISCOE, E. PELILLO and S.K. SINHA

335

Granular Lubrication

345

-

SESSION X

Numerical Experiments with Flows of Elongated Granules Part II H.G. ELROD

347

Particulate and Granular Simulation of the Third Body Behaviour A. GHAOUTI, M. CHAZE, P. DUBUJET and F. SIDOROFF

355

Measurements and Modeling of Granular Flows in the Collisional Lubrication Regime J. KIM, C.-M. YU and J. TICHY

367

A Simple Model for Granular Lubrication; Influence of Boundaries A.A. LUBRECHT, C. CHAN-TIEN and Y. BERTHIER

377

Solid Lubricants

387

Tribological Behaviour of Solid Lubricated Contacts in Air and HighVacuum Environments C. DONNET, M. BELIN, Th. le. MOGNE and J.M. MARTIN

389

Self-Lubricant "Mosaic" Surfaces of Type 316 Austenitic Stainless Steel G. ZAMBELLI, J.-F. CARTON, P. CHEVALLIER and J.-D. WAGNIeRE

401

Role of the Third Body in Life Enhancement of MoS, K.J. WAHL and I.L. SINGER

407

Significance of Transfer Layers for Dry Frictional Applications R. HOLlNSKl

415

xii

SESSION XI

Hydrodynamic Lubrication

42 1

Pressure Drop in Hydrostatic Pocket. Experimentaland Theoretical Results M. ARGHIR, S.E. ATTAR and D. NICOLAS

423

Application of the Homogenization to Thin Film Gas Lubrication G. BAYADA and M. JAI

433

Boundary Conditions for Reynolds Equation with Particular Reference to Piston Ring Lubrication M. PRIEST, R.I. TAYLOR, D. DOWSON and C.M. TAYLOR

44 1

Effect of Compliance on the Extent of Optimum Compliant Air Thrust Bearing Operating Range I. IORDANOFF, P. HERMEL and P. STEPHAN

453

Experimental Measuring of Velocity Profiles in Herringbone Grooved Journal Bearings J. ABSl and D. BONNEAU

46 1

SESSION XI1 Coatings

469

An Investigation Into the Properties of a Thin Solid Coating Using an Optical Method A.V. OLVER, P.M. CANN and J.-C. LORIC

471

Tribological Analysis of Friction Damage on Coated Plastics Through the Third Body Concept. J. DENAPE, P. ETIENNE, J.-Y. PARIS, J. PHALIPPOU and R. SEMPERE

479

Friction and Wear Behaviour of Plasma-Sprayed Cr203Coatings in Dry Sliding Against AlSl D2 Steel J.E. FERNANDEZ, YINGLONG WANG, R. TUCHO and A. RINCON

489

SESSION Xlll Dynamic EHL

499

Kinematics of Roughness in EHL G.E. MORALES-ESPEJEL, J.A. GREENWOOD and J.L. MELGAR

501

Influence of the Sliding Speed on the Elastohydrodynamically Lubricated Film Thickness Shape of Wavy Contacts F. COUHIER, A.A. LUBRECHT, D. NELIAS and L. FLAMAND

515

Surface Roughness Modelling for Piston Ring Lubrication : Solving the Problems M. VISSCHER, D.DOWSON, C.M. TAYLOR

527

Numerical Solution for Elastohydrodynamic Analysis of High Pressure Sleeve Seal H. XU, P.L. WONG and Z. ZHANG

539

The Evaluation of the Minimum Film Thickness in Ball-Plane Impact Experiments I. MUSCA, T. MOROSANU and E.N. DiACONESCU

545

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SESSION XIV Invited Lectures

553

How Lubricants Behave in EHL Contacts B. JACOBSON

555

Elastohydrodynamic Films with Emulsions Y. KIMURA, K. OKADA and W. LIU

563

Understanding Grease Lubrication P.M.E. CANN

573

SESSION XV Surface Degradations

583

Smoothing Effect of the Third Body Compaction on Alumina Surface in Sliding Contact K. ADACHI, K. KATO and R. TAKIZAWA

585

Friction in Abrasion of Alumina Fibre and Silicon Carbide Particle Reinforced Aluminium N. AXEN

597

Adhered Film Formation on Steel Surface by Impingement of Hard Particles N. HAYASHI, Y. KAGIMOTO and H. AKIYAMA

605

A Wear Mechanism of Ductile Metals by Slurries : Fatigue or Ratchetting? A.A. TORRANCE, Y. YANG BLAKE and B. CROSBY

615

Surface Degradationand Third Body Formation in Tribocorrosion Systems S. MISCHLER, S. DEBAUD, E.A. ROSSET and D. LANDOLT

623

Modelling Fluid Interactions in Magnetic Fluid Grinding T.H.C. CHILDS and F.Y. CHANG

631

SESSION XVI Friction

639

A Justification of Friction Laws J.-F. GANGHOFFER, A. BRILLARD and J. SCHULTZ

641

Friction of Sliding Surfaces Carrying Adsorbed Lubricant Layers J.A. WILLIAMS AND Y. XIE

651

Effects of Thin Layer on friction and Wear of Cast Iron Under Severe Sliding Conditions K. HAYASHI, K. HIRASATA, K. YAMAMOTO and K. SUGITA

665

-

An Elastic Plastic Model with Adhesion for the Sphere-Flat Contact A. TUDOR and L. SElClU

675

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SESSION XVll MixedlBoundary Lubrication

683

An Examination of Additive Debris to Give insight into Boundary Lubrication J.S. SHEASBY, T.A. CAUGHLIN, S. TERRANOVA and A. COHEN

685

The Influence of SlidelRoll Ratio on the Film Thickness of an EHD Contact Operating Within the Mixed Lubrication Regime M. SMEETH and H.A. SPIKES

695

The Influence of Plastic Bulk Deformation on Surface Roughness and Frictional Behaviour During Deep Drawing processes H. LUBBINGE, R. ter HAAR and D.J. SCHIPPER

705

Written Discussion

71 3

List of Delegates

749

SESSION I KEYNOTE ADDRESSES

Chairman :

Professor Gerard Dalmaz

Paper I (i)

Third Bodies : Perspectives on Modeling in Lubricated Contacts, in Close Fitting Contacts, etc: Following on the Concepts of Dr. Maurice Godet

Paper II (ii)

Maurice Godet's Third Body Approach

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

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THIRD BODIES: PERSPECTIVES ON MODELING IN LUBRICATED CONTACTS, IN CLOSE FITTING CONTACTS, ETC: FOLLOWING ON THE CONCEPTS OF DR. MAURICE GODET K. C Ludema Mechanical Engineering Department, University of Michigan G.G. Brown Building, Ann Arbor, MI, 48109-2125 The third-body concepts have advanced the field of contact mechanics, friction and wearto the point where broad-ranging modeling has begun. To date third-bodies have been modeled as powders or aggregates of solid particles. Several additional properties must be included in the future, including the role of two phase third-bodies, third-bodies that expand to fill restricted spaces and the sizes of third-body particles relative to clearance spaces. The latter is likely to be controlled by the surface free energy properties of the third-body substances. 1. INTRODUCTION Third-body mechanics is synonymous with Dr. MauriceGodet. He began in 1963 with an emphasis on hydrodynamic lubrication, often applied to such hardware as gears, cams, bearings,face seals etc. A year later A8 he wrote the first of several papers attempting to rationalize the many different equations for calculating wear rate. He next explored the composition and nature of boundary films *18 including wear particles. From the very start of his career he waspreparing the ground workfor the third-body concept, which was a major achievement. This paper offers a perspective on how materials oriented research can extend Godet’s concepts.

2. “THIRD-BODY CONCEPTS 2.1. Understanding third bodies In 1974 A64 Godet began a line of reasoning on the mechanics of friction, pointing out that interfaces have some content and are not simply the conjunction of two semi-infinite solids. The interface region consists of “an oil film, an oxide, an extreme pressure film, a thin coating, etc” and was referred to as the “third-body”. (By

indirection, the two macroscopic sliding members were both identified as “first-bodies”.) In most practical conditions the content of the third-body varies with time, with short term variations depending on operating conditions, and long term variations depending on duty cycles, amount of wear, etc. We do not see that the fluid constituents in the third-body are seriously considered, probably because o f modeling difficulties. In 1977 A82 Godet stated a most important caveat in the efficacy of third-bodies, “in all contact conditions which perform satisfactorilv,a thin film or third-body separates both machine elements.” From this work the conviction grew that contact shape and duty cycle of sliding are important. This has great bearing on theoretical equations on friction and wear. In 1977 A83 the first of the results appeared in which the wearing of chalk (sticks)was studied. The general flow of debris could be visualized by sliding chalk of various colors in repeat passes. To manyobservers these papers did not seem particularly relevant or scholarly, but they were rather graphic and proved to be most helpful in understanding wear. Chalkdebris was

4

found to contain particles with $.imensions t h a mav be less than 1%of the thinnest dimension of the third bodv film. 2.2. The Load Carrying Capacity of Third-Bodies In 1978 A92 third bodies were seen to cany loads just as hydrodynamic films do, and, by analogy with liquids there should be some way to calculate bad carryi* of third-body layers. To do so requires an estimate of a velocity field in the third-body bulk but there are serious impediments to doing so. First,there is too little material for measuring relevant properties. Secondly “the solid third bodies observed on the rubbing surfaces at the end of the experiment are not necessarily representativeof the operational materials which govern the test.” Thirdly, the flow field in thirdbodies are not likelyto be similarto that in fluids. These discussions were rather ethereal, but they did show that contact shape, machine rigidity, etc are probably as important in third body flow as it is in hydrodynamic lubrication. To this point it is difficult to discern in the papers just how the concepts of hydrodynamics could be applied to third-bodies composed of solid particles. In 1980 *loo Godet elaborates, “leaving aside the rather formidable mathematical difficulties that such a study subtends there seems to be, offhand, no fundamental reason why this extension could not be done if the necessary information were made available” He further points out that those with an interest in continuum mechanics have good potential for achieving this goal because they have already learned how to describe solids, liquids, visco-elastic materials, granular substances and powders in their own terms. In 1980 again, A102 and 1984 Godet points out that virtually all existing wear equations are built on the assumption that small bits of material are loosened from (an inexhaustible and steady supply from) one

surface or other, and immediately lost from the system, having served no useful purpose. However, if some particles remain to form the third-body, even those that are abrasive, then some of those variables that are important in hydro-dynamics must also be important in retaining particles in the contact region, such as shape of contact, entry conditions, path of sliding, system vibration, degrees of freedom, etc. A complete study of wear should therefore consider the ratesof particle entry into and loss from the third-body mass. In 1984 A1 l 6 attention turned to fretting and the load-carrying-capacityof fretting particles. Fretting is an attractive process to study because the loose particles can be formed quickly but are not a highly cohesive. Now the term “surface protection” appears. The fretting particles provide a load-carrying-capacitymuch like that of deliberately applied oxide particles and other powders. Inthe papers of the late 80’sthere are several on material analysis of third-bodies. Though particle size and morphology were reported, there was little progress on identifying the nature of the attractive forces between thirdbody particles, and little on those factors that induce a particle to leave the first body and become a part of the third-body. 2.3.Mechanisms of flow within the third bodies In 1990 A174 Godet showed how third-body “flow” (now described as “velocity accommodation”) differs from that in liquid. In liquid there is only one mechanismwhereas in third-bodies 20 were proposed. There are 5 sites, ie, 2 first-bodies, two screens (which control adhesion) and one third-body. In each there may be 4 velocity accommodation mechanisms, namely, elastic deformation, plastic shear, rupture and rolling. Berthier expands slightly on these points by pointing Out that some of the 20 are likely to not be

’

5 operative, eg., rolling of first-body materials, and several of the suggested modes in the screen layers because of their small size, = 10-9 m. 3. A MATERIALS RESPONSE TO THE THIRD BODY CONCEPT The third-body concept is interesting in itself and will doubtless contribute to the uttimate complete understanding of wear processes. However, it also reveals something about how thought is developed in the broader tribology community. For decades those in the materials disciplines have considered wear models based on continuum mechanics as incomplete. Existing models usually ignore those entities that materials people are keenly aware of, namely, oxides and adsorbed gas layerson all solid surfaces. The latter are essentially viscous in behavior, further complicating efforts to model. Materialspeople view “adhesion” as far more complicated than a binary phenomenon, rather, adhesion “strength” is highly variable from low values to high values depending on atomic structure and many other factors. Furthermore, adhesion exists throughout the entire third-body layer and not only at its boundaries. The materialscommunity had observed the behavior of “third bodies” for many years. Mailander and Dies in 1943 noted that when changes occur in contact pressure or sliding speed, there is a corresponding change in composition of the debris, which composition was presumed to exist also in the loose particles in the contact region. Johnson, Godfrey and Bisson in 1948 mentioned that “oxides (that) formed on rubbing surfaces. . . function as lubricants” and aFe304 is better than Fe2O3. Finch, Quarrel1 and Wilman showed in 1935 that wear is dominated by the specific properties of the oxide films formed by sliding and by the

*

manner in which the oxide is attached to the underlying metal. Tingle in 1947 showed the same but in fretting conditions. Some authors in the materials community have attempted to connect oxide properties, oxidation rates and other variables with their tribological behavior, but they have not developed general equations for wear rate or wear resistance from these observations. Several materials-oriented authors have developed equations in the manner of continuum mechanics, but emphasized the fracture properties of the materials in addition to those properties relating to the calculation of real contact area between surfaces. Returning to the two phase (liquid and solid) composition of third-bodies, some studies have shown that hydrocarbon lubricated iron and steel surfaces acquire coatings of Fe304 and a (non-polymeric) organo-iron compound. These latter could be referred to as “fourth-bodies’’ in that they are chemically and mechanically distinct from the oxide beneath. These coatings develop over time of sliding and are found to provide short time load carrying capacity until the total film thickness decreases to about 7 nm. In these experiment the coefficient of friction of dry steel on steel was about 0.25 whereas for the coatings, after removal of liquid phase oil friction was reduced to about 0.12. In experiments done over a range of sliding speed, the coefficient of friction was constant, suggesting that the composite film was behaving as a plastic solid rather than as a viscous liquid. Tichy has recently modeled the behavior of two viscous layers, which should help advance the cause of boundary lubrication. Third bodies of proper properties can prevent scuffing and galling, but in close fitting contacts, they can be detrimental. A coherent layer of Fe304 is about 3 times as thick as the “layer” of

’

original iron removed from a wearing surface, but a fragmented layer is about 5 times as thick,. Thus, if the radialclearance between ashaft and sleeve bearing is 50 pm, only 10 pm loss from the shaft will fill the clearance space. If oxide particles are not removed by large motion or by flow of lubricant the oxide willcontinue to grow and produce an interference fit (as in fretting). However, few such efforts have culminated in models incorporating the observed thirdbodies. The great majority of materials-based researchers prefer to express their observations in the form of micrographs and various (x-ray, electron, etc.) spectra. 4. THE MODELING IMPERATIVE The long term reality of topics in science and engineering is that the mathematical approach is mandatory. Virtually every topic relating to the design of mechanical products is described in the form of equations, including hydrodynamic lubrication. Dry friction and wear are not. Most modeled topics are relatively simple, involving few variables. By contrast, wear phenomena involve over 100 variables. In a search of the literature *, over 182 equations were found for predicting wear rates, and about 50 were found for friction. These equations were collected in the hope that some of them could be harmonized, particularly those “for a single mode of wear”. It was distressing to find that some parameters such as Youngs modulus, fracture toughness or hardness are found in the numerator of some equations but in the denominator of others! The many equations for solid particle erosion, a seemingly simple form of wear, were analyzed in detail. These were “graded” for reliability, applicability and completeness, and 28 were found to be useful as a basis for further analysis. These 28 equations contain 33 rational parameters: some contain additional constants of proportionality, lumped parametersand other

constants that represent phenomena that are not readily measurable. Table 1 shows the distribution of usage of the parameters in the 28 equations. No two equations for a given material pair contain the same array of parameters, thus harmonizing is not possible. It is instructive to consider the wide range of exponents on V, the particle velocity: these range from 2 to 5, averaging about 3. An exponent of 2 would accord with our intuition that erosion rate might be related to the momentum of the impacting particle. The wide range of exponents probably do show that momentum considerations are invalid, but may rather suggest other possibilities. These include: a. Some important parameter is missing and its omission is indicated by unexpected behavior of included variables, b. Relevant materialsproperties are not used. For example, the values of hardness, fracture toughness, flow stress and perhaps others were likely values taken from standard, quasi-static tests, whereas the operative properties in the vicinity of an impacting particle would be dynamic hardness, dynamic fracture toughness, et al. c. Not all of the material properties represented are unique or independent. Unfortunately, there are insufficient data accompanying published equations for in-depth analysis of the variables used by various authors.

a

5. THE CHALLENGE : THE GODET LEGACY Maurice Godet had seen very clearly that the modeling of friction and wear awaits better characterization of the existing substances in the interface between passing solids, particularly their dynamic changes. Godet and his highly competent colleagues have convinced us of the need to consider both the mechanical dynamics of the sliding system and

7 the need to consider the third-bodies as “flowing substances” of ever changing composition and “load carrying capacity”. Indirectly he has shown the inadequacy of equations for friction and wear based on the concepts of area of contact, constant surface topography and “mechanisms” of wear. lconcur in his assessment, and doubtless many others do too. 6. A FURTHER SUGGESTION Tribologists like to develop equations for friction and wear “from first principles”. Unfortunately we can never be assured that all relevant “first principles” are in hand or are properly represented. indeed, many authors of equations have attempted to validate their equations with experimental data, but the experiments are usually “contrived” to achieve reproducibility more than reality. When experiments do not validate an equation, reasons for mismatch are usually obscure. It may be helpful to try a new approach. System Identifi~ation,~ is a method used to characterize a mechanical or electrical “black box” from input data and output data only. An equation, or model of the “black box” properties is written as a first approximation, and this equation “operates upon” the input to the black box to see if the result matches the system output. If not, some rather well developed computer based methods are used to alterthe first model, and this proceeds until there is an adequate match. This can be done for friction and wear as well. The current and apparently solvable problem with the methods of System Identification relates to the need to “discretize” the models, in which case the parameters become sub-divided and difficult to reassemble at the end of the process. There are some very good data in the literature on the wearing of simple materials, in air, that can be used in analysis by the methods

of System Identification. These are the data of Lancaster l o shown in Figure 1, and of Welsh shown in Figure 2. These data have been confirmed by numerous duplicate tests done by students at the University of Michigan. The work would surely require treating the oxides and other third-body constituents on these sliding surfaces as flowing substances. I suggest that a new GODET TRIBOLOGY MODELING PRIZE be awarded for the development of equations that accurately model the wearing processes observed by Lancaster and Welsh. Such a prize, awarded annually, would revolutionize our field. REFERENCES 1. Y. Berthier Wear 139, 1990 p 77-92 2. R. Mailander and K. Dies, Archiv fur das Eisenhuttenwessen, v. 10, pp. 385 and 399, 1943 3. R.L. Johnson, D. Godfrey and E.E.Bisson, NACA Tech Note #1578, 1948 4. G.I. Finch, A.G. Quarrel1 and H. Wilman, Trans. Faraday SOC.v. 31, p. 1051, 1935 5. E. Tingle, Collected Research on Cylinder Wear, (UK) Inst. Auto. Engineers, 1947 6. B. Cavdar and K.C Ludema, WEAR, v 148, p. 305-361, 1991 7. J. Tichy, Tribology Transactions (STLE), V. 38, p. 377-381, 1995 8. H.C. Meng and K.C Ludema, WEAR, V. 181-183, p. 443-457, 1995 9. G. Hsu, “Stochastic Modelling and Identification of Lubricated Polymer Friction Dynamics”, PhD thesis, The University of Michigan, 1995 10. J.K. Lancaster, Proc. Roy. SOC.(Lond) V. A 273, p. 466-483, 1963 11. N.C. Welsh, Phil. Trans.Roy.Soc. (Lond.) v. A 257. (pt 1, p. 31), (pt 2, p. 51), 1965 Appendix: The Godet papers

8

APPENDIX

( "A"

references listed below)

PUBLICATIONS OF DR. MAURICE CODET AND COLLEAGUES, SUPPLIED BY DR. G. DALMAZ OF INSA 1. BORSOFF V.N. el GODET M.

A scoring factor for gears". ASLE Trans. 6, p. 147-153, 1963. 2. GODET M.

"La thhrie des deux lignes, la lubrification des engrenages". C.R. Acad. Sc., Paris, 1.257, p. 4851, 1963.

10. GODET M. et BORNEMANN R. "La lubrication avec les mttaux liquides ii bas point de fusion". Rev. I.F.P., vol. X X , no 10, p. 1575-1599,octobre 1965. 11. GODET M.

"Hydrodynamique et thermique dans la lubrification des engrenages". Rev. SOC.Belge Mec., vol. 11, p. 62-67, 1965 12. VICHARD J.P. el GODET M.

"Applicationsde quelques principes aux machines classiques d'essai d'usure". C.R. Acad. Sc., Paris, t. 262, p. 532-534, fevrier 1966.

3. GODET M. "Reflexion thtoriques et expCrimentales a propos dc la recherche sur la lubrication des engrenages dans les applications de la science a I'industrie". La Machine-Outil Franqaise: . lEre partic no 193 (1963) .2Cmc partie no 194 (1964) .3eme partie no 195 (1965)

13. VICHARD J.P. et GODET M.

4. GODET M.

14. RAFFY J.C. et GODET M. "Le calcul dcs engrenages coniqucs droits a

"La thCorie des deux ligncs. Essais des lubricants". C.R. Acad. Sc., Paris, 1. 258, p. 71-74, 1964. 5. GODET M.

"Elastohydrodynamics in lubricant testing". Eng. 334, f6vrier 1964. 6 . GODET M. "La notion de contact dans Ics engrenages IubrifCis". C.R. Acad. Sc., t. 258, p. 443 1-4433, mai, 1964.

7. GODET M. et BORNEMANN R. "Une nouvelle famillc de lubrifants, les mCtaux liquides. Essais 2 150" C sur machine a quatre billes". La Machinc-Outil Franqaise, no 201, aolt-septembre 1964. 8. GODET M.

"Les aspects modernes de I'hydrodynamique des contactS IubrifiCs". Rev. I.F.P., vol. XXI, no 7-8, p. 1088- 1 130.

dCveloppantc dc cercle sphtriquc". Bull. S.E.I.E., p. 30-49, octobre 1967. 15. VICHARD J.P. et GODET M.

"Le banc d'cssai e l la loi d'usure". J. GAMI, numtro spkial: le frottemcnt et I'usure", 1967. 16. RAFFY J.C. el GODET M.

"La validid de I'approxjmation de Tredgold pour les engrenages coniques droits". Bull. S.E.I.E., no 245, janvicr 1968. 17. GODET M. "Corrtlation et divergences des rnkthodes d'essai du pouvoir lubrifant des huiles". a) J.S.I.A., t, XL,no 12, p. 625-636, 1967. b) Rev. A.F.T.P. (rnars-avril 1968).

"Introduction aux fondements thkoriques du calcul de I'usure des pikes de machines", par Pronikov AS. La Machinc-Outil Franqaise, no 203, novembre 1964.

18. VICHARD J.P. et GODET M.

9. VICHARD J.P. et GODET M. "Conditions restrictives dans Ics dispositifs exp6rimentaux de I'ttudc dc I'usure". C.R. Acad. Sc., Paris, t. 260, p. 5472-5, rnai 1965.

19. GODET M. et VICHARD J.P.

"Comportemcnt de ccrtains films hydrodynamiqucs minces en regime transitoire". C.R. Acad. Sc., Paris, strie, A, t. 266, p. 254-258, 1968. "Mechanical aspects of boundry lubrication". Proc. Inst. Mcch. Engs. vol. 182. pt. 3A, pi. 3A, p. 389-390,1967-1068.

9

20. VICHARD J.P., RAFFY J.C. el GODET M. "Transient effects in the hydrodynamics of spurgear lubrication". Proc. Inst. Mech. Engs., vol. 182, pt. 3A, p. 257-258, 1967-1968. 21. VICHARD J.P. et GODET M. "Simultaneous measurements of load, friction and film thickness in a cam and lappet system". Proc.Inst. Mech. Engs., vol. 182, pt. 3G, p. 109-113, 1967-1968. 22. SCHAEFFER G. et GODET M. "Etude haute temptrature des paliers lisses fortement chargts". a) "Le frottement et I'usure". Journees d'Etudes des 20-21 mars 1968, Paris, p. 79-85, GAMI-ISMCM. b) "Mtcanique ElectricitC", revue GAMI no 240, p. 21-27, decembre 1969. 23. VICHARD J.P. et GODET M. "Lubrification hydrod ynamiquc des contacts hertziens". a) "Le frottement et I'usure". J d'Etudes des 20-21 mars 1968, Paris. b) "MCcanique Electricid". Revue GAMI, no 234-235, p. 35-46, juin-juillet 1969. 24. GODET M. "Gear lubrication". Mech. Eng., p.67-70, mai 1970. 25. FANTINO B., FRENE J. et GODET M.

"Conditions dutilisation de I'kquation de Reynolds en mkcanique des films minces visqueux". C.R. Acad. Sc., Paris, t. 272, p. 691-693, mars 1971. 26. DEYBER P. et GODET M. "Contact temperature in mixed friction". Tribology, vol. 4, n"3, p. 150-154, aodt 1971. 27. FRENE J. et GODET M. "Transition from laminar to laylor vortex flow in journal bearings". Tribology, vol. 4, no 4, p. 216-217, novembre 1971. 28. GODET M. "Sur le regroupement des probkmes qui traitent de la lubrification et du froltement". C.R. Acad. Sc., Paris, t. 273, p. 999-1002, novembre 1971.

29. GODET M. "Fondements mkaniques de la uibologie". a) Journees d'Etudes GAMI sur I'usure, Paris, 1970. b) Mecaniques Materiaux Electricile, I'usure, t. 2, p. 34-44, ler trimestre 1972. 30. BERTHE D. et GODET M. "Equation de I'koulement laminaire entre deux parois rapprochkes en mouvement relatif'. C.R. Acad. Sc.,Paris,t. 272,p. 1010-1013,avril 1973. 31. GODET M., FRENE I., BERTHE D., PLAY D. "Effets mkaniques inuoduits par la formation et la prtsence de films en surface". Memories Techniques CETIM, vol. 11, p. 7-14, mars 72. 32. DALMAZ G. et GODET M. "L'hydrodynamique du contact sphere-plan". Premiere partie solution thkorique numerique exacte en regime tqui et piCxovisqueux. Mtcanique MatCriaux ElcctricitC, revue GAMI, no 268, p. 32-34, avril 1972. 33. DALMAZ G. el GODET M. "An Apparatus for the simultaneous measurement of load, traction and film thickness in lubricated point contacts". Tribology, p. 1 1 1-1 17, vol. 5, no 3, juin 1972. 34. FANTINO B. FRENE J. el GODET M. "Reynolds equation in viscous film theory". ASME JOLT, v. 94, no 3, p. 287-288, juillct 1972. 35. GODET M. et PLAY D. "Les fondements de la uibologic". CAST, "Aspects modemes de la lubrification", p. 5-22, Lyon 20-22 septembre 1972. 36. GODET M. "Le frottement mixte ct lcs cssais mecaniques des huiles". CAST, "Aspects modcrnes de la lubrification", p. 173-196, Lyon 20-22 sept 1972. 37. DALMAZ G. et GODET M. "L'hydrodynamique du contact sph6re-plan". Deuxieme partie: Mcsure dc la charge, de la f orce de frottement ct dttermination de la ghmCtrie du contact en glisscmenl pur". Mtcanique MatCriaux ElcctricitC, revue GAMI, no 272-273, p. 9-18, aoih-septcmbre 1972.

10

38. NICOLAS D., FRENE J., et GODET M.

"Theory of tilting torque permissible in plain bearings". Int. Symp. on plain bearings, vol. 1, p. 105-120, Vysoke Tatry, TchCcoslovaquie, 24-26 octobre 1972. 39. FRENE J., NICOLAS D et GODET M.

"Characteristics of plain turbulent bearings". Int. Symp. on plain bearings, vol. 1, p. 173-186, VysokC Tauy, TchCcoslovaquie, 24-26 oct 1972. 40. FRENE J., NICOLAS D. et GODET M.

"Taylor vortices in Couette flow". Int. Symp. on plain bearings, VysokC Tatry, Tome 4. p. 989-992.24-26 octobre 1972.

48. FRENE J. et GODET M.

"DCtermination par sondc paribtale, du changement de regime de I'Ccoulement entre deux cylindres excentrts de rayons LrEs voisins". C.R. Acad.Sc.,Paris, 1.276, p.1133-1136,av. 1973. 49. GODET M.

"Le travail des forces et dcs couples extCrieurs en uibologie". C.R. Acad. Sc., Paris, t. 276, p. 1381-1383, mai 1973. 50. PLAY D. et GODET M.

"Le frottement: des fondements h I'application".' lbre partie, la Sussie HorlogCre, no 18, p. 513-S17,3 mai 1973., 2bme partie, la Sussie HorlogCre, no 20, p. 557-581, 17 mai 1973.

41. FRENE J. el GODET M.

"La prtance et le couple rCsistant d'un palier lisse fonctionnant en rCgime non laminaire". MCcanique Madriaux ElectricitC, revue GAMI, no 274, p. 18-29, octobre 1972. 42. GODET M.

"Hydrodynamics in lubricant testing". Wear, vol. 22, no 3, p. 4 15-417, dCcembre 1972.

51. DEYBER P. et GODET M.

"Le frottement et I'Climination des films exu&mc pression dans la lubrification mixte". Mkanique Mat&. Elec., revue GAMI, no 280, mai 1973. 52. FRENE J. et GODET M.

"Etude des regimes de wansition dans les paliers lisses". Rev. Roum. Sci. Techn. MCc. Appl., tome 18, no 4, p. 601-631, Bucarest, 1973.

43. DEYBER P. et GODET M.

"DCterminadon de la distribution de charge dans le frottement mixte par la mesure de la tempbrature de contact, application h I'essai d'huile". MCcanique Matbriaux ElectricitC, revue GAMI, no 276, p. 2-18, decembrc 1972.

53. GODET M.

"La mesure de forces el de couples de frottement purs". Rev. Roum. Sci. Techn. M k . Appl., t. 18, no 5, p. 1007-1016, Burcarest, 1973. 54. FRENE J. et GODET M.

44. LOHOU J., HAARDT R. et GODET M.

"Effects de porlance hydrodynamique dans les joints d'CLanchCitC h fuite radialc". MCcanique MatCriaux ElectricitC, revue GAMI, n026S, 46me uimesue 1972. 45. MICHAU B., BERTHE D. ct GODET M.

"Le pitting dans les mkcanisines IubrifiCs". Journal S.I.A., IngCnieurs de I'automobile, p. 34-43, no 1, janvier 1973. 46. GODET M.

"L'effet des dCformations dans la mesure de la force et du couple de rrottemcnt". C.R. Acad. Sc., Paris, t. 276, p. 771-774, mars 73. 47. LOHOU J. et GODET M. "Angular mi sa 1i gnem en t and squeeze-fi 1m effects

p. D2-Dl5 A D2-D28,1973.

"Detection of Taylor vortex transition in very small clearances by hot film wall anemomeay". Tribology, vol. 6, no 5 , p. 178-183, octobre 1973. 55. DALMAZ G. et GODET M. "Traction load and film thickness in lightly loaded

lubricated point contacts". J. Mech. Engr. Sci, I.M.E., v. 15, no 6, p. 400-400. dccembre 1973. 56. MICHAU B., LAFONT F., BERTHE D. et

GODET M. "Influence de la distribution de pression henzienne a I'intCriew d'un contact". Mechanique Materiaux Electricite. Revue GAMI, no 288, p. 14-19, dtccmbre 1973.

11

57. FRENE J. et GODET M.

"Performance of plain journal bearing operating under vortex flow conditions". ASME JOLT, vol. 96, no 1, p. 145-150, janvier 1974. 58. FRENE J. et GODET M.

"Flow transition criteria in a journal bearing". ASME JOLT, vol. 96, no 1, p. 135-140,jan. 1974.

67. GODET M., CAUBET J., BRUSSON J.P.,

CHAMF'IN B., VINCENT L., COQUILLET B., GUIRALDENQ P., LAFONT R., PENNEQUIN, MICHAU B. et BERTHE D. "La fatigue superficielle dans les mCcanismes lourdement chargb". Journee d'dtude du 23 nov. 1973, INSA Lyon. Revue Energie Fluids. . lCre partie no 68, p. 47-52, fevrier 1974. .2Cme partie no 69, p. 61-66, mars 1974.

59. MICHAU B., BERTHE D. et GODET M.

"Les avaries dans les roulements". Energie Fluide, no 67, p. 47-56. janvier 1974. 60. NICOLAS D. et GODET M.

"Comportement dun palier lisse soumis h un torseur de forces exttrieurcs quelconques". MCcanique MatCriaux ElectricitC, Revue GAMI, no 289, p. 22-28, janvier 1974. 61. NICOLAS D. et GODET M.

"Etude thdorique et expCrimentale du comportement d'un palier lisse soumis h une charge excen trdc" .MCcan ique Makri. Elect., revue GAMI, no 290, p. 34-39, fevrier 1974. 62. GODET M.

"Research reports". Laboratoire de Mecanique des Contacts. Tribology, v.7, no 1, p.33-36, fev 1974. 63. BERTHE D. el GODET M. "A more general form of Reynolds equation.

Application to rough surfaces". Wear, vol. 27, no 3, p. 345-357, mars 1974.

68. GODET M., PLAY D., BERTHE D. FRENE J. "Tribomvcanique". Rheological Acta, vol. 13, no 2, 1974. 69. MICHAU B. et GODET M.

"Observations of oil pressure effects in surface crack development". Tribology International, p. 119-122,juin 1974. 70. DALMAZ G. et GODET M.

"Effets des conditions d'alimentation sur 1'Cpaisseur du film dans les conkcts hcrwicns lubrifiis". MCcanique MatCriaux Elcctricitt5, Revue GAMI, no 269-297, p. 25-34, aofit-septembre 1974. 71. FANTINO B., FRENE J. et GODET M.

"Influence des dCfauts de [orme dans la lubrification hydrodynamique". MCcanique MatCriaux Electricitb, Revuc GAMI, no 296-297, p. 35-43, aoQt-septembre 1974. 72. BERTHE D., FANTINO B., FRENE J. "

64. GODET M.

"Surface and shape effccts in the measurement of friction forces". Wear, Vol. 28, no 1,p. 115-124, avril 1974. 65. BERTHE D. et GODET M.

"Elastohydrodynamic lubrication of rough surfaces in pure rolling". Tribology, v.7, p.67-69, av1974.

et GODET M. Influence of shape defects and surface roughncss on the hydrodynamics of lubricated systems". Journal of Mechanical Engineering Science, vol. 16, no 3, p. 156-159, 1974.

73. ROZEANU L. et GODET M.

"The phenomenology of friction thermal failure". Inter. conf. Proc. Eng., Toyko, p.396-401, 1974. 74. GODET M. et DEYBER P.

66. MICHAU B., BERTHE D. et GODET M. "Influence of pressure modulation in a linear

hertzian contact on the internal stress-fields" Wear, vol. 28, p. 187-195, 1974.

"La lubrification extr&me-pression: I'apport hydrodynamique et al formation de films". Specialists meeting on fretting in Aircraft systems, AGARD Conference proceedings, no 161.6-12 octobre 1974.

12 75. PLAY D. et GODET M.

"Frottement et usure de fibres de carbone dans une matrice tpoxy". Colloques internationaux du CNRS, no 233. PolymCres e l lubrification, 20-23 mai 1974. Brest.

85. BERTHE D., FLAMAND L. et GODET M.

"La lubrification dcs comcts hcrtziens et application aux engrenages". Congr mondial des Engrenages, v. 1, p.407-422,Paris,22-24 juin 1977. 86. FLAMAND L., BERTHE D. el GODET M.

76. GODET M. et PLAY D.

"Introduction to Tribology". Colloques intemationaux du CNRS, no 233. PolymCres el lubrification, 20-23 mai 1974. Brest. 77. PLAY D. et GODET M. "Etude des propritt6s lubrifiantes du monofluorure de graphite : (CFx). Colloques internationaux du CNRS, no 233. Polymbres el lubrification, 20-23 mai 1974. Brest. 78. BERTHE D. et GODET M.

"L'hydrodynamique dcs surfaces rugueses". Mecanique Materiaux Elcctricite, revue GAMI, no 298, p. 32-39, octobre 1974. 79. HAARDT R., NICOLAS D. et GODET M.

"Vibration axiale d'un joint radial m&salignt soumis ZI une force dc fermeture constante". Mtcanique Mattriaux ElectricitC, revue GAMI, no 299, novembre 1974. 80. HAARDT R. et GODET M. "Axial vibration of a misaligncd radial face seal under a constant closure force". ASLE Trans., vol. 18, no I , p. 55-61, janvier 1975. 81. PLAY D. el GODET M. "Thud body formation and elimination on carbon fiber epoxy composite". Space uibology proceedings of the first European Space Tribology. Fracasti, Italy, p. 165-173, avril 1975.

"Simulation sur machine h galets des avaries de fatigue superficielle des dents d'engrenages". Congres mondial des Engrenages, p. 603-617, Paris, 22-24 juin 1977. 87. FRENE J. et GODET M. "Plain journal operating under vortex and turbulent flow conditions ; comparison between experimental and theoretical results". Superlaminar flow in bearings. Edit6 par D. Dowson, M. Godct et C. M. Taylor, IME 1977, p. 194- 198.

88. DALMAZ G. et GODET M. "Film thickness and cffective viscosity of somc fire resistant fluids in sliding point contact". ASME JOLT, v 100, no 2, p. 304-308, avril 1978. 89. ROZEANU L. el GODET M.

"Model for gear scoring". ASME, 77-DET-60. juin 1978. 90. BERTHE D., FLAMAND L. et GODET M.

"L'tlasohydrodynamique et les avaries dans les contacts herlziens". Frottement Usure et lubrification dans I'indusuie. JournCes d'Ecully, p. C3-19, septembre 1978. 91. PLAY D., FLOQUET A. et GODET M.

"Relation between wcar of composite materials and both friction and surface composition". The wear of non-metallic materials. Edit6 par D. Dowson, M. Godct et C. M. Taylor, MEP 1978, p. 32-41.

82. PLAY D. et GODET M.

"Design of high performance dry bearings". Wear, vol. 41, no 1, p. 2544,Janvier 1977.

83. PLAY D. et GODET M. "Coexistence of diffcrcnt wear mechanisms in a simple contact". Wear. vol. 42, p. 197-198, 1977.

92. GODET M. el PLAY D.

"Mechanical aspects of dry friction and wear testing". The wear ol' non-mctallic materials. Edit6 par D. Dowson, M. Godct el C. M. Taylor, MEP 1978, p. 77-86. 93. PLAY D. et GODET M.

84. FLOQUET A., PLAY D. et GODET M.

"Surface temperatures in distributed contacts. Application to bcaring design". ASME JOLT, vol. 99, no 2, p. 277-283, 1977.

"Visualisation of chalk wear". The wear of nonmetallic materials. Edit6 par D. Dowson, M. Godet et C. M. Taylor, MEP 1978, p. 221-230.

13

94. BERTHE D., FLAMAND L., FOUCHER D.,

HASSOUN M. el GODET M. "Theoretical and experimental load division in an EHD contact". Surface roughness effects in lubrication. Edite par D. Dowson, M. Godel et C. M. Taylor, MEP 1978, p. 218-223. 95. BERTHE D., MICHAU B., FLAMAND L.

et GODET M. "Effects of roughness ratio and Hertz pressure on micropits and spalls in concentrated contacts. Theory and experiments". Surface roughness effects in lubrication, Edit6 par D. Dowson, M. godet et C. M. Taylor, MEP 1978, p. 233-238. 96. PLAY D. et GODET M. "Self-protection of high wear materials". ASLE Transactions, vol. 22, no 1, p. 56-64, 1979.

102. PLAY D. et GODET M.

"Relation between wear of CrNi steels and debris transport at high temperature (950" C)". ASME JOLT, v. 102, no 2, p. 247-252, avril 1980. 103. BERTHE D., FLAMAND L., FOUCHER D. et

GODET M. "Micropitting in hertzian contacts". ASME JOLT, vol. 102, no 4, p. 478-489, 1980. 104. GUPTA P.K., FLAMAND L., BERTHE D. et

GODET M. "On the traction behavior of several lubricants". ASME JOLT, v. 103, no 1, p. 55-64, janvier 1981. 105. FLAMAND L. BERTHE D. et GODET M.

"Simulation of herwian contacts found in spur gears with a high pcrformance disc machine". J. of Mechanical Design, v. 103, no 1, p. 204-209.

97. KOHEN I., PLAY D. et GODET M.

"Determination des contraintes dans les contacts larges par photoClasticit6 ct intcrf6rm6tric holographique". IUTAM Symposium Poitiers. Recueil dcs conferences, 10-14 septembre 1979. 98. FLAMAND L., FOUCHER D., BERTHE D. et GODET M.

"Les paramktres mCcaniqucs qui gouvernent les avaries de surface dans Ics engrenages lubrifits". Mtcanique Mattriaux Elcctricitt, revue GAMI, no 360, p. 433-442, dtcembrc 1979. 99. KOHEN I., PLAY D. ct GODET M.

"Effects of machine rigidity or degrees of freedom on the load-carrying capacity of wear debris". Wear, vol. 61, p. 381 -384, 1980.

106. GODET M., BERTHE D., DALMAZ G., FLAMAND L., FLOQUET A., GADALLA N. et PLAY D. "Tribo-testing". Tribological technology, vol. 11,

Proc.NAT0 Advances Study Institute on Tribological Technology, Maratea, Ibly, 13-26 septembre 1981. Edit6 par P. Senholzi. 107. GODET M. "Extrapolat ion in t ri bolog y

",

Wear, vol. 77, p. 29-44, 1982. 108. KOHEN I., VILLECHAISE B., PLAY D. ct

GODET M. "Displacemcnts and swesses in dry contacts third body and conformity effccts". ASME JOLT, vol. 105, p. 542-551, octobre 1983.

100. GODET M., PLAY D. et BERTHE D.

"An attempt to provide a unificd treatment of tribology through load carrying capacity, transport and continuum mechanics". ASME JOLT, v. 102, no 2, p. 153-164, avril 1980. 101. LANCASTER J.K., PLAY D., GODET M., VERRALL A.P. ct WAGHORNER R.

"Thud body formation and the wear PTFE fibrebased dry bearings". ASME JOLT, vol. 102, no 2, p. 236-246, avril 1980.

109. FANTINO B., GODET M. et FRENE J.

"Dynamic behaviour of an elastic connecting rod bearing. Theoretical study". Published by S A E : Society of Automotive Engineers in "Studies of Engine Bcarings and Lubrication SP 539, p. 23-32, fevrier 1983. 110. EL SANABARY A.F., PLAY D. et GODET M.

"Effects of bulk thermal properties on polymer transfer". ASME JOLT, vol. 105, no 2, p. 259-270, avril 1983.

14

111. COLOMBIE C., BERTHIER Y., FLOQUET A., VINCENT L. et GODET M.

"Portance des particules d'usurc. Analogic avec lcs lubrifianb solides". AUM, 6kme congrbs Francais de Mechanique. Resume des communications, p. 12.17 a 12.20, Lyon 1983.

119. PROGRI R., VILLECHAISE B. et GODET M. "Boundry Conditions in a Two-Body Contact

formcd by a Rcctangular Polyurethane Slab pressed against an Araldiic planc". ASME, JOLT, vol. 197, no 1, p. 138-141, 1985. 120. COLOMBIE C., BERTHIER Y., FLOQUET

112. GODET M.

"Aspects mechaniques de la tribologie". AUM &me congrks FranGais de Mdchanique. ConfCrence Gdnbrale, p. 1.1 h 1.24, Lyon 1983. 113. BERAUD C., BERTHIER Y., COLOMBIE C.,

VINCENT L. el GODET M. a) "Measurements of wcar using small amplitude movements: Formation and protcclive role of third body", p. 3.1 a 3.4 b) "Usure par pctits dCbatternents: Formation ei rBlc prolcctcur du troisiCmc corps", p. 3.5 2 3.1 1. Colloque International sur les MatCriaux rdsistant 2 I'usure. Cercle d'biude des M6taux. 23-24-25 novembre 1983, Saint-Etiennc.

A., VINCENT L. ci GODET M. "Portance des particules d'usure - Analogie avcc les lubrifiants solides". MatCriaux, Mkhanique Electricid. Acte des journks d'Ctudcs des outils de productique, 2Cmc partir, no 41 1, mars-avrilmai 1985, p. 29-36. 121. PROGRI R., VILLECHAISE B. et GODET M. "Etude expCrimentalc et thboriquc du

comportcment d'un contact a dcux corps soumis a un cycle dc charges normalcs at tangentiellcs". EUROTRIB, 9-12 scptcmbre 1985, Session DI: Transformations mcchaniques et physicochimiqucs supcrficicllcs, vol. 11, p.5.4.11.1-5.4.11.10. 122. BERTHIER Y., COLOMBlE C., GODET M.,

114. GODET M. ct BERTHIER

Y.

a) "Forgotten parameters which govern wear", p. 1.1 h 1.3 b) "Les parameters oubliCs qui conditionncnt I'usure", p. 1.4 a 1.7 Colloquc International sur Ics MatCriaux rCsislant a I'usure. Cercle d'Ctudc dcs Mdtaux. 23-24-25 novembrc 1983, Saint-Eticnnc. 115. GODET M.

"Extrapolation en Tribologic". Compte-rendu dcs journCes MatCriaux Etablissement Technique Central dc'lArmemcni. fbvrier 1984. p. 1-18.

LOFFICIAL G. ct VINCIENT L. "L'usure par pcli ts dtbattcmcnts: (corrosion de contact, frctting)". EUROTRIB, 9-12 sept. 1985, Session D V: Apports ihkoriqucs nouveaux: corrosion de contact, vol. 11, p. 5.5.1.1-5.5.1.8. 123. BERTHIER Y., COLOMBIE C . , LOFFICIAL

G., VINCENT L. cy GODET M. "First and third body effects in fretting. A source and sink problems". Leeds-Lyon 12. 3-6 sept. 1985. P. 81-90. Global studies of mechanisms and local analyses of surface distress phenomena. Edit6 par D. Dowson, C.M. Taylor, M. Godct et D. Berthe.

116. COLOMBIE C., BERTHIER Y., FLOQUET

A., VINCENT L. ct GODET M. "Fretting: load carrying capacity of wear debris". ASME Journal of Tribology. vol. 106, no 2, avril 19x4, p. 194-201. 117. GODET M.

"Mechanics versus or with Materials in the understanding of Tribology". Lubr. Engir., vol. 40, no 7,Juillct 1984, p. 410-414. 118. GODET M.

"The third body approach. A mcchanical view of Wear. Wear, vol. 100, p. 437-452 1984.

124. PROGRI R., VILLECHAISE B. et GODET M.

"Fracture mechanics and initial displacements". Leeds-Lyon 12. 3-6 Scpt. 1985. P. 47-54. Global studies of mcchanisms and local analyses of surface distress phcnomcna. Edit6 par D. Dowson, C.M. Taylor. M. Godct ct D. Benhe. 125. BERTHIER Y., COLOMBIE C., LOFFICIAL

G., VINCENT L. el GODET M. "Corrosion de contact ct usurc par petits dCbattements". 8Emc congrbs europkn de corrosion. 19-21 novembre 1985, Nice. p. 24. PrCsentaiion oralc.

Y.,COLOMBIE C., LOFFICIAL G., VINCENT L. ct GODET M. “Corrosion et corrosion de contact”. 8Eme congrks euopCen dc corrosion. 19-21 novembre 1985, Nice, p. CPl0.1 hCPl0.10.

126. BERTHIER

135. COLOMBIE C., BERTHIER Y., VINCENT L.

et GODET M. “How to choose coatings in rrctiing”. ASR 86 3/4 dkembre 1986. Paris, Palais dc Chaillot. 136. TARAVEL P., AEBY P., BOUVIER M.,

127. GODET M. et BERTHIER Y.

“La lubrifications dcs cannelures”. 2 h e congrks mondial des engrenagcs”. 3-5 mars 1986, vol. 1, p. 329-342. 128. GODET M., et BERTHIER Y.

“Les cannclures, une rcvuc bibliographique” Journks d‘ttudes GAMI, 6 mars 1986, Journal du GAMI, mars-avril 1986. 129. COLOMBIE C., BERTHIER Y., VINCENT L.

BERTHIER Y. et GODET M. “Simulateur d’usure induite par petis dCbatlcmenis participation au 8kme Congrks FranCais de MCcanique - Progrks et ProblEme des moyens d‘essais Industriels. Nantes 3 1 aout - 4 septembre 1987, p. 85-88 137. GODET M. “L‘usure et la fatigue induites en petis dkbattcments

la corrosion de contact”. Une action du Laboratoirc dc MCcanique dcs Contacts du deparment GMD, publiC par SPOT, I’actualitCde I’INSA dc Lyon, n”3, juin 1987 p. 10-12.

et GODET M. “Le choix d’un traitcmcnt dc surface en petis dbbattements”. Confkrencc TRS 86.Palais des Congres, Paris 17-18juin 1986.

138. MAGNIN A., FRENE J . BOIS. et GODET M.

130. COLOMBIE C., BERTHIER Y., VINCENT L.

“Hydrodynamic of a wire drum contact”. ASME-JOT, OCL.1987, v. 109, n”4. p.679-683.

et GODET M. “Corrosion dc contact, usure sous faible dCbattement”. Molkriaux et Tcchniques, juillet-a013 1986, p. 361 -368. 131. GODET M. et BERTHIER Y. “Continuity and friction : an Osborne Reynold’s

approach”. Leeds-Lyon I3 Symposium On Tribology - Fluid film Lubrication - Osborne Reynolds Centunary. Edit6 par D.Dowson, C.M. Taylor, M. Godct ct D. Bcrthc.

139. BERTHIER Y., VINCENT L. et GODET M.

“Fatigue et usure induitcs par petis d6battements, 6bme Colloque MCcaniquc el Mtlallurgie dc Tarbes. 18, 19 et 20 novembre 1987, endommagement-fiabilit6, session 1, pp. 1 h 28. 140. BERTHIER Y . ct GODET M.

“Mechanical Parameters in Fretting”. 3rd European space machanisms et tribology. Symposium, Madrid, Spain. 30 septembre a u 2 oct 1987. (ESA SP-279, D k 1987)~.333-336.

132. GODET M. ct BERTHIER Y .

“Mkaniquc dc la Tribologie - Application aux cbramiques”. L’industric CCramique no 808. sept. 1986. p. 565-568. 133. GODET M.

“Lettcr to thc Editor. Coniincnts on “The wear of copper in singlc-pas$ sliding”. Wear, vol. 113, n”2, p. 295-297, dCcembrc 1986.

141. COLOMBIE C., BERTHIER Y., VINCENT L.

et GODET M. “Fretting wear and frctting fatiguc damage”. FATIGUE 87, prCsentC au Third International Conference on Fatiguc and Fatigue Thresholds, UniversitC dc Virginie, Charlottesville, Virginia USA, 28juin - 4 juillct 1987, p. 567-575. 142, GODET M.

134. DELAINE P., MEURISSE M.H. et GODET M.

“Cintmatiquc dam Ics arbrcs cannel6s”. Journal du GAMI, M6caniquc MatCriaux Electricid. No 418, p. 40-46. novcmbre-dkembre 1986.

“Pourquoi Ctudicr le frottement et I’usure aujourd‘hui. Editorial. Rechcrche et Indusrtie. Lettre dinformation scientirique et technique. NO46 du 15 scptembrc 1987.

16

143. BERTHIER Y. et GODET M.

“Introduction B la uibologic d‘aujourd’hui”. Compte-rendu de la Socidtci Franpise de MCtallurgie. Paris, novembre 1987. 144. BADIA M., LASLAZ G., PICHARD J.P.,

BERTHIER Y. et GODET M. “Sliding wear tests on nickel coated aluminum alloys”. De la confcrcnce - Tribological Mechanisms and Wear Problems in Materials Publite par A.S.M. MI., ‘87 h Cincinnati, Ohio du 10 au 15 octobre 1987. 145. BERTHIER Y.,FLAMAND L., GODET M.,

SCHMUCK J. et VINCENT L. “Tribological behaviour of titanium alloy TA6V”. Poster present6 au 6th World Conference on Titani urn. Nice, 1997. 146. CHAMONT C., HONNORAT Y., BERTHIER

Y., GODET M. et VINCENT L. “Wear problems in small displacements encountercd in titanium alloy parts in aircraft turbomachines”. Poster present6 au 6th World Confercncc on Titanium. Nice, 1987.

151. MONTEIL G . , LONCHAMPT J., ROQUES

-CARMES C. ct GODET M. “Interface composition in Herwian contact : application to the cam-lappet system”. Interface Dynamics - 145me Lceds-Lyon Symposium. Ed. D. Dowson, C.M. Taylor, M. Godet, D. Berthe, Elsevier 1987, p. 355-365. 152. GODET M.

“Modeling of friction and wear phenomena”. Proceedings of thc Workshop on the use of surface dcforrnation models to predict Tribology behavior. Columbia University New-York, 17-19 ddcembre 1986. - Approaches to modeling of friction and wear. Editeurs FF Ling et CHT Pan, p. 12 h 36. Springer-Verlag 1988. 153. BERTHIER Y., VINCENT L., GODET M.

“L’usure et la fissuration induitcs en petis dtbattements, (U.I.P. ct F.I.P.) genEse, formalismes et remcdcs”. Journtcs innovation Technologique et Traitements de surfaces, 11-12 janvicr 1988. Paris. Journal du GAMI n”428 ocl/dCcembre 1988. P.P. 20-26. 154. BERTHIER Y., VINCENT L., GODET M.

147. BERTHIER Y., BRENDLE M. et GODET M.

“Boundary conditions adhesion in friction”. Interface Dynamics - 14Eme Leeds-Lyon Symposium. Ed. D. Dowson, C.M. Taylor, M. Godet, D. Berthe, Elscvier 1987, p. 19-25. 148. DUBOURG M.C., MOUWAKEH M.,

VILLECHAISE B. et GODET M. “Crack behaviour under cyclic loading”. Interface Dynamics - 14Eme Leeds-Lyon Symposium. Ed. D. Dowson, C.M. Taylor, M. Godet, D. Berthe, Elsevier 1987, p. 41-48.

“Fretting fatigue and I‘rctting wear”. Confercncc proceedings in Tribology Trends in the 90’s. Lisbonne, Portugal 5-6 mai 1988, p. 1-1 7. 155. BERTHEIR Y., FLAMAND L., GODET M.,

SCHMUCK J. et VINCENT L. “Tribological behaviour of titanium alloy Ti-6A1-4V”. Sixth world confcrcnce on Titanium, Canncs juin 1988, p. 18651870. 156. GODET M.

“Le frottemcnt scc”. Courrics du CNRS, n071, EtC 1988, p.105.

149. BERTHEIR Y., WEHBI D., WACK J.,

ROQUES-CARMES C. et GODET M. “Fractals : A Method of characterization of third body morphology”. Interface Dynamics - 14kme Leeds-Lyon Symposium. Ed. D. Dowson, C.M. Taylor, M. Godct, D. Berthe, Elsevier 1987, p. 105-108.

157. BERTHIER Y., COLOMBIE C., VINCENT

L.et GODET M. “Fretting wear mechanisms and thcir effects on fretting wear”. ASME, Journal of Tribology, vol. 1 10, n03, juillct 1988, p. 51 7-524. 158. BERTHIER Y., VINCENT L. et GODET M.

150. LOFFICIAL G., BERTHIER Y. et GODET M.

“Load carrying in slow reciprocating mechanisms” Interface Dynamics - 14Eme Leeds-Lyon Symposium. Ed. D. Dowson, C.M. Taylor, M. Godet, D. Berthe, Elsevier 1987, p. 28 1 -290.

“Velocity accomodation in fretting”. Wear , vol. 125, n”1-2, juillct 1988, p. 25-38.

17

159. BERTHIER Y ., VINCENT L. et GODET M. "Le Fretting corrosion : aspects fondamentaux

description des phCnombnes". Joumte CETIM Senlis, 16 novembre 1988. p. 5 h 23.

168. BERTHIER Y., VINCENT L. et GODET M.

"Fretting fatigue and fretting wear", Tribology International, AoOt 1989, v. 22, no 4, p. 235-242. 169. BERTHIER Y., GODET M. et VINCENT L.

160. BERTHIER Y., VINCENT L. et GODET M.

"L'usure et la fissuration induites en petis d6battements (UIP et FIP), gtnkse, formalismes et remtdes. Journal du GAMI, Mtcanique Matkriaux Electrici16, n"428, octobreldtcembre 1988, p. 20-26. 161. BERTHIER Y., VINCENT L.et GODET M. "Fatigue et usure induites en petis dtbattements".

Tribologie Mattriaux et Techniques,janvicr 1989, p. 41 h48. 162. HESHMAT H., PINKUS 0.et GODET M.

"On a common uibological mechanism between interacting surfaces". Tribology Transactions, vol. 32, no 1, janvicr 1989, p. 32-41.

"Velocity accommodation Mechanisms". Poster prestnte au Third International Conference on: Surface Modification Technologies. OrganisC par Society (TMS) et le Centre d'Electronique et microtechnique (CSEM). 28 AoWI er septembre 1989, Neuchatel, Sussie. 170. BERTHIER Y., BRENDLE M. et GODET M.

"Velocity accommodation in friction". STLE Tribology Transactions, vol. 32, no 4, octobre 1989, p. 490-496. 171. BERTHIER Y., VINCENT L. et GODET M.

"Velocity accommodation sites and modcs in tribology". Procecding surface and interface analysis. vol. 16, SociCtC Francaise du Vide, ECASIA 23-27 octobre 1989, Abtibes (France).

163. BERTHIER Y., VINCENT L. et GODET M.

"Interaction "MCcaniquc-Mattriaux" en frettingfatigue". Paru dans: Fatigue des structures industrielles. HP Liewrade, 15- 16 mars 1989, Journ organisks par I T T Transferts, Niku-Lari. 164. GODET M

"Le laboramire de MCcanique des Contacts". Letue d'information scicntifique et technique: "Chercher et communiquer". Recherche et Industrie no 66.31 mars 1989. 165. BERTHIER Y., VINCENT L. et GODET M.

"Degradation uibomkanique mecanismes d'accommodation dc vitesse et usure en frottement sec". 28kme journks des aciers sptciaux 24-25 mai 1989, Likge, Belgique. 166. VINCENT L., BERTHIER Y. et GODET M.

"Fretting-fatigue,compktition usure-fissuration". Journees de Printemps: SociCtt FranCaise de Metallurgie. Fatigue et Contacts mtcaniques. Paris 30-31 mai 1989, p. 9-31. 167. GODET M.

"Third-bodies in Tribology". Proceedings of the 5th International Congress on Tribology, EUROTRIB 89, 12-15juin 1989, vol. 1, p. 1-15.

172. GODET M.

"Grand Lyon - Colt Technique". Industries et Techniques, n"668, novembre 1989, p. 65-66. 173. BERTHIER Y., VINCENT L. et GODET M. "Vibrations and Fretting wear". Congr6s :

Vibration and Wear in high speed rotating machinery", by Montalvao et Pina da Silva, NATO/ASI, Lisbonne, p. 153-183,10-22 avril 1989, publication 1990. 174. GODET M.

"Third Bodies in Tribology". Wear, vol. 136, nol, 1990, p. 29-45. 175. FLAMAND L. el GODET M. "Mattriaux tribologiques : comment les tester?".

SPOT INSA, n"3, juin 1990, p. 8-9. 176. GODET M.,,BERTHIER Y., LEROY J.M.,

FLAMAND L. et VINCENT L. "Coating design Methodology". Tribology Series 17 : Mechanics of Coatings. Ed. D.Dowson, C.M. Taylor, M. Godet, Elsevier Pays-Bas, septembre 1990, p. 53-59.

18 177. GODET M., BERTHIER Y., LANCASTER J.

et VINCENT L. “Wear modcling : Haw far can we gct with first principles?”. Tribological Modeling for Mechanical Dcsigncrs, ASTM STP 1105, K.C. Ludema et R.G. Bayer, Eds. American Society for Testing and Materials, San Fraancisco, octobre 1990, p. 173-179. 178. BOCH P., PLATON F., KAPELSKI G., GODET M., BERTHIER Y., TRABELSI R., BRIGGS J., ARBABI H. et AZEMA 0.

“Tribology and velocity accomodation mechanisms of ceramics (Sic and Si3N4) as a function of temperature and environment”. Proceedings of the Japan International Tribology Conferencc, Nagoya, oct. -nov. 1990, p. 1395-1400.

184. GODET M., BERTHIER Y., LANCASTER J.

et VINCENT L. “Wear modcling : using fundamental under standing or prac t i ca I ex per i encc” . WEAR vol. 149, 1991, p. 325-340. 185. GODET M. et VINCENT L. “Proprittb trihologiqucs, Frottcment-usurc”. Pratique des matbriaux indusuicls. Les rbfbrentiels DUNOD. Partie 2, Chap. 2, souschapitre, scction 1 51 3., compltment no 4, Novembre 1991. 186. MOUWAKEH M., VILLECHAISE B. et

GODET M. “Quantitativc study of interface sliding phenomcna in a two-body contact”. Eur. J. Mcch., A/Solids, vol. 10, n”5, p. 545-555, 1991.

179. REYNAUD Ph., BERTHIER Y., FLAMAND

L., GODET M. ct BORRIEN A. “Solutions kibologiqucs pour frottcmcnt sous vide”. Journee CETlM : Frottcment sous sollicitations exutmcs. 21 nov. 1990, p. 43-65. 180. BERTHIER Y., VINCENT L. ct GODET M. “Frottement et usurc : Approchc multi-tkhcllcs”.

Reconlrcs Scicntifiqucs du Cinquantcnairc. “MCcaniquc, ModClisation NumCriquc ct Dynamiquc dcs MatCriaux”. Publications du L.M.A. no 124, avril 1991, p. 159-172.

187. GODET M., BERTHIER Y., VINCENT L. el

FXAMAND L. “Les revttcmenls durs cn tribologic : une approchc Pluridisciplinairc”. Colloque Bilan MRT, Expost 17, 16-17 dCccmbre 1991. 188. GODET M., BERTHIER Y., DUBOURG M.C.

et VINCENT L. “Contact mechanics, some nceds for broader application”. Journal of‘Applicd Physics D, Special Issuc : Frontiers of Tribology, vol. 25, nolA, janvicr 1992, p. A273 51 A278.

181. PLATON F., BERTHIER Y., KAPELSKI G.,

AZEMA 0. cl GODET M. “Frottement ii scc dcs ccramiques : realites el solutions”. 3cmc colloque intcrregional curopCes sur les ckramiqucs. Lyon 28-29 mai 1991, ECL, p. 21.

189. BERTHIER Y., VINCENT L. ct GODET M.

“Velocity accomodation sitcs and modcs in tribology”. Eur. J. Mcch., A/Solids, vol. 1 I , nO1,p. 35-47, 1992. 190. SICRE J., BERTHIER Y., FLAMAND L.,

182. PLATON F., KAPELSKI G.. BOCH P., GODET M., BERTHIER Y., TRABELSI R., BRIGGS J . , ARBABI H. e l AZEMA 0.

“Le frottcmcnt A haute tcmp6rature dcs ckramiqucs :lubrification solidc. Journal du GAMl : Mtcaniquc Mut6rinux ElcctricitC, n”439, p. 27-33, juin-juillct 1991. 183. GODET M., BERTHIER Y., VINCENT L. el

FLAMAND L. “Hard coatings for uibological applications : a pluridisciplinary approach”. Surface and Coatings Technology, vol. 45, 1991. p. 1-8.

GODET M., REYNAUD Ph. ct VERGNE Ph. “Caract6risation tribologique sous vidc dc lubrifianls fluides spatiaux”. 3Eme congrEs Mondial dcs Engrcnagcs et des Transmissions. Paris, 12/14 fkvricr 1992, p. 537-548. 191. VINCENT L., BERTHIER Y., DUBOURG M.C . et GODET M. “Mechanics and motcrials in fretting”. Wcar, no 153, p. 135-148, 1992. 192. GODET M., BERTHIER Y. ct VINCENT L.

“Mechanisms, first and third-bodics in Tribology”. Acta Tribologycn, vol. I , nO1, p. 71-75, 1902.

19

193. DUBOURG M.-C., GODET M. ~t VILLECHAISE B. “Analysis ofmultiplc fatigue cracks, Part I1 : Results”. ASME JOLT juillct 1992, vol. 114, p.462-468. 194. VINCENT L., BERTHIER Y. et GODET M. “Testing mcihods in frctting fatigue : a critical apparaisal - standardization of fretting fatiguc tcst methods and equipmcnt”. ASTM - publ. 1 159, Philadelphia 1992, p. 33-48. 195. DAHMANI N., VINCENT L., VANNES B., BERTHEIR Y. ct GODET M, “Velocity accomodation in polymer frctting”. Wear, vol. 158, 1992, p. 15-28. 196. BERTHIER Y., DUBOURG M.-C., GODET M. et VINCENT L. “Wear dala : what can bc made of it? Simulntion tuning. 18Emc Lccds-Lyon Symposium : Wear Particles : from thc cradlc to thc grave. Elscvier tribology scrics 21, Ed. D. Dowson, C.M. Taylor, T.H.C. Childs,G. Dalmaz, 1 9 9 2 , ~161-172. . 197. GODET M. “Simulation of friction and wcar”. Sovict Journal of Friction and Wcar. vol. 13, nO1,p.19-30, 1992. 198. SICRE J., BERTHIER Y., FLAMAND L., REYNAUD P., VERGNE P. ct GODET M. “Tribological charmcrization of spatial wei lubricanis undcr vi1cuuin”. Fifth European Spocc Mechanisms and Trihology Symposium. ESTEC Noordwijk, PB, du 28 H U 30 oct 1992, p. 157-163. 199. SUN Y., BERTHIER Y., FANTINO B. ct GODET M. “A quantitative invcstigntion of displaccmcnt accom oda tion in third - body con tact”. Wear, 165,123-131, 1993. 200. PICHON V., BOUCHAYER P. et GODET M. “Lubricating of O-ring seals in pneumatic applications with ulwa thin grease films”. Proceedings of thc 19th Lecds-Lyon Symposium : Thin films in tribology, Tribology series 25, ed. by D. Dowson, C.M. Taylor, T.H.C. Childs, M. Godct, G. Dolmm, 1993, p. 593-610.

201. CARTON J.F., VANNES A.B., VINCENT L., BERTHIER Y.,DUBOURG M.-C.,GODET M. “Coatings in frctting : a mechanical and material approach”. Proceedings of 1st International Symposium on Tribology, vol. 2, ed. Y.S. Jin. 19-23 octobrc 1993. 202. BERTHIER Y . , GODET M. ct VINCENT L. “Fretting : Usure ct fissuration induites par pctis dkbattemcnts”. De Conccption MCcanique ct Tnbologic. Journcc organisk par Ic CETIM ct le CAM1 Ic 15 mai 1991. p. 101-117 janvier 1994. 203. SICRE J., BERTHIER Y., FLAMAND L., REYNAUD P., VERGNE P. ct GODET M. “Rheological and tribological characterization of six wet lubricants for spacc”. Proceedings of thc 6th Intemationl congrcssc on tribology Eurotrib 93 : Friction, wcar, lubrication, dcsign, thcory and practice of tribology. 30 aoW2 scptcn~brc 1993, vol. 2, p. 273-378. Egalcmcnt publie dans Journal of Synthctic Lubrication, Leaf Coppin . Publishers, vol. 1 1 , n o l , avil 1 9 9 4 , ~35-44. 204. HESHMAT H., GODET M. ct BERTHIER Y. “On thc rolc and mcchnnisms of dry tribopartiulatc lubrication”. Lubrication Enginccring (STLE), vol. 51 ,n07, p. 557-564, 1995.

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

21

MAURICE GODET'S THIRD BODY Yves Berthier MSA Laboratoire de Mecanique des Contacts, UMR C 55 14 20, avenue Albert Einstein, 6962 1 Villeurbanne, France

This text is the transcription of the video pint presented during the congress, which explains the spoken style and the lock of illustrotions of third bodyjlows. Copies of the video cassette can be supplied on request.

I) INTRODUCTION

Beyond the interface between the first bodies, tlie 3rd body is the concept that provides tlie missing degrees of freedom necessary in order to approach the tribology in a coherent way from 3rd body fluids to 3rd body solids. Tlie morphological differences of these 3rd body solids (Fig. 1) having the same clieinical composition, suggests different rheologies and stresses.

This direction must not, however, obscure tlie generality of the third body concept, since :

-

solid 3rd bodies lag behind fluid 3rd bodies by half a century, and in extreme operating conditions, concerns regarding fluid third bodies merge with those regarding solid third bodies and come up against the same hurdles! II) FRICTION AND WEAR

Solid third bodies go together with friction and wear. The friction coefficient is simply the relationship between two components of a contact reaction. Tlie physical content of this coefficient is very limited! The "F law: kx'l is already physically richer!

Figure 1 Third bodies (steel) This suggestion demonstrates the level of ignorance and lack of progress concerning knowledge about 3rd body solids as compared to third body fluids. Consequently, this expost will focus on 3rd body solids.

How should wear be defined ? Wear can occur by a loss of inass as well as by a gain. This gain, for example, can occur during the oxidation of the third body! Should one distinguish the transformed inaterial froin the detached inaterial (Fig. 2), whose particles may, or may not, be load carrying ?

22 thickness of the ~ o l y ~ e n ubisulpliite m layer !! [3] What is the reality I! Let’s take the contact of a sphere on a disc coated with inoly~enumbisulphite (Fig. 3). Note the hertzian zone on the ball, and also the particles of the 3rd body.

Figure 2 : Wear ? Degradations ? When does degrada~io~i, wear and loss of ~iiclioii occur? For example, in a brake, tlie loss of iiiaterial froin a brake pad is “wear” that does not iI~itnediatelyimply a loss of ~iiictioIi.On the other hand, only slight loss of material from tlie balls of a bearing results in a loss of fuiiction. Do laws of wear have any iiieaiiiiig ? Yes. They at least represent themselves. Maurice Godet spoke of them being i i o i i ~ i ~ sin e their present form ! Furthermore, as Kenneth Ludema said, wear laws that include the Young’s t~iodtiliisof one of the materials i n contact feature it include them either in the numerator, or in the deiioiiiiiialor ! [I, 21 What a generality!

Moreover, tliere is no legal unit of wear, so wear is not a inagnit~ide!What do the interpretations and wear and friction provide?

Figure 3 : BalI /disc contact Let’s take a look along the race video which presents zones of very di~erentmorphology. What could the contact pressure be? Where is the speed accoinIn~~tion located between the disc and the ball ? What about a ball race which has several balls supplied by solid third bodies by rubbing and wear of the cage? These are teclinological contacts that have to be controIled!

111) INTERPRETATIONS

Let’s take friction in the case of iiiolybdei~~~i~i IVj HOW IS IT DONE I N D ~ S T ~ L L? Y bistilpliite. Sevemi worlds separate what Bragg iiiitialIy iinagiiied regarding shearing of the Here’s a plane (Fig. 4), the very latest thing in 1)e~agoi~aI grid, and iiiacroscopic frictioii electronic ii~onnatioii.It ‘s iionetl~elessa plane that i~icasure~~iei~ts. Iiiterpretatioiishave progressed from has a rudder, and therefore links from wliich the displaceii~eiit011 the atotnic level, which explains third body escapes! friction on the basis of atomic friction to macroscopic stress calculatioi~s using finite elcinetits that explain friction values on the basis of In~croscopicelastic elenletits and which ~iiietiiiies use elements whose size is greater than the

23 The solution : slight cooling, condensation and water. The hen moves on a film of water. Once again a solid third body is saved by a fluid third body ! Let’s not be pessimistic. Solutions with solid third bodies exist, as with the case of tlie friction fabrics used in dry bearings (Fig. 6). They have been designed to control :

- the detachment of the 3rd body “on the peaks”, - and the internal flow by trapping the 3rd body in the “hollows”.

3rd body Figure 4 : Third body escapes Here, the tribological solution is more accommodation of wear than a solution. It’s often a case of making do as well as possible with friction and wear! The tribological breakthroughs are not always what one imagines : the movement of this hen (Fig. 5 ) on a PTFE surface is a problem. Hygiene requires PTFE as do the tribological oracles. But the hen does not move the desired distance. It rubs too much!! !

This way of proceeding that goes from the tribology to the material is very rare.

V) TESTS AND MODELS So what should be retained from the tests, models and results of applications?

1)Tests and friction measurements! !

Figure 5 : Translation of hens

Naturally, all tlie results bear the signature of the tribometer used. The analysis of the VAMAS program results is eloquent : for theoretically the same test conditions, from one laboratory to another, friction varies by a ratio of 2, while wear by a ratio of loo!

24

2) Interpreting the tests!

This too often depends on tlie resources and culture of tlie researchers. 3) The models !! In tribology, the models are too often in advance of understanding of phenomena. Since modelling is not describing, tlie model coincides with reality, tliougli through tlie adjustment of a parameter tliat is not necessarily a pliysical variable !! hence the difficulty in using models, for technological means. By the way, one can only congratulate the tlieoretical efforts to take into account the mathematical singularities of tlie law 11 = TM. 4) Tlie applications As we saw before, it’s a question of liaving to live with a situation more tliaii real solutions. Tlie poor control of know-how stems from the poor perception of tlie dynamics of tlie 3rd body and tlie role of tlie meclianism tliat harbours tlie contact!

Figure 7 : Tribological weathercock This dispersion was one of the things Maurice Godet raged against.

VI) Video of dynontics of the 3rd body

Tlie balance sheet is quite simple : tlie results depend on tlie investigative tools cliosen or available and tlie culture of the researchers!! Friction and wear suffer from a dispersion of tlie ways of understanding the same problem! As time goes by, and under the breeze of ail idea, tribology is blown to and fro like a weatliercock (Fig. 7)!!

WHICH METHOD OF PRETATION SHOULD BE USED ?

INTER-

Let’s t‘ake tlie liistory of Solid Meclianics, in this case creep buckling. Euler noticed that the beliaviour of macliine parts depended more on iiiiposed conditions than on tlie nature of tlie materials. Tlius lie studied tliis beliaviour to formulate the generality, hence tlie model problem! Then Solid Meclianics described how the materials are integrated within this generality. What does tribology do? It seeks to cliaracterise materials, wliich leads to isolated works on a given material, and at tlie point where Solid Meclianics arrives at a generality, tribology provides blocks of information wliose generality is never tested. This sliows :

- tlie excessive emphasis material in tribology, - tlie absence of generality.

on tlie orientation of

25

VII) THIRD BODY CONCEPT

The first tool to bring to light this generality was the 3rd body concept formulated by Maurice Godet in 1970 on a beach on the island of Elba. This 3rd body on which he based his tribological convictions led him to regret : ‘‘In my presence, the generality ofthe 3rd body is open accepted out of courtesy, aJer which it is conjned to our works”.

Is bringing to light of this generality a utopia? No, witli viscosity, fluid 3rd bodies attained this generality within a few years. Viscosity, wliicli can be measured outside contacts is a function of niaterial/mechanical transfer. It combines the physics of the load carrying phenomenon by making an abstraction of the composition of the 3rd body! Model problems and clieniical formulations adaptable to tribological requirements are available for fluid third bodies. That’s true for the majority of applications. What advances can be made with regard to solid third bodies where it is not known:

- what their characteristic parameters are?

-

whether they can be cliaracterised outside contacts? The greatest and almost historic limitation in the study of solid 3rd bodies stenis from post-mortem observations that have based interpretations. Film of flow of 3rd body

VIII) POMPEI COMPLEX Particles of the third body in movement may seem to stick fast to the first bodies observed at standstill, wliicli vitiates the reconstitution of 3rd body flows! For want of being able to visualise the dynamics of the 3rd body, it is necessary to reconstitute it! We can call this the Pompei complex. Let’s continue this analogy with archaeology. Archaeology uses aerial reconnaissance. stratigraphic excavations, dendroclironology and different physical-chemistry analyses. It knows how to reconstruct reality, because it knows how to

integrate each scale and each discipline within the generality. As for tribology, and in particular solid third bodies, it also draws advantage from studies made on different scales carried out by different disciplines.

But through lack of a generality, tribology cannot rebuild reality. The third body solids tnust therefore solve its Pompei complex. Taking into account third body flows will contribute to the emergence of the generality and thus lead to model problems. In parallel, materials specialists must be channelled towards conceiving materials that satisfy tribological requirements! Maurice Godet spoke of coating birth control! The industrial needs must be satisfied and the methods of reading a tribological problems have to be overcome. That’s to say set up a real science of surface engineering. To resist sudden gusts of wind (Fig. 7), let us structure the great evens of the life of a contact in order to :

- place the right interpretations at the right moment in the contact’s life ! and then identify the basic assumptions of existing works and position them in relation to solid third body dynamics.

-

IX)THIRD BODY’S FUNCTIONS Obviously, the structuring element is the 3rd body that :

- transmits the load,

- accommodates the difference of speed, - separates the 1st bodies. Let’s have a look at those 3 functions. 1) Load transmission

As witli the fluid 3rd bodies, solid 3rd bodies present load carrying properties (Fig. 8), though the load carrying mechanisms vary from one application to another.

26

Each site can present 4 types of accommodation of speed or mode, Mj :

- elastic, mode MI, - normal breaking, mode M2, - shearing, mode M3. - rolling mode M4. that leads to a total of 20 possibilities of Velocity Accommodation Mechanism (VAM).

Figure 8 : Load carrying

Video : "Here are, and action in the SI site and 2 type cracks which is the VAM SIM2. Now in the S3 site an example of rolling. The rolls have a diameter of about a tenth of micrometer that's the S3M4 mechanism the third body separates the 1st bodies'!

2) Speed accommodation 3) Separation The third body accommodates tlie difference in speed between the first bodies. In a basic contact (Fig. 9) there are 5 possible sites, Si, for tlie location of accommodation of speed :

- tlie S 1 site wliicli is the skin of tlie first body, - the S2 site constituted by the screens, - tlie S3 site constituted by tlie volumic part of tlie tlii rd body, - tlie S4 and S5 sites are inducted by using symmetry.

Figure 9 : Velocity accommodation meclianisms WAM)

This separation controls the degradation of the 1st bodies. It is therefore necessary to distinguish (Fig. 10) :

- the detachment of particles, the source flow,

- the circulation of the 3rd body in the contact, the internal flow,

- the external flow. The 3rd body can be recycled in the contact, or else definitively lost for the contact. This is tlie wear flow,. This group of flows m'akes up the tribological circuit.

27

The first bodies are included in a m e c ~ n i s mthat applies force and ~novementto them, Forces and local inovemen~ induce normal and ~ n g e n t i ~ forces that in turn induce a stress field to which the first body responds. These local responses range from cracking to superficial ~ b o l o g i ~ t r a n ~ o ~ n a t i oleading ~, to the detachment of particles and thus to the birth of the third body which then lives its life. Fiim of cracks

Let’s get back to integration. Temporal integration concerns the three steps of the contact’s life, conception, birth and its life. It comes up against the effects of memory, incubation time, and most pa~cularlyto the great sensitivity of solid third bodies to mechanical and physical chemistry stresses ! Spatial integration ranges from elementary physics to the mechanism in which the contact is located. The integration tool is the tribological triplet constituted by:

-

the technotogical mechanism, the scale used is the centimetre ; the 1st bodies, here the scale used is the tnillimetre; the third body, and here the scale used is the micrometre.

-

Figure 10 : Tribological circuit This involves a transition front !he plate wilh the threefunctions and that following it. Video : this is an example of external flow, so our 3rd body is delnitively lost for the contact. This the “wearflow.I’ X) S T R U C T U ~ N GTOOLS

The VAM and tribological circuit are the elementary structuring tools allowing to describe life of an elementary contact 141. To create a model problem of a technological contact, these tools must be integrated in the area of the contact and within the contact’s lifetime. The life of a contact can be suinmarised as follows.

A priori, no scale can ignore the others. They

interact and it is not possible to eliminate one without e v a l ~ t i n gthe consequences on the two others! To the nearest scale factor, m e ~ r ~ ~ oand gy climatology attempt to solve adjacent problems:

- meteorology is credible on a scale of 5 days, - whereas climatology is credible on a scale of several years. The links between the two are not obvious. However, tecIinologi~lly,solid third bodies should have integrated all their scales! On the other hand,

28 solid first bodies don’t benefit of an in-situ measure of flow adjustment. On one side, the elementary tools with the tribological triplet and tlie free steps of tlie life of the contact and on the other side the complexity of tlie technological contacts. In this framework, how far can one go without getting lost! Faced with the complexity of the matter, what then is reasonable? Everything must be done to impose reproducible operation on the technological contact. The best results are obtained by focusing, in priority, on the mechanism. For example, the mountings of this clutch disc (Fig. 11) are grooved and supported by a flexible washer wliicli stabilises the flows of the third body, thus the contact’s life. It is only after ”simplifying” the physics that the elaboration of a model problem becomes realistic provided also that there is iteration between experimentation,modelling and surface engineering. The experimentation must establish - the problem’s physical content That is to my eliminate the sequels of post-mortem views, and therefore identify the flows and the relays between the VAM, either : _ ..

-

- directly by visualisation tests,

- or

indirectly by reconstitution on the basis of appraisal and simple calculations that establish the morphological atlas of the 3rd bodies and stresses. To link cinematic, contacts dynamic to applied mechanical loads physical, chemical effects and so on, and so on. .. Experimentation must also define the operational variables of each element of the tribological triplet. This is the biggest part of the work! XI) MODELLING

Existing models must be used to exacerbate phenomena, thus to identify and uncouple the significant parameters. It is often easier to parameterise a problem theoretically than physically. For example, in modelling this contact, [ S ] , (Fig. 12), it is possible to analyse tlie influences of:

- tlie particle size on the thicknesses of the 3rd body, - the wavelength of roughness, - the rigidity of the first bodies,

by changing only one parameter at a time, which is not always possible experimentally.

Figure 12 : Contact modelling These iterations must not leave out surface engineering, since it is the technological safety barrier that must structure the knowledge obtained

29 on the functional properties to avoid duplicating errors and gamer the know-how that enables simplification of the physics to stabilise the operation of the contacts.

- and take into account the rheology of the solid 3rd bodies.

Although the physical content pennits refinement of the models, the models aid experimental analysis by providing directions of interpretation. Even during a visualisation test, it is not clear what scale one should be looking at !

We may question ourselves as to :

The most reliable models, as with the calculation of stresses in coated masses, already enable the preselection of coatings. They are already used in surface engineering.

Should tribology create its modelling tools?

-

the pertinence of modelling surface problems using tools developed for volumes, such as finite elements, and still further in advance, how we tribologists should approach the notion of surface, which depends on the scales of studies and the disciplines concerned.

-

XII) CONCLUSION It is the interaction between experimentation, modelling and surface engineering that is the price to be paid in order to obtain :

- model problems, - and the development

of materials that satisfy

tribological requirements. To sum up, the creation of model problems occurs via solving the Pompei complex. The structuring concepts: VAM, tribological circuit and tribological triplet are merely intermediate steps which bring the generality to light.

Let's not anticipate too much. There are many tasks ahead! With the help of the "third body", the structuring element of tribology, let's try to build model problems together without forgetting the interactivity with arts. Remember Maurice Godet thanking the musicians after the previous symposium : "Thanks a lot for supplying this quality that the scientists, in spite of all their work, cannot reach alone ". Thanks once again to Maurice Godet and all those who work for the solid third bodies, and of course to all the people at the Laboratoire de Mtcanique des Contacts whose fields of application ranges from fluid third bodies to solid third bodies.

Surface engineering must :

- simplify physics, - reduce the orientation given by the material to its real value. The generality, first, then the materials. It must take care to develop materials that satisfy tribological requirements, which supposes the translation of tribological parameters into material parameters. This can only occur if the sciences of fiinctional properties are treated in the same way as the others! Then there will be a chance for true model problems to emerge! To solve them tribology must forge its own concepts that : - manage the interactivity between the elements of the tribological triplet,

XIII) REFERENCES [ I ] H.C. Meng, K.C. Ludema "Wear models and predictive equations : their form and content". Wear 181-183 (1995), p. 443-457.

[2] K. Ludema "Third bodies in close fitting contacts". 22nd Leeds-Lyon The third body concept : Interpretation of tribological phenomena". Lyon 59 Sept. 1995. [3] S. Descartes, M. Cassard, Y. Berthier, A. Ginet, A. Aubert "MoSx, a solid lubricant : yes, but which scales of tribological interperetation should be used ? The consequences on the friction of mechanisms". Sixth European Space Mechanisms & Tribology Symposium. Zurich, 4-6 October 1995.

30 [4] Y. Bertliier, P. Jacquemard, M.-H.Meurisse "From plienoinenology to the concepts which flow froin the third body. Application to radial Face seal". 22nd Leeds-Lyon Tlie third body concept : Interpretation of tribological phenomena". Lyon 5-9 Sept. 1995.

[ 5 ] A.A. Lubrecht, C. Chan-Tien, Y. Bertliier "A simple tnodel for granular lubrication". 22nd LeedsLyon Symposium "The tliird body concept : Interpretation of tribological phenomena". Lyon 5-8 septembre 1995.

SESSION II INVITED LECTURES

Chairman :

Emeritus Professor Harold Elrod

Paper I1 (i)

Stress Waves in a Sliding Contact Part 1 - Experimental Study

Paper I1 (ii)

Stress Waves in a Sliding Contact Part 2 Modelling

Paper I1 (iii)

Third Body Effect in Fretting

Paper I1 (iv)

Elastic Plastic Microcontact Modelling Using Dislocations

-

-

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

33

Stress waves in a sliding contact. Part 1 : Experimental study.

T. Zeghloul,B. Villechaise

Universitk de Poitiers, Laboratoire de Mkanique des Solides, URA CNRS 861, Av. du Recteur Pineau, 86022 Poitiers Cddex, France.

ABSTRACT A two-body contact is formed between a rectangular polyurethane slab and an epoxy rigid flat. A constant normal load is first applied by pressing the slab against the flat, a tangential load is then imposed by gradually driving the flat from left to right until gross sliding, detected by the sliding of the left or front edge of the slab, is observed. Sliding is established progressively following successive perturbations or waves located at the interface and which travel from the back (right) to the front (left) edge of the plate. These perturbations, called "sliding waves" or "stress waves", were attributed to the propagation of a shearing mode interface crack. This experimental study gives an accurate phenomenological description of the stress waves. Both loads and displacements are measured continuously and their variations are studied in relation with stress waves travelling.

1. INTRODUCTION An experimental study of friction and sliding phenomena between two frictional bodies is presented in this paper. A two-body contact is formed between a rectangular slab of birefringent polyurethane and an epoxy rigid flat. Figure 1 gives a schematic view of the experimental device, mechanical properties and geometrical dimensions of the contacting bodies. The slab is first pressed against the flat, then a tangential load is applied until gross sliding is detected. Sliding is due to successive perturbations or waves named "sliding waves" or ''stress waves". These waves are located at the interface and travel through this interface. Progri et al [ l ] have previously identified the experimental conditions for reproducing these phenomena similar to "Shallamach waves" [2]. Mouwakeh et al [3] show that the energy dissipated

during sliding (contact mechanics) is comparable to the energy associated with the propagation of a shearing mode interface crack (fracture mechanics). An accurate experiment study is necessary to understand friction and sliding phenomena. Numerical modelling [4,5, ...I requires a good knowledge of mechanisms, displacements evolution, contact forces and generalised forces.

2. APPARATUS AND EXPERIMENTAL TECHNIQUES

The system consists of a bench which houses a loading frame and supports of photoelastic experiment. The bench includes 4 functional groups, (cf. figure 2).

34

A :Compressed air supply Figure 1 : Experimental device. Mechanical proprieties and geometrical dimensions of the contacting bodies.

2

1

2

I

A

\

a[ # ] DLS MISURES

CARTE D'ACQUSITION

4 Figure 2 : Photoelastic bench.

35

2.1. The loading frame 1, is formed of two parts holding the test specimens. Displacements in two perpendicular directions are feasible (cf. figure 1). The vertical guide is performed by two ball columns, the horizontal one by a gas slider. The epoxy counterface is mounted on a car differential screw. A sensor T which controls the tangential force imposes this displacement.

2.2. The optical photoelastic device 2, allows the continuous observation of the isochromatic field. 2.3. Load and displacement system 3, containing :

measurement

- sensors for normal (N) and tangential (T) load measurements, sensors for flat travel (DT) (sliding and slab deflexion), for the left edge (DG) and right edge (DD) slab sliding measurements.

-

2.4. measured parameters acquisition and treatment 4 : all signals are recorded and monitored during tests on an informatic system. The picture acquisition for numerical treatment or continuous recording on video tape is performed with a CCD camera.

3. ANALYSIS OF TYPICAL TEST [4]

The following parameters are recorded continuously: - the counterface displacement DT, the left lateral edge displacement DG, - the right lateral edge displacement DD, the normal load N, - the tangential load T. Further, the isochromatic field is continuously monitored during loading. Stress waves sweep through the contact first entirely, then partially. Variations of T, N, DG, DD and DT versus time are given in figure 4. Several steps are noted during this test :

-

- Step 1 : loading to < t < t l . The normal load increases from zero to Nd=-85N. The tangential load is nil and the

counterface displacement DT is unchanged. A stick zone holds at the contact interface : there is no difference between the tangential displacements of the slab and the flat. Consequently the shape of the slab is changed into a barrel and the displacement of the lateral edges of the slab DG and DD increase. Note that the displacements sensors are situated 5 mm above the contact surface. The isochromatic field changes continuously and is symmetric.

- Step 2 : regular evolution t l < t S t 2 . The normal displacement and thus the normal load are kept constant until the end of the test. A tangential displacement is imposed to the right at constant speed V = 4,8.10-2 m d s . The tangential load increases progressively and continuously. No perceptible sliding is observed. The flat shift causes deflections of the lateral edges of the slab. These deflections mod@ the displacements DD and DG. Continuous evolution of the isochromatic field through the whole slab is observed, due to shearing.

-

Step 3 : occurrence of the waves and of the jumps t2 < t < t 3 . An open zone is situated at the right edge of the slab. At t = t2 , a stress wave starts at the right side of the slab and sweeps entirely through the contact (cf. figure 4). Tangential load drop is measured as the stress wave comes out of the interface. The gross sliding is clearly identified by the large variations of the displacements DD and DG. The travel of the stress wave from one side of the contact to the other is in the opposite direction to those of the imposed tangential displacement. (The speed of stress wave is evaluated as V 2: 6.10’2 d s ) . After this event, a part of the interface is again fully adherent. The tangential displacement and therefore the tangential load continue to increase. Three other sweeps are recorded and correspond also to gross slidings, resulting in tangentials unloadings and displacement DD and DG variations increases with the number of the sweeps. The normal load evolution is similar to those of the tangential load.

36

t (4

0

80

40

120

160

200

240

280

-50

"d\

-60

-70

-

10

0

'

40

80

120

160 200

240

=

=

11

280

1

0

40

80

120

160 200

240

Figure 4 : Recording versus t of : - the tangential load T - the normal load N - the left edge displacement DG - the right edge displacement DD - the flat displacement DT. Test running conditions WL = 0.5

V t 4.8.

I

Nd=-85N 0

40

80

120

160 200 240

280

mm/s

280

37

- Step 4 :partial waves t3 < t 5 t4 . At t = 1'4 , a stress wave travels partially through the contact interface, but without coming out. A short unloading, weaker than one corresponding to a gross sliding, is recorded. This is confirmed by the displacement DD and DG measurements.

Similar steps are observed until the end of the test. The maximum tangential load does not vary any more. The ratio of tangential load to normal load corresponding to the gross slidings is roughly constant and equal to 1.

The partial waves : increasing the tangential load causes stress waves at the contact interface. The stress wave travels partially through the contact interface, but without going through. No gross slidings are observed. Energy is dissipated during this step, which is irreversible. The waves go through the contact and jumps occur : the stress waves travel entirely through the contact interface in the opposite direction of the imposed displacement. Gross slidings are observed. A tangential load drop and sticking at the interface are associated to each gross sliding. The stress field is different before and after this event. Note that the velocity of the counterface is around m d s while the velocity of stress waves is around lom2d s .

REFERENCES :

Figure 3 : Stress waves

J

4. CONCLUSION

The contact evolution during cyclic loading was analysed accurately. The interface contact behaviour is summarised in three steps : The regular evolution : during the n o d loading and for small tangential loads, evolution of the stress and the displacements remains smooth. The tangential force increases without reaching a limit which would give either a global sliding or a perceptible local sliding.

1. Progri R., Villechaise B., Godet M. "Fracture mechanics and initial displacements", Mechanisms and surface distress, D. Dowson, C.M. Taylor, D. Berthe Eds., Butterworth London, p. 77-54, 1986. 2. Shallamach A. "How does rubber slide", Wear, 1971, V. 17, p. 301-312. 3. Mouwakeh M., Villechaise B., Godet M., "Quantitative study of interface sliding phenomena in a two-body contact", Eur. Jnl. Mech.. NSolids, 10, nos, p. 545-555, 1991. 4. Raous M., Chabrand P., Lebon F. "Numerical method for frictionnal contact problems and applications", Journ. Mec. t h h . et applic.. Spdcial issue, sup. nol to vol. 7, 1988, p. 111128. 5. Zeghloul T. "Etude des phenomenes d'adhdrences et de glissements dans un contact entre solides : Approche expdrimentale et modelisation", Thtse de Doctorat de I'Univ. de Poitiers, 1992, 188 p.

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

39

Stress waves in a sliding contact Part 2: modelling M . Raous, S. Barbarin Laboratoire de MCcanique et d’Acoustique, 3 1 Chemin Joseph Aiguier, 13402 Marseille Cedex 20, France

ABSTRACT : This study deals with the numerical modelling and prediction of instabilities induced by friction. Some techniques of stability analysis in structural mechanics are applied to friction problems. The models are used to characterize the occurrence of stress waves and jumps in the global tangential force observed by Villechaise and Zeghloul during the sliding of a polyurethane slab on a rigid epoxy flat. Consideration of energetic or dynamic criteria shows that the non smooth character of the solutions can be predicted even with a constant friction coefficient. 1. INTRODUCTION

This study deals with the experimental characterization and the numerical modelling of the occurrence of instabilities induced by friction. Some techniques of stability analysis in structural rt iechanics have been developed in collaboration with J.A.C. Martins for friction problems [1][2]. I n this paper, we present the numerical simulation and the previous stability analysis of the experiment carried out by Zeghloul and Villechaise PI[41[51. We are interested in the occurrence of isolated fast stress waves moving along the contact zone of a deformable block sliding on a rigid plane. The block is first pressed against the plane. A slow regular tangential displacement (about 0.05 mm/sec) is then applied to the plane. The waves, which are observed using a photoelasticity technique, move nearly a thousand times faster than the rigid plane. Jumps in the measured displacements and in the total tangential and normal forces occur at each of these events of fast wave propagation. A response with jumps is thus obtained for a quai-static loading program. For the analysis of the quasi-static evolution we use a variational formulation of the unilateral contact problem with Coulomb friction. We obtain a quasivariational inequality that can be

set as a sequence of variational inequalities. The quasi-static solution is computed using either a mathematical programming method or some minimization methods for non differentiable functionals with constraints. These methods give an accurate determination of the contact evolution during the tangential loading process : loss of contact on part of the contact zone and gradual expansion of the sliding zone. Various criteria are then introduced to characterize possible growing deviations from the quasistatic evolution : either an energetic criterion (a jump to another solution is possible without any external energy contribution) or dynamic criteria (where a divergent or oscillating dynamic growth of a given perturbation is possible). The implementation of these models requires computing sets of complex eigenvalues of large unsymmetrical matrices associated with the finite element discretization. Lanczos and Double QR methods are combined to compute these eigenvalues. This analysis is conducted with a Coulomb friction law with a constant coefficient. This is in contrast with the widely accepted idea connecting stick-slip phenomena to a friction coefficient depending on the sliding velocity. Nevertheless] we also studied the problem introducing a variable friction coefficient and we shall discuss the results. A film with the results of a numerical

40 simulation has been presented.

displacement increases. Changes in the contact conditions with time can be noted locally.

2. QUASI-STATIC SOLUTION 2.1. The Model For the modelling of the stress wave problem, we consider a linear elastic block with unilateral contact a.nd Coulomb friction. The quasi-static problem must be solved using an incremental formulation because of the Couloinb friction law involving velocity terms (see [6]). This formulation corresponds to the solution of a sequence of static problems. Both plane stress and small deformation hypotheses are adopted. The incremental loading is applied in two stages: first the normal load is applied (up to a prescribed normal displacement U k ) and then an increasing tangential load is applied ( a prescribed tangential displacement UT(t)) (cf Fig.1).

b

O.l ........_......_.._.. .........__ -..._. 0.0 0 10 20 30 40 50 60 70 80 U

Ut= 1.Omm 0.5

0.4

1 I

0 10 20 30 40 50 60 70 80

Lt'

Prescribed displacements

Ut=l . l m m

U

0.6

1

E = 7 MPa v = 0.48

I Unilateral Contact Zone I Figure 1. The model 2.2. Numerical Methods To deal with the unilateral contact and the friction, various numerical methods have been presented in "71. The most efficient one is the LEMKE mathematical programming method (direct method working only on the set of contact and friction equations by using a condensation process). With the results presented in section 2, the finite element mesh has 2576 nodes, 51 of which arc contact nodes. In section 3, the mesh has 431 nodes, 21 of which are contact nodes. 2.3. The quasi-static solution Figure 2 shows the computed changes in the contact stresses when t,he prescribed tangential

0 U

10 20 30 40 50 60 70 80

Ut=l.2mm

:::L 0.00 0

10 20 30 40 50 60 70 80

Contact boundary (mm)

Figure 2. Contact stress evolution with p = l . l . When a t some contact node the normal stress and consequently the friction stress UT are zero, the solid is not in contact with the obstacle. UN

41

l'Tl When l u ~ is l equal to -, P

l n ~ is l larger than

-,l'Tl

P

sliding occurs. When the solid remains stuck

1 0 the obstacle. The model therefore predicts a small non contact zone on the right part, and a sliding zone which increases when the prescribed I angential displacement increases. The predicted local sliding displacements are very small (about lo-' mm) and it is likely t o be difficult to measure tliem in the experiment. When no more nodes are stuck, a global sliding is obtained. As shown in figure 3, the evolution of the solution is smooth. Figure 3 gives the changes with time in the global tangential force (friction furce) when the prescribed tangential displaceiirent increases. Figure 4 presents the isochrome lcvels a t t=27s.

60.0

zv 40.0 LL

20.0 0.0

80.0 [ 60.0

2 40.0 L4

80.0 n

associated with variable coefficient models. It is possible t o introduce a model of this kind into our formulation and we give the results of the corresponding quasi-static analysis in this section. In section 3, it will be established that this is not necessary however and that a non smooth solution can be characterized by a specific approach using a constant friction coefficient. We first used a two level friction coefficient : p s (static) and ,UD (dynamic). A single j u m p is observed (see figure 5). In the same way, a single wave propagates over the contact zone (see figure 6).

1

f

0

20

60

40

t

20.0 0.0

t I 0

20

40

t

60

80

(s)

Figure 5. Evolution of the global tangential force with ps = 1.15 and p~ = 0.9 .

80

(s)

Figure 3. Evolution of the global tangential force with p = 1.1.

Figure 6 . Isochromes with = 0.9 a t t=26s.

/IS

= 1.15 and

p~

Figure 4. Isochromes with p = 1.1 a t t=27s. The global shapes of these curves fit those measured by Zeghloul and Villechaise. On the contact boundary, the small wave is induced by the complex contact conditions (stick zone, sliding zone and separate zone). 2.4 Use of a variable friction coefficient Stick slip phenomena and instabilities are often

We now use a smooth decrease of the friction coefficient with the local sliding velocity (see figure 7). Here, repetitive jumps are numerically obtained (see figure 8). A wave is observed together with the first j u m p (see figure 9). However, waves are not observed together with the following jumps : we can note that after the first jump the stress field remains high while the wave phenomenon has always had a small amplitude. These results tend to underline a dependence of the phenomenon on the choice of the variation

42

0.2 0.0

0

25

50

75

100

125

v (Pnw Figure 7. Evolution of the local friction coefficient relative to the sliding velocity. 80.0 r 60.0 -

z

40.0 -

cient model because multiple solutions are to be expected, and depending on the numerical treatments, one or another solution will be selected. In any case, the numerical wave h a s an amplitude smaller than that observed experimentally (the number of isochromes is 200 in figure 4 and 100 in figures 6 and 9 while it is about 15 in the experimental analysis). It is also difficult to give a mechanical reason for the choice of the law given in figure 7 except for the upper and lower limits, which can be approximately deduced from the experimental measurement of the jumps of the tangential and normal forces. Note also that the above numerical results were obtained under the quasi-static assumption. Clearly, inertia effects will play an important role along the fast evolutions occuring at each jump. Another approach will now be investigated, which consists of introducing instability criteria.

3. INSTABILITY CRITERIA FOR FRICTION t (s) Figure 8 . Evolution of the global tangential force using for p the variation given in figure 7 (PMIN = 0.9 , PMAX = 1.15).

Figure 9. Isochromes using for p the variation given in figure 7 ( ~ M I N= 0.9 , MAX = 1.15) a t t=26s. of the friction coefficient. However, the importance of an implicit numerical treatment of the velocity dependence of the friction coefficient has been noted in the computations. That implicit treament acts correctly only in the case corresponding to figures 7 to 9 and shows up new stick zones after a jump, which is a key point for obtaining repetitive jumps. We are still working on the mathematical study of the variable coeffi-

We now consider the smooth quasi-static solution with a constant friction coefficient given in section 2.3 . At each step in the solution, we check wether a jump or a non smooth solution (divergence, flutter) is liable to occur, depending on various criteria. On the basis of previous studies by Martins et a1 [8], an energetic criterion and two dynamic criteria have been developed for the finite dimensional problem (see [ 11, [2]). 3.1. Stability criteria A small perturbation is applied to the smooth solution and its possible dynamic increase is checked. But this development has to be compatible with the unilateral and friction conditions. Applying these restrictions leads to introducing matrices K' and M' deduced from the stiffness and mass matrices K and M , respectively. These unsymmetrical matrices depend on the friction coefficient p and on the contact conditions (number of stick, sliding and separate nodes) ; they change at each step where a change in the contact occurs. Details will be found in Barbarin et a1 [l] and in Martins et a1 [2].

43

Experimental: First jump -+

I I

3.75 4.50

1 0

I

I

16 17

I I

4 4

I -9.057 I I -10.367 I

So, at each given time T in the incremental evolution, we modify the stiffness matrix K and the mass matrix M depending on the current contact conditions of the quasi-static solution. Here we a.re interested only in the free nodes (f) and in t,he tangential components of the sliding contact nodes (sT) :

0.276 0.154

I

I

5 5

where KiTi,p = KsTi,p p sign(RsTi) KsNi,p

with a positive real part (this is expected to be physically relevant if it corresponds to a low frequency mode of the structure). The situation is summarized by : Sufficient condition for divergence instability : the smallest real eigenvalue of K' computed is non positive. Sufficient condition for flutter instability : a complex eigenvalue of K' corresponding to a low frequency mode is obtained. Energetic instability (necessary condition for divergence instability): the smallest eigenvalue of the symmetrized matrix K> is non positive.

with p=f or sT and R s ~ isi the tangential reaction a t the sliding nodes. If the mass matrix M is diagonal (using the classical mass concentration), the criteria will be based only on matrix K'. The energetic criterion (Hill's criterion, see [9], [lo]) characterizes instantaneous jump solutions which may occur without adding any extra external energy. It can be shown (see [l],[2]) that such a situation may occur if the symmetric part K*, of K* admits a non positive eigenvalue. The dynamic criteria show (see [l], [2]) that a divergence instability may occur if K' admits a real non positive eigenvalue and a flutter instability may occur if K' admits a complex eigenvalue

3.2. The results For the energetic criterion, several numerical methods have been compared. The most suitable one is the Power method applied once or twice to find the smallest eigenvalue of the symmetrized matrix K i together with the associated eigenvector (which gives us the possible direction for the evolution of the solution). For the dynamic instability, we compute the whole spectrum of K* using both Lanczos and Double QR methods. Table 1 summarizes the results obtained with a friction coefficient ,u=l.l . The changes in the contact conditions (number of stick, sliding and separate nodes) are given when the prescribed

K* =

[

Kf,f

Kf,sT

KzT,f

KzT,~T

1

(1)

+

44

tangential displacement UT increases. The lowest eigenvalue of K> and the lowest real eigenvalue of K' are given at each step. The mode number which may be excited by a flutter instability is also given. T h e steps corresponding to t h e occurrence of instabilities using the various criteria are mentioned in this table. The step corresponding to the experimental observation of the first j u m p is also mentioned. The deformation corresponding to the eigenvrc-tor associated with the smallest eigenvalue of the symmetrized problem is presented in figure 10. It is worth noting that the direction given in figure 10, which is the initial direction of the jump solution, has precisely the shape of the wave. This is a very encouraging result obtained with this 11cw approach t o the phenomenon. However this energetic criterion is just a necessary condition for divergence instability.

Figure 10. Eigenvector with p=1.1 at t=26s. 3.3. Conclusion The quasi-static forniulation and the numerical treatment give an accurate description of the evolution of the contact displacements and the contact stresses. We show in this paper that the instability due to friction can be characterized with a constant friction coefficient model using appropriate criteria. Tlie energetic criterion predicts the occurrence of instability earlier than in the experiment. The direction of the possible jump exactly fits the shape of the experimental waves. With the flutter dynamic criteria, instability also occurs earlier. This is probably due to the significant role of damping in this problem, a role that was neglected here. Dynamic divergence never occurs. Other computations have shown that divergence criterion

would give instability only with a much larger friction coefficient than the experimental one (P = 2).

REFERENCES S. Barbarin, J . h . C Martins and M . Raous, Friction and instabilities : stress waves i n a sliding contact, Contact Mechanics International Symposium, Curry-Le- Rouct, 10-23 Sept. (1994). J.A.C Martins, S. Barbarin, M. Raous, Instabilities and friction (in preparation). T. Zeghloul, B. Villechaise, Stress waves in a sliding contact Part 1 , Proceedings of 22eme Leeds-Lyon Symposium on Trihology, 5-8 September (1995), L y o ~ i . T. Zeghloul, B . Villechaise, PhGnomknes de glissements partiels dCcoulant de l'usage de la loi de Coulomb dans un contact non lubrifiC, Materiaux et Techniques, Special Tribologie, Ddc. (1991) pp. 10-14. T. Zeghloul, Etude des pfidnomtnes d'atlhdrences et de glissements d a m un contact entre solides: approche expdrimentale et modClisation, Thesis, Poitiers, 13 Nov. (1992). M. Cocu, E. Pratt and M . Raous, Existence of a solution for the quasistatic problem of unilateral contact with nonlocal friction C. R. Acad. Sci. (Se'rie I ) n0320 (1995) pp. 1413-1417. M. Raous, P. Chabrand, and F. Lebon, Numerical methods for frictional contact problems and applications, Journal de Me'canique ThCo. A p p l . , special issue, supplement nO1to vol 7 (1988). 8. J.A.C. Martins, M.D.P. Monteiro Marques and F. Gastaldi, On an example of nonexistence of solution to a quasistatic frictional contact problem, E m . J . Mech., A/Solids, 13(1), (1994) 113-133. 9 . R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of Ariechanics Physics Solids,6 , (1958) 236-249. 10. X . Chatcau and Q.S. Nguyen, Buckling of elastic structures i n unilateral contact with or without friction, Eur. J. Mech., A/Solids, 10(1), (1991) 71-89.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

45

Third body effects in fretting J Weia, S. F o u v g , Ph. Kapsab and L. Vincenta

Departement Materiaux Mecanique-Physique, URA CNRS 447, Ecole Centrale de Lyon, BP 163,69 131 Ecully Cedex, France Laboratoire de Tribologie et Dynamique des Systeme, URA CNRS 855, Ecole Centrale de Lyon, BP 163, 69 13 I Ecully Cedex, France Experiments have been carried out, using a tension-compression hydraulic machine, to investigate the fretting behavior of TIN coatings on iugh speed steel (HSS) against an alumina ball. In the experiments reported here, a range of different normal loads, displacement amplitudes and frequencies was used and the 50% (RH), 75% (RH) and 98% 0. relative humidity of the test atmosphere was held at 5% 0 , 2 5 % 0, Compared to uncoated HSS, the fretting maps were modified due to differences in the surface nature and to mechanical properties. With the exception of low relative humidity, the relative motion between TIN and alumina occurs under a gross slip regime and the shape of the friction force versus displacement loop is quasirectangular. In the 5% RH and 25% RH atmospheres, the relative motion between TiN and alumina went from partial slip to gross slip when increasing the displacement. All the curves showing the friction coefficient were characterised by an initial transient state where the friction coefficient increased rapidly, followed by a steady state. The coefficient of friction and the wear depth change with the experimental parameters due to different wear mechanisms. 1. INTRODUCTION

Fretting refers to any situation in which the contact between materials is subjected to a low amplitude oscillatory sliding motion. The displacement amplitudes encountered in fretting are smaller than those of reciprocating sliding. The transition between fretting and reciprocating sliding is usually quoted in the interval 150-300 pm [ 1) and can be described as the value which exposes the entire contact to the atmosphere. TiN coatings produced by different physical vapour-deposition techniques usually exhibit improved service behavior and increased lifetime due to their ultrahigh hardness and their good wear resistance. In the past, work as focused on the tribological behavior of TIN coatings subjected to reciprocating sliding or sliding wear [2-71. The relative humidity then appeared as one important factor for their tribological behavior. Fretting behavior of TiN coatings under high loads, small displacement amplitudes and different relative humidity has not yet been reported. Fretting damage mechanisms of materials differ according to fretting conditions as described by fretting maps [ 1, 81. For uncoated materials in the

mixed or partial slip region, the nucleation and propagation of cracks prevail. In the gross slip region, the materials are mainly subjected to wear. In the present investigation, experiments have been carried out to systematically study the fretting behavior of TiN coatings against alumina in ballon-flat fretting experiments for several relative humidities with various applied loads, displacements and frequencies. The coefficient of friction and the wear depth of TiN coatings have been determined. Based on the experimental data and the results of microscopic studies, the dominant mechanisms responsible for the fretting behavior have been evaluated. The effect of h r d body (particle debris, transfer layers) and tribochemical reactions are discussed. 2. EXPERIMENTS 2.1 Materials A high speed steel ASP 23-M3 containing 1.2 at.%C, 4.2 at.%Cr, 5.0 at.%Mo, 3.0 at.%V and 6.4

at.%W was used as a substrate material for the steel block and for the coated specimen. After thermal hardening to 63 HRC, a 3-4 pm thick TIN coating was deposited by a PVD steered arc ion plating

46 process (BAM). The coated samples were cut to 15XlOX6 mm3. Surface roughness was Ra=0.02 pm. Its elastic modulus was 330 GPa [9] and its microhardness was 2000 HV. The counterbody was a polycristalline alumina ball with a diameter D=25.4 mm and a surface roughness Ra=0.02 pm. All the surfaces were cleaned with acetone and ethanol before testing. 2.2 Fretting tests Fretting tests were camed out using a tensioncompression hydraulic machine, which has been described previously [8, lo]. The normal load Fn varied from 50 N to 200 N with an interval of 50 N. Displacement amplitudes of +/-lo pm, +/-25 pm and +/-50 pn were applied with frequencies of 1 Hz and 5 Hz. For all tests, 5000 fretting cycles were performed. During the test, the three dimensional friction log (tangential force-displacement-number of cycles) was automatically recorded. The recorded data are then analysed to produce fretting loops (friction force vs. displacement hysteresis loops) and to determine the coefficient of friction, which is a value averaged over one complete cycle. The shape of a fretting loop depends on the experimental conditions, such as normal load, displacement amplitude, frequency, test time (or number of cycles) and environment. Fretting loops can be linear, elliptic or quasi-rectangular corresponding to the following fretting conditions: stick, partial slip and gross slip [ 1, 81. The test specimens were enclosed in a chamber in which the relative humidity could be changed. In this study, the relative humidity was selected as 5% RH, 25% RH, 50% RH, 15% RH and 98% RH at room temperature. After the fretting tests, wear depths were measured by talysurf profilometer. Characterization of the wear scars was performed with the aid of an optical microscope and a scanning electron microscope (SEM). The worn surfaces and debris were analysed by energy-dispersive X-ray spectroscopy (EDX) and X-ray diffractometer. On the basis of comprehensive analysis, wear mechanisms were evaluated.

3. EXPERIMENTAL RESULTS

3.1 Determination of the fretting regimes The ball-on-flat geometq used in tlus study results in a circular contact area. According to Mindlin's theory [ 111, the contact pressure reaches a maximum at the contact center and falls to zero at the edges under elastic contact conditions. The normal force is applied first, then the tangential force increases monotonically from zero with the increase of the displacement. It is expected that microslip occurs at the outer edges of the contact circle where the contact pressure is lower. Due to the lower contact pressure, at the outer edges of contact the tangential force needed to overcome the friction forces is also smaller, so that the partial slip occurs. When the tangential force is high enough to overcome the friction force at the center of the contact, gross slip predominates. The applied tangential force can be transferred into a tangential displacement, which is a more convenient measure of the fretting condition. Depending on the displacement amplitude, two types of friction forcedisplacement loops occurred for TIN coating for tests with very small relative humidity (RH=5%), as shown in Fig. 1. The area of the fretting loop represents the energy dissipated during a loop. In the partial slip regime, the shape of the tangential force-displacement loop is elliptic (Fig. la). After the elastic motion, the relation between friction force and displacement is no longer linear. In the central region, TiN coating and alumina stick together and the asperities deform elasto-plastically. In the outer annular region, slip occurs. The energy dissipation was mainly caused by sliding. In the gross slip regime, the friction force-displacement loop presents a quasi-rectangular shape (Fig. lb). The tangential force remains constant during a very large part of the displacement amplitude. The ratio between the dissipated energy Ed during a loop and the corresponding total energy Et is larger than 0.2 which is the limit between partial and gross slip conditions [8]. So to compare the effect of humidity, only gross slip conditions obtained for all the humidity ranges are discussed in the following.

47

(a) (b) Tangential force-displacement loops measured in 5% RH atmosphere at displacement of ((a)+/-4 pm and (b) +A25 pm (Fn=500 N, F=5 Hz). Fig.

1.

Depending on the experimental conditions, there are usually three regimes: stick, partial slip and gross slip. The nrnning condition fretting map (RCFM) of TiN coating and HSS substrate in the atmosphere of Werent relative humidity is shown in Fig. 2. The transition between partial slip condition and gross slip condition was determined (by energy ratio 181. It can be seen that TiN coating favors gross slip and thus reduces the mixed regime which is the most detrimental one because of cracking, the stick regime was not observed even for the smaller displacement. The transition between partial slip and gross slip appears at much smaller displacement amplitudes for TiN coating than that for HSS substrate. The TiN coating displays a rapid Itransition toward a gross slip regime. The partial slip is observed for very small displacement ,amplitudes and high normal forces. Transition is known to depend on the properties and friction coefficient of materials. A higher friction coefficient implies a higher transition displacement amplitude. The friction coefficient of TiN coating is smaller than that of HSS. In the case of high relative humidity, the friction coefficient of TiN coating is reduced to 0.2and the partial slip regime is no long observed from the fretting map.

--*TIN RWZW

-HSS RW5% --- HSS RH=ZMI ..-.-.HSS R W W

0

5

10

15

20

3.2 Friction and wear results Fig. 3 shows the influence of relative humidity on the coefficient of friction and the wear depth. Up to 75% RH, all the friction curves show a similar pattern, characterised by an initial transient state corresponding to an increase in the coefficient of friction, followed by a steady state. The lower the relative humidity is, the higher is the coefficient of friction during the steady state. The number of cycles needed to reach the steady state increases with increasing the relative humidity. In the test atmosphere with very high humidity 98% RH, the coefficient of friction remains almost constant at 0.2. Sliding between the TiN coating and alumina ball induced the formation of debris. The debris formed a thin oxide layer separating TIN and alumina and acted as a three-body action. From Fig. 3b it is clear that the relative humidity has a great influence on the wear depth.

.gj

g

1 T 0.8

- - RH25W

0.6 OA

b

O; 0

2000

4000

8000

number of cycles I

(a)

I RH=98% RH=75% RH=50% RH=25% RH4%

1

-300

-200

-100

0

loo

200

300

latersl podtion (Irm)

(b)

-.-.HSS RH=75%

dwkernent (rrn)

Fig. 2. RCFM of TiN and HSS for various RH.

Fig. 3. Evolution of the coefficient of friction with the fretting test duration (a) and wear scar profiles (perpendicular to the sliding direction) (b) on TiN mating against alumina (Fn=lOO N, D=25 pm, F=5

48 Hz) in the test atmosphere of different relative humidity. For a very low relative humidity (RH=5%), the wear depth is the largest. The wear depth and the width of wear scar decreases with increasing the relative humidity. The wear depth is in the range of 0.44-1.1 pm which is smaller than the mean thickness of the TiN coating (3-4 pm). ' T Fn =50N

- -

Fn=lCON Fn 4 5 0 N

0

2000

4000

normal force. It is worthwhile noting that the maximum wear depth and the width of the wear scar increase whereas the wear depth in the central region decreases with increasing the normal force. Fig. 5 shows the evolution of the coefficient of friction and the wear depth with the displacement amplitude. The greater the displacement amplitude, the shorter the initial transient state lasts. The steady state coeficient of friction slightly increases with increasing displacement amplitude, which is probably due to the quick formation of an oxide on the wear surface. In addition, increasing displacement results in the increase of the maximum wear depth and the wear depth in the central region.

6000

number of cycles D = 25pm D =50pm

I0 N

0

2000

4000

6000

number of cycles

Fn=150 N Fn=100N Fn.50 -300

-200

-100

0

100

200

N

300

lateral position (pm)

Fig. 4. Influence of the normal force on the evolution of the coefficient of friction (a) and the wear scar profiles (perpendicular to the sliding direction) (b) (D=25 pm, F=5 Hz,RH=75%). Because the case of 75% RH is representative the medium humidity condition, 75% relative humidity was selected to investigate the respective influence of the applied load, the displacement and the frequency on the fretting behavior of TiN coatings. Fig. 4 shows the evolution of the coefficient of friction and wear depth with the normal load. It can be seen that the number of cycles needed to reach the steady state increases and that the steady state coefficient of friction decreases with increasing

I

-300 -200

I

-100

0

100

200

300

lateral position (pm)

Fig. 5 . Influence of the displacement on the coefficient of friction (a) and the wear scar profiles (perpendicular to the sliding direction) (b) (Fn= 100 N, F=5 Hz, RH=75%). The coefficient of friction and the wear depth of TiN coating are affected not only by normal force and displacement but also by frequency. The evolution of the coefficient of friction and the wear

49

depth are shown in Fig. 6. It can be seen that the steady state coefficient of friction of TiN coatings at 1 Hz is smaller than that at 5 Hz.

F =5H2 F =1Hz

0

1000 2000 3000 4000 5000

number of cycles

*.

-300 -200

-100

0

lateral position

100

200

300

urn)

Fig. 6. Influence of the frequency on the coefficient of friction (a) and the wear scar profiles (perpendicular to the sliding direction) (b) (Fn=100 N, D=25 pm, RH=75%)

In addtion, increasing the frequency results in a shorter initial transient stage and a reduction of the number of cycles before the steady state is reached. However, the wear depth at 1 Hz is much greater than that at 5 Hz, possibly due to more material transfer. 3.3 Surface studies A comparison of micrographs of wear scars on TiN coatings clearly shows the differences encountered when the humidity is modified (Fig. 7). With the lowest relative humidity (RH=5%), the TiN coating appears to have worn more than in humid atmosphere, the morphology of wear scar is the coarsest and more transfer has occurred in the central zone. The TiN coating is mainly removed by transfer and abrasion. For relative humidities tugher than 25%, wear scars present a similar morphology. The wear surface is divided into three regions: a central region, a transition region and an outer annular region. The wear scar in the central region prevails deformation because of the higher pressure at the beginning of the test. Very small transfers and sometimes micro-abrasion occur in this region and the surface is smooth. In the transition region, transfers are observed with some grooves. Abrasion is smaller than in the outer region but transfers are more numerous than in the central region. In the outer annular region, many parallel grooves are oriented in the sliding direction. The ratio between the surface area of the central region and the area of the outer region decreases with increasing the relative humidity. It is also clear that the higher the relative humidity is, the smaller the wear surface is.

(a) (b) (c) Fig. 7. SEM micrographs of wear scars after 5000 fretting cycles for 5% RH (a), 50% RH 0)and 98% RH (c) (Fn=100 N, D=25 pm, F=5 Hz).

50

(a) 0) (c) Fig. 8. SEM micrographs of wear scars on alumina ball after 5000 fretting cycles for 5% RH (a), 50% RH (b) and 98% RH (c) (Fn=100 N, D=25 pm, F=5 Hz). Fig. 8 shows typical micrographs of the wear scars on alumina balls. Great differences in morphology exist between the wear scars for low and high relative humidity. Morphologies of scars on alumina ball correspond well to those on TIN coating (Fig. 7). The size of the damaged area on the alumina ball increased for fretting at very low relative humidity. It is clear that TIN transfer layers exist. Optical microscopy shows that the colour of the transfer layer is the same as the colour of the TIN coating. With high relative humidities (RH>25%), wear scars are characterized by three regions. In the central region, the alumina ball appeared to be damaged by deformation, slight transfer and abrasion. In the outer annular region, the alumina ball presents important abrasion damage. Between these regions, transfers are more numerous than in the central region but abrasion is not very important As determined by energy dispersive analysis, the composition of the debris appears to be the same on the alumina ball and on the TIN coating. The displacement amplitude also has a great influence on the damage mechanisms. Fig. 9 shows SEM micrographs of the wear scars on the TiN coating for displacement amplitudes of +/-lo pm and +/-50 pm. For the former case, the greater central region appears polished and the smaller outer annular region abraded. The wear scars are characterized by parallel grooving oriented in the sliding direction with some slight traces of transfer when the displacement is equal to +/-50 pm. Abrasive damages the fretting couples to a greater extent in the outer annular region than in the central one.

3.4 Third body examination for different relative

humidities Fig. 10 shows SEM micrographs of debris for different relative humidities. It is noted that the debris is loose and more debris is ejected from the wear scar at low relative humidity (RH=5%). At high relative humity (RH=98%), the debris are compacted together. Almost all the debris adhere to the wear scar. Very few debris are ejected out of the wear scar. At medium relative humidity (RH=50%), the morphology of the debris is between those at low and high relative humidity. Some debris are compacted to form greater debris. When the fretting tests are completed, it is found that the debris are mainly pressed to the outer annular region of the wear scar on alumina ball after separating the tribocouples. Just at high relative humidity (RH=98%), part of the debris adheres to the wear scar on the TiN coating. It implies that high relative humidity favours the debris layer resting between the contact surfaces. Besides, the analysis of the debris with energy dispersive X-ray spectroscopy on the TiN coating indicates that the oxygen content in the debris increases with increasing the relative humidity. Xray diffraction of debris indicates that the ratio between oxygen and titanium is smaller than 2. The debris layer as the third body plays an important role during the fretting tests. At high relative humidity, the debris are oxidised to a greater extent. The oxide debris between the contact surfaces can separate the direct contact between TIN coating and alumina ball and reduce the coefficient of friction and wear.

51

(a)

(b)

Fig. 9.SEM micrographs of the wear scars on TiN Coating after 5000 fretting cycles with +/-lo pm (a) and +/50 pm (b) displacements (Fn=100 N, F=5 Hz,RH=75%).

Fig. 10. SEM micrographs of the debris for RH=5% (a), RH=50% (b) and RH=98% (c) relative humidities. 4. DISCUSSION

Fretting wear is well known to strongly depend on parameters, such as applied load, displacement amplitude, frequency, environment and properties of material surfaces. For a given material,the fretting condition can be stick, partial slip and gross slip which often correspond to the material response: no damage, crack and particle detachment [8]. For the range of parameters in this study, the TIN Coating exhibited the partial slip condition only with very low relative humidity due to its many

brittleness. The behaviour of the TiN coating against alumina was greatly influenced by the relative humidity when gross-slip fretting was imposed due to the tribochemical reaction and the lubricious action of humidity. During the fretting test with very low relative humidity, no lubricious action was observed, and the highest values of the coefficient of friction and the wear depth OCCUT. Because of the easier and greater transfer under such a condition, the profile of wear scar is more irregular. The wear mechanisms are mainly transfer and abrasion.

52

Tllc frctting behavior is very different in the atmospheres with higher relative humidity (,RH>2S%) due to the lubricious action of the humidity. The process of fretting wear is divided into three stages: (1) initial adhesion, with transfer and few abrasion (0-200 cycles); (2) abrasion and transfer resulting in oxidation wear with mixture of titanium oxide and alumina debris (about 200- 1000 cycles); (3) steady state wear, abrasion in the outer annular region, medium abrasion and transfer in the transition region and slight transfer and abrasion in the central region (above 1000 cycles). The duration of each stage is influenced by the experimental condition. In the first stage, the coefficient of friction remained very low (about 0.2) possibly due to the combining action of contaminant films and moisture adsorption. In the second stage the coefficient of friction rises quickly due to the removal of the natural film and the direct contact between TIN and alumina. The wear observed is mainly two-body wear. First stage and the second stage are called as running-in period. The direct contact between TiN and alumina induces a quick increase in the wear depth. In the third stage, the formation of lubricious layers plays an important role. The wear debris mainly form in the transition region and in the outer annular region. Debris are TiO,-, oxides which agrees with other results [2,12-141. The lubricating effect of the TiO,, layer reduces the coefficient of friction and wear depth to a certain extent. The typical shape of the wear scar on the TiN coating can then be related to the presence of wear debris which modifies the pressure distribution[151. The adsorption of moisture from the atmosphere to the TIN surface as well as the formation of lubricious reaction layers depends on the relative humidity. The higher the relative humidity, the more the formation of the lubricious layer is. Thus thc coefficient of friction and the wear depth decrease with increasing the relative humidity. With higher relative humidity, the greater combining action of the natural film and the adsorption of moisture on the TIN surface also delays the steady state. That is to say that the formation of the debris layer needs a longer time. The influence of other experimental parameters such as normal load, displacement and frequency depends on the duration of the debris formation and on the quantity of the debris. Under higher normal

forces, the displacement in the central region is to a greater extent accommodated by deformation and the area of the central region is largcr. The formation of the debris layer requires a long time. Howcver, the wear depth and the quantity of the debris increase slightly with increasing normal forccs due to the higher pressure and tangential force. The quantity of the debris influences the coefficient of friction. With a greater displacement amplitude, the deformation accommodation in the central region is not so effective, so the central region is greatly worn too. In addition, the exposure time of TiN in the humid atmosphere and the adsorption of moisture on TIN surface as well as the action of oxidation arc reduced with greater displacement, so that the coefficient of friction and wear depth increase. By reducing the test frequency, the exposure time of TIN surface in the humid atmosphere increases. so that the adsorption of moisture on TIN surfacc and the oxidation of TIN occur to a greater extent and this results in the low values of the coefficient of friction. However the wear depth is greater due to more transfer. 5. CONCLUSIONS

Ball-on-flat fretting wear behaviour of TIN coating against alumina was studied under high normal loads, small displacement amplitudes and for different relative humidity. The main conclusions are: (1) A partial slip regime occurs in the running condition fretting map of TIN coating only in the case of low relative humidity. The TiN coating modifies the fretting map of the steel substrate and favors gross slip. (2) The curves giving the coefficient of friction vs. the number of cycles for TIN are characterised by an initial transient state and a steady state. The coefficient of friction and the wear depth decrease with increasing relative humidity due to the adsorption of moisture on TIN surface and the oxidation of TiN. The lubricious action of humidity plays an important role during fretting wear. (3) The normal force has a small effect on the fretting wear of TIN. With increasing normal force, the coefficient of friction decreases and the wear depth increases.

53 (4) The displacement amplitude has a large effect on the fretting wear. The coefficient of friction and the wear depth increase with increasing displacement due to the exposure time of TiN in the atmosphere during each cycle being shorter and the accommodation of deformation to the displacement being smaller. ( 5 ) The coefficient of friction increases and the wear depth decreases with increasing test frequency. (6) The wear mechanisms differ in the different contact regions. In the central region, slight transfer, abrasion and deformation are observed. In the outer region, abrasion is the main controlling wear mechanism. In the transition region between the central region and the outer region, abrasion and transfer are the main wear mechanisms.

ACKNOWLEDGEMENTS The authors wish to thank the Commission of the European Community for financial support (project BRE 2-CT 92-0224), their colleagues in the CEC project for furnishing the coated samples, R. Vargiolu for performing the surface roughness niesurements and N. Chavent for performing the SEM observations.

REFERENCES 1. 0. Vingsbo and S. Soderberg, On fretting

maps,Wear, 126(1988)131-147.

2. I.L. Singer, S. Fayeulle and P.D. Ehni, Wear, 149(1991)375. 3. Z.P. Huang, Y. Sun and T. Bell, Wear, 173(1994)13-20. 4. B. Malliet, J.P. Celis, J.R. Roos, L.M. Stals and M. Van Stappen, Wear, 142(1991)151. 5 . S.J. Bull and P.R. Chalber, Surf. Coat. Technol., 41( 1990)269. 6. H.J. Boving and H.I. Hintermann. Thin Solid film, 153(1987)253. 7. H.J. Scheibe and D. KlatEe, Surf. Coat. Technol., 57(1993)111. 8. S. Fouvry, Ph. Kapsa and L. Vincent, Wear, 185(1995)35-46. 9. J.P. Celis, J.R. Roos, E. Vancoille, S. Boelens and J. Ebberink, Mater. Sci. Forum, 102104(2)(1992)599-613. 10.2. R. Zhou, S. Fayeulle and L. Vincent, Wear, 155(1992)317-320. 11. R.D. Mindlin and H. Deresiewicz, J. Appl. Mech., 20( 1953)327-344. 12. M. N. Gardos, in MRS Symp. Proc., 140(1989)325. 13. I. L. Singer, Surf. Coat. Technol., 49(1991)474. 14. H. Mohrbacher, B. Blanpain, J.-P. Celis and J.R. Roos, Wear, 180( 199943. 15. S. Fouvry, Ph. Kapsa and L. Vincent, ITC’95, Yakohama, Japan, 29 0ct.-2 Nov.. (1995).

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The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

55

Elastic-Plastic Microcontact Modeling Using Dislocations I. A. Polonsky and L. M. Keera

aDepartrnent of Civil Engineering, Northwestern University, Evanston, IL 60208-3109, USA A new method for simulation of microscopic elastic-plastic contacts is developed. Microcontact plastic deformation is described in terms of nucleation and motion of discrete crystal dislocations. The new method allows elastic-plastic microcontacts to be investigated on the scales too small to apply conventional continuum mechanics methods, but still too large for atomistic simulations, The model is scale-sensitive and allows scale effects of microcontact elastic-plastic behavior to be studied theoretically. Results of several two-dimensional elastic-plastic microcontact simulations performed using the developed method are presented in this paper.

1. INTRODUCTION

The friction and wear properties of most materials h a s historically been explained in terms of the interaction of niicroscopic asperities covering contacting surfaces (Bowden and Tabor, 1950; Moore, 1975). Traditionally, problems of microcontact deformation have been analyzed using tlie methods and concepts of conventional macroscopic plasticity theory and contact mechanics, such as tlie slip-line theory (Green, 1955; Avitzur et al., 1984; Hockenhull, et al., 1993, and many others), approximate semiempirical contact theories (e.g. Sin et al., 1979; Halling, 1976; Burnett and Rickerby, 1987; Chang et al., 1987) and recently the finite element method (Tangena and Wijnhoven, 1985; Ohmae, 1987; Komvopoulos, 1989; Montmitonnet et nl., 1993). However, tlie elastic-plastic response of an asperity microcontact can be different from that of a similar macroscopic contact if the microcontact is so small that its size is comparable with a cliarac tcristic niicrostructural length, such as thc avcrage dislocation cell size (Kuhlmann-Wilsdorf, 1981; see also Pollock, 1992). The fact that the behavior of microcontacts can be remarkably different from that of macrocontacts is also co r ro bo ra t ed by m o 1ec u 1a r d y n a mi c s

simulations of atomic-scale contacts (e.g., Sutton and Pethica, 1990; Belak and Stowers, 1992; Landman et al., 1992). However, such simulations are currently limited to modeling contacts not exceeding a few nanometers in size. In an attempt to close the gap between macroscopic, continuum mechanics based analyses and atomistic computations (the necessity of which has recently been emphasized by Johnson, 1992), a new theoretical approach to modeling elasticplastic microcontacts based on plasticity representation in terms of discrete dislocations was developed by the authors (Polonsky and Keer, 1995-1,111. Using the new method, a number of microcontact simulations were performed. The junction growth effect for a s pe r i t y mi c r o co n t a c t s w a s s t u d i ed ; peculiarities of subsurface stress distributions a t asperity microcontacts were analyzed; interaction between a pair of microasperities was simulated, which provided an estimation of the plastici ty contribution to friction (Polonsky and Keer, 1995-1). Apparently for the first time, scale effects of elastic-plastic asperity microcontact behavior were studied thcorctically (Polonsky and Keer, 1995-11). In the present paper the new simulation method is hricfly described, some of the previously rcportcd results a r e summarized, a n d

56

simulation results not included in our previous publications are presented. The authors realize that tlie concept of surface asperity, which is essential to the present work, is not easy to define in a clear and meaningful way (Greenwood, 1992). One major problem is that most real surfaces have very broad spectra containing roughness wavelengths ranging from the body length down to tlie interatomic distance. Another is that different wavelengths are generally not independent. However, the authors believe that useful insights into the nature of microcontact deformation processes occurring on various roughness scales can be attained by co 11 si d e r i ng i n tera c t ion of i 11d i vi d u a 1 asperi tics of corresponding dimensions having a smooth shape, thus disregarding the fcwtures pertaining to other roughness scales. I t can be noticed that even i n the theories of rough contact based o n modern concepts of su rfa cc topography (Majumd a r and Bhu shan, 1 9 9 1 ; Aramaki a/., 1993) the notion of individudl asperity had to bc introduced at some point. Thus, the present research is r c'st r ict cad to problems i nvo 1v i 11g i iid i v i d u a 1 asperities. A complete theory of rough contact should also incorporate the statistical nature of surface roughness and take into account the interaction between different roughness wavelengths, but these issues lic outside the scope of the present work.

2. SIMULATION METHOD

A detailed description of the new method can be found in Polonsky and Keer (10c~5-I). The method is currently limited to simulating two-dimensional (2D) contacts. Although inadequate in many rcspccts, 2D dislocation-based analyses can be successfully used to explore some of the peculiarities of extremely small plastic microcontacts, as the work of Gerberich et a/. (1995) exemplifies. In tlie present analysis one of the contacting bodics is assumed to be rigid, while the other is elastic-plastic. The plastic deformation of the latter body is described in terms of the

nucleation and motion of discrete crystal dislocations (rather than in terms of continuum plastic strain). These dislocations move along a fixed set of slip directions; hence, the body is plastically anisotropic. However, i t is assumed to be elastically homogeneous and isotropic. The following two features make the new method capable of studying scale effects: first, the subsurface crystal dislocations describing plastic deformation have a fixed Burgers vector length; second, they can be nucleated only at pre-existing dislocation sources (a 2D array of which is assumed to exist below the surface). Thus, there appear two characteristic lengths in addition to the microcontact size: tlie Burgers vector length of crystal dislocations b and the spacing between dislocation sources d . For typical machined and/or worn surfaces, d can be related to a first approximation to the average size of dislocation cells, subgrains or microbands in the near-surface material layer (Rigney, 1988). The scheme used in the present method for elastic field computation is related to the boundary element method. The contact elastic field in the elastic-plastic body is constructed by distributing fictitious dislocation dipoles over its surface (discretized in to straight-line surface elements). Each surface element bears two dislocation dipoles: o n e with the dislocation Burgers vectors collinear with the dipole line (glide dipole) and the other with the dislocation Burgers vectors normal to the dipole line (climb dipole); the dislocations forming these dipoles are located at thc extremities of the element. Elastic fields are also produced by red dislocations lying below tlie surface of the elastic-plastic body, and by image dislocations lying above the surface. The three types of dislocations contributing to the total elastic fields a r e s h o w n schematically in Fig. 1. Thus, the total stress at a field point x in the elastic-plastic body is obtained as follows:

57

Here N,,N,,N,,and Ni stand for the number of surface elements, slip systems, real crystal dislocations a n d image dislocations, respectively. The Burgers vector magnitudes of the glide and the climb dipoles associated with element k are bkt and bkn, respectively, and the locations of the ends of element k are xkl and xk2. The stresses produced at point x by a glide and a climb dislocation dipole with the ends at points x1 and x2 and a unit Burgers vector are T t i j ( x ;x , , x 2 ) and T n j j ( x x; l , x 2 ) , respectively. The Burgers vector magnitudes of real dislocation I and image dislocation m pertaining to slip direction p are bpr and bl"", respectively, and s,, is the unit vector of slip direction p. The stresses produced at x by a dislocation having a unit Burgers vector in direction s and located at xo are Tjj(x;xO;s). Similarly, the displacement increment at point x can be expressed as follows:

p=l I=1

Burgers vector and the ends located at points xl and x p are U ' ; ( x ;x , , x , ) and U " i ( x ; x l , x Z ) , respectively. The functions T'ij(x; X,,X~), 7"'ij(X; x , , x ~ ) , T$x; xo; s), Ut;(x;x1,x2)and Uni(x;xl,x2), which play a role of Green's functions in the present algorithm, are well-known (e.g., Hirth and Lothe, 1982). Using for this purpose full-space dislocation solutions, rather than any types of fundamental solutions for an elastic halfspace, makes it possible to consider contacting bodies of arbitrary shapes, without assuming them to be nominally flat.

ID

Figure 1. Scheme of the simulation method showing real crystal dislocations (RD), image dislocations (ID), fictitious surface dislocation dipoles (FD, shown for one surface element only), the slip directions ( sl,s2,s3) and the dislocation source pattern (asterisks). The rigid body is shaded. Discretization of the elastic-plasticsurface is exaggerated.

Here ribkt and ribknare the increments of bkt and hkn, respectively. The positions of real dislocation 1 at the beginning and at the end of the increment are xroand xI1, respectively. The corresponding quantities for image dislocation are xpn0and xrnl. The displacements produced by a glide and a climb dipole with a unit

Currently, i t is assumed that all energy dissipation at the microcontact is associated with microcontact plastic deformation, and no energy is dissipated directly in the interface. Thus, the familiar

boundary conditions for a frictionless contact are used in the simulations:

Here at(x), a,(x) and g(x) are the stress tangential to the surface, the stress normal to the surface and the gap between the contacting bodies at a surface point x, respectively; A, is the current contact area. The unknown Burgers vectors of surface elements (bkn and bkt) are determined by requiring that the equality boundary conditions be exactly satisfied at the collocation points (the geometrical centers of the surface elements). The current contact area is determined by iteration, until the inequality boundary conditions are satisfied. Dislocations are nucleated i n pairs of opposite sign (dipoles). A iwwly nuclea ted dipole is centered at the dislocation source and its arm equals to the source spacing d . Dislocation nucleation occurs if the resolved shear stress (calculated using equation (1)) exceeds the frictional stress T() both at the source location and at the dipole ends. This frictional stress characterizes the resistance of the crystal lattice of the modeled material to dislocation motion (apart from elastic dislocation interactions). When checking this condition, the mutual attraction of the two new dislocations is also taken into account. Dislocation motion is predictcd a s follows. The stress state a t the location of dislocation is calculated using formula (1) and resolved on the dislocation slip direction. If the absolute value of the resolved shear stress is less than q,, the dislocation position does not change; otherwise, the dislocation moves. I t is assumed that the dislocation velocity v obeys the following quasi-viscous law:

where p is a coefficient characterizing the drag force acting on the dislocation. Then, the incremental distance traveled by a dislocation is computed as dl = u df, where df is the timc step and v is given by formula (4). This motion

always occurs in the dislocation slip direction. Including the rate dependence of dislocation velocity is necessary to improve the model stability and to avoid the well-known nonuniqueness typical of crystal plasticity problems. When two dislocations with a negative scalar product of their Burgers vectors approach each other closely enough (a distance of a few Burgers vector lengths), a dislocation annihilation reaction is simulated. Multiple annihilations a r e treated a s sequences of pair annihilations. A dislocation is also annihilated when it approaches the surface closely enough. In the latter case, the dislocation is moved out of the body along the corresponding slip direction and then i s shifted to a predetermined position above the contact area, so that the dislocations belonging to the same slip system that have left the body form a single image super-dislocation. Such a coalescence of image dislocations allows the computation time to be reduced considerably. The displacements produced by thcse image dislocation shifts are taken into account in a usual way. Note that the dislocations leaving the surface cannot be shifted to infinity and then discarded, as this would result in a spurious behavior of the surface displacements at locations far from the contact area. The problem is solved incrementally. The time s t e p and the corresponding incremental change in either the rigid body position or the total force applied to the rigid body in the tangential and the normal directions are prescribed. In the beginning of each s t e p , nucleation, motion, a n d annihilation of real dislocations during the step is predictcd as described above. The corresponding incremental displacements are computed and the plastic body geometry is updated. Then, the rigid body coordinates and/or the total force components are updated using the prescribed increments and the Burgers vectors of surface elements a r e recomputed according to the above algorithm. Such an incremental formulation allows one to d e a l with t h e h i s t o r y d e p e n d e n c e

characteristic of plasticity problems. Relatively large asperity deformations can be considered; however, the plastic rotations are assumed to remain small throughout the body (so that rotation of the slip directions during microcontact deformation can be neglected). 3. PROBLEM FORMULATION

The type of asperity microcontact considered in the present study was that between an elastic-plastic body having an initially flat surface and a rigid asperity. The asperity was shaped as a segment of a sine wave of wavelength 212 and amplitude h/2, so that the asperity length was 2a and its height h (Fig. I). In order to study scale effects, the value of a (characterizing the asperity size) was varied, while the asperity shape was similar in these simulations. The asperity sharpness ratio h/a = 0.1 was used in the simulations. This value is somewhat greater than the values often cited in the literature and based on profilometric data (about 0.010.001). However, it is well-known that the average asperity slope increases with increasing profilometer resolution, i.e., with decreasing roughness scale (Sayles a nd Thomas, 1979). For example, the slope of microasperities produced by individual slip lines intersecting the surface (as discussed by Kuhlmann-Wilsdorf, 1981) can in principle be on the order of unity. Hence, at extremely small asperity scales for which the present method was developed the chosen value of h/u appears to be realistic. Another consideration is as that very shallow asperities will be flattened elastically. A rough estimate of contact stresses produced in this case is o = Eh/a, where E is the Young modulus (Westergaard, 1939). Hence, a n asperity can be flattened without plastic deformation if h/a < oJE, where o,, is the yield stress. Since a,/E can be about 0.01 for hard wear-resistant materials, asperities shallower than h/a = 0.01 should generally be of little interest a s far a s microcontact plasticity is concerned.

The elastic constants of the elasticplastic body were chosen as follows: the shear modulus G = 100 GPa; Poisson's ratio v = 0.3. These values roughly correspond to steel. However, the elastic modulus values are not themselves very important; it is the ratio z,/G that critically affects the dislocation activity a t the microcontact. In the present simulations, zo = 500 MPa (i.e., zo/G = 200) was used. This value appears to be a reasonable order estimate for high-carbon steels in the martensitic condition, as well as moderately hard ceramics (cf. data in McColm, 1990). The crystal structure considered was that with three easy slip directions making an angle of 120' with one another. One of the slip directions was normal to the boundary of the elastic-plastic half-plane (see Fig. 1). In the 2D case only two non-degenerate slip directions are sufficient to produce an arbitrary plastic strain. A third (redundant) slip direction was added in an attempt to represent better real 3D crystal structures. Indeed, even crystals lacking five independent primary slip systems are still capable of arbitrary plastic deformation (apparently by the activation of additional slip systems) under a contact loading, as is clear from microhardness indentation experiments. The dislocation source distribution in the elastic-plastic body was in the form of a hexagonal 2D lattice with the lattice spacing d and the hexagon sides parallel to the slip directions for the chosen 2D crystal orientation (Fig. 1). The dislocation source spacing used in the present simulations was d = 100b, where b is the dislocation Burgers vector length (typically, 2-5 A). This choice can be justified by the following considerations. Values of the Characteristic microstructural length of nearsurface layers (dislocation cell or microband size) cited in the literature are in the approximate range 50-500 nm (Samuels et al., 1981; Rigney, 1988). However, these values usually pertain to depths of a few microns, while the microstructure just next to the surface can be much finer (Rigney, 1988). Hence, although very different microstructures can certainly exist in various materials under

60 various conditions, the chosen value of d appears to be generally realistic. Two contact situations were considered for each asperity size: normal indentation and tangential ploughing. In the former case, the horizontal position of the rigid asperity was fixed. Simulation started by setting the vertical position of the asperity to a value at which the two bodies slightly touched each other; the corresponding normal load applied to the asperity (and equilibrating the contact force) was computed. Then, the normal load was increased stepwise to a prescribed value; the corresponding normal penetration was computed at the end of each step. Finally, the asperity was withdrawn upwards (in a single step). Note that in the present 2D model load is measured per unit width (the asperity being infinitely wide). Tangential ploughing simulations also began as a normal indentation to a prescribed normal load. After that, the asperity started ploughing the surface in the tangential direction with a prescribed (constant) tangential velocity. The normal load achieved by the end of indentation was maintained during ploughing, while the normal penetration was allowed to vary. After ploughing a distance equal to the asperity half-length a , the asperity was rapidly withdrawn upwards. In both types of simulations the prescribed normal load (per unit width) was directly proportional to the value of a , so that the maximum contact pressure would have been the same in all these simulations if the problem had been purely elastic (with no dislocations nucleated).

microcontact elastic-plastic behavior was observed in the case of tangential ploughing. As the ratio a / d decreases, contact plastic deformation becomes more difficult; below a certain threshold asperity size (about a/d.= .2), the microcon tact response becomes purely elastic.

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4. RESULTS AND DISCUSSION 4.1. Scale effects in normal elastic-plastic

microcontacts Normal indentation and tangential ploughing simulations were performed for the following eight microcontact situations: a/d = 10, 8, 6, 4, 3, 2.5, 2, and 1.5. The results pertaining to the latter type of contact were presented elsewhere (Polonsky and Keer, 1995-11). A remarkable scale effect of

The results of some of the normal indentation simulations are illustrated by Figs 2-5. These figures show the deformed profile of the initially flat elastic-plastic surface both under the peak load and upon unloading (Figs 2a-5.4, as well as the dislocation activity below the contact upon unloading (Figs 2b-5b). In the latter type of figures, dislocations are shown as black diamonds

61

with thin dotted traces connecting each dislocation with the location of its nucleation.

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Laaded profile:60 ...... {. . . . . . .; . . . . . . . . . . u . n ] w e dfirof!le.;--. . : Initial profile:

3b). As the asperity size is reduced to a/d = 3 (Fig. 4), the residual plastic indent becomes very shallow and only a few dislocations are nucleated. Finally, at a/d = 2 there is no dislocation activity (the contact remains perfectly elastic all the time) and no residual indent is produced.

42

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Figure 3. Indentation of an elastic-plastic surface by a rigid asperity; a = 600b, d = 100b. (a) Surface profiles. (b) Dislocation activity. It is seen from Figs. 2-5 that the scale effect of microcontact elastic-plastic behavior is as pronounced for normal microcontactsas for tangential ones. The relative residual indent depth 7o/a (where 70 is the absolute depth of the residual plastic indent produced by the rigid asperity in the elastic-plastic body) at first decreases rather slowly as a/d is reduced. However, with further reduction in a / d it begins to decrease noticeably: the value of w/a for a/d = 6 it is only about two thirds of its value for a/d = 10 (cf. Figs 2a and 3a). The dislocation activity below the contact also becomes much less pronounced (cf. Figs 2b and

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Figure 4. Indentation of an elastic-plastic surface by a rigid asperity; a = 300b, d = 100b. (a) Surface profiles. (b) Dislocation activity. The observed trend in the elasticplastic behavior of normal microcontacts is illustrated by Fig. 5, in which w/u is plotted as a function of asperity size. The corresponding dependence for tangential microcontacts (the relative depth of the residual track ploughed by the asperity versus a / b ) is also shown in this figure for comparison. It appears that the threshold

62 asperity size is somewhat greater in case of normal indentation than in case of ploughing. This is not surprising since in the latter case the asperity traveling along the surface can find the position with respect to the dislocation source array that corresponds to the optimum conditions for dislocation nucleation.

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alb Figure 5. Relative depth of the residual depression produced by normal indentation (diamonds) and tangential ploughing (crosses) versus asperity half-length. The present simulations (together with those reported in Polonsky and Keer, 199541) show that plastic deformation at normal as well as tangential asperity microcontacts becomes difficult and then impossible when the asperity size decreases below a certain threshold value on the order of the microstructural length. These results give some credence to the ideas of KuhlmannWilsdorf (1981) who suggested that nanometer-scale microasperi ties can resist plastic smearing and thus remain capable of transmitting tangential contact force to deeper layers because their size is comparable with the characteristic length of dislocation microstructure, which inhibits plastic deformation. However, our simulations cannot verify her theory of friction as a whole, as it

also involves a number of assumptions that lie outside the scope of the present research. An interesting feature of the plastic behavior of normal microcontacts can be seen from Figs 2-4. The plastically deformed surface profiles (both loaded and unloaded) as well as the dislocation activity patterns are not quite symmetric with respect to y-axis, despite the fact that the initial geometry and the applied loading are perfectly symmetric (Figs 2-4). This symmetry loss is apparently caused by inherent instabilities in the complex process of motion, nucleation and annihilation of interacting dislocations. Such instabilities were frequently observed in our simulations, even in cases where the 'global' microcontact response was rather stable. In initially perfectly symmetric problems they can be triggered by computation error. When the asperity size is very much greater than the microstructural length, these small-scale instabilities should tend to 'average out', and the associated asymmetry in nominally symmetric normal contacts (as well as any effects of the exact position of the indent with respect to the dislocation source array) should become relatively insignificant. This speculation can in principle be verified by performing microcontact simulations with large a/d ratios. Such simulations would be very compu tationally expensive, however. One might argue that the scale effect demonstrated above occurs on a scale too small to be of any interest to real applications. The following example shows that this is not so. The authors measured the C.L.A. roughness of bearing balls (with the waviness cutoff set at 10 pm) and obtained values about 2 nm (for regular bearing balls) and about 20 nm (for bead-blasted balls used in rolling contact fatigue testing). These values provide approximate upper bounds for the asperity height h (for asperities shorter than 10 pm). Then, asperities having sharpness about h/u = 0.1 (as in the above simulations) should have lengths not exceeding a < 20 nm (smooth bearing balls) and a c 2000 nm (rough bearing balls), or a < 60b and u < 600b, respectively (for steel b is about 3 A). These values of u

63 agree with those used in our work (150b < a < 1OOOb). Even if one assumes that h/a = 0.01 for the asperities of interest, the values of a used in our simulations will still be reasonable, at least for smooth bearing balls.

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Figure 6. Ploughing of an elastic-plastic surface by a rigid asperity; a = 600h, rf = 100b. (a) Surface profiles. (b) Dislocation activity. 4.2. Comparison of normal and tangential inicrocontacts A comparison of a normal asperity microcontact and the corresponding tangential one (for the same asperity size, load and model microstructure) shows that a greater amount of microcontact plastic deformation tends to be produced in the latter case. For cxample, compare Figs 3 and 6 showing indentation and ploughing, respectively, for dsperity size a = 60Ob (a/d = 6). It is seen from

these figures that the region of dislocation activity is not only broader (which is natural) but also much deeper in the case of tangential ploughing. The depth of the residual depression produced by the asperity in the elastic-plastic body is also noticeably greater in this case (which is also evident from Fig. 5). This phenomenon is essentially the familiar junction growth effect (Bowden and Tabor, 1950). A detailed analysis of this effect in microcontacts similar to the present ones was performed by the authors (Polonsky and Keer, 1995-1); in particular, the role of asperity sharpness ratio h/a was investigated. It was shown that the effect manifests itself even for quite shallow asperities ( h / a = 0.02) and becomes considerably more pronounced as h/a increases. The corresponding difference in dislocation activity was also found to be great. The present study shows that the junction growth effcct occurs in asperity microcontacts at various asperity scales (see Fig. 5). Thesc findings have interesting implications for some wear mechanisms of hard brittle materials such a s ceramics. A widely used theory of ceramic wear is based on an assumption that asperity microcontacts are qualitatively similar to a h a r d n e s s indentation, so that the models and the experimental data pertaining to indentation fracture can also be applied in this case (Evans and Marshall, 1981). This theory has been criticized by some authors, particularly on the ground that it does not take into account the tangential component of contact force (e.g., Ajayi and Ludema, 1992). However, in the theories recognizing the tangential nature of asperity microcontacts during sliding the effects of tangential contact force are limited to modification of the Hertzian contact stress field and the associated increase in stress intensity factors for Griffith (Rosenfield, 1980, Hokkirigawa, 1991) or Dugdale (Rosenfield, 1981) cracks beneath the contact. I t is also assumed that the tangential force is solely produced by friction at the microcontacts. However, the contact area, the plastic zone size and the normal penetration can markedly increase if a tangential component is

64 superimposed on the normal load applied to the indenter (Bowden and Tabor, 1950). The above results and those reported in Polonsky and Keer (1995-1) indicate that this effect is as prominent for asperity microcontacts of a size comparable to the characteristic microstructural length as it is for macroscopic contacts. Since the indentation-type cracking occurring at asperity microcontacts should be caused by contact plastic deformation (a fundamental proposition of Evans and Marshall, 19811, it appears that the potential for microcrack initiation a t asperity microcontacts should be significantly higher for tangential ploughing than for normal indentation (at the same normal load). It should be emphasized that in our simulations the tangential contact force was entirely due to the surface profile change associated with the contact plastic deformation. Hence, contrary to the wear theories mentioned above, the difference between normal and tangential microcontacts is not limited to the effects of microcontact friction (although the junction growth effect can undoubtedly be greatly amplified by such friction). Load-controlled conditions at asperity microcontacts (such a s those used in simulations on which Figs 5 and 6 are based) can be expected to arise when there are a few sharp asperities dominating the surface relief, and the total load is not too high to be supported by these asperities only. This situation may occur, for instance, if a small number of third bodies larger than the surface relief features are present in the macrocontact, or if one of the surfaces has a roughness structure similar to that of a grinding wheel. I n such situations, the junction growth effect must be incorporated explicitly into any wear model; otherwise, a strongly non-conservative wear rate estimation may be obtained. In many other situation, however, a normal penetration increase occurring at the beginning of ploughing can be expected to produce a rapid increase in the number of asperity microcontacts within the macrocontact and a corresponding normal load redistribution. Then, penetra tion-controlled (rather than

load-controlled) loading conditions will prevail at asperity microcontacts. In real situations junction growth will still occur in this case d u e to microcontact friction. However, results of Polonsky and Keer (1995I) imply that the plastic behavior of asperity microcontacts, and hence their proclivity to microcrack formation, may differ markedly depend i n g on the p r e va i 1i n g 1oa d i n g conditions at these microcontacts. 4.3. Penetration - sliding distance dependence

I t is of interest to consider the trajectory of the asperity tip during loadcontrolled ploughing (which is also shown in Fig. 6a), that is, the normal penetration dependence on the sliding distance. This curve corresponds to an output produced by some modern microscratch testing devices. It is seen from Fig 6a that the penetration achieved by the end of normal indentation stage starts to increase immediately after the beginning of ploughing. This increase is initially roughly linear with the ploughing distance. This behavior is consistent with the recent experimental observations of Komvopoulos (1994). However, after a certain penetration depth is achieved, the asperity tip trajectory levels off; i n fact, it even appears to go u p slightly in the end of test (Fig. 6). Obviously, the penetration increase in this situation must stop sooner or later, as the contact cannot completely loose its normal load bearing capacity. One could expect that after a sufficiently long sliding distance a certain steady-state should be attained, at which the penetration is approximately constant (apart from small-scale irregularities caused by dislocation instabilities of the kind discussed above). With these considerations in mind, another ploughing simulation was performed. It was similar to the one represented by Fig. 6, except the normal load was somewhat lighter and the sliding distance was more than three times greater. The corresponding surface profiles and asperity tip trajectory are shown in Fig. 7. One sees that the penetration indeed attains a roughly constant value. However, it is also seen that the unloaded profile does not

65

have an approximately uniform depth, but is conspicuously wavy. The authors do not have a ready explanation for this effect, which has not been observed in experiments to our knowledge. This is a n illustration of the fact that much work has yet to be done before the results obtained using the present approach c a n be easily related to experimental observations, and real physical effects can be separated from numerical artifacts reliably.

60

-401

-1000-500

.

*

o

.

*

-,

.

*

soo moo is00

. 1

.

.

J

becomes purely elastic. Therefore, small microasperities may be able to sustain considerably higher loads than those predicted by models developed for macroscopic contacts. A comparison of the simulation results for normal indentation and load-controlled ploughing at the same normal load shows that considerable junction growth occurs in the entire range of asperity scales studied. If such loading conditions at asperity microcontacts arise during sliding wear of brittle materials, wear rate predictions based on indentation fracture analogies may be highly nonconservative. The present model certainly requires considerable refinements, such as for example taking into account the 3D nature of real contacts. Nonetheless, the new methodology of microcontact simulation appears promising. REFERENCES

2000 2500 3000 3500

.ulb

Figure 7. Ploughing of an elastic-plastic surface by a rigid asperity; u = 600b, d = 100b. The case of a long sliding distance (2000b). Surface profiles and asperity tip trajectory.

Ajayi, 0. 0. and Ludema, K. C., 1992, Wear, Vol. 154, pp. 371-385. Aramaki, H., Cheng, H. S. and Chung, Y.-W., 1993, ASME lournal of TribologqL,Vol. 115, pp. 419-424. Avitzur, B., Huang, C. K. and Zhu, Y. D., 1984, Wear, Vol. 95, pp. 59-77.

5. CONCLUSION

Using a new method of microcontact simulation based on plasticity representation in terms of discrete dislocations, scale effects of the elastic-plastic behavior of asperity microcontacts can be studied. For normal a s well a s tangential asperity microcontacts plastic deformation becomes more difficult, and the residual depth of the plastic depression produced by the asperity decreases when the asperity size decreases and becomes comparable with the characteristic length of the material microstructure. Below a certain threshold asperity size, the microcontact response

Belak, J. a n d Stowers, I. F., 1992, Fundamentals of Friction: MacroscoDic a n d Microscouic Processes, I. L. Singer and H. M. Pollock, eds., Kluwer, Dordrecht, pp. 511-522. Bowden, F.P. and Tabor, D., 1950, The Friction and Lubrication of Solids, Clarendon Press, Oxford. Burnett, P. J. and Rickerby, D. S., 1987, Thin Solid Films, Vol. 154, pp. 403-416. Chang, W. R., Etsion, I. and Bogy, D. B., 1987, ASME lournal of Tribolog, Vol. 109, pp. 257263. Evans, A. G. and Marshall, D. B., 1981, Fundamentals of Friction and Wear of

66 Materials, D. A. Rigney, ed., ASM, Metals Park, pp. 439452. Cerberich, W. W., Venkataraman, S. K., Huang, H., Harvey, S. E. and Kohlstedt, D.L., 1995, Acta Metallurnica et Materialia, to be published. Green, A. P., 1955, Proceedings of the Royal Societv of London A, Vol. 228, pp. 191-204. Greenwood, J. A., 1992, Fundamentals of Friction: Macroscopic and M i c r o s c o p i c Processes, I. L. Singer and H. M. Pollock, eds., Kluwer, Dordrecht, pp. S7-76. Halling, J., 1976, Wear, Vol. 37, pp. 169-184.

Hirth, J. P. and Lothe, J., 1982, Theorv of Dislocations, Wiley, New York, NY. Hockenhull, B. S., Kopalinsky, E. M. and Oxley, P. L. B., 1993, ASME lournal of Applied Mechanics, Vol. 60, pp. 85-92.

Montmitonnet, P., Edlinger, M. L. and Felder, E., 1993, ASME lournal of Tribolom, -- Vol. 115, pp. 10-14; 15-19. Moore, D. F., 1975, Princiules and Auulications of Tribolow, Pergamon Press, Oxford. Ohmae, N., 1987, ASME lournal of Tribologv, Vol. 109, pp. 330-337. Pollock, H. M., 1992, Fundamentals of Friction: Macroscouic and Microscodc Processes, I. L. Singer and H. M. Pollock, eds., Kluwer, Dordrecht, pp. 77-94. Polonsky, 1. A . and Kecr, L. M., 1995-1, Proceedings - of the Roval Societv of London, submitted. Polonsky, I. A. and Keer, L. M., 1995-11, ASME Journal of Tribolom, to be published. Rigney, D. A., 1988, Annual Review of Materials Science, Vol. 18, pp. 141-163.

Hokkirigawa, K., 1991, Wear, Vol. 151, pp. 219-228.

Rosenfield, A. R., 1980, Wear, Vol. 61, pp. 125132.

Johnson, K. L., 1992, Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singcr and H. M. Pollock, eds., Kluwer, Dordrecht, p. 574.

Rosenfield, A. R., 1981, Wear, Vol. 72, pp. 97103.

Komvopoulos, K., 1989, ASME lournal of Tribolow, Vol. 111, pp. 430439. Komvopoulos, K., 1994, Private communication Kuhlmann-Wilsdorf, D., 1981, Fundamentals of Friction and Wear of Materials, D. A. Rigncy, cd., ASM, Metals Park, pp. 119-186. Landman, U., Luedtke, W. D. M., 1992, Fundamentals Macroscopic and Microscopic Singer and H. M. Pollock, Dordrecht, pp. 463410.

and Ringer, E. of Friction: Processes, I. L. eds., Kluwcr,

Majumdar, A. and Bhushan, B., 1991, ASME k)urnal of Tribolow, Vol. 113, pp. 1-1 1. McColm, I. I., 1990, Ceramic Hardness, Plenum Press, New York, NY.

Samuels, L. E., Doyle, E. D. and Turley, D. M., 1981, Fundamentals of Friction and Wear of Materials, D. A . Rigney, ed., ASM, Metals Park, pp. 13-41. Sayles, R. S. and Thomas, T. R., 1979, ASME Journal of Lubrication Technology, Vol. 101, pp. 409-418. Sin, H.-C., Saka, N. and Suh, N. P., 1979, Wear, Vol. 55, pp. 163-190. Sutton, A. P. and Pethica, J. B., 1990, Journal of Phvsics. Condensed Matter, Vol. 2, pp. 53175326. Tangena, A. C. and Wijnhoven, P. J. M., 1985, Wear, Vol. 103, pp. 345-354. Westergaard, H. M., 1939, ASME Tournal of Applied Mechanics, Vol. 49, pp. 49-53.

SESSION 111 THIRD BODIES

Chairman :

Professor Jean-Marie Georges

Paper 111 (i)

The Surface Plasticisation and Lubrication of Poly (ether ether ketone) by Third Body Formation

Paper 111 (ii)

Third Body Formation and Friction Reduction on Mo/SiC Sliding in Reactive Gases

Paper 111 (iii)

From the Phenomenology to the Concepts which Flow from the Third Body. Application to Radial Face Seal

Paper 111 (iv)

Mechanisms of Third Body Formation with Polymers. Role of Mechanical and Adhesive Interactions in the Friction and Transfer of Polyethylene

Paper 111 (v)

Elusive 'Third Bodies'

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

69

The surface plasticisation and lubrication of poly(ether ether ketone) by third body formation B. J. Briscoea and B. H. Stuartb aDepartment of Chemical Engineering, Imperial College, London SW7 2BY bDepartment of Materials Science, University of Technology, Sydney, PO Box 123, Broadway NSW 2007, Australia The paper describes selected data on the influence of internal and external lubricants upon the friction and hardness of a poly(etheretherketone)and two of its composites formulated with a poly(tetrafluoroethy1ene). The data are used to exemplify certain changes which may occur in the interface rheology and contact conditions for polymers and their composites. In each case, a modified interface region, or transformed body, is formed which largely controls the response of the system. 1.

INTRODUCTION

Polymers, and indeed polymeric composites, have been commonly used in unlubricated contacts because of what is termed their self-lubricating character, but significant improvement in bearing performance may often be obtained by conventional liquid lubrication. However, in some polymer systems lubricants are believed to cause plasticisation of the surface, which can be deleterious to good operation. When a lubricant is applied to a polymer it is possible for the lubricant molecules to penetrate the polymer and alter its mechanical properties. In certain cases surface softening may be useful as a means of improving efficiency, but bulk plasticisation obviously needs to be avoided. Thus, environmental plasticisation of polymers represents an important practical limitation in their effective utilisation. An understanding of how lubricants, or indeed how an active environment, can cause surface plasticisation is important in order to control and optimise this phenomenon. Essentially, this is the process of forming a third body with the most efficient characteristics. This paper describes a study of some of the consequences of the plasticisation of the surface of the polymer poly (ether ether ketone) (PEEK). PEEK is a relatively new tough aromatic thermoplastic polymer and is currently finding use as a matrix material for high performance composites and in applications in the fields of aerospace, automative engineering and bearings. One particularly important property of PEEK has been its ability to resist chemical attack; there are a

very limited number of solvents for PEEK. Despite this, a series of recent studies have shown that certain solventscan be absorbed by PEEK and cause detectable plasticisation and also induce crystallisation; the latter is described as antiplasticisation. One class of organic solvents which fall into this category is the chlorinated aliphatic hydrocarbons (for example, chloroform). The effect of exposure to chloroform, an established plasticiser of PEEK (I), on the friction and hardness properties of PEEK have been examined. An effective alternative approach to the problem of attenuating the friction generated at PEEK contacts, while maintaining the attractive mechanical properties, is to use internal phase lubrication. This may be achieved by blending PEEK with a polymer, or a range of solid or liquid lubricants, of appropriate properties. One such polymer is pol ytetrafluoroe t h y lene (PTFE). Composites involving PEEK and PTFE are useful as the friction of PEEK is significantly reduced in this particular composite (2); the PTFE forms a third body in the contact zone. The incorporation of PTFE into a PEEK composite has been investigated. The phenomenon of surface plasticisation has been examined using tribological techniques to examine how the surface mechanical properties of polymers are affected by plasticisation; sliding friction and hardness methods have been used. 2.

EXPERIMENTAL METHODS

2.1 Materials

Samples of PEEK and 92w% PEEK / 8w% PTFE blends were supplied in the form of plates by

70 ICI Materials, Wilton. U.K. Crystalline PEEK samples were produced by annealing the polymer at a temperature of 400420°C and then allowing the samples to cool gradually to ambient temperature. The crystallinity of the samples were estimated to be 25%. Amorphous samples were produced by heating the samples to 400-420°C and then quenching immediately in cold water. The crystalline content of the amorphous samples was estimated to be negligible. The PEEK in the blends was in a crystalline form and each blend sample was produced under the same conditions as those used to produce the corresponding semi crystalline homopol y mers. The effect of chloroform on the properties of PEEK was examined by immersing crystalline PEEK in chloroform (Aldrich) in a sealed container at room temperature for 14 days prior to the experiment. Crystalline PEEK was used in this particular study because it was found that the dimensions of the amorphous PEEK samples became extensively distorted after treatment with chloroform, making the friction experiments impracticable.

experiment senses, in a qualitative way, the ability of the contact configuration to dissipate the frictional work, as measured by a force transducer attached to the sample holder, as it evolves in the contact zone. There are several alternative ways of presenting the frictional data obtained using the apparatus described. First, simply plotting the frictional force as a function of the normal load provides information regarding the nature of the frictional response of the sample under examination. The result may be viewed in a different manner by nonnalising the frictional force by the normal load

2.2 Sliding friction studies The frictional response of PEEK against a high speed counterface was studied using the method described by Briscoe et al. (3). The apparatus used is shown schematically in Figure 1. Essentially, a

F=kW"

loading

Y

rotating shaft

beam measuring normal load 1

normalload

\

_.)

I

I

Figure 1. A schematic diagram of the high speed friction apparatus. small plaque of the polymer is loaded against a smooth rotating steel cylinder and the normal load is progressively increased. The shaft is not deliberately cooled and hence the contact temperature increases as the experiment evolves. The precise details of the procedure adopted are given in Ref. (3). The important point is that the

p = -F W

where p is the coefficient of friction, F is the frictional force and W is the normal load. The experimental data may also be presented in a more telling manner, by plotting the frictional force against the normal load on logarithmic axes. The supposition is that the frictional force is a function of the normal load of the form: (2)

where k and n are system-dependent constants. This produces a load index, n, which provides a simple quantitative representation of the characteristics of the experiment as it evolves. Conventionally this type of representation allows conclusions about the mode of interfacial material deformation during the whole experiment to be deduced from the local gradients of the plot. 2.3 Scratch hardness studies The apparatus used for the examination of the hardness of polymers is shown schematically in Figure 2. The indentor. a cone, was held on a pivoted beam so that it could be positioned orthogonally to the flat substrate. The polymer substrate was secured on the stage which was motor driven along one axis. The frictional force was measured by two strain gauges which monitored the motion of the indentor as the substrate was moved and the output was transferred to a computer. The normal load was obtained by applying known loads to the indentor support unit. The effect of indentor geometry was examined by using a series of conical indentors prepared from drill steel over a range of included angles (30",45", 60".90" and 150"). The width of the permanent scratch created by the indentor was then measured using an Olympus

71

microscope connected to an Optomax image analyser. counter balance

normal load

Dolvmer

balanced beam

pivot

strain gauges attached to leaf springs

3.

4 ' polymer substrate

Figure 2. A schematic diagram of the scratch friction apparatus. The frictional force produced as the indentor traversed the polymer surface was measured. The coefficient of friction, p, was obtained simply by dividing the frictional force by the applied normal load (Equation 1). Bowden and Tabor (4) developed a simple model for the plastic ploughing friction coefficient of a conical indentor was introduced: I

2tane

z

d

h=-tane 2

i

(5)

where h is the penetration depth.

counter balance

P=

recovery in the depth of the residual scratch after the experiment and the penetration depth was calculated using the simple geometric expression:

(3)

The coefficient of friction is thus plotted as a

RESULTS AND DISCUSSION

3.1 Sliding friction studies The nature of the frictional response exhibited by unlubricated (untreated) PEEK is shown in Figure 3. The frictional work of PEEK, when loaded against the sliding smooth steel counterface and subjected to incremental increasing loads is presented. After a load of about l00N is reached the friction in this contact increases quite dramatically until a load of around 200N,after which the friction decreases. A plot of the friction coefficient against load is shown in Figure 4 and this plot emphasises that the experiment proceeds in several parts. Initially, there is a decrease in the friction coefficient of the contact until a critical load for scuffing is reached, whereupon the friction coefficient increases in quite a dramatic way. This is followed by a decrease until the limit of the experiment is reached. The initial decrease in the friction coefficient is typical and characteristic of many polymeric materials, which generally exhibit a tendency to form weak, thermally softened, interfaces, or third bodies, in sliding contacts.

function of tan8: 8 is the semicompliment of the cone angle. For the ideal case of plastic ploughing the relationship between the friction coefficient and tane' is linear. Variations from this linear relationship in the experimental values were used to determine the tw of material response for the polymer. The scratch hardness, H, was calculated using the expression:

8W Icd

H " 7

(4)

where W is the applied load and d is the scratch width. The residual scratch width was measured after the experiment and the normal load was known. It was also possible to determine the scratch hardness as a function of the penetration depth of the indentor into the polymer surface. It was assumed, for this purpose, that there was no

0

100

-

200

normal load / N PEEK / chloroform untreatedPEEK

300

72 Figure 3. The frictional force of unlubricated PEEK and PEEK exposed to chloroform as a function of normal load.

8 'f3

5

0

0.6 0.5 0.4

EP) 0.3

4 .C(

0.2 Q 0.1 0.0 0

100 200 normal load / N

-

300

untreated PEEK

Figure 4. The coefficient of friction of unlubricated PEEK and PEEK exposed to chloroform as a function of normal load. Figure 5 shows the frictional force as a function of normal load on logarithmic axes. The

1

lo3>

lo'

I-

10

log normal load PEEK / chloroform untreated PEEK

I

Figure 5 . Log-log plot of the frictional force of unlubricated PEEK and PEEK exposed to chloroform as a function of normal load. trends in the load index, detailed in Figure 5 , show that the experiment proceeds from an initial gradient of ca. zero (the self-lubrication zone), through a

transitional zone to an intermediate stable value, of 0.63, before a critical point is reached, whereupon a much larger negative gradient is evident. The intermediate zone (n-0.6-1.O) is characteristic of a conventional or nonself-lubricating response. The frictional work increases with the load. The value of n of 0.63 is consistent with an isothermal single asperity elastically deforming contact, although this is not believed to be the contact condition in this system. The fact that n is less than unity, which is the expected value, is more likely to be associated with the preferential thermal softening of the interface and the development of a thermally softened surface zone. Frictional data were obtained for PEEK after treatment with chloroform and the results are also shown in Figures 3 and 4. Figure 3 shows the frictional force of PEEK as a function of normal load, before and after exposure to chloroform. Treatment with chloroform produces a similar frictional response to that observed when dodecane lubricants are applied to PEEK (3). That is, the frictional force slowly increases until a critical point is reached, beyond which the force rapidly rises. Notably, the critical point in the case of chloroform treated PEEK occurs at a significantly lower load than that observed for any of the dodecane-additive systems reported by Briscoe et al. (3). Figure 3 shows that the critical changes occur to the frictional response in the range 100-150N,much lower than that found for PEEK lubricated by decanoic acid in dodecane (200N)(3). The coefficient of friction for chloroform treated PEEK is shown as a function of normal load in Figure 4. The friction coefficient also follows a similar pattern to that observed for the dodecane lubricated samples. That is, there is a initial decrease in the friction coefficient until a critical load is applied, after which the friction As a coefficient increases dramatically. consequence when the frictional force data is plotted on logarithmic axes (shown in Figure 5 ) it also demonstrates a similar trend to those observed for the dodecane lubricated samples: a self-lubricating region (n-O) followed by the inception of scuffing (n=2.7). Significantly, the load index for chloroform treated PEEK during scuffing is notably greater than that determined when the dodecaneadditive systems were applied as lubricants to PEEK. The idea of thermally induced phenomenon occurring in the high speed contacts examined is a natural consequence of the frictional work expended in the contact being ultimately realised as heat. The temperature rise in the contact reflects the influence

73

of the cumulative frictional work and is therefore load dependent. Examination of the untreated PEEK-metal contact shows that at some critical point the frictional force increases dramatically and seemingly without limit. This is particularly true when the load is large and increasing. The nature of this experiment means that as it proceeds the load increases and as a consequence the frictional work increases also, with the cumulative frictional work not increasing in a linear manner (Equation 2). In all cases, untreated and treated, a similar trend in load indices with load is observed. Up to a critical load the indices are always near zero. Beyond the critical load there is an increase and its magnitude reflects the rate of increase of frictional work as the load increases. The magnitude of the load index, n, is thus an indication of the potential for catastrophic thermally induced contact failure. Low values of n infer a self-lubricatingcapacity and hence a stable frictional behaviour. For dry PEEK n is 0.63 in the simulation and the potential for failure exists. For the chloroform treated system n is 2.7; a significantly worse condition. The data produced for PEEK exposed to chloroform follow trends similar to those observed for PEEK lubricated with the dodecane solutions reported by Briscoe et al. (3). However, an important difference between the treatments is the critical load at which scuffing occurs. As the load is lower for the chloroform treated sample, compared to the decanoic acid in dodecane lubricant (n=2. I), it may be postulated that chloroform causes more extensive plasticisation of the PEEK surface and thus provides the greatest potential for failure at lower load conditions for the PEEK sample. In addition, the greater load index determined for the chloroform treated sample at the inception of scuffing indicates that the rate of the frictional work generated under these conditions is more rapid than any of the dodecane lubricants, as well as the dry contact. The general features in the friction simulation data may be interpreted by invoking the adhesion model of friction:

where z is is the interface shear stress and A is the area of asperity contact. Hence, if as is common

z=z,+aP

(7)

then

.=(:+a) where P is the mean contact pressure generated at the asperity contacts and P=W/A. a is not a strong function of temperature and the temperature dependence of z may be ascribed to the zo parameter (3). It is acceptable for a multiple asperity contact under a high load to identify P as the hardness of the solid in the subsurface regions (2). Thus zo will decrease as a function of the localised surface temperature (the surface rheology is associated with a thin surface layer) as the frictional heating is increased. Similarly, P will decrease as the subsurface temperature increases. Considering now the data shown in Figure 4 where p is plotted as a function of load assuming that the load increase produces corresponding increases in surface temperature. Initially 70 decreases because of localised interfacial heating and the friction coefficient decreases. This behaviour is characteristic of a thermally activated self-lubrication process and n-0. Because of the localised heating and the decrease of TO with increasing temperature, a stable weak narrow zone of polymer which is an effective third body, is created at the asperity junctions. The process will resemble the adiabatic shear generated in poly (methyl methacrylate) (PMMA)and titanium ( 5 ) . The supposition is that no extensive subsurface heating occurs and as a result P is unchanged. Eventually, the thermal front progresses into the bulk of the sample and the contact area increases due to the loss of asperity persistence. Essentially, the magnitude of P decreases and the contact area increases. In the experiments described the initial contact area is perhaps one hundredth of the apparent area so there is the prospect of a significant increase in the z d p term (Equations 2 and 7) and hence in the magnitude of p. For the dry contacts thermal degradation of the polymer seems to facilitate a reduction of the frictional force which may be interpreted as being caused by an effective reduction in the dependence of the bulk flow stress or hardness. The degradation products may increase or maintain the hardness of the polymer. It should also be noted, by comparison of the untreated and treated data sets, that the dry contacts appear to be able to recover their self-lubricating capacity; the so-called negative gradient region

74 mentioned earlier (see Figure 5 ) . Such recovery processes were not apparent in the case of the lubricated systems as the progress to failure was monotonic. A possible reason for this negative effect may be that the processes involving the generation of self-lubricating thermal gradients reoccur. However, it seems that significant chemical degradation of the dry PEEK frictional surfaces occur, evidenced by a black residue on the contacting surfaces at the conclusion of the experiment. Such effects are less apparent in the lubricated contacts. It may be concluded that the degraded debris produced in the dry contacts allow this system to recover the persistence of the surface asperities on the polymer sliding surface. In effect a localised composite formulation is generated from wear debris which induces self-lubrication; a transformed or chemical third body. Figure 6 shows the frictional force obtained when a 92w% PEEK / 8w% PTFE blend was slid

0

100 200 300 normal load / N

experiment is brought about by the considerable wear of the PTFE sample. The frictional behaviour of PEEK is clearly influenced by the presence of PTFE; Figures 6 and 7. The force observed for the blend increases slowly over the entire period of the experiment. The magnitude of the frictional force for the blend is higher than unblended PEEK at lower loads (<100N), while the friction is considerably less than that observed for the unblended PEEK for loads greater than 1OON. The amount of wear debris is increased by the incorporation of this relatively small percentage of PTFE. It is likely that the blend with scuff in the manner observed for unblended PEEK. Briscoe et al. (2) provide evidence for this, but clearly, if scuffing does occur, it does not manifest itself until very considerable loads are applied many times greater than the critical load determined for unblended PEEK. The coefficient of friction for the PEEK/PTFE blend has been calculated as a function of normal load and the results are presented in Figure 7. Data for unblended PEEK and unblended PTFE are also shown in Figure 7. The friction coefficient of the

400

0.0

: 0

7.

PEEK

Figure 6. The frictional force of PEEK, PTFE and a 92 w% PEEK / 8 w% PTFE blend as a function of normal load, against a steel counterface as a function of the applied normal load. This particular blend composition was chosen as it has been shown that a PTFE concentration of about low% is sufficient to produce the majority of the friction reduction (2). The frictional responses of unblended PEEK and PTFE are also shown for comparison. The frictional force of PTFE increases monotonically from the inception of the experiment. The termination of the

I

'

100

1

.

200

1

300

I 400

normal load / N PEEK

Figure 7. The coefficient of friction of PEEK, PTFE and a 92 w l PEEK / 8 w% PTFE blend as a function of normal load. blend behaves quite differently to that of unblended PEEK, gradually decreasing over the time span of the experiment.The observed phenomenon may also be interpreted by applying a simple analysis based on Equation 7. The values of TO and a for PTFE are

75 low: Briscoe and Smith (6) quotes the values ~ 0 . 0 and 8 T ~ 106 = Pa. The blending of PEEK with PTFE, produces large changes to the frictional properties of unblended PEEK. The decrease in the friction coefficient of the PEEK/PTFE blend is due to the formation of a third body in the contact. The low friction of PTFE is accompanied by high transfer wear. As the matrix wears, the PTFE transfers to the contacting surfaces. This type of phenomenon also occurs notably in the case of shear orienting polymers, such as polyethylene, and takes the form of the generation of a self-lubricating third body in the contact (6). This leads in effect to a selflubrication of the contact, since the amount of work expended compared to that of the virgin polymeric material is reduced. Thus, PTFE has been shown to attenuate the frictional properties of PEEK. However, the rate of wear for this composite, against smooth ferrous substrates, is greater than that observed for unblended PEEK. 3.2 Scratch hardness studies The coefficientsof friction for amorphous and crystalline PEEK as a function of tane' are shown in Figure 8. Also shown in Figure 8 is the predicted

case of the 90" and 150" indentors the friction values are greater than those calculated for plastic ploughing, although for the crystalline polymer the results are relatively close to the theoretical values. This additional friction is due to the work expended in brittle cracking or fracture of the polymer. The brittle fracture contribution to the friction has been observed for polymers such as PMMA (7). For the other indentors (160") the observed friction coefficients are much lower than the predicted values, and also tend to remain constant as the cone become shaqer. Evans (7) observed a similar effect for the friction coefficient of PMMA with indentor angles of 30 and 45". Evans explained the discrepancy with a machining mechanism. Chip formation occurs by shearing the material across an internal shear plane within the specimen. The shear plane angle is less than the attack angle of the indentor and is independent of the indentor used. Plastic flow then occurs at an angle less than the cone attack angle. The ploughing friction force is thus governed by the shear plane angle, rather than the attack angle of the cone. Figure 8 also shows that the values of the friction coefficientsof the two samples of PEEK are dependent on the crystallinity of the polymer. Where the friction coefficient is independent of the cone angle, the actual value is higher in the case of amorphous PEEK. This may indicate the the amorphous polymer responds in a manner more closely related to that of a purely plastic material.

0

0

1

-----

2

3

4

tan0'

theoretical crystalline PEEK treated with chloroform

Figure 8. The effect of crystallinity and chloroform on the coefficient of scratch friction of PEEK. friction coefficient due to plastic ploughing, calculated using Equation 3. There is poor agreement between the measured and theoretical ploughing values for most indentor angles. In the

0.02

0.04 0.06 0.08 depth of penetration / mm 0

0.10

amorphous PEEK crystalline PEEK treated with chloroform

Figure 9. The effect of crystallinity and chloroform on the scratch hardness of PEEK.

76 The scratch hardness of both amorphous and crystalline PEEK were calculated from the resulting scratch widths. Figure 9 shows the hardness of amorphous and Crystalline PEEK as a function of the depth of penetration of the indentor during sliding. The scatter amongst these results is relatively high, but when a linear fit is applied, a clear difference in the magnitude of the hardness is observed for the amorphous and crystalline polymers. The hardness of crystalline PEEK is notably higher than that of the amorphous material. The hardness in both cases appears to remain constant until depths of at least 1OOpm. Figure 8 illustrates the effect of chloroform on the coefficient of friction of PEEK. For indentor angles of 90" and 150" the friction values for PEEK treated with chloroform are slightly higher than those values observed for the untreated original PEEK sample. This indicates that there is a slight increase in the amount of brittle fracture occurring with these angles. The friction observed for the chloroform treated sample at 60" is significantly increased. The values is greater than that predicted for plastic ploughing and also indicates a significant contribution to the friction due to brittle fracture. The friction coefficients observed when 30" and 45" indentors are applied to chloroform treated PEEK are greater than those observed for the original crystalline samples. These increases indicate that there is a greater plastic ploughing contribution to the friction after PEEK is exposed to chloroform and the values approach those calculated for plastic ploughing. The effect of chloroform on the scratch hardness of PEEK has also been examined and is illustrated by Figure 9. The hardness values for untreated crystalline PEEK are shown, along with those determined for crystalline PEEK after exposure to chloroform. A linear fit indicates that the average the values calculated for the chloroform treated samples are lower than those of the original crystalline sample. This reduction may be explained by a significant softening of the PEEK surface due to the presence of chloroform. Chloroform acts as a strong plasticiser and the softening of PEEK allows the indentor to penetrate the polymer to a greater depth. This, in turn, produces a greater scratch width and hence decreases the hardness. There is no convergence of the hardness values for the untreated and treated samples and this observation indicates that the plasticisation of PEEK by chloroform occurs at depths greater than 100mm. which are beyond the scope of the hardness experiments carried out here.

The friction coefficients of PTFE and a 92w% PEEK / 8w% PTFE blend have also been determined as a function of tan@' and are shown in Figure 10. The coefficients of friction for crystalline PEEK and theoretically calculated plastic ploughing values discussed previously are also shown in Figure 10. The scratch friction of PTFE was reported by Evans (7). There are some differences observed between the PEEK friction and that of the

0

-----

1

2 tane'

3

4

theoretical 100w%PEEK loOw%PTFE 92w%PEEK/8w%PTFE

Figure 10. The effect of PTFE on the coefficient of scratch friction of PEEK. PEEblend, but these are not significant enough to indicate major changes to the material response of the polymer. Figure 11 shows the hardness values determined as a function of the indentor pentration depth for PTFE, a 92w% PEEK / 8w% PTFE blend and crystalline PEEK. The hardness values observed for PTFE are, not unexpectedly, much lower than those observed for crystalline PEEK. It has already been shown by the friction results that PTFE is a more ductile material. This property allows the indentor to penetrate the surface of PI'€% more easily than in the case of a polymer such as PEEK. The resulting scratch width is therefore greater and so the hardness value is less. The hardness values determined for the PEEKPTFE blend behave in an altogether different manner to those of the unblended component homopolymers. While the hardness of the constituent polymers is independent of the penetration of the indentor, the hardness of the blend

77

1-

250

0 0

0 0

50

0.00

0

on

0

0.05 0.10 0.15 depth of penetration / mm 0 0

100%PEEK 92% PEEK / 8% PTFE 100%PTFE

0.20

I

Figure 11. The effect of PTFE on the scratch hardness of PEEK. increases dramatically over a narrow range of depth. This trend indicates that the blend is softer close the surface, where hardness values are similar to those observed for unblended PTFE, and then become harder with hardness increasing to values greater to those observed for unblended crystalline PEEK. An explanation for these observations is that there is phase segregation of the constituent homopolymers near the surface of the blend. PTFE appears to migrate to the surface of the blend and hence the low hardness values observed at the surface. This leaves a higher concentrationof crystalline PEEK in the underlying regions where the hardness is observed to be considerably greater. The transition between the two phases occurs over a relatively narrow range (30-50pm). It is also interesting to note that the magnitude of the hardness values observed of the blend at the highest load is greater than that observed for the unblended crystalline PEEK. This indicates that the PEEK at these depths may be more crystalline than that in the unblended polymer, as greater hardness values indicate a higher percentage of crystalline material. It appears that the presence of PTFE induces more crystallinity in PEEK when these polymers are mixed in this immiscible blend. 4.

SUMMARY

The behaviour Of the frictional response Of PEEK in highly stressed contacts have been examined. In each case examined a similar trend in the load indices with load was observed. Up to a

critical load the indices were always near zero and infer a self-lubricatingcapacity. Beyond the critical load the rate of increase of the frictional work increased and the magnitude of the load index was an indication of the potential for thermally induced contact failure. Thus, the propensity, or not, of a system to scuff was indicated by the magnitude of the load index. Dry PEEK contacts appeared to be able to recover their self-lubricating capacity, probably due to a salubrious third body generation via wear debris inclusion. The adhesion model of friction provided a qualitative interpretation of the friction data obtained for the PEEK systems examined. Limited surface plasticisation induced self-lubrication whilst excessive subsurface plasticisation produced a loss of asperity persistence and induced scuffing. Examination of the frictional behaviour of PEEK when blended with FTFE into a PEEK composite provides substantial changes to the frictional properties of PEEK. Friction is greatly reduced by the presence of PTFE and this is due to the formation of a lubricating film of PTFE in the contact. The high transfer wear and low friction properties of PTFE combine to produce a selflubrication characteristic in these PEEK/PTFEferrous contacts. A comparison of the scratch hardness of amorphous and crystalline PEEK was carried out. Several friction mechanisms were observed for both forms of PEEK. When sharper indentors were applied a machining mechanism was observed, while for blunter indentors a brittle fracture contribution to the friction was observed. However, amorphous PEEK showed friction coefficients of magnitudes closer to those calculated for a theoretical plastic ploughing mechanism. An examination of the hardness values of both amorphous and crystalline PEEK showed that the hardness of crystalline PEEK is notably higher than that of amorphous PEEK. Both forms of PEEK have hardness values which are independent of the depth of penetration of the indentor. The effect of chloroform on the material properties of crystalline PEEK was also studied. Significant changes to the frictional behaviour of PEEK were observed due to the presence of chloroform. When sharper indentors were applied to the chloroform treated surface the friction coefficients produced approached those predicted for a plastic ploughing mechanism. Also, the hardness of PEEK was shown to be reduced after treatment with chloroform. It was concluded from these results that chloroform causes a surface plasticisationof PEEK.

78 The effect of blending PTFE. with PEEK on the hardness properties of the latter has also been investigated. PTFE is a more ductile material than PEEK. However, no significant changes were observed in the scratch frictional properties of PEEK due to the presence of PTFE. Significant changes were noted, however, to the hardness values of PEEK after blending with PTFE. The results of this study showed that phase segregation of the constituent polymers in this blend occur. PTFE migrates to the surface while PEEK preferentially occupies the underlying regions. The data also indicated that the PEEK in this blend is more crystalline than unblended crystalline PEEK produced under the same conditions. 5.

REFERENCES

1.

B.H. Stuart and D.R. Williams, Polymer, 35, (1994) 1326

2.

3.

4.

5.

6.

7.

B.J. Briscoe, L.H. Yao and T.A. Stolarski T.A.,Wear 108, (1986) 357 B.J. Briscoe, B.H. Stuart, S. Sebastian and PJ. Tweedale, Wear 1624 1983) 407 and also B.J. Briscoe,GJ. Davies and T.A. Stolarski, Tribology International, 17,1984,129. F.P. Bowden and D. Tabor, ‘The Friction and Lubrication of Solids’, Part 1, Clarendon Press, Oxford, 1954. Y. Bai and B. Dodd, ‘Adiabatic Shear Localisation’, Pergamon Press, Oxford, 1992. B.J. Briscoe and A.C. Smith, J. Appl. Polym. Sci 28, (1983) 3827 P.D. Evans, Doctor of Philosophy Thesis, Imperial College, London, 1987.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

79

Third body formation and friction reduction on Mo/SiC sliding in reactive gases. I.L. Singer", Th. le Mogneb, Ch. Donnetb and J.M. Martinb 'U.S. Naval Research Laboratory, Code 6176, Washington DC 20375 USA

bLaboratoire de Tribologie et Dynamique des Systbmes, Ecole Centrale de Lyon, B.P. 163, 69131 Ecully Cedex FRANCE Friction tests were performed in an UHV chamber with a SIC pin sliding against a Mo flat during and after exposure to SO,, 0, and H,S gas at pressures between 4 and 40 Pa. Steady state friction coefficients were between 0.1 and 0.15 in SO, and 0, and less than 0.01 in H,S. Third bodies generated by reactions with the gases and during sliding were identified in situ by x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) and ex situ by scanning electron microscopy (SEM), energy-dispersive x-ray analysis (EDX) and transmission electron microscopy (TEM). Tribochemical films were somewhat thicker but had the same compositions (MOO, and/or MoSJ as gas reaction layers. SEM showed tracks from SO, and 0, tests were covered and surrounded by small (1-5 pm), tlake-like particles, whereas tracks formed in H,S had long stretches of a smoothly burnished surface with much less debris. EDX and TEM of debris attached to both flat and pin surfaces detected only metallic Mo. The adhesive junction theory of Bowden and Tabor was shown to account for the friction and wear behavior in SO, and 0,. 1. INTRODUCTION

Surfaces in sliding contact are destined to become severely worn if a lubricant is not present at the interface. The lubricant need not be a liquid; it could be a soft solid or even a tilm no thicker than a monolayer [Refs. 1,2,3,4]. Even the ubiquitous "air-formed" surface tilm can prevent wear, hut not for long. What is needed for long life and low friction is interfacial material of low shear strength that remains within the interface as long as possible. And, to balance the material ejected from the interface, additional material must be replenished, either by producing new material [Ref. 51, recovering "worn" lubricant [Ref. 61 or delivering fresh lubricant from an external supply. Gas- or vapor-phase lubrication is a proven, if not exploited, means of lubricating sliding contacts. Years ago, it was found that gases like

H,S, I,, and CI, were capable of lubricating Mo, Ti and Cr, respectively, in vacuum [Ref. 71. More recently, vapors of tricresylphosphate and simple hydrocarbon and oxycarbon gases have been shown to lubricate steel [Ref. 81 and ceramics [Ref. 91, respectively, at temperatures (350-700°C) appropriate for adiabatic heat engines. The latter two studies have, in fact, demonstrated that lubrication is afforded by solid "tribochemical" films formed when surfaces are rubbed against each other in the presence of the reactive gases [Refs. 8,9], but no further explanations were given on how the films form or lubricate. Tribochemical films are one of many "third bodies" that facilitate sliding (and rolling) at moving interfaces, as explained by Godet [Ref. 101 and Berthier [Ref. 111. Two types of third bodies are commonly distinguished: surface films or "screens," present on the two counterfaces, and particles that reside at the

80

Mo-S-H

Mo-S-0

H

Fig. 1. Sketch of sut$acejilms urld other third-

0

Fig. 2. Ternary diagrams calculatedfor the MoS - 0 and Si-C-0systems at standard temperature (298K)and 1 atmosphere (0.I A4Pa) pressure.

body products formed before and during sliding in reactive gases. interface. Figure 1 illustrates the four third bodies investigated in the present experiments. Three of these are films: gas reaction films, formed when clean counterfaces (Mo and S i c in the present experiment) are exposed to a gas; tribochemical films, formed when chemical reactions are assisted by sliding-induced stresses; and transfer films, films that transfer from a counterface. The fourth body is wear particles, distinguished from films by their size, typically on the scale of micrometers. Singer [Ref. 51 has suggested that third-body reaction products often are thermochemical equilibrium products of the reactants and that they lubricate either by promoting interfacial sliding or by sacrificial wear. Otherwise, very little research has been devoted to the mechanisms of tribochemical film formation or its role in friction reduction. The present investigation examines the gasphase lubrication of Mo by H,S, SO, and 0,. These combinations were chosen to allow us to control the third-body products and perhaps correlate them with the environmentallydependent friction behavior of the solid lubricant MoS, [Refs. 12,13,14]. The third bodies produced by the reaction of Mo with the gases are suggested by the thermochemical equilibrium

diagrams for the ternary Mo-H-S and Mo-S-0 systems shown in Fig. 2. For those not familiar with such diagrams, the reaction of Mo + H,S is identified by the reaction line connecting Mo with H,S, and the products of the reaction are given by the compounds at the vertices of the internal triangles through which the reaction line passes. According to the diagram, MoS, is the only solid product. Similarly, the reaction products of Mo + SO, can by identified by following the reaction line connecting Mo with SO,. As seen in the diagram, MoS, + MOO, are the only solid products of this reaction. 0, gives MOO, Finally, the reaction of Mo andlor MOO,, depending on the relative concentrations of 0, and Mo. We will see later that the chemistry is considerably more complex than indicated here. The objectives of this research are: 1) to determine the friction and wear behavior of Mo in the three gases, 2) to identify the third bodies generated and 3) to describe the mechanical and chemical mechanisms by which they modify friction and wear behavior. Sliding friction tests were carried out in a multi-analytical UHV tribometer, in which polycrystalline Mo and S i c were cleaned, characterized, then exposed to

+

81

subatmospheric pressures of H,S, SO, and 0,. X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) were used to characterize the near-surface (= 1 nm) compositions in situ before and after sliding; the details of the in situ studies have been published elsewhere [Ref. 151 and only some of the results will be presented here. Transmission electron microscopy (TEM), scanning electron microscopy (SEM) and energy-dispersive x-ray analysis (EDX) were performed ex situ to analyze the wear behavior and identify wear particles of thicker (0.1 - 1 pm) third bodies after sliding. In the discussion section, the third-body products produced during sliding are identified and their role in wear and friction behavior are examined. Differences in the friction and behavior of the two oxygencontaining gases and H2S are correlated with the third bodies generated, and thermochemical arguments are presented to account for the friction and wear behavior. 2. EXPERIMENTAL 2.1 Apparatus and surface analysis

Friction tests and surface analysis were carried out in situ in a load-locked, multitechnique UHV chamber described in detail in previous papers [Ref. 161. Reciprocating sliding tests were performed with a pin-againstflat geometry. Friction coefficients were calculated as the ratio of the tangential to normal force, averaged over each cycle. Friction testing and data acquisition were controlled by computer. XPS and AES analyses were performed in situ using a VG hemispherical analyzer, and sputter cleaning with 5 keV Ar ions. Ex situ analyses were performed in two other chambers. An SEM equipped with a Kevex thin-window detector for EDX was used to examine wear tracks and scars. A Philips analytical electron microscope was used to examine debris particles by TEM and EDX.

2.2 Sample preparation and friction testing

The pin is a rod of a-Sic ground on one end to form a hemisphere of radius 1.8 mm. The pin and a 1 mm thick polycrystalline Mo flat were polished with successively finer pastes of 6 pm, 3 pm and 1 pm diamond. After solvent rinsing, both substrates were inserted through a load-locked chamber into the UHV chamber. The substrates were cleaned in situ, first by radiative heating to about 8 W C , then by Ar ion sputtering for 15 - 30 minutes; XPS and AES were used to establish the cleanliness of the two surfaces. Friction tests were run with each gas (SO2, O2or H2S) at three pressures between 4 and 40 Pa as follows. Tests were started after the gas pressure stabilized at 13 Pa. After about 16 sliding cycles, the gas pressure was lowered to 4 Pa; after 30 more cycles, it was raised to 40 Pa. Tests were performed with substrates loaded to 0.5 N, equivalent to an initial mean contact pressure of 0.7 GPa, well below the hardness (2.9 GPa) of the softer Mo counterface; stroke distance was 3 mm and the speed was 0.5 mm/s. After each round of gas exposure and friction tests, the counterfaces were analyzed by XPS andlor AES (see next paragraph). Finally, both counterfaces were recleaned by ion sputtering before starting a new test. Fresh, unworn areas of the pin and flat were aligned for each new test. Several friction tests were also performed under high vacuum conditions, 5: Pa, after the counterfaces had been exposed to H2S gas for several hours. 2.3 Surface analysis procedures Surface films were observed in situ by XPS and/or AES. However, XPS could only be used on the flat, not the pin, because the x-ray beam isn’t focused and the hemispherical analyzer samples a large area (ca. 5-10 mm). Both survey and high energy resolution XPS spectra were acquired on Mo. Phases associated with the Mo 3d and S 2p spectra were identified from binding energies of standards reported in the

82

1

l-

a0

0.1

B 5ir

j

++

"++

+++

0.01

+

1

*+*++*++++++,

++++

+ +++

fie++

+*++++++++++*++

Table 1. Chemical state and thickness of gas reaction films on vacuum-cleaned Mo surfaces. (from XPS binding energies and areal intensities of peaks) [Ref. 151. GAS

0

a LL 0.001 1

6

10

16

10

26

50

36

40

46

SO

S6

60

CYCLES

Fig. 3. Friction coeflcients for 4 gas conditions: SO, (o), 0,(A), HJ (+) and high vacuum (a) (after HJ exposure).

literature [Refs. 17,181. Spatially-resolved AES was performed on Mo and SIC, using secondary electron images to locate wear features . Wear features were examined ex situ in two separate instruments. First, wear tracks on Mo and wear scars on S i c were examined by SEM and EDX. EDX spectra were acquired with both 5 and 20 keV electron beams; the lower energy lowered the depth probed by a factor of 10 by decreasing the electron beam penetration in Mo from 1.4 pm to 0.14 pm [Ref. 191. Second, wear debris were analyzed by TEM and EDX. The debris were collected by gently wiping carbon-covered copper grids against Mo wear tracks and S i c wear scars. TEM was performed with a 120 keV beam in the selected area diffraction (SAD) mode. EDX was performed with the detector tilted at an angle of 25 degrees. EDX spectra of debris were compared to spectra of standard powders of MoS,, MOO, and MOO,.

3. RESULTS 3.1 Friction Fig. 3 shows semi-log plots of friction coefficients vs cycle for tests run in the three gases and in high vacuum. In SO, and O,, the

CHEMICAL STATE THICKNESS (nm)

I SO,

I I

MOO,, MoS, 0.5

I 0, I H,S

I

I I I MOO,

MoS,

0.7

0.3

friction coefficients began at p = 0.2 then fell to about 0.1, independent of the gas pressure. In H,S, the friction coefficient began at p = 0.1 then dropped to about p = 0.015. Subsequently, it rose with decreasing pressure then fell to p = 0.007 with increasing pressure. These two rather unusual effects in H,S -- a pressure-dependent friction coefficient and ultralow friction values (p < 0.01) -- have been confirmed over a range of pressures and loads; the results will be presented more fully in a later paper. The fourth curve in Fig. 3 shows friction coefficients taken under high vacuum conditions, about 3 x Pa, after both pin and flat had been exposed to H,S for several hours at pressures up to 40 Pa. During testing in high vacuum, the residual gas analyzer indicated H,O, H, and H,S to be the three most intense gas species present. The friction coefficient rose from p = 0.6, after one cycle, to a steady-state value of p = 1. Clearly, continuous exposure to high pressures of H,S is needed to sustain low friction. 3.2 Third-body analysis 3.2.1 In situ XPS and AES XPS analysis of gas reaction films on Mo are summarized in Table 1. Gas reactions converted a thin (< 1 nm) layer on Mo to the Mo4+ state. Compositions of the layer may be identitied with MOO,and MoS,, or mixtures of

83

I

Inside track

I

Oulsldetrack

A-

c

o imimsmmemem 0 w l KlNmC ENEMY (@V)

0

2

3

0

Fig. 4. In situ AES spectra taken inside and outside tracks on Mo.

the two in SO, gas. All 3 layers were considerably thinner than 2.4nm, the thickness of the air-formed oxide layer (MOO, on MoOJ on Mo produced by polishing. AES spectra were taken inside and outside the worn areas (wear tracks) of the Mo flat, but only inside wear scars on the S i c pin. Tracks on Mo: Representative spectra taken inside and outside tracks on Mo are shown in Fig. 4. The spectra indicate that the tribochemical films and gas reaction tilms had similar compositions. However, peak-to-peak intensities of the S(KLL) and O(KLL) spectra, where present, were larger inside the track than outside the track. The opposite was found for the C(KLL) intensity, which was larger outside than inside, suggesting that C was an adsorbed contaminant that was partially wiped off during

0

100

200 300 460 KINETIC WERQY (ow

6W

Sdo

Fig. 5. In situ AES spectra taken on a sputtercleaned area and on wear scars on the Sic pin.

~

the friction tests. In SO, tests, S/Mo and O/Mo ratios in the track were about twice that of ratios outside the track. In 0, tests, the track showed mainly oxidized Mo, with the O/Mo ratio in the track twice that outside the track. S was also detected, but since the S/Mo was about the same inside and outside, the S should be considered as a background contaminant. Finally, the S/Mo ~ ratio ~ ~of the tracks in H,S tests was about 1.5 times that outside the track; moreover, the oxygen contamination seen outside the tracks was not observed in the tracks. Scars on Sic: Spectra taken on clean S i c and in wear scars are shown in Fig. 5 ; note that the spectra shifted about + 30 eV above expected energies, due to charging. The clean pin showed Si(LVV) and C(KLL) characteristic of S i c and a small O(KLL) intensity. Spectra of scars in all three gases showed some S and/or 0 as well as changes in the shapes of the Si(LVV) and C(KLL) curves. The scar formed in SO, showed Mo as well as S and 0, and the S/Mo ratio (=4.5) was the same as found in the track on Mo. The C/Si ratio in the scar was only 60% of the ratio on clean Sic. Moreover, both the lineshapes of Si(LVV) and C(KLL) differed from that of Sic: the C(KLL) has a low-energy feature that makes it appear graphite-like [Refs. 20,211 and the Si(LVV) has a low energy peak that could be an oxide or a sulfide. These features suggest that some Sic converted to graphite plus Si oxide or Si sulfide. The scar formed in 0, showed mainly Mo and 0 with a very distorted Si(KLL) line, suggesting Si oxide and very little Sic. Here again the O/Mo ratios were nearly the same as on the Mo track. Finally, the scars formed in H,S consistently showed a strong S signal but little or no Mo, indicating that MoS, tilms did not transfer to Sic during sliding. The C(KLL) lineshape looked like a mixture of graphite and Sic, while the low energy shoulder on the Si(KLL) line might be that of Si sulphide since it was not

84

Mo flat

Sic pin

Fig. 6. SEM of wear tracks on Moflat and scars on Sic pin run in 0,. (Similar tracks were generated in SO,.) shifted enough to be Si oxide. Summaries of the compositions of tribochemical and transfer films inferred by AES analysis are shown later in Table 2.

3.2.2 ex situ SEM, EDX and TEM SEM photos in Fig. 6 show a wear track on Mo and a wear scar on SIC after 60 cycles in 0,. Both wear surfaces were almost covered

and surrounded by small (1-5 pm), flake-like particles and agglomerates of such particles. The width of the contact zone on both surfaces was 200 pm. Several narrow "scratches" inside the track are shown at higher magnification in the middle photo. The scratches appear to be a sequence of patches of Mo, all of which are lifted slightly above the surface of the substrate. Nearly identical wear tracks and scars were observed after 60 cycles in S @ (not shown). In contrast, tracks and scars generated in H,S were much narrower, about 50 pm wide, and had far fewer debris particles. The track seen in the SEM photo in Fig. 7 had long stretches of a smoothly burnished surface interspersed with deeper areas containing small particles. The latter areas were about 100 - 300 nm deep, as determined by Michelson interferometry. The scar on the Sic pin in Fig. 7 had a few particles imbedded in fracture pits, but mainly was covered by a surface film, indicated by its higher brightness. Debris attached to both flat and pin surfaces were analyzed by EDX (in the SEM) using both a 20 keV and a more surface sensitive 5 keV electron beam. Only metallic Mo was detected; there was no evidence of oxygen or sulfur in the debris. We point out that although sulfur is difficult to detect in Mo because the S(Ka) and

85

Fig. 7. SEM of weur trclcks on Moflat and scars on Sic pin run in H J . (Note the higher magngcations in Fig. 7 than in Fig. 6).

Mo(La) spectra overlap between 2.1 and 2.6 keV, it is possible to distinguish the two spectra visually by their lineshapes and by spectral deconvolution [Ref. 221. Deconvolution of the composite spectra into S and Mo components also indicated no signiticant S content. Debris were later collected from both wear surfaces and analyzed by TEM in imaging, SAD and EDX modes. Image analysis showed particles from 3 - 5 p m wide in H,S and 0,

Fig. 8. E M of particle from 0, track: SAD pattern, EDX spectrum and bright-field image oj a particle. tracks and somewhat smaller (1 - 5 pm) in SO, tracks. The particles, however, may themselves be made up of smaller crystallites; the bright tield image of a particle stripped from a track run in O,, in Fig. 8, shows features finer than 1 pm. Most particles were too thick to be analyzed by SAD; however, those that were thin enough, such as the aforementioned particle, indexed to metallic Mo as seen in the SAD pattern of Fig. 8. An EDX spectrum of the

86 same particle is also shown. It, like spectra of all particles analyzed, fit the spectrum of metallic Mo, and not of Mo oxide or sulfide. 4. DISCUSSION

Three very different friction and wear behaviors were observed for a S i c pin sliding against a Mo tlat, depending on gas type and gas pressure. Sliding in high vacuum after prolonged exposure to H,S at pressures from 4 to 40 Pa resulted in high friction (p = l), severe wear of the Mo substrate and transfer of large Mo particles to the pin. These results are consistent with earlier studies by Pepper, Miyoshi, Buckley and Wheeler [Refs. 2 3 , 2 4 , 2 5 , 2 6 , 2 7 ] , demonstrating that gas-reaction layers alone do not reduce kinetic friction much below p = 1 and usually result in the transfer of metal to the ceramic counterface. Sliding in SO, or 0, at pressures from 4 to 40 Pa led to a steady state friction coefficient of p = 0.1, with mild wear to the Mo track and smaller Mo particles covering both the track and the pin scar (see Fig. 6). Finally, sliding in H,S at the same pressure led to a steady state friction coefficient of p < 0.01, with a predominantly burnished Mo track and virtually no Mo particles on the burnished track or the pin scar (see Fig. 7). The latter friction coefficient is one of the lowest friction coefficients ever reported for "dry" sliding [Refs. 12,281. Surprisingly, it is also an order of magnitude lower than the lowest value reported in the 1950's studies of gas-phase lubrication of Mo vs Mo by H,S, p = 0.2 [Ref. 71. We suggest that the value of p = 0.2 seen earlier might have been due to oxygen contamination of the H,S in their vacuum chamber, consistent with the higher friction coefficients that we obtained in both SO, and 0, gases. Clearly, two distinct categories of reactive gas lubrication have been observed: low friction (p = 0.1) sliding in the two oxygen-containing gases and ultralow friction (p = 0.01) sliding in

H,S. In Section 4.1, we will discuss how the third bodies are formed by the gas-solid-sliding interaction. In Section 4.2, we will explain how the third bodies can account for the friction and wear behavior, where sliding is accommodated and why two friction levels are obtained. Finally, in Section 4.3, we will comment on several issues that need to be addressed in future studies. 4.1 Third-body lubricants Gas reaction films were formed before sliding, when the clean surfaces reacted with the gases introduced into the vacuum chamber. The films on Mo were identified by XPS to be thin ( < 1 nm), chemisorbed layers whose compositions are shown in Table 1 . They are not expected to be crystalline, based on more detailed analytical studies of gas reactions with single crystal Mo surfaces Gas reaction films [Refs .29,30,31,321. on S i c were not analyzed in the present experiment. However, based on literature reports of oxidized single crystal S i c [Ref. 331 and our earlier examination of SIC exposed to 0, at pressures up to 50 Pa [Ref. 161, only a thin physisorbed layer of oxygen exists on S i c at room temperature. No comparable studies of SO, or H,S reactions with S i c could be found in the literature. Tribochemical and transfer films are thirdbody "screens" generated by tribomechanical interaction of the two surfaces in the presence of gases; these films were identified by AES and are summarized in Table 2. Tribochemical films were formed on both counterfaces in all three gases. Note that the tilms on Mo had the same composition as the gas reaction films (Table l), but the AES intensities indicated that the tribochemical tilms might be thicker than the gas reaction films. It is unlikely, however, that the tribochemical tilms are more than several nm thick since TEM and EDX, with 10-100 nm sensitivity, indicated no phase other than metallic Mo. Transfer films were detected only

87

TABLE 2. Third-body products in the sliding contact inferred from AES, EDX and TEM. (2 4 x 4 3; y and z = 1 or 2; C refers to graphite] GAS

I SO2

I

0 2

I H*S

THIRD BODIES ON Mo:

1 ;; 1 ;:I IMoS,

TRANSFER PARTICLES

none none

THIRD BODIES ON Sic:

TRANSFER PARTICLES

I

MOO,

IMoS,

I Mo

I I

MOO,

MO

I

well. The agreement between observed and predicted compositions suggests thermochemical processes could have produced the tribochemical films during gas-phase lubrication, even at room temperature and low speeds (0.5 mm/s). Although solid-state equilibrium usually requires long times or high temperatures to permit diffusion into the bulk, it is speculated that these highly defective, thin films can reach equilibrium compositions, even at room temperature, by defect-enhanced diffusion [Refs. 5,341.

none

TABLE 3. Equilibrium reaction products predicted for gas reactions with Mo and Sic at room temperature and pressure of 13 Pa. Only solid products are shown [Ref. 151. 1

I

I none

on Sic wear scars formed in SO, and 0,. These tilms, Mo oxide and/or MoS,, were acquired either by transfer of tribochemical films from the Mo track or by tribochemical tilm formation directly on the Mo wear particles. Compositions of third-body films identified in Tables 1 and 2 have been compared to compositions predicted by thermochemical equilibrium calculations. Equilibrium reaction products of the gases with Mo and S i c were calculated assuming that the reactions occurred at room temperature and a pressure of p = 13 Pa (1 x l o 4 Atm). The calculated compositions, described in more detail in Ref. 15, are summarized in Table 3. We note that the simple calculations presented earlier, in Fig. 2, were verified in the more detailed calculations. However, earlier we didn't consider the possible reactions with the pin material, let alone possible reactions between Mo and S i c in the gases; clearly, those reactions must be considered as

THIRD BODY PRODUCTS ON:

SO,

MoS,, MOO,

C, SiO,, SiS, SiS,, S

0 2

MOO,, MOO,

SiO,, C

H,S

MoS,

SiS, C, SiS,

4.2 Wear and friction behavior The wear mechanism in oxygen-containing gases, SO, and O, can be inferred from their wear features and friction coefficients. The texture of the scratch track in the center of Fig. 6 (middle photo) is commonly attributed to an "adhesive" wear mode. The lifting of a patch of material slightly above the surface takes place when an "adhesive" junction forms across the sliding interface and the tangential force acting across the junction causes it to rupture and lift up around an edge [Refs. 35,361. The formation of copious amounts of Mo particles in the track and attached to Sic is consistent with the classical adhesive junction theory of Bowden

88 and Tabor [Ref. 371, which can account for the measured friction coefficient as well. According to theory, if a junction forms at the interface between two counterfaces, then during sliding, the junction will shear in the weaker material if its shear strength is less than the bond strength at the interface; this also leaves a transfer particle attached to the stronger counterface. The friction coeftlcient associated with shearing of the junction is given by p = a/P, where (I is the shear strength of the weaker material and P is the contact pressure. For ideally-plastic junctions with one counterface (metal) much softer than the other (ceramic), (I = H/6 and P = H, where H is the hardness of the softer contact [Ref. 371. Hence, p = 1/6, approximately the value obtained for Mo vs S i c sliding in SO, and 0,. In practice, not all velocity accommodation need take place by breaking junctions; plowing of particles against particles and transfer of tribochemical tilms will also contribute to friction. Thus, the classical adhesive junction model accounts for particle formation, Mo transfer to the Sic and the magnitude of the friction coefficient in SO, and 0, gases. In H,S, only a few Mo particles were found in the track and on the pin scar, and those were probably generated during the tirst few cycles at higher friction by adhesive junction formation, before tribochemical tilms covered both surfaces. In steady-state, sliding was accommodated between the smooth Mo and S i c surfaces, both of which were covered with tribochemical films. From the burnished appearance of the track, steady-state sliding in H,S took place without much wear at all! Since sliding occurred along a smooth interface, mechanical contributions to friction, like plowing [Refs. 1,381, were minimal. Moreover, the adhesive contribution to friction also had to be minimal because no transfer tilms were seen on the counterfaces. The ultralow friction coefficient in H,S may, therefore, be attributed to the near absence of mechanical and

chemical interactions across the sliding interface. 4.3 Final remarks

One may generalize the above results by saying that, as the counterfaces slide past each other, there is competition between junction formation and interfacial sliding. If a junction begins to form, but the energy to form it and resist fracture is less than the energy to shear the weaker counterface, then the junction won’t form; instead, the counterfaces will slide at the original interface. However, if the energy to form and maintain a junction is greater than the energy to shear the weaker material, then sliding will take place by rupturing the weaker material. Clearly, the former case (interfacial sliding) requires less energy, hence lower friction, than the latter. It would be useful if this competitive process could be modelled and quantified. Thermochemistry offers one approach for estimating the chemical bonding, thus adhesion energy, associated with the reaction of two materials. Alternatively, more detailed examination of real surface and/or interface structures may provide a more satisfying physical mechanism for why films formed in some gases protect better than those in other gases. Two other issues have been raised, but not answered, by the present study: I) what is the microstructure of the beneficial tribochemical tilms, like those found in H,S tests; and 2) what is the lubrication behavior of the Si sulfidegraphite films formed on Sic. To the authors’ knowledge, no studies of Si-based solid lubricating films have appeared in the literature, but the ultralow friction coefficients measured in the present experiments suggest that they might be very lubricious. 5 . SUMMARY AND CONCLUSIONS

o

Sliding S i c against Mo at room temperature in SO,, 0, and H,S, at gas pressures between 4 and 40 Pa, produced low friction,

89 lubricating films. In SO, and O, friction coefficients were about 0.1, but in H,S, they were less than 0.01. In contrast, gas reaction films formed in H,S could not sustain low friction sliding in high vacuum. o Three distinct third-body products were formed during sliding: * In all three gases, tribochemical films were formed, with compositions nominally those of corresponding gas reaction tilms. * In SO, and O,, metallic Mo particles were generated and transferred to the S i c counterface; in H,S, very few particles were formed. * In SO, and O,, Mo-based transfer tilins were found on both surfaces; in H,S, no transfer films were found on either counterface. o Compositions of gas reaction and tribochemical films were consistent with phases predicted by equilibrium thermochemical calculations. o The higher friction coefficient ( = 0.1) in SO, and 0, was attributed to the detachment and shearing of Mo particles during sliding, consistent with the adhesive junction model of Bowden and Tabor. The lower friction coefficient ( < 0.01) in H,S was attributed to absence of junctions and Mo particles, the smoothness of the Mo track and the apparently low chemical reactivity of the tribochemical films formed on the Mo and S i c counterfaces in H,S. ACKNOWLEDGEMENT. ILS wishes to acknowledge the Naval Research Laboratory for supporting a sabbatical stay at Ecole Centrale de Lyon during FY93 and to thank Nicolas Chavent for performing the SEM/EDX analysis.

2. 3.

4. 5. 6. 7.

8.

9.

10. 11. 12.

13.

14. 15. 16.

REFERENCES 17. 1.

F.P. Bowden and D. Tabor, The Friction and Lubrication of Solids (Clarendon Press,

Oxford) Part 1 (1950) and Part 2 (1964). D.H. Buckley, Surface effects in Adhesion, Friction. Wear and Lubrication (Elsevier, Amsterdam, 1981) I. Iliuc, Trihologv of Thin Lavers (Elsevier, Amsterdam, 1980). B. Bhushan and B.K. Gupta, Handbook of Tribology, McGraw-Hill, New York, NY (1991), Chapters 5 and 13. I.L. Singer, Surf. Coatings Technol., 49 (1991) 474. K.J. Wahl and I.L. Singer, Tribology Lett., I (1995) 59. F.P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part 2, (Clarendon Press, Oxford, 1964) p. 210. E.E. Graham and E.E. Klaus, ASLE Trans., 29 (1986) 229; E.E. Graham, A. Nesarikar, N. Forster and G. Givan, Lubr. Eng., 49 (1993) 713. J.L. Lauer, T.A. Blanchet, B.L. Vlcek and B. Sargent, Surf. Coat. Technol., 62 (1993) 399; J.L. Lauer, B.L. Vlcek and B. Sargent, Wear, 162 (1993) 498. M. Godet, Wear, 136 (1990) 23. Y Berthier, Wear, 139 (1990) 77. I.L. Singer, in New Materials Amroaches to Tribologv: Theory and ADDlications, edited by L. Pope, L. Fehrenbacher and W. Winer, MRS Symposium, 140 (MRS, Pgh. PA, 1989). p. 215. I.L. Singer, in Fundamentals of Friction eds. I.L. Singer and H.M. Pollock (Kluwer Academic Publishers, Dordrecht, 1992) p. 237. C. Donnet, T. LeMogne and J.M. Martin, Surf. Coat. Technol., 62 (1993) 406. I.L. Singer, T. Le Mogne, C. Donnet and J.M. Martin, to be published in J. Vac. Sci. Technol., Feb 1996. J. M. Martin and T. Le Mogne, Surf. Coat. Technol., 49 (1991) 427. Handbook of X-ray Photoelectron Spectroscopy, edited by C.D. Wagner, W.M. Riggs, L.E. Davis, J.F. Moulder

90

18.

19.

20. 21.

and G.E.Muilenberg (Perkin-Elmer, Eden Prairie, MN, 1979). NIST X-rav photoelectron spectroscony database, Version 1.0, edited by C.D. Wagner and written by D.M. Bickhain (NIST, Gaithersburg MD, 1989). J.I. Goldstein, D.E. Newbury, P. Echlin, D.C. Joy, C. Fiori, and E. Lifshin, Scanning Electron Microscopv and X-ray Microanalysis, (Plenum Press, New York, 1981) p. 72. T.W. Haas, J.T. Grant and G.J. Dooley, J. Appl. Phys., 43 (1972) 1853. L. Muehlhoff, W.J. Choyke, M.J. Bozack and J.T. Yates, Jr., J. Appl. Physics, fiJ (1986) 2842.

22. P.D. Ehni and I.L. Singer, Applied Surface (1992) 45. Science, 23. See Buckley, Ref. 2, Chap. 6. 24. S.V. Pepper, J. Appl. Phys., 47 (1976) 801. 25. K. Miyoshi and D.H. Buckley, ASLE Trans. , 22 (1979) 245. 26. D.R. Wheeler, J. Appl. Phys., 47 (1976) 1123. 27. S.V. Pepper, J . Appl. Phys., 47 (1976) 2579.

28. J.M. Martin, C. Donnet, T. Le Mogne and T. Epicier, Phys. Rev. B, (1993) 10583. 29. See series of papers by H.M. Kennett and A.E. Lee, Surface Sci. (1975) 591,606, 617, 624, 633. 30. G.H. Smudde, Jr. and P.C. Stair, Surf. Sci., 317 (1994) 65. 31. See series of papers by J.M. Wilson, Surface Sci. 53 (1975) 315 and 330 and Surf. Sci. 3 (1976) 499. 32. L.J. Clarke, Surf. Science, 142 (1981) 331. 33. J.M. Powers, G.A. Somorjai, Surf. Science, 244 (1991) 39. 34. T.E. Fischer, Ann. Rev. Mater. Sci., (1988) 303. 35. see, for example, Buckley, Ref. 2, p. 456. 36. T. Kayaba and K. Kato, ASLE Trans., 24 (1981) 164. 37. See Bowden and Tabor, in Ref. 7, Chapter

a

IV. 38. T.H.C. Childs in Fundamentals of Friction

eds. I.L. Singer and H.M. Pollock (Kluwer Academic Publishers, Dordrecht, 1992) p. 209.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

91

From Phenomenology to the Concepts which flow fiom the Third Body. Application to Radial Face Seal. Y. Berthier, P. Jacquemard and M.H. Meurisse

Laboratoire de Mkanique des Contacts CNRS URA 856 M. 1 13, MSA F6%2 1 VIUEURBANNE WX

-

Many parameters are involved in the tribological life of a contact. As they interad, the analysis of their contriions requires a systematic approach taking into accowlt all the elements of the tribological process : mechanism, first bodies and thirdbody. This systematic and original apgraach is illusbatcdby the case of radial face Seals. he mnstmction of its tritmlogi~allife enables us to model the sealing function using 3" body flaws. 1. INTRODUCTION

The behavim of a contact results from the interaction of many panunetem and the &&e comibu!ion of each one intervene-s at a scale ranging fromthe llanometre to the millimetre. This work praposes a systematic approach, taking into accoullt all these pmmetm in order to identiQ the pmceses which govern the efficiency adthe durability of a contact. In this appoach, the contriions of the various parameters invoh.ed in the contact ale first ranked in order ofappearance and scale. This ranking is achieved by means of a st~uchvln ' 8 c o w which is the bfbological hplet. Then the various contriions are decoupled and analysed by means of two other struchuing concepts which are the velocity occommodotion mechanisms and the tn'bological cimcit. This contact approach is applied to the whole contact on the macmscopic and microscopic scales.Finally the evolution ofthe a n t r i i o n of each element of the tribological triplet is taken intoaamlnt so as to fecollstNct the history ofthe contad which is called, in this paper, the contact's I# [l]. This original systematic approach is illustrated bytbecaseofradial Eace seals. This seal is studied by carrying out tests on an apparatus which simulates its geomeby and its dynamics. The friction torque, the leak flow and the film thickness of the sealed fluid are evatuated with an approsolution ofthe Reynolds model in the

case ofthe hydtodyaamc regime. Tbese calculated values are then compared with the experimental ones in order to select the operating conditions of the tests which involve mixed lubrication. In this paper, the general s(ructunn 'gconcePts used are first presented Then tbe case of radial face seals is studied, using the systematic approach

above&scriM 2. STRUCTURING CONCEPTS

2.1. The T n i d Triplet

The triiogical triplet i n c W the mechanism the Id bodies and the T'body. The mechanism (Fig. 1) includes all the elements which determrne ' thecontactoperating conditions by transmittiag static and dynamic loads to it and by imposing its kinematin and enviromnt The Pbodiesare them materials in contact. They react to the loads transmitted by the mechanism by bulk deformations and degradation which consist of cracks, particle detachments or more generally surface tribological transformations 121.- l'Lbodiescanaccommodateapartoftbe velocity difference between the la bodies. The 3" body (31 separates the 1" bodies and also controls their degradation, it transmits the loads imposed by the mechanism and accommodates the main part of the velocity Merence

92

MECHANISM

sealed fluid

&

rotating shaft

/

secondary seals

3* BODY

V bolder

I

b) Detail view of 1" and 3d bodies

t

a) A radial face seal assembly Figure 1. The Tribological Triplet.Application to Radial Face Seal.

2.2. The Velocity Accommodrtion Mechanisms In a contad, the velocity accommodation can be localid at Merent sites S, and achieved by difFerent modes M,. The accommodation sites are the ld bodies S, and s5, the b ~ l kofthe 3'" body ~3 and the frontiers between the 1" and 3d bodies, .SZet S,, called screens. The accommodation modes are

elastic deformation MI, normal fracrure M2, shearing M3 and roll formation MI.A velocity accommodation mechanism S,M, [4] groups the site andthemodeOf~mm0dati~ 2.3. The Tribologicrl C W Whatever the nature ofthe 3"' body, it is present throughout the contact in the form of Merent flows. First the 3'" body is either in$zcted (source flow of artificial 3"' body) or pro~ced in the contact (source flow of aah~al3"' body). The 3"' body is

without wear of the contact faces, and with a minimal leakage of a few millilitres per hour. when this leakage is not tolerated or when there is a lack of lubricant, the seals operate in a mixed lubrication regime, which implies interactions between the contact faces causing &gradation. A radial faEe seal aperating in a mixed lubrication regime with water was selected, because this operating regime can involve severe degradation of the contact fixes. Attention is dram to the fact that the manufacturer particularly wishes to correlate the leakage and the wear to the materials of the contact

faces. 4.

AN OTHER VIEW OF THE CONTACT

then trapped andcirculatesbetween the Id bodies (internal flow). F w the 3"' body, which flows from the contact, is either recycled in the contact (external recycled flow) or ejected (ejection flow). The triilogica~circuit expram the balance of 3'" body flows.

The comibutions of the various parameters which govern the sealing efiiciency and the seal durability are ranked using the tlibological triplet. Inthe same way, preceding works about radial face seals are reviewed and classified depending on which element of the tribological triplet they more Speafically highlight.

3. CONTACT STUDIED

4.1. The Mechanism

Radial face seals provide radial sealing between a static housing and a rotating shaft via the contact between two rings. In many cases, these seals operate in the hydroctynarmc lubrication regime,

The rotating shaft, the holders of the seal rings, the spring, the secondary seal, which ensure the sealing along the shalt etc., form the mechanism of aradialfaceseal (Fig. 1).

93 The leakage and wear of the seal are cbngedby its dynamics, which &pen& on misalignments between the contact faces and the rotation axis, and 011 the s t i t h s s Of tbe seal ring [MI. A 0.Lcbeck [9] suggests a mechanism design, which applies a varying cosinusoidally distributed moment to the stationary ring. This moment produces maving misalignment and tangential waviness which continuously control the gapbetween the seal rings. According to the author, this gap control leads to reduce leakage and wear. 4.2. The 1" B o d i

In a radial face seal, the Pbodies are the rings in contact (Fig. 1). In the case of the seal Wed, la bodies made of two carbon-grapbte materials, called c 1 and c2, are paired with 1" bodies made of silicon carbide and nitri&d stainless steel. Carboncan be described as a mixme of mimaymllites and amorphous phases. A resin m up the pores in order to achieve the bulk Epnlinn. The M e & constituents which compose the cmbn-grajhte have a grain size ranging h m 0.3 pmto 30 pm.

Through machining, the 1" bodies acquire their initial macro- a d microgecnneby, which are Charactensed by parallelism &kct between the two blccs ofthe dg,tangential waviness, radial profile and rouglums of the contact face. In the mechanism¶the 1"bodies read to the thermal and naechanical stresses by deformation. Tbe macm and microgeometry and the tdk &formations of the 1" bodies, which depend on their thennoelastic pmperties, change also the seal dynamics. The assessment of the I" bodies deformations and their comquence on seal performance have beenstradiedby~a\lthorS[10-15].I.Etsionand 0.MicWl[16] propose a partially p o r n 1* body, which reduces leakage and wear in the same way as a gap profile forming a taper in the radial direction. 4.3 The Third Body

In the hydrodynamic lubrication regime, the 3d body is a thick film of sealed fluid or arhJcial3"' body, whose rheobgy is known [lq. In the bounQry lubrication regime, the 3d body consists d a few molecular layers of d e d fluid [IS]. In a d e d mixed Iubrication regime, the artificial 3d body does not completely separate the 1" bodies

between xhich inteructions then occur, d n particle detachment, which produces the natural 33 body. Tbe m h U e Of the artificial and naturd 3d bodies forms a composite body. In this paper, the term interaction designates either direct localised contacts between the 1" body roughnesses, or lubricated microantacts [19-20). The formation and the function of a composite 3d body have been studied in a continuous slidmg clutch ojmahng with carboncarbon composite I" bodies [20]. concerning radial face seals, several authors mention the existewe of a natural 9 b ~ d yin the form of a thin layer composed of particles essentially detached fiom the carbon-graphite la body [21-2.21. R I. Longley [23] has studied the friction of carbn-graplutes running against mild steel in air (50 % relative humidity), using a ring on ringtestappatus. They report theexistence of thin debris layer on both 1" bodies. According to RR W o n [21], the debris layer accommodata the velocity by shearing with low frictionand low wear, because its shear strength is lower than those of the 1" bodies. Alternatively, according to R I. Longley and his COdUthOrS, the thin layer formed increases the real contact area by filling up the pores and hollows, which inQces friction and wear to increase. Only fkw works have studied the particular c o n t r i i o n of the natural 3d body to radialfaoesealbehavioltr.

The thidrness of the 3d body involved in these seals ranges from a few tenths ofa micrometer to a few manometers. consequently, we are not able to measure the rheology of the natural and composite 3d bodies using classid methods. We g a round this difficplty by creating a morphological atlas of Id and 3d bodies by means of various surface CharactensationtechniquesThisatlasenablesusto reconsbud the contact dynamics.

In the rest of this text, we will note the various flows of the triilogical Circuit in the following way:

-Qt a d Q:,

which

the sour~eflows of

the arlificial and natural 3d bodies;

-Q: and Q:, which tbe h t e d Of the natural and composite bodies; -Q:and QZ,which are the ejection flows of the artificial andcomposite 3d bodies.

94 were carried out replacing the stationary specimen made of silicon carbide or stainless steel with one made of glass and filmed at 3000 imagedsecond. With this visualisation rig, the field of observation (4mm x Smm) was actually magnified by x loo. 5.2. Operating Conditions

friction torque axial load

1" body

Figure2. TestApparatus 5. CONTACT SlMULATION 5.1. Test Apparatus

The tests were performed on an apparatus (Figure 2.) which simulates the sealing function of the

seal. The mechanism is simpler than the industrial one and permits a simple replacement of the 1' bodies.

Annular specimens, with an outer diameter of 55 mm, an inner diameter of 47 mm and a thickness of 8,s mm are used for the 1" bodies. The load applied on the Id bodies ranges from 128 N to 600 N. The velocity ranges from 2,7 m/s to 13,4 ds.The sealed fluid is water, whose pressure ranges from 0 and 0.4 Mpa. The 1" body holders were adjusted to minimhe misalignments with the rotation axis. The spring features (stBness, number

of turns, shape defects...) were selected in order to completely accommodatethe misalignments. The initial macro- and microgeometry of each specimen was characterised before test. The thermwlmic and physicalchemical bulk properties of each material were measured. Finally a test procedure including seal test assemMy and running in conditions was dehned In order to localise and iden@ the interactions occurrhg between the 1" bodies, visualisation tests

52.1. Apprdmate solution ofthe Reynolds model The test operating conditions involving a mixed

lubrication regime were defined using an approximate solution of the Reynolds [24] model by comparing the calculated values of friction torque C and leak flow Q: with the experimental ones. In the case of the seal studied, the apparent contact width AR is more than six times lower than the average radius R Consequently the assumption of the narrow bearing was used. The calculations were made in the case that one of the 1" bodies presents a tangential sinusoidal waviness. Whatever the material, each specimen presents an initial tangential waviness which can be assumed sinusoidal of amplitude d and period n (n=2). However the elastic modulus of carbon-graphite is at least ten times lower than that of silicon d i d e or steel. We have therefore assumed tbat the tangential waviness on the carbon-graphite specimen was totally flattened by the applied load. AU the notations used in the following expressions are defined in the nomenclature at the end of the text.The gap between the la bodies was assumed to be constant in the radial direction. The gap is expressed by the form : e=e,(l+acosn0)

(1)

With these assumpI1ons. the load generated in the fluid film is expressed as a function of its average thickness :

In this expression, the iirst term on the right hand side expmses the load generated by hydrostatic effects and the second one the load generated by hydrodynamic effects. Assuming tbat the sealed fluid perfectly separates the 1" bodies (N=W), the average thickness eo is calculated with (1). The friction torque is expressed as a function of

95

the square root of the dynanuc viscosity, the linear velocity and the thcoretical load support induced by the hydrodynamiceffects :

qmR2c3 a k2 (l-a2)* The leak flow isexpressedby : with F =

(3')

(4)

The Reynolds model has been used by many authors to provide quantitative assessment of the hyddynamic lubrication regime with various expressionsofthe gap between the 1" bodies, taking into accoullt misalignments with the rotation axis (5-81 andor tangential waviness [lo-151. AO. Lebeck [25] has established a solution of the Reynolds model with an expression of the gap taking into accouLlt tangential wayiness and radial roughness. The total load support is given by integration of the lrydrodynamc and pressure distrihtions. AO.Lebedr conctwieS that more than 99 per cents of the load may be supported hydrodyaamically though roughness interactions were expected which cause 1" bodies &gdatiOn. S.2.2 Comparison of tkeordcd and aprrimentol re.df.9

Figure 3 tepresents the way calculated and measured friction torque change with the square root of tbe linear velocity for Merent tests. At 2.7 ds,the tlwre!tical thickness ta ranges from 1 to 4 pn, depeadins on the amplitude of the tangential waviness and the load applied. At 13.4 ds,the increase in thickness is equal to 0.4 pm at 400 N and0.8 pm at 128 N.Thesevalues are usual in the hyddynamic lubrication regime. At a load of 400 N, the torque measured at 2.7 mh is in average ten times higher than the calculated value. This difference &creases when the velocity increases. These variations in torque are explained in the following way. At low velocity, the load supgorted by tbe artificial 3d body is lower than the applied load and interactions between the ld bodies a0 locally occur. When the velocity increases, the

hydrodynarmc load increases and relieves the interactions between the 1" Wes. At a load of 128 N, the measured torque increases with the velocity, according to the calculated values. Concerning the influence of the waviness amplitude. the higher the amplitude, the lower thc calculated Friction torque. Thcre is no similar trend concerning the measured values. At low velocities, the seal operates in a mixed lubrication regime and the smaller the average or minimal gap (at the top of the waviness), the mote interactions are expected Both calmlated and measured leak flow increases with the linear velocity and the amplitude of the tangential waviness. Concerning thesc results, we can conclude that the main part of the applied load may be supported hydrodynamically even at low velocities. However, in this last casc more inteructions occur,causing friction increase and I" bodies degradation These conclusions are in good agreement with AO. Lebeck's canclusiolw. As a c o v of these results, the linear velocity of 2.7 ds was selected for following systematic tests and all the test specimens employed had an amplit& of its tangential waviness smaller than 0.9 pm in order to limit the leakage. 6. ANALYSIS OF TEE TRII)OLOGICAL

LIFE OF THE CONTACT

The test resultsareandysedinordertodeoouplc the contriions of the mechanhq the 1" bodies and the 3"' body by means ofthe sbuctunn . gcoacept above presented. Through this contact analysis, tbe contact's Life is reconsbucted The contact's life is divided into three stages : conception, birth and proper l i f e Conception stage includes the initial set up of the mechanism and the bulk deformations of the 1" bodies. Birth stage &ect the volumes oftbe 1" bodies where the local stresses are the highest. A volume a f f i or elementary volume, ranges Erom one pm3 to 100 pm3. the scale of an elementary volume, the gap between the 1" bodies is d e r than in the rest of the contact and also infeructions may occur. The birth stage is the response ofthe elementary volumes to the local stresses. Proper life stage indudes the variations of the 1" bodies' response and 3"' body flows, This tecotlstNctionis illusbated by the case of a cadmn-graphite running against a nitrided stainless steel 1' body. Different tests were carried out with

96

0.70

-

0.60

E 0.so

E.

0 o 0.40

-.$8 8

0.30

2 0.20 0.10 0.00

1 .00

1.50

2.00

2.50

3 .OO

3.50

- measufed values -----

calculated values

4.00

W=400N W=128N

Figure 3. Friction Torque Variations as a Function of the square root Linear Velocity. ld ~ e : CIs/ Sic 100 - = 2. los Pa 6.1. Conception

F, : load applied by the secondary seal

W

F, : centrifugal load P. : applied pressure

s :

apparent contact

area I PO: water pressure Figure 4. Loads applied to the carbon-graphite 1" body

m g e operating CoBditiom and N M h g times ranging from 2 minuus to 500 hous. Only few results are presented in Table 2. Different techniques of mface charactmiation were used to gather the evidence from the 1" bodies : optical i v , secondaty electron microsaqy and X ray dispersive energy spectrometry,confocal miwith whicb the quantitative topography of the surfaces was achieved

41.1. 1" Bodjr Ddomdaits

The mechanism imposes a rotational relative movement on the 1" bodies and the loads (Fig.4) : ~lnnalload N (N=P,.S), load applied by the secondary seal F, and water pressure. The sealed fluid or artificial P body is water at the temperature of the laboratory. Thus the possible heating of the 1" bodies arises from the power dissipated in the contact. The loads imposed by the mechanism only incluce a significant coning deformation (Fig. 5 ) of the 1'' body made of carbongraphite, because its elastic modulus is a! least ten times lower than that of steel. This &formation was also clearly obsemd with the visualisation tests.

The 1" body Mormalions control W p p e and thereforethethicknessof'thearti6cial3 b0dy.A this stage of the contact's life, the 1" bodies intervene through their themnoelastic properties. 61.2 Gap bdwezn the I* h f & s The average gaps calculated for each test with the appmximate solution of the Reynolds model are pesented in Table 2. These.values correspond to the

97

I

I

Figure 5. Radial Coning values usually observed in the hydrodyxwc lubrication regime. Whatever the case, the measured torque is between three to six times tugher than the calculated torque. No leak flow was measured Furthermore, the rmnimal value of the gap calculated with (1) is equal to 0.6 pm or 0.7 pm depending on the initial amphtude of the tangential waviness d This value is of the same order of magnitude than the maximal roughness (RJ measured on both l* bodies. Interactions may consequently OONT between elementary volumes of the 1" bodies, that explains the difference between measued and calculated values of the toque. 6.2. Birtb

This stage of tbe contact's life is reconstNcted examining the contact faces for several tests of two minutes, carried out under the same conditions (Figure8. Zone 1). The carbon-pphte Id body presents a smoothed annular zone, 0.5 mm wide,located near the inner circumference of the I* body (Figure 6.). In this zone some natura~3d body is trappea in the mughness in the form of grooved plates. They have an average s u r f i ~of~ 100 p m z . his ~ t u r a 3d l body is formed by agglomeration of particles with a m i m e t e r size, detached from the carbon-graplute ld body. The opposite zone of the other 1" body presents circumferential grooves with an average depth of ap~~~ximately 0.5 pm. The elementary vo~umes of the 1" bodies respond to the local stresses by a source flow of natural 3d body (Qf).Near the inner cucumference of the 1" bodies, the velocity accommodation mechanism is localised in the lfl bod~es(S,,Ss)and achieved by shearing. In the rest of the contact, the velocity diHerence is

accommodated in the artificial 31d body by shearing (M3). At this stage of the contact's life, the microscopic mechanical characteristics of each constituent of the carbon-graphtte control the source flow of natural 3d body. 6.3. Proper Life The proper life of the contact is reconstructed examining the contact faces after running 60 minutes and 500 hours for several tests. The variations of the leak flow (QE)and the friction torque were correlated with the morphologcal changes of the 1" and 3d bodies. After running 60 minutes (Figure 8. Zone 2), the smoothed zone on the carbon-graphite I" body has grown (width : 1.5 mm). The mostly carbonaceous natural 3d body trapped between the 1" bodies forms a uniform layer of few tenths of a micrometer thuck. It presents a stratified morphology near the periphery of the smoothed zone indicating that it accommodates the velocity digerence by shearing (S&) (Figure 7.). This 3d body flows in the tangential direction : internal flow (QF). Near the inner circumference of the &ngraphite 1" body, the surface is much more shury due to the remova~ofalmost ail the MW3"' body. The structure of the cadmn-graphite clearly appears, as if it had been polished for observation. These surface observations display clearly that the mostly cart~~naceous 3d body produced is forced gradually outwards by the artificial 3d body pressure and the centrifugal effects. Near the outer circumfemce of the 1" bodies, some compste 3d body (mixture of artificial and ~ t u r a l3 body) is trapped between them. It is mainly composed of iron oxides which are produced by physicalchemical reaction between the artificial 3d body and either the steel 1" body or particles detached from it. Both 1" bodies are degraded by the tangentiat interna~flow of the composite 3d body (QF).The carbon-graphite I* body then presents circumferential tracks of several micrometers &ep.

The fiction torque reaches its high-

average

value (0.7 Nm) after running 100 hours, and

remains at this level dutlng approximately 100 hours, with sharp instabilities. f i r running 200 hours (Figure 8. Zone 3), the torque then &creases withsuddendropswhile composite 3"'body is

98

Table 2 1"bodies : C2 / Z 20 C 13 nitrided - W = 310 N -PO= 3.10' Pa - V = 8 d s TestReference time d

eo C,

C,

j mn/h j pm j p I N m i Nm

El

E2

2mn 0.3 0.9

2mn 0.3 0.9 0.38

0.45 0.15

0.15

E3 jlh i 0.3

2mn 0.8

j 0.9

i0.63 i 0.15

:-

1.5

lh 0.8 1.5

ilOOh ! 0.8 i 1.5

0.67

0.40

io.7

0.11

0.11

i4mh i 0.8 1 1.5 i:-0.30 i;-0.11

i:-0.11

t

SO p m

1

b) Sheme of the

smoothed zone details

oothed zone a) Carbon 1" body

c) Optical microscopic view of the smoothed zone Figure 6. Birth of the Contact ejected from the contact at periodic intervals of a few hours. The circulation of the composite 3"' body in the contact continues to degrade the carbongraphte 1"body.

After running 400 hours (Figure 8. Zone 4), the torque has demased and is equal to about 0.3 Nm. The ejection flow of the composite 3"' body is continuous at a rate of several millilitres per hour. The seal therefore does not fulfil its sealing -on. The la bodies are at present separated by a thick j l m of composite 3d body whose internal flowscauses &gradation of both 1' bodies. ~t this stage of the contact's life, the ejection flow of composite 3"' body (Q,")is almost equivalent to the sum of the source flows (Q:,Qt). The seal leaks and the la bodies wear : the contact has "died".

7. CONTROL OF THE SEALING FUNCTION

A phenomenological model of the sealing function is achieved by means of the reconstruction of the contact's life. This model describes the sealing function only using 3"' b ~ d yflows (Figwe 8.). Each flow is controlled by at least two of the three elements of the tribological triplet and the contributions of each element intervene at different scales.These contributions were identified by means of the reconstruction of the contact's life and can be

now listed The source flow ofthe artificial 3rdbody depends

on its "mechanical" characteristics (viscosity, density, etc...). It is also controlled by the mecharusm, via the e e s s of the spring and the operating conditions.The distribution of the applied

99 The source flow of the natural 3rdbody depends on the hibological reJponse of the elementary volumes of bodies. This response is controlled by the microscopicthe~oela~ccharac~nstics of the la bodies and by the chemical reactivity of the 1" bodies with the artificial 3d body (paragraph 6.3.).

pressure depends on the abihty of the rotating lst body assembly to accommodate the surface defects, via the stiffness of the spring. The spring stiffness also controls the ttuckness of 3d body and consequentty the variations of the applied load The 1' bodies equally control the source flow of artificial 3d body via their initial macro- and microgeometry resulting from machining and their deformations.

b) Scheme of the smoothed zone details V

/

Smoothed zone

c) Optical microscopic view of the smoothed mne a) Carbon 1" body Figure 7. Proper Life : Velocity Accommodation Mechanism S3M3

Figure 8. Reconstruction of the Tnbologcal Life

100

The internal and ejection flows of the natural and composite 3"' bodies are controlled by the trapping of the 3"' bodies in the contact and by the driving forccs which forced them outwards @ress~reof the artificial 3"' body, nor ma^ pressure applied centrifugal force, etc...). On the ~ ~ C ~ O S C O Pd~ Ce , the trapping ofthe 3"' bodies is controlled by the mechanism via the stifhess ofthe spin& the operatiog condjtions, and by the deformations ofthe 1" bodies via their therowelastic chamctmistics. on the microscapic d e , the 3"' body is trapped either mechanically, or physicalchemically. The mechanical trapping depends on the microgeometry ofthe 1" body (rwghaess and porosity) and on the texture of the 3"' body. he physicalchemical trapping depends on surface energies of both 1" and 3"' bodies and each constituent of the carbon-graph~tehas a s p e d c surf= energy. Furthennore, during the mntact's Me, the morphological, thennoelastic and physicalchemical -C ' 'csof the ld and 3"' bodies are modified. For example, during the birth of the contact, the carb~naceausnatural 3"' body, is cornposed of particles with a micrometer size. These particles are then ground between the 1" bodies. Their size is tedoced resulting in self-adherence increase that ~bengthensthe cohesion of the 3"' body. III the same time on the carbon-gra@te 1" body, the zones where natural 3"' body is produced become more and more smooth. ConseguenUy, to model the sealing function BmouLLts to quantlQ these different 3"' body flows. AS the thicknesses ofthe 3"' b ~ d yiov0ha-iare very thin, the quantification of these flows can only be done by visualisation tests.Furthermore,these flows results from the conmitions ofeach element ofthe triilogrcal triplet and these contributions are eqtxted to change during the contact's life. Thedore, in order to achieve a realistic contact model the number of interactions must be reduced

order to identify, rank and decouple the contributions of the different parameters to the life of the contact. This a p p W was applied to the analysis of the behaviour of radial face seals. An approximate solution of the Rqnolds model was established providing quantitative assessment of the hydmdyaamic regime. By means of this solution, the operating conditions involving mixed lubrication were identified This approach enabled us : -to &sign a rational test method by taking into 8ccosltll the effects of the mechanism and conlrolhg the macro- and microgeometry of the 1" bodies. -to understand what bulk and surface properties ofthe materials efkctively control 3"' b ~ d yflows during the whole contact's life. Furthermore, the 3"' body concept leads to an unified view of the lubrication regimes introducing the origin oftbe 3"' body : artificial, natural and composite. The sealing W o n of a radial face seal can also be compkteb & s c r i i using 3"' body flows. H o w e r the main di&culty is to quant@ thesefl0WsQeto: modification^ Of the C O ~ ~ ~ E D ~ S , and properties of the 3"' bodies dwing the contact's life; -smal13dbodythickaess. Consequently, quantification of the 3"' body flows can unly be achieved by visuatisation tests.

TheexampleofradialEacesealsalsohighlights the interactions between thc contriions of each element of the tribological triplet. J3y consequenoe, an approach which confines the analysis to the role of materials alone may lead to erroneous interpretationsofthe physical processes involved in the contact. A realistic contact model must take into account all the contrihtions of the triilogical

triplet.

ACKNOWLEDGEMENTS 8. CONCLUSION

In this paper, a systematicand original approach to iden* the physical processes, which govern efficiency and durability of a contad is presented This approach uses general struchuing concepts in

The authon would like to thank the CEA and Carbone Lorraine for their support to this work and especially Mr MAURY, at CE4 and Mrs COULON and MOREAU, at Carbone Lorraitae.

101

NOMENCLATURE ~~~~

R AR

: average radius (=2,55 10” m)

: surface width (410” rn)

c=--AR : geometricalparameter (=1,574 10’) R : dynarmc viscosity of water at 2OoC p (=103 pa.s) o

: angularvelocity

Po

waterpresswe

eo

d a = - : dimensionless waviness amplitude e0

W

: loadsupport

C

: frictiontorque

F

: partoftheappliedload,whichmustbe supportedbY~hY~odynamiccarrying

load

Q

: leakflow

:wavinessfreque~

REFERENCES I . Y.Berthier,MaurkGodet’sThirdBody Appoach, 22nd Leeds-Lyon Symposium on Tn’bology, Lyon, France (1995). 2. Y.Eerthier, MC.Dubourg, M Godet, L. Vincent, Wear Data : what can be made of it?, 18thLeeds-L~nSymposium 011Tribolog~, Lyon, France (1991). 3. M. Godet, Third Bodies in Tribology, Wear, Vol. 136, 1 (1990) 29-45. 4. Y.Berthier, Experhental Evidence for Friction and Wear Madeling, Wear, Vol. 139, 1 (1990) 77-92. 5 . R HaardtandM Godet, AxialVibationofa MisalignedRadialFace Seal, Undera Constant Closure Force, 29th ASLE Annual Meetin& Cleveland, USA (1974). 6. J. Lohou andM Godet, Angular

Misalignmentand!3tp4Z-~Effectsin Radial Face Seal 6th International Conference on Fluid Sealing, Munich, Gzxmaqj (1973). 7. R Metcalfe, Dynamic Tracking of Angular Misalignment in Liquid-Lubricated End-Fe seals, ASLE T m . , Vol. 24,4 (1980) 5095 16.

A S.LeeandI. Green, Rotordynamicsofa Mechanical Face Seal Riding on a Flexible Sbaft, J. Tn’bol., Vol. 116 (1994) 345-351. 9. A 0.L&e& Design ofan Optimum Moving Wawe and Tilt Mechanical Face Seal for

8.

5 :scaleparameter R

: average thickness ofthe artificial 3d

body n

€=

Liquid Applications, 9th International Conference on Fluid sealin& Noordwij&erhout,Netherhds (1981). 10.I. E t ~ i and ~ n A Sharoni, Perfonnan~eOf EndFace Seals with Diametral Tilt and Coning Hydrostatic Effects,ASLE Trans., Vol. 23,3 (1979) 279-288. II.AO.Lebe&FaceSeal Waviness.prediction, Measurement,Causes and Effects, 10th International Conference 011 Fluid sealin& Indmck, Austria (1984). 12.T. G.Doust and A Parmar,An Emrimental and Theoretical Study of Ressure and Thermal Distorsions in a Mechanical Seal,ASLE Trans., Vol. 29,2 (1985) 151-159. 13.I. Etsion and M.Groper,The Accuracy of Ahalytical Solutions for the TemperaDistn’buton in Mechanical Face Seals, 14th nternational Conference on Fluid sealing, Fireme, Italy (1994). 14.R A Burton, Cmvedon of Heat in ShortBearings and Face seals, Tn’bol. Trans., Vol. 37,4 (1994) 876-880. IS. B.N. Banejee and R A Burton, Experimental Studies on Thermoelastic Effects in Hyddynamically Lubricated Face Seals, 1. Lub. Tech, Vol. 101 (1979) 275-282. 16.I. Etsion and 0. Michael, Enhancing sealing andDynamicperformancewithPartially PorousMechanical Face Seals,Tribol. Trans., Vol. 37,4 (1994) 701-710.

-

102 17. J. Fdne, D.Nicolas, 8. Degueurce, D.Berthe and M.Godet, Lubrification hydrodynamique, Eyrolles (eds),1990. 18.D.F. Moore,Boundary Lubrication. Principles

23. R I. Longley, J. W. Midgley, A Strang and D.G.Teer. Mechanism of the Frictional Behaviw of High, Low and Non-Graphitic

and Applications of Tribology, Oxford R ~ ~ I IPress, I O UChap. 7 (1970) 132-148. 19. A Jullien, M.H Meurisse and Y. Berthier, Fractionated Thin Film Lubrication, 19th Leeds-Lyon Symposium, Lyon, France (1993). 20. A Jullien, Analyse tribologique d b mecanisme & glissement dans I‘huile. Lubrification fractionde, These : doctorat INSAL, (1992). 21. R R Paxton, Manufactured carbon : a selflubricating material for mechanical devices, CRC Press (eds),(1979). 22.B. S. Nau, Research in mechanical seals, e x Mechanical Seal practice for unproved performance, J.D. S~mmers-Smith(eds),

(1963). 24. M.H.MMsse, P. Jacquemard, Modelisation Tribologique de garnitures mdcaniques d’dtanchditd, rapport de travaux C.E.A. (1995). 25. A 0.J-ebeck A Study of Mixed Lubrication in Contacting Mechanical Face seals, 4th

( 1992).

Carbon. Lubrication and Wear Convention

Leeds-Lyon Symposiumon Tribology, Lyon,

France (1977).

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

103

Mechanisms of third body formation with polymers Role of mechanical and adhesive interactions in the friction and transfer of polyethylene M . Brendlk and S. Lamouri Centre de Recherche s u r la Physico-Chimie des Surfaces Solides, C N R S 24, Avenue du Prbsident Kennedy, 68200 Mulhouse, France

This work is part of a systematic investigation concerning the mechanisms of transfer film formation in dry friction and their influence on frictional forces. This paper deals mainly with discontinuous films and is characterised by a n experimental approach using image analysis to quantify the discrete particles formed on smooth surfaces, combined with the analysis of the parameters controlling transfer particle stability. This work aims to complete the previous investigations in the case of polymers, and check to what extent adhesion (measured by peel test) affects transfer particle density. I t is based on the use of four well characterised films of polyethylene, differing mainly by the amount of grafted acrylic acid (respectively 0.0, 0.5, 1.0, and 2.0%). The variations of particle density with normal load, displaying either positive or negative slopes are of great interest. In agreement with previous hypotheses, these variations may be interpreted in terms of shear stresses T, provided that they include the well known pressure dependence o f t .

1. Introduction Introduced in 1987 by M. Godet e t a1 (0,the third body concept is now generally accepted, and its actual existence recognised in most tribocontacts. In 1989 it was completed by the concepts of m e c h a n i s m s of velocity accommodation by Y. Berthier e t a1 (2). Based on the simple statement that within a given contact, velocity may be accommodated at 5 different sites, by 4 d i s t i n c t modes (elastic d i s p l a c e m e n t , normal fracture, rolling, shearing), they predict 20 different mechanisms able to accommodate velocity within a dry contact. While the actual occurrence of each of these mechanisms was demonstrated for a given system, one or several mechanisms may be activated either simultaneously or consecutively. A t this stage, the utility of the 3rd body

concept r e m a i n s p u r e l y d e s c r i p t i v e , generally restricted to describing the l a s t activated mechanism before opening t h e contact. Indeed, although the activation of a given mechanism is governed by t h e principle of minimal energy dissipation, it i s seldom possible to p r e d i c t which mechanism will predominate. I n some particular cases, this minimisation implies a change in topography, i.e., the activation of different sites within t h e same contact, depending on t h e l a t e r a l position. T h e formation of a discontinuous transfer film is t h u s simply t h e r e s u l t of a l t e r n a t e d activation of two different sites located either at the interface or within the 3rd body (or even the opposed 1st body). The distribution of the corresponding a r e a s is not random, but d e t e r m i n e d by complex i n t e r a c t i o n s involving p a r a m e t e r s of physical n a t u r e (normal load, temperature, speed, etc.) and of physico-chemical nature (surface energy,

104 environment-controlled surface adsorption, etc.). Recently (3-5)we pointed to the interest of studying these discontinuous films by image a n a l y s i s , which e n a b l e s t h e extraction of s t a t i s t i c a l i nf or m a t i ons already contained in their transfer patterns. Moreover, these transfer characteristics were revealed to be very sensitive towards a n y of t h e involved p a r a m e t e r s . A systematic study of t he s e interactions allowed us to obtain a comprehensive view of these phenomena, described in a previous paper (6). The easiest way to summarise these findings is to consider t h e c a s e of discontinuous transfer on a flat surface: as soon as discrete particles a r e permanently attached to a smooth surface, each particle m u s t be considered a s a n a s p e r i t y interacting both mechanically and physicochemically with t h e countersurface. A simple analysis then reveals t ha t the forces acting on such particles a r e of two kinds: those acting in favour of their formation or s t a b i l i t y , i.e., m a i nl y t h e a dhe s i ve interactions bonding the particles onto the surface; a nd those acting against, either before their detachment from the first body (of cohesive nature), or after their formation (frictional interactions tending to remove them from the surface). The conditions of equilibrium may simply be expressed in terms of the shear stresses developed along t h e interfaces involved, a s illustrated schematically in Fig. 1.

1

. . . , . . , . . . . . . . . . ,

,

. , , , , ,

.

. . .

.

.

,

T=

kW,

where W a is th e corresponding work of adhesion. T h u s , despite t h e complexity of t h e interactions involved, it i s possible to assume that the limiting particle density and size of the transfer particles a r e primarily determined by the intensity of the adhesive interactions and the cohesive strength of the materials in contact, i.e., something close to W a . The aim of this work is to complete previous investigations on graphite by t h e systematic study of polymer transfer, an d to take advantage of the possibility offered by polymers to assess the work of adhesion W a by peel tests. Theoretically, t h e surface energy of a polymer can be modified without affectin g i t s m e c h a n i c a l p r o p e r t i e s . Therefore, for reasons of clarity, a first attempt was made to modify Wa by changing only t h e surface characteristics. In a previous paper (91, this w a s achieved by modifying only the uppermost surface layer of high density polyethylene (HDPE) by various plasma treatments. However, th is method did not ensure t h e constancy of surface energy with wear depth, nor that of the mechanical properties which were altered by superficial crosslinking. In this work, we therefore chose to modify the polymers in the bulk, by incorporating small amounts of polar chemical groups. 2. EXPERIMENTAL PART

\

.

actual adhesive interactions, by the simple relationship:

I

.

.

,

.

.

,

.

. .

Fig. 1: Schematic representation of a transfer particle. Finally, referring to Cox e t a1 (7-81, we have shown that it is even possible to link the various critical shear stresses T w i t h the

2.1. Principle Keeping the previous considerations in mind, this work aims both to investigate the friction and transfer behaviour of PE sliding against thoroughly polished steel, an d to establish in a more quantitative manner any possible correlation between th e transfer characteristics and the adhesive properties of

105

PE. It is mainly based on the use of 4 PE films, 50 pm thick, essentially differing by the a m o u n t of polar groups. These a r e commercially available films obtained by mixing various amounts of acrylic acid (AA) (respectively 0.0 ; 0.5 ; l . O , and 2.0% in weight) with finely powdered PE, followed by UV-induced chemical grafting prior to film manufacture. Although all these products were obtained from a PE of identical molecular weight (120 000 g/mol), a slight change of their mechanical properties with AA content cannot be discarded. Therefore, these films were thoroughly characterised, with respect to their surface and adhesive properties, as for their mechanical properties. 2.2. Material characterisations Using standardised traction tests, we determined systematically the Young's , at modulus E , the yield strain P ~ elongation rupture +, and the corresponding stresses uo and or of the polymer films. The surface characteristics were determined using the 2 liquid method (8,0), based on wetting contact angle measurements of water in the presence of various n-alcanes. The work of adhesion W a , involving both surface energy and rheological properties, were measured by peeling a t 180" adhesive assemblies of the various films with metallic substrates. Since the frictional tests a r e carried on steel, the peel tests should ideally be carried o u t on t h e s a m e s u b s t r a t e . However, peeling of steel assemblies proved unsuccessful: adhesion is either negligible (on polished a n d solvent cleaned metal as such) or too high (after additional plasma cleaning). In the case of plasma cleanings most films failed by rupture. Therefore, the results presented were obtained for peeling of assemblies with aluminium foils. T h e samples, typically of dimension 20 mm x 100 mm , are obtained by pressing the assemblies a t 130°C successively for 5 minutes under 2 bars and then 10 minutes under 4 bars, followed by rapid cooling (6 minutes).

2.3.Trilmmeter The tribometer used in these studies is schematically illustrated in Fig. 2 and h a s been described elsewhere (3). The frictional force m e a s u r e d by a d i s p l a c e m e n t transducer is continuously recorded by computer. All experiments were performed using the pin-on-disc geometry, at constant speed (1.6 mm/s, i.e., 1 rpm), a n d room temperature. Typically, the duration of a n experiment is 120 minutes, while the normal load, constant for a given experiment, may be varied from 10 to 50 N . As in previous studies, the experiments a r e carried o u t using a s e r i e s of 6 discs, polished simultaneously. This method w a s the only which allowed us to obtain discs having not only t h e required roughness, b u t also identical surface properties. The polyethylene films, of 50 pm thickness, a r e glued on a polymer pin (6 mm x 6 mm). Because pure PE is unable to form strong adhesive bonds, one face of the film had to be plasma treated as described in (9) prior to being bonded to the supporting pin.

lranstluce r

Fig. 2: S c h e m a t i c tri bome ter.

representation

of

106

2.4. I m a g e analysis After the experiments, the friction tracks a r e systematically examined by optical microscopy a n d t h e t r a n s f e r particles c h a r a c t e r i s e d by image a n a l y s i s . On polished steel, satisfactory results were obtained by direct coupling of the image a n a l y s e r with t h e optical microscope. Typically, 25 or 50 fields at a magnification of 200 were required to obtain representative results. The parameters considered a r e the particle density N (number of particles per m m 2 ) , the a r e a fraction covered by the transfer particles X (in %), and the particle size distribution curves ni = f(si),where ni is the number of particles per unit area having a n area within the categoiy S i .

contrast to the initial aim, the mechanical properties vary to a relatively large extent with acrylic acid content, a n d even display quite linear variations as a function of the s u r f a c e c h a r a c t e r i s tics. While t h e s e concomitant variations do not favour a n easy interpretation of t h e experimental results, it is interesting to note the existence of a n inversion concerning t h e mechanical properties of the polymers containing 1 a n d 2%AA. Also of interest is the observation that, in contrast to common belief, the role of acid-base interactions in controlling adhesive interactions and work of adhesion seems to be less important than expected.

2.5. Visualisation of particle mobility I t is possible to visualise the evolution of the transfer particles within a specific area on the disc by using the following method: during the whole frictional experiment, a camera continuously records on video tape the images corresponding to the friction track rotating under the camera. In fact, owing to the use of a relatively large magnification (x 400), only a small band of t h e circular friction track is actually , r is the radius visualised, i.e., S ~ r . d r where of this band a n d d r its width. Typically, r = 15 mm, d r = 150 pm, and the number of frames per rotation = 1440. After completion of the experiment, the frames corresponding to a given area (in practice, a distinctive defect on the metallic surface is chosen as a reference to ensure a n accurate localisation of the area studied) of the frictional track a r e selected and assembled to build the sequence corresponding to the evolution of a given disc area with the number of rubbing cycles.

3.2.1. Influence of rubbing time Fig. 3 illustrates typical variations of the coefficient of friction p as a function of the number of rubbing cycles, respectively in the cases where the experiment is started by lowering the pin onto a rotating disc or by starting disc rotation after one minute of static contact between pin and disc. While in the first case the variations are characterised by a progressive increase towards a limiting value, in the second case they systematically display a maximum, generally reached after 3 rotations, followed by a decrease to the same limiting value.

3.2. Frictional results

c

0,30

0 .c, V

with initial static

'C

g 0,20

p120

c,

.-ti

c

G 0,lO without initial static contact

3. RESULTS 3.1. Material characteristics Tables 1 and 2 summarise the main results concerning respectively the surface properties and the mechanical properties. They require the following comments: in

60 90 12 Number of cycles Fig. 3: Typical evolution of the coefficient of friction with rubbing time (here for PE). 0

30

107

Table 1 Mechanical DroDerties

PEhd

1390+60

30+4

2.5 0.7

+

37+5

68of60

PEg (0.5%AA)

1360+80

27f4

3.9f 0.5

32f7

620 f 95

PEg (1Yo AA)

125Of30

24k2

4.6 f. 0.4

28f5

64ok50

PEg (2% AA)

1030f 50

25+3

5.8 f 0.5

28+5

700 f 70

Table 2 Surface DroDerties

YSD

P

I sw

(mJ/m2)

rsP

WO

Wa

(mJ/m2)

(mJ/m2)

(mJ/m2)

(J/m2)

PEhd

30?2

1.08

0

33

62

100+50

PEg (0.5%AA)

35+2

1.75

(0.015)

36

&3

2oof.50

PEg (1% AA)

39+2

2.25

(0.025)

39

68

570 k 60

PEg (2% AA)

42f2

2.35

(0.027)

42

53

mf.40

where

Y sD and Y sP are respectively the dispersive and polar component of total surface energy

y s, Wo the thermodynamic work of adhesion, and Wa the work of adhesion determined by peel test. While this behaviour suggests t h a t a n equilibrium has been reached, we will later see that this is not true for transfer. The existence of a m a x i m u m is surprising: appearing only after 3 cycles, i t cannot be related to the rupture of the initial adhesive bond. On the other hand, it also seems difficult to associate it with the onset of load carrying capacity (LCC), a s proposed previously for g r a p h i t e (5). A closer examination of the variations of friction reveals that in the case of pure PE, p remains constant during the whole first rotation and begins to increase progressively only during the second revolution. In contrast, grafted PE

already displays a continuous increase already within the first rotation. Identifying the limiting value with the value reached after 120 rotations: ~ 1 2 0 , we observe that aside the anomaly displayed by the polymer containing 2%AA, these values increase practically linearly with t h e acrylic acid content from 0.16 to 0.25. This discrepancy however v a n i s h e s if we consider the variations of p120 a s a function of the work of adhesion Wa.

3.2.2. Influence of normal load The variations of tangential force F ~ 1 2 0

108 as a function of the normal load, for the various P E films, a r e illustrated in Fig. 4. In this graph, each point corresponds to the mean value of at least three experimental results.

14

2

12

* 10

v

c4

possible to assume t h a t these particles are actually the primary transfer particles, detached from the pin by direct adhesive bonding. Within this category it is again possible to distinguish transparent particles, free of a n y iron (designated a ) , a n d d a r k coloured particles (designated b). Obviously the dark particles are not made up of pure PE, but rather of a mixture of P E with finely divided iron particles, either limited to the superficial regions (b') or mixed in bulk (b).

g 8

5

6

L d

g

c,

.d

4

V

2

2

0 20 30 40 50 60 Normal load (N) Fig. 4: Variations of F ~ 1 2 0with normal load for various AA contents. 0

10

In agreement with Coulomb's law, w e observe that the values corresponding to a given polymer define a straight line, having a n intercept on the x and y axes nearly equal to zero, The real coefficient of friction pr generally associated with the slope of these lines, is a function of the AA. content and even appears to be linearly related with the work of adhesion W,, illustrated in Fig. 9 (10). For instance, it is interesting t h a t the inversion observed for the values of W, for 1 and 2%AA is also displayed by the values of pr. However, since the intercept of p r = f(W,) is far from zero, it is not possible to consider t h a t W a alone is sufficient to account for friction.

3.3. Optical microscopy The systematic observation of the friction track reveals the presence of a t least two different types of t r a n s f e r particles, schematically illustrated in Fig. 5. Firstly a large number of small particles, displaying a more or less regular form. I t is

Secondly a small n u m b e r of large, irregularly shaped, black coloured particles (designated c). These particles a r e already present after the first 3 rotations, a n d a r e apparently formed by the agglomeration of previously formed s m a l l e r particles of type b. iron con tamination nil full partial a b b'

....".' ....... ,. _.

C

, .2..-.

primary particles

large agglomerate

Fig.5: Schematic representation of t h e different types of transfer particles. These observations suggest t h a t the initial interactions occur between PE and the steel surface which is coated with loosely bonded iron d e b r i s formed d u r i n g polishing. Apparently less bonded, these particles a r e removed a n d mixed with t h e polymer, rapidly leading to the large bulk-modified agglomerates. After this first cleaning phase of the disc surface, iron debris become s c a r c e r a n d l e a d only t o p a r t i a l l y contaminated polymer particles, often via a double disc-to -pin transfer particle, and thus to particles of type b'. The strength of the adhesive bonds, formed later with a debris free steel surface and the cohesion of the iron reinforced polymer a r e seemingly improved in such a way that these large particles a r e able to groove the film. These grooves enable further particles growth by a n agglomeration

process without any increase in the adverse stresses, provided the growth takes place in the direction of the grooves. A better and more quantitative description of transfer is possible by image analysis. 3.4. Transfer characteristics 3.4.1. Influence of rubbing time

The variations of the area fraction X with increasing rubbing times, either as obtained by the continuous method (i.e., to each rubbing time corresponds a n experiment performed without any interruption) or by the d i s c o n t i n u o u s m e t h o d , (i.e., a given experiment is interrupted several times in order to permit the corresponding image analyses) a r e illustrated in Fig. 6. In agreement with previous observations, the extent of transfer is generally larger in the absence of any interruption.

observe the existence of a population of small particles (Population I), the number of which steadily increases. This last observation allows us to discard the possibility t h a t the limiting value displayed by the frictional force corresponds t o a t r u e equilibrium, including surface topography.

3.4.2. Normal load From Fig. 7 we can s e e t h a t for all polymer properties, t h e a r e a fraction X increases l i n e a r l y with n o r m a l load. However, in contrast to the corresponding variations in friction, the intercept of these lines with the y-axis are different from zero. Consequently, no direct proportionality can exist between the frictional force FN and the a r e a fraction X as previously found for graphite (5). This is not surprising, since as described previously a n d in contrast to graphite, no LCC and no equilibrium were reached.

continuous method h

8 3

v

8

.3

c,

discontinuous method

2 2 +I

03

2 0,5 0

$ 1

30

0

60 90 120 Number of cycles Fig. 6: Typical evolution of the area fraction X with rubbing time for PEg (l%AA). 0

Furthermore, while X seems to reach a limiting value when determined by t h e discontinuous method, X increases steadily when determined by the continuous method. These differences a r e also reflected by the particle size distribution curves described below, showing t h a t in t h e absence of interruption, transfer particles grow in larger number t h a n in the case of t h e discontinuous method. In both cases, we

0 -80 -60 -40 -20 0 20 40 60 Normal load (N) Fig. 7: Evolution of the area fraction X (after 120 min of rubbing) with normal load and the AA content.

The marked difference in the slope of

X = f ( F N ) for pure a n d grafted P E is very striking. This behaviour already suggests t h a t in the case of pure PE transfer particles grow larger, because they are subject to lower frictional forces and hence withstand more easily than the grafted polymers.

110 This is even better illustrated in Fig. 8 showing t h e corresponding variations of particle density N a s a function of normal load. They again are linear but the slopes may be of opposite sign: positive in the case of pure PE or grafted with 0.5%AA, or negative in the case of PE grafted with 1 or 2%AA.

0 0

2 3 100200300400500600

Fig. 9: Linear relationship illustrating the good correlation between t h e work of adhesion and the real coefficient of friction and the slope a.

10

20 30 40 50 60 Normal load (N) Fig. 8: Evolution of particle density N (after 120 min of rubbing) with normal load and AA content. 0

Considering the intercepts on the y-axis, i.e., t h e extrapolated values of particle density a t zero normal load No, we observe in agreement with a previous simple analysis, No is a linear function of AA con tent. However, this ranking is progressively modified with increasing normal load. Remarkably, the algebraic values of these slopes a fit linearly with the corresponding work of adhesion W a , as illustrated in Fig. 9, rather than with the thermodynamic work of adhesion W o . The opposite variations of t h e area fraction X (always increasing) a n d the particle density N (sometimes decreasing with normal load) is difficult to understand without considering t h e particle size distribution.

3.4.3. Particle size distribution In Fig. 10 a r e shown typical particle size distribution histograms a n d their evolution either as a function of rubbing time or of normal load. Sometimes, these distributions a r e bimodal, a n d comprise two types of population: Population I of s m a l l particles, displaying a maximum centred a r o u n d 20 pm2; Population I1 of larger particles, much less numerous, encompassing roughly all particles larger than 100 pm2, with a slight tendency to display a maximum around of 700 pm2. Referring to our previous microscopic o b s e r v a t i o n s , t h e y may be a s c r i b e d respectively to the primary particles and to t h e large iron-enriched agglomerates. Despite the semi-logarithmic scale, which normally suppresses the small categories, Population I is dominant. However, owing to the small particle size, its contribution to the total area fraction X is so small that a change in Population I is not necessarily reflected in X.

111

hl

40

c.l 0

t

E

3min 6min

25

10N

A 30min I 75min

i

2 3 4 log (si) Fig. 10: Evolution of p a r t i c l e size distribution with rubbing time for continuous experiment with PEg (1%AA).

0

The above r e m a r k s account for t h e following observations. As shown in Fig. 10, Population I increases continuously with increasing rubbing time, a n d accounts for the slight increase in area fraction or particle density displayed in Fig. 6. In contrast, the opposite variations of particle density illustrated in Fig. 1 1 a n d 12 seemingly have no incidence on t h e variations of a r e a fraction X , always increasing with normal load as shown by Fig. 7. c\l

E

25

1

+

10N

2 3 log(si) Fig. 1 1 : Evolution of p a r t i c l e distribution with normal load for PE.

0

1

4 size

1 log (si) Fig. 12: Evolution of p a r t i c l e s i z e distribution with n o r m a l load for PEg (l%AA).

Although s o m e t i m e s v i s i b l e , a n d suggested by the actual existence of two (or three) types of transfer particles, the bimodal nature of the particle size distribution is not always apparent. For instance, the absence of any marked inflection in the variations of the cumulated relative area fraction is not in favour of the existence of two distinct populations, but r a t h e r in favour of a single population s u b m i t t e d t o t h e s a m e controlling parameters. However, such a situation may also result from a continuous change in particle properties, as for example a continuous increase in t h e iron contamination of the transfer particles. In addition to the particle size distribution itself, which is only a description of t h e population at a given moment, it would be interesting to assess the lifetime of t h e particles. Indeed, since large particles result from the agglomeration of smaller primary particles, they necessarily display a limited lifetime or period during which growth is permitted. The shorter this lifetime is, the higher is the rate of large-particle formation, provided t h a t the r a t e of replacement is constant and they do not escape from the contact as wear particles. In order to assess particle mobility, a n attempt was made to visualise the evolution of transfer.

112 3.5. Visualisation of particle mobility

Owing to the difficulty of transfer particle discrimination, t h e method of direct visua l i sa t i on could not be a ppl i e d in the case of PE. In contrast, the method was revealed to be successful in the case of Polyethylene terephtalate (PET), similarly characterised by a bimodal particle size distribution. This allowed us to confirm that at the beginning the transfer particles a r e p i n n e d on t h e s u r f a c e a n d grow progressively up to a given size, and then suddenly disappear. Simultaneously, the app e a ra nc e of l a r ge r agglomerates is observed at other places along the friction track. The same process probably occurs in the case of polyethylene, but owing to its smaller refractive index, the discrimination of the particles becomes more difficult with this type of optical system.

particle density N , normal load, adhesive interactions, mechanical properties, etc., is still out of reach. Nevertheless, the general tren d s of t h e experimentally observed variations appear to be difficult to explain without taking into account the criteria of transfer particle stability as developed in a previous paper (6). We therefore propose a simplified mechanism of particle formation based on two determining phases : establishment of t h e a c t u a l area of co n tact, a n d t h e effectiveness of transfer. Considering the initial situation, i t is possible to conceive t h a t normal load does indeed affect the real area of contact sr , and even, since we a r e in a flat-on-flat contact, the number of spots where actual contact occurs: Nr

.

Nr = k FN / H

4. DISCUSSION

4.1.New hypothesis Previous results, and in particular the fact t h a t t he particle distribution of Population I is totally independent of experimental conditions a n d t h a t their number may vary in contradiction with trends normally expected, lead us to assume t h a t Population I consists of elementary particles having their own conditions of stability. They m u s t be considered as elementary particles pinned to the surface over a given period of time, after which they become mobile a n d lead either t o the formation of wear particles or to the formation of larger transfer particles by a n agglomeration process. In order to demonstrate the validity of this hypothesis, a n a t t e m p t was made to experimentally visualise particle mobility. The theoretically reasons accounting for the decrease in particle density with increasing normal load were then explored. 4.2. Theoretical approach

Despite numerous previous investigations in t hi s field, a general formulation of the relationship between

A t each point of actual contact, adhesive interactions take place, but not all of them a r e necessarily broken cohesively. T h e probability p for such a n event to occur (and hence lead to the formation of a transfer particle) logically increases with t h e strength of adhesive interactions . Obviously, the number of actual contact spots can only be a n increasing function of normal load. For the number of transfer particles to decrease with increasing normal load, it is necessary to assume that it is the probability of transfer particle formation or particle stability which may decrease. Such a possibility is offered by t h e p ressu re dependence of the various s h ear stresses applied to a transfer particle. Indeed, referring to Briscoe e t a1 (ll), th e shear resistance of a polymer may be expressed in the form: t

= to (1 + ) ' l a

or T: = toexp.aP

Hence, if we assume that the probability of transfer is controlled by the aforementioned ratio ti /ts which then becomes:

113

and its differential with pressure:

-

d(ti /t,H dP = tio /tso (ai as) / (1 + as P)2

From this expression we see t h a t the probability of transfer may indeed decrease with increasing pressure, provided t h a t ( a i as) becomes negative. Although not assessed experimentally, it is plausible t h a t a i differs from a, for the same polymer because it concerns a different interface. More obviously ai and a, may vary from one polymer to another. In order to account for the actual slopes tlN/dFN, it is also necessary to know the relationship between FN and the pressure P actually applied to the particles. This is again very difficult. Even in the simplest case, i.e., when transfer-particle growth is sufficient to ensure full LCC on the transfer particles, and hence the pressure normally only controlled by the hardness of the softer substrate, the situation is more complex and still depends of the particle size distribution. I n all other cases, the normal pressure applied to the particles remains a function of the applied normal load.

-

5.CONCLUSION

As in the case of graphite, when rubbing a g a i n s t thoroughly polished s t e e l , polyethylene was shown to form discrete transfer particles. Quantification of these particles by image analysis places this work i n t h e p e r s p e c t i v e of o u r g e n e r a l investigation of p a r a m e t e r s controlling discontinuous transfer-film formation. As expected, the grafting of small amounts of a c r y l i c a c i d , allowed t h e a d h e s i v e interactions of polyethylene to be modified, and actually influences the corresponding frictional and transfer characteristics. With increasing rubbing t i m e , t h e frictional forces were shown to rapidly reach

limiting values which, in agreement with Coulomb's law, a r e directly proportional to t h e n o r m a l load. Although t h e r e a l coefficient of friction t h u s defined is linearly related to the corresponding work of adhesion W a , no direct proportionality exists. A s expected, t h e c h a r a c t e r i s t i c s of transfer actually reflect t h e influence of rubbing time, normal load, adhesive interactions, etc. However, their evolution may appear complex. Thus, while the total area fraction displays linear variations with normal load, the direct proportionality is lost. Moreover, t h e r a n k i n g of t h e corresponding values remains a function of both the adhesive interactions a n d the normal load. Similarly, the particle density was shown to be a linear function of normal load, displaying either positive or negative slopes, themselves linearly related to the work of adhesion. The previous results were shown to be in agreement with o u r analysis of transfer particle stability, and even to complete them. For instance, they confirm the dual control of transfer particle stability by the ratio: t i /tS, i.e., the ratio of the shear stresses applied respectively at the bottom a n d top of the particles. Alone, the pressure dependence of the above ratio of polymer shear stresses is able to account for the decrease in particle density with increasing normal load, observed for some polymers. These criteria were also shown to apply to a population of small particles revealed by image analysis. Therefore, i t becomes possible to extend their application not only to the control of particle growth, but also to the control of particle mobility. While in this work, this mobility generated a population of larger agglomerated secondary particles, the same considerations may apply to particles which escape from the contact a n d t h u s account for the wear rate. Similarly, the a p p a r e n t effect of iron contamination on transfer phenomena may be of general significance.

114

REFERENCES (1) M . Godet a n d Y . B e r t h i e r , “Continuity on dry friction: a n Osborne Reynolds approach”, 1 3 t h Leeds-Lyon Symposium on tribology, “Fluid film lubrication, Osborne Reynolds Centuary”, edited by Dowson, D., Taylor, C. M., Godet, M. and Berthe, D., pp 653-661 (1987). Y . B e r t h i e r , M . Godet a n d (2) M . BrendlB, “Velocity accommodation in friction”, Tribology Trans. 32 (4) pp 490-496 (1989). (3) M. BrendlB, J. Fatkin, P. Turgis and R. Gilmore, “Mechanisms of Graphite Transfer on Steel as Studied by Image Analysis”, Tribology transactions 33 (4) pp 471-480, (1990). (4) M. BrendlB, P. Turgis, “Friction and T r a n s f e r Behaviour in Discontinuous T r a n s f e r Films”, 1 8 t h Leeds Lyon Symposium on Tribology ‘‘Wear Particles From the Cradle to the Grave” Ed. D. Dowson e t al. Elsevier pp 313-321, (1992). (5) M . BrendlC, P. Turgis, R. Gilmore “Modelling of Discontinuous Transfer Films”, D. Dowson e t al., Ed 1993, Elsevier Science Publishers B.V pp 649-659. (6) M. Brendlb, P. T u r g i s a n d S. Lamouri, “A g e n e r a l approach t o discontinuous transfer films-The respective role of mechanical a n d physico-chemical interactions”, 1994 ASME/STLE Tribology Conference, October 16-19, 1994, Lahaina, HAWAI. (to be published in Tribology Trans.). (7) H. L. Cox, “The elasticity a n d s t r e n g t h of paper a n d o t h e r fibrous materials”, Brit. J. App. Phys., 3, 1952, pp. 72-79. M. Nardin and J . Schultz, (8) “Re1a tion ship between the fibre -matrix adhesion and the interfacial shear strength in polymer based composites”, Composite Interfaces 1 (2), 177-192, 1993. (9) M . Brendlb, P. Starck, B. Monasse, J.M. Haudin, “Influence of molecular weight a n d crystallinity of HDPE upon initial friction and transfer behaviour”, ASLE Transactions, 27 (4), pp. 389-397 (1984).

L . La v i e 11e , “ Po 1y m e r - po 1y m e r (10) friction: relation to adhesion”, Wear, 151 pp 63-75, (1991). (11) B. J. Briscoe and A. C. Smith, “The interfacial shear strength of molybdenum disulfide and graphite films”, ASLE Trans. 25 (3) pp 349-354.

ACKNOWLEDGMENTS The authors wish to express their thanks to the Ministry of Education of Algeria for the grant made available to Dr. Lamouri. The authors are indebted to Lonza-Alusuisse a n d especially Dr. W. Hotz for having allowed them to perform the image analysis.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

115

Elusive 'Third Bodies' L. Rozeanua and F.E. Kennedyb a Department of Materials Engineering, Technion - Israel Institute of Technology, Haifa, Israel

b Thayer School of Engineering, Dartmouth College

Hanover,NH USA The Third Body Concept is a very useful tool for simplifyingand unifying the identification of tribelogical system. In its initial formulation by Godet, it was implied that the system could be defined like a hydrodynamic system, with the number and behavior of the constituents being initially specified. Then the interfacial interactionsare identified to allow velocity accommodation within the system. In a variety of sliding systems, though. the friction behavior of the system changes in time in a way that is hard to predict with normal third body models. This paper will discuss several cases in which either the interfacial conditions or the behavior of the first or third bodies varies during sliding. Those changes in behavior could be included in an expanded third body concept which includes various velocity accomodation mechanisms within the model.

1. INTRODUCTION The concept of 'Third Bodies' in tribology was introduced by M. Godet [1.21 in order to define physically the components of a friction system and the mechanical interaction between them. The thirdbody concept was inspired by fluid film lubrication theory, so when applying the concept to friction systems it is natural to consider that the three bodies and the interfaces between them will behave in accordance with traditional lubrication assumptions. If those simplifying assumptions are invoked, however, it may be impossible to accommodate changes in velocity between sliding surfaces, as was pointed out clearly by Berthier, et al, several years ago [3]. In this paper, several cases will be presented which demonstrate the necessity of including various velocity accommodation mechanisms in any thirdbody model of a sliding system.

2.

INTERFACIAL SLIP

In classical fluid film lubrication, it is almost always assumed that there is no slip at the interface between a solid (first body) and the fluid (third body), and one is tempted to apply the same no-slip condition in three-body contacts. That assumption can be fallacious,however, whether the third body is a liquid lubricant or solid particles.

This interfacial slip can be included in a three-body contact model as long as an interfacial screen is included between the first and third bodies and velocity changes are allowed to occur across the screen.

1.1.

Boundary Slippage of Liquid Lubricants

The shear profile in a liquid lubricant film is assumed to satisfy the boundary condition that at the wall the velocity of the fluid is equal to that of the wall. This presumes perfect 'wetting' of the wall by the fluid. In the case of mineral oils, this assumption has been challenged by tests which have shown that mineral oils can develop boundary layers on solid surfaces that enable the liquid to slip with respect to the surface [4]. This can be demonstrated by the following experiment: If a metallic plate is immersed in mineral oil and then taken out and drained of oil such that only a b o u n w layer is left. a drop of the same oil put on the surface would not wet the surface. In essence, the normally liophilic oil would develop an autophobic boundary layer, which is shown schematically in Figure l(c). This phenomenon, and its application to lubrication, has been studied from various points of view at INSA [a and Technion [6,7].A demonstration of the effect of an autophobic boundary layer in mineral oil is shown in Figure 2. It can be seen that

116 the resulting oil film is quite different when the boundary layer has been scraped off. One possible explanation for the autophcbic boundary layer phenomenon is as follows: When the polar molecules of the lubricant are adsorbed on a clean surface, they liberate a certain amount of energy (heat of adsorption) which could be designated as Lad. This amount of energy can be responsible for a temperature decrease DT = Lad / Cp, where Cp is the specific heat. This temperature decrease can be sufficient to stiffen the molecules engaged in the adsorption process, causing a solidlike region near the wall. This boundary layer is composed of closely-packed, ordered molecules which will not move easily unless they get an amount of energy higher than Lad. Beyond the boundary layer will be non-adsorbed molecules possessing their original morphology and energy. The forces which would normally attract those fluid molecules decay exponentially away from the wall and are effectively shielded by the adsorbed layer. A number of experiments, some of which were reported earlier [6,7] have shown that the bulk of a lubricating oil film can exhibit different behavior once the boundary layer has formed. As can be seen in Figure 2, the oil film may have a different appearance. Even more importantly, the hydrodynamic pressure in the oil film may decrease significantly [7]. The reason for these effects has been shown to be a change in the velocity distribution in the film [8]. The bulk of the fluid may slip over the adsorbed layer because the interfacial bonds between the energetic lubricant molecules in the oil film and the adsorbed molecules in the boundary layer are too weak. Thus, the no-slip boundary condition may no longer hold at the interface between oil film and boundary layer. If the lubricating oil film is disrupted and oil droplets are produced, those droplets would tend to become spherical in shape in order to decrease their surface energy by reducing their surface area. Those droplets could fail to wet the boundary layer, as in Figure l(c), and this would also lead to slip between the oil drop and the boundary layer. Further evidence for the autophoby of boundary layers can be found by removing the boundary layer, either by mechanical means, as in

Figure 2, or by thermal or chemical action. In actual bearing operation, heating the bearing can cause desorption or melting of the boundary layer, wear particles could scrape off the adsorbed layer, or chemical degradation of the lubricant film could produce surface active agents which could change the behavior of the boundary layer. Experiments have shown that once the boundary layer is removed, boundary slippage no longer occurs, and higher hydrodynamic pressures result in the oil film [71. Kaneta and others have observed boundary slip in elastohydrodynamicfilms [9]. As was the case with the hydrodynamic films described above, the consequences of boundary slip include a modified velocity profile in the film, the pressure distribution, and the film thickness. In the EHL case, the slip occurs when the lubricating oil exhibits solidlike behavior. Slip was found to occur at or near the wall when the film thickness was small, but the slip region moved away from the surface when the film thickness increased. The boundary slip in EHL films has been attributed to the limiting shear strength of the lubricant [lo]. That explanation does not appear to apply to the hydrodynamic films described above. The above comments do not challenge the 'third-body concept' as long as one includes a 'screen' at the interface between lubricant film (third body) and solid surface (first body). The screen would allow velocity changes to occur between the two bodies, as described by Berthier, et al[3]. The modified velocity profiles in the lubricating film could be analyzed using a slippage parameter to account for the boundary slippage effect [8]. The complication is that the velocity accommodation behavior of the screen could change in time, as the boundary layer forms and/or is removed.

1.2.

Boundary Slippage of Solid Particles

There has been considerable interest in recent years in lubrication by dry particles 1111. Experimental studies have shown that dry particle lubrication can exhibit many of the same chmcteristics as fluid film lubrication. Triboparticulate films can, for example, show a pressure profile

117

which is quite similar to hydrodynamic film pressures [ 121. The solid particle films are even more likely than fluid films to exhibit slippage at or near the boundaries with the solid first bodies [ 121. In the case of solid films, in addition to its effects on pressure distribution and velocity profiles, the boundary slippage can also give rise to wear of the fmt bodies. It has been hypothesized that boundary slip in solid films may be due to limiting shear stress, somewhat akin to that for EHL films [12], although some recent successes in modelling powder lubrication has been based instead on collisional characteristicsof particles and their intemctions at the boundaries [ 131.

2.

MULTI-PHASE THIRD BODIES.

The Third Body Concept is meant to improve the identificationof tribological systems. It implies that each body is a well-defined entity, generally of a single phase. The friction process can produce new phases, such as wear debris, which become independent bodies and behave according to their own rules. In general, this is a one-way sequence of events, and the overall system behavior can be considered by an outside observer to be a chronological sign of the system history. It is inconceivable for the process to spontaneously reverse itself, such as by relocation of the wear particles into their original sites on the worn body. Similarly, the deterioration or contamination of a lubricant film is also generally an irreversible process. When the third body is a liquid lubricant. its viscosity is easily determined and can be used in predicting performance. When the lubricant is a twophase system, though, as is the case with multi-grade lubricants, the flow behavior is not as easy to predict and the rule of monotonous or one-way change or evolution may no longer be valid. The popular multigrade lubricants are dispersions of long chain polymers in a low viscosity mineral oil. Their flow behavior at low rates of shear is similar to that of a mono-grade lubricant, either synthetic or mineral oil. At high rates of shear, however, the two phases can separate, with each one behaving in its own way [14]. One consequenceof this independentbehavior of each phase is the spatial orientation of the deployed long chain molecules responsible for the decrease of

viscosity with increases in the rate of shear [15]. There are situations in which the two-phase lubricant deviates from linear or predictable behavior, and one such case is shown in Figure 3. Here a multigrade lubricant separates two flat circular plates or radius R which are in oscillatory motion. It is well known [ 161 that the force on the plates in a Newtonian squeeze-film,such as the one shown in Fig. 3. is given by:

Therefore, the absolute value of the force f should be the same at a given film thickness h, as long as the viscosity p and the velocity v are the same, no matter what the sign of the velocity. If the plates are vibrating very rapidly, however, the fluid will be subjected to a very high shear rate at small film thicknesses. For approaching plates, the fluid will be squeezed out at a high rate, starting with the phase which can respond fastest, i.e., the dispersing medium. The fluid left behind will be a dispersion with a continuously increasing concentration of the long-chain dispersed phase, and the effective viscosity of the fluid will continuously increase (non-linearly). Eventually the lubricant film may be only a wet deposit of dispersed phase and will have a very high viscosity. When the velocity reverses and the plates begin to separate, the fluid will be drawn back in, with the low viscosity phase being the first to enter the gap. Thus the effecive viscosity and the force required will be lower at the same point when the plates are being separated than when the plates were coming together. Because of this, there is no longer a unique relationship between fluid behavior and plate position (or chronological time). One must also consider the history of the multi-phase fluid deformation in order to determine the fluid (third body) behavior at a given point in time. To some extent this is similar to plasticity theory, in which the deformation history, as well as the current strain state, must be used to determine the stress state in a plastically deformed solid. When the multi-phase lubricant has been squeezed out, the boundary layer which remains has a high composition of long-chain molecules. This layer offers better boundary lubricant protection than a boundary layer composed only of mineral oil hydro-

118

carbon molecules. That this is so can be seen in Figure 4. which shows electrical resistance contact measurements made in an oscillatory squeeze film situation. Three different lubricants, two mineral oils of different viscosity (SAE 10 and S A E 30) and a multi-grade lubricant (SAE 1OW-30)were used between the oscillating bearing pad and the rotating shaft. The results show that there was less metal-tometal contact with the multi-grade lubricant than with either of the mono-grade oils. In systems such as gears or rolling bearings, an analogous rapid 'squeeze-outldraw-in'flow is required, with the lubricant being squeezed out at the front of the contact and drawn in at the rear (Figure 5). In this case the lower viscosity dispersant phase gets squeezed out fust and later is drawn in first. The changes in viscosity follow the pattern described above, increasing steadily both for the squeezed-out fraction and for that left behind. The zone of minimum film thickness is one in which the lubricant film is a carpet with a high concentration long-chain polymer molecules. Eventually the lubricant emerging from the contact has recovered its original constituentsand for all practical purposes is the same multi-grade lubricant. Treated as a 'third-body', the behavior of the multi-grade lubricant appears unusual because, although its overall composition and steadly flow properties remain unchanged, during the localized squeeze-out / drawin action it demonstrates some 'elusive' behavior. As a result of this behavior, the total frictional work required in the rolling or rollinghliding contact is reduced. This is demonstrated in Figure 6, which shows frictional torque measurements in a viscometer that had been modified to test lubricated gear teeth [17]. There is a considerablereduction in frictional torque by changing from a mono-grade lubricant (SAE 30) to a multi-grade ( S A E 10W-30),even though the shear rates (up to 40,000/s) were not really high. It might be noted that there was a considerable increase in torque for the S A E 30 oil when the rate of shear increased, a finding which should be further investigated. It is believed that non-linear or discontinuous behavior can also occur when a solid third body is composed of two different phases or even particles of two different sizes, but such systems have

not yet been tested.

3.

THE MECHANICALLY AFFECTED LAYER.

It is well known that in many sliding systems much of the frictional energy is dissipated through plastic deformation of the near-surface regions in the two first bodies [181. When sliding tractions are applied to the surface at high velocities, the mechanically affected layer (MAL) experiences high rates of shear and heat is generated therein. This shear deformation could be considered to be a velocity accommodation mechanism. The mechanical behavior at a point within the MAL depends on its temperature and its deformation history, but it is generally not possible to draw a map of the temperature and shear rate distribution which could help in understanding the performance of the system. The frictional performance of the system is determined by the surface temperature, which is related to what is happening at the frictional interface, and by the near-surface temperature gradients. which determine the properties of the materials in the high shear region. With the aid of inhared thermography or thin film thermocouples, one may be able to get measurements of surface temperatures in sliding contacts [ 191, and the background temperature (of the non-contacting surfaces)can be measured without difficulty. However, near-surface temperature gradients cannot be determined accurately, even with the use of subsurface thermocouples. In addition, since the background temperature depends on cooling and attachment conditions unrelated to friction,the temperature gradient cannot be determined with knowledge of only the surface and background temperatures.

3.1.

The Two Temperature Gradients Model.

In order to solve this dilemma, it was necessary to divide the sliding component into two regions (Figure 7). an upper, mechanically-affected layer (MAL) and a lower, mechanically-passive layer (MPL). The most important feature of this concept is that each layer can have its own tempera-

I19

ture gradient, a high gradient in the MAL and a low gradient in the MPL [20]. The upper temperature gradient is anchored to the frictionally controlled surface temperature Ts,and the lower one is anchored to the externally controlled background temperature Te. It was recently shown that the two temperature gradients are related to the concepts of small scale and large scale heat flow restrictions [21]. By invoking these concepts, the gradient in the MAL results in a local temperature rise which is related to frictional conditions within the real area of contact, and the gradient in the MPL is related to the overall thermal conductivity of the body and this results in a nominal surface temperature risc. In the two-temperature gradient concept, all shear deformation (or velocity accommodation) is assumed to occur within the MAL [20]. The partition plane which separates MAL from MPL is assumed to be that point where the shear velocity is zero and where the temperature, Tss, is the lower temperature for the high Grad.T in the MAL and upper limit for the low Grad.T in the MPL. The location of the partition will shift upward or downward until the two gradients cross. Since each of the temperature gradients satisfiesFourier's law for heat conduction within its region, it is possible to calculate both gradients using measured data and available temperature analysis expressions, e.g.. [21]. Therefore, the thickness of the MAL can be determined. This thickness and the temperature gradient within the MAL determine the variation of rate of shear with depth. In turn, the shear rate vs. depth distribution controls the performance of the rribosystem,including friction force, wear particle generation, and surface appearance. Once the map of the MAL is known it is easy to understand why a change of a particular system variable can produce a given performance change. For example, it is possible to obtain improved performance by lowering the background temperature, causing a decrease in the thickness of the MAL. It can be shown that thermal steady state can be maintained only if a certain relationship exists between the MAL parameters [20]. Arbitrary change of a single parameter, such as surface temperature, requires readjustment of the other parameters, such as shear rate or MAL thickness. Material selection and change of thermal conditions can affect friction performance, although the effect on wear may not be as easy to predict.

The MAL. is part of a first body, but considerable velocity accommodation occurs within it through shear deformation. That velocity accommodation must be considered carefully if an accurate third-body model of the sliding system is to be developed. One possible way to accomplish this would be to consider the MAL as a new third body, with its own behavioral rules, different From those of the first body from which it evolved. An alternative would be to expand the consideration of velocity accommodation mechanisms in the top region (the MAL) of the first body to include the large shear deformations which occur in that region.

3.2.

Low-Friction Coatings.

By analysis of the mechanically affected layer, it can be shown that low friction is achieved if the shear gradients are steep and the MAL is thin. The best friction performance is obtained when shear is confined to a very thin surface layer in a sliding solid. Material beneath the MAL (in the mechanically passive layer) is essentially not involved in the friction process. One way to achieve thermal steady state with the thinnest possible MAL would be to increase the sliding speed [20]. For example, if the sliding speed is of the order of 10 m/s, the h4AL may be less than 10 pm thick. Such a thin mechanically affected layer would reach a very high temperature and the material within it would be softened to provide a lower resistance to shear. However, it is seldom either advisable or possible to increase the sliding speed sufficiently to reduce the thickness of the MAL to such low values. In general, the MAL thickness is the result of a complex process by which the temperature and shear rate gradients are determined by external operating variables and the properties of the contacting materials. Therefore, the MAL thickness is a dependent variable; it cannot be changed arbitrarily. There is a way to 'cheat' the system: coat the friction part ('first body') with a very thin layer of a soft material (Figure 8). If a friction force is applied to the surface, the resulting shear deformation will be confined within the soft surface layer because of the strength discontinuity. Velocity accommodation will therefore occur within the soft coating, as will frictional heat generation. The friction part will then become a mechanically passive layer for the very soft

120 coating. which becomes a 'clone MAL'. By means of such a soft coating, a very thin MAL (on the order of a few microns) can be obtained at moderate sliding speeds. By a trial and error process, the benefits of using thin soft coating were discovered long ago, well before the two temperature gradients theory was developed. In many hydrodynamic bearings the regular bearing material is covered with a thin layer of a softer material like lead, and sometimes with an even thinner overlay of soft indium. Such coatings help achieve low friction during startup or other conditions in which solidholid contact can occur. Thin soft overlays mimic the performance of natural mechanically affected layers; by their features and performance they are real 'third bodies', and could be modelled as such. The shear behavior of the coating would have to be taken into account in a three-body model of the sliding contact.

4.

CONCLUSION

Friction is a complex subject. Various forms of surface interactions are encountered,along with various contacting materials, various demands, and unlimited types of enigmatic failures. The vast amount of research in the field of tribology excels in its diversity. In any issue of the Journal of Tribology, for example, few of the papers will deal with the same topic or use the same approach. The Third Body concept makes a gallant attempt to offer a rational guide for planning and executing tribology research and modelling. It is evident that not all tribology problems are amenable to being modelled by the same velocity accommodation approach. It must be recognized, however, that friction implies mechanical intraction at interfaces, and at least one way one can find common features is with the 'Third Body' line of reasoning. The friction systems discussed in this paper show that the third body can undergo shorter or longer range changes by which it is no longer valid to assume continuity of interaction along a monotonous path. It is possible to extend the third body approach to include second order effects; this would enable beaer correspondence between expectation and performance in cases such as those discussed in

this paper. For example, in case 3 the friction interaction is controlled by events taking place below the surface of the first bodies. If either the mechanically affected layer was allowed to become a third body, or velocity accommodation mechanisms within the first bodies were expanded to include large shear deformations, the third body approach could model the system completely. It is particularly important to introduce the number of constituents and velocity accommodation mechanisms within and between them as primary identification features of friction systems, and to allow the rules governing the behavior of those features to change during the tribological operation. In that way, even the most apparently 'elusive' systems could easily be modelled by third body methodology.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15.

M. Godet, Wear, 100 (1984). 437. M. Godet, Wear, 136 (1990), 29. Y. Berthier, M. Godet and M. Brendle,, Tribology Transactions,32 (1989), 490. E.G. Shafrin and W.A. Zisman, J. of Phys. Chem., 64 (1960), 519. G. Dalmaz, private communication, 1973. L. Rozeanu and L. Snarsky, Wear, 43 (1977), 117. L. Rozeanu and L. Snarsky, J. Lubrication Technology, 100 (1978). 167. L. Rozeanu and N. Tipei, Wear, 64 (1980), 245. M. Kaneta, H. Nishikawa and K. Kameishi, J. of Tribology, 112 (1990). 447. S. Bair and W.O. Winer, J. of Tribology, 114 (1992). 1. H. Heshmat, M. Godet and Y.Berthier, Lubrication Engineering, 5 1 (1995). 557. H. Heshmat, Lubrication Engineering, 48 (1992), 373. K.T. McTeague and M.M. Khonsari, J. of Tribology, in press, 1996. L. Rozeanu and M. Maayan, in Interface Dynamics, Proc.of 14th Leeds-Lyon Symposium on Tribology, Lyon, France, Elsevier, 1988, p. 177. L. Rozeanu. M. Maayan and F.E. Kennedy, Tribology Tms., 34 (1991), 389.

121

16.

17.

18.

D. Fuller, Theory and Practice of Lubrication for Engineers, 2nd ed., J. Wiley & Sons, New York, 1984, p.177. L. Rozeanu, M. Maayan, and FE. Kennedy, Roc. 5th European Congress on Tribology, Espoo, Finland, 1989, v. 4, p. 126. F.E. Kennedy, J. Lubrication Technology, 104 (1982), 582.

19.

20. 21.

F.E. Kennedy, in Friction, Lubrication and Wear Technology, Metals Handbook, v. 4, 10th ed., PJ. Blau, ed.. ASM International, 1992, p. 438. L. Rozeanu and D. Pnueli, J. Lubrication Technology, lo0 (1978), 479. X. Tian and FE. Kennedy, J. of Tribology, 115 (1993),411.

FIGURES

~~

~

~

_

_

_

Figure 1. Physical meaning of autophoby: a) Liophilic; b) Liophobic; c) Autophobic.

a.

b.

C.

Figure 2. a). Experimental partial sliding bearing with means to scrape the boundary layer before shaft enters oil bath. b). Oil film before scraping. c). Oil film after scraping.

122

I

f

Figure 3. Squeeze film between two flat circular plates. V

Lubricant

-

-

% Current flow

I

SAE 10 8.5 SAE 30 7.5 MGL (10/30) 6.1 (Normalized t o 100% for direct metal-metal contact).

-

Figure 4. Experimental setup and elecmcal contact measurements between friction surfaces under pulsating loading for multi-grade and mono-grade lubricants.

1

REAR

WOW M ORAW-IN

EHL

OIL

WORK

snsu

WORK'TO SOUEEZEOUT=

Figure 5. Squeeze film situation in a rolling contact.

123

----

I

MONO GRPSE LUBRICANT , , MULTI GRAOE LUBRICANT/ LUBRICANT

0

/

/

60°C I

I

I

20

I

30

I

40

Figure 6. Variation of friction torque (normalizedaverage) for multi-grade and mono-grade lubricants in a spur gear system.

I Figure 7. The two-temperaturegradients model for mechanically affected layer (MAL) and mechanically passive layer (MPL).

Te

Figure 8. A very soft coating applied on a friction surface performs like a MAL with imposed thickness.

This Page Intentionally Left Blank

SESSION IV THIRD BODIES IN E.H.L. Chairman :

Emeritus Professor Duncan Dowson

Paper IV (i)

Direct Observation of Particle Entry and Deformation in a Rolling E.H.D. Contact

Paper IV (ii)

The Entrainment of Solid Particles into Rolling Elastohydrodynamic Contacts

Paper IV (iii)

Behaviour of PTFE Suspensions in RolIinglSliding Contacts

Paper IV (iv)

Third Bodies in Wet Friction Couples-in-situMeasurement with Electrical Impedance

Paper IV (v)

A Ball-in-Socket Apparatus for the Test of Hip Joint Prosthesis. Influence of the Third Body on the Friction Behaviour

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

127

Direct observation of particle entry and deformation in a rolling EHD contact 1

2

1

1

P.M.E. Cann ,J.C.Hamer ,R.S. Sayles , H.A. Spikes & E. Ioannides

I .3

.

I

Tribology Section, Department of Mechanical Engineering, Imperial College, London SW7 2BX PCS Ltd, Imperial College, London SW7 2BX SKF ERC, Neiuwegein. The Netherlands

’

In the last few years there has been increasing awareness of the problem of debris entrainment, and subsequent damage, in rolling element bearing contacts. Such debris is in the form of wear particles or solid contaminants and the ensuing plastic deformation of the steel surfaces can lead to premature fatigue failure. The problem has been studied both experimentally, through direct observation of particle entry and surface deformation, and theoretically by the modelling of dents as initiation sites for fatigue. Experimentally one of the best methods for studying such effects is by direct observation of particle behaviour in an elastohydrodynamic contact. The contact is formed by a steel ball loaded, and rolling, against a glass disc and a microscope is used to observe particle flow in and around the lubricated contact. Such work has shown qualitatively the entry of particles into the contact and the surface damage induced by their passage through the contact. This approach has also been applied in the current work, however, instead of a simple glass or chromium coated disc, a disc with a silica spacer layer is used. The advantage of this is that particle entry can be seen more clearly and the resulting dents measured. In addition, it is also possible, to infer the local pressure e.xperiencedby the particle as it passes through the contact. Images are shown for different types of ductile particle passing through a rolling point contact. The local pressure experienced by each particle is deduced and profiles of the surface dents caused by their passage are plotted.

1. INTRODUCTION

Whilst considerable advances have been made in the design and manufacture of rolling bearings premature failure still occurs. This can be due to a number of reasons; poor lubrication, misalignment, or operation outside design limits. There is, however, a significant contribution from the damage caused by foreign contaminants present within the lubricant and this can result in failure, or excessive wear, of both balls and raceways (1)(2). Attention has therefore turned to the problem of surface initiated failure due to damage caused by the passage of debris through the bearing contact. Such debris is in the form of generated wear particles; both metallic and ceramic. It is classified as ductile or friable depending upon the nature of the material. Particles entrained into the rolling contact are subjected to very high loads

and this can cause indentation (3) of ball andor raceway. Such damage generates a high local stress concentration in subsequent overrolling that can initiate spa11 formation and thus affect bearing life (1). There have been two main approaches to the study of this problem; firstly through experimental investigation of the behaviour of particles in rolling contacts and quantification of the ensuing damage. In most experimental work, a model bearing contact, formed by a steel ball loaded, and rolling, against a glass disc, has been used (4)(5). The passage of particles, suspended in lubricant, can thus be observed through the contact. In most work ‘model’ particles of different materials with known size and hardness properties are studied. These experimental studies ( 5 ) have confirmed that relatively large particles, many times the size of the film thickness,

128

can enter EHD contacts. They have also shown that the behaviour of ductile and friable particles is markedly different (6). The current paper concentrates on ductile behaviour and only these particles will be considered here. Ductile particles plastically deform in the inlet region and pass into the contact as platelets (6). As they do so the contacting surfaces conform around the particle. Whether a particle causes damage to the surface is determined by its size, shape and relative hardness. If yield of the surfaces does occur then the resulting dents are rounded, with a smooth surface (6). The second approach has been to model debris damage to hard bearing surfaces by softer particles as an extrusion problem (7). From this it is possible to predict the onset of plastic deformation and the frnal dent shape of the counterface. These results have been compared to those from experimental studies (6) and good agreement found for the depth of the dents. The analysis does, however, underestimate the dent width found experimentally (6). If the underside of the glass disc is coated with a semi-reflective chromium coating it is also possible to measure the perturbation of EHD films by the passage of dents through a rolling contact. This technique has been used to map rough surface EHD film formation (8). Measurements (9)(10) for surfaces with dents have shown that a significant modification of the film shape occurs as the dent passes through the contact. In particular there is a local reduction in film thickness at the leading edge; this is thought to be due to a local loss of pressure build up in the inlet region (10). The current paper has applied a new technique, based on classical optical interferometry, to observe particle entry into rolling EHD contacts. The chromium coated disc used in the earlier work is replaced with a silica layer/chromium disc. This approach was first exploited by Westlake (11) and further developed by Johnston et al (12). The presence of the silica layer augments thin EHD films formed in the contact making them visible as 3rd or 4th order interference colours. The image can now be viewed in the normal way by a CCD video camera and images of the contact captured for subsequent analysis. From this analysis, based on hue quantification, film thickness maps, down to 10 nm, can be generated from the entire contact. The technique is detailed in reference 13. The aim of this study was, therefore, to develop a technique which would give improved visualisation

of particle capture and behaviour in EHD contacts. In addition, to map both the ensuing dents and the EHD film perturbation due to their passage through a rolling contact. The application of the spacer layer technique is described in section 2 and the particle imaging and dent analysis in section 3. 2. EXPERIMENTAL A modified optical interferometry technique was used to observe particle behaviour in a rolling contact. A simplified diagram of the experimental design is shown in Figure 1. The contact is formed by a steel ball rolling against a glass disc. the underside of the disc is coated with a chromium layer overlaid with silica. A microscope coupled to a CCD video camera is positioned directly above the contact and this is used to observe particle behaviour within the contact. A shutter speed of 0.0005 seconds is used. The camera is coupled to a capture board so that images from the contact can be taken and stored for subsequent analysis. Examples of these are shown in Figures 3-5. Earlier work (13) has established a ‘colour’hilm thickness calibration and this has been used in this paper to map EHD film thickness in the rolling contact. The effect of dents on local film thickness can thus be determined.

I microscope ’$ Glass , disc

5=?

chromium/ silica layer

0

steel ball

particles entering contact

Figure 1 Visualisation of particles in an EHL contact 2.1 Test conditions

The test conditions are summarised below in Table 1. A poly-alpha-olefm oil (viscosity 23.8 CPat 25°C) was used as a canier fluid for all tests. The rolling speed was kept as low as possible to ensure

129

sharp images of the particles passing through the contact. The seocnd advantage of this is that the particles are more likely to cause damage in the thin EHD film regime (6). Table 1 EHD test conditions

I

I28N Max.Hertz pressure I 0.47 GPa EHD film thickness I 4 0 nm Rolling meed I 0.005 m/s Particle conc. I 1%w/w

Load

I

I

The properties of the EHD test specimens are given in Table 2. Table 2 EHD test specimens

I Propem Diameter Young’s modulus

I Ball

1 Disc

I 25.4 mm I 100 mm I 210 GPa I 75 GPa

I

ratio The debris particles (supplied by Goodfellow Metals Ltd) were chosen to have very different hardness values. These are listed below in Table 3.

applied and the microscope focused on the contact area. The experimental procedure was as follows: (i) the rig was set rolling at the desired speed. (ii) the test lubricant was applied to the disc (iii) images taken of new debris as it enters the contact.

Images were also taken of the debris in a static contact. In a later series of tests dent formation was examined. In these experiments, the ball and disc were run for an extended period to ensure damage had occurred. The disc and ball were then dismantled and cleaned thoroughly to remove the particles. The components were then reassembled and experiments carried out to observe, and quantify, the debris damage. 3. RESULTS

3.1 Images captured from a rolling contact A series of images are shown below in Figures 2 to 6. These were taken of particles as they passed through the inlet and contact region. Figure 2 shows the type of image obtained for a glass disc coated with chromium. The debris appears as colourless particles and it is difficult to follow their progress through the contact.

Table 3 Properties of debris particles Particle Pure iron Tungsten

I

Hardness

I 70Hv

I 500Hv

The particles were sieved before use to give a restricted size range of 30-60 pm diameter. This is a typical diameter range for wear particles found in practice (6). 2.2 Experimental procedure The debris was suspended in the base oil at l%w/w concentration. Prior to testing, a new ball in and the glass disc were and then acetone, ah dried and assembled. The load was then

of iron particles passing through a rolling contact interferometry.

using

conventional

optical

Figures 3 to 6 show images taken using a silica spacer layer. The green colom in the centre of the contact is due to the silica spacer layer which is 450 nm thick. fieinlet is to the right of the picture.

130 Figure 3 shows a series of images of an iron particle passing through the contact. In 3a the particle is just entering the inlet region. As it approaches the contact its colour changes from grey to green and finally to dark blue. Its width also changes from 65 pm, when first observed, to 105 pm in the contact. In Figure 3c the contact is heavily distorted by the particle. A second particle is also seen at the top of the picture; it does not enter the contact but still appears trapped by the rolling surfaces. It colour also changes as it approaches the contact. As it passes out of the contact the particle reverts to green and then colourless. Similar experiments were performed with tungsten particles. Figure 4 is an image of a tungsten particle trapped in a static contact. The light coloured ring around the particle is oil trapped in the local pocket of deformation.

Figure 4 Tungsten particle in static contact It is also possible to observe and measure dents as they pass through the contact. Figure 5 shows three dents in the contact - these appear as yellow spots. There are also four iron particles around the contact.

(d) Particle leaving contact Figure 3 Iron particle passing through a rolling contact

Figure 5 Iron particles and dents in a rolling contact

131

3.2 Pressure aod dent measurement from images It is also possible to measure particle contact pressure and dent size from the captured images. This is described below. 3.2.1 Calibration of pressure measurement One of the observations from this work was that as the particles first moved into the contact zone they became coloured. This is due to the trapped particles becoming squashed against the glass surface and plastically deforming to produce a highly reflective surface. This was confumed by optical examination of the rolled track after the experiment. Figure 6 is a photograph of ovemlled particles surrounded by fresh ones. The deformed particles have a greater cross sectional area, typically 100-120 pm wide, and are silver in appearance. The new particles are much smaller, typically 40 - 60 p wide and dark. This is shown schematically in Figure 7. . The ‘colour ’ of the particles therefore is due to reflection of light at the particle/silica interface and thus corresponds to the silica layer thickness. With this technique therefore it is possible to see exactly where contact, and deformation, of the particles takes place.

thickness. layer. To verify this a direct colour change/pressure calibration was undertaken. To calibrate the silica coloudpressure change a steel ball of 1 mm radius was loaded statically against the silica-coated disc. The loads were chosen to give a range of maximum Hertzian contact pressures from 0.5 to 2 GPa. A series of images were taken with increasing load and the interference colour change in the centre of the contact recorded. The results were translated into percentage silica layer thickness change per GPa. The experimental result was 1.38 YO per Gpa and this was used to estimate local particle pressures.

Figure 7 Schematic diagram of particle accommodation with a spacer layer surface.

Figure 6 Photograph of overolled iron particles Further observation showed that. as the particle moves into the Hertzian region, this colour changes indicating a local decrease in the silica layer thickness. This is thought to be due to compression of the silica layer caused by the very high local pressures (see Figure 7). The change in interference colour is quantifiable and is a measure of the local pressure experienced by the particle during its passage through the contact. The pressure can thus be estimated from the relative change in silica layer

3.2.2 Particle pressure profiles The observed changes in the silica layer thickness were thus used to calculate the local pressure on the particles. Examples of the local spacer layer compression in a static contact are shown for a tungsten particle in Figure 8 (curve (ii)) from the image shown in Figure 4. The curves are plotted as displacement (instead of film thickness) across the contact. The zero level in Figures 8 and 9 is the contact surface for the smooth Hertzian condition. Thus the silica layer thickness measured in the centre of the contact is subtracted from these results. The plot therefore shows the perturbation of the silica layer in the presence of a particle. The static profile, when there is no particle present, is also given (curve

0).

132 The graph for tungsten is for a particle of 60 pm (measured in the contact). The increase in displacement close to the particle is due to the local deformation of the surfaces which accommodates the particle (see Figure 7). This is filled with oil and the height rapidly becomes too great (>250 nm) to be measured by this technique. Consequently the deformation height is not a true measurement: the width however can be estimated. The width of local deformation around the particle is 120 pm. In Figure 8 there is a (-10%) decrease in the width of the Hertzian contact for the particle case so that significant load is being supported by the tungsten. On top of the particle there is no oil present therefore the colour observed is a measure of the local silica layer thickness. This decreased by 32 nm from the static Hertzian measurement of (i). From this can be calculated the maximum pressure on the particle which is 5.4 GPa.

3 v

8

m

3

a

2ool

I 0

-100 I -300-200-100 0 100 200 300 Contact position (pm) Figure 9 Contact deformation and local spacer layer compression around iron particle (90 pm diameter) 3.2.3 Measurement of surface damage It is also possible to measure surface damage using this technique. In Figures 10 profiles of a typical dent formed by iron particles are shown. Cross-sectional profiles are plotted for the static case for both the dry and lubricated condition. Typical cross-section dimensions were 40 pm wide and 0.132 pm deep for the dry case. When lubricant was present the depth reduced to 0.108 pm. 2001

-50

-300-200-100 0

I

lubricated

I

100 200 300

Contact position (pm) Figure 8 Contact deformation and local spacer layer compression around tungsten particle (60 pm diameter), static contact. In Figure 9 a similar graph is shown for an iron particle in a static contact. This is 9Opm in diameter and the estimated maximum pressure is 3.3 GPa. The particle is much flatter suggesting that substantial deformation has taken place.

0

100 Position (pm)

50

150

Figure 10 Cross-sectional profile of dent formed by iron particle. Generally the dents formed by tungsten were deeper and naRT)wer. Although the profiles shown in Figure 11 are similar to the iron dents. In Figure 11

133 the dent profiles for two different positions (middle and edge) within the contact are shown. Both are for the static condition.

c

8

CI

-300-200-100 0

100 200 300

Contact position (pm) Figure 11 Tungsten dent profiles for different positions in the contact The profile at the edge of the contact is significantly deeper (0.110 pm) than in the middle (0.085 pm). There is also a slight width increase from 40 pm at the edge to 50 pm in the middle. 4. DISCUSSION & CONCLUSIONS 1.1 Discussion

Previous work (6) has shown how relatively large ductile particles can enter rolling contacts. The plastic extrusion of these particles and the elastic and ultimately plastic deformation of the hard rolling surfaces has been modelled numerically (7) and (8). This indentation mechanism by relatively soft particles has also been demonstrated experimentally using large (1 mm diameter) particles (8). However observation of the extrusion mechanism and measurement of the extrusion pressures has proved more difficult. Using conventional chrome layer interferometry, the absence of a film between the squashed particle and the semi-reflecting layer means no interference colour will occur at the particle disc interface. Consequently it is difficult to determine when a particle first makes contact with the disc and the subsequent passage of the particle through the contact is poorly defined.

If a spacer layer disc is used however. a sharp, bright interference pattern can be generated between the conformal squashed particle and the semi reflecting layer. This means that the progress of the particle through the contact can be closely monitored and the dimensions of the extruding particle can be accurately measured. Additionally the silica layer is compressed as the contact pressure on the particle rises. From the reduction in the spacer layer thickness and consequent change in the interference colour an estimate of the strain and therefore pressure in the spacer layer can be made. The colour change to contact pressure relationship has been calibrated using a series of small highly polished steel balls loaded against the glass disc. These of c o m e produce a Hemian pressure distribution in which the normal strain to stress relationship will differ slightly from that found under an e.xtruding particle. However the shape of the extrusion pressure distributions predicted in the theoretical models of (7) and (8) are not dissimilar to Hertz and it seems reasonable therefore that this calibration should provide a good first approximation. The measured contact pressures of 3.3 and 5.4 GPa with iron and tungsten particles respectively compare well with the contact pressures predicted in the theoretical model. Permanent indentation of the 850 Hv, 25 mm steel balls used in these experiments c o n f i i s that the maximum particle contact pressures often exceed 4 GPa. Using the spacer layer technique it was also possible to observe the passage of a dent through the contact. By observing the dent with both a dry and lubricated contact, the dent shape and reduction in film thickness at the periphery of the dent could be calculated. This information will prove valuable in improving fatigue life prediction in debris dented bearings. 4.2 Conclusions This paper has described the application of an optical interferometric technique using a spacer layer disc to the study of particle entrainment in rolling EHD contacts. The technique;

(i)greatly improves visualisation of the particle as it enters the contact. (ii) gives a direct measure of dent size and resulting film thickness perturbation.

134 “The Behaviour of Suspended Solid Particles in Rolling and Sliding Elastohydrodvnamic Contacts.”, ASLE Trans., 3 l , pp 12-2 1, ( 1987). Dwyer-Joyce, R.S., “The Effects of Lubricant Contamination on Rolling bearing Operntion.”, PhD Thesis, London University, (1992). Hamer. J.C.. Sayles, R.S. & Ioannides, E., “DeformationMechanisms and Stresses Created by 3rd Body Debris Contacts and their Egects on Rolling Bearing Fatigue.” Roc. 14th LeedsLyon Symposium on Tribology, 14, pp 201-208.

(iii) allows estimation of local particle pressures within the contact Experimental work in the future will seek to relate individual particle entrainment with local particle pressure and subsequent damage in the contact. The technique therefore provides us with a valuable tool with which to verify existing debris dent models and improve prediction of which type and size of particles will enter rolling contacts. REFERENCES

Webster, M.N., Ioannides, E. & Sayles, R.S., ”TheEfsects of Topographical Defects on the Contact Stress and Fatigue Li$e in Rolling Element Bearings.”, Proc. 12th Leeds-Lyon Symposium on Tribology, Butterworths, 12, pp 121-131. (1985). Dwyer-Joyce, R. S., Hamer, J.C., Sayles, R.S, & Ioannides, E.. “Surface damage efsects caused by debris in rolling bearing lubricants, with an emphasis on friable materials”, “Rolling element bearings towards the 21st century”. 1.Mec.E. Seminar. pp 1-8, (1990). Sayles. R.S., Hamer, J.C. & Ioannides, E., “The efsects of particulate contamination in rolling bearings - a state of the art review. ’’ Paper presented at the Institution of Mechanical Engineers’ Seminar “Aerospace Bearing Technology”, Birmingham, UK, May, 1989. Also published in the Proceedings of IMechE,. 204, pp 29-36. Sliney, H.E., “Dynamicsof Solid Lubrication as Observed by Optical Microscopv.”, ASLE Trans., 2 l , pp 109-1 17, (1978).

Wan,G.T.Y. & Spikes, H.A.,

( 1987).

Hamer, J.C., Sayles, R.S. & Ioannides, E., “Particle Deformation and Counterface Damage when Relative& SoJ Particles are Squashed between Hard Anvils.”, ASLE Trans, 32 pp 281-288. (1989). Jackson, A. & Cameron, A., “ A nInterferometric Study of EHL of Rough Surfaces.”, ASLE Trans., l9,pp 40-50, (1976). (10) Wedeven, L.D., ‘’Influenceof Debris Dent on EHD Lubrication.”, ASLE Trans., a,pp 41-52, -?

(1 977). (1 1) Wedeven, L.D. & Cusano, C.,

“ElastohvdrodynamicFilm Thickness of ArtiJcially Produced Surface Dents and Grooves.”, ASLE Trans., 22, pp 369-381, (1979).

Westlake, F.J., “AnInterferometric Study of Ultra Thin Fluid Films.” PhD Thesis London University, (1970). (1 3). ’ Johnston, G.J., Wayte, R.C. and Spikes, H.A., “The Measurement and Study of Vew Thin Lubricant Films in Concentrated Contacts.” ASLE Trans, 34, pp 187-194, (1991) Cann, P.M., Hutchinson, J. & Spikes, H.A. ( 14) “TheDevelopment of a Spacer Layer Imaging Method (SL&$ for Mapping Elastohydrodvnamic Contacts”,accepted for presentation ASMEISTLE Joint Conference Oct.(1 995).

( 12)

The Third Body Concept / D. Dowson et al. (Editors) (0 1996 Elsevier Science B.V. All rights reserved.

135

The Entrainment o f Solid Particles into Rolling Elastohydrodynamic Contacts R S Dyer-Joyce and J Heymer

Department of Mechanical and Process Engineering, University of Shcflield, Mappin Street, Sheffield, S1 3JD, United Kingdom ABSTRACT

The entry of lubricant borne solid particles into machine element contacts is important, both for prediction of three body abrasive wear, and for an understanding of the behaviour of solid lubricant additives. This paper describes a quantitative study of particle entrainment into a rolling elastohydrodynamic contact. The level of surface indentation is used as an indication of the number of particles entrained into the contact. It is shown that over the range of test conditions considcred; concentrations of particles in the contact can be many times higher than those in the bulk, larger particles are more likely to become entrained, and at higher speed less particles of all sizes become entrained 1. INTRODUCTION

Solid particles suspended in a bulk lubricant may be an intentional addition or a potentially harmful contaminant. Molybdenum Disulphide and PTFE particles are commonly added to oils to improve their lubricity. These soft materials are thought to form a film adhered to the component surfaces. On the other hand, solid contaminating particles are also frequently present in industrial lubrication systems. These particles may originate as wear debris, carbon combustion products, or environmental contaminants. These particles enter into machine element contacts (such as bearings, gears, and seals) and cause surface damage. This damage frequently leads to premature failure through abrasive wear [ l ] or surface initiatcd rolling contact fatigue [2]. Both the beneficial effects of the former category and the deleterious effects of the latter are controlled by the ability of the solid, lubricant borne, particles to enter into the conjunctions of lubricated machine elements. In the past, the interferometric method has proved a useful tool to study the behaviour of particles in thc region of an elastohydrodynamic contact. One of the contacting elements is replaced by glass giving a ‘window’ on the contact area and lubricant entry region.

Wan and Spikes [3] and Dwyer-Joyce et al [4] showed how particles of various size and material behaved in and around ehl contacts. Ductile metals were shown to deform and the flattened platelets enter the contact. Brittle materials were found to fracture in the contact entry region and the fragments pass through the contact. The fragment size being controlled by the fracture toughness of the debris material. High speed video photography was uscd to show the motion of particles in the contact enlry region. A mass of particles tended to build up in the inlet region, with some flowing around the contact sides, and those on a central streamline passing through. It was also noted [4] that brittle particles below their critical crack size passed through the contact unfractured. This fact was later used [ 5 ] in a study of the three body abrasive wear process. Finely graded small size diamond particles were uscd as test contaminants, These did not breakdown in the lubricated contact and so abrasive mass loss could be directly attributable lo a particle of known geometry. A quantitative study of the particle entry process using this optical method is diflicult. Particle concentrations in practical lubrication systems are relatively low, such that the probability that there is a particle i n the contact at any one time is typically much less than unity. Sufficient high clarity imaging

136 to magnify small sized particles travelling at contact speeds is costly (requiring short duration photography or high speed video). In this study a relatively simple (although somewhat tedious) approach is followed. The level of surface indentation generated by the particles is used to quantify the entrainment process. The study is limited to a nominally pure rolling axisymmetric elastohydrodynamic contact. Small size diamond particles have been used, so that each entrained particle is responsible for a single surface indentation. 2. TEST APPARATUS & METHOD

The test geometry consists of a steel ball (diameter 25.4 mm) loaded and freely rolling on the upper surface of a flat rotating steel disk. Figure I shows a sketch of the apparatus. The ball is supported by rollers and spring loaded onto the disk. The upper surface of the disk is polished to facilitate the inspection of surface indentation. spring loaded

1

ba\w

polished disk s p e c i m y

additive) was thoroughly mixed with the required quantity of diamond powder. The mixture was continuously fed, using a constant flow syringe, onto the' disk, so as to become directly entrained into the contact. After testing, the disk is removed and examined under a microscope. Several photomicrographs of each test track wcre made. The number of surface indentations in each was recorded and then scaled to give a number of indentations per unit area of test track. For each test, a new ball and track on the disk was used. Test durations (1.c. number of disk revolutions) were chosen such that a measurable number of surface indentations were generated. Too few indentations give statistically poor results. Too many indentations result in a lengthy counting process. 3. RESULTS

The first test series was designed to investigate the validity of the method. The particle size and Concentration was maintained constant and the duration of each test varied. Figure 2 shows the result; the number of indentations counted per unit area is plotted as a function of test duration. 2000

belt drive to variable speed mo!or

I U

Figure 1. Diagrammatic skctch of the test apparatus. Finely graded diamond powder (DeBcers type MDA) was used as test particles. The size ranges used were 1-2 pm, 2-4 pm, 3-6 pm, 4-8 p i , and 6-12 pni. In addition a test series was carried out with 26-32 pm spherical particles of M50 steel. The test lubricant, Shell Turbo T68 (a mineral base stock without EP

20

30

40 50 Number of disk revolutions

60

Figure 2. Number of indentations per unit area against test duration (espressed as a number of disk revolutions). Panicle concentration 0.15 @I, contact rolling speed 0.2 m/s. Each test condition was repeated three times. The rcsulls are typically within less than 30% of the mean. This high degree of scatter is likely to be

137 caused by the difficulty in maintaining a uniform particle concentration in the mixture presented at the contact inlet. Within the scatter in the data the number of indentations per unit area appears to be approximately linear with test duration. This suggests that particles are not remaining imbedded in the surfaces; and a single entrained particle does indeed cause a single indent. However, the best line fit does not tend to zero (as of course it should). The results for low test revolutions suffer from high statistical inaccuracy (they are based on only a few indentation counts per photomicrograph), and are likely to represent an underestimate. To verify that particles were not left imbedded in the rolling element surfaces; a used test specimen pair were lightly cleaned and re-run with fresh uncontaminated lubricant. No further indentations were observed. The number of indentations per unit area can be cspressed as a number of particles in the contact at any instant, N, (by dividing by the nuniber of revolutions and multiplying by the contact area). If we assume the particles are cubic in shape of side length, d, the mass of particles in the contact is given by i)iC

= Ncp/

negligable compared with the total volume in the contact. The lubricant film thickness, h is determined from the relations of Hamrock and Dowson [7]. The division of these expressions then leads to a n effective concentration of particles in the contact (expressed as particle mass per unit fluid volume).

4 is defined here as the ratio of the particle concentration in the contact to that in the bulk, x, thus; A useful parameter 'particle entry ratio',

(3)

The effect of a variation of particle size on particle entrainment is shown in Figure 3 . The plot shows the particle entry ratio (defined by equation 3 above) plotted against particle size (a mean for each size range has been used). Each test series was repeated at three contact rolling speeds. Error bars are drawn on only one data set for clarity. The solid lines join the mean data points. 10000 0 2arll/s I

(1)

where p is the density of the particle material. The volume of oil entrained into the contact (corrected for the compressibility of the fluid using the empirical relation of [ 6 ] )is given approsimatcly by:

0

10

20 30 40 50 60 70 80 90 Particle size to film thickness ratio, dlh

100

Figure 3 . Plot of particle entry ratio, 4 against the mean particle size for three contact rolling speeds. Particle concentration 0.15 g/l. where pm is the mean contact pressure (in GPa) and a I S the contact radius (both determined from Hertzian analysis). The volume of fluid/particle mis in the contact is increased by the particles embedding in the contacting surfaces. However the number of particles prcsent in the contact at any instant is so small that this extra volume embedded in the surfaces is

The trend is clear; the contact has a significant particle concentrating effect across the whole range of particle sizes. Further more, the larger particles are many times more likely to be entrained into the contact than the smaller.

138

The effect of increasing rolling spccd is shown in Figure 4. The plot shows the particle entry ratio plotted against the contact rolling spccd for two sizcs of particle. As the speed increases the particles become less able to enter the contact. 10000 1000

nionotonically increasing curve. Clearly from this data no deductions can be made concerning the effects of particle density, material, or indced shape.

-. 6 - 12 micron

I

- 2 micron

1

10 1

0000

0200 0400 0600 0800 Contact rolling speed, m/s

1

OW

Figure 4. Plot of the particle cntry ratio, 4 against the contact rolling speed for two sizes of particle. Particlc concentration 0.15 dl. The presence of diamond particles in an industrial lubrication system is obviously unlikely. This material was chosen since it would not fraclurc in the contact (and so allow the prediction of particle entrainment directly from an indentation count). Ductile materials are deformed but also do not fragnicnt [4]. Therefore, they may also be tested for entrainmcnt bchaviour in this way Industrial lubrication systems frcquently contain hard steel fragments (originating from work hardened wear debris) typically in concentrations of the order 0.5 to 1 g/l. To provide a simplified analogue of this environmental condition, a 1 g/I concentration of 2634 pm particles of M50 steel was tcstcd for particle entry.

I

J

0000

0200 0400 0600 0800 Contact rolling speed, rn/s

1000

Figure 5 . Plot of the particle entry ratio against contact rolling speed for 26-34 pm particles of M50 steel. 4. DISCUSSION

Perhaps the most surprising result is that concentrations in the contact reached as high as 8000 times that in the bulk. Under certain test conditions the contact is exerting an enormous concentrating effect (like a stcamrollcr compressing everything in its path!). smaller particles off central flow line swmt to

Figure 5 shows a plot of the particlc entry ratio with increasing contact speed. Again, we see that the contact has a significant concentrating effect. The trcnd, as in the previous tests, is for particle cntry to reduce with increasing contact rolling speed.

Figure 7.Plan view of the circular contact and the motion of entrained particles.

The entrainment ratio for 30 pm steel particles is lower than that for 9 pin diamond particles (comparing figures 4 and 5). The relalionship between particle size and entry rario is not simply a

From the results presented it is clear that both particle size and speed of rolling have a significant effect on particle entrainment. When the fluidparticle mixture enters the inlet region of this type of flooded point

0

0

0

0

O

O

139 contact, most of the fluid is swept around the contact sides (see figure 7).

concentrating effect which is more marked for larger particle sizes.

However particles whose trajectory follows the central streamline will be subjected to lower off-asis fluid drag forces. Particles on the central streamline thus enter the contact whilst those travelling off-axis tend to get swept around the sides.

These features were observed, qualitatively, in the high speed video studies of [4]. Particles were observed building up in the inlet region. Smaller sized particles tended to pass around the contact sides, with only those on a central streamline becoming entrained. Larger particles were observed to be far less mobile; becoming trapped by the surfaces and thus directed by large friction forces before significant fluid forces could cause contact evasion.

Those that reach the nip as the two rolling elements approach will be subjected to high frictional forces in the direction of entrainment (see figure 8). These friction forces will incrcase as the particle is entrained further into the cntry zone and causes plastic indentation of the contacting surfaces. When the particle is trapped in the entry region the Stokes’ viscous drag forces are likely to bc small in magnitude compared to these friction forces.

Figure 8. Forces acting on particles in the contact entry region. The magnitude of fluid drag is small compared with the frictional entrainmcnt forces. It is suggested therefore, that the entrainment process is governed by fluid motion around the contact, until the particles are trapped in thc entry region when friction forces cause their inevitable entrainmcnt. Thus, high contact rolling speeds result in increased drag forces on the particles and a greater dcgrce of contact evasion. The effect of particle size is tivofold. Drag forces are greater on larger particles tending towards contact evasion. However, more importantly large particles become trapped in the inlet region, and subjected to frictional entrainment forces, further from the contact. It is this that results in the

These tests have only dealt with the case of a nominally pure rolling circular point contact. Without firther espcriment or computational fluid dynamics analysis, it is only possible to surmise as to entrainment behaviour of other lubricated contact cases. The flow of fluid around the contact is clearly a dominating factor. Thus for line, transverse elliptical (ball bearings for esample), and starved contacts where fluid flow around the contact is reduced, the particle entry ratio is likely to be even higher than the fully flooded asisymmetric case. The effect of contact sliding may also be significant; one of the frictional entrainment forces (shown in figure 8) will act in the opposite direction, reducing the likelihood of particle entry. 5. CONCLUSION

The aim of this work has been to quantify the entrainment of solid lubricant borne particles into elastohydrodynamic contacts. A simple flexible mcthod, of using surface indentation to measure particle entry, has been developed. Over a limited range of test conditions some interesting results have ensued. Broadly, over this limited test range, the conclusions

are summarised thus; (i)

The contact acts to concentrate the suspended particles; such that the concentration in the contact can be several thousand times higher than that in the bulk lubricant.

140

(ii)

Larger particles are more likely be entrained into a contact than smaller particles.

(iii)

The entrainment of particles is reduced as the speed of rolling increases.

(iv)

Large steel particles, of a size commensurate with the debris commonly found in industrial lubrication systems, show similar behaviour.

Therefore, a larger particle may be more suitable for the design of a solid lubricant additive; and the operation of low speed contacts would promote particle entry. Conversely, the designer of a filtration system may be advised to concentrate on filtering out large particles since these show a greater likelihood of particle entry (although of course there are a great many small particles which, although a lesser proportion are entrained, may cumulatively result in high levels of surface damage and wear). The scope for hture work is great. A variety of contact geometries under combined rolling and sliding would generalisc the work to be more industrially applicable; as would a more detailed study of the size and speed effect on ductile panicles.

REFERENCES Lorosch, H. K, (1983), “Research on Longer Life for Rolling Element Bearings”, Trnns. ASLE, Vol. 41, No.1, pp. 37-43. Sayles, R S. and Macphcrson, P. B., (1982), “The Influence of Wear Debris on Rolling Contact Fatigue”, ASTM STP 771, J.J.C.Hoo, Ed, Anrerican Society Test & A4nterinls, pp. 255-275. Wan, G. T. Y. and Spikes, H. A,, (1987), “The Behaviour of Suspended Solid Particles in Rolling and Sliding Elastohydrodynamic Contacts”, Trans. ASLE, Vol. 31, No.1, pp. 1221. Dwycr-Joycc, R S., Hamer, J. C., Saylcs, R S. and Iornnides, E., (1991), “Lubricant Screening for Debris Effects to Improve Fatigue and Wear Life”, Proc. 18th Leecls-Lyon Svirrp. Tribologv.

[ S ] Dwycr-Joyce, R S. ,Saylcs, R S., and

Ioannidcs, E., (1991), “An Investigation into the Mechanisms of Closed Three Body Abrasive Wear”, Wear, Vol. 175, pp 133-142. 161 Dowson, D. and Higginson, G. R, (1977), “Elasto-HydrodynamicLubrication, 2nd ed.”, Pergamon Press. [7] Hamrock, B.J. and Dowson, D., (1977), “Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 111, Fully Flooded Results”, ASME J. Lub. Tech., Vol. 99, pp 264-276.

The Third Body Concept / D. Dowson et al. (Editors) (D 1996 Elsevier Science B.V. All rights reserved.

141

Behaviour of PTFE suspensions in rollinghliding contacts S Palios, P M Cann and H A Spikes Tribology Section, Department of Mechanical Engineering, Imperial College of Science Technology and Medicine, London SW7 2BX, United Kingdom

PTFE (polytetrafluoroethylene)powders are quite widely used as concentrated dispersions in liquid lubricants where they form pastes or greases. It has also been suggested that they can be used to reduce friction and wear when suspended at quite low concentrations in oils. Thus a number of PTFE-containing products are currently marketed which, it is claimed, improve crankcase engine performance when added to conventional motor oils. The way that such PTFE particles might function in lubricated contacts is disputed. Some workers suggest that they adhere to rubbing surfaces and are smeared out to form a protective, low friction coating. Other authors propose that the particles pass individually through contacts without adhering, serving to bodily separate the two opposing surfaces. Another suggestion is that PTFE particles have no practical beneficial effects whatsoever on either friction or wear. This paper measures both the film-forming properties of lubricants containing suspended PTFE particles and also their friction and wear properties in order to investigate the effectivenessand mechanism of behaviour of these panicles.

1. INTRODUCTION

The last two decades have seen a rapidly developing interest in the production and use of low fiiction. highly efficient, liquid lubricants. The initial impetus for this was fuel shortages resulting from conflicts in the Middle East in the 1970s. More recently. the main driving force has been the need to reduce global fossil fuel consumption and thus to limit carbon dioxide emissions. Most attention has focused on crankcase engine lubricants and modem engine oil specificationsnow include engine tests, such as the ASTM Sequence VI, to quantify fuel efficiency. However there is also considerable interest in reducing friction and thus increasing the efficiency of transmission lubricants. Lubricant manufacturers have adopted two main approaches to producing high efficiency lubricants. One has been to lower the dynamic viscosity of the lubricant and thus the hydrodynamic friction. This has resulted in a steady reduction in the viscosity of multigrade engine oils over the last fifteen years. A

second, complementary, approach has been to employ soluble, friction modifying additives to reduce friction in the boundary lubrication regime. Typical examples are molybdenum compounds and long chain, unsaturated organic acid salts. A third approach, which is the subject of this paper, is far more contentious. This is to add to the liquid lubricant tiny insoluble particles of polytetrafluoroethylene (PTFE). This material, when used in solid-coating form on the surfaces of components such as dry bearings and non-stick frying pans, is known to show very low friction and it has been suggested that a similar benefit is conferred by dispersed particles in an oil. At present, PTFE dispersions are provided primarily by specialist lubricant suppliers as concentrates, to be added, by the user, to conventional engine, transmission or other lubricants. Their efficacy is controversial. Some studies suggest that they significantly reduce friction and also wear in engines and other systems (1). Other studies have found very little, if any benefit (2).

142

This paper describes an investigation into the friction and film-forming properties of PTFE suspensions in lubricating oils. The aim of the work was to investigate the conditions, if any, under which such PTFE particles can reduce friction and wear and to explore the mechanisms by which such benefits may be produced. 2. BACKGROUND

Dispersed, solid particles have been used as dilute solutions in liquid lubricants for many years (3). The most widely employed materials are graphite and molybdenum disulphide (MoS,) although many other substances such as metal salts and even glass particles have also been used (4)(5). Both graphite and MoS, are lamellar solids which reduce friction when supplied as dry, solid coatings. It is generally presumed that their low friction results from preferential slip parallel to the solids’ low shear strength basal plane. The effectiveness of suspensions of graphite and MoS2 in oils is disputed. Some workers have found that they reduce friction and wear whilst others have found an increase (6). One reason for these observed differences may lie in the fact that, depending upon how graphite and MoS, are manufactured, both of these solids can exist in different forms with differing particle shapes and surface adhesive properties (7). A second possible origin of contradictory results is that the behaviour of suspended solid particles may depend critically upon the geometry, kinematics and surface roughness of the rubbing system used. Thus a number of workers have studied the behaviour of both graphite and MoS, in and around contacts visually, by making one of the rubbing bodies Lransparent; usually of glass (8)(11). This has shown that both types of particle are canied into the contact in pure rolliig conditions and adhere to the surfaces to form a concentrated layer of solid lubricant in the contact track. In high slide-roll ratio contacts, however, particles tend to accumulate in the inlet, causing Starvation and thus loss of lubricant film. Studies of the effects of temperature, lubricant viscosity and of the influence of other additives present support the principle that, to be effective,

graphite and M0S2 particles must adhere to the rubbing surfaces and thus form, due to the mechanical effects of sliding, a solid lubricant coating (12)-(15). By comparison with graphite and MoS,, the behaviour and effectiveness of dispersed PTFE is far from clear. Although PTFE has been used at high concentration in pastes and greases for many years, its use as a low concentration dispersion in oils is quite recent. The concept was first patented by Reick in 1976 (16) and has beem promoted as a means of reducing friction and wear in a number of applications, including crankcase engines, chain WWS,Wire drawing and penetrant lubricants (17)(21).

There has been considerable conmversy concerning the effectiveness of PTFE in this form. Thus reference (22) cites a note from Du Pont, one of the main manufacturers of PTFE who circulated a letter to all news media and customers in 1980 “E$ective February 1, 1980, ‘Teflon’fluorocarbon resins or untrademarked DLX-6000 fluorocarbon micropowder will not be supplied for use as ingredients of oils or oil additives for the lubrication of internal combustion engines. This decision is based on our conviction that these polymers are not useful ingredients in such products. ”

Just over ten years later, another main manufacturer of PTFE powders, ICI states (23) “One of the more recent applications for PTFE lubricant powders has been their inclusion in internal combustion engine lubricating oils. A considerable amount of literature has already been published on this application which has highlighted the role that PTFE particles may play in filling the irregularities in the metal counterface and providing a smooth, low piction sugace between the moving parts. Once the lubricant is in place, the oil base provides a bawierjllm which bonds the PTFE to the sugace to give a very low boundary piction coeflcient which reduces the total running piction of the engine. Further developments are awaited in this expanding automotive applications area. ’’

143 Despite the above statement, surprisingly little scientific work has been carried out on the behaviour of suspended PTFE particles in oils. The most detailed study is due to Reick (22). This work examined the influence of fine, dispersed PTFE particles, of diameter 0.05 to 0.5 tun, on the heat generated in a sliding steelkeel contact. The presence of PTFE particles resulted in significantly lower temperature rises than found with PTFE-free oils, implying lower friction, and also postponed the onset of scuffing. Reick noted that when the steel surfaces were pretreated with a comsion inhibitor. the effectiveness of the PTFE was reduced. Reick also canied out Auger and ESCA analysis of the rubbed steel surfaces. When these were vigorously degreased. no fluorine was found to be present, but after only mild degreasing there was evidence of individual particles of fluorine-rich material in and around the wear track. From this study, Reick concluded that FTFE particles do not adhere strongly to the solid surfaces, nor get smeared out, as is found with graphite and MoS2. but rather pass individually through the contact; “floating particles rolling and sliding between the surfaces”. Reick’s work was carried out in a low pressure, conforming contact. Reick also mentions, without further details. that PTFE particles are ineffective in high pressure contacts such as in the four ball or Fales machine. This was confiied in a study by Cusano et a1 who examined the effect of surface roughness on dispersed solid lubricant behaviour (6). They found that the addition of dispersed PTFE to a mineral oil had negligible effect on friction and wear in a point contact pin on disc machine. Similar findings have also been described by Horsmans who found large wear and friction reduction by dispersed PTFE in a pin of disc machine but very little effect in a four ball tester (24). Li and coworkers used X-ray photoelectron spectroscopy and Auger to analyse the surface films present on specimens from a Falex test lubricated with a PTFE dispersion (25). They confirmed observation of distributed microparticles of PTFE in the contact region but also found that PTFE formed a very thin, structured surface layer under boundary lubrication conditions. This consisted of

M y fluorinated carbon chains in the topmost layer

with partiauy hydrogenated chains mixed with FeF, below this. One major practical problem in using dispersed PTFE particles which may explain some of the differing views as to their ef€icacy is that of dispersion stability. Clearly, to be effective, the PTFE particles must remain in suspension during storage and use. This is achieved in part by using very small particle diameters, so that Brownian motion becomes significant and also by using dispersants. It has also been claimed that electron bombardment of the PTFE can provide a permanent negative charge, which enhances interparticle repulsion as well as promoting particldmetal surface bonding (24)(26). 3. TESTMATERIALS

One problem in studying the behaviour of PTFE particles used in commercial oils is that the particles are very small, typically less than 0.1 pm diameter, which makes them very difficult to observe visually. Most commercial samples also contain additives which are incorjwmted to help disperse the PTFE particles and it may be difficult to distinguish the effects of these additives on friction and wear from the contribution of the PTFE particles themselves. To help tackle these problems, in the current study tests were made on two M e r e n t types of suspended PTFE system. One consisted of a fully-formulated, commercial oil, with and without PTFE particles. The other was a set of dispersions of well-characterised, quite large PTFE particles in very simple base fluids. 3.1 Wellcbaracterised blends Table 1 lists the two types of PTFE particle employed in simple blend).

I FL1700 I VydaxHD

t

Particle size. um d a c e area. m‘/g I

.

1=1

1

I

I 1.0

3.1

I 5-

I

Table 1. PTFE powders employed One. FL1700, Erom ICI Fluorochemicals, had quite fine particle size of about 1 pm, and, it was

144

claimed, could be broken down to submicron-sized particles in high shear conditions and was suitable for use in oil dispersions. The other, Vydax HD from Du Pont Chemicals had somewhat coarser particle size. These PTFE particles were dispersed in additive-free, polyalphaolefm, synthetic hydroc h o n base fluids of differing viscosities, as listed in table 2.

I Viscosity at I SHF41 SHF401

4OoC (cSt) 14.9 440

Viscosity at 100°C (cSt) 3.12 49.5

I

Figure l(a)

1% wt. Vydax in SHF41

Table 2. Characteristics of base oils employed The PTFE particles were dispersed at 1% and 5% wt. in both fluids. The blends were placed in a

beaker on a magnetic stirrer or in an ultrasonic bath for 5 minutes to uniformly disperse the particles. It was more difficult to achieve a uniform mixture with the more viscous oil (SHF401) where the fluid was preheated with a magnetic stirrer and hot plate. In some cases, a Silverson heavy duty laboratory mixer/emulsifier was used in order to ensure an evenly-dispersed solution. The dispersions obtained using these simple systems were not fully stable and settled slowly with time; especially for the larger particle size system. Therefore they were well-dispersed prior to each test and care was taken to periodically agitate the blends during a test to ensure that particles did not settle. Figures la and lb show optical images (x170) of suspended particles of 1% wt. dispersions of the two PTFE powders in SHF41, taken using a differential interference contrast microscope. The PTFE particles, which clearly have a range of sizes, appear white against a dark background 3.2 Commercial materials A fully-formulated 10W/30 engine oil was also tested, with and without the addition of 1% wt. of commercial PTFE particles. The particle size of these particles was not known but was estimated to lie in the range 0.05 to 0.1 pm. The engine oil had a viscosity of 10.6 cSt at 100OC. These dispersions appeared to be fully stable over time.

Figure 1@) 1% wt. FL1700 in SHF41 4. TEST METHODS

A number of different experimental test methods were used in this study. These divide into two groups;

(i) Boundary friction and wear (ii) EHD film thickness, traction and imaging

4.1 Boundary Friction and Wear Tests A reciprocating test rig was used. In this, a 6.0 mm diameter steel ball is held in a chuck and loaded downwards on the flat face of a 10.0 mm diameter steel disc. The disc is held in a bath which is two thirds filled with test lubricant so that the contact between the ball and flat is fully immersed. The bath temperature is controlled to f 0.5OC. During a test, an electrical vibrator is employed to oscillate the ball backwards and forwards in contact with the flat at a stroke length and frequency that can be set by the user. A control

. 145

a precision o f f 1 nm. A highly polished steel ball (AISI 52100, 19.05 mm diameter) is loaded against the underside of a glass disc which is coated with a chromium semi-reflecting layer and a silica spacer layer. In the w e n t study the thickness of the spacer layer was approximately 510 om. The surface of the glass disc was optically smooth and the composite roughness of the undeformed surfaces was 11 nm. The disc is driven by an accurate motor via a series of speed-reduction gears, which provides controlled speeds over a m g e from 0.0002 m/s to 5 d s . The rotating glass disc drives the steel ball in nominal pure rolling. The test rig is shown schematically in figure 2. In these tests, the ball was half-immersed in lubricant Which ens~reedfully-flooded conditions. Test temperature was maintained using thermocouples around the chamber and measured near the contact inlet using a digital thermometer.

circuit maintains constant stroke length regardless of the friction value. Friction between the ball and flat is measured using a load cell attached to the lower specimen holder. The friction coefficient was logged continuously throughout a test and at the end of some tests, the wear scar size on the ball was determined using a microscope. This was taken as the average of the major and minor axes of the elliptical wear scar. Friction tests were carried out according to the following conditions:

1 Strokelength

I

Stroke frequency

1000 wn 20 Hz,50 Hz

Temperature staees Ball properties Disc properties Time interval

4OoC, 6OoC, 8OoC, 100OC. 12OOC AISI 52100,800 VPN AISI 52 100,200 VPN 10 min

I

Table 3. Friction test conditions used in this study

The temperature was raised in stages, with 10 minutes at each stage. Friction coefficient was averaged over the 10 minutes of the test. Wear tests were canied out according to the following conditions:

1000 pn Stroke length Stroke frequency 20 Hz Load 400 g 8OoCor 12OOC Temperature AISI 52100,800 VPN Ball properties Disc ~rotmties AISI 52 100.200 VPN 1Time interval 175min

Table 4. Wear test conditions for wear testing New specimens were used for each test and the temperature was held constant for the duration of the test. 4.2

EHD Film Thickness, Traction and Imaging Methods

EHD film thickness meaSUfementS were made using ultrathin film interferometry (26). This can measure central film thickness as low as 2 nm with

Figure 2. Diagram of EHD Film Thickness Rig

I

The whole test rig operates under microcomputer control. Before the start of the test, prior to the addition of lubricant, the silica spacer layer thickness is measured at a number of Merent positions around the glass disc. Lubricant is then added, temperature stabilized and motion started. During the test, a disc position encoder is used in conjunction with the microcomputer to enable film thicknesses to be measured at the locations on the glass disc where the spacer layer thickness has been praiously detennined. In the current study, film thickness tests were Carried out at temperatures of 40°C, 8OoC and

146 120OC. at a load of 20 N, corresponding to a maximum contact pressure of 0.52 GPa and in nominally pure rolling. The rig used for EHD traction measurements was the same as the one used for the film thickness measurements, except that the glass disc was replaced by a smooth hardened, polished steel disc, with a similar surface finish to that of the ball and both the ball and the disc wete driven by separate DC motors, enabling the sliddroll ratio to be controlled. Traction measurements were made between a 19.0 mm diameter, AISI 5200 steel ball in sliding contact with a steel disc. The Young's moduli of the two surfaces were 2 10 GPa for both. In order to observe the bebaviour of individual particles of PTFE in contacts, a spacer layer imaging method was used. This is fully described in (28). The optical test rig used is essentially the same as in figure 2. However a solid state, colour camdframe grabber is used to capture interference images of the EHD contact. A high speed electronic shutter enables images to be captured within 0.25 ms. From the images thus obtained it is also possible to produce maps of film thickness over the contact using a colour analysis technique (28). 5.

Friction is seen to rise with temperature, presumably because the contact operates more fully in the boundary as opposed to the mixed regime as the viscosity decreases with increasing temperawe. Table 6 shows wear results at two test temperatures. It can be seen that the FL1700 PTFE dispersion reduces both friction coefficient and wear but the V ~ I Y fine PTFE dispersion in the commercial oil has negligible effect on performance. SHF41 SHF41+5% FL 1700 Commercial Oil corn. oil +

4OoC 334 265 164 165

12OOC 419 336 215 19 1

1

Table 6. Wear scar results from reciprocating rig 5.2 EHD Film Thickness Figure 3 contains EHD film thickness plots for a 1% wt. dispersion of FL1700 in SHF41 at two temperatures, 40 and 8OOC. The figure also shows some results for SHF41 without PTFEat 4OOC.

RESULTS 0 1% FL17OO,4O0C

5.1 Boundary Friction and Wear Table 5 summarises friction coefficient results for the lubricants tested.

_FL1700 _

X 1% FL700,80°C

~

SHF401 SHF401+ 5% FL1700 Comm.Oil Comm.Oi1

0.09 0.07

0.10 0.07

0.12 0.07

0.12 0.08

0.13 0.09

o.Ooo1 0.001 0.01 0.1 1 Entrainment speed, mls

0.12 0.12

0.12 0.13

0.13 0.13

0.14 0.14

0.14 0.14

Figure 3. EHD Film Thickness of SHF4 1 with and without 1% wt. PTFE

Table 5. Friction coefficients in reciprocatiug rig

10

It can be seen that at high speeds, log(film thickness) vetrms log(speed) is linear, in accord with EHD theory. Comparison with the PTFE-free fluid shows that there is no measurable contribution

147

from the PTFE at high speeds. At slow speeds, however. the PTFE-containing oils showed evidence that PTFE was passing through the contact to momentarily increase the film thickness. The fdm thickness measurements were irregular, and quite random, spanning the range from a lower bound corresponding to the PTFE fluid film thickness up to an upper bound of approximately 70

EHD Traction Figure 6 compares the traction behaviour of a 1% wt. and a 5% wt. dispersion of FL1700 in SHF41 with the corresponding PTFE-free base fluid. All measurements were taken at a fied slide-roll ratio of 50%. 5.3

nm.

0.1

Figures 4 and 5 compare results for the commercial oil with and without dispersed PTFE at 80 and 120OC. The PTFE-cOntaining oil appears to form a slightly thicker film than the PTFE-free one at very slow speeds, especially at 120OC.

I

E

aa

'E 0.06 8 8 0.04

H

I

E No PTFE, 80°C

0.08

0.02

O l 0.001

I

I

I

0.01

0.1

1

Entrainment Speed, m/s

10

Figure 6. Tractiodentrainment Speed Plots for SHF41 with FL 1700 PTFE at 80°C o.Ooo1 0.001 0.01 0.1 1 Entrainment speed, m/s

10

Figure 4. EHD Film Thickness Results at 80°C for Commercial Oil with and without PTFE No PTFE, 120°C

E 100 d

!i

F

10

E

E l o.Ooo1 0.001 0.01 0.1 1 Entrainment speed, m/s

Figure 5. EHD Film thickness results at 12OOC for Commercial Oil with and without PTFE

10

The results illustrate how traction coefficient varies with entrainment speed. For the base fluid, this m e is effectively a Stribeck-type plot, showing how traction coefficient varies with EHD film thickness. At high speeds, the traction corresponds to an EHD limiting traction value. As the speed and thus the film thickness is reduced, however, the traction rises progressively towards the b o u n d a ~friction ~ value as the film thickness decreases. With the PTFE-containing fluids, the EHD traction coefficient at high entxainment speed is somewhat higher than the PTFE-free value. possibly because the PTFE particles are blocking the inlet slightly to cause starvation and thus reducing film thickness. In the slow speed,thin film regime however, the traction coefficient of the PTFE-containing oils falls. This collapse is irregular, with the traction rising and falling apparently randomly with time. Figures 7 and 8 compare the traction behaviour of the commercial oil with and without PTFE.

148 Negligible contribution by PTFE can be seen at either temperature. No PTFE, 80°C '5 0.1

and Vydax. No evidence was seen of the accumulation of particles in the contact track, suggesting strongly that PTFE particles do not adhere to or become smeared out on the rolling track.

1% PTFE, 80°C

i= .T-

E5 0*08 0.06

..tj 0.04 c! b- 0.02

01 0.001

I

I

I

0.01 0.1 1 Entrainment Speed, m/s

10

Figure 7. Tractiodentrainment Speed Plots for Commercial Oil with and without PTFE 0.14 1

I

E 0.12

I a No PTFE, 120°C

a, 'J 0.1

1% PTFE, 120°C

E

1

I

Figure 9. Spacer Layer Image of Contact with 1% wt. of Vydax HD in SHF41 at 0.012m/s

3c 0.06 0.08

0

10.04

c 0.02 0.001

0.01

0.1

1

10

Entrainment Speed, m/s

Figure 8. Tractiodentrainment Speed Plots for Commercial Oil with and without PTFE 5.4 Spacer Layer Imaging of EHD Contact

Spacer layer imaging showed that FL1700 and Vydax HD particles (1% wt. in SHF41) pass through slow speed rolling contacts when tested at room temperature. At very slow speeds (less than LO &second) large quantities of particles pass through. As the speed is raised however, the numbers entering the contact diminish sharply and at high speed (greater than 0.1 d s ) very few, if any, particles are entrained. Figures 9 and 10 show interference images taken from the contact, the inlet is on the right. The local colour variations within the contact are PTFE particles of El700

Figure 10. Spacer Layer Image of Contact with 1% wt. of FL1700 in SHF41 at 0.012 m/s It is possible to map the film thickness across these contacts using interference colour analysis. Figures 11 and 12 show the film thickness profiles, taken along the centre line, in the direction of rolling. The corresponding profiles for the base oil are also shown. Figure 1 1 shows a profile for 1% Vydax at slow speeds. The presence of a particle can be clearly seen. It is possible to estimate the volume of this indentation which is about 120 pm3, corresponding to a 6 pm diameter spherical particle. It can be seen that the particles produce a

149

local elastic impression in the two surfaces but that the surrounding contact region remains quite flat. 0.1 m/s

180 :

200 h

I I

160:

8 120

8

100 40 . 20 : 0 -200

SHF 41 1

-100

'

1

0

.

1

.

-200

'

100

200

Contact position (pm)

Figures 12 to 14 show similar profiles for FL1700 at three speeds. At very slow speeds many particles pass through the contact and individual ones cannot be easily distinguished. As the speed is raised. fewer particles pass through so that at 0.2 m/s the film thickness is similar to the base fluid.

1

200

Figure 13. Fdm Thickness Profile with 1% wt. of FL17OO in SHF41 at 0.1d s .

Figure 11. Film Thickness Profile with 1% wt. of Vydas HD in SHF41 at 0.012m / s .

300

-100 0 100 Contact position (pm)

200 180

--

3- 1601 140 v1

8 120-

4

100: 80: 60: iz 40 : 20 0 : -200

3

-

4

I

-

I

I

-100

0

.

1

100

.

1

200

Contact position (pm) Figure 14. Film Thickness Profile With 1% wt. of FL1700 in SHF41 at 0.2 d s .

-200

-100 0 100 Contact position (pm)

200

Figure 12. Film Thickness Profile with 1% wt. of FL1700 in SHF41 at 0.012ds.

With the commercial oil the particles are much smaller and difficult to distinguish. The spacer layer images suggested that particles were passing through at low speeds where some perturbation of the EHD N m shape was observed.

150 6. DISCUSSION

This study shows quite clearly that PTFE particles of about 1 p diameter are able pass through slow speed, rolling, elastohydrodynamic contacts. However they appear to be largely rejected from high speed contacts. These PTFE particles also appear to penetrate slow speed,mixed rolling/sliding contacts where they help reduce friction in the thin film regime. They may, however, promote higher friction at higher rolling speeds, perhaps by promoting starvation. The behaviour of the much finer particles supplied for use in commercial engine lubricants is far less clear. Contact imaging suggests that some particles may pass through low speed rolling contacts. However traction, boundary friction and wear tests all show no contribution from the dispersed PTFE. If, as appears the case, PTFE particles are unable to adhere and smear on the surfaces to form a reasonably coherent layer on the solid surfaces, then two possible reasons for the lack of effectiveness of tiny, dispersed PTFE particles can be considered. One is that very small PTFE particles are rejected from the contact even down to very low speeds. below those attainable in the current study. If this were the case then the particles will simply not pass through EHD contacts. It has been suggested previously that the mechanism by which particles are drawn into contacts involves their being trapped by friction forces between the converging solid surfaces (11). Very small PTFE particles would both have low friction and would, by virtue of their small size, have to penetrate the inlet a long way before becoming trapped. Thus their almost complete rejection Erom the contact could easily be envisaged. On the other hand, EHD film thickness measurements do show a small enhancement of film thickness due to the PTFE at very slow speeds, suggesting that particles may pass through the contact under these conditions. An alternative explanation for the inability of very small PTFE particles to reduce friction in this study is that the particles may pass through the contact but not support a signifkant propoxtion of the applied load in the process. It should be noted that the friction in a contact derives from the integral, over the whole contact area,of the ratio of

local shear stress to local supported load. In the EHD imaging work it was seen for the large PTFE particles, that the solid surfaces deformed around the particles to fom localised elastic indentations of about 50 nm in depth. The total Hertzian flattening under these ConditioILS is about 2 p. Thus the proportion of the load supported by even these large FTFE particles will be quite small. If tiny, 75 nm diameter, particles pass through the contact, the amount of elastic deformation they will produce, and thus the proportion of the load supported will be very small. Thus they would be expected to cause only a tiny decrease in overall friction. In summary, it is no use having an easily sheared region of the contact if this does not support any of the load. If this is the origin of the lack of effectiveness of small PTFE particles in this study, then it supports the contention made by previous workers that PTFE particles may be more effective in “area contacts” (22). Such contacts will have much lower contact pressures than those in the current study and in such systems, the proportion of the load supported by deforming PTFE particles may become much more significant. In consequence the particles may contribute to reduced friction and wear in such systems. 7. CONCLUSIONS A study has been made of the behaviour of dispersed PTFE particles in high pressure, boundary and EHD contact conditions. It has been found that large, micron-sized PTFE particles appear to reduce friction and wear in reciprocating tests. These particles also reduce friction in slow speed, thin film, mixed sliding/rolling conditions. Optical studies show that these large particles are able to pass through slow speed, rolling contacts where they cause significant elastic deformation of the solid surfaces. The reduction in friction and wear can be ascribed to this behaviour. There is no evidence of the particles adhering m n g l y to the rubbing surfaces to form a pennanent coating. Very small PTFE particles in fully-formulated oil, appear to make no measurable con~butionto friction and wear reduction. This may be because

151 the particles are unable to enter the contact. Alternatively, they may be so small and weak that in passing through the contact they are unable to bear a significant fraction of the applied load. In such a case they would not be expected to reduce friction or wear to any useful extent.

WFERENCES 1.

2. 3. 4.

5.

16.

7.

8.

a

Saunders, J. “Slick 50 Breaks Boundaries”, Lubricants World, pp. 27-31, May 1995. Winfield, B., “Oil Additives: the Pitch is Slick but do they Work?”, letter to Car and Driver, p. 23, March 1994. Smith E.A. “Colloidal Graphite in Assembly Lubrication”, Engineering 165, pp. 505-507, (1948). Middleton, K. “A Comparative Examination of Some Potential Inorganic Lubricants on the Shell Four-Ball Tester and on a CrossedCyliider Wear Machine”, Paper 7, I. Mech. E. Lubr. and Wear Convention, May 1964. Arizmendi, L., Palacios, J.M. and de la Cruz M., “A Very Ememe-Pressure non-Lamellar Additive for Special Mechanical Designs, Proc.1.Mech.E. C2%/73,pp. 307-311, (1973). Cusano, C. and Goglia, P.R. “Surface Roughness Effects with Solid Lubricants Dispersed in Mineral Oils”, ASLE Trans. 27. pp. 227-236, (1984). Groszek, A.J. and Witheridge, R.E. “Surface Properties and Lubricating Action of Graphite and MoSP, ASLE Trans.14.pp. 254- 266, (1971). C.Cusano and H. E. Sliney “Dynamics of Solid Dispersions in Oil During the Lubrication of Point Contacts, Part I Graphite.” ASLE Trans. 25.pp.183-189, (1981). Cusano,C. and Sliney, H. E. “Dynamicsof Solid Dispersions in Oil During the Lubrication of Point Contacts,Part II Molybdenum Disulphide.” ASLE Trans.25. pp. 190-197, (1981).

-

9.

10. Wan, G.T.Y. and Spikes, H. A., “Two Phase Lubricants in Elastohydrodynamic Contacts Graphite in Oil, Dispersions”, Proc. 12th Leeds-Lyon Symposium on Tribology, Lyon Sept. 1985, “Mechauismsand Surface Distress”, ed. D Dowson et al. ,publ. Butterworths, 1986. 11. Wan,G.T.Y. and Spikes, H.A. “The Behaviour of Suspended Solid Particles in Rolling Sliding Elastohydrodynamic Contacts” STLE Trans. pp.12-24, (1987). 12. H O W ,R. “Lubrication Mechanisms of Solid Lubricants in Oils”, ASLE Trans. 18. pp. 263-269, (1975). 13. Bartz, W.J. and Muller, K. “Investigationsof the Lubricating Effectiveness of Molybdenum Disulphide”, Wear-02 pp. 377-379, (1972). 14. Scott, D. and Jamieson, D. “Molybdenum Disulphide as a Lubricant Additive in Rolling Contact a Study of Compatibility with Other Additives, J. Inst. Pet. 48.pp. 91-97, (1962). 15. Rolek, R.J., Cusano, C.and Sliiey, “The Influence of Temperature on the Lubricating Effectiveness Of MoS2Dispersed In M i n d Oils” ASLE Tran~.28.pp. 493502, (1984). 16. Reick, F., “Lubricating Oil with Fluorocarbon Additives”, US Patent 3933656, Jan., (1976). 17. Gutman, M. and Stotter, A. “The Influence of Oil Additives on Engine Friction and Fuel Consumption” Lubr. Eng. -4l pp. 150-154, (1985). 18. Wilson, B. ”PTFEas a Friction Modifier in Engine Oil” Ind. Lubr. and Trib. 44,pp. 35, (1992) 19. Shaub, H., Pandosh, J., Searle, A. and Sprague, S. “Engine Durability, Emissions and Fuel Economy Studies with Special Boundary Lubricant Chemistry”,SAE 941983, (1994). 20. “(Polytctraflwmethylene)Lubricant Saves Energy” Wire Tech, 10.p.20, (1982). 21. Dehlsen, J. and Ferguson, J., “Multipurpose -Lubricant“, Tribolog~Int. p ~282-285, . (1979).

-

-

152 22. Reick, F.G.“Energy-savingLubricants Containing Colloidal FTFE”,Lub. Eng. pp. 635-646.(1982). 23. “Fluoroglide Fluompolymer Lubricants, a Guide to: Applications, Properties and Processing”, 1C1 Fluoropolymers, Blackpool, Lancashire, UK, 1992. 24. Horsmans, J. “NewDevelopments in FTFE Additives for Lubricating Oils”, Proc. 5th Int. Colloq., Esslingen, Jan. 1986,pp 6.5.14.5.8, ed. W.J. Bartz. 25. Li L.C., Yang, M.S. and Ling, Q.Z. “Chemical Structure Characterisationof the Boundary Lubrication Film Using X-ray Photoelectron Spectroscopy and Scanning Auger Microscope Probes”. Wear 140.345357. (1990).

a,

26. Stewart, C.W. Letter in response to Mr B Winfield’s article in Car and Driver, March 1994,Du Pont Central Research, P.O.Box 80323,Wilmington, DE,Feb. 18th 1994. 27. Johnston, G.J, Wayte, R.and Spikes, H.A. “The Measurement and Study of Very Thin Films In Concentrated Contacts” Trib. Trans., 34,pp.187-194,(1991). 28. & , I P.M., Hutchinson, J. aud Spikes,H.A. “The Development of a Spacer Layer Imaging Method (SLIM) for Mapping Elastohydmdynamic Contacts”. To be presented at STLWASME Joint Meeting, (1995).

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

153

-

Phird bodies in wet friction couples In-situ-measurementwith electrical impedance

4. Pauschitz, G. Mikolasch, F. Franek and G. Abraham Institute of Precision Engineering - Department of Tribology, Technical University Vienna, Floragasse 7,1040Vienna, Austria

This paper describes the possibilities and advantages of in-situ determination of the changes pnto the friction surface during transition from liquid lubrication to solid body friction. A porous friction layer is used as first body (test body) with a steel disc as counteracting body. In order to estimate the contact intensity a High-Frequency-Impedance-Measuring-System (HIFIMS) is used. The application of the measuring system has been carried out using a Disc-Friction-andWear-Apparatus. For the verification of the HIFIMS results additional measuring methods in iorder to characterize the surfaces are used.

1. INDRODUCTION

The ,,third body" idea [l]is to characterize the interface of a friction pair, i.e. a zone which is characterized by the friction in terms of material: couple, as a zone of material changes

or in terms ofkinematic: as a layer in which the difference in velocity of the particular friction partner is accomodated.

j

Thus the third body usually includes all different types of friction, from liquid lubrication friction to solid body friction. The in-situ determination of the transition from the liquid lubrication friction along semi liquid and boundary lubrication to solid body friction needs a corresponding measuring system. For this purpose a new application of the High-Frequency-Impedance-MeasuringSystem for experimental investigations is used. The HIFIMS was developed at the Institute of Precision Engineering (IFWT). Using a dynamic frequency measuring system (variation of frequency) enables at

once an evaluation algorithm in opposite to static resistance systems. This measuring system enables to determine and classify lubricant and boundary layers as well as the influences caused by a certain pressure. The main capability of the HIFIMS to determine the variation of a lubricating film between the first body and the counteracting body of different tribological systems has been described for several applications, e.g. gear wheels, journal bearings or roller bearings [2] - [3]. For the series of tests described in this paper the application of the measuring system has been carried out using a DiscFriction-and-Wear-Apparatus. 1.1. Contact situation in the interface Different contact situations between a solid friction pair with o r without lubricant are shown schematically in the diagram friction-coefficientvs. velocity (figure 1).

The diagram shows the zone of internal solid body friction (A), boundary friction (B), semi liquid friction (C)and liquid lubrication (D). The zone of boundary friction is characterized by an almost constant friction coefficient [41. This is due t o a balanced

154 generation and destruction of reaction layers (figure 1).

Figure 1: Friction conditions Using friction for velocity traction or braking, the zones A to C are the most important ones. GODET et al. call them as the jest", which is not enough investigated and understood [ll.

A constant and high friction coefficient is the most important aim for the development of rubbing materials. Supposing the two mating bodies are brought into contact (i.e. loaded) at a certain relative speed at the starting point of the friction process, liquid lubrication between the two first bodies is significant for the regime. The conditions of lubrication change with increasing load to semi liquid friction and to boundary friction, which is the goal condition for this application. The primary task of the tested friction layers and materials is to guarantee a high and constant friction moment and avoid wear. For this reason attention is paid to the transition from semi liquid friction to solid body friction, particularly to the changes and behaviour of the third body as a function of the load regime and the intermediate body.

1.2. Test apparatus and test samples The principle of the measuring unit is shown in figure 2. The test rig is based on the twin disc principle. The basic body is fixed on a clamping unit which is connected

with the friction measurement device. The counteracting disc is driven by a motor unit at the desired rotating speed. The center of the fixed basic body is connected with a separate lubrication tank and so the gap between the friction plates is supplied with a lubrication liquid respectively cooling liquid. The fixing devices of the discs are electrically isolated from each other and from the bench, and electrically connected to the measuring device. A voltage signal for the HIFIMS is transmitted to the disc in motion by means of a coupling capacitor. The test body (first body) is a steel disc with a porous friction layer, which is made of a blend of different metal powders. A steel disc is used as counteracting body with a Universal Tractor Transmission Oil (UTTO) as intermediate liquid.

Figure 2: Measuring unit application on a Disc-Friction-and-WearApparatus 2. DESCRIPTION A N D APPLICATION

OFTHEHIJ?IMS 2.1. Electric circuit arrangement

The ,,heart" of HIFIMS consists of a HFoscillator, which oscillates as a function of the electrical impedance connected to the oscillator input. The HF-oscillator drives two external capacitors at a frequency of 100 kHz up to 10 MHz. One of the capacitors (C,) is formed by the metal mating samples and the intermediate liquid. The oscillator frequency

155 depends, on the one hand, on the distance of two electrical conducting metal surfaces and

of the lubricant performance, on the other hand, on the series capacitor and additional parallel capacitors. Using an additional series capacitor a precise adjustment is possible, which means a higher resolution in the relevant measuring range. Thus a detraction of intermediate liquid is avoided and a falsification of the measured value is excluded (also if there is only a small clearance between the two plates and the gap is filled with a nonconducting dielectric), because the measuring voltage on the series capacitor decreases to very low values and thus avoids critical electric field intensities. This means that errors can be avoided.

Parallel coupled series capacitor enables a suitable working range of the oscillator frequency. An adequate choice of this parameter is important, because resonance effects in the electrical measuring circuit may occur and lead to unsatisfying conditions and to an ,,inverse“ measuring behaviour. A determination of the working frequency just before starting the measurement is necessary t o find the optimal performance.

of the ohmic part. If there is only a small gap between the two first bodies, especially at conditions of semi liquid friction or boundary friction, the ohmic part of the impedance dominates. The value of the capacity is determined by (Using a geometric model of infinite plates under simplification and of ideal conditions)

>

the geometry of the two rubbing surfaces (electrodes),

> >

the space between them and the electrical dielectric.

characteristic

of

the

Nonconductive boundary layers build up a multilayer capacitor, as shown in figure 3. 2.2. Interpretation of the high frequency signal The signal of the HF-oscillator is the output frequency which is influenced by the impedance input. Looking only the dominating part of the impedance by liquid lubrication, one can get the relation shown in equation (1). fo

“c1

(1)

The total capacity C is calculated by the equation (2):

C = ‘M

*‘S

(2)

+ S‘

Equation (1)and equation (2) leads to the f, characteristic which is shown in figure 4. The total capacity C varies in a defined range, which is limited by following two extreme values.

>

Maximum capacity C,, (C, -> infinity) by short circuit of the measure impedance (full metallic contact between the rubbing parts).

>

Minimal capacity C,, of the measure impedance at a certain film thickness (= calibration point (Y);lubrication film

Figure 3: Tribological contact During liquid lubrication the impedance , evaluated by the high frequency oscillator circuit consists of the capacity part as well as

156 separates completely the two rubbing parts). Thus the minimal capacity can be expressed as: (3)

distance (at a certain gap width). Decreasing frequency indicates a smaller gap or that there are more ,,disadvantageous" friction conditions, e.g. semi liquid friction or boundary friction. Thus, under defined conditions, the generating of a boundary layer onto an electrical conductible friction layer may be measured and described by the change of the electrical impedance between the basic body and the counteracting body. The generation of a boundary layer leads to an additional increasing of the reference frequency. This behaviour can be explained by the oscillator circuit. A simple equivalent circuit is shown in figure 6.

Figure 4: Characteristic oscillator frequency vs. total capacity Trigger

Yet one can determine the variation of the capacity as a function of specific geometrical parameters as well as of the specific electrical characteristics of the lubricant. The relation for the tested rubbing couple is shown in figure 5. Figure 6: Equivalent circuit of the HIFIMS

d 1

0 solid body

Cantact

oapacltor discs di8tancfi

m1

100 calibration distance

Figure 5: Oscillator frequency vs. capacitor disc distance The slope of the curve (figure 5) depends on the relation d to A. The reference frequency f, one gets at the calibration

The boundary layers behave as series resistance Rs to the total capacity C. Because of an appearing voltage drop across a resistance R, during the discharging/ recharging process of C, as a function of the direction of the alternating current, the switching threshold of the inverter will be arrived earlier and this leads to an increase of oscillator frequency f,. The amount of the frequency increase is a function of RJRFratio. From the decreasing frequency output of the HF-oscillator one can assume semi liquid conditions and an increasing frequency output to the generation of a boundary layer. The material constitution and thus the impedance of the third body are also

157

distinctly influenced by different additives of the intermediate body. In opposition to the HIFIMS other measuring systems probable show a measurable increase of the friction coefficient to late, because of inertia effects of the test rig. Though sophisticated measurement techniques are available, an optical wear measurement in order to detect material transfer between the basic body and the counteracting body is usually done afker the test. In both cases one cannot determine the start of wear process exactly enough.

3. ADDITIONAL INVESTIGATIONS FOR THE INTERPRETATION OF THE HIFIMS RESULTS

For the interpretation of the HIFIMS results, additional investigations to describe the behaviour of the third body in the layers concerned are recommendable. Indeed at I F " surface structures of the friction layer (e.g. optical analysis, scanning electron microscope, figure7 and figure8) and permeabilities of the sintered friction coats are analyzed before and aRer the test run.

Figure 7 shows a distribution of material elements onto the surface (porous layer) of the first body. It was determined by scanning electron microscope and energy dissipation spectroscopy. 3.1. Significancy of the pores in the

friction body The tribological behaviour of porous friction bodies is mainly influenced by the system of pores (figure 8 and figure 9). The pores enable the liquid intermediate body flow in the contact zone. Thereby in the boundary friction zone (figure 1, zone B) the quantity of pores (relation between pore volume and body volume) and also the quality of the pores (size, geometry and frequency of the pores) are of great importance to prevent from hydrodynamic lubrication. No or little porosity favours hydrodynamics and thereby a reduction of the friction coefficient may occur [5]. A comparable situation occurs if the pores are closed with wear particles, dirt or particles of oil crack process. 3.2. Determination of the pores size

distribution The estimation of the pores geometry onto the surface of porous layers is possible by microscope analysis.

Figure 7: Distribution of material elements (surface of first body)

Figure 8: Pores structure on the contact zone (bright zones are pores)

158 smooth surface and the pore) [91. The values derived from the material portion curve are only an integral parameter and thus only one part for a correct interpretation of the surface profile (figure 10 and figure 11).

DU=-U Ic

4* A

Dh =-

U

Figure 10:Roughness profil along one surface line

Figure 9: Pores size distribution For this purpose an image analysis system is used at the IFWT. The system consists of a micro position desk, microscope, video camera, control monitor, computer and a special analysis software.

3.3. Roughness measurement The surface topography represents a three-dimensional stochastically distributed amount of asperities and grooves as a function of the production process. The topography in the contact zone of the basic and the counteracting body influences the time interval1 between the partial destruction and the new generation of reaction layers. Thua the conformity of the roughness on the contact zone mainly influences the generation of the third body and the tribological behaviour as well [61. The essential features of the surface profilometry are described in DIN 4768 [71 and DIN 4776 [8].But the description of a porous layer surface by the data output of a modern profilometer is not sufficient, The shape of the material portion curve is particularly determined by the geometry of the pores (size and number of pores along the measurement line as well as the geometry of the pore edge at the transition between the

0,lO

nm

Figure 11: Material portion curve [ABBOTTI (figure 10) 3.4. Permeability measurement

The estimation of the integral effect of the pores or the structure of the pores to describe the properties of material and structure is possible by measuring the permeability of the porous body. Permeability can be determined by a measurement system which was developed at IFWT [lo]. For the relations between permeability and tribological behaviour (load carrying capacity, transition speed) there are several theoretical approaches, but it is not possible to determine an exact relation, because of the technological conditions (e.g. the inhomogeneous pressure distribution).

159

4. TRIBOLOGICAL TEST AND

MEASUREMENT PROCESS 4.1. Test set up The basic body is pressed by a static load against the counteracting body which is rotating at a chosen speed of maximum 50 s.'. Specific pressure of 0,33 MPa is reached with a maximum load of 750N. The resulting friction torque (maximum 22,5Nm) is measured using a spring bar with strain gauges.

With the HIFIMS a metallic contact, and thus the intensity of wear process, are detectable by a decreasing output signal. An in-situ measurement is thereby possible.

FRICTION TORQUE SIGNAL

HlFlMS SIGNAL (OUTPUT FREQUENCW

Under these conditions the measured friction coefficient was in the range of 0,08to 0,12. While measuring the friction torque, the output frequency of the HIFIMS is measured, too. The lubrication temperature which rises up to 130 "C till 150 "C, is measured with a thermo couple near the gap between the two discs. 4.2. Test results For users of tribological systems it is important to detect metallic contact in the tribo-system concerned. The friction torque and thus the friction coefficient usually cannot clearly indicate critical tribological situations, yet results from the HIFIMS show that changes in the friction coefficient correlate with HIFIMS signal changes (figure 12).

Physical and chemical variations of the intermediate body or of the friction layers respectively, which appear during the friction process, lead t o a change in the impedance, in some cases advantageous slightly before the coefficient of friction announces a remarkable change in the tribological conditions. From the decreasing frequency output of the HF-oscillator one can assume ,,disadvantageous" conditions and an increasing frequency output to the generation of a boundary layer. Boundary layers, which are formed by physical and/or chemical reactions, are destroyed by solid body friction process and wear particles.

HIGH-

LOW

Figure 12: Measurement results

5. CONCLUSIONS

The HIFIMS may indicate the changes of the third body during a certain period of motion with constant velocity or a single cycle with starting from a certain relative velocity till stand-still contact of the mating couple. One may also detect the modifications during several repetitions of this process (i.e. running-in-process). Limited application of the HIFIMS is recognized if the conditions of the measured

160

system may shift from mild abrasive wear to severe abrasive wear. An interpretation of the HIFIMS signal for special test situations is possible but one cannot correlate it clearly enough t o surface effects, thus further works are needed to explain several behaviours of combinations of lubricants, additives, geometry, load, temperature and other parameters. We will do this works in a new research project which starts from december 1995.

NOTATION f

[-I

fcJ

[sY

C

[Fl

C, C,

[Fl [Fl

d A R, Rp

[ml [m'] [QI [QI

friction coefficient oscillator output frequency total capacity series capacity measuring capacity capacitor disc distance surface of capacitor series resistance feedback resistance

REFERENCES [l]M.Godet, Third-bodies in tribology,

Wear 136, Elsevier Sequoia, The Netherlands (1990). [2] F. Franek and G. Abraham, Equipment for measuring the distance between at least two elements in relative motion, European patent 0412974 (1988). [3] G. Abraham, F. Franek and J. Ebrecht, Evaluation on lubricant quality by monitoring the electrical impedance of

lubricating film, Proceedings of the 6* International Congress on Tribology, EUROTRIB '93, Budapest, Vo1.4, Pages 99-105 (1993). [41 G. Polzer and F. Meiher, Grundlagen zu Reibung und Verschleifi. VEB Deutscher Verlag fur Grundstoffindustrie Leipzig, 2. A d a g e (1982). [51 A. Jullien, Y. Berthier, D. Menard and M.H. Meurisses, Behaviour of wet clutches operating under continuous running conditions with a new carbon based material, Proceedings of the 18* Leeds-Lyon Symposium on Tribology, Leeds University, Pages 303 312 (1990). [61 J.A. Williams, Engineering Tribology, Oxford University Press (1994). [71 DIN 4768, Ermittlung der RauheitsmeRgroRen Ra, R,, Rm, mit elektrischen Tastschnittgeraten. [81 DIN 4776, KenngroSen zur Beschreibung des Materialanteils im Rauheitsprofil(1990). [9] A. Pauschitz, W. Zhang, A. Matzner and F. Franek, Oberflachenbeurteilung und Rauheitsmessung an tribologischen Funktionsflachen von Sinterteilen, Vortrag Tribologie-Fachtagung 94, Gesellschaft fir Tribologie: Reibungsund VerschleiRminderung in Maschinen und Anlagen. Gottingen (1994). [lo] F. Franek and A. Matzner, Quality Parameters of PM-Part's Structure with Respect to Tribologic Behaviour, Proceedings, 6* International Congress on Tribology. Eurotrib '93, Budapest, Vol. 5, Pages 441 - 446 (1993).

-

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

161

A ball-in-socket apparatus for the test of hip joint prosthesis.

Influence of the third body on the friction behaviour. F. Bernard, C. Annarclli, J. Bcn, J. Dupuy-Philonand J. Fornazero. DCprlcmcnt Physiquc dcs MalCriaux, UnivcrsilC Claude Bernard - Lyonl ,69622 Villeurbanne CEDEX,France R. C'ohcn Laboratoirc dc Biophysiquc, Facult6 dc Pharmacie, Universitk Lyon I, France

Expcritncnts arc run with alumina/alumina hip implants in order to investigate the influence of a third body on thc friction bchaviour of thc proslhcsis. Thanks to thc vcrsatility of the physiological test rig developed in the Ddpartcinctit dc Physiquc dcs MatCriaux, various mcchanical and lubricating conditions were allowed to be applied to thc prosthetic couplc. I1 appcarcd that depending on the mechanical test conditions, the mating surfaces can cridurc scvcr dctcriorations due to rclcasc of alumina grains. The interaction between the lubricant and the surlacc mawrial can bc ol'grcat impormcc as wcll, as found with a salinc solution supplemented with additives (protcins),coinparcd U, lubrication with a simple saline solution.

1. IN'I'RODUCTION

Chi purposc to charactcrizc matcrials uscd for ptostlictic hip joints, it is now admitted that

physiological tribological tcst conditions are coinpulsory. Sincc most of thc simulalors currently dcscrihcci in thc litteraturc havc only onc or two axis ol' motion I1,2,3,4],an applicd load which docs not correspond to thc physiological onc I11 or even an sockct that is situatcd undcr thc ball I1,3,4,5], we dcstgncd an apparatusallowing thc thrcc-dimcnsional molion of a ball-in-stxkct contact 161, to reproduce accuratcly thc sollicitations cndurcd by thc human hip. Thc physiological conditions arc fullfilled through the typc of lubrication, the applicd load and thc typc of motion (spccd and amplitude of the niovcmcnls). The first cxpcrimcnts wcrc run with an alumina/alumina couplc. This couplc is said to be one o f thc most cfficicnt for prosthctic application, duc to iLs vcry high mcchanical characlcristics and its vcry good rcsistancc to thc agrcssivity of the physiological mcdium. Thc aim of this study was to point out thc inilucncc of thc tcsting conditions on thc friction bchaviour or lhc couplc. This was pcrinittcd by thc vcrsalility of thc simulator, which allowed us to apply various mcchanical test contlitions, as wcll as by ihc usc of two kinds of lubricant, sincc it can act as a third body. The intcraction of thc lubricant with thc mating surfaces

is in that case of great importance in the friction behavior 17, 81, hcnce it was investigated prior to the tribological test, by means of wettability measurements. 2. MATERIAL AND METHODS 2.1. The tribological test rig 2.1.1. Apparalus The ball-in-socket apparatus was developed in the laboratory for the wear test of materials for total hip joint replacements. The in-vivo behaviour of such couples is best approached when studied on a model reproducing thc hip movements and h e load endured by a prosthesis while inside the human body. Therefore we designed our simulator according to the advice of orthopaedic surgeons. It presents the following specifications:

- acetabular cup on top of the femoral head. - 3 movements corresponding to the three axis of motion of the joint: flexion-extension,abductionadduction and internal external rotation (figure 1). - variable speeds and amplitudes of the movcments. - lubricant maintained at 37"C, filtered throughout the test and made of a saline solution (0.9% NaCI) with or without additives (proteins). - load applied by means of a pneumatic power system controlled by a computer. We can thus reproduce any kind of sollicitations.

liltlustrial prtncr: MEDINOV (M. Colombicr, J.M.Pcguet), Roannc, France

162

Abduction 3otaiion Lubrican L: 37°C fi I tcrcd

)=Load 1

igure I : Situation of Ihc hctlring couplc inside the sim tilator

This simulator pcrmits thc mcasurcmcnt of a I'rictioii couplc C along thc flcxion-cxtcnsion axis at

givcn time by mcms of a strain gaugc transducer. 7'11~applied load F is mwsurcd at thc siunc time. We ; I

diuh

tlcl'inc a I'riction cocl'ficient p:

2.1.3. Experimental procedure Three different conditions were used in order to generate various third bodies. They were issued from a combination of various loads and various lubricants. The computer controllcd pneumatic system enable us to reproduce the load applied on a hip joint during a normal walk, according to the results obtained by G. Bergmann et al. [9], as shown in figure 2. This type of loading together with appropriatc amplitudes of the movements are called the physiological Lest conditions. Harder conditions were also applied, which consisted in a constant 1200N load and wider amplitudes of movements. This value of 1200N is approximately the average load applied on the hip of a 600N person walking at a normal speed. This situation will be further called the cxtremc test conditions. For both tests, the averagc frcqucncy of the movements was set to 0 . 8 3 k wich is supposed to bc the mean walking freqWCY.

- Physiological load (N)

I

p=- C

o

Simulator I d (N) . .

R. F Whcrc R stands for thc ball radius. Othcr paramclcrs arc acccssiblc as well, such as the pH and thc Lcinpcraturc of thc lubricant and the rcsl pltcntial of thc mcullic implants 161. 2.1.2. Couple resred Thrcc aluinina couplc wcrc tcstcd, with roughly the same dirncnsions and surfacc finish (Lablc l), in ordcr to cxcludc any olhcr sourcc of diffcrcnces in the rcsults than thc mcchanical conditions and the nature ol' thc lubricant. Thc mcan arithmctic roughness is less than 0.0Spm for all thc iinplanls.

2*rh 2*rs dr

Tcst 1

Tcst 2

Tat 3

27.990 28.044 0.027

27.950 2H.037 0.044

27.958 28.040 0.04 I

'ruble I

Diiiiciisions of thc Alumina/Alumina couplc. rh-=h;iIt radius, r,=sockct radius, Ar=diffcrencc of the r i i d i i . Mrasurcincnts arc givcn in mm.

During thc wcar kst, thc cups arc hcld in the siinulator by mcans of orthopacdic ccmcnt (p)lyiiicthylmclhacrylalc).

0

04

0.8

Time (I)

1.2

1.6

I 2

Figure 2: Comparison of the physiological load applied during the wear test and the physiological load measured by G. Bergmann et d. I91

The couples studied under physiological and extreme test conditions were lubricated with a saline solution. A third type of test has been performed under physiological test conditions with a lubricant supplemcntcd with proteins, in order to approach more closely the in-vivo situation of a hip joint. This type of lubrication is standardzed. As a matter of fact, according to the I S O m 9325 (November 1989), thc lubricant should consist of bovine Serum dilulcd thrcc timcs and addcd with a bactericid agent and kept at a physiological pH. Furthermore. this solution should be kept frozen until use. Few authors used such a lubricant [10,11,12],

163

Amp1i tudcs

'I'cst I Tc.st 2 Tcst3

Lubricant

Ilcx-cxt

atxl-ruld

int-cxt rot.

40P SW

5(r

10"

1OP S(P . 10P

4r

10"

saline solution salinc solution saline solution+ proteins

Load physiological constant physiological

0.83Hz 0.83Hz 0.83Hz

'lahlr 2 'I'CSI conditions cntlurcd by thc aluniina/illumina couples

but it docs not sccm to us that it is thc bcst fluid Ibr physiological wear tests. As a maltcr of fact, hovinc scrum is a complex mixturc which may be difl'crcnt from batch to batch. Thcrcforc the rcproducibility of such a scrum is difficult LO ensure whi Is conducting cxpcrimcnts. At last, according to the I S 0 standard, the lubricant should have properties similar to Lhose of thc synovial fluid. But the liquid surrounding thc prosthetic joint in thc human body is still unknown ilnd its charactcristics might bc difrcrcnt than those cxpcctcd. One can think anyway that protcins are present, and cspccially serumalbumin, sincc this ubiquitous inolcculc can bc met in any cxuaccllular mcdiuin. The dcnaturation of' the protcins can lcad to thc itggrcgiition ol' thc molcculcs, which is likcly to modil'y thc friction rcsults. Thcrcforc our aim was to SCI up ii solution close to the onc that may be ciicountcrcd in the human body, in Lhc surrounding ol' llic prosthcsis, and with a satisfying stability in order to run the simulator for a ling timc without chonging the lubricant. Furthcrmorc, this solution hid lo he easy to rcproducc from one cxpcrimcnt to thc odicr. Hcncc thc lubricant uscd in test 3 was a phosphate buffcrcd sali nc solution (pH=7.4) containing bovinc scrumalbumin (BSA) and antihiotics in ordcr to maintain a physiological pH ml inhihit microbial prolifcration. Thanks to this wlirtion. no dcnaturation of' thc protcins could bc noticed bcl'orc 400,000 cyclcs which means approximatcly IS days of tcst. Af'tcr that timc, the lubricant had to bc changcd. The tcst conditions of the thrcc cxpcrimcnts are suinmarizcd in table 2.

2.2. Viscosity measurements In ordcr to point out the changc in viscosity rclatcd to thc presence of bovinc scrumalbumin, we

used a simple viscosimeter of the falling ball type. The viscosity is givcn by:

Wherc q is the dynamic viscosity (Pas), t the time of the ball fall, ps the density of the ball, p the density of the fluid and K a constant that is calculated with a fluid of well known viscosity. After calculations with demineralized water, the preceding equation bccomcs: "rl3.397.10-6(8.02-p)t

2.3. Wettability measurements Thc wcttability of a material surface has a non negligeable influence on the friction behaviour of a tribological system and is an indicator of its biocompatibility as well: the more the material is wcttablc, thc better it is tolerated by the human MY. 2.3.1. Method of the sessile drop The solid/liquid intcrfacc is charactcrized by two physical parameters: the liquid surfacc tcnsion 0 and the contact angle 8 (figure 3). 8 depends on the value of the surface tension comparcd to the solidlliquid adhesivc forces; the higher (r is, the less thc material surface is wettable. Thesc two parametcrs are strongly dependent on tcmpcrature, liquid phasc composition, vapor phase composition, nature of thc substrate and size of the drop. 2.3.2. Experimental procedure The test conditions are kcpt identical from one tcst to another, in order to prevent any perturbations and to cnsurc the rcproducibility of the measurcmcnts: - room tcmpcrature (22°C Lo 24°C)

164

I'irtcire I : Swlircc finish ol ihc I H ) I I ~ I I I ~w a i c l i c s .

luw)riil

hcad al'icr icst 1. Highcr concentration o f rcmovcd grains can bc wen along

obtitincd for sphcrcs truncatcd "abovc" thcir cqualor as wcll; thal is for valucs of thc contact anglc lcss than 90". This cquation supposcs that thc volumc rcmains constant. This is controllcd through the mcasurcmcnt of thc hcight and thc surfacc of thc drop.

- siiinplc and droplcl maiiitiiincd in an argon auiiosplicrc ( I am). - drop volurnc: I SpI - 0 incasurcd at t=O. 2 and 5 ininulcs in ordcr to ohscrvc the evaporation of the drop. 0 is dctcrmincd at t=?inin, hcausc thc droplci in then subilizcd. - surl'acc finish of the llat suhstratcs idcntical to tha1 of the prosthctic implants. - itic surfaccs arc clcancd kliirc cach tcst with inctliatiol and distillul watcr. - I'iw nicasurcincntspcr wmplc. Thc conlac1 anglc is caculatcil according to thc mcllicxl tlcwribcd by Young I13 I: cos c)

:

.

(

2 nh3

-

q$

f

3]

With I' the volumc o f the drop and h thc drop IwighI. To ;I I'irsi approxitnation, drops ol' liquid on a ~ ) l i I i I ~surfxc b which is not wcttcd hy lhc liquid i1sslllb\c it sliilpc similar 10 dial of a truncatcd sphcrc

that ih wincwhat fattcr around the equator ban a uuc trutic'iitqd sphcrc. Thc abovc expression can hc

3. INFLUENC'K OF I H E MECHANICAL CONDITIONS Thc cvolulion of Lhc friction cocflicicnt is plotid with rcspcct to thc timc cxpresscd in million cyclcs, considcring that it Lakcs 1.2s to cornplclc a full cyclc. Sincc thc mcasurcmcnts arc donc in a discrctc way, onc will scc that thc cxpcrimcnlal data appcar as a points cloud, which givcs a statistical crror. 3.1. Results Thc rcsults oC icst 1 and tcsi 2 arc shown in figure 4. Onc can scc that thc cvolutions of the friction cocfl'icicntarc toully diffcrcnt.

3.I . 1. Physiologicul simulation At thc bcginning of thc tcst, thc valuc of the friction cocfficicnt is quitc high (0.12), but il dccrwscs rapidly to rcach a valuc of 0.03 after 0.4 million cyclcs. This cvolulion rcmains on its dccrcasing slopc until thc cnd of thc tcst, which ukcs placc altcr 2 million cyclcs, whcrc p is a litllc lcss than 0.02 (rcal valuc: 0.016).

165

0

0 .

00

0.

mo

. 0.5

I Million cycle\

1.5

*-

7

L

Figure 4: Expcririicnlitl results of tcsts 1 and 2. Friciion cocl'ficisni ;IS ;I function of tinic. ( )ptical observations of

Lhc couplc after the w a r show little damage o f thc hearing surfaccs (IJicm-c I ) . Scvcral missing alumina grains can bc PL*'CII. 7'hc.y arc distributed hoinogcncously on thc wlacc. with ncvcrthclcss it higher conccntraiion uloiig scratchcs. Thcsc lines arc attributcd to thc polidiing ot the surl'acc kl'orc the tcst, sincc thcy ;ippciir inucli lhinncr that thc avcragc siLc of thc t i k i n g grains (5 to IOpm). OIW will noticc two pciiks iit 0.1 and 0.25 w l l i o i i cyclcs. AI'tcr picturc I , onc ciin attributc Ihcii) to aluinina grains. hut thcy could hc duc to 1;viiitxt piirticulcs as wcll. ICSI

2. I 2 . Exlreme condilions sirnululion Thc first valuc of p is around 0.05, and its cvolution exhibits a lorming pcriod that lasts 0.3 million cycles, whcrc p is cqual to 0.035. Such a period was not appcarcnt during the physiological simulation. The lowcst l'riction mcasurcd is 0.01 after 0.1 million cyclcs. Thc valuc of 0.035 is slilbilizcd until I million cyclcs, whcrc it starts to risc. Al'tcr 1.6 million cyclcs p is alrcady 0.06 in valuc and thc couplc starts scixing up. Aftcr 1.8 million cycles, Lhc scizing is tolal (crcaking sounds wcrc hcard) and p is more Lhan 0.1 2 in valuc. Thc optical magnifications of thc two implants havc nothing in common with those of thc physiological simulation (picturc 2). In this casc, thc surfaccs appcar scvcrcly damagcd. Numcrous holcs can bc sccn as wcll as scratchcs due to thc trapping o f alumina grains bctwccn thc rubbing surfaccs. Thc avcragc sixc of thcsc grains is around 20 to 40pm. Discussion Aftcr thc picturcs, i t appcars that numcrous alumina grains wcrc rubbcd out in thc casc of thc cxtrcmc test conditions, lcading most probably to thc high risc in friction altcr 1.8 millions cyclcs, cvcn with an uppcr cup situation. Sincc thc contact mcchanics rclatcd to thc simulations arc vcry complcx, only simplc idcas arc given hcrc as a first cxplanation of thc phcnomcna observcd.

3.2.

(a) aluniin;~cij)

I'icturcs 2: High tlctcrioration of ihc iii;iting surraccs a

(b) alumina femoral head h t&t 2.

166 3.2. I . Conrucl geornclry Evcn il' thcrc arc aspcritics on thc surfaccs and the contact IS lubricatcd, thc Hcrw thcory is uscd to inotlcl thc contact gcomctry I 14,lS 1. Considcring at l i n t that thcrc is no movcmcnt, thc dcformation of thc \urlilcc undcr thc applicd load lcads to a circular sllrtilcc ol conkict (figurc 5 ) of radius u such as:

Wlicrc I; stands for the applied load, E thc Young's modulus and v thc Poisson's ratio. Siiicc tlic movcmcnts arc altcrnativc, cach timc h * y stop altogcthcr thc mating surfaccs find iliciiisclvcs in lhis situation. Whcn thc motion starts again. it seems that thc most strcssfull inovcmcnts iirc thosc of roution and abduction. According U, G. Hainillon I Ihl, whcn sliding ukcs placc a maximum tensile strcss dcvclopcs at thc back cdgc of the ct)llIilct, lor x=-u and y=z=O (figurc 5 ) considcring a clockwise rotation of thc ball. Sincc thc amplitudcs 01' thcsc movcmcnts arc much highcr in thc case of thc c'xtrcinc tcsi conditions, this will rcsult in a largcr area of thc bcaring surface cnduring thc high triisilc strcsscs. Thus thc likclihtwd of a failure, of grailis removal, is incrcascd in this lattcr casc. Purthcrniorc, thc cyclic supprcsion of thc load in tcst I Icads to lowcr strcsscs, comparcd to thosc duc to tlic conslant load of tcst 2. It sccins that thc diffcrcncc ol' congrucnccs (table I ) docs not play any rolc, sincc almost the same friction cocfficicnt could bc mcasurcd until one million cyclcs, whcrc scizing up Likcs placc. 3 2 . 2 . Rcbrive speed The rclativc spwd of thc mating surfaccs has no inl'lucncc on thc strcsscs dcalt with abovc, but is of ; Igreat inil)orlanccin thc risc of hcat duc to friction. Sincc tlic ccrimics arc poor thcrmal conductors, this risc in tciiq)cruturc at thc contact can damagc thc grain joints and rcsult in thc rclcasc of thc grains 1171.

'l'hc variation ol' spccd ol' the movcmcnts is a siiiusoitlal law of thc timc. Thc maximum angular v i l l l l ~is ~ given hy:

GM= Ann With A the ainplitudc and 'I' the pcriod of the consitlcrctl movcmcnt. If we considcr only onc of tlicsc inovcnicnts without any motion of thc stxkct, ~Iiciii;IxiiIiuiii rclativc spwd is:

L

Figure 5: Enlargement of the surface of contact between the ccramic ball and cup.

According to Bowdcn and Tabor 1181, a lower value of the risc in temperature can be reached through the following cquation, which does not take into account the fact that there are aspcrities in the contact leading to high flash thermal cxcursions:

Whcrc F stands for the applied load, Pm the mean pressure (F/7ta2),g thc constant of gravity and k thc thcrmal conductivity. Thus we can calculate the ratio ATdATp, where ATe is thc thermal cxcursion under severe test conditions and ATp the one under physiological condiLions:

Which gives a value of 6 at 0.8 million cycles. This rcsult has been calculated using the maximum rclative specd. In fact, the presence of the salinc solution leads to a lubricating film that separates the two surfaces. As a matter of fact, the evolution of the friction couple during the flexioncxlcnsion movcmcnt reveals two phases (figure 6). During lhc first third of each semi-cycle, one can see the high friction due to boundary lubrication conditions. Thcn the friction dccreases because of a fluid lubrication duc to a highcr speed [18,191. Lct us suppose the same typc of lubrication for the sliding movcmcnts. The highest rise of

167

kiiqwraturc will lakc placc during this first third of Ihc .wtni-cyclc,whcn thc spccd is not thc maximum o i i ~ > From . thc prcvious cquation wc thus obtain ATcz7ATp. This ratio could bc high cnough to cxplain partly thc grcatcr gcncration of alumina grains under cxirctnc tcst conditions, by cnhancing thc initiation of dcfccts in lhc wcakcr grain bondarics. ~~

~

tribological system, we introduced additives in the lubricant of a third experiment (table 2). 4.1. Wettability measurements

Thc wcttability experiments (pictures 3-a and 3b) show a greater contact angle of the saline solution supplemcnted with proteins. The results (table 3) indicate a significant decrease of the contact angle with h e protein supplemenlcd lubricant (student t test: t=3.36, ~ 1 % ) .

liiction couplc

Picture 3-a: Saline solution droplet

Figure 6: Evolution o f thc friction couplc along the flexion-cxtcnsion axis. 1 : bondary lubrication. 2: fluid luhrtc;ilion.

2 2 . 3 . Condusion 7'hc cxtrcmc tcst conditions rcsult in a highcr libclihtx)d of failurc bccausc of widcr amplitudcs of sircwfull sliding friction of thc ball in thc socket. Fiirthcrinorc this is cnhanccd by a much highcr rise in icinlxraturc duc to fastcr rclativc spccds of h e c.lcincnts.Thcsc charactcristicslcad aftcr onc million cyclcs to thc rcmoval of alumina grains. These grains will hclp in a furthcr dcgradation of the b r i n g surfaccs by inuducing high strcsscs in the contact. Thcsc damagcd surfaccs cxhibit a higher liliclihood of aspcrity contact, which could be an cxplanation to thc scizing that tcwk placc aftcr 1.6 million cyclcs. Tcinturicr ct al. 151 madc thc same ohscrvation during lhcir study of alumina couple; it was run with a similar simulator (thc sockct being bus bclow thc ball) and it lcad to ncgligeable wear 01 thc mating surfaces until thc spccd was increased ovcr IOmm/s, whcrc lhcy got scizing of the couple. 4.

INFLUENCE OF THE LUBRICANT

In ordcr to invcsligalc thc influcncc of lhe nature of thc third body on lhc friction bchaviour of the

Picture 3-b: Droplet of saline solution supplemenlcd wilh additives. Naturc of the solution Saline 8 mcanvaluc 60.2" 1.7O SD

Saline+BSA Saline+BSA initial 0.5 M cycles 53.4O 4.2'

77

mcan valuc (Pas* I 03) 1.O49 SD 0.0528

1.161

1.156

0.0545

0.0360

Table 3: Wettability and viscosity measurements.

This phenomenon can be observed in the friction couple measurement curves. The friction coefficient is measured after the mean value of C, which acquisition lasts four to five cycles (figure 7). One can see that during lest 1 measurements, the friction couplc rapidly exhibits a shape as shown in figure 6, with a proeminent phase 1 (figure 7-a and 7-b). On the contrary, this phase cannot be observed during

168

Salinc solution N.ni

0.012 million cyclcs

Saline solution 0.741 million cycles

N.m n

-3

N.111

Sulinc solution t RSA 0.015 million cyclcs

tl

100

200 300 400 1/I 00 swonds Figure 7-b: test 1

I

500

Salinc solulion + BSA 0.737 million cycles

N.m

2r-----7 I 1 1

0

0 .

I 1

L

.

-1

-2

’

1/100 sccontls

Figure 7-c:

test

.

1/100 seconds

3

Figure 7-d: test 3

Figure 7: Evolution ol‘ llic friction couple during Lhe measurement of experimental points.

icst 3 iiicasurcincnts (figurc 7-c and 7 4 . Thcsc Icsults can lead to thc conclusion that thcrc is no

chaiigc in the lubricating conditions in thc casc of t~”si 3 . I n order to give an cxplanation to these obscrvaiions, data about thc plasma protcins havc lo bc lakcii into account. Thcy can he considcrcd as spherical molecules of 10 to 20 n m in diarnctcr w i l t i ii Icntlcncy to adsorb on matcrial surfaces, as showii tiy Ihc wcttability incasurcincnts (tablc 4). As ;I iiiattcr o l fact, the scrun\ulhuinin consists of a siriglc chain madc of amino-acid groups linkcd Logclllcr by peptidc bonds. This chain is foldcd on ilscll Ihanks to weak bonds (hydrogcn, Van dcr Wilals) and strongcr disulfidc bonds 1201. Thcse

polar groups will be able to adsorb on charged surfaces, which is thc case of alumina, that exhibits A13+ and 02sites [21]. Since thc roughness R, of the mating surface is less than 0.05pm, one can then imagine that the protcins will be able to fill the valleys, and act as a cushion, thus prcventing asperity contacts at low rclativc speed, and allowing thc friction to be constant during a semi-cyclc. This cffect can be cnhanced by thc denaturation of the proteins. Thcsc globular inolccules can bc disrupted under the high charge density that arises at cxlreme pH values [221, or under tcmperaturcs higher than 70°C. If this happcns, they loose their spherical shape and tend

169

to aggrcgutc. But the pH rcinaincd constant around thc istlclcctric point (pH at which thc protcins arc no11 charged and stablc) throughout thc tcst. Mirthcriiiorc, thcrc was no significant changc of thc viscosity of thc lubricant, froin thc beginning of Ihc tcst until 0.5 million cyclcs, whcrc thc solution hccainc whilcr. Thcsc obscrvations indicalc that no tlctliituriltion of thc protcins did happen.

4.2. The tribological test Thc rcsults of LCSLSonc and thrcc arc prcscnted in I'igurc 8. The rcadcr can rcfcr to paragraph 3. I. I lOr dclails about the rcsults of tcst 2 with a saline wlulion without any additives. Considering tcst 3, the evolution of p points ciut a forming pcriod o f thc alumina/alumina couplc, that lasts 0.2 million cyclcs. During this pcritxl. one can scc thrcc pcaks (0.01,0.09 and 0.13 niillion cyclcs with p. bcing rcspcctivcly 0.106, 0. I20 and 0.125 in valuc). After 0.2 million cycles (p=O.OX), thc friction dccrcascs until thc cnd of thc ~.cst,whcrc p is cqual to 0.05 after 0.74 million cyclcs. During thc lcst, thc tcinpcraturc of thc lubricant rcmaincd al. 37+2"C and its pH bctwccn 7.3 and 7.4. It had to bc changcd after 0.5 million cyclcs, hccausc it bccamc whilcr.

I.1

o

Saline solution Saline solulion + proleins

').',I 0.12 0. I

II'

() L . - -

0

'

I;,,

- ,

0.5

1

1 .s

Million cyclcs igure 8 : Experimental rcsults or tests 2 and test t i c t i o n cocrficicnl as a function or time.

Thc gcncral shape of thc cxpcrimcnlal curvc is siniilar to thc onc obtained with a salinc solution as a lubricant, with a shift of thc friction ctxfficicnt toward highcr values. One can SCC that pclrks takc placc during the forniing pcriod, as obscrvcd with tcst 1. Both tcsts

have bcen pcrformcd under the same mcchanical conditions, unlikc tcst 2 where no peaks were visible. This can be rclated to the easiness to climinatc particulatcs uappcd between the mating surfaccs. This is morc likcly to happen with high amplitudcs of movcmcnts, which is the case of tcst 2. According to paragraph 4.1., it seems that the lubricating conditions arc more favourablc during test 3, thanks to the prcsencc of proteins. How come thcn that the friction coefficient is higher in that than without proteins. This is probably due to the highcr viscosity of the physiological scrum (table 4). As a matter of fact, this leads to higher shcar sucsscs in the contact, thus incrcasing the friction couple. Furthermore, since the proteins tends to adsorb on alumina implants, one can think that thcy will "link" the mating surfaces. In that casc, energy will bc needed to break the numerous wcak bonds and unfold thc molecules. 5. CONCLUSION

The studies have shown thc great influence of the testing conditions of thc friction and wear behaviour of total hip prosthesis. The differences observed could be relatcd to the gcneration of various hird bodies. In one case it was generated by strong mechanical conditions lcading to high stresses dcvclopcd in thc contact; the initiation of defects being probably enhanccd by a higer rise in tcmperaturc than in the casc of the physiological situation. In an other case, the lubricant itsclf acted as a third body through h c prolcins which were added into it. Thcse proteins were supposed to form a "cushion" between the mating alumina surfaces, thus providing better lubrication. But at the same time, the friction cocfficicnt was found to be twice as high as in the casc of saline solution, because of thc highcr viscosity as well as the ability of the protcins to adsorb on h c surfaccs. Besidc thc fact that generation of alumina grains can have a vcry ncgativc effect on h e friction, or that protcins arc of great importance in lubricating cffects, thcsc results show that the ball in socket alumina couplc is very sensitive to the testing conditions during a uibological test. Hence one should choosc carefully these conditions when rcproducing the physiological situation.

170

111 I)1. I O(; R A PH Y I I I V. Saikko, P. Paavolaincn, M. Klcimola, P.

Sliilis; Proc. Instn. Mcch. Engrs.; 1992, vol. 206, l~5-20(~ 121 V . Saikko; Proc. Insln. Mcch. Engrs.; 1992, vol. 206, 20 1-21 1 131 t1.A. McKcllop, T.V. Riistlund; J. of Biomcd.

Rc's.: 1900, VOI.24, 141.3-1425 131 S. Sandrolini, A. Gatti, L. Cini, P. Caldcralc; in Evaluation ol' Biomatcrials, cd. G.D. Wintcr, J.L. l ~ r i ~ Ky . , dc (;root: 1980, 147-156 151 P. Tcinturicr, S. Tcrvcr, J . Li, A. Taussat, A. Caillot: Rcv. Chir. Orthop.; 1990, zh,383-390. 161 F. Bcrnard, J. Dupuy-Philon, J . Bert, D. Rcmy, R. Moycn and J.L. Bcssc, in "Advanccs i n M a tc r i ;I Is Sc i cn cc and I in p I a n t 0rt ho pacd i c Surgery", NATO AS1 Scric E, R. Kossowsky and N . Kossowsky (cd), Kluwcr Acadcmic Publishcrs, 294 ( 1005) 171 Wc*i-'l'c Lu, J.L. Duda and E.E. Klaus, J. Am. ('crani. Soc., 73(8). 2247-2254 ( 1090) 1x1 (;.M. McClclland, in "Atlhcsion and Friction", M. ( i r u n ~ c and ' H.J. Krcuzcr (cd). Springer Scrics in Surl'i~ Scicncc, Springcr-Vcrlag. 17 (1989) I01 ( i . Bcrginanri ct al. J. Biomcch., 26, No8, 969000 (199.3). 1 101 'I'.Kiistlund, B. Albrcktsson, T. Albrcktsson iIIItl 11. McKcllop, Bioinalcrials, 1 0 , 176-181 ( 10%'))

I11 I H.A. McKcllop and T.V. Riistlund, J. of Biomcd. Mat. Rcscarch, 24, 1413-1425 (1990) 1121 H. McKellop, I. Clarke, K. Markolf and H. Amstutz, J. of Biomcd. Mat. Rcscarch, 15, 619653 (1981) 1131 J.A. Young, R.J. Phillips, J. of Chcm. Education, 43( l ) , 36-37 (1966) I141 D. FranGois, A. Pincau and A. Zaoui, "Comprtcmcni mkcxaniquc dcs matkriaux, Hcrmcs (cd) ( 1993) 1151 Ph. Frain, Rcv. Chir. Orthop., 69(2), 95-10 (1 983) 1161 G. M. Hamilton, Proc. Instn. Mcch. Engrs., 197C, 53-59 (1983) (171 K.-H. Zum Gahr, Wcar, 133, 1-22 (1989) I181 F.P. Bowden and D. Tabor, "The friction and lubrication of solids", Fowler, Kapiua, Mott and Bullard (cd), Oxford University Prcss (1950) 1191 D.F. Moorc, "Principlcs and applications of tribology", Intcrnational Serics in Materials Scicnce and Tcchnology, D.W. Hopkins (cd), Pergamon Prcss, 14 (1975) 1201 Phclps and Putnam, "The plasma proteins", F.W. Pulnam (cd), Acadcmic Prcss New York and London, 1 (1 960) (21I J. Oscik, "Adsorption", Ellis Horwood Series in Physical Chcmislry, Dr T.M. Sugdcn (ed) 1221 C.L. Brooks 111, M. Karplus and B.M. Pettilt, "Protcins", Wilcy Scrics on Advances in Chemical Physics, I. Prigoginc and S. Rice (ed), 71 (1988)

SESSION V NANOTRIBOLOGY

Chairman :

Professor Irwin Singer

Paper V (i)

Nanometer Scale Mechanical Properties of Tribochemical Films

Paper V (ii)

In-situ Measurement of the Visco-Elastic Properties of a Sliding Lubricated Contact

Paper V (iii)

Nanorheological Behaviour of Confined Liquid Layers for Normal Contact

Paper V (iv)

How to Achieve Contact Recording with a Low Stiction Force

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

173

Nanometer Scale Mechanical Properties of Tribochemical Films S. Bec and A. Tonck Laboratoire de Tribologie et Dynamique des SystBmes, URA CNRS 855, Ecole Centrale de Lyon, B.P. 163,69131 Ecully Cedex, France In boundary lubrication, the anti-wear effect of lubricant additives is associated with the formation of films on friction surfaces. The inhomogeneous nature of these tribochemical films makes it difficult to measure of their elastic and plastic properties. The aim of this paper is to report the method we have developed, coupling nanoindentation experiments and imaging procedures, to measure t h e hardness and the Young modulus of friction films. Special care is taken for the calculation of the actual tip/film contact area. We use a new instrument, also designed for friction experiments at the molecular scale and derived from a Surface Force Apparatus. Our experimental procedure includes four main stages performed with the same apparatus : 1) survey of a large area to detect the position of islands and valleys on the surface film with a tapping method, 2) local choice of the indention point with a preliminary image of the surface topography (tangential displacement of the diamond indenter on the surface), 3) indentation with continuous and simultaneous quasi-static measurements of the load and dynamic measurements of the contact stiffness and 4) observation of the residual indent with a second topographic image of the indented area to accurately measure the contact area a t maximum load without having to move the sample. In addition to the optically obtained hardness value, it gives t h e equivalent plastic depth of a n ideal indenter an d t h u s t h e equivalent tip defect and also the correction due to pile-up formation and due to local roughness. The tested tribochemical films were formed in boundary lubrication on a plane on plane tribometer with two lubricants : pure n-dodecane and n-dodecane + 1% of zinc sec butyl dithiophosphate (ZDTP) on AISI 52100 steel. At small loads, there is no pile-up of t h e film formed with n-dodecane (oxide film). On high areas of the film (islands), a t a plastic depth of 3 nm, the hardness of this film is 6.7 GPa and the reduced modulus is about 134 GPa. These properties are higher than those measured in low areas of the films (valleys) where we measure a t the same depth of 3 nm a hardness of 5.2 GPa and a reduced modulus of 106 GPa. On the film formed with n-dodecane + ZDTP, there is a large pile-up around the residual indents, even a t very small loads. The film is heterogeneous : the surface properties are lower t h an the bulk properties and may vary depending on the islands. The hardness, at 3 nm depth, is between 2 GPa and 4.5 GPa and the reduced modulus (at 3 nm depth) is between 78 GPa and 115 GPa. 1. INTRODUCTION

In boundary lubrication, the anti-wear effect of lubricant additives is associated with the formation of tribochemical films on friction surfaces [l-31. The knowledge of t h e mechanical properties of these tribochemical films would be useful to understand their anti-wear mechanism. A low wear rate of the film itself could contribute to its efficiency and such a behaviour may be obtained if the film has high bulk mechanical properties, a good adhesion and also lower surface properties, which allows the shear plane to

be well defined. The measurement of t h e mechanical properties of friction films is a fi rs t s t e p t o v al i d at e t h e s e simple assumptions. But the small thickness (few tens of nanometers) and the inhomogeneous nature of these tribochemical films (the films formed i n t h e wear scar a r e not usually continuous but often very patchy) makes it difficult to measure of their elastic and plastic properties. So, in the literature, only very few studies present such results [4-5]. In this paper, we present t h e method we have developed to measure the hardness and the Young modulus of friction films. This

174 method couples nanoindentation experiments a n d imaging procedures, both performed with the same apparatus derived from the Surface Force Apparatus developed in our laboratory. This allows a precise calculation of the actual tip/film contact area, which is necessary for this type of surfaces. It is applied to the measurement of the mechanical properties of two friction films formed in boundary lubrication on a plane on plane tribometer with two simple lubricants, pure n-dodecane and n-dodecane + zinc dithiophosphate (extensively used in engine oils). 2. EXPERIMENTAL

2.1. Apparatus Nanoindentation experiments and images of the surface topography are performed with a three-axial instrument derived from the Surface Force Apparatus [Sl,developed in our laboratory. I t is also extensively used with a sphere to do nanofriction experiments and visco-elastic characterizations of interfaces 171.

Figure 1 shows a schematic diagram of the apparatus. Three piezoelectric elements are used to move the diamond tip (or the sphere in the case of interface studies) in the three directions X, Y and Z. They allow a displacement of 10 pm when they are supplied with a high voltage of 300 V. Three sensitive capacitive transducers measure the relative displacements of the diamond tip and sample holders in the three directions. These three transducers and the very low compliance of the sample and tip mountings (lower than 2.lO-’ m/N allow the relative displacements t o be measured without any further displacements which may occur when displacement transducers are far away from the samples. The resolutions reached are better than 0.1 nm. Two force transducers specially built and based on the capacitive measurement of elastic bending of two double cantilevers are used to measure the normal and tangential forces Fz and Fx. They have a high resolution in spite of very low compliances, N and 25.10-6m/N respectively.

Figure 1. Schematic diagram of the three-axial instrument derived from Surface Force Apparatus

175 Three closed loops are used to feed the high voltage amplifiers via PI controllers and then supply the three piezoelectric elements. Two displacement closed loops control the tangential displacements X and Y while the operation in the normal direction Z can be selected either in displacement or normal force control. The standard set-up used in this test obviously includes the continuous quasistatic measurements of the displacement Z and the resulting normal force Fz, at a slow penetration speed, generally 0.1 to 0.5 nm/s. But it also includes the simultaneous measurements of the rheological behaviour of the tested surface. In order to do that, small sinusoidal motions are added to normal and tangential displacements. Extremely small dynamic motions of 0.1 nm can be used. The resulting displacements and forces are measured using double phase synchronous analysers which give the in-phase and out of phase signals of both the normal and tangential mechanical transfer functions of the contact between the tip and the sample. The out of phase signals are related to the dissipative phenomena as viscous o r frictional effect and the in-phase signals are related to t h e conservative or elastic contributions. In this first stage, we are interested in the elastic contributions which are directly related t o the elastic properties of the sample. Using the Z feedback in the constant force mode, we can image the surface topography, before and after the indentation test, with the same diamond tip. This is possible because of the partial elastic recovery in the print. The applied load is 0.5 pN. The scan rate is limited due to the frequency response of the force sensors. It typically gives a linear speed of about lpm/s, depending on the slope of the surface, the normal load and on the mechanical impedance of the tip/sample contact. Therefore the acquisition time for an area of l p m x l p m with 256x256 pixels is about 10 minutes. Nevertheless, it is very efficient because with the same apparatus, one may obtain very accurate mechanical measurements a t a chosen place and take images without having to move the sample. Simple scanning lines through t h e indentation point are also made at speed as

low as 1to 10 nm/s. Different measurements are recorded during the scan : an accurate topography profile, normal and tangential mechanical impedance and static tangential force. However, while this procedure is well suited to image a small area such as an indentation print, we cannot use it t o image a large area in the case of rough and soft material and i n case of bad friction behaviour often due to adhesion phenomena. So, we improved the instrument to obtain a well adapted and non-destructive method when we need to have a survey of an enlarged area, as in the case of patchy reactional surfaces for which we have to map globally and then choose the islands of interest. It is a feature commonly used in Atomic Force Microscopy : the tapping method which is based on the measurement of altitudes at given points without friction. Successive landings every 0.5pm on an area of 18x11 pm produce an image that allows one t o choose a desired island on these tribochemical films. The landings a r e performed in constant normal force mode and in between, the displacement is carried out in constant displacement mode. A test for a desired stabilization is made before acquisition of the altitude and coordinates, using stable and precise numerical measurements. Therefore our experimental procedure includes four main stages performed with the same apparatus as shown figure 2 : a) survey of a large area to detect the position of islands and valleys on the surface film (tapping method) (figure 2a), b) local choice of the indentation point on the chosen island ( o r valley) using a preliminary image of the surface topography and an accurate topography profile (figure 2b), c) indentation test : continuous and simultaneous quasi-static (normal load) and dynamic measurements (contact stiffness) (figure 2c), d) observation of the residual indent using a second topographic image of the indented area in order to accurately measure the contact area at maximum load (figure 2d).

176

5

5

4-

@ Indentation : static measurements

-1 iav 2

t

160

v

1

An

@ Indentation : dynamic measurements

k

9

s

3-

i21 0 1 2

0 50 100 15C 0 TOTAL PENETRATION DEPTH Z (nm)

-

15 TOTAL PENETRATION DEPTH Z (nm)

Scan and image after the test

X (nm)

Figure 2. Description of the 4 stages of the experimental procedure used to characterize friction films. Example of test made on ZDTP film, the maximum load of the indentation is 5 mN. a) survey of a large area to detect the position of high areas and low areas (valleys) on the surface film (tapping method) , b) local choice of the indentation point using a preliminary image of the surface topography and an accurate topography profile, c) indentation test : continuous and simultaneous quasi-static (normal load) and dynamic measurements (contact stiffness), d) observation of the residual indent using an accurate line profile and a topographic image of the indented area to measure the actual contact area at maximum load.

177

2.2. Samples The tested friction films were formed on AISI 52100 steel planes i n boundary lubrication on a plane on plane tribometer. The second plane was made of lamellar graphite cast iron. The apparent contact pressure was 4 MPa, the apparent contact area was m2, the average sliding speed was loq2 m/s and the temperature was 80°C. Two simple lubricants were used : pure n-dodecane, which forms an oxide film, and n-dodecane + 1% of zinc sec butyl dithiophosphate (ZDTP), which is an antiwear additive extensively used in engine oil and forms a reactional film. The procedure and conditions to form the films are described with more details in reference [4]. An uncovered plane was also tested t o give reference values for the 52100 steel.

be determined. At the nanometer scale, different phenomena affect this actual area : the geometrical tip defect, the formation of pile-up around the indent and, in the case of rough surfaces, the local geometry of the surface. Concerning the tip defect, several techniques can be used for tip shape calibration [8-9], including Transmission Electron Microscopy techniques [lo] and AFM observation of the tip shape [ 111. With the capability of our apparatus to take images of the surface topography before and after indentation, we can perform tip shape calibration directly on the tested sample in order to obtain an equivalent height of the tip defect, noted ho. As this method was already precisely described [12], we will focus, in this paper, on the measurement of piling-up effects, ho is known and equal to 4 nm for our indenter.

3. METHOD

The actual contact area, A, and the equivalent radius of contact, a, are related t o the theoretical plastic penetration depth 6 by :

The aim is to extract quantitative values of hardness and Young modulus from the depth-sensing measurements of normal load Fz and dynamic normal contact stiffness Kz.

Case of homogeneous bulk materials The hardness H and the reduced Young modulus E*=E/(1-v2)of a bulk material are given by equation (1)to (3) : 3.1.

H = -Fz A

(1)

a

(4)

6

2a=F where a and p are two constant factors from the geometry of the indenter. For the Berkovitch type tip used in this study, a = 0.03646 and p = 0.1731. The last value includes a shape correction to account for a triangular shape instead of a circular one D31.

where Eappis the apparent modulus, E i * is the reduced modulus of the diamond indenter (we take Ei* = 1150 GPa), A is the actual contact area, a is the equivalent radius of contact.

To determine the theoretical plastic depth 6, we need to relate it to the measured experimental plastic depth hF. At maximum load, the plastic depth, hR9, is obtained by drawing the tangent to the unloading part of the indentation curve [14-151. In the case of dynamic measurements of the contact stiffness, this tangent and so the plastic p e n e t r a t i o n d e p t h a r e calculated continuously during the test 116-171.

So, the actual contact area, A, which is related to the plastic penetration depth must

For material without plastic pile-up, the theoretical plastic depth is simply calculated

1

Eapp =

(3)

’

178

by adding the height of the tip defect to the measured plastic penetration depth (equation 6 ) : 6=hw+ho

(6)

When plastic pile-up exists, it affects the contact area, so the theoretical plastic depth must include an equivalent height of pile-up noted hb, and we can write :

The notations are explained figure 3.

after unloading Corresponding perfectly sharp indenter 6 : plastic depth for the perfect indenter hR : plastic depth ho : equivalent height of the tip defect hb : height of the plastic pile-up a : equivalent radius of contact

3.2. Compliant thin film on a stiffer

Figure 3. Determination of the theoretical plastic penetration depth 6 from the plastic depth measured during the test (hRl), the equivalent height of the tip defect (ho) and the equivalent height of plastic pile-up (hb). To continue, assumptions must be made about how hb varies with hR9 + ho. On materials such as sapphire 1161, silica [171 or pyrolyzed polymer coatings [171, we have obtained good results with the hypothesis t h a t h b is proportional to the plastic penetration depth hR1 + ho. Using a constant coefficient noted b, we can write : hb = b x (hw + ho)

(8)

and then

6 = (1+ b) x (hR + ho)

simulations with a finite element method in the literature [181. We determine it experimentally from the image of the indents. On the image of an indent, the accurate measurement of the print area allows one to determine an optically induced hardness value. In case of plastic pile-up, the higher actual area corresponds to a hardness value smaller than the one calculated with equation (6), considering there is no pile-up. The ratio of these two values is then equal to (1 + b)2. It is assumed to be constant using the plastic depth. We will see later in the results part that this last assumption is valid in our case. Then, 6 , the hardness H and the reduced Young modulus E* can be calculated continuously during the test. With our diamond tips, this approach is valid for plastic indentation depth hw greater than 3 nm. The error on the values of hardness and reduced Young modulus calculated with this method is less than 5%.

(9)

The coefficient ( l + b ) corresponds to the average increase of penetration depth due to pile-up around the indent. Such a coefficient (then called form factor) is also used in

substrate Much more t h a n the hardness, t h e measurement of the elastic properties of a thin layer is largely influenced by the elastic properties of the substrate, even a t penetration depths very small compared to the film thickness (t).The measured contact stiffness is a global stiffness that includes the stiffness of the substrate. The reduced Young modulus (E*) calculated from this global stiffness appears to increase continuously with the penetration depth. A first rough estimation of the modulus of the film can be obtained by extrapolating the global increasing curve to t h e zero penetration depth. As this method is not very precise, we have built a simple model to extract a value of film modulus (Ef*) from the global measurements. It is detailed in reference [171. We consider the case of a cylindrical punch of radius a and we suppose that both the film (thickness t) and the substrate are homogeneous materials. In case of adherent film, the global stiffness corresponds t o the reciprocal sum of t h e film stiffness (Kf = na2Ef*/t) and the substrate stiffness (Ks= 2ES*a). To ensure correct boundary

179

conditions, we correct the expressions of the film and substrate stiffnesses with a polynomial function. These boundary conditions are : 1)the film must behave like a bulk material when the radius of contact is very small compared to the film thickness (a<&),2) if the film and the substrate have the same elastic properties, the global stiffness must be equal t o the substrate stifmess Ks. It gives the following equation : 1 --

K,

t

fi(a)na2Ef *

+

1

f2(a)2aES*

Indentation tests a r e made in 'dry' conditions (no lubricant), a t room temperature. At the frequency used for dynamic measurements, 37 Hz,we did not observe viscous effects. Examples of loading-unloading curves obtained with the medium loads on the three samples are shown figure 4. 500

(10)

where Kg is the measured global stiffness, t is the film thickness, a is the radius of contact, Ef * is the reduced Young modulus of the film, Es* is the reduced Young modulus of the substrate, f l ( a ) and fi(a) are two polynomial functions in the form : 1+ aan. 2t Calculations give fi(a) = fi(a) = 1+ - . na This simple model can then be used to estimate the reduced modulus of a thin film if the thickness of the film and the reduced modulus of the substrate are known. T h e t e s t e d friction films a r e heterogeneous in thickness. To estimate the film thickness locally, in the tested area, we use the corresponding large survey, assuming that the local film thickness is nearly equal to the difference between the altitude of the tested point and the lowest altitude on the survey. The obtained thicknesses are in the range of thicknesses evaluated with other techniques on the same films 141 and give good results when used in the model. The reduced Young modulus of the 52100 steel substrate is obtained with preliminary measurements presented in the following part. 4. RESULTS

The maximum loads used for the indentation tests were 65 pN, 400 to 500 pN and 5000 pN.

0

10 20 30 40 50 TOTAL PENETRATION DEPTH 2 (nm)

Figure 4. Example of indentation curves obtained on the 52100 steel plane and on the oxide and ZDTP friction films. The indentation curves obtained at comparable loads on the steel plane and on the ZDTP film are not very different. The other noticeable fact is t h a t the loading curves of the two friction films intersect, which indicates t h a t t h e mechanical properties of these films are probably non constant with thickness. We will show in the following parts that the careful determination of the actual contact area through the quantification of the plastic pile-up allows to clearly differentiate the properties of the three materials. 4.1. 52100 steel plane Line profiles through the indents (400 pN and 5000 pN load) show pile-up formation. around the prints. We also observe on the images that the shape of the indents can be schematically described by a triangle. This indicates that pile-up effects occur almost uniformly around the indents.

180 On the images, we measure the actual contact area A, which allows to calculate hardness values at maximum load. These values take into account pile-up effects. We find H = 9.3 f 0.5 GPa. The calculation of the hardness from the corresponding experimental curves and taking b = 0 (considering no pile-up) gives, at the same maximum load, a higher hardness value of 11.5 f 0.6 GPa. The ratio of these two values is used t o calculate the correcting factor due t o pile-up, ( 1 + b). This gives ( l + b ) = 1.11 (which corresponds to 11% of increase of depth due to plastic pile-up). I n terms of contact areas, ( l + b ) 2 corresponds to the ratio between the actual contact area A and a calculated theoretical contact area Ao which should have been measured if no pile-up had occurred (calculated taking b = 0 in the equations). These areas are drawn figure 5 . Pile-up effects result in this case to an increase of contact area of 23%.

Using this value, the reduced Young modulus is equal to 260 f 13 GPa, which is a rather high value. This value will be used to apply the thin film model described before. At smaller plastic depths, the mechanical properties of the substrate are a little lower : at a plastic depth of 3 nm, we measure a hardness of 6 . 6 f 0.3 GPa and a reduced modulus of 217 k 11 GPa. 4.2. Oxide film

Both high areas, where the film thickness is estimated a t about 120 nm, and low areas (valleys), where the film thickness is estimated at about 50 nm, are tested. Examples of images of indents on a high area and on a low area at a maximum load of 400 pN are shown figure 6.

Figure 6. Indentation prints on the oxide film (maximum load 400 pN). (a) on a high area (thickness about 120 nm) (b) on a low area (thickness about 50 nm) The topographic profiles show that in both cases, there is no plastic pile-up around the indentation prints made with 400 pN maximum load. This is a n unusual behaviour for a thin film softer than the substrate. I t may be explained by a compaction of the film beneath the indenter. Figure 5 . Image of an indent on the 52100 steel plane, a t a maximum load of 5000 pN. The corresponding plastic depth is 121 nm. The thick line indicates the actual contact area A. The fine line indicates the calculated theoretical contact area Ao which should have been measured if no pile-up had occurred (calculated taking b = 0 in the equations).

On high areas, the hardness value calculated from picture measurement of the print area and the value calculated from the indentation curve at maximum load are the same and equal to 7 . 8 f 0.4 GPa. At a plastic depth of 3 nm, the hardness is equal to about 6.7 f 0.3 GPa. Then it increases to about 9 f 0.5 GPa before decreasing and stabilizing to about 7.8 GPa (figure 7). The

181

curve of the reduced modulus of the film Efh varies in a similar way (figure 7). At 3 nm depth, the modulus is equal to 134 f 7 GPa.

- 100

H

ti;2

0

I

1

1

I

I

I

1

-80

3 J

-60

8

3

-40

2

-20

5

Comparing the shape of the diamond tip and the initial surface profile, we can estimate from which plastic depth onwards there is a n increase of contact area due to the geometric shape of the valley. We find 7 nm. For plastic depths smaller than this value, we can calculate the hardness and the reduced modulus as described before for high areas. The hardness value calculated at a plastic depth of 7 nm is about 6.2 f 0.3 GPa. This value is comparable to the value we can determine from optical measurements of the actual contact area which is about 6.4GPa. At smaller plastic depths, the mechanical properties appear to be lower. At 3 nm, we find a hardness of 5.2f 0.3 GPa and a reduced modulus of 106f 5 GPa. These values are lower than those measured on high areas. This difference may be related t o different contact conditions between high and low areas during film formation. At large plastic depths, t h e same calculations give overestimated values because of the non negligible error on the calculation of the contact area (figure 9).

At the same load, the actual contact area in a valley may be greater than on a plane surface because of the shape of the valley itself as illustrated by figure 8.

x

ll24 I

140

r

120

*

w

3 100 J 3 80

8

60

'

2

-I

0

-20

0

I

-300

I

-200

5

I

40 120 I I I I I I 0 10 15 20 25 30 35 40 PLASTIC DEPTH h w (nm)

7nm

5

E

I

-100

0

100

200

300

X (nm)

Figure 8. Illustration of the increase of actual contact area (A compared to Ao) in the case of indentation of a low area on the oxide film, due t o the initial toPograPhic Profile of the surface.

Figure 9. Calculated hardness (HI and reduced Young modulus (EP) of the oxide film on a low area without any correction due to the profile of the surface. At small plastic depths (<7nm), these calculations are valid. At large plastic depths, the values are overestimated because of wrong calculation of the contact area.

182

4.3. ZDTP film

The experiments involved measurements of the properties of several different high areas of the film. Attempts were made on valleys but because they are very small, only few small indents (65 p N ) could be performed. They show the presence of a film in the valleys. Its mechanical properties seem comparable to those measured on high areas of the film. In the following, we present the results we obtained on high areas of the ZDTP film. Figure 10 shows a n example of indents made at 500 pN and 65 pN on one of the high areas. At these loads, the maximum penetration depth is smaller than the film thickness. Large pile-up is clearly visible around both indents. Contrary t o the steel substrate, the actual contact area (A) has not a triangular shape but can be described more precisely by a main triangle (area Ao) plus 3 smaller triangles corresponding to the non negligible part of contact area due to plastic pile-up. Such type of plastic flow is typically observed for soft thin layers on a harder substrate.

The ratio of the total contact area A over gives the term (l+b)2used to calculate the hardness and the reduced Young modulus continuously versus the penetration depth. Results are detailed for three of the tested high areas, representative of all results we obtained on this film (figure 11). Their estimated thicknesses and the values for AIAo are given in table 1. Table 1 Tested islands on the ZDTP film High areas Thickness (nm) #1 #2 #3

1.32 1.51 1.49

60 90 70

I

20 I o

high area# 1

A

higharea#2 high area # 3

O

' Figure 10.Image of indents (500 and 65 pN) on a high area on the ZDTP film. The actual contact area (A) can be approximated by a main triangle (area Ao) plus 3 smaller ones due to the large plastic pile-up. The relative part of contact area due to pile-up seems comparable for both indents.

NAo

g

b

2b

60' 40.

20. 01 0

3b

o: 5: 2'5 PLASTICDEPTH h R (nm)

I

5

I

I

I

315

o

high area # 1

A

high area # 2

n

high area # 3

I

I

10 15 20 25 30 PLASTIC DEPTH h R' (nm)

4d

I

35

4

Figure 12. Calculated hardness (H) and reduced Young modulus (Ef9 versus plastic depth on high areas on the ZDTP film.

183 Results differ significantly depending on the areas. This indicates that the ZDTP film is heterogeneous. An important result is that the properties also vary with the penetration depth. They are significantly lower at small plastic depths. The plastic flow observed for this film is coherent with these low values. Furthermore, t h e difficulties we have encountered to make the topographic profiles and the images (instabilities, film sweeping away locally...) indicate that the mechanical properties are probably even lower in surface. Further experiments have t o be made to quantify this. At larger plastic depths, the hardness and the Young modulus increase rapidly to rather high values. 6. CONCLUSIONS

The development of a specific indentation test procedure makes it currently possible to characterize the mechanical properties of friction films. These surface films accumulate a number of difficulties : very small thickness, high surface roughness, heterogeneity in surface and in thickness, plastic pile-up effect on the actual contact area. The important point of our method is the capability of our apparatus t o generate images which allow to solve these difficulties while performing quantitative mechanical

measurements with a good accuracy. So reliable values can be given for plastic depths as small as 3 nm. The quantification of plastic pile-up effect and values of hardness and reduced Young modulus measured on the two films tested are summarized in table 2. There is no pile-up effect for the oxide film. This may indicate a compaction of the film beneath the indenter. Its mechanical properties are rather high and almost constant with thickness. On the other hand, the ZDTP film exhibits, at its surface, a very low hardness value, which rapidly increases with the penetration depth. This low surface hardness leads to an important plastic flow around the indenter which results in a large and typical pile-up. These first results are encouraging. The lower surface mechanical properties of the ZDTP film may be related t o its good antiwear properties, by allowing the shear plane to be localized at the surface of the film. The oxide film which h a s bad anti-wear properties [ll does not exhibits such low surface properties. Using this specifically developed test procedure, further experiments can now be conducted on tribochemical films with different chemistry and formed under different conditions, in order to contribute to the understanding of anti-wear mechanisms.

Table 2 Recapitulative of the parameters used for calculations and measured mechanical properties (the error on the values of hardness and reduced Young modulus is about 5%) Thickness NAo At a plastic depth of At a plastic depth of (nm) (pile-up effect) 3 nm 30 nm

H (GPa) Ef* (GPa) H (GPa) 52100 steel plane Oxide film high area low area ZDTP film high area (*)

(**I

I 120 50 60 t o 90

1.23 1 1 1.32 to 1.51

Ef* (GPa)

6.6 217"' 9.3 260") 6.7 134 7.8 132 1 (**) 5.2 106 1 (**) 2 to 4.5 78 to 115 8.4to 11 127 to 156

For the steel substrate, the given modulii are E*. No value (wrong calculation of the contact area due to the initial shape of the surface).

184

Acknowledgements The authors wish to thank Ph. Kapsa for his constant interest for these friction films and J.-M. Georges for his helpful discussions and advice.

REFERENCES 1. Ph. Kapsa, These d'Etat n"8219, Ecole Centrale de Lyon, France (1982). 2. P. Cann, H.A. Spikes and A. Cameron, ASLE Transactions, 26 (11, 48 (1983). 3. Dan-ping Wei, Lubrication Science 7-3, 211, April 1995. 4. A. Tonck, Ph. Kapsa and J . Sabot, Transactions of t h e ASME, 108, 117, January 1986. 5 . J.-M. Georges, D. Mazuyer, J.-L. Loubet an d A. Tonck, in Fundamentals of . . riction : Macroscopic a n d r o s c o p i c Process, 263-286, I.L. Singer and H.M. Pollock (eds.), Kluwer Academic Publishers, The Netherlands, 1992. 6. J.-M. Georges, S. Millot, J L . Loubet, and A. Tonck, J. Chem. Phys, 98 (9), 7345 (1993). 7. J.-M. Georges, A. Tonck a n d D. Mazuyer, Wear, 175 (11,59 (1994). 8. M. F. Doerner and W. D. Nix, J. Mater. Res. 1 (41, 601 (1986). 9. W.C. Oliver and G. M. Pharr, J. Mater. Res. 7 (6), 1564 (1992). 10 J. B. Pethica, R. Hutchinson and W.C. Oliver, Philos. Mag. A, 48,593 (1983).

M. G . Gee, D. J . Hall, 11. N. J. .McCormick, . in Thin W s : S t r w and M e d u n i d P r o p e r t i e s IV, edited by P. H. Townsend, T. P. Weihs, J . E. Sanchez Jr, P. Bergesen (Mater. Res. SOC.Proc. 308,Pittsburgh, PA, 1993) pp 195-555. 12. S.Bec, A. Tonck and J.L. Loubet, Mat. Res. SOC.Symp. Proc. Vol. 356, 657-662, (1995). 13. R. B. King, Int. Solids Structures, 23 (121, 1657 (1987). J. M. Georges, G. Meille in 14. J.-L. . Loubet, . i c r o in d en t a t i on T e chnrz. ue s 1n Materials Science a n d Eneineeriu, ASTM STP 889, edited by P. J. Blau and B. R. Lawn, American Society for Testing and Materials, Philadelphia (1986) pp 72-89. 15. J.-L. Loubet, M. Bauer, A. Tonck, S. Bec and B. Gauthier-Manuel, in Mechan ical ProDert ies and Deformat ion Behavior of Materials HavinP Ultra-Fine Micros t r u c t u r e s , NATO Advanced St u d y Institute, edited by. M. A. Nastasi, Kluwer Academic Publishers, Netherlands (1993) pp 429-447. 16. M. Bauer, thesis, Ecole Centrale de Lyon, France, n"91-28, 1991. 17. S. Bec, thesis, Ecole Centrale de Lyon, France, n"92-62, 1992. 18. P. Laval, thesis, Ecole Nationale Supkrieure des Mines de Paris, France, May 1995.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

185

In-situ measurement of the visco-elastic properties of a sliding lubricated contact A. Tonck, D. Mazuyer, J.-M. Georges

Laboratoire de Tribologie et Dynamique des SystBmes, URA CNRS 855, Ecole Centrale de Lyons B.P. 163, F-69131 Ecully Cedex, France In this paper, a new type of experiment is presented which was enable by the recent development of the surface force apparatus and of the molecular tribometer used in our Laboratory. In a single test, we obtain the pertinent parameters involved in boundary lubrication and about third body behaviour. To the now classical stage of characterisation using surface force procedure (bulk viscosity measurements, thickness of immobile layer, adhesion and confined layer under load), is added a frictional test with continuous measurement of the viscoelastic properties of the interface layer under shear. This in-situ characterisation is made in both the normal and the tangential directions using very low superimposed vibrations and gives both the compressive and shear modulus. The appropriate choice of the amplitudes and frequencies used allows these extra measurements to be performed without any perturbance towards the friction process and also with a good accuracy. Thanks to this procedure, i t is now possible t o know precisely the rheological behaviour of the interface during the friction process and not only after the sliding, where the interface can be modified by molecular relaxation process of the lubricant. The method is applied to a sphereplane contact lubricated with self-assembled stearic acid monolayers whose thickness remains almost constant during the loading. 1. INTRODUCTION

To understand t h e mechanism of lubrication in a boundary regime, the lubricants a r e generally tested on tribometers measuring the evolution of the frictional force a s a function of various external parameters such as sliding speed, normal load, temperature, that can be easily obtainedll-31. Yet, t h e friction force is governed, in t he absence of ploughing friction due t o the solid asperities, by adhesive bonding and hence from the mechanical shear strength of the sliding interface 141. Furthermore, a molecularly thin film is present in the interface whose shearing behaviour and structure control the sliding process that can give viscous or

friction forces [51. This behaviour strongly depends on the variations during the sliding, of internal properties of the film such as thickness, its viscosity, its elastic shear modulus [61. So, the knowledge of the evolution of these properties under shearing is necessary for a better understanding of the dissipative process i n boundary lubrication. For example, in a sphere-plane contact lubricated with two monolayers of stearic acid which is the lubricant also used in the present work, it has been shown [61 that the shear process seems to be related to : 1-the elastic shear modulus of the bilayer, 2- the limit of the shear elastic deformation of the bi-layer before sliding characterised by a critical length X*,

186

3- small variations of the thickness of the bi-layer. Variations of the order of O.Olnm are observed at each changes of the state of the film : beginning of sliding, changes of speed, stops, reverse sliding (dilatance phenomena observed when the speed is lower than about lOnm/s). These variations are interpreted as to be due to the interdigitation processes between the two mono 1ay er s . After sliding, the interface thickness is also modified by a molecular relaxation process of the lubricant. The great problem then encountered is that the rheological behaviours of the interface (point 1 and 2) are measured only before or after the friction test, whereas they change during friction, like the thickness does. The precise measurement of these internal parameters, at a molecular scale and under shear, leads t o two main difficulties. The first problem arises from a

structural effect : the compliance of the interface is very often much lower than the compliance of the solids or of the experimental device used, so the elastic behaviour is dominated by these external parts. The second is related t o the accuracy needed for the measurement of very low compliances in a linear regime response. To minimise the structural effect, the only possible way is a reduction of the ratio 2db (diameter of the contact (2aYthickness of the film B) either using of a very low radius as with AFM technique [7-91 or using a low normal load, with an apparatus especially designed to measure such compliances. Our device, first used as surface force apparatus and then as molecular tribometer [61, has been developed to work at low loads, as a surface viscoelasticimeter in order to obtain valid i n - s i t u rheological measurements during all the friction test.

Figure 1. Schematic diagram of the molecular tribometer derived from Surface Force Apparatus

187 2. EXPERIMENTAL DEVICE

Nanofriction experiments and in-situ viscoelastic characterisations a r e performed with a three-axial instrument derived from a Surface Force Apparatus, developed in our laboratory [SI. Figure 1. shows a schematic diagram of the apparatus. Three piezoelectric elements are used to move the sphere in the three directions x, y and z. They make possible a maximum displacement of 10mm when they are supplied with an high voltage of 300V.Three sensitive capacitive transducers measure the relative displacements of the samples holders in the three directions. These three transducers and the very low compliance of the samples as well as their mountings (lower than 2.10-7 m/N) allow the relative displacements to be measured without any further displacements. Bending due to load frame compliances is negligible. The resolutions reached are better than 0. lnm. Two force transducers specially built and based on the capacitive measurement of elastic bending of two double cantilevers are used t o measure the normal and tangential forces : Fz and Fx. They have a high resolution in spite of very low compliances, 10-8 N and 25.10m6m / N respectively. Three closed loops are used to feed the high voltage amplifiers via PI controllers and then supply the three piezoelectric elements. Two displacement closed loops control the tangential displacements x and y, while the operation in the normal direction z can be selected either in displacement or normal force control. The standard set-up used in the tests obviously includes the continuous quasistatic measurements of the displacements and the resulting normal and tangential forces. But it also includes the simultaneous measurements of t h e rheological behaviours of the contact. In order to do that, small sinusoidal motions can be added to normal and tangential displacements.

Extremely light dynamic motions such as 0.1 nm can be used. The resulting displacements and forces are measured using double phase synchronous analysers which give the in-phase and out of phase signals of both the normal and tangential mechanical transfer functions of the contact between the sphere and the sample. The out of phase signals are related to the dissipative phenomena a s viscous or friction effect and the in-phase signals are related t o the conservative or elastic contribution. For dynamical measurements, the frequency response of the complete measurement chain is carefully recorded as the apparatus transfer functions. These transfer functions are then used to calculate from the measured dynamical forces and displacements, the behaviour of the interface or of the contact itself. We are thus able to obtain a rheological analysis in the two axis, on a frequency range of 0.01 up to 500Hz. The normal behaviour either for tip or sphere-plane indentation is obviously a non-linear process, first by the about square law for tip behaviour or Hertzian law for sphere-plane behaviour of the repulsive force. Thanks to the low level of dynamical motion, the behaviour can be considered as locally linear. The surfaces used in this work are cobalt coatings on fused boro-silicate glass for the sphere (radius R = 2.45 mm) and on silicon wafer for the plane. This cobalt layer is deposited under a low argon pressure using cathodic sputtering. Before deposition, the chamber is pumped for 8 hours at a pressure of Pa. Atomic force microscopy observations show that the surfaces consist of irregular connected clusters leading to a corrugated "blackberry"-like roughness (0.8 nm peak to valley with a wave length of 70 nm). A droplet of 1 m M solution of stearic acid (Aldrich) in anhydrous n-dodecane (pure grade from Aldrich Sure Seal : grade 99 96) is deposited between the two cobalt surfaces. This droplet forms a meniscus of radius r = 1-2 mm in the sphere/plane interface. A monolayer of stearic acid is

188 obtained after one hour adsorption 110-113. All the experiments were performed in dry air at a temperature of 24.3 f 0.2 "C.

3.EXPERIMENTAL PROCEDURE The aim is t o obtain, in a single friction test, rheological information about the contact on a wide range of normal loads (from 1 pN to 10 mN), including in-situ normal and tangential viscoelastic characterisation. The experiment is carried out by making a normal approach of the sphere t o the plane while a tangential displacement is simultaneously applied between the two solids (figure 2.).

t

Z

x

fhPBa

The evolution of the frictional force can then be continuously measured as function of the normal load, The speed of the motion of the sphere along the Z direction is sufficiently slow to consider that the friction of the interface is in its steady state phase. The superimposed vibrating motions both in the X and 2 directions are also used to characterise the surface stearic acid layer before contact and then to perform the insitu viscoelastic measurements of the interface under shearing. The simultaneous t a n g e n t i a l stiffness measurement of a sliding contact is not obvious and precautions must be taken t o insure the validity of the rheological measurement. In order to successfully do that, we have to carefully take into account some problems listed below, that will lead to the choice of the range of the suited amplitudes and frequencies. Tangential visco-elastic characterhtion d a static contact Even for a static contact, the measurement of the tangential visco-elastic properties may be af'fected by the sliding or the micro-sliding of the contact, resulting of the dynamical tangential sollicitation. This well known and already studied phenomenon [121 leads t o the formation of hysteresis cycles in the tangential forcedisplacement curves. The effect on the measured transfer function is a reduction of the visible measured stiffness and the occurrence of a frictional dissipative part which may be mistaken as a viscous effect. In order to avoid this problem, the only possible way is the use of a very low tangential amplitude, t o stay in a linear regime. At low loads, classical mechanical behaviour of a contact between two solids [121 predicts extremely low tangential sollicitation. But fortunately, at this scale of load, the behaviour appears t o be often dominated by t h e interface layers themselves, for which we have already shown that the sliding occurs only after a critical distance X* having a molecular 3.1.

g

stearic acid molecule

dodecane molecule

Figure 2. Schematic description of the experimental procedure of the friction test. The sphere is simultaneously displaced in the directions X and Z at different speed (Vx=O.l nm/s and Vz=O.Ol nm/s). A sinusoidal vibration with different a m p l i t u d e s a n d frequencies is superimposed t o the continuous motion along these 2 directions. Then, tangential and normal forces, tangential and normal stiffnesses can be continuously measured during the experiment.

189

scale (figure 3.). This distance is almost independent of the normal load and the tangential sollicitation selected is taken t o be its tenth part. The estimation of the value of X* 0.3 nm) in a previous work [61 leads to an amplitude of 0.03nm. (5

Fx

f x* (I

FXP

X

Figure 3. Characteristic evolution of the frictional force with the sliding distance when the stearic acid bi-layer is sheared. After an linear period characterised by an elastic stiffness Kx, the force Fx becomes non-linear and reaches a limiting value Fxc. The transition between these 2 periods occurs a t the critical distance X*=Fxe/Kx. The superimposed vibration (amplitude Ax) to the sliding motion causes small linear returns of the friction force with a slope Kx. This stiffness is continuously measured during sliding thanks t o the appropriate amplitude Ax and frequency Rx.

3.2. Friction and superimposed viscoelastic characterisation In addition to the previous points, the intrinsic non linear behaviour of a sliding contact appears clearly in the case of friction experiment superimposed with tangential visco-elastic characterisation and must be well considered. The dynamic displacement of amplitude A x and frequency Rx results in little cycles such as those shown in figure 3., assuming there is no significant speed effect and that the friction behaviour is well described by a

tangential stiffness Kx (elastic reversible part) and a plateau (non-linear part)(figure 3.). These highly non linear responses have needed a peculiar analysis based on a first harmonic method that has been already used for nano-indentation experiment (case of superimposed elastic measurements) 1131 and extended to a friction test. This method exhibits a criterion t h a t ensures an accuracy on the viscoelastic measurements better than 1% when the following relation is checked :

where Vx is the tangential speed. This method shows the non-linearity causes a phase of 0.36" that does not affect the measurement of the damping of the film. According to relation (l),it is seen that the higher the frequency is, the higher the average tangential speed might be. So the maximum speed that can be applied for a frequency of 220 Hz and an amplitude of 0.03 nm is 0.7 nm/s. This value could appear very low for a conventional friction test, but preceding tribology experiments at a molecular scale, show that the physical phenomena in the sliding process occur for this order of magnitude of speed and even lower [61. In a liquid medium, when the dynamic behaviour of the interface is measured under a normal solicitation, the in-phase component of the transfer function is not only due t o the elasticity of the compressed layer but also to the elastic deformation of the solid surfaces. Therefore in order to minimise this contribution and to obtain directly the normal contact stiffness, a low frequency is used for the normal vibrating motion. On the opposite, the use of high frequency is very convenient for the measurement of the tangential stiffness of a squeezed layer, because in a tangential solicitation, no similar flow pressure is created and the measured tangential stiffness represents the real stiffness of the contact.

190

Table 1 Experimental conditions used for the quasi-static motion and the superimposed vibrating solicitations both in the normal and tangential directions

Quasi-static speed (rids) Vibration frequency (Hz) Vibration amplitude (nm)

Normal motion

Tangential motion

0.01 (VZ)

0.1 (VX) 220 (ax) 0.03 (Ax)

37 ( n z ) 0.1 (Az)

The experimental conditions that have been chosen, after accounting for the main sources of disturbance, caused by dynamic measurements both in the normal and tangential directions, on the friction process are given in table 1 .

deduced from the evolution of the normal force, assuming t h a t the contact is equivalent to a Hertzian sphere/plane contact separated by a rigid layer of thickness D and is given by the relation :

a2 D=Z+R

4. RESULTEl AND DISCUSSION

Before the friction experiment, the lubricant is squeezed in a normal approach in order to measure the evolution of the static force versus displacement and the transfer function of the contact (with the superimposed sinusoidal vibration). The difference between the measured inverse damping function and the measured inverse of the derivative of the contact capacitance [141 show that the thickness of the hydrodynamic layer is 4.9 nm (twice the length of a stearic acid molecule). The attractive part of the normal force is very small (adhesion force : -2.5 pN) is well described by a Van der Waals law whose value suggest that the contact between the layers is made through methyl groups [61, [151, [161. The evolution of the repulsive normal force versus the sphere/plane distance shows the contact behaves as if the interface were a rigid wall 6 nm thick. These measurements in a simple squeeze experiment mean that the interface can be considered as the contact between one monolayer adsorbed onto each surface. The variations of the average thickness is

where a is the Hertzian contact radius and R is the sphere radius. In relation (2), the a2 term - represents the total elastic

R

deformation of the solids according t o Hertz's law. The measurement of the electrical spherdplane contact capacitance during the experiment is also a useful control of the value the thickness D given by relation (2). During a friction experiment in which the loading is increased in a quasi-static way, the normal and tangential forces, Fz and Fx, respectively , the normal and tangential elastic stiffnesses, Kz and Kx, respectively are simultaneously measured versus time, In a classical nanotribology experiment at constant normal load Fzo, the evolution of the tangential force F x versus the sliding distance is characterised by two periods 161: -an linear period described by a tangential stiffness Kx, -a non-linear period, where the tangential force increases until an equilibrium value

Fx~.

191

The ratio Fxt/Kx is a length noted X * (figure 3.) that is characteristic of the transition between the linear and the nonlinear period of friction process and can be viewed as the critical distance above which sliding occurs. Then, the two parameters Kx (elastic parameter) and length X * (plasticity onset) can be used to describe the frictional behaviour of the monolayers. Thanks t o the experimental procedure detailed in this paper, it is possible t o continuously measure the stiffness Kx and the characteristic length during the sliding process by the evolution of the ratio F a x . Therefore, the tangential force Fx can be written as : FX = FX! = KX x X*

(3)

According to the relation (81,the friction coefficient is made of two components :

E

-the first term (-)is a conservative part P given by the average tangential elasticity of the monolayers in contact relative to the pressure, -the second term is a dissipative part described by the molecular length X * adimensionnalized by the thickness of the interface and defined as the minimum sliding distance from which sliding starts.

So, the friction coefficient p is given by : 0.02

I

(4) L

0.015

The previous relation may be regarded in terms of elastic shear modulus/contact pressure rather t h a n in terms of stiffness/normal force using the following relationship :

- KXXB a=----;;xxaz

0

where -d is the mean elastic shear modulus of the interface. So, relation ( 5 ) implies : (6)

therefore,

1

2 3 4 NORMAL FORCE Fz ( mN )

5

Figure 4. Continuous evolution of the friction coefficient with normal load . The friction coefficient becomes independent of the load when the two monolayers are in contact (at loads greater than 50 pN) which corresponds t o constant sphere/plane distance of 4.9 nm. Then, the friction coefficient reaches a very low value of 0.0075.

where is the mean contact pressure. Combining relations (4) and (71,the friction coefficient can be expressed as :

The simultaneous measurements during the sliding, of tangential force Fx, thickness of the interface and tangential

192

stiffness Kx allows us, according t o relations (3) and (71,t o determine these two components. Figure 4. shows the continuous evolution of the friction coefficient as a function of the loading force. This curve exhibits a very low friction coefficient (about 0.0075) that is independent of load in the range 50 pN5000pN (pressure range from 4 MPa t o 5OMPa). In this pressure range, these selfassembled monolayers of stearic acid obey the Amontons law but give only half the friction coefficient than that previously measured on the same contact [61. This difference may be due to an increase of the density of the monolayers in the experiments presented in this work. L

31.5

'

to another evolution of the length X* and of

the ratio

B P

with Fz, as shown in figure 5.

These curves are both derived from tangential stiffness measurement t h a t includes not only the stiffness of the squeezed monolayers but also the stiffness Kc of the Hertzian spherdplane contact [121. This contribution becomes important especially at high loads and the measured stiffness is then given by : (9)

The curves plotted in figure 5. are based on corrected values of the stiffness K x by the relation (9). It is noted that length X * increases with the loading, from 0.06 nm and 0.1 nm. This slight increase in X* is

E

balanced by a simultaneous decrease of = P

from 1to 0.5 leading to a friction coefficient independent of normal load - Fz. The G measured values of X* and = are quite P

1 2 3 4 NORMAL FORCE Fz ( mN )

0

5

Figure 5 . Simultaneous evolutions of the G and the critical length X* versus ratio

P

normal load.

-G P

is experimentally obtained

by the measurements of tangential Stiffness Kx, normal force Fz and distance Band

-

=&xD.X*is P Fz the ratio of tangential force Fx to tangential stiffness Kx. X* increases from 0.05 to 0.1

derived from the relation

nm while

-G P

. I

decreases from 1 to 0.5.

This different molecular structure leads

different from those that have been obtained in other experiments for only three states of loading [61 (in that case, X*=0.5 nm and G -=r=O.l). As for the reduction of the friction P

coefficient, these significant quantitative differences are attributed t o a higher ordering of the monolayers and do not modify the qualitative analysis of our results. These observations show t h a t the intrinsic length X* is not only related to the molecular nature of the lubricant but also to the structure of the molecular layers it forms at the neighbourhood of the surfaces, depending on the interactions lubricantlsurface. These results are confirmed by friction experiments in which the normal force is maintained constant (figure 6.).

193

0 0 v

U

4

-0.5 150 ~.

".l

0

50

100 TIME (s)

Figure 6. Correlated evolutions of the frictional force and tangential stiffness in a friction test at constant load (Fz=500pN), for different sliding speed Vx. When the sliding speed is increased the stiffness decreases while the tangential force slightly decreases (after a small increase). When the sliding motion is stopped the friction force suddenly relaxes to a nonzero value while the stiffness Kx increases on a much longer time. These variations are associated with slight changes (0.5 m) in the thickness of the interface that cannot totally explain the important variation of Kx, especially when the sliding is stopped. This effect might be due t o the interdigitation between the monolayers. In this type of experiment, it is possible to check that the value of the measured tangential stiffness Kx is not far from the value of the static stiffness given by the slope

(%)=o

= Kx.

As shown in figure 6.,

x

the evolution of the friction force (for a normal load equal to 500p.N), is associated with variations of both the tangential stiffness and the electrical capacitance. This effect is sensitive to the change in the tangential speed and is particularly exhibited when the sliding is stopped suddenly resulting in a relaxation

experiment : the frictional force drops steeply to a minimum non-zero value in a few seconds whilst tangential stiffness Kx increases by 40% over a longer period. A slight increase in the electrical contact capacitance is simultaneously observed. If we assume that the capacitance variation is only due to a decrease of the interface thickness, this latter would be about 0.0004 nm. This very small value cannot lead to the significant increase of stiffness measured in this experiment. This gap suggests that stiffness Kx is certainly related not to the elasticity of the whole interface but to the behaviour of the shear plane (small interdigitating zone between the sliding monolayers [171). 5. CONCLUSIONS

The original experimental procedure used in this work associated with an appropriate choice of the amplitude and the frequencies of the vibrating motions (limited by microsliding effects and the non-linearity of the sliding process) both in the normal and in the tangential directions make now possible the in-situ measurement of the visco-elastic behaviour of a sliding contact at a molecular level, in a single test. The molecular tribometer is used a s a viscoelasticimeter of surfaces and interfaces that can be used in a spherdplane contact as well as in tip/plane geometry. The preliminary experiments carried out on sliding stearic acid monolayers adsorbed on cobalt surfaces show the interest of measuring the rheological properties of the interface under shearing and not only after or before the friction test and their evolution with the normal load. Thanks t o the measurements of the thickness of the interface, the tangential stiffness and the tangential force during the shearing, i t is possible t o completely describe the friction coefficient. It has been shown t h a t the

194

friction coefficient can then be written as :

G , directly obtained from P Kx is related to the experimental data - x 6 Fz the elastic behaviour of the interface or of a p a r t of the interface. The length X* experimentally obtained by the ratio Fx/Kx is a critical length over which sliding starts and strongly depends on the structure of the layer. The mean thickness D of the interface changes during sliding in the case of these stearic acid boundary layers while X* increases from 0.06 nm to 0.1 nm where the term

and

7

a decreases from 1 to 0.5 with the load

-c

P leading to a low constant friction coefficient. The variations of may be more important for polymeric lubricant 1181, for example. So, t h e simultaneous

D, X* and ti

during the P friction process govern the evolution of the friction coefficient. Last, the amplitudes of the tangential vibrating motion necessary to obtain precisely the dynamic response of the sliding contact have initially been chosen to be much lower than the critical length X* in a ratio 1 t o 10. Actually, in the experiments presented in this paper and for the layer we have characterised, X* is found to be 0.06 nm while the amplitude of the tangential vibration is 0.03 nm (half of X*). These particular experimental conditions do not disturb the measurement of the frictional force nor the tangential stiffness. This means that the value of the amplitude to make precise measurements of the viscoelastic response of an interface under shearing can be high and is only limited by the intrinsic length X*. evolutions of

-e

REFERENCES 1. F. P. Bowden, D. Tabor, The Friction and Lubrication of Solids, Clarendon, Oxford, 1964. 2. R. C. Bowers, W. A. Zisman, J. Applied Physics, 39,12 (1968)5385. 3. B. J. Briscoe, D. Tabor, J. of Adhesion, 9 (1978)145. 4. A. M. Homola, J. N. Israelachvili, M. L. Gee and P. J. Mac Guiggan, Tribology, 111 (1989)675. 5 . H. Yoshizawa, Y. L. Chen, J. N. Israelachvili, J. Chem. Phys., 97 (1993) 4128. 6. J. M. Georges, A. Tonck, D. Mazuyer, Wear, 175 (1994)59. 7. C. Mate, Phys. Rev. Lett., 68 (1992)3323. 8. R.Overney, E. Meyer, J. Frommer, H. J. Giintherodt, M. Fujihira, H. Takano, Y. Gotoh, Langmuir, 10 (1994)1281. 9. S. A. Joyce, R. C. Thomas, J. E. Houston, T. A. Michalske, R. Crooks, Phys. Rev. Lett.. 68. 18 (1992)2790. 10. M.-Jacquet , J: M. Georges, J. Chimie Physique (Paris), 11 (1974)1529. 11. E. Smith, C. A. Alves, J. W. Anderegg, F. Porter a n d M. D. Siperko, Langmuir, 9 (1993). 12. R. D. Mindlin, ASME J. Applied Mechanics, 16 (1949)259. 13. S. Bec, These de doctorat no 92.62,Ecole Centrale de Lyon (1992). 14. J. M. Georges, S. Millot, J. L. Loubet and A. Tonck, J. Chem. Phys., 98, 8 (1993)7345. 15. B. V. Derjaguin, V.M. Muller and Y. P. Toporov, J. of Coll. and Inter. Sci., 53 (1975)314. 16. J. N. Israelachvili, Intermolecular and Surface Forces, 2nd Edition, Academic Press, 1992. 17. J. F.Joanny, Langmuir, 8 (1992)989. 18. J. M. Georges, A.Tonck, D. Mazuyer, J. L. Loubet, E. Georges, Proceedings of the 21st Leeds-Lyon Symposium on Tribology : Lubricants and Lubrication, T. Childs, D. Dowson, C. Taylor, G. Dalmaz (Eds), Elsevier Science Publishers B. V., Amsterdam, 1995.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

195

Nanorheological behaviour of confined liquid layers for normal contact F. Auslender and F. Sidoroff Laboratoire de Tribologie et Dynamique des Systhmes, URA CNRS 855, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, B.P. 131, F 69131 Ecully Cedex, France The rheological analysis of surface force apparatus experiments, usually based on lubrication theory, requires a refined modelisation taking into account the heterogeneity resulting from confinement effects. Such a model is developed and applied both in the incompressible and compressible case. It is shown that compressibility effects are essential for very thin layers. This finally leads to an oedometric thin film model to be applied for analysing the experimental resu 1ts. 1. INTRODUCTION

1.1 Surface force experiments

Surface force experiments as initiated by Tabor, and later Israelachvili [ 11, have now a rather long history and it has now become an essential experimental tool for characterizing the nanorheological behaviour of polymers and lubricants, in particular when cmfinement effects may play a significant part. More recently the ECL machine dftveloped by A. Ton& and J.M. Georges (21 has progress in the understandmg and characterization of confined liquids 131. In their principle these experiments are rather simple : two solids with well defined geometry (sphere-plane in the ECL machine, which is geometrically equivalent to the crossed cylinders used by Israelachvili) are brought close together and then moved under controlled kinematics. In the present state of the apparatus both normal and tangential motion can be imposed (3 axes machine) but attention will be focused here on the purely normal problem. These experiments are classically malysed through Chan & Horn formula 141

F=---6xpR2 ,j D which is derived from lubrication theory and Reynolds equation and which gives the drainage force F between a plane and a sphere of r a d u s R as a function of the separating h t a n c e D (Figure 1) and its time derivative D for a viscous newtonian fluid of viscosity p. This is however not sufficient for a correct analysis of the real problem which a more rheo10k3 and structure of the interfacial liquid.

Figure 1. Sphere-plane squeeze.

196 1.2 Some experimental facts

The imposed relative motion consists of a very slow evolution of D superposed with a small amplitude harmonic motion D( t) =

D(t) + 6D eiwt

(2)

A standard signal processing technique then provides the harmonic part of the response

P = F(t) + 6F eiot

8F = (K + iA) 6D

obtained by extrapolation of the 1/A curve. This reflects the presence of a solid-like confined layer (hydrodynamic layer) which for various liquids roughly corresponds to one molecular layer on each solid 131. 3. A deviation from Chan and Horn's result for small D. This will be discussed later. 20

-

(3)

z

where K and A respectively denotes the structural stiffness and damping of the system which can then be measured. Extension of Chan and Horn formula ( 1 ) for the viscoelastic harmonic case leads to the following relationships 151

ir

r---

----7ll

I

2trCR--

16

....... . K . .. A . . . . . . *

5=

*. . . . . . . . . . . . .P . . . . . . . . .

12

6, C:'(o) R2 K= D

6n C:"(o) R2 A= D

c

Lr.

a <

8-

-

I

2

-0.4

.'.

--.R E R V ~. / .F ,.= D I

-

N

,

,

- 0.2

,,/

I

I

8

(4)

0.6 ;

- .-?mRdD/dC . . . . . . . .=.D.

1. 2

z

r,

'

!

b

I

12

L

I

t

16

O

20

_'

"e DISPLACEMENT APPROACH H =D (nm)

where G(o) = G ' ( o )+ iG"(o) is the complex shear stiffness of the material (Coulombs modulus). The basic experiment consists in slowly varying D at constant o and a typical result is presented in Figure 2 giving as a function of the separating distance D the inverse of the damping A together with the inverse of the derivative dC/dD of the electrical capacity which according to the classical sphere plane condensator theory is proportional to D. These results essentially show 1. A good agreement for large D with Chan and Horn's formula (1) or (4) with G " ( o ) =po which prechcts 1/A to be proportional to D. The resulting value for p agrees well with more macroscopic measurement. 2. A significant discrepancy between the electrical zero (resulting from capacity measurements) and the mechanical zero

Figure 2. A typical experimental result from 131 (Georges - Millot - Loubet - Tonck).

A second type of experiment of viscoelasticimetric type can be performed by varying o at constant D. Using (4), this allows to measure G'(o) and G"(o). Experiments then result in a unique determination of G"(o) while the real part G ' ( o ) is found to depend significantly of D. This again will be discussed later. 1.3 Nanorheology as a structural problem The model leading to (4) is essentially based on the following assumptions a) linear isotropic viscoelasticity b) thin film approximation (lubrication model) c) rigid sphere and plane d) homogeneity e) incompressibility

197

( )bviously the homogeneity assumption d) is not reasonable and the heterogeneity rtsulting from the solid-like confined layer should be taken into account. The rheological problem to be solved then becomes a s1,ructural problem in the sense of continuum mnchanics and requires the solution of a houndary value problem for the dsplacement or velocity and for the stress field. It will however be shown later that heterogeneity alone is not sufficient to explain the observed experimental results and that compressibility must also be taken into account. The purpose of the present work therefore is to develop, under the thin film iipproximation, a consistent model for the hchaviour of an heterogeneous compressible viscoelastic material squeezed between a plane and a sphere both being supposed

rigid.

where W' is the prescribed vertical dsplacement. In particular the plane sphere squeeze will be described in polar coordmates (r,z) by

r

u = w = ~

z=o

In the thin film approximation, the basic variable is the flux vector

which can be related to the z-integral of' the volumetric strain by the mass balance equation

2. BASIC EQUATIONS

2.1 The elastic problem

We consider an heterogeneous elastic body confined between two substrates x = Z*(x,) (standard notations are used : a,P...= 1,2 for greek index, while i, j = 1,3 for latin index, with x3 = z . Summation wnvcntion is used). The displacement field u = (u,,w) and the stress tensor ~ i must j be

found satisfying - the equilibrium equation - the local elastic law (Hooke's law)

2.2 Thin film approximation In the thin film approximation, the slress tensor is postulated as

Olj =

O

0 1'

0

O

52

52

(5

1'

with two complementary assumptions A. The hydrostatic stress does not depend on z,

where

Eij

and q j respectively denotes the

strain tensor and its deviatoric part. Here the elastic bulk and shear moduli K and CI Iwlh may depend on xi = (x,,z). -- the boundary conditions which for the squeeze problem considered here will be taken as

(5

= O(X,)

B. The dominant terms in the deviatoric part of the strain tensor are i3uu I & . It then follows from Hooke's law (5)

The left hand side of the mass balance equation (9) then follows as

198 Chan and Horn's formula (1) drectly follows for this equation for the sphere plane system with h given by (7). while q is obtained starting from the equilibrium equations ( 13)

2.3 Harmonic viscoelastic response These elastic results a r e easily extended to linear viscoelasticity by use of the Laplace Carson transform in the general case (correspondence principle). We are interested here in an harmonic solicitation

Integrating twice with respect to z gives u, as

All quantities can then be found as harmonic functions with C and D to be determined from the Iwundary conhtions (6). Integrating ua with respect to z finally gives the flux q as

J G(x,,z)

Substituting (15) and (12) in the mass halance equation results in

an elliptic partial differential equation which with appropriate boundary con& tions will give the hydrostatic stress dmtribution ~ ( x , ) . In case of homogeneous elasticity (2 and K are constant and (16) becomes

with G(x,) a complex field. The viscoelastic constitutive equations in particular assume the complex form

with fi(x,,z.o) and ~ ( x , , z , o ) the bulk and shear complex moduli. The model constructed above is drectly transposed and finally leads to

with c o a n d D,still given by (12) and (15) from the bulk and shear moduli k and For a given viscoelastic heterogeneous will be known as configuration fi and function of x a , z and o so that it only remains to solve the complex partial ddferential equation (21) to obtain G and by

c.

-

(17)

which in turn gives the usual Reynolds equation for K +oo (or more precisely the c h t i c counterpart of Reynolds equation).

integration the normal force F and the correspondlng structural stiffness K and dampin g A. The plane sphere problem investigated here is axisymmetric so that (21) reduces to a n ordnary differential equation

199

-

G

(

I d r TI rdr

- --

dG

%) = SD

3. INCOMPRESSIBLE ANALYSIS 3.1 The layered NH configuration In the incompressible case vanishes so that (22) can be integrated once da r -~

dr

2D0(r)

SD

Figure 3. Layered configuration

Since the confinement effects essentially rrsults in the presence of a confined layer we shall limit ourselves in the following to a layered configuration with two layers of thickness D0/2 attached to each surface (Figure 3). The heterogeneous viscoelastic titructure will then be described by the complex shear modulus and 62(o)of the bulk and layer respectively. A dwect computation then gives as

G(o)

g = - DO h

r2 h=D+2R

The standard configuration consists in a viscous (N) bulk material (viscosity p) with elastic (H) layers (stiffness G) : the NH configuration is therefore defined as

-

(>(a) = iop

QO)

=

c

The corresponding results will presented in adimensional variables

be

The Merential equation (23) is numerically integrated by standard techniques with boundary condition cr + 0 for r + 0 0 , so that finally the real and imaginary parts F‘ and F” of F are determined as function of the achmensional separation D ( B = 1 when the two solid layers are in contact at r = 0) and pulsation R. 3.2 Near field analysis The dependence of A with respect to D (Cf. Figure2) is shown on Figure 4 which represents 1/A = S2/F” as a function of D for Mferent values of R (for an homogeneous For small values newtonian fluid 1/A =

n).

(25)

of this relation tends to 1/A = D- I and the system behaves as if the two layers were rigid. For increasing values of R this relation is still obtained for large but the layer thickness significantly modifies the behaviour for D close to 1, i.e. when the two solid layers are close together.

200

1.2-

..:......

2 1 __ Log F

10.8 -

0.60.4 0.2 W

-

.‘/.’ , f,’

--

I’

c

WDO

I

I

I

I

I

I

I

0.8

1

1.2

1.4

1.6

1.8

2

Figure 4. Relation 1/A vs. D for different R.

-4

1

I

I

I

I

I

I

I

-3

- 2

-1

0

1

2

3

4

Figure 5. R dependence of F’ and F“ . Comparing these curvcs with the experimental results described above shows a good qualitative agreement and allows identification of the layer stiffness G. For instance we can adjust SZ t,o fit the c?xperimentally observed value KO of for -

I) = I ( Do is known from the electrical zero and p from the behaviour at large D). Since p and o are known, this value of R determines (;. For a Santotrac 40 oil the value of (; = 100 Pa is obtained which is obviously unreasonable and much too small. 3.3 Far field analysis The dependence of F’ and F” with respect to R for ddferent values of D is rnpresonted on Figure 5, showing a rather complex behaviour. The experimentally observed range however corresponds to SZ tmtwcen and 10-6. In this range the I X ~andF llog;“ vs. LogR curves are straight lines with slope 1 and 2 respectively. Accordmg to (4) these curves can be used to determine Log(:’ and Log(>” as a function of Log a.

Again these curves are in good qualitative agreement with experiments : using the h i d separation D - Do instead of D the curve for (3” is found independent of D while G’ does depend on D. Fitting our model with tho experimental results again provides identification of the layer stlffness which is again found to be 100 Pa for the Santotrac 40. It is worth noting that these two chfferent identification procedures relating onc to contacting elastic layers, the other to significantly separated layers, provide indeed the same wrong value. 4. THE COMPRESSIBLE CASE

4.1 The importance of compressibility All the preceding results are based on incompressibility and this assumption may explain the very small value obtained for (1. Indeed the shear stiffness of the layer may contribute to the global response of the system but the layers will primarily bc loaded in compression. The role of compressibility in this problem must be clarified. Before coming back to the general problem let us start with the case of an homogeneous elastic body which is governed by (17), which of course cannot be integrated analytically. Introducing adimensional

20 1 variables it is however possible to show that this problem only depends on one ixhmensional parameter a = -G- R

identified. Practically we have to fix one of them and it is then possible to determine the other. Again both methods give similar results which are represented in Figure 6. 16-

K D

15-

In particular the elastic stiffness can be shown to be

Y

3

141312-

F=k6D

11-

where i(a) is an adunensional function which can be computed numerically and which is equal to 1 for a = O ( K -+a,the incompressible case) and which decreases with a. Thls Lt a first evidence of the essential role of compressibility in this kind of problem. Even if K is much greater than G the incompressible approximation a = 0 cannot be used for very thin layer i.e. where I)/R is also very small (typically 10-7 in the surface force experiments). 4.2 Compressible viscoelastic analysis The general compressible viscoelastic case requires the solution of (22) with the houndary conditions a+O

for r - + m

do -=0 dr

for r = O

In the elastic case o is a real function and the problem has been solved by finite ddferences und finite elements but in viscoelasticity 0 is complex and the finite ddference method is more convenient. Computation has been performed by assuming an incompressible newtonian fluid between compressible elastic layers (RNHH configuration). The two identification procedures described in sections 3.2 and 3.3 for the layer stiffness can still be developed. However there are now two elastic constants to be det.ermined K and G which cannot be both

lo 9$

L LO6 G

8 l 0

I

I

I

I

i

2

4

6

8

10

Figure 6. Elastic stiffness identification. The vertical asymptote corresponds to thr incompressible limit but the obtained numerical values show that if the ratio W K is in order 1, it is the horizontal asymptote which is relevant. This confirms the conclusion of section 4.1. Compressibility. even small, plays an essential role in the squeeze of very thin layers.

4.3 A simple problem In order to clarlfy this compressibility influence a very simple model will bc considered [7][8] : the squeeze of an elastic thin layer (length 21, thickness 2h, width L) under plane strain conchtions (Figure 7).

Tzh I

~

.

Figure 7. Squeeze of a plane thin layer. The equation (17) can then be solved exactly giving the following expression for the elastic stiffness

202

k=

which after integration in x gives (29). For t,hin films p >> 1 , oz is almost constant everywhere but in a boundary layer about x = 51. This is in agreement with the exact solution except for the value of this constant stress which for the exact solution is found to be

3(1- 2 ~ h)

and in the incompressible case

These two relations again confirm the singular character of the incompressible case. Now the elastic problem still cannot be exactly solved but M e r e n t analytical techniques can be used to investigate its structure [7][8]. Essentially the elastic stiffness is obtained as

k=

- i-e(v,-)

( 1 +Ev()l(-l v - )2 ~ ‘.hI[)

h

0,

=

E(1-V) (1

vo/(l - v )

0 . .=

l J [

5. OEDOMETRIC THIN FILM MODEL 6.1 The homogeneous elastic case In order to improve the compressible thin film model ( 1 7), let us start from the normal stress dutribution oz for the problem of section 4.3

E 6D c h p x / l oz = 3(1-2v)%{ chl

-’}

(33)

The reason for this obviously lies in the assumed form (10) for the stress tensor. It therefore appears natural to modify this assumption in

] (31)/a ],

with a function 8 which increases from 0 to -0.55 when v varies from 0 to 0.5. For a very thin layer h/l + 0 , the oedometric solution is obtained (no lateral motion ux =O). The correspondmg stiffness is given by the oedometric modulus differing from the value (29) obtained from the compressible model (17), which therefore appears as not satisfactory to describe the compressible case and therefore has to be modified. Equation (31) also clearly shows again the singular character of the incompressible limit.

6D

+ v)(l - 2v) 2h

71 O

“I

0 vo/(l- v)

T2

‘2

o

(34)

which reduces to (10) in the incompressible case ( v = 1/2) and which corresponds to the oedometric state ( E~ = E~ = 0). Keeping all other assumptions unchanged, the oedometric thin film model is finally obtained as

instead of (17). When applied to the problem of section 4.3 this equation gives chaxI1

3(1 - 2 ~ I) h

in agreement with what is known about the exact solution. In particular, near the boundary x = 1

203 so that the side effect is limited to a boundary layer of width 6 . Again the incompressible limit v -+ 1 / 2 is singular.

between relatively smooth surfaces, J. Chem. Phys., 98 (1993) 7345-7360. 4. D.Y. Chan and F.G. Horn, Drainage of thin liquid films, J. Chem. Phys., 83 1985)

5.2 The general case Extension of this model to the elastic heterogeneous case and later to the v iscoelastic harmonic heterogeneous case is straightforward - even if somewhat clumsy it is still based on (34) with

53 11-5324. 5. J.P. Montfort

= (3E - 26)/(6g

+ 26)

and finally leads to the equation (21) with different, more complicated, expressions for f!,and%, but which can be treated exactly in the same way. The identification procedure for G or K can then be applied as in section 4.2. The resulting curve Log K, Log G is practically inbtinguishable from Figure 7. This analysis however provides a more satisfactory description of compressibihty and should be used instead of the previous one. 6. CONCLUSION

A complete model is now available for dacribing the nanorheology of confined liquids in surface force experiments including compressibility effects in the layers which, somewhat to our surprise, appears to be quite essential. It will provide an adequate framework for interpretation of experiments as well as a reference to assess the validity of t.he simplified models presently used.

REFERENCES

J.N. Israelachvili, Intermolecular and surface forces, Academic Press, New York, 1992.

A. Tonck, J.M. Georges and J.L. Loubet, J. Colloid Interface Sci., 126 (1988) 1540. J.M. Georges, S. Millot, J.L. Loubet and A. Tonck, Drainage of thin liquid films

and G. Hadziioannou, Equilibrium and dynamic behaviour of thin films of a perfluorinated polyether, J. Chem. Phys., 88 (1988) 7187. 6 A. Cameron, The principle of lubrication, Wiley, New York, 1967. 7. F. Auslender, G. Armengaud, F. Sidoroff and J.M. Sbgura, Ride de la compressibilitb dans I'Bcrasement des couches minces, 126me CongrBs FranCais de Mbcanique, Strasbourg, 1995. 8. G. Armengaud, F. Auslender, J.M. Sbgura and F. Sidoroff, Mbthodes hergbtiques appliqubes A l'btude du comportement des couches minces Blastiques, 126me Congr6s FranCais de MBcanique, Strasbourg, 1995.

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205

How to achieve contact recording with a low stiction force L. Tosi

B. Bou-Said

a SILMAG Research and Development group, 17, Rue des Martyrs, 38000 Grenoble, France. b Laboratoire de Mecanique des Contacts, URA CNRS 856, INSA de Lyon France.

An increase in magnetic density of hard disk drives involves a reduction of the head-disk separation. Today the current separation is around 40 nm. This paper presents a new type of slider in order to reduce the head-disk separation to zero manometer and which generates a low stiction force. These sliders are the most advanced in the disk drive industry. Using the microelectronics' techniques we inlay protrusions on the Air Bearing Surface (ABS) of the slider. With the Flying Height (FH) machine (currently used in the drive industry) we can measure the gap bctween the disk and the sensor of the standard sliders and the advanced sliders. A (( Zygo )) and a G Tencor )) are used to correlate the thickness of the protrusion. The Stiction Force (SF) machine is used to measure the stiction of the slider with protrusions and without protrusions on one type of disk. In this paper we present new experimental results in order to validate the concept of the protrusions on the ABS and we compare the results obtained with advanced sliders to those from standard sliders. 1. INTRODUCTION

The first techniques to perform contact recordings with high glide disks were a high Gram Load (GL) and a low linear velocity. But the extremely high wear rate of the slider and of the disk make this solution obsolete. In 1990 J. LEMKE [ 1 ] suggested to use hydrodynamic lubrication where the slider is in continuous contact with the lubricant (full contact approach). But numerous problems (lubricant Icakage, ...) make this technique hard to implement in the industry. In 1990 the industry proposed to manufacture a slider flying at a small distance from the disk (less than 20 nm) to study the real problems of contact. The disks have to be very smooth. Both a liquid lubricant and a smooth disk increase stiction which can lead to stalling of the drive motor. Therefore this solution needs a device which lifts the slider upon start-up (dynamic loading). Nevertheless only one company introduced this technique in manufacturing drives

because of to the cost and many problems related to the dynamic loading. In 199 1 the tendency was to dramatically reduce the slider area, mass and load (35 'YO for the M pic0 D, 25% for the (( femto N, ....) but a lot of difficulties in manufacturing (dicing, assembly,...) stopped the implementation in the industry. With our solution the dynamic loading is not necessary because of a smaller contact area between the disk and the head. Using the bonded disk FOSTER [ 2 ] with a very smooth surface the FH is less than 10 nm and the wear is low. The main problems with this solution are coming from the microelectronic technology (thickness of the protrusion, ...) and the difficulty to develop a correct theoretical model to obtain a numerical simulation of these sliders. Protrusion

206 2. EXPERIMENT

We present in the following section the geometry of the slider and the measurement techniques. 2.1 Sliders Two types

of sliders are used in these experiments. Standard sliders without protrusions and advanced sliders with protrusions. The sliders are coated with TiW. Ten sliders of the two types are used in these experiments. These sliders are (( picos 25 % )).

Measurement of the protrusion heights. The protrusion height is measured with a contact stylus profiler (DEKTAK) and a non-contacting optical profiler (ZYGO) (Bushan, 1990) [ 3 1.

Representative values of the height obtained with stylus and optical profiler are presented in table 1. The stylus radius is 2.5 pm and the measurement presented gives the results of a 100 pm line scan, while the optical profiler characterizes a 100 pm by 100 pm area. Table 1

I SLIDERS I Th (nm) I 1 2 3

Th (nm) I(ZYG0)I (DEKTAK) I 72.9 I 14.2 I 73.4 I 72.5 73.3

I I I I I

Yo

I

98.25 101.24 98.91

Standard slider The heights measured with the two methods are in good agreement.

Advanced Slider (Note the four protrusions on the ABS)

Measurement with (( DEKTAK ))

207

Flying height measurement.

Our Flpng Height Tester is a Cambrian Digital Flying Height Tester.

We present in table 2 the results obtained from ten standard sliders (no protrusions).

The flying height is obtained from the analysis of a color interference pattern due to the separation between the disk and the slider. Light reflected from the bottom of the glass disk and light reflected from the flying surface of the head (ABS) travels a slightly different &stance before reaciung the optical assembly of the tester. This path difference is equal to twice the distance between the bottom surface of the glass disk and the ABS, which is the definition of flpng height. The difference in the optical path results in a phase Merence as light reaches the optical assembly of the tester. The interaction of the phase s M e d light causes the color patterns which are visible on the television monitor. The tester determines the flying height of the head by analyzing the relative intensity of the various wavelengths of light.

FLYING HEIGHT MEASUREMENT Flying height bin)

1-

[

1-1

0.28

I

0.47

I

i

0.66

1.73 1.65

2.09 2.17

2.32 2.32

1.65 1.69

2.28 2.13 2.17 2.28

2.32 2.17 2.17 2.32-1

Head # 3 Head ## 4

I

Head # 8

I

I I

I

I I

Head # 10

m] -

c

I-I

I

1.69 0.03 1.73

2.19 0.06

i

2.28

2.25 0.08

I I

Glass Disk

Flyng Height Tester

i

2.36

I

208 As the distance between the disk and the slider becomes large compared to the limit of the FH machme the measurement of the flying height (the gap) of standard sliders is easy to perform. We can note that the FH increases with increasing radius, For the advanced sliders (with protrusions) the distance is too small to get correct

measurements with the FH machine. Then as we cannot obtain the distance between the disk and the sensor we only measure the distance between the A B S (near the bottom of the protrusion) and the disk. So to obtain the distance between the sensor and the disk we have to extrapolate.

We present in table 3 the results obtained from ten advanced sliders (with protrusions).

1

Flying height @in)

1 Radii (inch) I

0.28

1

I

I I I I I I I

Head # 6

1-1 I

1-1 I

=I

I Mean

Max. Min.

3.02 2.89 2.97 3.01 3.13 2.95 3.18 3.13 .~ 3.16 ~~

~

2.88

I I

0.47

I

3.21 3.33 3.34 3.37 3.29 3.18 3.44 3.39 3.34

I

3.19

I I

I I

I

I I I I

I

.

I I

0.66

I

Thickness of the protrusion

I

Zrgo

I

Dektak

I

2.87 2.89

I

2.92 2.85

2.85 2.82

I

2.86 2.88

I

I

3.39 3.48 3.36 3.58 3.54 3.50 3.52 3.57 3.53

I

3.41

I

3.36 0.22

II

I I

I I I

I I I

I I I

I

I

I I I

I I I

I

I I

2.88 0.30

I

I I

I

3.18 0.26

I I

I

I I

I I

2.89 2.79 2.89 2.92 ~

2.87 2.83

I

I

I I

2.89 2.88

I

2.81

I I

2.85

2.85

I

2.76

I

I 0.32 3.1 8

I

I 1

1

I

I I I I I I 1

I

209

FLYING HEIGHT MEASUREMIWI"T

From our results we can note that with the advanced sliders the &stance between the sensor and the disk is very small I 1 nm. The importance of the pressures which are generated by the protrusions prevent the gap to be reduced to zero. We note also that the curves have the same tendencies with respect to the radius. Then we can conclude that the introduction of the protrusions does not change the flying characteristics. We believe that the number and the height of the protrusions can be optimized in order to obtain better results.

disk surface when the disk starts to rotate after the slider has been sitting on the surface for a fixed amount of time. A load cell is used to make th~s measurement. The force that the disk applies on the head is transferred to a semiconductor load cell through a frictionless air slide. The load cell is a resistance bridge. The disks are 2.0 pnch glide height and are covered by 3.2 nm of AM2001 lubricant. The stiction tests are performed in the ID crash zone. Both sliders (standard, advanced) are used in these tests. 3.1 Description of the tests

3. STICTION TESTS

The tests are obtained from a NUPHASE MEGASSIS ANALYSER. The stiction tester measures the forces (in grams) required to break loose a head slider from a

For all sliders one start/stop is performed. After the s W s t o p the slider stays on the disk during one minute and the stiction test is performed after this dwell time.

2 10 The Hga is the Head Gimbal Assembly. Sum G ~ g r

vleasurement device for the stiction force

Looking at the values we note that there is a sigruficant difference in the stiction forces but the difference is not proportional to the surface in " contact " with the disk. The surface of the 4 protrusions is : S = 4 * ~ * ( d f 2 ) ~ with d=60 pm S=l1310 pmz. The surfaces of the 2 ABS are near 1 000 000 pm2. We think that if we introduce a crowning on the ABS we can probably obtain a response which could be closer to a linear one. The results obtained by the Stictioflriction tester show that the presence of the protrusions on the ABS tends to minimize the stiction force. T h s is due to a smaller contact surface with the disk.

Table 4 4. CONCLUSION

All the stiction forces are expressed in grams.

I

Sliders

Head # 8

1 IStandard lAdvanced1

2. I

This paper deals with experimental results concerning flying height and stiction force obtained from standard sliders and advanced sliders for magnetic contact recording. From these results we observe that with the advanced sliders we obtain a lower gap between the sensor and the disk as well as a lower stiction force and this is due to the presence of the protrusions. With this new type of slider we believe an increased magnetic density of hard disk drives can be obtained even if the thickness and the number of the protrusions are at the present time not fully optimized. We are still working on the following three problems : - optimization of the number and the shape of the protrusions from an experimental point of view. - wear test experiments. - numerical modeling and simulation for proximity recordmg.

REFERENCES [ 1 1 Lemke, James U. U.S. patent No 314999 02.24.89. [ 2 ] Foster, J S. U.S. patent No 681272 04.08.91. [ 3 1 Bushan B. Tribology and Mechanics of

Magnetic Storage Devices.

SESSION VI STARVED E.H.L. Chairman :

Professor Bo Jacobson

Paper VI (i)

Starvation Phenomena in E.H.L. Point Contacts: Influence of Inlet Flow Distribution

Paper VI (ii)

Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and VI Improvers

-

Paper VI (iii)

-

Waviness Orientation in E.H.L. Point Contact

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

213

StsawationPhenomena in E.H.L. Point Contacts: Influence of Inlet Flow Dist,r ibu t ion. F. ('hevalier ", A.A. Lubrecht ', P.M.E. Cann ', F. Colina and G . Dalmaz'. "Laboratoire de Mecanique des Contacts, URA CNRS 856, INSA de Lyon, France. 'Department of Mechanical Engineering, Tribology Section, Imperial College, London SW7 2BX, UK. In comparison to the fully flooded Elastohydrodynamic (EHL) regime, it is difficult to predict the complete film thickness distribution under starved lubrication conditions. Starvation of the contact results in an overall reduction, and a shape modification, of the film in the contact. Existing models cannot fully predict these changes, as the boundary conditions used do not represent physical reality. Experiments show that the film thickness distribution in the Hertzian zone depends on the amount and distribution of the lubricant in the inlet zone. The area where the pressure build-up starts; the inlet meniscus, is a result of the supply condition rather

than the fundamental physical parameter determining starvation. The aim of this paper is to present numerical EHL results based on the amount of lubricant locally available 011 the surfaces. The results of two different simulations of the inlet film are presented. The first model assumes a constant inlet oil film and gives "classical" film shapes when sufficient oil is available. As the oil quantity decreases, variations in film thickness are reduced, eventually tending to the d r y contact shape. The second approach adopts a more realistic inlet oil distribution, pairing film depletion in the centre of the track with a polynomial distribution elsewhere. A complete modification of the film shape is observed when the width of the central depletion increases and when the oil quantity in the central part decreases. The minimum thickness no longer appears in the side lobe area but in the central region; the sides remain abundantly lubricated. Thr numerical results are compared to film distributions obtained experimentally and good agreement is found.

1. INTRODUCTION Most concentrated contacts still require an adequate lubricating film t o operate reliably over long periods. To build and maintain this film requires a sufficient supply of lubricant. In a starved contact the inlet gap is not completely filled and as a result pressure build-up begins closer t o the contact. The ensuing EHL film can therefore be much thinner than predicted by fully-flooded analysis, and consequently the risk of asperity contact increases. This can result in surface damage and premature component failure. The degree of lubricant film reduction depends on the amount of oil on the contact surfaces and the operating conditions. It is import,ant therefore t o be able to predict the degree of film thickness reduction in order to adjust the predicted life, the operating conditions or to augment the surface finish. On the other hand, it would also be advantageous t o know the mini-

mum quantity of oil required to adequately lubricate a contact under given operating conditions. It was the early work of Wedeven et al. [16], Chiu [5] and Pemberton et al. [14] that defined the starved lubrication problem. They studied starvation visually, using optical interferometry t o measure film distribution within the contact and to simultaneously observe the supply condition. One observation was that as starvation proceeded an oil-air meniscus is formed in the inlet region and this moves towards the Hertzian contact circle as the severity of the condition increases. Figure 1 shows three inlet meniscus positions representing the evolution from fully flooded through classically starved t o fully starved. Film thickness reduction coefficients were thus derived based upon the relative inlet meniscus position. The supply condition was defined in terms of the position of the inlet meniscus rather than the amount of oil present on the surfaces. The latter would be a more direct way of describing the

214 contact behaviour as it controls both the shape and location of the inlet meniscus and the ensuing film thickness distribution.

I

2

0

Figure 1 Inlet meniscus position : 1 fully ffooded - 2 classically starved - 3 fully starved. The circle represents the Hertzian contact area.

In numerical studies of the problem (Hamrock and Dowson [ll])the inlet meniscus position was again adopted to describe starvation. The inlet meniscus was modelled as a straight line. Formulae relating the position of the inlet meniscus to a coefficient of film thickness reduction were established. This approach can only be applied to the “classically” starved regime where the menis(’us is still outside the Hertzian radius (Figure 1). I t breaks down for the “fully” starved condition where the meniscus position touches the Hertzian contact. The application of the experimental film depletion factors to realistic cases is difficult since it is hard to establish the position of the inlet meniscus. The limitations of the numerical work are similar. The assumption of a straight line meniscus is contradicted by experimental observations [ 1,2,6,9,16]. Recent experimental observations [3,4] show that a contact can be locally estremely starved and nearly fully flooded, due t,o large differences in local oil supply. T h e earlier studies are therefore limited, since t,liey cannot take into account the precise geometry of the inlet meniscus. The current work by the authors represents a new approach to the problem. It was introduced in an earlier paper [4] where a physical boundary condition was used;

the oil inlet film thickness distribution on the surface. Results were presented for the hydrodynamic case for different inlet film distributions and the effect of repeated passes examined. In this paper the approach has been extended to the EHL regime. The supply condition has been modelled by both a constant and polynomial inlet distribution. EHL film thickness results have been obtained for a range of inlet supply and operating conditions. The results are presented as 2-D line graphs and pseudo-interference plots. The latter gives a pictorial representation of the results in a form comparable to the usual optical interference measurements. The numerical results from this work are also compared to experimentally measured starved EHL film thickness distributions. 2. THEORY

The theoretical formulation is based on the algorithm established by Elrod [7] [8]. A new variable 0, which represents the lubricant concentration within the gap has been included in the Reynolds equation. This variable allows conservation of couette flow in the cavitated region. The problem is thus treated as a complementarity problem where 0 5 0 < 1 , P = 0 or 0 = 1,P > 0. Consequently, the calculational domain is divided in two distinct zones: pressurized and cavitated. The boundary between these zones, i.e. film formation and subsequent rupture, is determined automatically by the calculation. Its position depends directly on the amount of lubricant initially adhering to the surfaces.

2.1. Notation b

radius of Hertzian contact, b = v(3wRz)/(2E‘) D domain E’ reduced modulus of elasticity, 2 / E ’ (1 - .;)/El (1 - ~ i ) / E 2 G material parameter, G = aE’ h film thickness AH film thickness difference between two consecutive black lines in the pseudo -interference plot. H , dimensionless central film thickness

+

215

H,, dimensionless fully flooded central film thickness H, dimensionless minimum film thickness H dimensionless film thickness, H = hRx/b2 Ha dimensionless rigid body displacement H,,r,-dimensionless inlet oil film thickness, Hoilm = Hi,/ L dimensionless material parameter (Moes), L =~ ( 2 ~ ) 1 / 4 M dimensionless load parameter (Moes), M = w(2~)-3/4 n number of discretisation points p pressure ph maximum Hertzian pressure, yh = (3w)/(2b2) po constant (Roelands), po = 1.98 10’ P dimensionless pressure, ‘f = P / p h €2, reduced radius of curvature in x direction, 1/Rx = 1/Rx1+ 1/Rx2 R, reduced radius of curvature in y direction, R, = Rx mean velocity in 2 , urn = ( u ~ u2)/2 u,, IJ dimensionless speed parameter, U = (qourn)/(E’Rx) W dimensionless load parameter, = w/(E’R:) X ,Y dimensionless coordinates, X = x/b, Y = y/b 2 pressure viscosity index (Roelands) u pressure viscosity coefficient, [Pu-’1 w external load 710 viscosity at ambient pressure, [Pas] fi dimensionless viscosity, i j = ~ / Q O p dimensionless density, p = p/po 0 concentration or relative oil quantity X dimensionless parameter, = ( 1 2 ~R:0 um)/(phb3)

+

w

2.2. Mathematical Model The modified dimensionless Reynolds equation, which is valid in both zones, can be written as:

The film thickness is given by:

H ( X , Y ) = Ho+

-x2 + 2

Y2 2

-

The rigid body displacement Ho is coupled to the force balance equation which, for a circular contact reads:

(3) The viscosity pressure relation proposed by Roelands is used: ?j(P)= e x p ( % ( - l + ( 1 -)*)) PPh (4) z Po with

+

(5) The compressibility is taken into account with the density pressure relation proposed by Dowson and Higginson:

The formulation enables us to take any lubricant inlet profile and the boundary conditions are P = 0 and 0 ( X o ,Y ) = H o i , m ( Y ) / H ( X o ,Y ) . 2.3. Numerical Techniques The starved model, including the additional parameter 6 , thus becomes a free boundary problem. This additional variable slows down the numerical EHL solution, which is already difficult to solve. Moreover, as starvation increases the meniscus approaches the Hertzian region and the solution becomes very sensitive to its position. A relatively fine mesh is thus required to predict the film thickness accurately. Furthermore, in order to limit the influence of the boundary conditions in the y direction, it is necessary to use a large calculational domain. For these reasons a multigrid solution method has been applied to the problem and a multilevel multi-integration method has been used to limit the computing time in the calculation of the elastic deformations. These numerical techniques and the theory are developed in references [13] and [15].

216

3. N U M E R I C A L R E S U L T S

I n t.he following section starvation will be studied for two lubricant inlet profiles. Firstly, the oil film a.vailable on the surface is assunied to be constant., i.e. it does not vary with Y . Three numerical operating conditions, see Table 1, are treated wit,li different inlet film thicknesses. The last case, i.e. hl = 291 L = 3.28, is also solved with a varying inlet distribution, having a depleted centre. It corresponds to an experimental operating condit,ioti and the numerical findings will be compared tmothe experimental results described in section 4.

thickness distribution tends to a flat, Hertzian shape. While under fully flooded EHL conditions the ratio H , / H , tends to increase with load [15], this ratio tends asymptotically to unity for all operating conditions, as starvation increases (Hoilm decreases), see Table 2. A constant inlet distribution is useful to study, in a simple way, the influence of starvation on the contact behaviour and it confirms the established starved results. However, experimental observation of starved contacts indicate far more complicated inlet distributions. A constant film thickness can not represent this physical reality. More complex inlet film distributions are thus used in the following section to simulate a more realistic lubrication condition.

M = 10, L = 10, H,, = 0.687 Hoiim I 00 I 1.26 I 0.63 I 0.25 I 0.13 ..... H , / H , I 1.35 I 1.34 I 1.28 I 1.12 I 1.03 M = 100. L = 10. H,,_ _ _ = 0.137 Hoilm I 00 I 0.27 I 0.14 I 0.054 I H ,”,/ H ,.._ I 1.87 I 1.83 I 1.66 I 1.29 I M = 291, L = 3.28, H,,... = 0.0361 I1 Hoiloo 00 I 0.78 I 0.39 0.019 I 0.0078 H , / H , 1 2.26 I 2.22 I 2.02 1 1.50 I 1.09 Table 2 H , / H , as a function of Hojloo. ,

I

-2,2 66049

66049 1 Table 1 Parameters used. 71

I

I

-2,2 66049

3.1. Constant inlet film Figures 2-4 represent the pseudo-interference plots of the film thickness distribution and the central cross sections for different values of inlet oil supply and for the three operating conditions. The IIert,zian circle is plotted with a dashed line and the boundary of the pressure zone with a solid line. On t.he pseudo-interference plots the inIrt’ meniscus is observed moving towards the I-Icrtzian circle when the inlet film diminishes. 1 his meniscus conserves a simple, circular, shape c.onccnt.ric with the Hertzian zone. At the outlet, (‘liefilni rupture location is hardly affected by the supply condition. On each cross section plot, H , is observed to decrease faster than H , with HOil,. When Hoiloo becomes very small compared to H,, the film I

/

I

I

I

I

I

I

I

’

3.2. Depleted inlet distribution In order to simulate the “classically” starved EHL condition a polynomial distribution hoiIm(Y) = (Y4/2 t 0.1) ,urn has been used. This is a “mildly ” starved case which shows a more realistic inlet meniscus, see Figure 5. The pressure develops upstream of the Hertzian area and starts earlier on the sides than in the centre of the track (concave shape). There is no significant modification in film thickness distribution compared to the fully flooded case. Only a small reduction of the thickness is observed in the central part. Figure 6 shows a “fully” starved condition. This result has been obtained by setting an inlet film distribution defined by hoiloc)(Y)= max( ( Y 4 - 0.1)/2,0.035) ,urn,. It means that a

217

Hoilm=0.63

Hoilm=0.25 0.2

0.8 0.7

-..... ..... ........ .....

0.6

-

-p:

0.18

Hink + i

0.16

I

-?

'.... .........

..... ... .. _.

,I

1

0.5

Hinki ,+ Hinf=l, 3';...... HinkO . .. .

-$

0.12

0.4

0.3

2

0.08

m

r

5 I

0.14

0.1

0.06

0.2 0.04 0. 1

0.02

n -1.5

0 -1

-0.5

0 Y-yla

0.5

1

Figure 2 Case M=IO L=IO : Pseudo interference plots, with film formation and cavitation boundaries, and central film thickness distribution as a function of HOilm. AH = 0.1

~~

-1.5

-1

-0.5

0 Y =y/a

05

1

1 .5

Figure 3 Case M=I00 L=10 : Pseudo interference plots, with film formation and cavitation boundaries, and central film thickness distribution as a function of HOilm. AH = 0.04

218 very thin constant layer of lubricant of 3 5 n m is present in the central part of the track. The inlet meniscus has reached the Hertzian zone, and a significant change occurs in the central part of the contact. The pressure now builds up very close t o the Hertzian circle. The central part is therefore heavily starved, whilst the sides are abundantly lubricated. This results in a complete modification of the contact geometry. A flat zone of minimum film thickness occurs in the central region of the contact. Two distinct regimes are observed: the centre maintains the same lubrication level as a contact with a supply thickness of 3 5 n m , whilst the sides behave as if they were fully lubricated. No significant reduction of the film thickness is observed in the side lobe region, see Figure 7. 4. EXPERIMENTAL MEASUREMENTS OF STARVED EHL FILMS 4.1. Experimental method

-1.5

-1

-0.5

0

Y-vla

0.5

1

Figure 4 Case M=291 L=3.28 : Pseudo interference plots, with film formation and cavitation boundaries, and central film thickness distribution as a function of Hojloo. AH = 0.02

In a parallel study, film thickness distributions were measured in a starved EHL contact. As in earlier experimental studies a visual technique is used to study film formation and the supply condition. The contact is formed by a steel ball loaded and rolling against a glass disc and a modified optical interferometry technique is used to measure the film distribution within the contact. Pictures of the starved EHL contact were taken and the images translated into film thickness maps. The basis for this technique is the thin film optical system developed by [12]. This method allows film thickness measurements down to 1 nm with a resolution of 1 nm. Thus providing the sensitivity necessary to measure the very thin films formed in heavily starved contacts [lo]. The improvement in film thickness resolution, compared to conventional interferometry (25 nm), is due t o the silica spacer layer which overcoats the chromium and thus augments films formed within the contact. The disadvantage of this technique is that only single or line contact measurements can be taken; it is not possible to map the full contact. The technique [3] used in this paper also uses the silica spacer layer, however, now a CCD camera coupled to an video capture board is used to grab an image of the contact. The presence of the silica

2 19

0.06

a

2

0.03 0.02

O.O1

0

t

-1.5

0.06

-

0.05

-

0.04

-

0.03 -

0.02

.

0.01

-

0' -1

-0.5

0 Y =y/a

0.5

1

1.5

Figure 5 Case M=291 Jk3.28 : Pseudo interference plots, with film formation and cavitation boundaries, and film thickness distribution for different abscissa with hojlm(Y) = ( Y 4 / 2 + 0.1) pm. AH = 0.02

-1.5

I

-1

-0.5

0 Y ?la

0.5

1

1.5

Figure 6 Case M=291 ~ k 3 . 2 8: Pseudo interference plots, with film formation and cavitation boundaries, and film thickness distribution for different abscissa with hojlm(Y) = max((Y4 0.1)/2,0.035)pm. AH = 0.02

220

001

1

01

-1.5

-1

-0.5

0 Y=y/a

0.5

1

I

1.5

Figure 7 Case M=291 k 3 . 2 8 : comparison of the central cross section of the three cases: fully flooded - classically starved - fully starved.

layer enhances the lubricant film making it visible as a second or third order interference film. Subsequent colour analysis of the image gives a map of film thickness variation within the contact. The starvation experiments were carried out at a constant rolling speed of 0.155 m/s and a maximum Hertzian pressure of 0.53 GPa. Starvation was induced by progressively removing oil from the rolling track. Film thickness profiles for different starvation conditions can thus be directly compared. The lubricant used was a poly-alphaolefin with a viscosity of 0.0587Pa s. 4.2. Results In Figure 8 three images are shown; the inlet is on the left hand side and they show progressive starvation of the contact. I n these images the contact moves from the fully flooded (8a) to the “classically” starved (8b), where the meniscus is still outside the contact, and then the fully starved (8c) regime. The consequent local depletion of film in the centre of the contact is indicated by the colour change. These images were then translated into film thickness distributjions and these are shown in Figures 9-10, predicted film thickness profiles, using the polynomial model, are also shown for comparison. Figures 9a-l0a show a typical profile for a fully flooded contact and the usual features of a central film with minimum side lobes and constriclion a t t,he rear are seen. Figures 911-10b repre-

Figure 8 Experimental interference plou: ( u ) fully flooded - ( b ) classically starved - ( c ) fully s t arved.

22 1

200

200

150

150

100

100

I

50

50

I

I

0

0

200

1

Numerlcrl

-

ExperimentrI --.-.. 150

100

I

I

50

a

200

200

150

150

100

100

50

5c

0

c

Figure 9 Comparison between numerical and experimental thicknesses at t = 0 for the three cases: ( a ) fully flooded - ( b ) classically starved - ( c ) fully starved.

Figure 10 Comparison between numerical and experimental thicknesses at y = 0 for the three cases: ( a ) fully flooded - ( b ) classically starved ( c ) fully starved.

222 sents the “classically” starved condition, in this case an overall decrease in the central region is observed. The side lobe film thickness decreases very slightly. Figures 9c-1Oc represent the heavily starved contact, a substantial modification of the film shape occurs with loss of the film in the central region. The side lobes remain well lubricated and the minimum now occurs along the centre line. 5. DISCUSSION A N D CONCLUSION

5.1. Discussion From experimental observations, see Figure 8, the inlet meniscus position is seen to be governed by the initial oil quantity available on the surface. This meniscus position results in an equilibrium between side flow due to the pressure and in flow due the replenishment action which is greatly dependant on the oil quantity in the side reservoirs. Since it is not yet possible to measure the experimental inlet oil distribution resulting from this equilibrium, this profile had to be approximated. The stabilized inlet oil distribution (Figure 6) is simulated by a constant thickness in the central area of the contact, combined with a rapidly increasing part further away from the central line which represents the slope of the side reservoirs. With this assumption, a reasonable agreement between experiments and theory is obtained in the entire contact for the different conditions, see Figures 9-10. One of the main questions remains, however, if this hypothesis can be verified by direct measurements. Another extension of the theoretical model should try to model the forces redistributing the outlet oil profile. Such an extension could allow the calculation of the oil film decay with continuous overrolling, and to establish whether there is a finite asymptote to this decay. 5.2. Conclusion This paper has presented a new approach to numerical modelling of the starved EHL regime and the following conclusions have been drawn from the work. (i) The authors have presented a new model which they feel is more realistic as it is based on

the amount of oil locally available and it is this, rather than the position of the inlet meniscus, that determines the degree of starvation. The residual oil film adhering to the rolling track is also an easier property to measure in practice than the position of the inlet meniscus. (ii) The film thickness distributions from the constant inlet film model give an overall decrease in film thickness converging to the Hertzian shape, with reducing oil inlet thickness. (iii) The polynomial distribution produces a very different EHL map. The minimum film thickness is now situated in the centre which is heavily starved, whilst the side lobes remain fully flooded. (iv) The polynomial shape approximates the inlet distribution found in practice and reproduces closely the film thickness measured experimentally. (v) The authors believe that this work allows a quantitative description of starvation in an EHL contact based on the oil film present on the contacting surfaces.

REFERENCES 1. AstrSm, H., Ostensen, J.O., and HSglund, E., 1993, “Lubricating Grease Replenishment in an ElastoHydrodynamic Point Contact,” ASME J O T , 115,pp. 501-506. 2. Cann, P.M., and Spikes, H.A., 1992, “Film Thickness Measurements of Greases Under Normally Starved Conditions” NLGI Spokesman, 56,pp. 21-26. 3. Cann, P.M., Hutchinson, J. and Spikes, H.A., 1995, “The Development of a Spacer Layer Imaging Method (SLIM) for Mapping Elastohydrodynamic Contacts” , accepted for presentation at the ASME/STLE joint conference, October 1995. 4. Chevalier, F., Lubrecht, A.A., C a n , P.M.E., Colin, F., Dalmas, G., 1994, “Starved Film Thickness: A Qualitative Explanation”, Proceedings of the Zfst LeedsLyon Symposium on Tribology. 5 . Chiu, Y.P., 1974, “An Analysis and Prediction of Lubricant Film Starvation in Rolling Contact Systems,” ASLE Tmns., 17, 1,

223

1 ) ~ . 22-35.

Dalmaz, G., 1978, “Film Thickness and ‘Traction measurements in small Elastohydrodynamic Elliptical Contacts,” Proceedzngs of the 5th Leeds-Lyon Symposium on Trabology, pp. 71-80. Elrod, H.G., and Adams, M.L., 1974, “ A Computer Program for Cavitation and Slarvation Problems,” Proceedangs of the ist Leeds-Lyon Symposaum on Trabology, pp. 374 1.

Elrod, H.G., 1981, “A Cavitation Algorithm,” ASME J . Lub. Tech., 103, pp. 350354. Gadallah, N., and Dalmaz, G., 1984, “Hydrodynamic Lubrication of the Rib-Roller I h d Contact of a Tapered Roller Bearing,” .IISME J O T , 106,_pp. _ 265-274. 10. Guangteng, G., Cann, P.M., and Spikes, H.A., 1992, “A Study of Parched Luhication”, WEAR, 153,pp. 91-105. 11. Hamrock, B.J., and Dowson D., 1977, “Isothermal Elastohydrodynamic Lubrication o f Point Contacts, part IV, Starvation Rehiilts,” ASME J . Lub. Tech., 99, pp. 15-23. 12 Johnston, G.J., Wayte, R.C., and Spikes, H.A., 1991, “The Measurement and Study of Very Thin Lubricant Films in Conrentrated Contacts,” S T L E Trib. Trans., 34, pp. 187-194. 13. Lubrecht, A.A., 1987, “Numerical Solution of the EHL Line and Point Contact Problem Using Multigrid Techniques,” PhD. Thesis, University of Twente, Enschede, The Netherlands. ISBN 90-9001583-3. 14. Pemberton, J., Evans, D., and Cameron, A., 1976, “A Mechanism of Fluid Replenishment in ElastoHydrodynamic Cont,acts”, WEAR, 37,pp. 184-190. 15. Venner, C.H., 1991, “Multilevel Solution of the EHL Line and Point Contact Problems,” PhD. Thesis, University of Twente, Enschede, The Netherlands. ISBN 90-9003974-0. 18. Wedeven, L.D., Evans, D., and Cameron, A., 1971, “Optical Analysis of Ball Bearing Starvation,” Trans. A S M E , Series F, 93,pp. 349-363.

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

225

Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and Vl-Improvers B.-R. HOhn, K. Michaelis and U. Mann') Rchnical University of Munich Gear Research Centre (FZG), Arcisstrasse 21, 80333 Munich, Germany The objective of the research was the investigation of lubricant film formation in elastohydrodynamic contacts for oils of different origin (paraffinic, naphthenic, polyalphaolefin) and various types of VIimprovers (polymethacrylate, olefin copolymer, styrene butadiene copolymer). An essential part of the research was to find out whether VI-improvers maintain their thickening effect under contact conditions of high pressure (p > 8000 bar), temperature ( a > 100 "C), high shear rate (y > los s-l) and short time of contact, all these conditions occurring simultaneously. A twin disk machine was used to determine mean (integral) values of film thickness as well as film profile in the contact zone for line contact. For these measurements, two electrical capacitance methods were used. Important lubricant properties both for interpretation of the electrical data and for the corresponding EHL calculations were determined. In addition to a thermal viscosity loss, high shear rate y leads to considerably reduced film thicknesses due to non-Newtonian viscosity loss. 1

lntroductlon

Calculations of EHL film parameters depend very much on the assumptions and input values of lubricant properties into the calculation methods ([2], [l], [12]). Therefore thin film sensors were developed and applied to measure these values in disks and gear contacts ([15], [lOl). Foord, Hammann, and Cameron [5] mixed different base oils with polymethacrylates in different concentrations. An optical method (steel ball versus glass plate) was used to determine film thickness in point contacts. For conditions of y,=4.1O7 s-' and pm,=450 N/mm2 they prove, that the thickening effect of polymers was lower than expected.

'I

Hirata and Cameron [7] showed that the viscosity loss of polymer containing oils under contact conditions is higher than for measurements in high pressure viscometers. Schrader [13] performed film thickness measurements with different oils under pure rolling conditions. He showed that already at low temperatures (Boj,=35"C) polymer containing oils build up lower film thickness than calculated. In the described investigations film thickness was measured under conditions as they occur in anti friction bearings and gear contacts of highly loaded transmissions.

Prof. Dr.-Ing. Bernd-Robert HOhn is head of the Institute of Machine Elements and the Gear Research Centre (FZG). Dr.-Ing. Klaus Michaelis is chief engineer at the FZG. Dr.-Ing. Ulrich Mann has written his thesis on the basis of the reported results.

226 2

Experlmental Procedures

rolling friction between the test disks, by the bearings or by any other elements.

2.1 Test Rlg

.

The oil injection temperature Ooil and the oil volume flow rate Veil are controlled by an external oil pump and control unit. The oil is heated to a constant temperature using an oil heating unit with low thermal power density. The temperature is controlled to max. AOoi, k 0.5 K. The investigations run at constant oil temperature Ooi,, while the oil is directly injected between the test disks at a constant flow rate Voi,. The investigations were performed with constant rolling velocity vc

Fig. k

'Mn Disk Machine,

FZG.

The film thickness measurements were performed in a twin disk machine (Fig. 1). The test disks (1) and (2) are separately driven by two AC motors. For continuous variation of speed, friction drives are mounted between motors and driving shafts. The upper shaft is arranged in anti friction bearings in bench (3). The upper bench (3) is attached to the frame by two flat springs (4). These springs (4) allow only a horizontal translation of the upper bench which is restricted by a load cell (11) without an affection by hysteresis. The lower shaft is also arranged in anti friction bearings in the lower bench (6), which is fixed to link (7). The link (7)swivels around axis (8). The disks are loaded by the helical spring (9) and the load applier (10). For a velocity difference (vl + v2) between the two disks a frictional force FRis measured by the load cell (11). The measuring of a frictional force instead of a frictional torque allows the measurement of the tractional portion of the frictional force. The measured value FR does not contain any other losses e.g. caused by

vz = v l + v2

(1)

For measurements under sliding conditions the velocity of one disk is increased while the other is decreased simultaneously. The slide ratio s is defined as

2.2 Capacltance Fllm Thlckness Measure-

ments

W o electrical capacitance methods were used to determine film thickness. The first method allows to measure a capacitance between the test disks (Fig. 2). The disks are electrically isolated from each other. Both disks are arranged in a RC-resonance circuit. Considering the elastic deformation of the contact zone it is possible to convert the capacitance to a mean (integral) film thickness. For details refer to [14].

227 contact conditions. The smaller the size of the sensor the better the resolution of the film profile. The bulk temperature is measured with a Pt-100 thermoresistor, near the surface of the disk.

2.3 Test Conditions

film profile integral measurements

Fig 2: Principle of Capacitance Oil Film Thickness Measurements.

'Ib measure a film profile the condenser area is reduced to a small stripe which is sputtered on the surface of the disk. The result is a variable capacitance signal C,(x) while the sensor passes through the contact zone. The thin film sensors are deposited by using a ion beam sputtering technique ([15], [lo]). insulating layer A1203 sensqr strip

The case-carburized steel disks are 80 mm in diameter. The relative radius of curvature is 20 mm and the reduced Young's modulus E' is assumed as 2.2740" N/m2. The contact length is 5 mm. The disks are ground and polished to a surface roughness of R, = 0.06 pm. The measurements were made for oil injection temperatures aOi, = 40, 60 and 90 "C. The Hertzian stress was varied in the range of pH = 800 to 1200 N/mm*. The measurements were performed for pure rolling conditions and f o r d i f f e r e n t values of s l i d e r a t i o s (s,,, = 30 %). Depending on rolling speed, the maximum sliding speed is vg = 3 m/s. The maximum rolling speed v, is 16 m/s.

/

2.4 Test 011s

'lbble 1 shows some characteristic parameters of the test oils. The viscosity pressure coefficient a is given for a pressure of 2000 bar.

Fig. 3: Sensor for Film Thickness Measurements (Film Profile). Fig. 3 shows the geometry of a sensor for film thickness measurements. The sensor is electrically isolated from the steel test specimen. Both, insulating layer and sensor should be as thin as possible in order not to influence the

A paraffinic mineral oil (IS0 VG 100) was chosen as a reference oil for all measurements. First the nominal viscosity was varied (M32 and M460). Different chemical structure were tested using a naphthenic oil NlOO and a poly-alphaolefin PAO. Both oils have the some nominal viscosity (IS0 V G 100).

Four typical polymers were tested. The base oil MlOO was mixed with polymethacxylate (PMA),

228 olefin copolymer (OCP) and styrol butadiene copolymer (SBC)('l?ible 1). To verify the influence of shear stability on film formation, the polymethacrylate was used in two molecular weights.

For the evaluation of capacitance film thickness measurements it is necessary to measure the dielectric constant of all test oils. For these measurements, a high pressure apparatus was used. A detailed description is given in [8].

3

Measurements

3.1 Pure Rolllng

The next figures show some results of integral film thickness measurements.

Table 1 Some Properties of Test Oils

rolling velocity vy

Fig. 4:

Influence of Rolling Velocity vn and Nominal Viscosity on Film Thickness.

Fig. 4 shows the measurements for the paraffinic oils under pure rolling conditions (s=O %). As expected, the measured film thickness increases with increasing rolling velocity vn. The oil M460 builds the highest oil films. For a better understanding the measured bulk temperature Voi, is also indicated in Fig. 4. It

229

can be seen, that the temperature rises with increasing rolling velocity va and increasing viscosity. A direct comparison of different oils is difficult because of the different bulk temperature. Under pure rolling conditions the bulk temperature UM is effected by shear and compression in the inlet zone of the contact. These effects were observed by Murch/Wilson [ll]. For practical applications they introduced a thermal correction factor C into isothermal EHL film thickness equation of Dowson/Higginson [2].

3.2 Sliding The next measurements were performed for sliding conditions.

0.0;

Fig. 6

rolling velocity vy

Fig. 5:

Influence of Rolling Velocity vn on Film Thickness (VI Improved Oils).

Fig. 5 shows the measurements for the polymer containing oils. Only for the oils PMAl and PMA2 a higher film thickness than for the reference oil MlOO can be observed. The increase of oil film thickness is lower than expected from the higher viscosity. Interesting is a comparison of the oils PMA2 and M460 (Fig. 4). In spite of the higher nominal viscosity of oil PMA2, the measured film thickness is lower than for the oil M460. This represents a certain viscosity loss because of high shear rate y in the inlet zone of the contact. Similar effects were investigated by Dyson/Wilson [3]. They derived an equation for the maximum shear rate y, in the inlet zone. Calculations show, that the shear rate is approx. lo6s-'. This shear rate is high enough to reduce the viscosity of polymer containing oils.

'

5:

10 :

'

15 :

' 20 : ' 25 : slide ratio s

'

30 :

'

X:

'

40 I

Influence of Slide Ratio s on Film Thickness (Chemical Structure).

Fig. 6 represents the measurements for oils with different chemical structure. It can be seen, that oil PA0 with a low pressure viscosity coefficient a, low coefficient of friction p and high VI for lower slide ratio s builds lower film thickness than the base oil M100. For higher slide ratio s the film thickness of the PA0 is higher. The measured bulk temperature fiM is lower than for the oil M100, the result is a higher film thickness. The oil NlOO is an oil with a higher viscosity pressure coefficient, higher coefficient of friction and low VI ("hble 1). The bulk temperature is higher and the film thickness is lower than for the reference oil M100. The measurements for the polymer containing oils are shown in Fig. 7. A significant higher film thickness can be observed for the oil PMA2. For higher values of slide ratio s the bulk temperature for all oils is on a similar level. The measurements of film profile were performed for control of integral film thickness measurements. Fig. 8 shows the measurements

230

slide ratio s

Flg. 7:

Influence of Slide Ratio s on Film Thickness (VIImprover). 1.0

Fig. 9

1 3 pm 3.0

film thickness hprofile Comparison of Integral and Film Profile Measurements.

shear rate effected viscosity loss. The next step is to compare the viscosity of the oils at the same relevant temperature in the contact. relative distance x/b,

Fig. 8

Measurement of Oil Film Profile for Oil M100.

4

Results

4.1 Relatlve Film Thlckness

for oil M100. The minimum film thickness at the end of the parallel gap decreases with increasing slide ratio. This can be interpreted as a result of viscosity decrease while the oil is passing through the contact zone. Fig. 9 compares the two methods. For the film profile measurements the height of the parallel gap was evaluated. For the oil PMAl the measurements fit within a range of & 20 %. The film profile measurements for the other oils confirm the results. Considering the measurements, it is very important to distinguish between temperature and

The film thickness measurements were performed at different oil temperatures. If all other test parameters are kept constant, the film thickness can be described as a function of measured bulk temperature 6,. Fig. 10 shows the results for the oil M100. With a logarithmic scale for film thickness axis, the measured results can be interpolated with a straight line. This gives the possibility to compare film thickness for the tested oils at a constant chosen bulk temperature. Fig. 11 shows the comparison of relative film thickness for the polymer containing oils. The

23 1 polymer PMA2 is sensitive to shear rate because of its high molecular weight. The relative film thickness of oil SBC slightly increases with rising temperature. The polymer of this oil is shear stable, so the effect can be explained with a better viscosity-temperature behavior of oil SBC. 0

bulk temperature 4,

Fig. 10: Measured Film Thickness as a Function of Bulk Temperature.

O*O,L,

1I

.

.

'

200 ! '

.

! . ' ' 400 ! . . 'mPos ! . -600 -I

' 300

nominal viscosity

C

s

Fig. 12: Thickening Effect of Polymers.

2.0

E

E

p

1.0

c

0.0

30

40

50

60

80

70

bulk temperature

C

100

$

Fig. 11: Relative Film Thickness of Polymer Containing Oils.

relative film thickness is the ratio between tested oil and reference oil MlOO and can be interpreted as an effective viscosity related to the base oil. The oil PMAl builds higher film thickness as the reference oil M100. The film thickness is approx. 50 % higher for the whole temperature range. The film thickness of oil PMA2 is also higher than for the reference oil. The relative film thickness shows a dependence on rolling velocity v,,. First and foremost is this a result of different shear rates y in the inlet zone, which is a function of rolling velocity [ll]. The

The statements with respect to the thickening effect of VI-improvers are summarized in Fig. 12. The relative film thickness is shown as a function of the nominal viscosity. The oils are compared at a bulk temperature of 80 "C. It can be stated, that all polymer containing oils build up lower films than a straight mineral oil with the same nominal viscosity. The influence of rolling velocity v,, on relative film thickness for polymer containing oils is higher than for the straight mineral oils. In both cases this effect increases with increasing viscosity. This is mainly affected by a temperature rise in the inlet zone, which is higher for higher oil viscosities. High shear rate in the inlet zone reduces the effective viscosity of polymer containing oils.

4.2 EHL-Calculatlons

For the conditions of the measurements film thickness was calculated. The calculations were

232 performed with an EHL program of Oster [12]. Film thickness calculations in the parallel gap were made acc. to Ertl/Grubin ([4], [6]). The temperature for the calculations is the measured bulk temperature OM.For thermal correction the temperature measurements in disk contacts of Kagerer ([9], [16]) were evaluated. He measured a typical temperature rise AO,,, in the inlet zone of the contact. This temperature increase was added to the bulk temperature

The oil inlet temperature O(.l) is mainly influenced by oil viscosity and rolling velocity. Oil: MlOO

-

&-

60 ’C

p~

1000 N/n

wL

= 16 m/s

2

--

.

\ 3.0. 0

8

Calculation acc. Ostsr Correction of inlet temp.

I

.

I

I

Oil: M460 pH= 1000 N/mm’

I

s - o x

-

rolling velocity vE

Fig. 14: Comparison of Measured and Calculated Film Thickness for Oil M460.

Fig. 15 shows the results for the oil PMM. The calculation without thermal correction shows a considerable increase of calculated film thickness relative to measured film thickness with increasing rolling velocity. Considering the thermal correction, the calculated film thickness is two times higher than measured. A shear rate based viscosity loss is not taken into account in these calculations.

h

3d

\ 3.0 8 0

60.1 X

o.oJ

-2.0

!

-1.5

!

-1.0

1

!

-0.5

!

0.0

74.2 ‘C

!

0.5

!

1.0

!

1.5

I

2.0

relative distance x/bH

Fig. 13: Calculations of Film Profile.

2.5 0 Y

.-u r

2.0

c

E -

1.5

.-P

1.0

?

0.5

G

With the program system of Oster [12] it is possible to calculate a film profile (Fig. 13). For a comparison with the measurements, the calculations were evaluated in the parallel gap. Fig. 14 shows the results of film thickness calculation for oil M460. The ratio of measured to calculated film thickness is displayed. With increasing rolling velocity vp the calculated film thickness is always higher than the measured film thickness. Introducing the inlet temperature increase Atr(.l) the influence of rolling speed on calculated film thickness can be compensa ted.

r

0

2

4

6

8

10

12

14

16

m/s

20

rolling velocity vL

Fig. 15: Comparison of Measured and Calculated Film Thickness for Oil PMA2. Film thickness calculations acc. Ertl [4] and Grubin [6] and a thermal correction according to MurchNilson [ l l ] led to comparable statements. From the measured film thickness using the Ertl/Grubin equation an effective viscosity in the contact can be calculated.

233

0 viscosity

calculated from film thickness

2

100 'C 160 50 oil temperature 29 Fig. 16 Recalculated Viscosity.

the contact. For all oils, a temperature increase caused by compression and shear effects in the inlet zone leads to lower inlet viscosity and therefore to lower film thickness. In particular for high oil viscosities (> I S 0 VG 100) and high surface velocities, the measured values of film thickness are lower than expected. In case of polymer containing oils the high shear rate in the inlet zone (p i~ lo6 S') leads to an additional reduction of inlet viscosity. The result is that most of the polymer containing oils build up only marginally higher film thicknesses than their base oil. This tendency can be observed even more clearly from the measurements under sliding conditions. Measurements show that straight mineral oils, with a nominal viscosity equal to that of the polymer containing oils build up thicker films.

30

Fig. 16 displays the comparison of recalculated and measured viscosity of oil PMA2. The measurements of viscosity were performed for two shear rates. Viscosity measured at low shear rate (y = lo3 s-') and the recalculated viscosity do not correspond. Thinking of the comparison between measured and calculated film thickness, this result would have been expected. The recalculated viscosity corresponds better with the viscosity measurements at high shear rate (4 = lo6 s-*). For straight mineral oils and synthetic oils no difference is observed. This means, that the use of viscosity data from high shear measurements leads to better calculation results also for polymer containing oils.

5

Summary

The measurements prove that film thickness is influenced mainly by effects in the inlet zone of

EHL calculations carried out in parallel with the experimental work show the limits of the isothermal film thickness calculation method. It is known, that the predicted film thickness is too high especially for high oil viscosities and high surface velocities. By introducing a thermal correction factor C [ 111 or an inlet oil temperature, the influence of self heating in the inlet zone can be taken into account. Because of that, calculations for the Newtonian oils show a good correspondence with the measurements. Even with these refinements, the calculations for VI-improved oils lead to results, which are up to 100 % higher than the measured values. Rmporary viscosity loss caused by high shear rate is not taken into account in the calculation method. Corresponding results for measurement and calculation can be obtained by considering the viscosity of polymer containing oils at high shear rates. Further, for VI-improved oils a permanent viscosity loss caused by continuous shear stress in practical applications must also be taken into account.

234 6

Acknowledgement

Oils. ASLE llans., Vol. 27 (1984), pp. 114-121.

The authors would like to thank the German Society for Petroleum and Coal Science and Rchnology (DGMK) for their kind sponsorship of this project.

HOhn, B.-R.; Mann, U.: Measurement of Oil Film Thickness in EHD Contacts, Influence of various Base Oils and VI Improvers. Final Report, DGMK Project 466 (1995).

References

Cheng, H.S.; Sternlicht, B.: A numerical solution for the pressure, temperature and filmthickness between two infinitely long lubricated rolling and sliding cylinders under heavy loads. 'Ifans. ASME, J. Basic Eng. (1965), vol. 3, pp. 695-705. Dowson, D.; Higginson, G.R.: Elastohydrodynamic Lubrication. Oxford: Pergamon Press (1966). Dyson, A; Wilson, AR.: Film Thickness in Elastohydrodynamic Lubrication by Silicone Fluids. Proc. Instn. Mech. Engrs., Vol. 180 Pt. 3K, (1965-1966), pp. 97-112. Ertl-Mohrenstein, A.: Die Berechnung der hydrodynamischen Schmierung gekrilmmter Oberfliichen unter hoher Belastung und Relativbewegung. VDI-Fortschrittsbericht Reihe 1, Nr. 115 (1984). Foord, C.A; Hammann, W.C.; Cameron, A: Evaluation of Lubricants Using Optical Elastohydrodynamics. ASLE ?fans. 11, (1968), pp. 31-43. Grubin, AN.; Vinogradova, J.E.: Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces. Symposium: Investigation of the contact machine components. Cent. Sci. Res. Inst. Rch. Mech. Eng. Moscow, Book No. 30 (1949). Hirata, M.; Cameron, A: The Use of Optical Elastohydrodynamics to Investigate Viscosity Loss in Polymer-thickened

Kagerer, E.: Messung von elastohydrodynamischen Parametern im hochbelasteten Scheiben- und Zahnkontakt. Thesis TU Munich (1991). Kagerer, E.; KOniger, M.: Ion Beam Sputter Deposition of Thin Film Sensors for Applications in Highly Loaded Contacts. Thin Solid Films, 182 (1989), pp. 333-344.

Murch, L.E.; Wilson, W.R.D.: A Thermal Elastohydrodynamic Inlet Zone Analysis. Pans. ASME F, J. Lubr. Rchn. 97 (1975) 2, pp. 212-216. Oster, R: Beanspruchung der Zahnflanken unter Bedingungen der Elastohydrodynamik. Thesis TU Munich (1982). Schrader, R.: EHD-61- und Fettschmierung und Mikro-EHD - AbschluObericht, FVA-Report 291 (1989). Simon, M.: Messung von elastohydrodynamischen Parametern und ihre Auswirkung auf die Griibchentragfahigkeit vergilteter Scheiben und Zahnriider. Thesis TU Munich (1984). Simon, M.; KOniger, M.E.; Reithmeier, G.:Ion Beam Sputter Deposition of Thin Insulating Layers for Applications in Highly Loaded Contacts. Thin Solid Films, 109 (1983), pp. 19-25. Winter, H.; HOhn, B.-R.; Michaelis, K.; Kagerer, E.: Measurement of Pressure, Rmperature and Film Thickness in Disk and Gear Contacts. JSME International Conference on Motion and Power 'Ifansmissions, pp. 474-479, Nov. 23-26 (1991) Hiroshima, Japan.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V. All rights reserved.

235

Waviness Orientation in EHL Point Contact P. Ehret, D. Dowson, and C.M Taylor a a

Institute of Tribology, Department of Mechanical Engineering. The University of Leeds

In recent years, EHL point contact analysis has greatly benefited from the development of new numerical techniques. Amongst these, the multigrid multi-integration method has opened real perspectives not only in simulations of smooth surface contacts, but also in the consideration of rough surfaces and transient effects. Brandt [l], Lubrecht [2] and Venner [3] have demonstrated the quality of such a solver, which allows high levels of discretisation, and enhances stability and robustness. Using this technique, an investigation on the effect of waviness orientation in EHL point contacts under high load situations has been carried out. Pure sliding is considered and the waviness is placed on the stationary surface. Under severe loading conditions the maxima of waviness are largely flattened and large pressure ripples are produced. The orientation of the waviness strongly influences the behaviour of the flow at the entrance of the contact, which in turn considerably effects the deformation of the surfaces inside the contact area. Leakage flows and accumulation of lubricant at the inlet introduce surface constrictions and grooves, which propagate all along the contact in the direction of the flow. Results show that the transverse waviness presents the best lubrication capability. The lowest minimum film thickness is obtained when the waviness is orientated at about 60° compared to the direction of the surface velocity.

1. INTRODUCTION Both roughness surface features, and the orientation of texture represent a major concern in EHL contact analysis. Machine elements such as ball bearings, gears, cams and followers never exhibit a perfectly smooth surface. The surface topography reflects to a certain extent the conditions and the processes used t o generate it. In many practical contacts, the surface reveals a strong orientated texture, in t h e direction in which it has been finished. The influence of this privileged direction on the EHL predictions has been the focus of many studies over the past years. In the 1970s, Patir and Cheng [4] wrote a series of paper on surface roughness in lubrication and presented an analysis on surface roughness orientation in EHL contacts. They concluded that the film thickness increases as the surface texture varies from longitudinally to isotropic, and to transversally orientated pattern, although their study was limited to half of the contact, and only considered the variation in the central film thickness. The considerable improvement in numerical

methods, obtained in recent years, allows one to re-address the subject in a more comprehensive form. In contrast with their stochastic approach, a deterministic definition of the surfaces can be taken into account. This leads to important consequences. Firstly, the analysis no longer relies on a set of statistic parameters which characterize the surface. Above all, the surface texture can be deformed under high pressures, which in turn may strongly modify the behaviour of the flow in the contact. Only a few papers deal with the 3D microgeometry surface problem. T h e main reasons are: first of all, the need for a refined discretisation to represent accurately the micro-geometry, and secondly the demands of a stable and robust solver to handle the strongly non-linear Reynolds Equation, The works of Seabra, [5], Barrangan de Ling [6], Kweh [7], and Lubrecht [8] can be considered as the pioneer analyses of a deterministic approach in a 3D surface problem. Nevertheless the recent enhancement of the multigrid method, and the development of the multi-integration by Venner, Lubrecht and Brandt [3], [9] have led to robust low complexity solvers, which offer real

236 perspectives in the EHL analysis of full 3D roughness surface features. Until recently, 3D micro-EHL studies have mainly concentrated on transverse and longitudinal waviness in order to model the main scale of the roughness. Venner [3] has extensively studied these both cases as function of the wavelength of the waviness in an heavy loaded situation, and has shown that the maximaof pressures are about the same in these two configurations. Furthermore, for the longitudinal case, he reported large variations of the minimum film thickness. These results, however, point out the importance of the location of the waviness in the contact. When a minimum line of the waviness lies on the off-side of the contact, where the minimum film thickness occurs, Venner's computations show an increase of 40 % in the film thickness in comparison to the values predicted in smooth surface. On the contrary, his worst case predicts a decrease of 60 ?6 in the film thickness compared to the smooth solution, when a maximum line of the waviness is located in the off-side of the contact. Venner's results for transverse waviness are more homogeneous. In all cases, the minimum film thickness remains higher than that of the smooth surface, and decreases gently as the wavelength increases. The purpose of this present work is to extend the analysis of the transverse and longitudinal waviness to that of an arbitrary direction of the waviness compared to the surface velocity. Therefore, this study rejoins the original interest, presented more than fifteen years ago by Patir and Cheng.

G = oE' hh

H L

P Ph

PR

XIY

.Y,Y z W

7zI

W W

rl 3FR

4

= (m) A Dimensionless amplitude, A = uinp/hh amp Waviness amplitude [in] E' Reduced Elasticity M O ~ L I ~[U P Sa ] ,

-E' 2

El

Ez

G

(1-4

El'

+

(1-4)

Err

Elasticity Modulus of Body 1 [ P a ] Elasticity Modulus of Body 2 [Pu] Dimensionless Material Parameter,

Dimensionless Load Parameter (Moes), M = w(2~)-3/4 Pressure [Pu] Maximum Hertzian Pressure [ P u ] , 3F P h = 2aaa Reference Pressure [ P u ] , p~ = 0.198 l o 9 P a Dimensionless pressure P = p / p h Radius of the Ball [m] Velocity [m./s] Dimensionless Velocity Parameter, = 122% 2 E'R Coordinates [m] Dimensionless coordinates, = x/u,Y = y/u Pressure Viscosity Parameter Load [ N ] Wavelength [m] Dimensionless Load Parameter,

u

1.1. Notations radius of the Hertzian contact [m],

Central Film Thickness [m] Minimum Film Thickness [m] Rigid Motion [m] Constant of integration Hoo = hoo/hh Dimensionless film thickness, H = h/hh Dimensionless Material Parameter (Moes),

L =G(~u)'/~

M

N

u

Maximum Hertzian Deformation [m], hh --- K'a

rl0

rlR

e

x

x

W=" E ' P Dimensionless wavelength, = &/a Pressure Viscosity Index [Pu-'1 -=In% Viscosity [ P a s] Viscosity at Ambient Pressure [ P a s] Reference Viscosity [Pa s], VR = 6.32 1 0 - 5 ~ s ~ Reynolds Equation Coefficients,

w

Dimensionless parameter A=* Poisson Coefficient of Body 1 Poisson Coefficient of Body 2

237 2. THEORY

The traditional Reynolds equation is used in t h e present study. The isothermal and steady statmeconditions are assumed. The lubricant is considered as a Newtonian compressible and piezoviscous fluid. The change of density with prcssure is given by the Dowson and Higginson r d ntion [ 101:

0.6~

1

+ 1.711

‘rhe viscosity variation obeys the Roelands rquation [ 111 :

The problem may be described as a contact of a ball on a wavy surface. A pure sliding condition is considered; the wavy surface is motionless, while the ball, animated with a circumferential velocity !is, draws the lubricant into the contact. The domain of study is rectangular, and the inordinates are defined such that the axis Ox has t.he same direction as the surface velocity. The origin of the frame is located at the centre of the (-oilt act. For the sake of clarity the same dimensionless numbers and same notations as Venner [3] are rctained in this present study. The dimensionless Reynolds equation can now be written as follows

be treated with this mathematical model. In order to avoid this problem, a sufficient number of ridges are placed inside the Hertzian region, and large loads are imposed. The boundary conditions for the Reynolds equation are :

P =0

on each side of the computation domain

aP P = -= 0

The wavy surface is represented by a succession of ridges and grooves, orientated at a given angle q5 compared to the direction of the surface velocity. Considering the contact area small in relation to the radius of the ball, each body can be replaced by an elastic semi-infinite space. The material is assumed homogeneous and perfectly elastic. Hence, the dimensionless equation for the film thickness is :

H ( X ,Y ) = Hoo 2

tm

FS-,

R ( X , Y ) = dcos

Ail

A=

1 2 7 1 0R2 ~~ a3ph

At the boundary cavitation, the Reynolds condition is imposed in order to take into account the conservation of mass. Pressures are set to zero in the cavitation area. Nevertheless, because the continuity of the flow inside the cavitation area does not appear in the analysis, the cases where a reformation of the lubricant film occurs cannot

P(X‘,Y’)dX’dY’

(4)

J( X - X ’ ) a t ( Y - Y ’ ) z

)

Scos(q5) - Ysin(q5)

W

(5)

The integral part corresponds to the elastic deflection due to the pressures. The constant Hoo represents the rigid motion between the two surfaces, and is obtained from the resolution of the Force Balance equation. In a dimensionless form, this equation can be read as :

s_, 1, pH3 (=-

s-,

+ 9 + f- R(X,Y ) +

tm

with

+,

with

at the boundary cavitation

ax

t m

2n P ( X , Y ) d X d Y- - = 0 3

(6)

In order t,o ensure the accuracy of the microdeformations, the number of points used in this present analysis is 513 x 513. A multigrid scheme is employed to solve the Reynolds equation and the Force Balance equation, and the multi-integration algorithm is used to perform the integration required by the Elasticity equation. This scheme and a full comparison of results obtained with the EIN method [la] will be detailed elsewhere. As an example, Figure 1 displays the minimum and central film thickness predicted by

238

I

1

II Surface N1 I Surface N2 I 20

amp

RMS

CLA

II II

0.250 0.495 0.350 0.315

I

0.125 0.125 0.088 0.079

I

II

2.26 10”

I Pal

1

I [mm] I luml

bmj Iuml

40 10-3 3.5

90

U.

[PaSI Ims-’I

Table 1 Waviness characteristics

both multigrid multi-integration method and EIN method for the smooth point contact problem. In this example, the Moes parameter L equals to 28.28, and the second Moes parameter M varies in the range of 10 to 1000. Good agreement has been found which validates results obtained by both these independent methods.

L

M L W

PI

1

Mlnlmun PUn l l k h

100

loo0

M

Figure 1 Comparison of central and minimum film thickness for L=28.28, ElN : Effective lnAuence Newton method, M l M : multigrid multiintegration method

3. RESULTS 3.1. Conditions of study Two different surface features have been investigated. Their characteristics are presented in Table 1. The waviness only,allows a very coarse description of the real surface. The random nature

I/

(1

1008.2 II 12.04 I 1.4310-’ I 1.72 lo-”

I

I

I I

126.0 I 12.04 I 1.7901OVb 1.72 lo-’’

J

of the roughness is lost, while only the mean surface features are modeled. With such limitations in mind, the first surface can be related to a gear tooth finish surface, whereas the second surface may be referred to as a roller or a ball bearing surface. Two different loads are also examined. These are characterized respectively by an Hertzian pressure equal to 2 Gpa and 1 Gpa. The parameters of the study, and the solutions obtained in the smooth surface problem are given in Table 2. Since all the other parameters are considered constant, the variation in load only affects the dimension of the contact, and changes very little the central film thickness. For the highest load, the number of ridges in the contact equals 5 and 9, respectively for the surface N1 , and N 2 , while 3 and 5 ridges are found in the Hertzian area for the lowest load situation. For the wavy surface analyses, the computation domain has been kept constant for all cases. It is equal to -2.5 5 X 5 1.5 and -2 5 Y 5 2.

239

ph

Figure 2 Pressure distribution and film thickness = 1.0 Gpa 4 = 45" amplitude = 0.495 p i , wavelength = 0.25 mm

ph

Figure 3 Pressure distribution and film thickness = 2.0 Gpa 4 = 45" amplitude = 0.495 prn, wavelength = 0.25 mrn

3.2. Description of the Results Figure 2 and Figure 3 represent the pressure distribution and the film thickness for the longest wavelength surface and for the two load situations. The orientation of the waviness is taken at 45' compared to the direction of the surface velocity. In order to improve the representation of the film thickness, an inverse scale is used. Furthermore the plots are orientated so that the entrance o f the flow is situated at the left side of the plot. For these two cases, the ridges of the waviness are almost flattened, and produce a succession of elliptical contacts on which large pressure ripples are built up. More importantly, new surfaces features have been created. As Figure 4 displays on a larger scale for the highest load, ridges and val-

leys propagate all along the contact in a perfect straight line in the direction of the surface velocity. These features result from the behaviour of the flow at the entrance of the contact. As in the smooth surface problem, the film thickness depends mainly upon the condition of the flow at the entrance of the contact. Inside the high pressure domain, the change in pressure no longer reflects a change in the flow because of the high viscosity of the lubricant. The flow is then predominantly a Couette flow and the Reynolds equation ( p H ) = 0. It is reduced to the wedge term follows that a surface feature which has been introduced or generated at the entrance of contact propagates undisturbed in the contact according to the direction of the surface velocity. The val-

&

240 entrance where the viscosity is low. T h e transverse pressure gradient is then large enough to create transverse flows. These in turn produce surface constrictions which travel all along in the contact and form the ridges. With the lowest load, the elliptical contacts are almost detached from each other, in contrast with the 2 Gpa case where these micro-contacts overlap. Nevertheless the aforementioned nature of the flow has not changed. As part of the lubricant avoids the first ridge, it is entrapped in the groove before the central ridge. This then generates the large elastic deformation on this ridge. Further on, following the same direction, the large surface constriction at the exit of the contact, and the high spikes of pressure can also be attributed t o this amount of lubricant.

Film Thickness Contour

Figure 4 Enlargement of film thickness, and film thickness contour. Description of the flow in the contact. p h = 2.0 Gpa 4 = 45" amplitude = 0.495 pm, wavelength = 0.25 nam

leys are thus produced by an accumulation of the lubricant, in the grooves of the waviness at the entrance to the contact. This only occurs in the part of the inlet where the minimum lines of the waviness cut the Hertzian contact circle. In the other part of the inlet, however, the flow is hampered by the ridges of the waviness tangent to the Hertzian contact. This subsequently reduces the film thickness in the direction of the surface velocity. Therefore it is in this half of the domain that the minimum film thickness is located. On the other hand, the waviness also brings about large flow disturbances, or leakage flows at the

3.3. Minimum Film Thickness Figure 9 shows the variations of the relative minimum film thickness, hm,n/h,in,moo,hversus the orientation angle 4. As q5 increases from 0", the surface feature varies from transverse to orientated, and finally to longitudinal waviness when q5 = 90". A close similarity in the shape of the curves can be seen. The minimum film thickness attains it highest value for the transverse waviness, then decreases gradually as the orientation angle q5 increases. The angle 4 = 60" indicates a transition in the behaviour of the flow. After this point, the minimum film thickness is stabilized or even increased again. These orientations correspond t o the configurations where the waviness is no longer an obstacle for the flow. The valleys are then no longer concentrated in one part of the contact, but they facilitate the flow through the contact from all the positions of the inlet. This, however, does not imply a better lubrication, since the lubricant flows essentially through the valleys to the detriment of the other parts of the contact. 3.4. Average Film Thickness The average film thickness in the Hertzian contact area has been computed for the different cases. This value can be related to the volume of lubricant inside the contact, but also to some extent to the flow of lubricant in this part of the do-

24 1

1.2

2 1.0 z zI 0.8 0.6 0.4

1 . .

~

..

.

. ... .. .. . ... . I

Su&r N1 pb=lGp

SPrbrcNl ph=lcpS

1.05

!

..

0.95

...........i ..............:.................,... . . .,,.. ~ .. , ... . ... ,, ... ... ... ...

.

~

0.0 20.0 40.0 60.0 80.0 100.0

0.0 20.0 40.0 60.0 80.0 100.0

0.85

'

;

. "

..

..

'

J

f

0.0 20.0 40.0 60.0 80.0 100.0

0.85 0.0 20.0 40.0 60.0 80.0 100.0

0.0 20.0 40.0 60.0 80.0 100.0

0.85' ' ' ' ' 0.0 20.0 40.0 60.0 80.0 100.0 OllenhtiooAn&

I

'

"

stvbrtN2 ph:ZcpS

0.4

0.4

I l ( l l I l . l

0.0 20.0 40.0 60.0 80.0 100.0 0.0 20.0 40.0 60.0 80.0 100.0 orknllum Angk OritntPtioPAngk Figure 5 Relative minimum film thickness versus the orientation angle

main. Figure 6 displays the variations of the relat ive average film thickness, have/have,,,,,,, versus the orientation angle 4. The transverse case contains the lowest amount of lubricant. As the orientation angle 4 increases, the capability of the valleys to draw the flow into the contact also increases and seems to contradict t,he poor lubrication conditions obtained for these orientations, compared to the transverse waviness. The transition angle obtained in the previous section can be again related to the orientat,ion angle where the volume of lubricant become higher than that of the smooth surface. 3.5. Maximum Pressure Figure 7 represents the variations of the relative maximum pressure pmuE/pmQl,,,,,,, versus the orientation angle. For the highest load, the values remain almost unchanged. The pressure distribution is then close to that of a dry con-

-58.0

OrkntPtioa hgk

'

'

'

'

Figure 6 Relative average film thickness versus the orientation angle

tact and therefore it becomes nearly independent upon the orientation of the waviness compared to the direction of the surface velocity. In contrast the lowest load situations exhibit larger variations of the maximum pressures. These values particularly concern the spikes of pressure which are formed when the flow exits the contact. In particular for the surface N"1 these large spikes have to be related to the important amount of lubricant which has to exit from the contact. 3.6. Cumdative Height Distribution Cumulative height distributions in the contact area have been computed for the highest load situation and the longest wavelength surface. This analysis presents many advantages since it allows us to compare globally the changes in the film thickness compared to the orientation angle. Figure 8 displays the cumulative height distributions for five different angles; the abscissa represents

3.r

242

i

___r

,

sprbrtN2

. .. .. , ,

3.0.

a

j

.. ..... ..... . .. ,

1

2.0

.

..............;.

.. ..... .. . .

. ,

.

.

. ...

. I

.

j

. ... ..,. ... .. ,.. , I

.

;. .. ..... . ... I

.

.

.

.

I

,

.

.

.. ,.

.

.

I

I .

. .

.

.

I

.

.

,

I

.

hblbpAngk

.

.

.

0.6 0.4 0.2 0.0 0.00

; . . . . .. . . . . ... . . . . L...

.

.

. .. . .. .. ...

pb=2Cp . . ,. .. ... ... ; , . . . i. ........ . . ... ... .... .... ... ... . .. .. ... ... .. .. ;...............i. ........... . . .... .... .. .. . . ... ...

0.050

.. .

I

0.0 20.0 40.0 60.0 80.0 100.0

'lhnrrverse Film Thickam

Cumulative Height Distribution

2.0

2.0

,

3.0p1 SuWNI pblCp

LWNI pb:@

.

. .,, , ... ... .

.

I

.

I

. .. .

.

.

.

.

. .. .

.

.

.

....

....

.

.

SurhrrN2 . ..,. .. ..

. 3.0 . . i. . .... .,. .. I

.

.

j

.. ..... . .

.

.. ....

pb=lGp . . ... .,... ,. .. .

...

.

.

..... . ..

,

.; . . !. ' .

... ,

.

I

.

,

.

,

I

....

....

...

..... . ..

... .

... ... .

0.02

0.04

0.WO -2.00

HfvJ

0.0 20.0 40,o 60.0 80.0 100.0 ... ..

0.025

, .

0.6 0.4 0.2 0.0 0.00

0.00

2.00

Dimtim Oy

0.02

0.04

0.m

-

-2.00

0.00

2.00

.

I

Olitnbhhgk

Figure 7 Relative maximum pressure versus the orientation angle

the dimensionless film thickness, and the ordinate represents the proportion of the points in the Hertzian area whose film thickness is lower than the value given in abscissa. The dotted lines are the cumulative height distributions for the smooth surface problem. The vertical lines indicate the average values of the film thickness. Furthermore the film thickness profile at X = 0.22 and the location of the minimum film thickness Figure 9 are given as a reference for each case. In the transverse case, 4 = 0", the majority of points have essentially the same film thickness. They correspond to the central plateau of the film thickness profile. The width of this plateau results from the length of the first ridge of the waviness that the lubricant has flattened in entering the contact. The ridges and grooves, located at the proximity of the plateau, have then been pro-

0.6 0.4 0.2 0.0 0.00

0.025

:::%m .....

0.6

O.OO0

-2.00

0.00

2.00

0.00

2.00

..

0.4 0.2 0.0 0.00

o.6 0.4

0.04

0.02

.. .. . .

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

0.02

'

0.04

0.m

-2.00

i HfXY)

Dimtim Oy

Figure 8 Cumulative height distribution in the Hertzian region and film thickness profile at X=0.22, p h = 2.0 Gpa amplitude = 0.495 pm, wavelength = 0.25 m m

243 lp = 30"

duced by the lubricant which has flowed round this first difficulty. As the orientation angle increases, the dimension of the plateau decreases, and valleys appears in a part of the contact. Furthermore a large surface constriction arises at one side of the plateau, which replaces one of the previous grooves. Consequently the part of the contact, which is already poorly lubricated, does not benefit any longer from the leakage flows of the first elliptical contact. This surface constriction then corresponds to the extremity of the longer elliptical contacts where the flow cannot access. The situation worsens as 4 increases because legs lubricant passes through the first elliptical contact. E'rom the cumulative height distributions, it can be seen that the film thickness attributed to the plateau decreases. A plausible explanation is that the flow which used to go to this area of the contact is diverted at the entrance of the contact by the orientation of the first obstacle. This amount of lubricant then goes directly to the nearby valley of the plateau which has deepened, or even is lost outside the contact. After 60') the plateau can no longer be distinguished. The valleys then begin to be superimposed on the minimum lines of the waviness and readily enhance the circulation of the lubricant through the contact. This, however, does not improve the lubrication as an increase in the number of points with a low film thickness can be clearly seen in the cumulative height distribution for 4 equals 60' and 90°. 4. CONCLUSION

This study has focused on the effects of waviness orientation in an EHL contact. The configuration in question has considered the waviness to be motionless, and has involved pure sliding conditions. Results obtained show that the transverse waviness provides the best lubrication capability. In this configuration, the valleys created by the leakage flows at the entrance give access to the extremity of the long elliptical contacts, located at the centre of the Hertzian region. On the other hand, the orientation of the waviness

1.51

X Y

1

-

i

'

I

'

-1.5 ' ' ' -1.5 -0.5 0.5 1.5 Y

lp = 45"

x

lp = 60"

1.5 1_~111

0.5 -0.5

'

I -1.5 ' ' ' ' -1.5 -0.5 0.5 1.5 X

Y

-1.5 -0.5

*

."

-1.5 -0.5 0.5 1.5 X

H 4 = 900

-1.5 -0.5 0.5 1.5

x

Figure 9 Location of the minimum film thickness = 2.0 Gpa amplitude = 0.495pm, wavelength = 0.25 m m

ph

leads to a strong non-homogeneous lubrication of the contact. Although the flow is facilitated by the creation of valleys in one part of the contact, the other part exhibits poor lubricated conditions, due to the diversion of the lubricant in the valleys and outside the contact. The minimum film thickness decreases as the orientation angle increases and attains its lowest value for an orientation angle equal to 4 = 60'. In the following configurations, the major part of the lubricant flow through the valleys and the rest of the contact is poorly lubricated. It should be remembered that in all the cases treated, a maximum line of waviness has been placed a t the centre of the contact. A translation of this surface feature compared to the cen-

244 tre of the contact should seriously affect the niinimum film thickness predicted. Furthermore, as the Newtonian behaviour of the lubricant, and the isothermal conditions seems the more questionable assumptions in this present work, further studies should investigate the influence of such effects, i n conjunction with the orientation of real rough surfaces.

5. ACKNOWLEDGEMENT

This research was funded by a research grant from EPSRC under a project to study NonNewtonian Lubrication of Elastohydrodynamic Elliptical Contact with 3D Surface Roughness.

REFERENCES 1. Brandt, A. Multi-Level Adaptive Solutions

2.

3.

4.

5.

6.

to Boundary-Value Problems. Mathematics of Computation, 31( 138):333-389, 1977. Lubrecht, A.A., ten Napel, W.E., and Bosma, R. Multigrid, an Alternative Method of Solution for Two-Dimension Elastohydrodynamically Lubricated Point Contact Calculations. J. Trib. (Trans. ASME F), 108(3) :551-556, 1986. Venner, C.H. Multilevel Solution of the EHL Line and Point Contact Problems. PhD thesis, Twente University, T h e Netherlands, 1991. Path, N., and Cheng, H.S. Effectof Surface Orientation on the Central Film Thickness in EHD Contacts. 5th Leeds-Lyon Symp. (Leeds) (ed Dowson D., Taylor C.M, Godet M., and Berthe D.), pages 15-21, 1978. Seabra, J., and Berthe, D. Elastohydrodynamic Point Contacts part 2 : Influence of Surface Speeds, Surface Waviness and Load on the Contact Behaviour. Wear, 130:319335, 1989. Barrangan de Ling, Fdm., Evans, H.P, and Sniddle R.W. Micro Elastohydrodynamic Lubrication of Circumferentially Finished Rollers : The Influence of Temperature and Roughness . J . Trib. (Trans. ASME F), 11 1 :730-736, 1989.

Kweh, C.C., Evans, H.P, and Sniddle R.W. Micro-Elastohydrodynamic Lubrication of Elliptical Contact with Transverse and Three-Dimensional Roughness . J. Trib. (Trans. A S M E F), 111:577-584, 1989. Lubrecht, A.A., ten Napel, W.E., and Bosma, R . The Influence of Longitudibal and Transverse Roughness on the Elastohydrodynamic Lubrication of Circular Contacts. J . Trib. (Trans. A S M E F), 110(3):421-426, 1988. Brandt, A., and Lubrecht, A.A. Multilevel Matrix Multiplication and Fast Solution of Integral Equations. J.of Comp. Phys., 2:348-370. 1990. 10. Dowson, D., and Higginson, G.R. Elasto-Hydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication. Pergamon Press, Oxford, Great Britain, 1966. 11 Roelands, C. Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils. PhD thesis, Delft University, (V.R.B Groningen) The Netherlands, 1966. 12. Wang, D. Elastohydrodynamic Lubrication of Point Contacts f o r Layers of Soft Solids and for Monolithic Hard Materials in the Transient Bouncing Ball Problem. PhD thesis, The University of Leeds, Great-Britain, 1994.

SESSION VII THERMAL ASPECTS Chairman :

Professor Francis Kennedy

Paper VII (i)

Study on Heat Transfer and Temperature Field of Rotating Friction Interface

Paper VII (ii)

Three-Body Contact Temperature in Fretting Conditions

Paper VII (iii)

Infrared Technique for Measuring Temperature Distributions in E.H.D. Contact Zone. Part One : Technique. Part Two : Experimental Results

Paper VII (iv)

An Iterative Heat Balance Technique for Rapid Estimation of Engine Bearing Temperatures

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

241

Study on heat transfer and temperature field of rotating friction interface M.Sato', T.Wataraib, K.Miyata', T.Inagakid and Y.Okamoto'

' Oiles Cooperation, 8, Kirihara-machi, Fujisawa-City, Kanagawa-ken, Japan, 252 Department of Mechanical Engineering, Faculty of Engineering, Ibaraki University,

4-12-1, Nakanarusawa-machi, Hitachi-City, Ibaraki-ken, Japan, 314 An experimental study was conducted to visualize and analyze heat mass transfer and temperature fields of

a rotating dry-friction interface. The friction temperature distribution of selflubricated plastic materials was observed by means of the infrared radiometer. In a combination of POM-POM, and POM-PPS materials, the transient temperature distribution along the axis is expressed in the error function and the temperature rise of the friction interface AT was correlated to the friction value pFV/A, which means the heat flux by friction heat generation. Finally, it was clear from a series of experiments that the surface temperature rise, heat flux of the friction and rubbing time played a significant role in our experiment. 1 INTRODUCTION

temperature, can increase by several hundred degree centigrade and cause shearing destruction of both

A tribological surface under rotating and reciprocal

interfaces.'),*)

motion is widely used in bearings and sealing

Those phenomena which play an important role on

elements to eliminate the friction force of the moving

engineering damages, such as interface rupture,

interface. The friction force at the interface produces

seizing and heavy wear have been reported by

the heat generation and a temperature increase. An

Bowden and

excess heat generation of the friction interface

In order to analyze the surface temperature, the

increases the temperature and friction forces. In the

point temperature near the friction interface was

case where the interface temperature becomes larger

measured by thermocouple.6)But it is very difficult

than the limiting value like softening and melting

to measure and visualize the two-dimensional and

temperatures,the friction interface generates a higher

transient temperature distribution of the interface.

friction coefficient with wearing and an increase in

In this paper@ experimental study was conducted

the generated heat which influences stable operation

to visualize and analyze thermal and wear

and life of mechanical components.

phenomena of the rotating dry friction thrust

The temperature of the friction interface under wearing conditions, so called hot spot and flash

interface of two plastic materials

which are

polyoxymethylene (POM) and pol yphenylene sulfide

248

In the combination of POM-POM and POM-PPS

(PP9 That temperature distribution was visualized and

materials, it was clear that transient temperature

measured by an infrared radiometer, as a remote

distribution along the axis was expressed in the error

sensing device. Data was recorded by the data

hnction. The temperature rise of the friction

recorder.

interface AT was clearly correlated to friction I n f r a r e d Radiometer

Camera

-

I-

I-

I

I I

1 I

F

I I I

I I

I I

Computer

I

Tlic roocoup 1e - S t a t i o n a r y

rL_i

Part

-I-.

Specific

gravity conductivity - ....__ ._

Tsnaile

strength

W/(m

___-

Elongation Bending

strength - .. ..... .. - -. ._.. - .- _.- _

Impact

strength

~

-. .

.-I-----_..._.

Elastic

Compressive

N/m'

7 6 . 5 X

J/m

58. 8

2. ~

N/m'

strength -

Hardness

Specific

25

- .. . -

__

_

__-_

diffusivitly

heat

lo-'

_

k J / ( k p -

lo-'

0 . 4 8

5 3 . 9 X ~ 1 0 ' '

--

8 3 . 3 X 10'' 1 4 . 7

lo-'

6 X

3 . 4 x l o - '

_

--.

2 1 . 2 x

lo-'

72

I. I 3 X l o - '

m'/s

-

2. 5

HRY

-

--___ Thermal

%

N/m' -

I. 6 X l o - ' 0 . 2 7 -

51.ox

_______

modulus .. .

0 . 2 3 2

K)

N/m'

-

__-

-

-

.~

lo-'

I . 4 l X

ke/m'

-

..-__

Thermal

PPS

~-

__.. ..-.

_ _ L

POY

Unit

Mechanical and physical Properties

K)

'I'ihlc 1 'Iliermel propcrlics of lesled resiri nialerials

6 8 , 6 X l o - '

IIRA

110

I . 2 9 - I. 7 6 x lo-' I . 32-

I . 5 7

-

249

value /LFV/A which means the heat flux generated by

part is made of POM, and PPS resin. The thrust load F and revolution speed V was

friction energy. Finally, it was clear from a series of experiments

controlled by the reciproca!ing motor. Chrome1 and

that the surface temperature rise, the friction heat

Alumel thermocouple

were embedded in the

flux and rubbing time played a significant role in our

stationary part at the depths of 1,5,10,20 mm.

experiment. From a direct thermal visualization using

The axial temperature distribution was measured

the infrared radiometer, the relation between friction

by thermocouple and recorded on a data recorder.

energy and a surface temperature was studied as a

The friction force

function of the tribological behavior of the surface.

torque meter and we could calculate the friction

Lastly, the transient behavior of the temperature

F was also measured by the

coefficient p.”) Table 1 shows thermal properties of tested plastic

and the friction coefficient was measured under

resin materials POM and PPS used.’)

friction and wearing conditions.

Table 2 illustrates several experimental conditions

2

EXPERIMENTAL

APPARATUS

AND

in combination with the tested materials.

METHOD

The remote-sensing

infrared radiometer was

installed on the side of the cylindrical test piece and A schematic illustration of the experimental

measured

the

two-dimensional

temperature

apparatus is shown in Figure 1.@#’) This figure shows

distribution. The radiation temperature distribution of

the test piece of the rotating thrust bearing.8) The

the friction interface was visualized and displayed on

upper rotating and lower stationary cylindrical parts

the CRT.

are 25mm in diameter and 25mm in height. The rotating part is made of POM resin and the stationary F (N)

w

V

( r pm)

No. 1

98

No. 2

Experiments were performed to measure the thrust force F, friction force pF, rotating speed V and

(m/m i n)

P (MPa)

r (mi n)

1 5 0

12. 1

0. 4 9

60

POM

POM, P P S

98

200

16. 1

0. 4 9

60

POM

POM, P P S

No. 3

98

250

20. 1

0. 4 9

60

POM

POM, P P S

No. 4

98

300

2 4. 1

0. 4 9

60

POM

POM, P P S

2 8. 1

0. 4 9

60

POM

POM, P P S

32. 2

0. 4 9

60

POM

POM, P P S

Test

IN11881350 No. 6

98

400

R o t a t i n g

Stationary

p a r t

p a r t

Table 2 Test condition of POM-POM and POM-PPS materials

250

temperatures by thermocouple at constant time intervals after start up. The thermographs which display the two-dimensional temperature distribution was recorded and played back by the personal computer. 3 EXPERIMENTAL RESULTS 3.1 Calibration of radiation temperature and

uncertainty of measurement

PPS; ~=58.4+0.804xTs (2)

Using measured values of T,, T,’, and T,, the emissivity

E

I

is expressed by

(T9TJ4.08-(TJTJ4.08 ES=

1 -(TJTJ4.08

(3)

Generally, the measured radiation temperature Ti, by means of the infrared radiometer is affected by the radiation reflection from surrounding surfaces and does not coincide with the real temperature of the test piece T,. So it is necessary to calibrate the radiation temperature Ti, to the real temperature T, using the environment temperature T,. Figure 2 shows the calibration correlation between the radiation temperature Ti, and the real temperature T,.As the emissivity of the test piece is smaller than unity, the radiation temperature Ti, is smaller than the real temperature T,, in case when T, is larger than the environment temperature T,.lolB1l) From this figure, the radiation temperature Ti, can

a) t = O S min

be expressed by the real temperature T, as follows

POW T:=63.0+0.707xTs (1)

0424

0

POM PPS

--I 340

3/30

Radiaton temperature T,‘ (K) Fig. 2 Calibration of the correlation between radiation and real temperature

b) t=l min Fig. 3 ‘Ihermograyh of POM-POM friction interface @=98 N, V=16.1 m/min)

25 1

Temperature

is

increasing with

increasing

Applying equation (3), emissivities of POM and

operation time. As shown in the longitudinal cursor

PPS are found to be 0.60 and 0.74 respectively in

line of the figure, the axial temperature distribution

temperature range of 283 to 400 k. Uncertainty of

of the rotating and stationary cylinder becomes

the temperature and emissivity was 3% by applying

mountainous and symmetrical, because of same

ANSVASME code.

thermal conductivity and emissivity of both tested materials. Therefore, the generated friction heat equally transfer to both parts.

3.2 "hernograph of friction interface The thermograph of the friction interface using the infrared radiometer is shown in Figure 3 in

Figure 4 shows the thermograph of the friction interface POM-PPS after 0.5 and 1 min. The upper rotatinn and lower stationary parts consist of POM Y

combination of POM and POM materials.

.-

~

10.08

C 0

.02:5 YL

o

ioloo

*OOO

.

Time

a) t=0.5 min

T

(sec)

Fig. 5 Time-dependent point temperature of

POM-POM materials (F=98 N, V=16.1 m/min) I

i

,

.

,

"

'

i k-700

d

,

I !

l

,0.1 I

*

I

1

-

!

= .a,

1

0

i g

b) r=l min Fig. 4 'llermognph of POM-PPS friction interface @=98

N,V=12.1 m/min)

0

(sec) Fig. 6 Time-depcndent point temperature of Time

T

POM-PPS materials @=98 N, V=16.1 m/min)

252 and PPS materials. The axial temperature gradient of

The thermal behavior of the transient temperature

the PPS material is larger than that of the POM

distribution

material, because the thermal conductivity of PPS is

one-dimensional heat conduction equation along axis

larger than that of POM.

of the tested cylinder, as shown in

was

analyzed

by

applying

a

3.3 Temperature distribution of the friction

interface material and its thermal analysis The time-dependent

local temperature was

measured by thermocouple, changing the distance H from the friction surface. Figures 5 and 6 show the time-dependent point temperature of the POM-POM and POM-PPS

where a is thermal diffusivity. The boundary condition is expressed as

materials with the distance H as a parameter. The temperature rise of POM-POM at H = l mm is gradually increasing and becomes maximal after 1000 to 2000 sec. On the other hand, the temperature rise of POM-PPS at H = l mm is gradually increasing up to

Solving the equation (4). the temperature T=T(x,t) is expressed as

over 3000 sec. The time-dependent axial radiation temperature distribution of friction side walls in the combination

of POM-POM and POM-PPS is shown in Figure 7 and 8. Axial mountainous temperature is increasing

31

with increasing in time r and revolution velocity V. I

I

1

I

I

1

1

31 -

c

.-0

+ I

cp .U

a

-0c

2Qi Location (mm)

0

Fig. 7 Time-dependent axial radiation temperature

_ .

.

Fig. 8 Time-dependent axial radiation temperature

distribution of POM-POM materials

distribution of POM-PPS materials

(F=98 N,V=16.1 mdmin)

(F=98 N, V=16.1 d m i n )

253 cylinder.

where erf means the error function. The relation between the dimensionless Fourier number x/(2J(ar )) and the dimensionless

The interface generates the heat flux qi by friction heat dissipation and qi is expressed in

temperature of the POM-POM and POM-PPS interfaces was summarized in Figure 9 and 10. It is clear that the curved line of equation (6) shows a good correlation with the transient temperature

In the case when the heat qi generated at the

distribution T(x,z). The plotted data of PPS is

interface is generatied transfered the heat into an

scattered around the correlated curved line because

infinite space, the transfer solution of the equation 4

of the heat conduction rate of upper and lower

1

I

1 2 Fourier number x/( a

Fourier number x/( a

Fig.11 The relation between Fourier number and

T )lI2

dimensionless temperature for the POM-POM

9 Relation between dimensionless Fourier

number and dimensionless temperature of th,e POM-POM materials

' I

I'

K

L

friction interface

r i

I

I

1

I

2

Fourier number x/( a

3 T )In

T )ln

Fig.10 The rtlation between dimensionless Fourier

Fig.12 The relation between Fourier number and

number and dimensionless temperature of the

dimensionless temperature for the POM-PPS

POM-PPS materials

friction interface

254 can be is represented in dimensionless form.

V46.1 dmin

,

The temperature rise AT was

measured by thermocouple with the distance H as a parameter. The temperature rise AT and friction coefficient ,u is gradually increasing and reaches a Figures 11 and 12 show the relation between the Fourier number and the dimensionless temperature and of the POM-POM and POM-PPS friction interfaces. It is clear that the curved line of equation

(8) shows good correlation with the plotted data of the dimensionless temperature distribution T(x,r).

But the plotted data of the PPS is scattered around the correlated curved line because of the heat conduction rate of upper and lower cylinders, as shown in Figure 9 and 10.

maximum after 1000 to 2000 sec. After that, AT and ,u gradually decrease with time. In this case, the

friction interface operates under normal film lubrication conditions. Figure 14 shows the time-dependent temperature rise and friction coefficient of the POM-POM friction interface at a normal force of at 98 N and a vrlocity of 28.1 d m i n . The temperature rise AT becomes twice as high in case of V 4 6 . 1 d m i n and the friction coefficient ,u shows nearly the same value in case of a velocity of

3.4 Time-dependent temperature rise and friction

V d 6 . 1 d m i n , as shown in Figure 15. But AT and

,u are largely fluctuating with time. Especially, the

coemcient under wear condition The time-dependent behavior of the temperature rise and friction coefficient of the POM-POM and

POM-PPS friction interfaces under wear condition

surface temperature rise AT alternatively changes its value from 40 to 60 K at time intervals of about 1500 sec. The friction interface produced a wear powder under heavy wear conditions. It was

was studied. Figure 13 shows time-dependent temperature rise and friction coefficient of the POM-POM friction interface at a normal force of 98 N and a velocity of

observed that the temperature rise AT increased during the wear powder production and decreased after releasing the powder from the friction interface. Figure 15 shows the time-dependent temperature 1041

.

I '

.

I

.

1

.

I 0.1

c

C

I /--

P)

a

E

L

'1-

:*

.05

5

?i Q

C

;E

-1 0

Time

T

(sec)

Fig.13 The time-depenlrrrl( temperature rise and friction coefficient of the POM-POM friction

Time

T (sec)

Fig.14 The time-dependent temperature rise and friction coefficient of the POM-POM friction

255

rise and friction coefficient of POM-PPS friction interface at 98 N in friction force and V=16.1 d m i n

means of the infrared radiometer. Friction heat generated in the rotating interface is transfered to the upper and lower materials. The

in velocity. The temperature rise AT and friction coefficient p

transient temperature distribution of the cylindrical

are gradually increasing with time. In this case, the

test piece was measured and analyzed by solving the

friction interface is in normal film lubrication

heat balance equation. It was concluded that the

condition.

dimensionless transient temperature correlates to all

Figure 16 shows time-dependent temperature rise and friction coefficient of POM-PPS at 98 N in

experimental data. The transient behavior of temperature and friction coefficient of the dry interface under wearing

normal force and V=28.1 d m i n in velocity.

As already shown in Figure 15, the fluctuation of

condition was measured simultaneously. It was clear

the temperature rise AT and friction coefficient p a r e

that the fluctuations of the temperature rise AT and

mainly caused by the wear powder production and

friction coefficient p are mainly caused by the wear

the release of the powder in the interface.

powder production and release of the powder interface.

4 CONCLUSION

REFERENCES

Tribological and thermal behavior of the dry rotating interface was measured and analyzed by

1) OECD,Wear and lubrication, (1963)

2) Y.Kimura et al, Introduction of tribology,

0.04 C

.-0)

E QE

0.02 8

0 Time

T

(sec)

Time

f

(sec)

Fig. 15 l'ime-dependent temperature rise and friction

Fig.16 Time-dependent temperature rise and friction

coefficient of POM-PPS friction interface at 98

coefficient of POM-PPS friclion interface at 98

N and V=16.1 Wmin

N and V=28.1 d m i n

256 Yokendo Publisher, (1994), 145

8) Thagaki et al, SPIE Thermosense, 16, (1994),

3) F.P.Bowden et al, The friction and wear of solid,

262

Oxford, (1954), 31

9) Y.Okamoto, Infrared remote-sensing thermal

4) H.Blok, ME2, (1937), 14

measurement, (1994), Corona Publishers, 26

5) K.C.Ludema et al, JSLE, (1988), 500

10) Y.Okamoto et al, Remote-sensing thermal image

6) Thagaki et al, 3rd world Conf. on Experimental

method, (1995), Corona Publishers, 96

Heat Transfer Mechanics and Thermodynamics,

11) ASME, ANSVASME test codes supplement on

(1993), 793

instruction part measurement uncertainty, (1987)

7) MSato et al, Asian Symp. of Visualization, (1994), 262

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

257

Three-body contact temperature in fretting conditions J. Pezdimik’, B. Podgornik],J. Viiintin’, M. Kalin’ and F. Vodopivec* 1

University of Ljubljana, Faculty of Mechanical Engineering, Center of Tribology and Technical Diagnostics, BogiSiEeva ul. 8, Ljubljana, Slovenia ‘Institute of Materials and Technologies, Lepi pot 11, Ljubljana, Slovenia

In fretting wear, t,he microstructure and the mechanical properties of t,he surface and subsurface layer depend significantly on the temperature field produced in the fretting zone. InformatZions reported in the literature indicate contradictsing values for the temperature produced at the interface. In the present study, the results of a successive grinding technique used to examine the microstruct,ure changes generat,ed by fret,ting of a AISI 52100 steel were compared to the mathematically calculated contact temperatures generated in interface using Archards model and equations developed in Centre of Tribology and Technical Diagnostics (CTT)). 1. INTRODUCTION

In tribology the term fretting is used to refer to any contact situation where two surfaces in mechanical contact are subjected to low amplitude oscillatory displacements. This type of contact is frequently encountered in industry where machine vibrations may induce minute movements between parts intended to be fixed with respect to each other. The effect of fretting is to cause surface damage by wear, corrosion and fatigue crack initiation, which may cause eventual failure of the part and significantly limits the life of machine elements and structures. The main reason for the lack of a stringent definition of fretting is the complexity of the fretting process, and the difficulty of comparing the effects of the prevailing contact conditions . (geometry, normal and tangential forces, displacement amplitude, frequency and number of cycles), as well as of the surrounding atmosphere. The contact surface temperature is a dependent variable, being a function of the size and shape of the real contact area, along with the friction coefficient, normal load, sliding velocity and thermal properties of the contacting bodies. The frictional heating,

which is only generated in real contact, regions, resuks in a relatively steep temperature gradient in t,he subsurface layer. In any sliding system, the temperature of the contact interface may have a significant effect on the tribological behaviour of the contacting materials because the temperature dependence of the microstructure and the mechanical and physical properties of the contacting solids affect considerably the contact configuration and the wear process. The extent of the temperature rise in the fretting contact zone has been a subject of considerable interest, but the literature reports vary significantsly in this matter. Some authors reported very low contact temperatures in fretting conditions [1,2], even bellow lOOC [3], meanwhile the others reported temperatures in the range from 500 to lOOOOC [4 - 61. The present study is primarily concerned with the presence of wear debris in the contact at fretting conditions and with their effect on temperature rise and changes of microstructure caused by the heat generated on the worn area. The tests were carried out at different loads, frequencies and amplitudes with one material combination under lubricated conditions.

258 2. THEORETICAL BASIS

The contact. surface temperature model used in most engineering applications of dry and boundary lubricated sliding has been the classical Blok model. This model considers the contact surface temperature problem as a semi-infinite body subject to a concentrated heat source. The validity of this assumption may be questionable for many practical dry and boundary lubricated sliding conditions. In many sliding situations the size of the contacting bodies is finite and contact occurs at several microscopic contact, spots within the nominal contact area. The frictional heating causes a high flash temperature at those spots. The temperature of the entire nominal contact area is affected by the hot spots, resulting in a mean temperature wit,hin the nominal contact area which can be significantly above the bulk temperature of the contacting bodies. Shearing of asperities in the initial stage of fretting causes detachment of the particles from the sliding bodies in the contact. We suppose that those particles are trapped in the contact. The real contact area consists of the limited number of contact spots between asperities of both contact bodies and particles trapped in t,he interface. Therefore the real contact area is the sum of those contact spots. With simplification we can calculate the real contact area as;

where n is the number of contact spots and al, is contact radius o f a single contact spot. The frictional heat generated at the interface is concentrated over a limited number of contact spots with radius air (Fig. 1-A). Consequently very high flash temperatures occur at those randomly located contact spots. The rapid heating on contact spots and subsequent quenching caused by the cold bulk of the surrounding material cause local changes in the surface and subsurface structure. Temperature affected area starts to form by heat flashes

under contact spots and then grows by coalescence of single isolated elementary areas (Fig. I-B). We suppose that the conduction of the generated heat is much faster in the vertical than in the horizontal direction.

c

2a

Figure 1. Distribution of the t,emperature on the real contact, area For the estimation of contact temperature an equation first proposed by Archard [lo] has been used. In his model Archard replaced real contact area consisted of the contact spots by a single circular contact area of a radius “a” and considered that the temperature in the contact is equal for both contact bodies. Archard also made a distinction between the cases of low and high sliding speeds. The difference being that the heat flux becomes more effective at high sliding speeds owing to the rapid introduction of new contact surface to the interface. In fretting this effect does not occur since the same contact surface is in contact all the test time. In this case the Archard equation for low speeds (2) can be used;

259

In eqn. (2) F is normal load, p is the coefficient of friction in the contact,, v is the relative velocity, a is t,he radius of contact area and h is the thermal conductivity. For fretting Archard eqn. (t2) can be rewritten as; (3) where f is frequency and A is amplitude. Than the contact temperature is the sum of Ihe bulk temperature of the contact bodies and the average flash temperature (eqn. 4);

Extended Archard formulation [ 1 1J for estimation of the temperature distribution was used to determine the subsurface temperature as a function of depth. In the case of fret,ting where low speeds occur the situation is analogue to the flow of current through an area of xa2. Therefore equation for low speeds (5) can be used; 7 ( 2 ) = T c * 1[

I

2 * arctan( z/a) z

In eqn. (5) Tc is contact, temperature, a is contact radius and z is the dept,h. A s a comparison to the Archard model C‘I‘L) developed the equations which consider the contact of two rough surfaces. In this case the contact consists of the individual cont.act, spots as a result, of contacts of asperities and/or particles detached from one of the sliding bodies in the init,ial stage of frett,ing. Frictional heat generated in the contact is dependent on coefficient of friction (p), normal load (F) and relative velocity (v). We discuss the frictional heat generation in the single contact spot. We also consider the hstribution of the normal load on the contact spots. Therefore the frictional heat generated in single contact spot is;

F n

CD 1 -- - - p * v In eqn. 6 “n” is the number of contact spots. Archard has considered some average angle of inclination of the asperities in the contact. In our equations the effect of actual angle of inclination of the asperities is included. Archard has supposed the conduct,ionof the generated heat to t.he depth equal contact radius. Our equations consider the conduction to the actual dept.h where the t<emperature ddference becomes zero and that the thermal conductivity is dependent on temperature (h = L O ) . In accordance to the Archard theory we consider the case of low sliding speeds where the simplified circular cont,act of the single cont,act spot, (Fig.2) is in the contact almost all the time:

Heat, flux generated by friction in single cont,act spot (@I) is conducted in the elements “A” and “R” (Fig.2) over the areas which are changing with depth. Value of the area on the depth zI for element A (Fig.3) is;

Heat flux generated in t,he single contact spot is divided between both elemenh in t,he con tact;

and can be treated through differentially thin layers with area A, and thickness ti;

260

Figure 2. Contact of tho single contact, spot

Figure 3. Conduction of t.he generated frictional heat in the single contact spot

26 1 Solving equation (10) we get for element A on thcb depth ZA, and layer of thickness;

Analogically we can write equations for element B.

temperature difference o f

3. RESULTS OF THE CALCULATION 3.1 Calculation procedure

r

(;

= ~2.(l-cosp,)

~

(1Xa)

( 12b)

lf the value of the area A, is const.ant. for t,he h y e r of thickness 6, the equation for t,he temperature difference calculation get t,he Himpldied form;

Temperature rise in single contact spot for element. A is equal to the whole t.emperat,ure difference t,o the depth ZAn (eqn. 14). where the temperature difference over one layer become almost zero (ATA P 0). n

AT, =

CAT^^ r=l

The contact temperature in single contact spot is equal to the sum of the temperature rise and bulk temperature of the element ,4T A(eqn. ~ 15); = ATA 4- TAb

:lnd t,he subsurface temperature dist,ribution can be calculated as;

the

same

Average con (,act,temperature genera t,ed in t,he interface in dependence on the real contact area was calculated for Archard‘s model and by our equations. For t.he calculat.ion by Archard’s model we used equations (3) and (4). In the Archard’s model t,he real con t,act sp0t.s are replaced with single circular contact, area, so the calculat,ctl temperature in the contact is average cont,act temperature. At, the calculat,ion by our equat,ions we used simplified equation (13) and equation (14) for the c a l c u l a t h of the temperature rise in single contact. spot. If the thickness & is small enough t.he error caused by the simplification used in the equation (13) is negligible. Equation (15) was used for contact kmperature calculation. For the normal load distribution on the single contact spot we used equat.ion (6). The calculat,etl con t,act, temperat.ure in single contact spot using equation (13) and (14) is equal to t.he average contact temperat,ure in the real contact. area. Subsurface t,emperature distribution was in both cases calculated for single contract spot,. For the calculat,ion by Archard’s model equation (5) was used. In t.he case of our equat,ions we first det.ermined using equation (13) the dept,h where the t,emperature difference over one layer becomes less than 0.01”c (depth ZAn). The subsurface temperature distribution was calculated from the depth ZAn to the surface using equation (16). The temperature on the certain depth “z” is equal t.o t.he sum of the bulk temperature of the element A and the sum of the temperature differences from the depth ZAn to the cert.ain dept.h “z”. Because of t,heir structure equat.ions (12) or (13) can be used for contact temperature calculation a s well a s for calculation of subsurface temperature distribution.

262

10000

1000

s

I

t 3

3 --

0

5

10

15

20

25

30

Ar Irdl

Figure 4a. Average Contact Temperature (Amplitude 6 pm; alr = 1 pm)

10000

100

0

26

50

75

100

125

150

175

Ar IPm21 Figure 4b. Average Contact Temperature (~lmplitude75 pm: a i r = 1 pm)

200

263

0

5

10 z [pml

15

20

Figure 5a. Subsurface Temperature Ilistribution (Amplitude 5 pm; alr = 1 pm; n = 5 ) 10000

1000

a

L

h

3

B

100

10

0

40

20 z

60

80

Irml

Figure 5b. Subsurface Temperature Distribution (Amplitude 75 pm; air = 1 pm; n = 5)

264 3.2 Presentation

of

the

calculated

results Calculat.ions were made for Mferent frequencies, normal loads antl amplitudes but only two of them are present.ed in t.his paper. Present,ed result,s were calculated at frequency of 50Hz, load of l00N antl amplitucte of 5 and 75 pm. Figure 4a,b shows average cont.act, temperature generated in the int,erface in dependence on the size of t.he real contact area (eqn. 1). Effect of the angle of inclination of t.he asperit,ies is also shown in Fig.4a,b. Subsurface temperature distribution under single contact, slmt. antl effect of angle of inclination on the heat conduct,ion are shown on Figure 5a,b.

3. EXPERIMENTAL AND OPERATING PROCEDURES The experiments were performed using a high frequency SRV fretting test rig. The test parameters are shown on Fig. 6. f “174

Experiments were conduct.ed using a ballflat combinat,ion of AISI 52100 (100 Cr6) steel against AISI 52100 steel. Ball specimens were of st,andard diameter of 9.525 mm, while flat specimens were machined from rod st,wk. The specimens were heat treated to a final hardness of approximately 850 I-IV and surface ground t.o Ha = 0.05 antl R,,,, = 0.44 microns. Aft.er cleaning, the t,est specimens were placed in the fretting t,est, rig. The m h o n was then transmitked t,o the ball t,hrough the drive units. Diferent, input amplit.udes, normal loads and frequencies were used. The duration of the t,est was from 10 t,o 360 minutes. The test temperature was 50%. IS0 VG 220 lubricant was spread on the surface of the specimen before the test (Fig.6). At (.he end of t,he t.est, specimens were removed and examined. The microstruct.ura1 examinations were performed on t,he flat specimens. Surface layers of thickness 3 to 7 pm were grounded off carefully and then the surface polished and nital etched. The microstruct,ure was examined with an optical (OM) and a scanning electron (SEM) microscope.

IF M

4. EXPERIMENTAL RESULTS AISI 52 100 (100 Cr 6 )

_.

I

A@ ?-I+’: _ _ m _ _m_

..

1,ubricant S 0 VG ~ _ _ I_ _ 220 ~

__.

(spread on the contact surface)

Figure 6. Test parameters

A successive grinding t.ochnique was used to examine the microstructure changes generated by fretting of a N S I 52100 streelat! tlifferen 1. amplihdes. The resu1t.s indicate that. the while phase is the precipitation hardened aus1.enit.e and that it, grows lat,erally by coalescence of init,ial areas of a few pm2. Frequent.ly very small modification of the init,ial microst.ructure was found near t.he white phase. In t.his paper experimental results of 5 antl 75 pm amplit.ucles, normal load of l00N and frequency of 50Hz are shown.

265

4.1 Specimen A, testing amplitude 5 pm

Figs. A1 show t,he worn area and the m icrost,ructure at, increasing distance below t,he initial (contact,)surface. Aft,er grinding off a layer of st,eel of thickness 5.4 pm the heat affected white area is virt,ually circular with prolongations in the form of short point,ed laths. These show the changes of microstructure due to the increase of' t.emperature caused by the fret,t,ingmotion of wear particles trapped in the contact. The microstruct,ure of the whit.e area consists of nn irregular central island of a white etching phase embedded in an area in which differences in grey coloration reveal Mferen t microstructures. At high magnification the white phase, which is found in the central island of irregular shape, shows a microstructure with a homogeneous matrix and small precipit,ates with a sharp boundary toward the neighbouring microst,ruct.ure (Fig. A2). This consists of mart,ensite tempered a t a t,emperat,ure of around 700% and shows fine carbide particles produced by the tempering as well as coarser non dissolved carbide particles of the same shape and size as in t,he initial microstructure. On t,he heat affected area M e r e n t stages of tempering are found, up to the complete spheroidisation, that is a microstructure of carbide particles ernbedded in ferrite. The initial size of the white area o n the surface was 240 pm, and the dept,h changed microstructure from the surface was less than 20 pm.

appeared on both sides of the ellipsoidal heat affect,ed area. In the protractions the wear damage was of different form than that in tbe main whit,e phase area. At. higher magnificat,ion the protaraction appeared whit,er and t,he transition boundary t.o t,he steel mat,rix, with virtually unchanged microstructure, was step like. At greater depth the protraction was separat,ed from the elliptical white area by a narrow region of steel with a slightly changed initial microstructure. At st,ill greater distance from the surface the white area broke u p into three parts. At the depth of 32 pm a band of white phase of length appr. 120 pm and widt,h of 10 pm wit,h a step Ilke boundary toward the matrix microstructure was still found. The microstructure of the white phase consist,ed of a homogeneous matrix wit,hout grain boundaries and numerous equiaxed precipitat,es of size below 0.05 pm. More rarely rodlike precipitates and precipitate free areas were found. Generally, the boundary between t,he white phase and the matrix microstructure was abrupt,. The great difference in microst,ructure, namely a matrix with tempered martensite with non dissolved carbide part,icles and in the whit,e phase, a dispersion of precipitates smaller by more than one order of magnitude in an uniform matrix, shows the great difference in temperature experienced over a distance of some pm. 5. DISCUSSION

4.2 Specimen B, testing amplitude 75 pm

The wear damage was much greater than on previous specimens (Figs. Bl). The defects in form of pits and microcracks of different width and dept,h were distributed over the whole white phase area. The maximum depth of pits was up to 16 pm, while microcracks orthogonal to the fretting motion were observed up to a depth of 27 pm. After the first.grinding two protract,ions with a flat, border toward the initial microstructure

High pressures and very low velocities in the init,ial st,age of fret.t.ing result in mainly dry contacts and shearing of asperities occur. Consequently, passage from two to a three body contact is obt.ained. Calculations of cont,act temperature using Archard's and in CTD developed equations indicate that t.he average contact t,emperat,ure can reach very high values, depending on the size and t.he shape of t,he real contact area and the amplitude (Fig. 4a,b).

266

Figure Al. Micrographies on the contact surface (uper left) and an increasing distance from this surface (amplitude 5 pm)

Figure A2.Microstructure in an area of white phase and tempered martensite (amplitude 5 pm)

267

Figure B1. Micrographies on the contact surface (uper left) and an increasing distance from this surface (amplitude 75 pm)

1000

100

10

Figure 7. Subsurface Temperature Distribution (Amplitude 75 pm; alr = 10 pm; n = 1)

Archard's model and our equations for average contact temperature calculalion are based on the similar bases, which are already explained in the paper. Considering the real cont,act area in the main equations differences between calculated values of both models are evident from t,he Fig. 4a,b. With the comparison of the calculated results of Archard's model and our equations (Fig. 4a,b) we can see that the Archard's equation for average con tact temperature can be used for estimation of the contact temperature generated in real contact area. For more accurate determination of the contact temperature we must consider the dependence of thermal conductivity on the temperature as well as influence of angle of inclination of t,he asperities. In the most cases the real contact area is very thfficult, to calculate therefore in the many cases Hertzian contact, radius is used. Using Hertzian contact, radius in Archard's equation for contact temperature calculation in fretting conditions (eqn. 3 and 4) results in very low average contact temperatures [ 1.231.

Archard's equat,ion for subsurface t.emperature distribution is suitable for estimation of the subsurface temperatures because it does not consider the changing of t,hermal conductivity of the contact bodies and act,ual angle of inclinat.ion of the asperities. Our equations include the effect of real angle of inclination which can be changed with depth and thermal conductivity in dependence on temperahre. Because of that we believe that, our equations could be suitable for more accurate calculation of subsurface temperature distribution. Average contact, t.emperature as well as the subsurface temperature distribution is dependent on real contact area and number of contact spots (Fig. 5a,b). With decreasing the real contact area and angle of inclination of the asperit.ies the average contact temperature increases and becomes even higher than 1000°C (Fig. k 7 ) . As consequence of the high pressures and rapid heating, as well as subsequent quenching caused by the cold bulk of the

surrounding material, a white phase layer is produced. In this white phase layer a microhardness in the range from 950 to 1200 w 0 5 was measured, what is higher than that of the surrounding bulk of the mat,erial (850 HV). In the white phase a completely different microstructure from that, of t,he temperature unaffected steel was found. The basic microstructure of the steel consisted of a matrix of low tempered martensite with mostly spherical carbide particles with an average linear size from 0.2 to 0.8 microns. The white phase microstructure consisted of a homogenous matrix (if microcracks and micropores are neglected) without, grain boundaries and a uniform dispersion of carbide precipates in the form of microbranchlets and spheres or polyhedra, and without secondary carbide particles. A sharp boundary between the white phase layer and the unchanged basic st.ruct,ure of the material is also evident from the experimental results (Fig. A2). The carbide particles found in the initial microstructure dissolve in austenite above 1OOOOC [12]. No such particles were found in the white phase independently of its shape and size what suggests that in areas of white phase the steel was heated to a temperature above 1OOOOC. The white phase startast,o form on several isolated points under con tact, spots. With increasing the test time single islands of white phase did grow by coalescence to the large single area. By increasing the fretting amplitude the quantity of t,he white phase in the heat affected area increases by formation and growth on new isolated points. A considerable drop of temperature occurs at. the boundary between the white phase and initial microstruct,ure. The small depth of the affected volume of met,al as well as the sharp boundary between the white phase and initial microstructure shows that the heat generated under single cont,act,spots by flashes was limited to volume of t.he order of a few pm3. The white phase clearly grows much faster near the surface of t,he specimen than in it depth, because some part of the frictional heating from those hot spots is

269 conducted in depth under contact spots but the main part is extended near the surface of real contact regions. A logical explanation for such behaviour is that the generated heat is dissipated very fast in the surrounding matrix producing slight tempering and that the white phase area grows by coalescence of single isolated areas produced under real contact regions by heat flashes. All the previously formed white phase was maint,ained at the virtually maximal temperature during the test. If not, a signlficant ddference in the size of carbide precipitates would be expected between the init,ial and the final stages of growth, which was not found in our cases. The experimental results indicate that the average contact temperatures generated in fretting conditions are very high (over 1000°C). From the comparison of the experimental and mathematically calculated results we can conclude, that, for the generation of very high contact temperatures the real contact area must be very small. As evident from the Fig. A1 and D1 the real contact area is much smaller than t.he Iiertzian contact area. The real contact area can not be exactly determined but on the other side its actual size is very important for accurate contact temperature calculation. The angle of inclination of the asperities has also great influence on the heat conduction and consequently on the contact temperatures. Therefore different way for contact, temperature calculation should be determined. By our opinion contact temperatures generated in the interface can be determined by measuring the actual depth of the temperature affected structure and by considering the real angle of inclination of the asperities. 6. CONCLUSIONS 0

In the initial stage of frett,ing passage from two to a three-body cont,act is obtained. The real contact area is very small consisting from the individual contact spot,s.

In virhally all cases, the microstructure of the white phase was identical and showed a homogeneous mat,rix with a dense dispersion of carbide precipitates of size below 0.05 pm. No carbide particles present in the initial microstructure were found in the white phase which suggests that in areas of white phase the steel was heated to a temperature above 1OOOOC. Archard’s model for the contact as well as for subsurface temperature distribution calculation can be used for estimation of the average contact temperature and subsurface temperature distribution. Because our equations considering the effect of real angle of inclination of the asperities and dependence of the thermal conductivity on the temperature they can be used for more accurate determination of average contact, temperature and subsurface temperature dist,ribution.

REFERENCES 1. Sproles and D.J. Duquette, Interface temperature measurements in the fretting of a medium carbon steel, Wear, 47 (1 978) 387. 2. Gaul and D.,J. Duquette, Cyclic wear behaviour (fretting) of a tempered martensite steel, Metall. Trans. A, IlA, (1980) 1581. 3. Attia and N.S. D’Silva, Effect of mode of motion and process parameters on the prediction of temperature rise in fretting wear, Wear, 106 (1985) 203. 4. Attia andP.L. KO, On the thermal aspect of fretting wear - temp. measurement in the subsurface layer, International Conference “Wear of Materials”, Vancouver, Canada, Procee. (1985) 363. 5. Kennedy Jr., Thermal and thermo mechanical effect in dry sliding, Wear, 100 (1984) 453. 6. Griffiths, White layer formations at machined surfaces and their relationship to white layer formation a t worn surfaces, J. of Tribology, 107 (1985) 165.

270 7. Bryggman and S. Soderberg, Contact conditions in frett,ing, Wear, 110 (1986) 1. 8. Berthier, L. Vincent and M .Godet, Fretting fatique and fretting wear, Tribology international, 22 (1989) 235. 9. Dobromirski, I.O.Smith, Metalographic aspect of surface damage, surface temperature and crack initiat,ion in fretting fatigue, Wear, 117 (1987) 347 10. Archard, The temperature of rubbing surfaces, Wear, 2 (1958159) 438 11. Archard,R.A.Rowntree, The temperature of rubbing bodies; The distribution of temperature, Wear, 128 (1988) 1. 12. Usami, K. Funabashi and T. Nakamura, Experimental study of surface temperat. during friction and wear test, Proceeding "Eurotrib 1993, Vol. 3 (1993) 440. 13. Vodopivec, J. Viiintin and R. SuBtarGiE, Effect of fretting amplitude on the microstructure of a l%C and 1.5%Cr steel, accepted for publication in "Materials Science and Technology" 14. J. Pezdirnik, J. Vii;intin, Influence of frequency and amplitude oscillations on surface damages in line contact, Proceedings of the 20th Leeds-Lyon Symposium on Tribology, Elsevier, 1994

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

27 1

Infrared technique for measuring temperature distributions Part one : Technique in EHD contact zone W.X.Qju a , S.Z.Wen b and A.K.Tieu a a Department of Mechanical Engineering, University of Wollongong, Northfields Avenue, Wollongong, NSW 25 22, Australia

bNational Tribology Laboratory, Tsinghua University, Beijing 100084, P.R.China This paper theoretically analyses the possibility of using infrared technique to measure the temperature distributions in EHD contact zone and turns it into operation. It is shown that this non-contact measuring method can be applied to measure the temperature in a very small contact area. 1. INTRODUCTION Temperature, a sensitive factor in EHD (elastohydrodynamic) problem, can significantly affect viscosity and load carrying capacity, etc. [1,2,3,4]. To measure the temperature in such a small area like EHD contact zone, there are two types of reliable methods at present. A micron-thin sensor [5,6,7] coated on a workpiece's surface can be used in practice, but its strength and error of performance can not be controlled easily; Infrared radiation method [8] is mainly used in labratory because one surface must be transparent to infrared rays. This paper theoretically analyses the problem involved in designing an EHD Temperature Test Rig using the infrared radiation technique, shown in Fig.1.

Fig.1 Photo of test rig Detector

2. CONTACT SURFACES IN EXPERIMENT

int

The contact surfaces, as shown in Fig.2, consist of a sapphire plate, a steel ball or cylinder and an oil film filled between them.

Fig.2 Contact model and components of

radiation

272 of temperature at the two interfaces and in the oil film that makes measurement by infrared technique possible.

Sapphire, with a structure of monocrystal hexahedron, was selected as the transparent material due to the following desirable characteristics

PI:

(a) higher hardness and strength, (b) high melting point (2040 O C ) and good thermal stability, (c) higher transmissivity to visible light, infrared and ultraviolet rays (Fig. 4 shows its transmissivity curve of infrared r a y ) without chromatic dispersion, (d) anti-wear, shock and erosion, (e) thermal property similar to steel, thus a metal to metal contact can be simulated realistically. The roughness parameters of the sapphire plate and steel ball or cylinder in use are shown in Table.1

I

Steel Ball

Fig.3 Heat model in EHD contact zone

3.2. Analysis of infrared radiation It is known from the basic theory of physics that any object of a certain temperature, usually higher than 0 degree Kelvin, radiates electromagnetic wave because of continuing movement of inner charged particles. The infrared spectrum band is located in the electromagnetic spectrum from 0.76 pm to 1000 pm. It is assumed that the radiator in the experiment has the Lambert radiator characteristics, i.e. its radiancy N has no relation with radiation directions.

3. ANALYSIS OF INFRARED RADIATION 3.1. Heat generated in EHD

contact zone In Fig.2, when relative motion occurs between the sapphire plate and steel ball or cylinder, heat will be generated due to viscous shearing of the lubricant and/or local friction and film compression. Hence, these heat energies can be considered as a comprehensive heat source located in the oil film, with heat conduction occuring a t interfaces 2 and 3, as shown in Fig.3. The temperature of interface 3 can be regarded as the temperature at the surface of the steel ball (i.e. temperature at the lower surface of oil film); while the temperature of interface 2 as the one at the lower surface of sapphire plate (i.e. temperature at the upper surface of oil film). It is the existence

3.2.1. Infrared radiation from each source The radiation received by the probe from the target spot in a n EHD contact zone is the summation of four parts as shown in Fig.2: Nb from the steel ball or cylinder, Nf from the oil film, Ns from the sapphire and Ne from environment.

Table. 1 Surface roughness parameters of Steel Ball (or cylinder) and Sapphire Plate (pm)

Items stee1 ball sapphire

Ra

0.012 0.002

I

Rtm

0.100 0.030

Rmax 0.200 0.124

R,

0.200 0.007

273

If attenuations of each parts denoted by Ab, Af, A s , and respectively, the total rate radiation can be calculated following:

N = AbNb + AsNs + A,N,

+ A,N,

are Ae,

of as

(1)

The attenuations introduced here indicate a set of transmission loss, such as reflection by interfaces and absorption by mediums. For Lambert radiator, there is a relation as following:

where R is the emissive energy radiated per unit area per unit time. Eq.( 1)can be written as

R = AbRb + AsRs + A,R,

+ A,R,

(3)

The effectiveness of various factors can be seen from this equation. The problem is how to separate these factors effectively. 3.2.2. Infrared transmissivity of each source Fig.4 shows the transmissivity curves of oil and sapphire as well as the infrared response curve of InSb probe used in the detector HCX-1 ( I S 0 40 and IS0 10 oils were used in the experiment). From the figure, the transmissivity of

the oil reaches the lowest point at the wavelength of 3.4 pm within a band from 3.1 pm to 3.7 pm. Beyond this band, it is almost 100 % transmission. According to the equilibrium of energy [lo]:

a,+p,+2, = 1

(4)

a,----absorptivity of oil,

where

pf ----reflectivity of oil, zf----transmissivity of oil. Under a certain temperature, emissivity, denoted by e, equals to the absorptivity at the same temperature: e,

=a,

(5)

It means that the radiation from high transmiting band approaches zero. In addition, infrared transmissivity of sapphire is about 90 %, so its emissivity can be neglected. A steel ball or cylinder specimen can usually be treated as a graybody,i.e. its emissivity e does not change with wavelength.

3.3. Applied filter In the above analysis, it is clear that there exists no infrared radiation of oil film beyond the range of wavelength from 3.1 pm to 3.7 pm. A band filter can be used to filter the film radiation from between 3.1 pm

Wavelength (pm)

Fig.4 Transmissive curves of oil and sapphire & spectrum response curve of the Infrared Detector HCX-1

274

3.5

a. Photo of filter

4

4.5

5

5.5

Wavelength (pm) b. Transmissive curve of

Fig 5 Filter

c. Filter location in light path

the filter

to 3.7 Fm wavelength when measuring the temperature of the steel ball surface. (A filter with a band width from 3.7 pm to 5.6 pm will be used in experiment, as shown in Fig.5.) 3.4. Emissive energy of

each radiator The emissive energy of ball surface, Rb, will follow such a formula:

eb---emissivity of ball surface Tb--surface temperature of ball. Fig.6 shows the measured eb curve of the ball surface, which is almost a constant, about 0.20. And that is the characteristic of a graybody.

the filter and received by the probe at a temperature T. Its value can be determined by calculation or calibration. The attenuation coefficient of ball surface radiation, denoted by Ab as shown in Fig.2, includes four parts: absorptive attenuation when passing through oil film; reflective losses at interfaces 1 and 2, respectively; and loss when passing through the sapphire. Thus,

where

2.5

3

3.5

4

4.5 5

5.5 Wavelength (urn)

where

r, --- transmissivity of the

sapphire reflectivity of interface 1 and 2 , which can be calculated by the Fresnel formula: (8) p = (n,- n 2 y / (n, + n2)2 where n l and n2 represent the refractivities of two kinds of media, which can be obtained from reference [lo]. Meanwhile, the second interfacereflection is neglected because of its very small magnitude [lo]. According to Fig.4 and Eq.(4), there exists the following relation:

Fig.6 Emissivity of steel bal1,eb

RB(T) represents the emissive energy of a blackbody which passes through

eLf = ef , zLf = l-eef, when 3.1< LC3.7 Fm (L=Wavelength) eLf = O , zLf = 1,

275

when 2.5 < L< 3.7 pm , 3.7< L< 5.5 pm

or,

(9)

Environmental emssive energy Re is generally known as the radiation of a blackbody at room temperature To, that is

The attenuation coefficient Ae is more complex as shown in Fig.2. A fraction of environmental radiant beams is reflected at the interfaces 1 and 2, with an attenuation A1 subjects to the following conditions: a part of the beams is reflected by interface 1 ; the other part is, after passing through the sapphire, reflected by interface 2, then returns through the sapphire again. Thus

If experiments are conducted under the same environmental condition, Re can be determined by calibration and treated as a constant later on. As for the oil film , the following formula can be derived in terms of the same method as the steel ball and environment:

4. CALIBRATION

The other fraction of environmental radiation passes through the oil film, is reflected by the ball surface, then returns through the film and sapphire to the probe. So

Considering the equilibrium energy:

where

2,

of

The calibrations curves are shown in Figs. 7,8. A blackbody has a standard emissivity eg, which does not change with wavelength. Furthermore, with known testing wavelength known, the relationship between the emissive energy and temperature can then be obtained. Therefore, a certain relationship can be established between the emissive energies and the output voltage signals.

is close to zero, then

Pb = 1-a,,while

e6 = ab,so

Pb = 1-e, (14)

Now that eb has a constant value of 0.20, and P,=0.80, then Ae, the comprehensive attenuation coefficient of environment, can be written as:

1601

20

30

40

50

60

70

80

90

1 I

276 Eq.( 20) then can be written as:

-i: v

Initial Outpuc

210

u

-I"

200

5

190

n=l

Vollagc 170 mv

8

n

3x2 / n 2 + 6 x / n 3 + 6 / n 4 ) e - " ] k f }

I

I60

30

20

40

50

60

70

80 90 Temperature (Oc)

Fig. 8 Calibration curve of blackbody with filter

(22)

Substitute L1 and L2 with filter's limiting wavelength, R( L ~ - L ~ ) Ba t various temperatures can be determined, as shown in Fig.9. Moreover, the transmissive loss of the filter must be considered, which is about 10 % as shown in Fig.5. ?.

: :

From Planck's law [ l o ] , a spectrum emissive energy of an absolute blackbody can be written as

N

5

30

/ I

s

20

10

where

L, wavelength T, temperature of blackbody cl, first constant of radiation c 1=2 hc2 c2, second constant of radiation ~2=ch/k h, Planck's constant k, Boltzmann's constant c, speed of light in vacuum

If the emissive energy power over a wavelength range from L1 to L2 is desired, integrate Eq.(18):

8 0 50 50

-

70 70

90 90

110 110

130 130

150 150

Temperature 170 190 (Oc) 170 190 Temperature ( O c )

Firr.9 Radiation of blackbody-temperature curve with filter

The emissive energy of t h e environment should be calibrated by the following procedure: Supply the contact zone with a circulated oil flow at a constant temperature and last long enough to establish a thermo-equilibrium in the zone. Then the total emissive energy, emitted from target spot and received by the infrared detector (with the filter), will be determined as following:

let x=cz/LT, then L=c2/xT, equation ( 19) becomes: where R can be obtained from the calibration curve (Fig.8) according to the temperature of the oil bath:

This value can be considered as a constant in later experiments.

277 5.2. Temperatures of oil film The temperatures of the oil film can be determined in terms of the method described above. Firstly, measure the emissive energy without the filter,

5. TEMPERATURE OF BALL OR CYLINDER SURFACE AND OIL

FILM 5.1. Temperature of Ball or cylinder surface By using the filter, the radiation of the oil film is filtered away and no longer enters the detector. So, ef=O and r,=l, the total emissive energy can be written as following by Eq.( 3):

4

= A,R,

+ AbRb + A f R f

(26)

then, with the filter,

R = A,Re, +

(27)

where Re1 and Rbl represent the emissive energy with filter sacrifice, that is All parameters on the right side of E q . ( 2 5 ) can be determined by comparing with the calibration curve of Fig. 8 and 9 after calculation or measurement. Therefore, RB(Tb) can be obtained, and then used to obtain Tb from Fig.9.

I86 a

170

PH=1.12 GPa PH=O.8 GP3

I

16C

vb= 0.33 d s .

150 Q

80 70

PH=1.12 GPa

---

-

I

Vbd.24 m i s

140 130

0

-.- Vb= 0.33 m i ~

5

120

'a

110

L

IC€

90 80 70

HZ Conhcr Zone (PH=O.SGPa)

10

I

0-

-0.2

-0.1

Entrance

0

(mm)

60

I 0.I

50

0.2

Exit

Fig.10 Steel ball's temperature rise ATb, along the centre line of contact zone under point contact with pure sliding

Fig.10 presents the temperature rise curves of the ball surface, based on the above analysis a n d data processing.

-0.2

I

H e m Contact Zone (PH=O.BGPa)

-0.1

Entrance

0

(mm)

0.1

0.

Exit

Fig.11 Oil film's temperature rise ATf, along the centre line of contact zone under point contact with pure sliding

Then Tfdetermined by the same method as that for Tb. Fig.11 shows the temperature rise of the oil film in the contact zone.

278

6. ERRORS IN EXPERIMENT The errors in the experiment involve many factors, for example, the error of detector performance, the error of data processing, neglect of the sapphire's radiation, the assumption of the oil film as a graybody and the slight vibration of the apparatus, etc. 7. CONCLUSION a. The infrared technique has been shown a practical method to measure the temperature distribution in EHD contact zone. b. More attention should be paid to minimise the error of experimental data in later research.

REFERENCES 1. B. W. Kelly and E. F. Leach, Preprint No.64 LC-13, ASLE/ASME

Lubrication Conference, Washington, D.C., 13-16, Oct. 1964. 2. H. S. Cheng and B. Sternlicht, J. of Basic Engineering, Trans. ASME, Vol. 87,NO.3, 1965, pp.695-707. 3. D. Dowson and A. V. Whitaker, Proc. Instn. Mech. Eng., Vol.180, Pt. 3B, 1965-1966,pp.57-71. 4. D. Zhu and S. Z. Wen, J.Trib. Trans. ASME, Vol. 106, 1984,pp.246-254. 5 . H. S. Cheng and F. K. Orcutt, Proc. Instn. Mech. Engrs., Vo1.180, Pt. 3B, 1 9 6 5 - 1 9 6 6 , ~158-168. ~. 6. G. M. Hamilton and S. L. Moore, Proc. Roy. SOC. , London, A322, 197l,pp.3 13-330. 7. L. Ma, Ph. D Thesis of Tsinghua University,Beijing, China, 1985. 8. W. 0. Winer, D. M. Sanborn and H. S. Nagaraj, Wear,Vol. 49, pp.43-59, 1978. 9. F. Schmid and C. P. Khattak, Laser Focus, Sept., 1983. 10. S. Jones and Chasmar, The detection and measurement of infrared radiation, Oxford University Press, 1968.

The Third Body Concept / D. Dowson et at. (Editors) 61 1996 Elsevier Science B.V. All rights reserved.

279

Infrared technique for measuring temperature distributions in EHD contact zone Part two: Experimental results W.X.Qiua, S.Z.Wenb and A.K.Tieua a Department of Mechanical Engineering, University of Wollongong,

Northfields Avenue, Wollongong, NSW 2 5 2 2 ,Australia National Tribology Laboratory, Tsinghua University, Beijing 100084,P.R.China The paper aims at showing the results of experiments on measuring temperature distributions in EHD contact zone by the infrared radiation technique. The effects of lubricant viscosity, velocity, load and slide-roll ratio on the temperatures have been considered. Also, the experimental data are compared with others results.

1. EHD TEMPERATURE TEST RIG According to the infrared radiation technique introduced in Part one of the paper, temperature distributions in EHD (Elastohydrodynamic) contact zone can be measured by using the EHD Temperature Test Rig shown in Fig.1 (its photo can be found in Part one). The object of measurement is an EHD

contact zone formed by a steel ball or cylinder made of bearing s tee1 with diameter of 25 mm, a sapphire plate of 30 mm diameter x 4mm thickness, and an oil film separating them. The steel ball specimen, in fact, is a piece of ball-part with a thickness of 15 mm, formed by cutting away symmetrically in the middle plane of a ball. A central hole has been made to fit a small shaft. Then they are

* Amplifier

Spindle

’,

C Y

Aluminium~Iate-wiihJ

oox

I

b .C.Motor I

X. Y Scanning table

I

Fig.1 Systematic sketch of test rig

280

connected as an integral component to a universal coupling, and a gearbox with a gear-ratio of 3:1, driven by a D. C. motor 1. The sapphire plate, forming a window to transmit infrared rays, is inlaid in an aluminium alloy plate with 280 mm diameter, which is mounted on the spindle and driven by a motor 2. The properties of sapphire and roughness parameters of both sapphire and steel ball or cylinder were presented in Part one. The contact couple, motor 2 and the loading part are assembled on an X-Y scanning worktable. The load in the experiment is applied by calibrated spring assembled under the ball holder, of the value up to 10 Kg. Two kinds of oil used in the experiment ( I S 0 10 and I S 0 40 oil) are heated to a desired temperature by Model 501 Thermostat and are introduced to the contact zone by siphonage. The oil then flows into a cup through the oil tray and pipe underneath, and finally, returns to the Thermostat. A model HCX-1 Infrared Microscope Detector consists of a unit (InSb Probe) for collecting and converting radiant energy and a set of signal processor with the following specifications : ( i ) Measurement range: room temperature to 350 OC (ii ) Relative error: + 4 % (iii) Resolving power for temperature: 1% (at room temperature) (iv) Resolving power for target: round spot with a diameter of 40 pm (v ) Visual field of scanning: 10mmx10mm (vi) Focus length: 40 mm (vii) Response time: in the order of microseconds (viii) Response wavelength of InSb probe: 2.5 pm to 5.5 pm (ix) Refrigeration of probe: liquefied nitrogen (77OK) ( x) Environmental condition:

relative humidity < 70 %, temperature +5 to +40 OC. Model 8520A Digital Multifunctional Electrometer was used to obtain data directly, while Model LF-802A Speedometer and Model TEM-2 2 50 Digital Thermometer were used to measure the rotational speed and the temperature of the oil bath in the experiment, respectively. 2 .DETERMINATION OF RADIANT

ENERGY FROM ENVIRONMENT The method introduced in Part one is used to calibrate environmental radiation. The data can be obtained as following: the output voltage of the detector is 0.175 v, the corresponding temperature of the blackbody 38OC, and the radiant energy R 1.49 x 10 -3W. cm -2. Then , from the temperature of the oil bath, 50 O C , RB(Tb ) can be read from the calibration curve as 2.13 x 1 0 -3 W cm -2, thus:

From Eq.( 7) in Part one:

Ab = ~ , (-p,)(1 l -p,)Zf = 0.84 with eb=0.20 so Ae&=1.13 x 10 -3 W.cm -2 This value will be used in later calculation.

3. TEMPERATURE DISTRIBUTION IN EHD POINT CONTACT ZONE UNDER CONDITION OF PURE SLIDING During the experiment, InSb probe receives continuous signals through the sapphire "window" when steel ball rotates against the stationary sapphire plate. The applied loads were 2 1 N and 60 N, which correspond to a Hertzian

28 1

stress of 0.8 GPa and 1.12 GPa, and a Hertzian contact radius of 0.11 mm and 0.16 mm, respectively. The three sliding speeds in the experiments were 0.24 m/s, 0.33 m/s and 0.53 m/s.

Entrance

Exit

Fig 4 Temperature distribution of ball surface, Tb ( O C ) , point contact, P~=1.12GPa,Is0 10 Oil, vbz0.53 m/S

Fig.2 Scanning sequence

The worktable moves along the X and Y directions with a step length of 20 pm, as shown in Fig.2. Considering the symmetry of two parts of contact zone divided by its central line, only half of the contact zone needs to be investigated in the experiment, so there are 288 points for each map, where 24 points along the Y direction and 1 2 points along the X direction. The inlet temperature of oil bath in all experiments was 50 OC. Fig.3 to Fig,8 show some of the maps representing the temperature distributions of the steel ball and the oil film.

Entrance

Exit

Fig.5 Temperature distribution of ball surface, Tb ( O C ) , point contact, P~=1.12GPa, Is0 40 Oil, Vb=0.24m/S

-

c

-EE

E

0.15

0.15

0.10

0.10

1 0

0

-0.15 -0.10

Entrance

0

0.10 0.15

Exit

Fig.3 Temperature distribution of ball surface, Tb(OC) , point contact, p~=0.8GPa,Is0 10 Oil, vb=O.33 m/S

Entrance

vb=0.24m/s

Exit

Fig.6 Temperature distribution of oil film, Tf ( O C ) , point contact, P H = O . ~ G PIs0 ~ , 10 oil, vb=O.24 m/s

282 between the central contact zone and outlet. The highest temperature reaches 135 O C for IS0 10 oil and 155OC for IS0 40, when vb=0.53 m/s a n d PH = 1 . 1 2 G P a , with corresponding outlet temperatures of 120 O C and 130 O C , respectively. Temperature increases with higher velocity, load and viscosity of lubricant, which can be seen in the inlet, contact and outlet zones.

1

E

-E

0.15 0.10

-n.i5 -0.10

0

0.10 0.15(mrn) 100

Entrance

Exit Vbd.14 m/s

Fig 7 Temperature distribution of oil film, Tf ( O C ) , point contact, P~=1,12GPa, Is0 10 Oil, ~ b = 0 . 5 3m/S

-.-

70

Vb= 0.33 m/r

A

Entrance

Entrance

Exit

Exit

Fig.9 Temperature rise of ball surface, ATb,alOng the centre line of contact zone point contact, pure sliding, IS0 10 oil

Fig 8 Temperature distribution of oil film, Tf ( O C ) , point contact, PH=0.8GPa, Is0 40 Oil, Vb=0.24m/S

I

90

3.1. Temperature distribution of ball surface Fig.9 to Fig. 12 show the curves of ball surface's temperature rise, ATb, along the central line of contact zone and the effect of sliding speeds on ATbmax. From these figures, a temperature rise over 10 O C (relative to the temperature of the oil bath, 50 O C ) exists at Hertzian contact boundary because of shearing and compression of the lubricant at inlet. In general, the t e m p e r a t u r e distributions of the ball surface shows regular peaks of temperature

ao

<-

70

60

c

Q 50

40

30

,

20 10

-*

I

'k0.8GPa

Hrruinn Doundary

n L

u--

-0.20

-0.10

Entrance

0

0.10 (mm) 0.;

Exit

Fig.10 Temperature rise of ball surface, ATb,along the centre line of contact zone point contact , pure sliding, IS0 40 oil

283 Generally, the oil film temperatures are higher than that of the steel ball surface. In the experiment, the highest temperature of oil film reaches 205 O C for IS0 10 oil and 235% for IS0 40 oil, when vb =0.53 m/s and PH = 1.12 GPa.

90 S 70

3E

n so f-

a

30 1C

0

0.1

0.2

0.3

0.4

0.5

Vb (m/s) Fig. 11 Sliding speed effect on ATbmax, point contact , pure sliding, IS0 10 oil

Entrance 20 L 0

I 0.1

0.2

0.3

0.4

0.5

Exit

Fig. 13 Temperature rise of oil film ATf, along the centre line of contact zone , point contact , pure sliding, IS0 10 oil

v b (m/s) Fig.12 Sliding speed effect on ATbmax,

point contact , pure sliding, IS0 40 oil

3.2. Temperature distribution of oil film Fig.13 to Fig.16 show the curves of temperature rise of oil film, ATf, along the central line of contact zone and the effect of sliding speeds on ATfmax.

Unlike the temperature distributions of the ball surface, that of the oil film shows some dramatic undulation in the contact zone. But by comparing with the film thickness and stress distribution of EHD condition [S], it can be found that they have a certain relation, that is, temperature peaks exist corresponding to the second pressure peak and the area of the minimum thickness.

Fig.14 Temperature rise of oil film ATf, along the centre line of contact zone , point contact , pure sliding, IS0'40oil

284

I

experimental results matched on both distribution and trend, although individual values differ from each o t h e r because of d i f f e r e n t experimental conditions.

U

5

,/'

120

vb (m/s) Fig.15 Sliding speed effect on ATfmax, point contact pure sliding, IS0 10 oil

130 -170 U

OPH-1.12CPiI A

PH=O.~CP~I

: 1

150

c

Q

130 110

90

20

40

60

80

100 1 2 0

ATbmax Calculated Data

(OC)

Fig.17 Experimental data comparing with Calculated data

Within the speed range of the experiment, the temperature rise of the oil film decreases with a n increase of velocity. This trend becomes more obvious in the case of higher viscosity. Also, an increase of the load leads to a n increase temperature rise of the oil film. The above phenomenon appears at the inlet, contact and outlet zone. In addition, the temperature of the oil film drops more sharply at the outlet.

3.3. Comparing with the other's results Comparing with the results calculated according to Jaeger [l], the experimental data shown in Fig.17 is about 15OC higher than the latter, but is showing the same trend. From the experimental curve by Nagaraj et a1 [2] shown in Fig.18, it can be seen t h a t the two

Fig.18 Experimental curve by Nagaraj [2] (steel ball RaO.O11 pm, pure sliding, oil bath temperature 4OOC)

It should be said , however, that the results obtained by the experiment approach the real values more closely than those by calculation.

2 85 The applied load is 2 1 N, which corresponds to a Hertzian stress of 0.8 GPa. Keeping the linear velocity of ball unchanged at 0.33 m/s, three sliding-rolling ratios of 0.5, 1 and 4 can be obtained after adjusting the linear velocity of the plate to values of 0.20 m/s, 0.11 m/s and -0.11 m/s, respectively . Moreover, the case of pure sliding has a sliding-rolling ratio of 2. Therefore, four different ratios are then available in the experiment. Fig.19 and 20 show two of the temperature distribution maps of steel ball and oil film in this type of experiments.

4. TEMPERATURE DISTRIBUTION

IN EHD POINT CONTACT ZONE UNDER CONDITION OF SLIDING-ROLLING In this experiment, InSb probe receives discontinued signals through the sapphire "window" when steel ball and plate are driven respectively by two motors. The slide-roll ratio will be given as following: c = 2 ( V b -Vs)/(Vb +Vs)

(1)

where V b and vs represent the linear velocities of steel ball and plate, respectively. The lubricant used in experiment is IS0 4 0 .

4.1.Temperature distribution of ball surface Fig.2 1 presents the temperature rise of the ball surface, ATb, along the central line of contact zone for the four ratios.

60

< so c

Entrance

Exit

Fig 19 Temperature distribution of oil film, Tf ( O C ) , point contact, p~=0.8GPa, Is0 40 Oil, c=1

a

40

30 20 10

1'11-0.8CPa llertzian Boundary

0 -0.20

-0.10

Entrance

0

(mm 1

0.10 (mm) 0.20

Exit

Fig.2 1 Temperature rise of ball surface, ATb,along the centre line of contact zone, point contact, slide-roll case , IS0 40 oil

Entrance

Exit

Fig 20 Temperature distribution of oil film, Tf ( O C ) , point contact, p~=0.8GPa, Is0 40 Oil, c=o.5

From the data shown in reference [2,3], the temperature rise in pure rolling (i.e. C=O) is low, with the value between 5 to 8 O C . By the experimental curve shown in Fig.21, A T b m a x is about 2 5 O C with its position approaching the centre of

286

the Hertzian contact zone when C=O.5, and moves gradually towards the outlet with an increase of C until the ratio equals to 2, then moves backwards to the centre of the contact zone when C > 2. The temperature of the oil film drops sharply at the outlet. 4.2. Temperature distribution

of oil film Fig.22 shows the temperature rise of the oil film, ATf , along the central line of the contact zone under the four ratios.

-0.20

-0.10

Entrance

0

(mm)

0.10

(mm) 0.20

Exit

Fig.22 Temperature rise of oil film, ATf ,along the centre line of contact zone, point contact , slide-roll case , IS0 40 oil 10

I

The maximum temperature rise of the oil film reaches about 140 O C when C=4. 4.3. Comparing with the other’s

results By comparing the experimental results by the author with the one by Nagaraj et a1 [2,3], as shown in Fig.23, it can be found that they have the same trend. 5 .TEMPERATURE MEASUREMENT

UNDER CONDITION OF LINE CONTACT Using the same test rig and changing the specimen of steel ball to a steel cylinder made of bearing steel with a diameter of 25 mm, the condition of EHD line contact can be simulated. I S 0 40 oil is used as the lubricant in the experiment. The applied loads are 60 N and 100 N, which correspond to Hertzian stresses of 0.46 GPa and 0.59 GPa, respectively. The linear velocities i n t h e experiment were 0.24 m/s, 0.33 m/s and 0.53 m/s. 5.1. Temperature distribution under condition of pure sliding

I

‘--c-0.33d --Vc-O..53d

-------

-0.11 -0.08

Entrance Entrance (mm) Exit Fig.23 Experimental curve by Nagaraj [2] (steel ball Ra 0.011 pm, P~1.02GPa,oil bath temperature 4OOC)

0

0.08 0.11 (mi

Exit

Fig.24 Temperature rise of steel cylinder AT,,along the line perpendicular to the contact zone, line contact, pure sliding, IS0 40 oil

287 Fig.24,25 show the curves of temperature rises of steel cylinder and oil film, along the line perpendicular to the contact zone. vc-0.2lrn/s A

Ij1-0.46CPa

180

I70

'

vc-0.3 3 rn/s

lI

vc-0.53rn/s

a n d the maximum measured temperature was 140 O C when P ~ = 0 . 5 9GPa and vc=0.53 m/s In general, the t e m p e r a t u r e distribution of the line contact shows similar feature as the one for the point contact except for lower values and more gradual change. The reason is that there exists an enlarged contact area in the case of line contact.

.

vc (m/s) Fig.27 Sliding speed effect on ATcmax, line contact, pure sliding, IS0 40 oil -0.1 1 -0.08

n.08 0.1 I (rnrn)

0

Entrance

Exit

Fig.25 Temperature rise of oil film, ATf ,along the line perpendicular to the contact zone, line contact, pure sliding, IS0 40 oil

160

4

PH=O.j9GP3.

130

5.2. Temperature distribution under condition of slidingrolling Like the condition of pure sliding described above, I S 0 40 oil is selected as the lubricant. The applied load is 60 N, which corresponds to PH =0.46

GPa. The measurements are conducted under four ratios of 0.5,1,2,4.

2130

80

2 110

60

100 90

0.10 0.20 0.30 0.40 0.50

vc (m/s) Fig.26 Sliding speed effect on ATfmaY, line contact, pure sliding, IS0 40 oil

I

50

-5

40 30 20 10

OL

The effects of sliding speed on the temperature rises of steel cylinder and oil film are shown in Fig.26,27. For line contact, the temperature rise in contact zone changes gradually,

A

P11-0.36CPa

70

L

$dg P11-0.46CPa Hertzian Boundary 1

I

I

-0.08

0

Entrance

(mm)

I

0.08

(rnrn)

Exit

Fig.28 ATCalong the line perpendicular to contact zone, line contact, slide-roll IS0 40 oil

288

En trance

Exit

Fig.29 ATf along the line perpendicular to contact zone, line contact, slide-roll IS0 40 oil

Fig.28 a n d 29 present the temperature rises of steel cylinder and oil film, ATc and ATf , along the line perpendicular to the contact zone.

6 . DISCUSSION ON EXPERIMENTAL RESULTS (a) The temperature rise of the oil film is reduced with an increase of speed in the speed range of the experiment. As generally known, at low speed, a

small film thickness increases gradually with a rise in speed. In this case, a local boundary lubrication might occur, so the temperature will be higher. The condition will be improved when the oil film becomes thicker with an increase in speed. Consequently, the temperature rise of the oil film may decrease. The condition will be more complex

when the speed continuously increases. To understand completely the process of temperature rise of an oil film changing in relation to speeds, an assumption of five stages may be put forward as shown in Fig.30. The results shown in Fig.15 have demonstrated the first stage. The following two stages have been verified by the experiment conducted by the others [2,3]; while the other stages still remain unknown, especially the criteria level of speed. (b) The phenomenon ( a ) became more obvious when using an oil of a higher viscosity. The reason is that, in the speed range considered, a more viscous oil may result in a thicker oil film, and its thickness increasing with speed will become more obvious than that of thinner oil. (c) The temperature of the oil film rose steeply at the inlet and dropped sharply at outlet In the experiment, only the average film temperature in the direction of film thickness was measured. But it still can be concluded that the heat model, mentioned in section 3.1 of Part one, is correct. That means there exists a heat layer with high temperature in the oil film, parallel to the contact surface and generated by shearing, friction and compression of lubricant. The heat energy of this layer will be transferred by convection of oil and conduction of both interfaces of the oil-steel ball (or

dVb(rn/S)

Fig. 30 Possible changing process of Tf with vb

289

cylinder) and the oil-sapphire plate. According to reference [5,6], there is the following relation: Heat transferred to solid Pe=

Heat taken away by fluid and

P, = ( Vh2)-'

where Pe represents Peclet Number, V,h represent velocity and oil film thickness. The value of Pe is very large as h* is very small in EHD condition, so the main method of heat transfer here is conduction. In other words, the proportion of heat taken away by fluid is smaller. This is the reason why the temperature of oil film rose steeply at the inlet and dropped sharply at the outlet.

( d ) The temperature distribution of the ball surface showed no peak which corresponds directly to the temperature peaks of the oil film and the stress peak described in reference [51. It is clear that heat is transferred to

the interface of the ball and oil film through a large temperature gradient from the heat layer in the oil film. In addition, the oil conductivity is small. So the peak of temperature would be lowered and change smoothly. Furthermore, the highest peaks of film temperature situated near the contact boundary, that facilitates more heat exchange. So a new heat balance will be established at the surface of ball, which will not correspond to the temperature distributions of the oil film and the stress distribution described in reference [S]. ( e ) The temperature of the sapphire surface could be higher than that of the ball surface.

This is a deduction that can not be seen directly from the experiments,

but it will help us to understand the heat balance in the contact zone. In the case of pure sliding, the ball rotated while the sapphire plate stood still. The diffusivity of sapphire is smaller than that of steel. So the surface temperature of the sapphire would have been higher than that of the ball.

7.CONCLUSION (1) In the case of EHD point contact, the temperature distributions of the ball surface show that there is a peak appearing between the centre of the contact zone and outlet , and no obvious second peak.

( 2 ) The temperatures of oil film are 60 OC higher than that of steel ball in the contact zone. Its variation shows similar trend as the film thickness described in reference [5].

( 3 ) The contact temperature varies in direct proportion to load and viscosity of lubricant. (4) For the speed range considered in the experiment, the temperature rise of the oil film is in inverse proportion to sliding speed under condition of pure sliding, while the temperature rise of the ball surface is in direct proportion to sliding speed.

( 5 ) Sliding-rolling ratio greatly affects the temperature distributions. The peak of temperature moves towards the outlet and increases with the ratio value when C <2; it moves back towards the centre of contact zone with a higher value of C>2.

(6) In the case of line contact, the temperatures are far less than that of point contact under the same condition and show smoother change in the contact zone. It also has the same variation as the case of point contact.

290

( 7 ) The main method of heat transfer is conduction a t both interfaces of the oil film-ball (or cylinder) and the oil film-sapphire plate. (8) During the experiments, the temperatures in EHD contact zone were generally less than 300 OC.

REFERENCE 1. J.C.Jeager, Proc. Royal SOC. New

South Wales, Vo1.56, pp.204, 1942. 2. H.S. Nagaraj, D.M. Sanborn and W.O. Winer, Trans. ASME, J. of

Lubrication Technology, pp. 2 54, April, 1977. 3. V.K.Ausherman, H.S.Nagaraj, D.M.Sanborn and W.O.Winer, Trans. ASME , J. of Lubrication Technology, pp.254, April, 1976. 4. K.P.Hou, Thesis for Ph.D of Tsinghua University, Beijing, China, 1987. 5. A.N.Grubin and I.E.Vinogradova, Investigation of contact of machine components, Kh.F.Ketova(ed.) Central Scientific Research Institute for Technology and Mechanical Engineering (Moscow),Book No.30 (DSIR translation No. 337) ,1949. 6. D.Dowson, Proc. Instn. Mech.Engrs. 1965-66, V01.180, Pt.3B., pp.7-16.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

29 1

AN ITERATIVE HEAT BALANCE TECHNIQUE FOR RAPID ESTIMATION OF ENGINE BEARING TEMPERATURES A 0 Miana and G J Jonesb 'Engineering Analysis Department, T&N Technology Ltd, Cawston, Rugby, CV22 7SA, UK bGlacier-VandervellLtd, Argyle House, Northwood Hills, Middlesex, HA6 ILN, UK This paper describes a technique for obtaining improved estimates of the operating temperatures of engine crankshaft bearings(bigendhod and main bearings). An accurate estimate of temperatures is essential in determining the operating

viscosity of the lubricant and hence predicting the performance of each bearing in terms of the minimum oil film thickness, power loss and oil flow. The method presented here consisted of formulating equations of heat conduction and convection for each bearing. The resulting set of simultaneous equations were then solved by employing matrix algebra in an iterative algorithm. This ensured that the heat generated within all the bearing films was accounted for as being dissipated to the immediate surroundings, i.e. the oil sump, the oil gallery, the engine block and the connecting rods. In addition to data for the material, geometry and loading, the analysis employed curve fitted performance data for each bearing. The new 'beat balance" algorithm was found to be very robust and rapid, offering the possibility of a wide range of "what if' type calculations. 1 INTRODUCTION

Operating temperature is one of the major influences on the performance of an engine crankshaft bearing, since this determines the viscosity of the lubricant and thus the hydrodynamic performance of the bearing. Thus it is necessary to have a good estimate of effective operating tcmperature in order to obtain reliable predictions of bearing performance.

In order to achieve a stable temperature in a hydrodynamic bearing there needs to be a balance between the heat generated by friction and the heat carried away by convection into the lubricant and by conduction to the bearing components. Often a simplified form of 'heat balance" is used, where it is assumed that a fixed proportion of the heat generated is carried away by the lubricant. Thus only the power loss generated and the oil flow for the bearing need to be calculated and these can be determined from the hydrcdynamic analysis alone. To further speed solution times, approximate values of power loss and oil flow can be utilised to determine operating temperature. These are calculated using a representative fixed eccentricity instead of performing a full orbit analysis.

One of the major limitations of the above approach is that each bearing in an engine is treated in isolation. No account is taken of any interaction between bearings such as that produced by heat conducted through the crankshaft. Improved prediction of bearing temperatures can only be achieved by using a more sophisticated thermal model of the total bearing system. This includes the use of values of oil flow and power loss calculated from a full orbit analysis of each bearing. Heat conduction within the crankshaft and in the bearing support structure has to be calculated together with convective and radiative losses from the crankshaft and connecting rods. Performing a thermal analysis of the complete engine would be prohibitively time-consuming. However, it has been found from experimental studies that the bearing temperatures are very dependent on the oil gallery temperature. By utilising this as a datum, only the 'bottom-end"of the engine needs to be modelled, which significantly reduces the complexity of the problem.

292 2 FORMULATION OF HEAT BALANCE 2.1 Heat balance in a bearing For a hydrodynamic bearing to operate at a stable temperature the following heat balance must be satisfied. heat generated in bearing = heat convected away by oilflow through bearing + heat conducted to crankshufr + heat conducted to bearing structure

The heat generated in a bearing and the oil flow through it can be derived from an oil film analysis of the bearing. Heat conducted away from the bearing oil film into the Crankshaft and bearing can be evaluated by creating a thermal model of the complete bottom-end of the engine. Figure 1 shows diagrammatically the main heat flows for a part of an engine bay.

It should be noted that heat may be conducted into the oil film rather than away from it. For example, if the temperature of a big-end bearing is significantly higher than that in the adjacent main, then heat may flow through the crankshaft from the big-end to the main.

2.2 Thermal conductance The heat transmitted, by conduction, convection or radiation can be expressed as product of a thermal conductance G and a temperature rise AT:

The heat convected away by the oil flow through the bearing can be calculated from the following:

In order to obtain thermal conductances in the engine components, ie the crankshaft, the connecting rods and the crankcase panels, approximate thermal models were created using simplified geometry so that standard heat conduction formulae could be utilised.

2.3 Heat conduction in crankshaft The crankshaft was modelled by breaking it down into the bearing journals and the webs connecting them. Each journal was modelled as a solid cylinder, with heat being conducted from the journal surface to the journaVweb interfaces on each side of the journal. The value for conductance for one half of the journal was given by: G - k

4~ D

(L

+

D)(2L

~ +

L D)

(3)

Each web was represented as an equivalent solid cylinder having a diameter equal to the mean of the diameters of the adjoining journals and a length equal to distance between the centres of the journaVweb interfaces. The value of conductance between theinterfaces was: n Dz

+ Conduatlon In components

- -b

Conveotlon vle oll now

er) Conveotlon from eurteoes

-

Figure 1. Heat flow from crankshaft bearings

G - k -

4 L

(4)

293 2.4 Convective and radiative losses The heat transfer coefficient for convective losses from the crankshaft webs was calculated using the equation for a rotating cylinder but using the mean surface speed of the web Us: a

- 4.04

It was assumed that only radial heat flow occurred through the bearing lining and the bearing backing, so the conductance of each layer of the bearing half could be calculated using the following equation : G - k -

2 1

u ( - 3 3

D

r L

(7)

(5)

The crankshailcounter weights were approximated to a sector shape and the heat transfer coefficient calculated from the above equation, again using the mean surface speed. Radiative losses from the crankshaft webs and counterweights were calculated using the following relationship for conductance:

This equation could also be used for the bearing cap, by approximating its shape to a semi-cylindrical shell of uniform thickness. The conductance across the interface between the bearing shell and its housing was calculated from: G

- 1400A (1

+

(-).‘ j

0.39

075

)

(8)

where Pj is the contact pressure. where A was the effective surface area of each component

2.5 Heat conduction into big-end bearing A simplified heat flow model for a big-end bearing is shown in Figure 2.

It was assumed that the heat conducted through the cap was dissipated from its outer surface via convection and radiation. The convective heat transfer coefficient was calculated using Equation 5, using a value of surface speed equal to the mean velocity of the big-end journal.

For the rod half, the big-end shoulders, which were assumed to account for 80% of the bearing arc in the rod, were modelled on the same basis as the cap half. The remainder of the bearing arc was assumed to conduct heat to the shank of the rod, which was represented by an equivalent rectangular block.

2.6 Heat conduction into main bearing The cap half the main bearing was modelled in exactly the same way as the big-end bearing cap except that a different value of heat transfer coefficient for the outer surface was used, since this was stationary.

Figure 2. Approximate model of big-end

Heat from the block half of the main bearing was assumedto be conducted into the supporting crankcase panel. This panel was represented by a semi-cylindrical shell so that Equation 7 could still be applied. The outer surface of this shell was assumed to be at the same temperature as the engine block.

294 2.7 Assembly of equations

7. The front of the engine was assumed to be insulated (no axial heat flow). 8. An approximation was made for the heat lost from the rear main via the flywheel.

Having obtained expressions for the various heat flow terms for each bearing, the heat balance equations were then assembled into a set of simultaneous equations for the complete engine. Using an electrical analogy, Kirchoffs current law was applied to the heat flow (electrical current) whereby heat flowing into the fluid film (node) was taken to be positive.

Since the effective bearing temperatures were the only unknown points of interest, the thermal conductances between bearings and to reference conditions could be combined into overall values. This reduced the number of simultaneous equations to be solved to that of the number of bearings in the engine. (Intermediate temperatures, e.g. at the joint between the bush and engine block, could be calculated as a post-processing exercise if required.)

Figure 3 shows the assembly of the thermal network for an engine bay containing a single cylinder. The following boundary conditions and assumptions were employed in order to complete the thermal model:

This set of simultaneous equations was expressed in matrix format, with bearing temperatures as the unknown variables:

The main gallery/block temperature was defined. Each bearing operated with a lubricant at an effective uniform temperature. 3. The oil feed temperature to each main bearing was defined. 4 The oil feed temperature to each big-end bearing was defined as a function of the oil feed and effective temperatures of the feeding main bearing. 5 . A representative temperature was employed for heat convection from the surface of components. 6 . Of the heat lost from the crankshaft webs and counter-weights the 90% originated from the adjacent bearing. 1. 2.

I 1

1

-

'

bnductlon through metal __* Convection by oil I Convecdon by airinrump I ~~

-

-

[rl [WSI

(9) The bearings (bothbig-ends and mains) were numbered consecutively from the front of the engine in order to produce a diagonally dominant three banded matrix [A]. The inverse [A]' could therefore be obtained efficiently and a solution for bearing temperatures obtained with negligible computer processing time: [A1

$?: piston

BIG END

Figure 3. Assembly of thermal conductances

295

3 IMPLEMENTATION OF IMPROVED HEAT BALANCE MODEL The heat balance model described in the previous section has been incorporated into a "rapid" design technique for crankshaft bearings.

3.1 Bearing orbit calculation The analysis of the oil film in a dynamically loaded engine bearing requires the solution of the governing Reynolds equation throughout a complete cycle of the engine. This results in the prediction of the motion of the journal centre relative to the bearing and hence values of oil film thickness. Also values for oil film pressure, power loss and oil flow can be obtained from such an analysis. This ''orbit" analysis is potentially very time-consuming since it involves many hundreds of solutions to the Reynolds equation. However computationally efficient solutions can be obtained by applying a number of simplifying assumptions. i.e. a. b. c.

the journal and bearing are rigid, cylindrical and aligned the lubricant is isoviscous and Newtonian 'mass conservation' effects in the lubricant film are ignored

In this implementation, the oil film analysis was carried out using a technique based on Booker's Mobility method but utilising a 'Finite Bearing' Mobility map due to Goenka (1).

3.4 Oil flow calculation The values for oil flow in the big-end bearings were calculated using the modified Martin equation (3) which takes account of mass conservation:

Q, -

For a crankshaft bearings in high speed automotive engines, the oil film thickness can become so low that the bearing potentially operates in a mixed lubrication regime. Under these conditions, the use of viscous shear alone for calculating power loss may result in an under-estimation. Accordingly, a correction term, as indicated by Conway-Jones et al(2), was applied to the power loss calculation to account for this effect.

1s

(11)

The exponent S takes a value of 0.7 for single oil hole and 0 for a full 360 deg. groove. For partial grooves, the value is interpolated on the basis of groove extent. Where such bearings were fed from a partially grooved main bearing, a correction was applied to take account of the crankshaft drilling being occluded by the plain part of the main bearing during parts of the engine cycle. The above equation was also employed for the main bearings, using an appropriate value for the factor S.

3.5 Bearing oil supply pressure The expressions for oil flow above require the value of the oil supply pressure P,, For the main bearings, it was assumed that the feed pressure was equal to the oil gallery pressure. Calculations using simple pipe theory indicated that any pressure drop through the crankcase oilways could be neglected. In calculating the feed pressure to the big-end supply holdgroove, the inertial effects of crankshaft rotation were taken into account by adding the centrifugal head generated in the crank drilling. This was estimated from the following formula:

AP 3.2 Power loss calculation Values of power loss for each bearing were obtained from the orbit analysis by determining the viscous shear torque from the film thickness predicted by the orbit.

QA QH

- 2%'

p

N~ ( r o2 - r 2i )

(12)

3.6 Interpolation of Power Loss and Oil Flow

To reduce overhead of re-calculating power loss and oil flow at each stage of the heat balance, which would involve another complete orbit analysis for every bearing, values were calculated for these parameters for a number of different values of effective temperature covering the potential range of operating temperature. Then, during the iterative process to determine the actual bearing temperatures, values of power loss and oil flow could be interpolated from these results.

296 3.3 Solution Algorithm The iterative technique used to obtain a solution for the bearing temperatures is shown in Figure 4.

For each bearing, calculate performance for a range of effective temperatures

I

Specify initial values of effective temperature for each bearing

I

I

Interpolate values of power loss and oil flow for each bearing

I

r

1I

Calculate conductances and assemble the heat balance equations in matrix form

For each bearing, update values of effective temperature to new values

I

1

Invert coefficient matrix and multiply out to obtain solution for bearing temperatures

in bearing temperatures

N

Using temperatures from heat balance perform full orbit analysis for all bearings

Figure 4. Flow chart for determining bearing operating temperatures The "heat balance" algorithm presented above was found to be very stable and converged within a few iterations. The measurable speed of calculations was

governed only by the time required for the orbit calculations.

297 4 COMPARISON OF PREDICTED AND MEASURED TEMPERATURES

-

a) Speed: 2500 rpm Gallery Temperature: 113 C

-

b) Speed: 4500 rpm Gallery Temperature: 129 C

150

3 145

Experimental data was available from tests on a 2-litre, 4-cylinder, fuel injected, naturally aspirated gasoline engine. Temperatures had been measured at a number of locations on one connecting rod, including four close to the surface of the large-end bearing, via a two-bar telemetry linkage. Thermocouples had also been placed in each of the main bearings and in parts of the engine block. Figure 5 shows comparisons of predicted and measured bearing temperatures for three speed conditions, all with the engine operating at full power (Measured assembled clearances were used as data for the predictions). Calculated values based on only viscous power loss are shown as well as those where the boundary layer correction was included. Agreement between the measured values and the predictions of the model was very good. Only in the case of the big-end bearing at high speed did the boundary layer effect have any significant influence on the predicted temperature and then it resulted in much better agreement with experiment.

t

f ::

5 CONCLUSIONS

130

P‘gdsp‘ *$@+a

@/’

@>* *9

-

c) Speed: 6500 rpm Gallery Temperature: 141 C

An improved technique for estimating crankshaft bearing temperatures has been formulated and successfully incorporated into a ‘rapid’ bearing design analysis program. Comparison of predicted temperatures with those measured in a modem highspeed gasoline engine gave very good agreement, despite the simplified thermal model employed. However, fUrther validation is required, in particular for the power loss correction term, which was empirically based. Experimental data is required from different types and sizes of engine to ensure that this approach can be applied generally.

Figure 5. Comparison of experimental and predicted values of crankshaft bearing temperatures in a 2.0 litre gasoline engine

The primary objective of this work was to improve the prediction of bearing performance at the design stage, rather than to provide a tool for the thermal analysis of the bottom end of an engine. The resulting design technique allows for rapid assessment of the influence of a number of bearing parameters on predicted performance. These include bearing diameter, length, clearance and grooving arrangement.

298 REFERENCES

APPENDIX

( 1 ) GOENKA, P.K. Analytical curve fits for solution

The following table summarises the defaults used in calculating the results shown in Figure 6. These defaults can be modified in they are not appropriate for a specific engines.

parameters of journal bearings, Trans ASME J, of Triboloev. Sen'es F, 1984, October, 42 1-428 (2) CONWAY-JONES, J.M., MARTIN, F.A. and GOJON, R. Refinement of engine bearing design techniques, Tribolo~vIntemati o d , 199 I , 24.2, 119-127 (3) MARTIN, F.A and XU, H. Improved oil flow prediction method for connecting rod bearings fed by a single hole in the crankpin, Tribolo~ -v of m e s and Eng ine OiL, 1993, (SP-959), S A E Technical Paper 93079 1,95- 104

NOTATION an NxN matrix of conductance coefficients area lubricant specific heat inner diameter of bearing layer outer diameter of bearing layer bearing diameter, effective web diameter thermal conductance heat generated within the fluid film, heat flow through an '%lement" thermal conductivity of material bearing length, effective length of web rotational frequency of crankshaft change of pressure along crank drilling side-leakage flow from bearing the "hydrodynamic" oil flow the "feed pressure" oil flow radius of drilling inlet about crankshaft axis radius of drilling exit about crankshaft axis a column matrix, size N, including the power generated at each bearing flow exponent temperature rise of the lubricant through the bearing or the difference between the supply and effective temperature, temperature difference across an "element" temperature a column mamx, size N, of unknown bearing temperatures lubricant density heat transfer coefficient surface emissivity the Stefan Boltzman constant

I ITEM

I DEFAULT

I

Big-End Feed Temperature

0.5 x Feed Main Temp. Rise

Big-End Feed Pressure

Main Gallery Plus Inertia Head

Main Feed Temperature

Main Gallery

Main Feed Pressure

Main Gallery

Block Temperature

Main Gallery at 1.4 x Joumal Diameter From Film

Sump Temperature

Main Gallery

Rod Conductivity

17.3 W/mK

~~

~

. Lining . . Conductivity I 17 I W/mK I Beanng

: Bearing Backing Conductivity

17.3 W/mK

Engine Block Conductivity

56.7 W/mK

Bearing Lining Thickness

0.01 x Joumal Diameter

I Bearing Shell thickness

I 0.05

x Journal Diameter

Flywheel Aspect Ratio (Disc) Flywheel Density

7854 kg/m3

Table 1 Defaults Assumed For Analysis

ACKNOWLEDGEMENTS The helpful advice and suggestions from Dr J M Conway-Jones (The Glacier Metal Company Ltd) and Mr F A Martin (consultant to T&N Technology Ltd) are gratefully acknowledged.

I

I

SESSION Vlll INVITED LECTURES Chairman :

Dr Jim Greenwood

Paper Vlll (i)

Friction Modelling for Internal Combustion Engines

Paper Vlll (ii)

Non-Laminar Flow in Hydrodynamic Lubrication

Paper VIII (iii)

Third Body Formation in Soft Solid Processing

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

30 1

Friction Modelling for Internal Combustion Engines D. Dowson, C.M. Taylor and Lisheng Yang Institute of Tribology, Department of Mechanical Engineering, The University of Leeds, Leeds, LS2 9JT, United Kingdom. A friction model of the internal combustion engine has been developed which takes account of the three major tribological components contributing to power loss; the engine bearings, the valve train and the piston assembly. All these components have been analysed in detail in earlier and separate studies, but this initial approach to the synthesis of procedures for friction and power loss prediction in complete engines enables the influence of engine design changes and the selection of alternative lubricants or lubricant modifiers to be assessed. The authors believe that the lubricant should be considered as an engineering material in the engine and component design process.

1. INTRODUCTION For some twenty years engine and component manufacturers have been placed under increasing pressure from governments and consumers to design vehicles that not only exhibit good reliability and durability, but also improved fuel consumption. Environmental considerations have also forced many countries to introduce tight regulations to limit the pollution attributable to motor vehicles. World political, economic and environmental pressures continue to influence the design of new generations of engines and the formulation of new lubricants, with the intention of improving even further the efficiency of automobile engines. The most effective design approach to the reduction of undesirable emissions is to reduce the level of he1 consumption. It is well known that only about 12% of the energy input to an automobile engine is made available as propulsive energy to overcome tyre friction and aerodynamic drag [ 1,2]. The indicated power of about 40%, obtained after deducting the losses associated with cylinder cooling (:. 30%) and the exhaust gases (= 30%), is further reduced to an engine brake power of about 25% due to air pumping in the engine (=3-6'%0) and friction losses in the tribological components such as the bearings, valve train and piston assemblies (~12-9%).It is the latter quantities that are the subject of this paper and although they typically represents only about 9% of the initial energy release, they do account for

some 30%-40% of the all important engine brake power. In this paper the development of a procedure for the prediction of friction and power loss in an automobile engine is outlined. The major frictional components of the engine bearings, the valve train and the piston assemblies have been analysed separately and then combined to provide estimates of the total engine power loss. The analysis of these tribological components can be a complex analytical task, but suitable simplifications have been made to facilitate the development of a robust and reliable model. The simplifications introduced are explained and justified and an estimate is made of the power loss attributable to accessories such as the alternator, water and air pumps, cooling fan and power steering. The engine data considered are representative of a modem 1.8 litre, four cylinder engine with four valves per cylinder and double overhead camshafts. The predictions of the model have been compared with experimental findings obtained by an engine manufacturer. The measure of agreement between the predictions from the model and the test results and issues requiring further refinement in the model are discussed. The development of a satisfactory engine friction model, based upon sound analysis of the major tribological components, offers a major attraction in terms of the initial screening of new engine designs and new lubricant formulations. Engine testing is very expensive and it is expected that if some of the

302 initial screening can be undertaken through the computer modelling route, substantial savings in total engine development and lubricant formulation costs will be possible. 2. POWER LOSSES IN ENGINE BEARINGS

The major bearing power losses in reciprocating engines are associated with the bigend and main bearings. Both are dynamically loaded bearings in which the applied load varies cyclically in both magnitude and direction. The determination of power loss in these bearings requires the solution of the Reynolds equation for dynamic conditions. This, in turn, requires a knowledge of the connecting rod and bearing geometry, the speed of rotation, the lubricant properties and the loading cycles. The problem has been analysed extensively over the years, but with the major emphasis being on minimum film thickness, rather than friction and power loss. 2.1. Big-end Bearing Loadings

The major sources of loading on the big-end bearings arise from the gas forces on the piston and inertia forces associated with the reciprocating and rotating masses, with the inertia forces often being dominant. The gas force, which acts along the cylinder axis, is calculated simply from the known cyclic variation of the cylinder pressure and the crosssectional area of the piston. The inertia of the piston assembly is readily determined from a knowledge of the kinematics of the crank and the engine speed. The usual method of dealing with the contribution of the connecting rod to the inertia forces is to share the connecting rod mass between the piston assembly and the rotating crank. For the reciprocating inertia force, a fraction of the connecting rod mass, typically about one third, is associated with the piston assembly mass. The remaining two thirds mass of the connecting rod is assumed to be on the crank and located at the bigend bearing. This mass contributes to the rotating inertia force on the bearing. The vector sums of the gas forces and the inertia forces are then displayed as a function of crank angle, usually as polar diagrams, to provide input

data to the equations for force balance with the hydrodynamic reactions. 2.2. Main Bearing Loadings

The forces acting on the main bearings arise partly from out of balance masses rotating with the crank and partly from reactions along the crank from the big-end bearings. Since the latter are determined from the procedure outlined above, and the rotating inertia forces can be calculated for a known out of balance, the cyclic variation of main bearing loads can be calculated. The major practical difficulty is that in multicylinder engines, the interactions between forces from all the cylinders makes the main bearing loading problem indeterminate. A full treatment of the elastic structure of the engine assembly would not be justified for the present purposes. The approximation adopted in the present analysis was, therefore, to assume that the crankshafts for each cylinder were separate, simply supported, rigid beams; thus making the problem statically determinate. 2.3. The Reynolds Equation

For a dynamically loaded journal bearing, the Reynolds equation can be written in the form;

'"I

[;

q l + E M S a ) - +r'da aa

(I+ECOS

'"I

a) JY

At the edges of the bearing the pressures are ambient everywhere and hence the external boundary condition on pressure is that;

The full solution of equation (1) at successive crank angles, for an appropriate cavitation boundary condition, requires considerable and ~ ~ e ~ e computational effort. Fortunately, the delightful short bearing approximation developed by Dubois and Ocvirk [3] in 1953 provides a good approximation to the full solutions, if the ratio of the axial length of the bearing to the journal diameter (b/d) is less than about 0.7. This is the

~ ~ a

303 approach adopted in the present analysis, but it should be noted that short bearing theory is inaccurate at large eccentricity ratios, irrespective of the @Id) ratio. The short bearing approximation to the pressure distribution in a dynamically loaded journal bearing is given by;

In the 'Mobility' method of solution for the orbits of journals in dynamically loaded bearings subjected to a specified loading, introduced so effectively by Booker [4] some thirty years ago, the velocity of the journal at any instant is given by;

-

- ..........................................

dZ dt

V=-=E+&(j

i c o s a +E($-m)sin a

p=-y[$-yl]

(1 + ECOS a)' ..................................

(3 1

In a later paper, Booker et a1 [ 5 ] demonstrated that the power loss in the bearing could be written as;

where;

m=

( 0b

+

0

is the mean angular velocity of

1 )

H - qr'b

J,m(m,

- a,)'+

e . .............(7)

C

2

the journal and the bush. The half-Sommerfeld cavitation boundary condition was adopted, resulting in an effective fluid film of extent n-radians, from ( a ,) to (01 ). Integration of the pressure distribution under these conditions enables components of the force applied to the lubricating film by the journal to be ascertained along and perpendicular to the line of centres, as follows; F"=FCOS

(6)

@=jpcos a d A

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

where ( 5 ) represents a co-ordinate along the load line and ( J , " " ) is a journal bearing integral evaluated and tabulated by Booker[6]. Equation (7) is a particularly convenient relationship for the evaluation of power loss in a dynamically loaded journal bearing, since it can also be shown that;

(4)

F " = F s ~ @~ = j p s i n a d A

3. POWER LOSSES in the VALVE TRAIN

The resulting expressions can be combined to give the total load, which is known at any crank angle as explained earlier, as a function of the journal centre velocities along and normal to the line of centres. Inversion of these expressions allows the journal velocity components at any crank angle to be written as;

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

(5)

where, ( M ' ) and ( M * ) are 'Mobilities', representing dimensionless ratios of velocity to force.

A model has been developed which enables the complete valve train friction to be estimated. This model includes the cam and follower interface; the camshaft bearings; the follower-guide and the valve-guide, although the former dominates the total valve train power loss in most circumstances. 3.1. Cam and Follower Power Loss In the present case, a tapered cam and nonrotating domed follower was considered, although the analytical procedure adopted is applicable to any other configuration. This geometry is somewhat more complex than that presented by a flat faced follower, but it is representative of modem automotive valve trains. For a cam and follower of given geometry, the evaluation of power loss in the lubricated conjunction requires careful analyses of the

304

kinematics and dynamic loading between the cam and follower.

(Fd) and the taper of the cam (F,) act in mutually perpendicular directions. The total, instantaneous, contact force (W) is given by;

3.1.1. Kinematics Dyson and Naylor [7] presented

a full analysis of the kinematics of the problem in 1960. They found that the velocity of the point of contact relative to the cam (V,) and follower (Vf) respectively could be written as;

w =[( F")Z + ( F J + (Fy]......................(14) The force component (Fv) represents the sum of the spring (S) and inertia forces (Ic). The former is simply given by; S = K, (Lc + S).................................................. (15)

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

.(9)

where (K,) is the spring stiffness, (L,) is the cam lift and (6) is the initial compression of the spring. The inertia force is determined by the mass of the follower (M) and a proportion of the spring mass (m). Dowson et a1 [8] proposed that one third of the spring mass should be used in this calculation to yield; Lc = (M + d 3 ) a, ............................................ (16).

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

(10)

where the distance (Z) represents the sum of the radii of the domed follower (Rf) and cam base circle (R,),together with the cam lift (Lc). Thus; Z = Rf + R, +Lc ....................

the force components (Ft) and (Fv) can be related to the geometry and written as;

F, = F, tan (y,- 0 , ) ................................. ................................. F, = F, tan y

(17)

(18)

(1 1) Hence,

The mean entraining velocity (Ve), required for the calculation of film thickness, and the sliding velocity (V,). used in the calculation of viscous friction, are given by; Ve = % ( Vc + Vf ) ........................................... (12) v, = vc -v, ................................................ (13) 3.1.2. Loading. The principal forces associated with

the operation of the cam and follower are the spring force; the inertia force, the friction force in the region of load transmission and the forces resulting from the stiffness and damping characteristics of the overall structure. The resulting load can readily be estimated with fair accuracy by neglecting the latter two forces. The inertia (I,) and spring (S) forces act along the axis of the follower, while the contact forces associated with the domed shape of the follower

In the application of this analysis, it was assumed that the cam and follower remained in contact throughout the operating cycle, as would be the case for a valve train fitted with a hydraulic lash adjuster. Lubrication. It can readily be seen by reference to the lubrication regime chart presented by Chittenden et al. [9], that the cam and follower operate in the piezo-viscous-elastic regime of elastohydrodynamic lubrication over the base circle. The central film thickness (hce,,) in this region was calculated from the formula by Hamrock and Dowson [lo]. 3.1.3.

305

hc,,=4.31ReUeo"GO4'y-007'

Around the nose of the cam, where the geometry, kinematics and loading mitigate against effective fluid film lubrication, boundary lubrication can almost always be expected. 3.1.4. Friction and Power Loss. Once the central film thickness has been calculated from equation [20]and the sliding velocity from equation [ 131, the force of friction can readily be estimated in the vicinity of the Hertzian contact zone from the expression; =

JJ

rl V h mn

..................................... (21)

The simple Barus relationship ( q= q,ee) was used for the viscosity-pressure relationship and a Hertzian pressure distribution was assumed to apply over the elliptical contact region. This relationship greatly overestimates the viscosity at high pressures, but this is of limited significance in the present approach, since a limiting shear stress, or coefficient of friction, was adopted. The value of the limiting coefficient of friction was assumed to be 0.08 and whenever the elasto-hydrodynamic coefficient of friction exceeded this value, it was assumed that a limiting shear stress prevailed, such t h a t ( F = 0.OSW). The average frictional power loss over the cam operating cycle was thus given by;

where, ( r f ) is the distance from the cam centre of rotation to the friction force vector. 3.2. Camshaft Bearing Power Loss

The l.SL, four cylinder engine considered in this study had two camshafts, one for the inlet and the other for the exhaust, each presenting eight cams. The camshafts were driven by a toothed belt from

the crankshaft and each was supported by five plain bearings. 3.2.1. Camshaft Bearing Loadings. Each camshaft is subjected to reaction forces from the followers, friction forces from the cardfollower interfaces and pulley forces from the driving belt. The cadfollower forces can be calculated according to the procedures outlined above, while the belt forces can be estimated from a force and moment analysis and knowledge of the belt configuration and the tension in the belt. The full problem is indeterminate, hence a procedure similar to that employed for the crankshaft bearings, in which successive portions of the shaft were assumed to be rigid, was adopted. The resulting forces on the camshaft were resolved into components acting along and perpendicular to the cylinder bore axes. Knowledge of the angular relations of all the cams and the &stances between the cam lobes and bearings enabled cam bearing loadings to be estimated throughout the cam operating cycle. The length-todiameter ratios of the camshaft bearings were well within the normally accepted limit of 0.7 and hence the 'Short Bearing Mobility' method outlined in Section 2 was used to evaluate the camshaft bearing power loss. The bearings were pressure fed and the power loss equations for a complete 2n film were adopted. Isothermal conditions were assumed, with the lubricant viscosity being determined for some specified average temperature. 3.3. Follower/Guide and Valve/Guide Friction

Neither the follower nor the valve guides contribute significantly to the overall camshaft power loss, but they were analysed as follows for completeness. The forces exerted upon the followers by the cams can lead to tilting moments as well as axial loads. The simplest approach to the calculation of friction force and power loss is to assume that the tilted follower experiences boundary lubrication, with a constant coefficient of friction (p) of, say, 0.08. A force balance for the situation reveals that; -

F, f p F , ] ....................... ...(22)

306

An alternative approach, which can bz used to

estimate the friction in hydrodynamically lubricated guides for both the follower and valve stem, is to assume concentric movement within the guides, with radial clearance (c) such that;

( n & ) ..................................... (23) 4. POWER LOSS in an ENGINE PISTON

ASSEMBLY The piston assembly is the largest contributor to mechanical power loss in a reciprocating engine. Losses arise from the piston ring pack; typically consisting of a top compression ring, a second compression or scraper ring and an oil control ring and the piston skirt. The analysis of compression ring lubrication and friction became established in the 1970's, but the essential features will be recalled in the following section. The procedure adopted to account for multiple compression rings will also be recalled. The oil control rings present a greater analytical challenge owing to their more complex construction, geometry and mechanics, but a useful simple approximation to their contribution to power loss will be outlined. 4.1. The Friction and Power Loss of Compression

Rings. The compression rings act as gas seals to the combustion chamber and there is thus a substantial variation of pressure throughout the ring pack at certain times in the engine operating cycle. The principle of operation of the compression rings in modem reciprocating internal combustion engines, still follows that of the original Ramsbottom [ 111 ring developed for steam engines in the 19th. century. Each ring has a modest spring force pushing it against the cylinder liner, but this sealing force is supplemented by the gas pressures acting on the inner face of the ring, whenever high cylinder pressures are encountered. The simplicity of this arrangement has stood the test of time and since rings very rarely break in operation, emphasis has been placed upon their tribological and sealing characteristics in recent times.

If the surfaces of the cylinder liner and rings are assumed to be perfectly smooth, the tiuckness of the lubricating films between them can now be calculated throughout the operating cycle. If the films are thick compared to the composite surface roughness, the friction and power loss can be calculated from the shearing of the viscous films, but if the theoretical film thicknesses fall to, or below, the composite roughnesses, mixed or boundary lubrication will prevail. In the present analysis, the latter condition was represented by a constant coefficient of friction of 0.08, 4.1.1. Inter-Ring Pressures. Since the loading on

the compression rings is intimately linked to the gas pressures acting on the inner faces of the rings at the back of the grooves, it is essential that the interring pressures are ascertained in order to determine the loading on the rings. Few measurements exist of the inter-ring pressures, but reasonable agreement has been noted between experimental measurements and theoretical predictions based upon the orifice and volume model first introduced by Eweis [12], developed by Ting and Meyer [13] and applied extensively by Ruddy et a1 [ 141 and Kuo et a1 [ 151. In this model, the volumes occupied by gases between adjacent rings, including the clearance between piston lands and the cylinder liner and the free volumes in the ring grooves, are assumed to communicate with each other via orifices represented by the ring gaps. The fluctuating flow of gases through the set of inter-connecting chambers thus formed is assumed to be isentropic, with the gas obeying the ideal gas law. The temperature in any given volume is equated to the wall temperature on the cylinder liner and the piston and cylinder liner are assumed to be of circular cross-section and concentric. The pressure above the top compression ring is taken to be the cylinder pressure, while the pressures on either side of the oil control ring are deemed to be equal to that of the crankcase, say atmospheric. If the mass rates of flow through successive orifices of areas (A,) and (An+1) are (mn-l) and (m,) respectively in the labyrinth model, the rate of change of pressure (pn) in the volume between the rings is given by;

307

where the mass flow rates for either orifice are givcn by;

If the calculated film thickness failed to exceed the composite surface roughness, it was simply assumed that boundary lubrication prevailed and that the coefficient of friction was 0.08. The frictional power loss developed by each compression ring over the complete cycle was; H =--!---IF n D U , d f j ............................

2a

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

(25)

where, (ps) represents the pressure at a stagnation point. The pressure change in each volume can be calculated as a function of crank angle throughout the operating cycle from equations (24) and (25). 4.1.2.

Compression Ring Friction and Power

Loss. Full details of the calculation of the cyclic variation of film thickness in the compression rings have been given elsewhere [ 161. The procedure calls for the representation of each ring face profile by a parabola. However, if a scraper ring is fitted, it can be assumed that boundary lubrication applies on the downstroke, while hydrodynamic action often dominates the upstroke. If a film thickness in excess of the composite roughness of the ring and liner was developed at any crank angle, it was assumed that the ring was lubricated hydrodynamically and that the friction was associated with the shearing of the lubricating film. The frictional force per unit circumferential length was then given by; I,

F =

dx .....................................................

(26)

5,

where the limits (XI) and (x4) represent the limits of the wetted length of the ring with a cavitated film extending from (x2) to (x3) such that;

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

(27)

The factor (p) represents the width of the film occupied by lubricant, as opposed to air or gas in the cavitated region.

0

where (D) is the cylinder bore.

The Complete Pack of Compression Rings. There are one or two important points to consider when the above general analysis for the power loss of a single ring is integrated into a procedure for the determination of the power loss of the complete pack of sealing rings. The main problem is to take account of the distribution of lubricant within the pack, while satisfying the requirements of flow continuity. It is clearly quite unrealistic to assume that all the rings in a pack are fully flooded with lubricant, although the analysis offers this as an option. It is, therefore, essential to consider lubricant starvation, or the limited supply of lubricant, to some rings. In the past and in the absence of any specific information, it was often assumed that the top ring was fully flooded on the upstroke, but this is by no means certain, even in diesel engines with direct supply of lubricant to the ring pack through a quill. In the present analysis, it was assumed that the top compression ring encountered a layer of lubricant equal in thickness to the lubricant which it left behind on the cylinder wall on the downstroke. It was further assumed that on the upstroke, the second and subsequent rings encountered a thin layer of lubricant consistent with the quantity of lubricant passing beneath the previous ring. T h s often leads to severe starvation, which means that, although the second and subsequent rings are generally less highly loaded than the top compression ring, the film thicknesses in each ring are remarkably similar. In modern engines, the bottom of the piston is generally liberally bathed in lubricant supplied by a splash system from the sump. It has therefore been assumed that the bottom ring in a pack is fully flooded on the downstroke. Subsequent rings 4.1.3.

308 were again assumed to be starved on the downstroke, as determined by the continuity requirement outlined above. An interesting problem arose near to the dead centre positions, since the top and bottom rings traverse short lengths of the cylinder liner before meeting the layer of lubricant left behind by the adjacent rings. This can give rise to instabilities in the calculation if the physics of the problem is not adequately recognised. The boundary conditions on pressure for the complete pack of compression rings are that the top of the upper ring is subjected to the combustion chamber pressure, while the bottom of the lower ring is exposed to the constant crankcase pressure. The pressures on each side of the intermediate rings, whether they be starved or not, are determined from the gas flow analysis outlined in Section 4.1.1. 4.2. The Oil Control Ring. The compression rings provide the sealing action, while the oil control ring fitted nearest to the sump, restricts the amount of lubricant made available to the compression rings and distributes it circumferentially to lubricate the ring pack and the piston skirt. The oil control ring is spring loaded against the cylinder wall, usually with greater pressure than that inherent in the compression rings, since it does not enjoy the additional loading associated with the gas pressures. Many oil control rings have two narrow lands, each being typically only 0.5mm to 1 mm high, and hydrodynamic analysis invariably predicts theoretical film thicknesses less than the composite surface roughness 117,181. The full hydrodynamic analysis of the oil control ring is complex and time consuming and for the present purpose it was deemed to be adequate to assume that boundary lubrication prevailed. This restriction could, however, be relaxed and hydrodynamic analysis incorporated into the procedure if desired. The coefficient of boundary lubrication was assumed to be 0.08, as for the cam and follower calculation., and the radial loading on the ring was assumed to be entirely due to the inherent elastic compression of the ring. The cyclic power loss was thus readily computed for this component.

4.3. Piston Skirt Power Loss. The piston is not only subjected to high axial loadings, but also to significant side-thrusts resulting from the obliquity of the connecting rod to the axis of the cylinder. The piston skirt, which is that portion of the piston beneath the ring zone, helps to take the side loads and to ensure that the piston glides smoothly up and down the cylinder. The piston is of complex shape, being generally of oval cross-section, with the smallest diameter across the gudgeon-pin boss in the cold state, to permit thermal expansion to yield a near circular section at the engine operating temperature. The diameter of the piston also varies along its length, to accommodate the severe temperature gradient from the combustion chamber to the crankcase and to prevent edge loading on tilted pistons. This usually leads to a barrelled shape, or a simple tapered form, with the minimum diameter at the top of the piston. The large bearing area offered to the cylinder wall by the piston skirt leads to modest mean pressures and it is generally agreed that if edge contact can be avoided, the skirt is effectively lubricated by fluid film action. The full solution of this hydrodynamic[ 191, or even the elastohydrodynamic problem[20], considering the detailed geometry of the piston mentioned above and taking account of the varying angle of piston tilt throughout the cycle and cavitation in the divergent space, is a complex problem. A much simplified approach, which nevertheless represents a reasonable model for the prediction of piston skirt friction and power loss under hydrodynamic conditions, was therefore adopted in this initial analysis. It was assumed that the piston and cylinder were concentric throughout the cycle and that the resistance to motion arose from the shearing of the lubricant filling the clearance space. Account was taken of the barrelled shape of the piston, but it was assumed that the viscous friotion was attributable to Couette action alone, such that the total piston skirt friction at any instant was given by;................................................ F = =& o

c

where (c) is the radial clearance at any axial location (x). The viscosity at each axial location was

also assumed to be determined by the local cylinder liner temperature, since this also varied substantially along the liner. 4.4. Piston Assembly Friction and Power Loss The calculation of complete piston assembly friction and power loss in the present model calls for the integration throughout the cycle of the contributions from the compression rings, the oil control ring and the piston skirt according to the simplified procedures outlined above.

5. ENGINE DETAILS The power loss model for reciprocating engines outlined above has been applied to a 1.8 L (Litre) engine. Details of the engine required as input to the model were kindly supplied by the manufacturer, and these are summarised below. 5.1. Details of 1.8 L (Litre) Engine The four cylinder, four stroke petrol engine had a cylinder bore of 80.62 mm, a crank radius of 38.35 mm and a connecting rod length of 136.19mm. The masses of the piston, connecting rod and flywheel were 0.48kg, 0.60kg and 8.26 kg. respectively. 5.1.1. Bearing Dimensions. The main bearings were of diameter 58mm and length 18.30mm, with twin lands (7.175mm) and partial arc circumferential grooving. The radial clearance was 0.0175 mm. The big-end bearing was 19.lOmm long, with a diameter of 46.9mm and a radial clearance of 0.0210mm. 5.1.2. Valve Train Data. Cam- The camshaft speeds ranged from 500 to 3,500 rpm and the valves were inclined at 20" to the cylinder axes. The valve timing was 246" and the operating temperature was about 95°C. The cam width was 1lmm, the base circle radius 18mm and the cam taper 0.01667O. The elastic modulus and Poisson's ratio of the cam were 170GPa and 0.28 respectively, while the load over the base circle was 64.251N. Cam lift data for both the intake and exhaust valves were available at 1" intervals.

The camshaft bearings were all of diameter 25.97 mm and radial clearance 0.0225mm. Their lengths were 17mm, except for bearing number 1, which was slightly longer at 20.0mm. All were circumferentially grooved, with twin lands of width 7.5mm (bearing no.l-9.0mm). Follower and Follower Guide- The diameter of the follower was 28.4mm and the radius of the domed face 8.0m. Its height and mass were 26.5mm and 0.054 kg respective1y.The elastic modulus and Poisson's ratio were slightly higher than those for the cams, at 204.0 GPa and 0.29 respectively.The follower guide had a length of 22.0mm and a radial clearance of 0.024mm. Valve and Valve Guide- The valve guides were 36mm long with a radial clearance of 0.02mm on the intake and exhaust stems of diameters 6.043mm and 6.025mm respectively. The valve spring had a stiffness of 37.634kN/m, a mass of 0.035 kg and an initial compression of 5.580 lmm. Piston Assembly. The piston in this four stroke engine was fitted with two compression rings and one oil control ring. The mean radial clearance between the piston and cylinder wall was 0.22785mm and the axial separation of the compression rings was 4.046mm. Rings. Both compression ring gaps were 0.4628mm, but the radii of curvature of the top and second rings were quite different at 0.063m and 0.50m respectively. An orifice discharge coefficient of 0.65 was assumed for the ring gaps in the calculation of inter-ring pressures. The heights of the top and second compression rings were 1.484mm and 1.184mm respectively, while that of the oil control ring was 0.50mm. The elastic tensions for the same three rings were 0.200MPa, 0.134MPa and 1.890MPa respectively. The dimensionless offsets, defining the lines of closest approach to the cylinder wall in the unloaded condition, of the top and second rings were 0.00 and 5.1.3.

-0.85.

The initial surface roughness of the cylinder liner was 0.70pm, while those of the top and second compression rings were 0.72pm and 2.56pm.

310 Cylinder Pressures. The measured combustion chamber pressures and temperatures were available for every 10" of crank anglc and these were interpolated to provide input data at 1" intervals. 5.1.4. Engine Temperature and Lubricant Data-

Engine Temperatures.The estimated tempcratures over the speed range 2,000 rpm to 7,000 rpm are shown in Table 1.

I

Combustion Chamber TopRmg Groove SecondRing Groove Liner-Maxm. -Medm. I 'I -Minm.

I

'I

Table 1.

I

Engine Speed - rpm 2,000 I 3,000 I 5,000 I 7,000 700 750 850 950

I

I

I

170

195

220

240

160

180

210

230

165

185

200

220

150 140

I

170 160

185

I

175

I

and their effectively separate fluid film bearings of restricted length collectively offering the greater power loss. The cumulative power losses in the engine bearings have been calculated by three methods for seven speeds in the range 2,000 rpm to 7,000 rpm. and the results are shown in Figurel. The full dynamic load equations outlined in Section 2.3 yield the greatest power losses, but the simplified approach based upon equivalent steady loading conditions at any instant give remarkably similar predictions. The simple Petroff solution, in which the journal is assumed to be concentric with the bearing at all times underestimates the friction at all speeds. '

I

251

205

I

195

I

Estimated Engine Tempcratures ("C)

Engine Lubricant. The 5W/30 Lubricant had dynamic viscosities of 0.009865 Pa.s and 0.005123 P a s at 95°C and 135°C respectively. The viscositypressure coefficient was taken as 2 . 2 ~lo-* m2/N. 6. ANALYSIS O F POWER LOSSES IN A 1.8 LITRE, FOUR CYLINDER, FOUR STROKE PETROL ENGINE.

The input data listed in Section 5 has been used to compute the power losses in thc three main dissipative systems in the four cylindcr, four stroke, petrol engine, namely, the cngine bearings, the valve trains and the piston assembly. An allowance for the power losses in the engine accessories will also be included. Engine Bearings. The cngine had four ungroovcd big-end bearings and five partially grooved main bearings. The partially grooved bearings were not analysed in detail, but limiting situations for ungrooved and fully circumferentially grooved bearings were considered. The grooving arrangement certainly makes a difference to the predicted power loss, with the twin bearing lands 6.1

Figure 1.

Predicted Power Losses in Engine Bearings

The results displayed in Figurel indicate that the relatively simple quasi-static load approach provides a good estimate of bearing power loss over the range of conditions considered. Even the very simple Petroff concept can be adapted to give a reasonable estimate of the bearing power losses, since the ratios of the full computed results from the dynamic loading analysis to the concentric journal predictions, varied over only the relatively narrow ranged of 1.74 to 2.0 for ungrooved bearings over the full speed range considered. For the grooved bearings the ratios were 2.3 to 2.8 respectively. The computed power losses in the grooved bearing were

31 1 27% and 34% greater than those in the ungrooved bearing at 3,000 rpm and 6,000rpm respectively. 6.2. Valve Train. The initial analysis of cam operating conditions, including the calculation of Hertzian contact stresses and elasto-hydrodynamic film thicknesses, followed the procedures developed by Dowson et a1 [S] and Ball et a1 [2 I ] in the 1980's. Camshaft bearing loads were calculated at one degree intervals of camshaft rotation and the software used for the engine bearings was modified to suit the camshaft bearing problem. In the analysis of cadfollower interface power loss, allowance was made for the full kinematics of the situation, including rotation of the follower. However, it was found that little error was introduced if follower rotation was neglected and this represented a useful simplification. 0.1

p 0

I

0.e

. A

/-

;

0.5

R 0.4

L 0

0.3

S

6.3. Piston Assembly. The initial calculation of inter-ring pressures is important, not only because it determines the loading on the compression rings throughout the four-stroke cycle, but because the pressure differences between the crankcase, the ring zone and the combustion chamber determine the direction of gas flow. The pressure differences also contribute to the axial force balance which influences ring lift. The peak cylinder pressure of almost 7MPa at full load and 3,000 rprn occurred some 10" after top-dead-centre (tdc), while the maximum interring pressure of 0.8MPa was encountered about 70" after tdc. The difference between the combustion chamber and inter-ring pressures testifies to the efficacy of the top ring sealing process. The surface roughness of the rings and cylinder will vary throughout the lifetime of the engine, with major changes taking place in the first few hours of operation. On the basis of the surface roughnesses mentioned in section 5.1.3, it was concluded that the ring pack experienced primarily mixed or boundary lubrication under the starved lubrication conditions encountered in the complete piston assembly. Traces of the cyclic variation of power loss for the compression rings at 3,000rpm are shown in Figure 3

0.2

two

45m

2ow

2500

3 m

3500

Camshaft Speed ( rpm )

Figure 2.

Predicted Power Losses in the Intake Valve Train.

I *.I

nM 0.1

The total predicted intake valve train power loss at various camshaft speeds is shown in Figure 2. The cadfollower interface provides the main source of power loss in the valve train, while the valve and follower guides make relatively minor contributions. At a speed of 1500 rpm the combined power loss of the five camshaft bearings represents only 7% of the cdfollower loss. It should be remembered, however, that shaft deflection and bearing distortion were neglected in the present analysis.

0

Figure 3. Predicted Cyclic Variation of Power Loss for the Compression Rings at 3,000 rprn Under Starved Lubrication Conditions. The predicted power losses in a complete , single piston assembly are shown in Figure 4. Attention is drawn to the major contribution to power loss by the oil control ring. The similarity

312 between the power losses from the piston skirt and the individual compression rings is also evident.

L 0 S

s

a4

about 40%, with the experimental values increasing more rapidly with speed than indicated by the analysis. For a concentric journal and bearing operating under isothermal conditions, the power loss should increase in proportion to the square of the speed and this relationship is followed reasonably well by the experimental results shown in Figure 5. In this Figure the 'square' law traces have been superimposed on both the experimental results and the model predictions such that the values coincide at 3000 rpm.

a1

a

Figure 4. Predicted Power Losses in the Piston Assembly at Various Engine Speeds. 6.4. ACCESSORIES. The present engine friction model does not include analyses of the power losses in particular forms of accessories such as the oil and water pumps. The published literature suggests that the accessories account for about 20% of total engine friction over the operating speed range and experimental studies on the engine indicated that a figure of 25% should be adopted. 7. COMPARISON BETWEEN PREDICTED POWER LOSSES AND MEASUREMENTS ON A MOTORED FOUR CYLINDER, FOURSTROKE 1.8L ENGINE

The simple friction model outlined above has been evaluated against motored test results for a four cylinder, four-stroke engine. The tests enabled main bearing, valve train, piston assembly and accessories power losses to be estimated over a range of engine speeds. The total motored power losses were also recorded and these have been compared to the predictions of the model. 7.1. Engine Main Bearings. The measured power losses are compared with the predictions of the model outlined in section 2 in Figure 5. The agreement at the lower speeds is reasonable, but the model underestimates the measured power loss at the higher speeds. At 6,000 rpm the model underestimates the engine bearing power loss by

Figure 5 .

Friction Model and Motored Test Results for Engine Main Bearings.

7.2. Valve Train. The valve train made the smallest contribution to the total engine power loss, but the model and test data were in close accord as shown in Figure 6. Neither the engine bearings nor the valve train developed losses in excess of twenty 1.4

E R

i 0.8

1

Figure 6.

1

Motored Test and Friction Model Results for the Valve Train.

313 percent of the total engine friction over the speed range considered. 7.3. Piston Assembly. The individual contributions to the total piston assembly power losses from the compression rings, oil control ring and piston skirt, as predicted by the friction model, have been illustrated in Section 6.3. The comparison between the total predicted losses for all four cylinders at the temperatures recorded in Table 1 and the measured losses deduced from the motoring tests are shown for a range of speeds in Figure 7. The measured and predicted losses are of similar magnitudes, but the power loss-speed characteristics display rather different forms. The motoring test results showed that the total piston assembly power loss increased quite rapidly as the engine speed increased, whereas the predicted losses were almost linearly related to speed. The latter result is expected since the oil control ring, which makes a major contribution to the total power loss, has been found to experience boundary lubrication. Furthermore, it has been predicted that the compression rings were operating within the mixed or boundary lubrication regimes for much of the time, if the surface roughnesses reported in Section 5.1.3 were maintained throughout the test. If boundary lubrication dominates the operation of the components making major contributions to the piston assembly power loss, the relationship with speed will be almost linear. 8

P 0

7.4. Accessories. In the present model the accessories were assumed to contribute 25% of the total power loss at any speed. Analysis of individual components will be necessary if the contributions of the accessories are to be included in an enhanced engine friction model. The present global representation of losses associated with the accessories appears to provide good first estimates of their contribution to engine performance. 7.5. Total Engine Power Losses. The calculated power losses for the individual components, including the allowance of 25% for the accessories, can now be summed and the predictions of the Friction Model compared with the results from the the Motored Test. This comparison is shown in Figure 8. It can be seen that encouraging agreement is found, although the experimentally measured losses increase more quickly with speed than the model predicts, particularly at the higher speeds.

-+Motorad Test +Frlctbn

lwc

mw

Model

YIW

4aw

YIW

rn

ma0

ENGINE SPEED ( rpm )

'

w e

Figure 8. Motored Test and Friction Model Results for the Complete Engine.

E R

3 4

L 0

It is also instructive to review the proportions of the predicted losses attributable to the four major classifications at two different engine speeds and this is illustrated in Figure 9.

3

S s

2

(W 1 1wo

moo

swo

4000

5000

m a

ENQINE SPEED ( rpm j

Figure 7. Motored Test and Friction Model Results for the Piston Assembly.

?ma

I

8. DISCUSSION

A model of engine friction and power loss has been developed which is based upon analyses of the three major tribological components in modern

3 14

(b)

Figure 9.

Power Losses in the Engine Under Full Load at (a) 3000 rpm (50Hz) and (b) 6000 rpm (100Hz).

engines; the bearings, the valve train and the piston assembly. The objective was not to produce more sophisticated analyses of these components, but rather to integrate existing knowledge into a robust model of engine power loss. Indeed, in this process a number of simplifications have been advanced where these were thought to be justified. It is most important to represent the operating conditions in engines as accurately as possible if realistic predictions of power loss are to be achieved. A major part of the effort reported in this paper was devoted to the analysis of the kinematics and the cyclic loading patterns on the bearings, valve train and piston assembly. This is an essential preliminary step in engine power loss analysis. Thermal effects strongly influence the outcome of the predictive models, particularly through the

their effects upon lubricant viscosity. In this initial model, isothermal conditions have been assumed in the analysis of the engine bearings and the valve train, while the variation of temperature along the cylinder wall has been introduced into the piston assembly analysis. In the latter case, however, the temperature at a given crank angle was assumed to be constant when the compression rings, oil control ring and piston skirt were analysed. It was assumed that the lubricant was a Newtonian fluid, with the viscosity being determined by the pressure and temperature. It is now recognised that the shear rates in all three components are so high that some shear thinning of the lubricant will result. We would therefore propose to introduce non-Newtonian lubricant characteristics into future developments of the model. This has already been achieved in a limited way in the analysis of the cam-follower conjunction, where a limiting shear stress was introduced into the estimation of friction in the present analysis. The components were represented by simple, perfect geometries. For example, both the cylinder liner and the pistons were assumed to be circular in section, even though the variation in diameter of the piston along its length was considered in the analysis. Furthermore, no attempt has been made to consider the effects of engine elastic or thermal distortion upon power loss in the tribological components. This is a complex problem and although it was not felt that an extension of the analysis in this direction was justified at the present stage of development, it was recognised that the effects could be significant. It was particularly useful to be able to compare the predictions of the friction model with motored test results made available by the engine manufacturer. The analysis of engine bearings depicted in Figure 5 shows that the theoretical and experimental results have similar forms, although the model results underestimate the experimentally determined power loss. This is particularly evident at the higher speeds. The valve train is a complex tribological structure, but the friction model provides quite good predictions of its power loss over a wide range of speeds, as shown in Figure 6. In this case the agreement between theory and experiment improves as the speed increases.

3 15

The dominant role of the piston assembly in determining total engine power loss has been noted. The quantitative agreement between the piston assembly model predictions and the experimental results shown in Figure 7 appear to be quite good over the full speed range. However, the model overestimates the piston assembly friction at the lower speeds and underestimates it at the higher speeds, due to the different forms of the two characteristics. The most striking feature of the predictions is the near linearity of the power loss with speed. This results from the dominance of boundary lubrication. It was assumed that the oil control ring, which makes a significant contribution to the total piston assembly power loss, operated in the boundary lubrication regime, while the compression rings found relief through fluid film lubrication for only a small part of the operating cycle. It was further assumed that the roughness of the rings remained constant over the full speed range, but it is known that polishing usually takes place during running of the engine. It will clearly be important to take account of progressive changes in surface roughness with engine running time in further developments of the friction model. The final agreement between the predictions of this initial engine friction model and the motored engine results is encouraging. Good agreement is evident in Figure 8 over most of the speed range, which embrace the normal engine operating conditions. The results presented in this paper show that it is possible to develop a reasonable, relatively simple friction model for engines, by considering the three main tribological components of the engine bearings, the valve train and the piston assembly. The simple allocation of a fixed percentage of the total friction to the accessories represents no more than a first step towards the generation of a more complete model, but the procedure does not appear to lead to gross errors. The comparison between predictions from the model and motored engine tests focuses attention on areas requiring further attention as the model is refined. These include more complete representation of the thermal situation in running engines, an allowance for the progressive changes in surface topography, the inclusion of nowNewtonian behaviour of the lubricant and an improved approach to the calculation of losses in the accessories.

9. CONCLUSIONS

An engine friction model has been developed which is based upon predictive procedures for the power losses in the engine bearings, the valve train and the piston assembly and an assumption that the accessories contribute a fixed percentage to the total engine power loss. Studies of the predicted contributions from the individual tribological components and a comparison between predictions from the model for the complete engine and the results from motored engine tests carried out by the engine manufacturer enable the following conclusions to be drawn. The piston assembly accounts for most of the power losses (:. 55%) in the engine at all the speeds considered. The piston skirt and even the compression rings make relatively modest contributions to the total piston assembly power loss if it is assumed that the oil control ring experiences boundary lubrication throughout the cycle. The power losses attributable to the engine bearings are well predicted by the 'quasistatic' approach to the analysis. The losses increase roughly in proportion to the square of the engine speed. Losses associated with the cam-follower interface greatly exceed those from the crankshaft bearings and the cam and follower guides. The percentage contributions to the total power losses from the engine bearings and the valve train are about 9 'YOand 13 'YOat the lower speeds. This is reversed to 14 'YO and 10% at the higher speeds. Further development of the model calls for closer attention to the thermal conditions in the engine, an improved understanding of the surface topography of the piston assembly components throughout the operating period of the engine, the

316 inclusion of nowNewtonian lubricant behaviour in all the tribological components and an improved representation of the losses associated with the accessories. It may also be necessary to include the effects of thermal and elastic distortions in relation to the bearings and the piston assembly.

.

APPENDIX Nomenclature

b C

d h ken m P Ps r f' t

bearing length radial clearance bearing diameter film thickness elastohydrodynamic central film thickness spring mass pressure stagnation pressure radius of journal distance from cam centre to friction force vector time

Rs S T U V

Vc Ve Vf Vs W We

z

a

P Y E

6

F Ffl,n F(d,t,v) F(c,v,z) FE F'P

D G H I,

JpO

KC KS LC M

R R, R, Rf

bearing load friction forces on follower guidc contact force components (cam) force components on follower Force component on lubricant along line of centres (bearings) Force component on lubricant perpendicular to the line of centres (bearings) cylinder bore dimensionless materials parameter power loss inertia force journal bearing integral discharge coefficient spring stiffness cam lift mobility; follower mass universal gas constant radius of cam base circle equivalent radius ( also effective radius in entraining direction) radius of dome on follower

v qo 0, z cp

P yc ob OJ

a

effective radius in side leakage direction spring force absolute temperature dimensionless speed parameter velocity of journal centre within the clearance space velocity of the contact relative to the cam entraining velocity velocity of the contact relative to the follower sliding velocity instantaneous contact force (cam) dimensionless load parameter sum of the radius of the domed follower and the cam base circle together with the cam lift angular coordinate from line of centres (journal bearings); also viscosity-pressure exponent in Barus equation fraction of compression ring circumference filled with lubricant in the cavitated region cam taper angle eccentricity angle initial compression on valve spring dynamic viscosity of lubricant (Pas) dynamic viscosity at atmospheric pressure cam rotation from top lift position shear stress attitude angle coefficient of friction angle between the common tangent at the contact and the X axis (cams) angular velocity of bush angular velocity of journal mean angular velocity of journal and bush

REFERENCES 1.

Pinkus, 0. and Wilcock, D.F., 'The Role of Tribology in Energy Conservation', Lub. Eng., (1978), Vol. 34, No. 11, 599-610.

2.

Dorgham, M.A., 'Ford Energy Report, Proc.Int. Association for Vehicle Design', Special Publication SP1, (1982).

317

3.

4.

5.

6.

7.

11.

Ramsbotton, J. ' On an Improved Piston for Steam Engines', Proc. Instn. Mech. Engrs., (1854), 70-74.

12.

Eweis, M. 'Reibungs und Undichtigkeitsverluste an Kolbenringen ', Forschungshefte des Vereins Deutscher Ingenieure, (19 3 9 , No. 37 1.

13.

Ting, L.L. and Meyer, J.E., ' Piston Ring Lubrication and Cylinder Bore Wear Analysis, Part 1-Theory', J . Lub. Tech., Trans., A.S.M.E., (1974), Vo1.96, Ser.F., N0.3, 305-314.

14.

Booker, J.F., 'A Table of the Journal Bearing Integral', (1965), J.Basic Eng., Trans. ASME, Ser. D., Vol. 187, 533-535.

Ruddy, B.L., Dowson, D. and Economu, P., ' The Prediction of Gas Pressures Within the Ring Packs of Large Bore Diesel Engines', J. Mech. Eng. Sci., (1981), Vo1.23, No.6,295-304.

15.

Dyson, A. and Naylor,H., 'Application of the Flash Temperature Concept to Cam and Tappet Wear Problems', Proc. lnstn. Mech. Engrs., (1961), A.D.,No.8, 255280.

Kuo, T., Sellnau, M., Theobald,M. and Jones,J. 'Calculation of Flow in the PistonCylinder-Ring Crevices of a Homogeneous Charge Engine and Comparison with Experiment', (1989), S A E , 890838.

16.

Dowson,D., Economou, P.N., Ruddy, B.L., Strachan, P.J. and Baker, A.J. S., ' Piston Ring Lubrication. PartII- Theoretical Analysis of a Single Ring and a Complete Ring Pack', In 'Energy Conservation Through Fluid Film Lubrication Technology: Frontiers in Research and Design', Ed. Rohde, S.M., Wilcock, D.F. and Cheng, H.S., (1973), ASME, 23-52.

17.

Pachernegg, S.J., 'The Hydraulics of Oil Scraping', (1971), SAE, 710816.

18.

Ruddy, B.L., Dowson, D. and Economou, P.N., ' A Theoretical Analysis of the TwinLand Type of Oil Control Ring', (1981), 1nst.Mech. Eng., Journal of Mechanical Engineering Science, Volume 23, Number 2, 51-62.

Dubois, G.B. and Ocvirk, F.W., Analytical Derivation and Experimental Evaluation of Short Bearing Approximation for Full Journal Bearings', NACA Techn. Note 1157, (1953). Booker, J.F., 'Dynamically Loaded Journal Bearings: Mobility Method of Solution', (1965),J.Basic Eng., Trans. ASME, Ser.D, Vol. 187, 537-546. Booker, J.F., Goenka, P.K. and van Leeuwen, H.J., 'Dynamically Loaded Journal Bearings: Numerical Application of the Mobility Method', (1982), J.Lub.Tech., Trans. ASME, Vol. 104,478490, addendum (1983), Vol. 105, p220.

8.

Dowson, D.,Harrison, P. and Taylor. C.M., ' The Lubrication ofAutomotive Cams and Followers', Proceedings of the 12th. LeedsLyon Symposium on Tribology, (1986), 'Mechanisms and Surface Distress', Butterworths, London, 305-322.

9.

Chttenden, R.J., Dowson, D. and Taylor, C.M.,' The Estimation of Minimum Film Thickness in the Design of Concentrated Contacts', Proc. Instn. Mech. Engrs. Conference on Tribology-Friction, Lubrication and Wear-Fifty Years On', (1987), V01.2., 807-818.

10

Hamrock, B.J. and Dowson, D., 'Ball Bearing Lubrication- the Elastohydrodynamics of Elliptical Contacts', (198 l), John Wiley & Sons.

318 19.

Knoll, G.D. and Peeken, H.J., 'HydrodynamicLubrication of Piston Skirts', (1982), J. Lub. Tech., Trans. ASME, Vol. 104, No.4, 504-509.

20.

Oh, K.P., Li, C.H. and Goenka, P.K., Elastohydrodynamic Lubrication of Piston Skirts', (1987), J. Trib., Trans. ASME, Vol. 109, No.2, 356-362.

21.

Ball,A.D., Dowson,D. and Taylor, C.M., ' Cam and Follower Design', Proc. 15th. Leeds-Lyon Symposium on Tribology,' Tribological Design of Machine Elements', (1989), Elsevier, 1 1 1-130.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

319

Non - Laminar Flow in Hydrodynamic Lubrication J . Frtnea and V. N. Constantinescub

"Laboratoirede Mecanique des Solides - URA CNRS, Universite de Poitiers 40, Avenue du Recteur Pineau, 86022 POITIERS Cedex b

University "Politehnica" of Bucharest, Romania

The classical theory of hydrodynamic lubrication assumes that the flow regime is laminar and the inertia forces in the fluid film are negligible. For large bearings using low viscosity lubricant or for high speed, the inertia forces could be important and non laminar flow occurs. In that presentation a general view of non laminar lubrication is presented. The different flow regimes which occur in bearings are shown. The transition criteria between laminar and Taylor vortices and turbulence are given. The theories to obtain the characteristics of bearings operating in turbulent flow regime are presented. The effects of inertia forces in laminar and in turbulent flows are shown. I . INTRODUCTION

An over century old well known viscous fluid mechanics problem (Reynolds, 1886) is that of hydrodynamic lubrication, i.e., the laminar flow in a thin film bounded by solid surfaces in relative motion. Lubrication led and still leads to applications of economic implications at least comparable to another famous problem of viscous fluid mechanics, namely the boundary layer theory. Non laminar lubrication is a comparatively more recent problem that became important in special fields of contemporary technology, particularly in high speed and/or large size bearings and seals, especially when lubricated by liquids of low kinematic viscosity. Thus, if h is the thickness of a lubricating film and I is the characteristic length in the tangential direction of the moving surfaces, then llie small parameter of the problem is

and a typical Reynolds numbcr may be defined as pVh

Re = -

P where p is the fluid density, p is the viscosity while V is a characteristic velocity, for example the relative velocity of the two surfaces.

Typical values of the Reynolds number (2) encountered in various applications are: Re 3,000 in medium size, low speed water lubricated bearings and seals (Smith and Fuller, 1956); - Re 5,000 in large size oil lubricated bearings used in large power turbo-generating units (Capitao, 1974); - Re 10,000 in liquid sodium bearings and seals (Constantinescu, 1968); - Re lo5 or more in high speed bearings and seals lubricated with liquefied gases, used for example in liquid hydrogen or liquid oxygen turbopumps for space applications (Childs, 1994). Obviously, the mentioned conditions can not be considered by using the classical assumptions of hydrodynamic lubrication theory, namely laminar and almost inertialess viscous flow. As a consequence, research efforts appeared as early as in the 50's (Wilcock, 1950; Smith and Fuller, 1956; Constantinescu, 1958, 1959) in order to pose and tackle this problem and to produce a reasonable engineering theory of turbulent lubrication under almost parallel flow conditions and later on (Constantinescu, 1962, 1968,1969, 1970; Constantinescu el. al, 1985; Constantinescu and Galetuse, 1974; Frtne, 1974; Frtne et. al., 1990) to include also the iiauence of convective and time dependent inertia forces.

- -

-

-

-

320

t’

\ \

Figure 1. Taylor vortices between rotating cylinders 2. NON LAMINAR FLOW REGIMES

In spite of the fact that one deals with motions taking place in layers of very sinall absolute thickness (h ... 10” m), any fluid, particularly a liquid still behaves as a continuum medium. Consequently, a stable laminar flow takes place as long as the Reynolds number does not exceed a certain critical value (Re < Re, ), as shown experimentally by FrCne (1974). Various kinds of laminar flow instabilities may occur at larger Reynolds numbers. Particularly, a more complex laminar flow with vortices is produced when Re > Re, if centrifugal forces are present (Taylor vortices in journal bearings and radial seals Figures 1, 2, 3, 4 - spiral vortices in thrust bearings and radial seals - Figure 5 , etc.). When the Reynolds number is further on increased more instabilities are occurring leading to fully turbulent flow (Constantinescu,

-

-

1993).

A number of studies were produced during the years in order to evaluate Re, , e.g., Taylor (1923) for co-axial cylinders, DiPrinia and Stuart (1974) for eccentric cylinders, phenomenological

lR

0 4

Figure 6. Notations interpolation procedures (Constantinescu et. al., 1971; FrCne and Constantinescu, 1975) The important result of all mentioned attempts is that turbulence is produced in thin film flow, which is basically a combined Poiseuille-Couette almost parallel flow. 3. EQUATIONS

Let consider the geometrical configuration of Figure 6 and let assume, in order to s i m p l e the presentation, that only surface 1 is moving with velocity V. Let also consider a fully turbulent flow and a standard averaging procedure. Then x, z will be the orthogonal coordinates in the tangential directions while y is the coordinate upon the

32 1

Figure 2. Visudisation of Taylor vortex flow (large h; FrCne, 1970)

Figure 3 . Unstable Taylor vortices leading to turbulence (large 11; Frtne, 1970)

322

Figure 4. Taylor vortices between co-axial cylinders (small h; Frhe, 1975)

Figure 5. Spiral vortices in a self-acting thrust bearing (Frhe, 1975)

323 normal to surface 1 ; the fluid film is comprised then in the interval y = [0, h], where h = h(x, z). Under the mentioned circumstances, admiensionless analysis of the Navier-Stokes equations leads to a system of equations identical to that used in the boundary layer theory (Schlichting, 197X), namely

for an incompressible fluid with constant properties. Variables u, v, w are average velocity components and - p stands for the average prcssure while u", t2

aii

aii

-aii

-aii)

ay

an

E*Re y + z - + V - + W (at ax

=

(34

--

-

v , v'w' are Reynolds stresses. The mentioncd system must bc integrated by using appropriate boundary and initial conditions and a proper model in order to evaluate the turbulent stresses. 4. ALMOST FLOW

(3c)

PARALLEL

(INERTIALESS)

Equations (3) simplify to

-_

where (4)

aiid I, b, po are some characteristic values for Icngth, viscosity and pressure. The same system in diiiieiisional variables reads p

(

au

au

au

-1

--ndpx + p ay y + - -puV a2u aay

(

()=--+-

p

-

aY ap aY "IP7) aw aw aw

--dP + p- a2w az ay*

a

( ")

'5- p v w

and the continuity equation is

leading to a combined Couette-Poiseuille flow problein. Historically, first the Prandtl's mixing length approach was used together with some additional approximations in order to obtain analytical solutions (Constantinescu, 1958, 1959). The errors introduced by the mentioned additional simplifying assumptions were later on corrected (Constantinescu, 1967, 1968) through comparisons with experimental data for pure Couette and pure Poiseuille flows. Typical qualitative velocity profiles are presented in Figure 7 showing the strong departure from laminar parabolic velocity profiles. The main result (that was confirmed in all later on published turbulcnt lubrication thcories) is that in tcrins of some global paranietcrs

u=u

V 2

--

m . h

324

-r

' 0.a

0.6 OA

0.2

0

-2

-a

- 1 6-15

-u

.I

- O B .oh -a- 0 2

o 02

0.4 0.6

oa + I

(a)

R.160

Y

- 0 6 - 0 . 4 -0.2 0 0 2 0 . 4 06 O B E 1 fb)

0.4

02

0

O t c ) 0 . 4 06

I

..

B *, 0

t

0.6

0.6

0 .4

0.E:

LAMINAR

on

TURBULENT

0.4

-

L W I M

TURBULENT *

,

.

0.2 I/

/

/

/

0

0 2 0.4 06 0 8 :

0 I

0 2 0.4 06 0 8

lzulr

I.

0

0 1 OA 06

08

-

V

-,-y

LAMINAR

0.6

c

. ----

0.4

0.2

I.

12

I

(0

R=160 E*= 20

--_ '.

\

'

0

0 2 OI O h 0 8

I

I2

1.4

I8

(9 1

IB 2 .

22

24

26 28,

-

3

V

Figure 7. Velocity distribution for R = k*2Re and prcssure gradicnts Bx = -(h2/pV)(L3p/aX). Constant k* = 0.4 in Prandtl's theory but k* = k*(Re) in the present theory (Constantinescu, 1958)

(8b) then almost linear relationships such as

B, = k,(Re)--,U V

B, = k,(Re)- w m V

(9)

are found to be valid. Relations (7) hold true for the laminar regime too; then k, = k, = 12. Consequently, an inertialess pressure differential

325

1.0

-

- _

' -%vwv 0

Theoretical laminni curve (no inertia forces)

~

: g o ,

-,Q.

0.8

-

Load

.-G ,

.-0

2

_

~

.

.\

120N

Y

c -\

A

Q) Q)

.i -

\.

60N

0.6 -

_

P

0.4 -

2

0.2 -

0 0

v x

200N 250N

m \

k, = k, = 12

m\

m

410N

and for turbulent flow

IOOON 1.000

Figure 8. Journal bearing; C/R = 0.003, L/D = 1. Eccentricity ratio versus Sommerfcld number for lleRc<3 (FrCne, 1974) equation quite similar to the classical Reynolds equation can be obtained as

for the usual steady boundary conditions

y=h,

(14a)

730N

0.0 +-----r----r--T 0.001 0.010 0.100 Sominerfeld number S

y=o,

The mentioned results are valid for Couette dominant flow. However, Poiseuille dominant flow may take place in some areas of externallypressurized bearings as well as in some seals. Then for laminar flow

u=v,

v=w=o u=v=w=O

nW (lla) (1lb)

Coefficients k,, k, may be approximately expressed as (Constantinescu, 1968, 1985)

k, = 12 +0.0136Reo9, k, = 12 +0.0044Reog6(12) lor Re < 50,000 while Couette tangential stress is

The two wall stresses TO h are then

In hybrid situations (coupled Couette and Poiseuille flows, either in line or normal to each other), as is oftcn the case, thcn the largest k,, values are t
where W is the applied load, L - the bearing width, D - the shaft diameter and R - the sh'lft radius. The theory includes laminar flow, an interpolation for the transition region (FrCne and Constantinescu, 1977) and fully turbulent inertialess flow according to the mentioned mixing length turbulent lubrication theory. Similarly, Figure 10 shows the dependency of the friction torque versus tangential speed for various loads. The quite satisfactory agreement with the experimental data indicates that inertia forces do not play an important role for relatively small Reynolds numbers (Re < SO00 for the mentioned experimental data), although &Re>> 1, reaching values up to ERe = 15. As already mentioned (8), this type of bulk flow behavior allowed bulk flow theories to be proposed, by starting from experimental data for channel

326 1.o

0.8

.-

4c

50

8

‘

0.6

0

>

testA

\

0.4

testA

0

testB

0.2 I .oo

0.100 Sotlunerfeld number S

0.001

theoreticnl

z

0.010

0.00 1

0.010

0.100

1.oo

Sommerfeld number S

b)Re=2370

a) Re=ll85 1.o

2. 0.8 .-0 ’e c

5

’‘ 4 3

theoretical test A

0

0.4

theoretical testA

testB

0.2 -7 0.001

0.6

e

1

0.010

0.100

rnl

1.oo

Soinnierfeld number S

c) Re=3555

d)Re=4740

Figure 9. Journal hiring; C/R = 0.003, WD = 1. Eccentricity ratio versus Sommerfeld number. Comparison between inertialess theory (laminar, transition, turbulent) and experimental data for various Reynolds numbers (FrCne, 1974) flows (I-hrs, 1974). Alternatively, an almost parallel Couette flow type was developed by Ng and Pan (1965), based by the law of wall. In this theory ZXY = 2,

+6zx,

ZYZ = 62,

where 6zx, 62, are small as compared to ‘cC The final result is a pressure equation identical to (a), with only a slight difference in notations

327

1

0.4

“O 0.8 theoretical

:I E

g

0.2

c

n

test A

0

test B

E

sP

0.0

T

0

2000 4000 velocity (thin)

6000

i

9

//

theoretical test A

0

test B

I

I

0

4000

0

I

I

8000

I

I

12000

velocity (Vmn)

Figure 10. Journal bearing; C/R = 0.003, L/D = 1 . Friction torque versus tangential spccd. Comparison between inertialess theory (laminar, transition, turbulent) and cxperiinental data for various loads Trike, 1974)

theoretical

c

A

test A

0

test B

A

d 0.2 c

0.0

1

A

c) Load 4700 N

a) Load 430 N

0.8

0.6

1-1

1

I

I

I

I

I

I

I

I

b) Load 2300 N where obviously G,=l/k,, G,=l/k,. Numerical values are provided for Gx, G, for Re<100,000. A non linear theory, proposed by Elrod and Ng (1967), further on uses the law of wall but the friction velocity is defined hnction of the local stress t, instead of the wall stress zw.

Additional alternate models were also used, such as the Prandtl-Kolmogorov model (Ho and Vohr, 1974) and standard k- E models (Launder and Leschziner, 1978; Ku and Tichy, 1987). All mentioned models are still subjected to some criticism. Thus, first, there is a strong interaction of the two solid walls that is not directly taken into account. I n addition, there is a strong non linear coupling between the Couette flow and the Poiseuille flow (both in line and perpendicular) leading for example to regions of reverse flow. Moreover, lines of tw = 0 occur on both surfaces that again are subjected to some comments. Finally, due to (l), the characteristics of viscous sublayers and transition layers close to walls are important and should be taken care in a more appropriate way. Two additional turbulence models will be briefly mentioned. First, an up-dated classical mixing length model (Lucas, Danaila, Boiineau and Frhe, 1994), based on Prandtl’s suggestion that

328

0.10 V. Lucas, Rh=l1224.32, gradpx=-5E3

V . Lucas, Rh=12209.74, gradpx=-lES

Mixing length

~

--ft V. Lucas, Rhzl1446.2, gradpx--2.5E5

~*

V. L U S ~ SKl1=10444.17, , gradpx=-513 V. Lucns, N1=9398.4, gradpx=-I Eb

. ...

8

0.01

H. G . Elrod, C. W.Ng

1.0

0.00 1E+2

0.8

1 E+3

I E+4

1E+5

Rh 0.6

Figure 12. Coeffcicnt G, for dp/dx>>dpP/az.(Lucas et. al., 1994)

0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 UIV

Figure 1 1. Velocity profiles for ii planc, r a l l efor l Couette-Poiseuilleflow for Rl,=hU/v= 10g aand various pressure gradients

p v ax:

By using van Driest's formula 1, = key[ 1 - exp(

where y+

= uty/v

-$)I

and A is a constant, one obtains

(Lucas el. al., 1994)

so that total local turbulent stress is (20) Substitution in (16) yiclds

A comparison with experimental data suggests that A = 38.2 for this problem. The obtained results are in good agreement with the rcsults obtained by Elrod and Ng (1967), as seen from Figures 11 and 12. The second model is rather recent (Danaila, 1995) and pays care for low Reynolds numbers in the vicinity of the wall. For cxample the first equation ( 5 ) is coiisidcred togetlicr with

329 where is the turbulent viscosity, k is the turbulent kinetic energy while other coefficients are constants and interpolation functions to be determined. The transport equations for turbulent kinetic energy k and for turbulent dissipation E (Jones and Launder, 1973; Patel, Rodi and Scheuerer, 1985; Cousteix, 1988; Wilcox, 1993) are

where the turbulent pseudo-dissipation rate E is rclated to dissipation E as

or, more precisely, for example in the tangential x direction. on dh R'= Redx This last observation separates from the beginning the problem of continuously distributed inertia effects (due to the continuous film thickness variation h(x, 2)) from areas of almost concentrated inertia effects (dNdx -P f 00, such as steps or the entrance area into a lubricating film). The first mentioned problcin can be tackled in an approximate manner by using a procedure similar to momentum integral approach in the boundary layer theory (Constantinescu, 1962, 1969, 1970; Constantinescu and Galetuse, 1974). Thus, let integrate, term by term with respect to y equations (3). By taking into account the continuity equation (6) one obtains

-Ja

h

u2dy + puv(g + p-1a

5. INFLUENCE OF CONVECTWE INERTIA FORCES

uwdy

=

(29a)

az 0

ax

The constants and various approximation functions are then deduced by including some tiine scales accepted to exist in a turbulent flow structure near a wall and far from the wall (Cousteix, 1988). The local time scale is expressed as a function of the two mentioned scales while some constants are determined from limiting situations, such as y -+ 0 , y + 00, etc. The obtained results are i n good agreement with both direct Navier-Stokes simulations (DNS) (Spalart, 1988), as well as with some experimental data.

h

h

h

p-Juwdy+pvwlo a ax 0

h

+p-jw a

2 dy

=

0

By proceeding in a similar way the continuity equation may be expressed as

-I

h

+-I

a udy + v((, h as

h

a

wdy = 0 0

When usual steady boundary conditions (1 1) are used, then the last relation expresses that

An order of magiiitudc analysis shows that the irnportance of convective inertia terms i n (3) as compared to viscous terms depends on

h 1

K'= Re- = E *Re

(27)

where average velocities U,,,, WIl1 are defined in (8).

330 The integrals from equations (29) may be evaluated for some prescribed velocity profiles. The simplest assumption is to consider that the velocity profiles retain the same shape as for the previous inertialess situation. Then h

Iu’dy = a U i h + PV’h- yUmVh

(32a)

0

h

I uwdy

Y

= OLU,Wmh- -UmVh

0

In laminar flow the assumption of parabolic velocity profiles gives 6 a=5’

p=-

5

12’

y=-

0

(32b)

2

1

H,O

0

I

100

20 lo

(33)

5

0

while in turbulent flow (Constantinescu and Galetuse, 1974)

Approximations (30)-(32) might be considered as acceptable since integrals (30) are less sensitive to errors in the evaluation of the velocity profiles. The comparatively weaker point of this approach is the need to evaluate friction stresses on tlic two surfaces, i.e., the last terms of (27). Indeed, TX I ’ =..y are depending on the derivatives of the ve octty profiles. When the same assumption is made (namely velocity profiles having the same shape as in the inertialess case), then TyI0 xy 0

=

kZP --w, h

mm

0

I

I

0

00

I

0 ClV

I

(35)

where kx = k, = 12 in laminar flow and assume values (10) in turbulent flow. An attempt to improve the accuracy of the first formula (33) was done (Constantinescu, Galetuse and Kennedy, 1975) by considering some flows close to the lubrication one, for which both laminar and turbulent analyses can be done directly. It was

I

la

K h,/h,

Figure 13. Comparison with experimental data for the pressure distribution in an air lubricated step bearing (Constantinescu and Galetuse, 1976).

33 1

found that while formulas (30) do not need additional corrections, the first formula (33) may be improved as

A system of three equations for the unknowns

Wm, P can thus be written and solved numerically. Moreover, a direct iterative procedure can be employed by starting from the inertialess case, in all situations when inertia effects are not very important (Kennedy, Constantinescu and Galetuse, 1975; Constantinescu, 1995). This procedure was consistently used by various authors in evaluating inertia effects (Kings and Taylor, 1975; Launder and Leschziner, 1975; FrCne et. al., 1990). An example concerning an experimental air lubricated step configuration is given in Figure 13 (Constantinescu and Galetuse, 1976). Note however that an inlet ram pressure is occurring, due to inertial entrance effects. 6. CONCENTRATED INERTIA EFFECTS

Such effects may be of importance in certain applications, for example in radial seals of turbopumps (Figure 14) as well as in any externally pressurized bearing operating at high Reynolds numbers (Childs, 1994). Several viscous siniplified models are available (Pan, 1974; Constantinescu, Galetuse and Kennedy, 1975; Constantinescu, 1987, 1988) and even inviscid models (Tipei, 1982; Buckholtz, 1987). Basically, the qualitative influence of inertia forces at the entrance of a narrow gap is similar to the inviscid Bernoulli effect. Thus, any time the fluid is accelerated, a pressure drop is occurring while a pressure rise takes place when the flow is decelerated. However, the local flow conditions are strongly departing from the simplifying lubrication assumptions A proper answer to this problem can therefore be furnished only by direct numerical simulation of

High pressure

I

Figure 14. Inertia effects in a radial seal 1: Sudden area change 2: Convective inertia forces 3: Labyrinth Navier-Stokes equations with an appropriate turbulence model. At the same time there is a strong need for detailed, careful and contident experimental data that are still missing in the technical literature on this subject. 7. CONCLUSIONS It is emphasized that bearings and seals operating at large Reynolds numbers are subjected to loss of stability of the initial laminar flow, to transition and turbulence as well as to non negligible influence of inertia forces. Therefore, the non laminar lubrication of such machine components poses basic problems that are similar to another important subject of viscous fluid dynamics, namely the boundary layer flow. Some of the significant systematic research efforts devoted in the last decades to this problem are briefly outlined. Such efforts allowed the analysis and the design of a number of applications, especially in aerospace and in nuclear engineering. The mentioned results concern the evaluation of non laminar regimes, turbulence models for almost parallel (inertialess) Couette-Poiseuille flows, a method for estimating the effect of convective inertia forces as well as the effect of local inertial flows taking place for example at the entrance in a narrow passage. The last effect is of utmost importance in externally-pressurized bearings in radial seals and can be properly tackled only

332 through comprehensive nunicrical simulations with appropiate turbulencc models. Indced, as alrcady mentioned, the turbulence model necd to accoiint for the simultaneous existence of two walls closely placed each other as well as for strong pressure gradients (favorable and especially adverse, leading to zero wall shear stress and to reverse flow). Finally, the need for appropiate careful and confident experimental data concerning details of such turbulent flows is emphasized.

REFERENCES Buckholtz, R. H. (1987). The Effects of Lubricant Inertia Near the Leading Edge of a Plane Slider, Trans. of the ASME, Journ. of Tribologv, 109, 60-64. Capitao, J. W. (1974). Influence of Turbulcnce on Performance Characteristics of the Tilting-Pad Thrust Bearings, 7’rans. ASME, Journ. of Lubrication Technology, 96, 110-117. Childs, D. (1993). Turboinachinery Rotor Dynamics, John Wiley. New York. Constantincscu, V. N. (1958). Influence of Turbulence on the Motion in the Lubricating Film (in Romanian), Sf. Cerc. Mec. Apl., 9, 103-137. Constantinescu, V. N. (1959). On Turbulciit Lubrication, Proc. Inst. Mech. Engs. London 173, 88 1-900. Constantinescu, V. N. (1962). On High Spccd Flow of Gases in thin Layers (in Romanian), St. Cerc. Mec. Apl., 13, 383-400. Constantinescu, V. N. (1967). On the Pressure Equation for Turbulent Lubrication, Proc. of the (bnference on Lubrication anti Wear. 1. Mech. Engs, London, 132-134. Constantinescu, V. N. ( 1 968). Lubrication In Turbulent Regime, AEC-tr-6959, U.S. Atomic Energy CommissiodDivision of Technical Information, National Bureau of Standards, U.S. Department of Commerce, Springfield, Virginia 22151. Constantinescu, V. N. (1969). Gas Lubrication, ASME Publications, New York. Constantinescu, V. N. (1970). On the Iiflucnce of Inertia Forces in Turbulent and Laminar SclfActing Films, Trans. ASME, Journ. of Lubrication Technology, 92,473-481. Constantinescu, V. N., Pan, C. H. T. and Hsing, F. C. (1971). A Procedure for the Analysis of

Bearings Operating i n the Transition Range Betwccn Laminar and Fully Developed Turbulent Flow, Rev. Roirm. Sci. Techn. - Mec. Appl., 16, 945 982. Constantinescu, V. N. and Galetuse, S. (1974). On the Possibilities of Improving the Accuracy of the Evaluation of Inertia Forces in Laminar and Turbulent Films, Trans. ASME, Journ. of Lubrication Technology, 96,69-79. Constantinescu, V. N., Galetuse, S. and Kennedy, F. E. (1975). On the Comparison between Lubrication Theory Including Turbulence and Inertia Forces and some Existing Experimental Data, Trans. ASME, Journ. of Lubrication Technology, 97, 439-449. Constantinescu, V. N. and Galetuse, S. (1976). Pressure Drop due to lnertia Forces in a Step Bearing, Trans. ASME, Journ. of Lubricatron Technology, 98, 167-174. Constantinescu, V. N., Nica, A,, Pascovici, M. D., Ccptureanu, G. and Nedelcu, S. (1985). Sliding Bearings, Allerton Press, New York. Constantinescu, V. N. (1987). Influence of Inertia Forces in Externally-Pressurized Journal Bearings Operating at Large Rcyiiolds Numbers , Rev. Rouni. Scr. Techn. - Serie Mec. Appl., Bucharest, 32,625-638, Constantinescu, V. N. (1988). On Entrance Conditions i n Lubricating Films at Large Reynolds Numbers (in Romanian), St. Cerc. Mec. Apl., 47. 369-376. Constantinescu, V. N. (1995). Laminar Viscous Flow,Springer, New York. Coustcix, J. (1988). Aerodynamics of Viscous Fluids; Turbulence and Boundary Layers (in French), ENSAE. France. Danaila, S. (1995). A Turbulence k E Model for Boundary Layer Flow (in Romanian), S t . Cerc. Mec. Apl., 54 (undcr press). DiPrinia, R. C. and Stuart, J. T. (1974). Developiricnt and Effects of Supercritical TaylorVortex Flow in a Lightly Loaded Journal Bearing, Trans. ASME, Journal of Lubrication Technology, 87,28 - 35. Elrod, H. G. and Ng. C. W. (1967). A Theory for Turbulent Fluid Films and its Application to Bcarings, Trans. ASME, Journ. of Lubrication Technology, 89, 346-362. FrCnc, J. (1970). Contract Report No. HC.061.E.750, Electricit6 dc France. FrCne, J. (1 974). Non Laminar Flow Regimes in

-

-

333

Thin Layers. Application to Sliding Bearings (in Freiich), Ph. D. Thesis, Claude Bernard University, Lyon, France Frtne, J. (1975) General Discussion on Thrust Bearings, Proc. Leed-Lyon Synlposium on Superlaminar Flow in Bearings, I . Mech. I.. London, 166 167. FrCne, J. and Constantinescu, V. N. ( 1 975). Operating Characteristics of Journal Bearings in the Transition Regime, Leeds-Lyon Symp. on Superlaminar Flow in Bearings, I. Mech. E. Publ., London, 121 -124. FrCne, J., Nicolas, D., Degyerce, B., Berthe. D. and Godet, M. (1990), Hydrodynamic Lubrication (in French), Eyrolles, Paris. Hirs, G. G. (1974). A Systematic Study of Turbulent Film Flow, 7’rans. A.YME, Journ. of hhricafion Technology, 96, 1 18-126. Ho, M. K. and Vohr, J. H. (1974). Application of the Energy Model of Turbulence to Calculation of Lubricant Flow, Trans. ASME, Journ. of Lubrication Technology, 96, 95-102. Jones, W. P. and Launder, B. E. (1973). The Calculation of Low Reynolds Number Phenomena vith a Two-Equation Model of Turbulence, /ntern. ./ourn. ofHeat Trans..r, 16, 1 119-1130. Kennedy, F. E., Constantinescu, V. N. and Galetuse, S. (1975). A Numerical Method for Studying Inertia Effects in thin Filiii Lubrication, I’roc. Leeds-Lyon Syinp. on Superlatninor Flow in Mcarings, I. Mech. Engs. Publ., London, 174-182. King, K. F. and Taylor, C. M. (1 975). Laniiiiar and Turbulent Lubrication of the Finite Width Plane Inclined Slider Bearing Including a Consideration of Mean Convective Inertia Effects, Proc. LeedsLyon Symp. on Superlaniinor Flow in Bearings, I. Mech. Engs. Publ., London, 144-149. Ku, C. P. and Tichy. J. A. (1987). Applicatioii of tlic k - E Turbulence Modcl to Squeeze Filin Dampers, Trans. ASME, Jour.n. of Tribology, 109, 164-168. Launder, B. E. and Leschziner, M. A. (1975). An Efficient Nuiiierical Scliciiie for the Prediction of Turbulent Flow in Thrust Bearings, Proc. LeedsLyon Symp. on Superlatriinar Flow in Bearings, I. Mech. Engs. Publ., London, 137-143.

-

Lucas, V., Danaila, S., Bonneau, 0. and Frene, J. (1994). Roughness Influence on Turbulent Flow through Annular Seals, Trans. ASME, Journ. of Tribology, 116, 321-329. Ng, C. W. and Pan, C. H. T. (1965). A Linearized Turbulent Lubrication Theory, Trans. ASME, Journ. of Basic Engineering, 87,675-681. Pan, C . H. T. (1974). Calculation of Pressure, Shear, and Flow in Lubricating Films for High Speed Bearings, Trans. AWE, Journal of Lubrication Technology, 96, 80 94. Patel, V. C., Rodi, W. and Scheuerer, G. (1985). Turbulence Models for Near-Wall and Low Reynolds Numbers Flows, AIAA Journal, 23, 13081319. Reynolds, 0. (1886). On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experimental Determination of the Viscosity of Olive Oil, Phil. Trans. Roy. SOC. London, 177, part, 1.57-234. Smith, M. I. and Fuller, D. D. (1956). Journal Bearing Operation at Superlaminar Speeds, Trans. ASME, 78, 469-474. Spalart, P. R. (1988). Direct Simulation of a Turbulent Boundary Layer up to Reg= 1410, Journ. of FIuidMechanics, 187,61-98. Taylor, G . I. (1923). Stability of a Viscous Liquid Contained Between Two Rotating Cylinders, Phil. Trans. Roy. SOC.London, A223, 289 - 343. Tipei, N. (1982) Flow and Pressure Head at the Iiilet of a Narrow Passage without Upstream Free Surface, Trans. ASME, Journ. of Lubrication Technology, 104, 196-202. Vohr, J. H. (1968). Experimental Study of Taylor Vortices and Turbulence in Flow Between Eccentric Rotating Cylinders, Trans. ASME, Journal of Lubrication Technology, 90,285 - 296. Wilcock, D. F. (1950). Turbulence in HighSpeed Journal Bearings, Trans. ASME, 72, 825-834. Wilcox, D. C. (1993). Comparison of TwoEquation Turbulence Models for Boundary Layers with Prcssure Gradient, A I M Journal, 31, 14141421.

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The Third Body Concept / D. Dowson et al. (Editors)

335

1996 Elsevier Science B.V.

Third body formation in soft solid processing M. J. Adamsa, B. J. Briscoeb, E. Pelillob and S. K. Sinhab

a Unilever Research, Port Sunlight. Bebington, Wmal L63 3JW. UK. bDepartmentof Chemical Engineering and Chemical Technology, Imperial College, London SW7 2BY, UK. This paper reviews and examines third body formation in the technologically important area of soft solid (paste) processing. On the basis of analyses applied to a number of experimental procedures, it is shown that in paste processing the wall boundary evolves as the material flows and takes its own characteristics which are quite different from that of the bulk of the material. A third body in the form of a thin lubricating layer is formed at the interface between rigid wall and the paste material. The thickness of this layer depends upon the parameters such as the wall stress, temperature and the roughness of the rigid wall. This phenomenon has precedence in tribology but an important difference is that the real contact area approaches the apparent values unlike in many conventional tribological contacts.

1. INTRODUCTION

In all tribological phenomena it is well known that, whether it be metallic, polymeric or ceramic systems, an important and frequent consequence of the action of the sliding motion, between two interacting surfaces, is the formation of an interphase whose properties, chemical and physical, are different to those of the adjacent (or first) bodies; a third body [ 1, 23. The tribological characteristicsof such systems are greatly dependent upon the response of this resultant third body. For example, the steady state friction is modified and controlled according to the dynamics and properties of the third body that is produced. For elastic and brittle materials, the third body is generally in the form of particulate debris, which may or may not affect the friction process. For more plastic and viscous materials, the sliding motion often gives rise to the formation of a transformed film, the properties of which are generally different from those of the contacting bodies. Such interface films are genedly formed from a moltenhoftened surface layer at the contacting point of the two bodies. In some cases, they are generated also by the presence of a lubricant or humidity in the vicinity of the contact. For instance, the presence of humidity or water can lead to the formation of hydroxides for ceramic systems. These hydroxides act as a third body which may lead to an increase in the wear of the material 131. Surface

melting is a common occurrence in polymeric contacts sliding and this molten layer behaves more or less in a viscous manner [4]. Thin film formation between two solid bodies has often been treated as a case of hydrodynamic or boundary lubrication [5]. Generally, such interactions are engineered between a coherent rough soft material sliding against a hard substrate. A soft material, for example a polymer sliding against a hard metal, shows localised surface melting at elevated temperatures due to frictional heating and this molten layer facilitates the localised frictional energy dissipation by a viscous flow process[4]. Similarly, isothermal strain softening may occur due to the localised interfacial restructuring or reorientation: PTFE is the classical example [6]. A similar observation of a third body formation has also been reported in the different but important area of material processing involving paste deformation and flow. Pastes are an example of soft solids; that is they exhibit comparatively low yield stresses. They are normally constituted from fine particles dispersed in a liquid phase; the solid phase volume fraction is typically 60%. The boundary layer formation in paste flow is the result of the presence of a liquid-richregion near the rigid wall due to the large shearing action between the solid particles present in the paste and the rigid wall [7]. The formation of a “third body” in soft-solid processing is of special significance as this phase, in

336 a large part, controls the efficiency of the processing operations [8]. The present paper reviews three experimental methods, and their associated analyses, for the determination of the prevailing wall boundary condition which occur during the deformation and flow of pastes. The methods to be described are wedge indentation, cylinder upsetting and capillary extrusion. The corresponding analyses have been drawn from those established in engineering plasticity and rheological analyses. The approach ha$ certain precedents in conventional tribology but it is distinguished by the fact that in these systems the contact area is nominally the same as the apparent contact area. The data derived from the three methods are compared and the current capacity to characterise the wall boundary condition in these systems is critically evaluated. Any deformation process, whether it be the sliding of two bodies separated by a third body or a manufacturing operation, may be regarded as arising from the action of the imposed wall boundary conditions upon a set of material properties to induce a set of flow fields. Thus, for example, the throughput of a manufacturing operation may be judged on its throughput which is the integral of the velocity field. In order to implement numerical simulations of such processes, a knowledge of the wall stress boundary conditions and the associated material flow parameters is necessary. The aim of the current paper is to evaluate the applicability of two possible prescriptions of the wall boundary conditions. Cylinder upsetting and wedge indentation are commonly analysed using a Coulombic relationship where the wall yield stress is some fraction of the uniaxial yield stress (the maximum permissible value of the wall normal stress). The available analysis for the capillary extrusion method incorporates a Tresca condition which states that the wall shear stress is some fraction of the shear yield stress. Actually, a variation of this condition is employed where the wall shear stress is also a function of the wall slip velocity; the important point being that it is assumed :c) be independent of the wall normal smss. If at large strains, the elastic component of the response is neglected then an effective constitutive relationship for a paste may be considered to be composed of a plastic (yield) and a viscous (flow) term [9]. For the upsetting work, the strain rates involved were relatively small which allows the viscous term to be neglected for the

current purposes. At strain rates corresponding to those at which this flow term is the most significant, it is a good approximation to represent the resulting viscoplastic response by a power law relationship which, in uniaxial stress induced flow, may be written as:

where o is the flow stress, k is the flow consistency, n is the flow index and & is the shear rate. 2.

EXPERIMENTAL METHODS

2.1

Material

The experiments were carried out using a model paste material known as “Plasticine”. This material is a dispersion of clay particles (78% w/w phase volume of kaoline, AlqSi4010(OH)g), in a liquid (hydrocarbon)medium. It was homogenised in a z-blade mixer before making the specimens. Cylindrical specimens,of specified dimensions, were prepared from blocks by the use of mould cutters. These blocks were prepared by compressing the material between parallel platens using an Instron universal testing machine (model 1122). In order to facilitate the removal of the blocks from the platens, waxed paper inserts were used. For the wedge indentation experiments, blocks of accurately defined geometries were used. The specimens were thermally equilibrated for at least 2 hours at 21 O C prior to the measurements. 2.2 2.2.1

Experimental procedure Cylinder Upsetting

Cylindrical specimens of 60 mm diameter and 20 mm height were prepared. The cylinders were compressed between two “over-hanging’’parallel smooth steel platens. The interface traction was changed by introducing lubricants between the model paste and the steel surface of the platens. Talcum powder (Mg(jSi8020(0H)4) and a proprietary silicone grease were used for this purpose. The unequivocal stick wall boundary condition was achieved by utilising “emery” (carborundum) paper as the interface. The cylinders were compressed at a constant velocity of 0.833 mm/s and the mean

337 compressive stresses as a function of the imposed n a t d strain were recorded.

V-@

Figure 1:

Geometry of extrusion

Capillary Extrusion The capillary or die-land extrusion experiments were also carried out by using an Instron machine which was fitted with a ram extruder attachment having capillary tubes attached to the barrel. A 63 mm inner diameter barrel was used with a number of orifice dies and capillary die-lands (30 and 50 mm) of different diameter (1, 2, 3, 4 and 5 nun). For each experiment, the "Plasticine" was placed into the barrel and the extrusion pressure, Pt, was rnlded. In order to obtain the extrusion pressure in the die-land, the following technique was adopted [9]. I'he total extrusion pressure, Pt, operating upon the die-land may be described as (seefigure 1); 2.2.2

indentation depth of 6 m m and the indentation loads were recorded for a range of indentation velocities. Finally, the wedges were removed from the samples and the actual area of contact was measured by observing the residue impressions of the "Plasticine" on the wedge faces; "Plasticine" naturally transfers a film of oil and particulate material to contacting surfaces; actually a part of the third body residue. The mction between the "Plasticine" and the wedges was modified by heating the wedges. 3. RESULTS AND ANALYSES 3.1 Interface Friction in Upsetting The parallel plate geometry, where a cylindrical sample is used in compression, has been used previously as a means for the rheological characterisationof plastic and visco-plastic materials [lo]. The boundary condition defined by the friction between the platen wall and the deforming material plays a critical role in determining the processing parameters such as the reaction load and also the geomey of the deformation resulting from the flow patterns or the velocity profiles occurring within the bulk of the sample. The velocity profile provides a measure of the variation of the local shear rate. Figure 2 shows, in a schematic manner, the influence of the boundary friction upon the material flow of a typical paste material in upsetting.

t moving platen

where Pf is the pressure due to the bulk flow and wall friction in the capillary die-land and Po is the orifice pressure. For each diameter of the die-land, measurements were also performed with orifices of the same diameter. Finally, the pressure required for the initiation of orifice extrusion was subtracted from the total extrusion pressure in order to obtain the pressure generated within the die-land. Wedge Indentation Wedge indentations were carried out on thick "Plasticine" blocks where the ratio of the thickness of the sample to the indentation depth was more than 15. This geometry was chosen to ensure that a condition of almost plane strain deformation prevailed. Stainless steel wedges of included angles 30°, 60°, 90°, 1200 and 1500 and of widths 180 mnm were employed. Using the Instron device, the wedges were driven into the samples to a fixed

stationary platen Ir

d=2R (a)

2.2.3

shear b

(

L b m l l i n astationary platen (b)

Figure 2: Upsetting of paste cylinders between two parallel platens with (a) frictionless, and (b) finite friction wall boundary conditions.

338 There are two main theories currently available which take into account the influence of wall frictional effects; a plasticity approach and a visco-plastic approach [ 111. The plasticity analysis includes a wall friction coefficient between the material and the platen surface whereas the viscoplastic solution has been derived only for a stick wall boundary condition. Consequently, we will consider a plasticity approach which is based upon the upper bound theorem. The method does not explicitly account for the rate dependent properties associated with the viscoplastic characteristics. However, by only considering a constant platen velocity it is possible to exemplify how changing the wall traction influences the compressive reaction force. Unfortunately any influence of the wall slip velocity upon the friction cannot be established. The upper bound method assumes that the material deforms homogeneously. This may be the case with hard material such as metals where the interfacial shear stress is much less than the bulk shear yield stress of the material. However, for soft visco-plastic solids the magnitude of shear stress generated at the wall is comparable to the strength of the material itself. Hence, the wall stress is readily capable of introducing inhomogeneous flow during the compression process (figure 2 b). Nevertheless, the upper bound method does provide a fmt order description of the compression process. The corresponding solution may be written in the following form [12];

natural strain (lnh/ho) for the three interface conditions. The figure indicates that there is an additional energy dissipation at, or induced by, the boundary in the absence of an externally applied lubricant which gives rise to a significant increase in the working stress, 5.For the case of the “emery” paper wall, the wall boundary condition was near to a stick condition [8] which, according to plasticity theory, correspond to a value of 0.577 (seelater). If a lubricant is applied, or if a third body (thin lubricating layer) evolves due to the action of a high wall stress, the mean stress decreases due to a reduction in the frictional work at the boundary and a corresponding reduction in the inhomogeneity of the deformation within the bulk. The friction coefficients may be estimated from these plots by using equation (3). The value of the yield stress is obtained as an apparent value from the curve associated with the “emery” paper data. The calculated coefficients of friction are shown in the figure. A critical evaluation of this procedure compared to the others examined for detecting and charactensing the thud body, will be presented later.

1 .o

0.8

0.6

(3) 0.4

where ?f is the mean normal pressure acting on the platen, G~ is the uniaxial yield stress of the material, p is the coefficient of friction, is the initial diameter of the cylinder and E is the strain which is defined as (1-E) = h/kwhere h and are the current and initial heights respectively of the cylinder. As was indicated previously, the above solution applies only to rigid perfectly-plastic materials. It is not clear whether or not the flow stress is also generally dependent upon the imposed strain in the plastic region. However, at low strains such materials often show a strain dependence due to an elastic compliance effect. Figure 3 illustrates the measured mean normal stress for a compressive velocity of 0.833 mm/s as a function of the imposed

0.2

0.0

0.0

0.2

0.4

0.6

0.8

1.0

2

Natural Strain (1nh.h)

Figure 3: Mean normal pressure as a function of natural strain for the upsetting of “Plasticine” cylinders at different interface conditions. The full lines show the experimental data and the points are calculated using equation (3).

339 3.2 Wall slip in Capillary Extrusion

Capillary extrusion has been used extensively in polymer and paste processing for obtaining material flow or yield parameters such as the bulk flow stress. In dilute suspension flows, it is generally assumed that the material sticks to the rigid wall of the tube during the flow. However, at high concentrationsof the solid phase, wall slip may often occur under different combinations of the wall shear stress and the wall temperature [13]. In a capillary flow, the greatest shear stress occurs near the wall and decreases towards the bulk of the material.High wall stresses and high shear rates near the wall induce the movement of solid particles away from this region which causes a particle depleted layer to form. Another reason for the existence of such a thin lubricating layer, or third body, may be the shear induced heating of the soft solid during the flow. The high energy dissipations involved in the flow processes gives rise to an increase in the wall temperature. Most of the heat which is generated is produced near to the wall due to the creation of a localised high shear zone. An increase in the interface temperature reduces the viscosity of the liquid phase in contact with the wall and thus effectively provides a lubricating thin boundary layer between the wall and the hulk of the material. In the present study, the capillary extrusion experiment has been carried out with the model paste material in order to examine the effects of high shear stresses (high extrusion velocities) upon the wall slip in paste flows. The wall stress generated in a capillary tube is given as [14]; 2,

- APD

-- 4L

0.50

I

0.45

-

0.40 -

0.30 0.35

0.25 0

50 100 150 200 250 300 350 400

Wall Slip Velocity, mm/s Figure 4: Wall shear stress as a function of the computed wall slip velocity for the capillary extrusion of “Plasticine”. graphical procedure is adopted to obtain the wall slip velocity and the wall shear stress. This procedure is now well established and has been fully described in reference [14]. Figure 4 shows a plot of the wall slip velocity as a function of the wall shear stress in capillary flow for the present system. The figure shows that there is a critical wall stress below which there was no observable wall slip. Above the critical value, the slip velocity increases linearly with the wall smss. These data may be represented by the following relationship;

(4)

where zw is the wall stress, AP is the pressure difference across the tube, D is the diameter and L is the length of the tube. The wall shear rate for a power law fluid (equation l), is defined as;

r=R where v is the mean extrusion velocity and R is the radius of the capillary tube. This analysis for the capillary extrusion does not explicitly take the potential wall slip effects into account. Normally, a

where zWo is the wall shear yield stress, u is the wall slip velocity, 4 is the viscosity of the liquid phase in the paste and t is the film thickness of the wall boundary layer. From equation (6), a plot of T~ as a function of u will be predicted as being linear and the film thickness may be obtained from the gradient. If we assume that the fluid viscosity is 12 Pa. s, a reasonable estimate based upon the paste formulation, then we obtain a value of 25 pm for the fluid film thickness at the wall.

340 3.3 Effects of Interface Temperature in Wedge Indentation In the previous two sections, the effects of surface lubrication and wall velocity were considered.

Another effect which may be important in paste processing is that of the interface or container wall temperature. As was explained previously, heat generated at the wall, due to shear heating may increase the wall temperature. A high wall temperature induces wall slip apparently due to the generation of a thin and low viscosity lubricating layer. In many paste processing operations, such as those for foods, the wall of the equipment is either heated or cooled depending upon the type of process involved and hence provide the boundary characteristicsare required for optimisation purposes. In this section, the effects of the interface temperature are evaluated using the data obtained from the wedge indentation measurements. For the interpretation of the data, an analysis has been derived from a slip line field solution for plastic materials. This solution provides an interrelationship between the ratio of indentation pressure, p, to the apparent yield stress of the material, the semi wedge angle, (half of the wedge included angle) and the Coulombic coefficient of friction, p, between the deforming paste and the wedge surface [15]. This relationship is given as follows;

w,

(7) where c is known as the constraint factor which is a function of both p and For the viscoplastic material considered here we assume that von Mises yield criterion applies so that we may write;

w.

Hence, in order to obtain the friction coefficient fiom a measurement of the indentation pressure, for a given wedge angle, it is necessary to establish the values of the constraint factor and also the yield strength of the material. One approach to resolve this problem is to use an analysis developed for creeping solids which leads to the following relationship[16, 171;

(9)

lnlsrllce ernpruwes

(p)

.R.%.C

A

0.5

25 degC (0.577) 40degC(0.175) 50 degC (0.075) 60 degC (0.025) 70degC(O00)

-

0.0.' 0

' 10

"

20

'

. ' .

'

30

40

50

'

I

60

.

' . 70

I 80

Semi wedge angle, deg.

Figure 5: The constraint factor, c', as a function of the semi wedge angle in a wedge indentation test for different (wedge) interface temperatures. The solid lines show analytically (slip line) computed values. The numbers within the brackets are the predicted Coulombic friction coefficients for the corresponding interface temperams. where C' is equal to 1.155 c(p,w). EeRis a mean strain rate of the sort that would be experienced by the material in a simple tensile or compressive deformation and b represents the ratio of the true to the apparent contact width. These two analyses and their application for the bulk and boundary characterisations for paste materials are described elsewhere [17]. Figure 5 is a plot of the computed value of the parameter c' as a function of the semi wedge angle for several different interface temperatures. The application of the above analysis to such data is rather problematic but does enable both the elastoplastic stress-strain and vim-plastic stress-strain rate constitutive relationships to be directly derived in addition to the wall boundary conditions. Here, we will focus only upon the latter. Essentially, at a given indentation velocity the data obtained at 2loC were fitted to the slip line field solution on the basis that a stick wall boundary condition was supposed to exist. This enabled an apparent yield stress (the flow stress normalised with respect to strain rate) to be

34 1

determined which was used to estimate the wall friction component at the elevated wall temperatures using the slip line field solution. The friction coefficients obtained on this basis are shown in figure 5 . It may be seen that there is a systematic reduction in the wall friction coefficient values with an increasing of the wall temperature until at ca. 70 O C where an apparently frictionless interface condition is achieved. 4. DISCUSSION In the current work, a soft solid has been subjected to three rather different modes of deformation. While it has been shown that sensible trends in the wall friction may be sensed for the variations of the wall surface topography, the state of lubrication, the sliding velocity and the wall temperature, the analyses do not discriminate between those wall boundary condition relationships which are a function of the normal stress or those that are not a function of this parameter. There is here an analogy with the work of Tanaka and Uchiyama [4] concerning the influence of surface melting upon the friction of thermoplastics. They were able to rationalise their data by a relationship similar to equation (6) except that the zwo was taken as zero. However, the thickness of the layer might be expected to depend upon the normal stress if a simple hydrodynamic lubrication theory was adopted. They actually calculated the film thicknesses as a function of a number of experimental parameters but did not comment upon the significance of their computed values. Unlike relatively soft quasi-homogeneous materials such as polymers, the interface friction of soft solids cannot be measured using conventional sliding measurements against a hard counterface. This is because there would be a very substantial bulk deformation component ok the friction. A more useful approach is to employ wall stress transducer and this is currently under development. A possible cause of the current failure to discriminate between the two options for the wall boundary condition is that only the mean quantities were measured. More detailed measurements involving stress distribution or displacement fields may be required. Kudo [18] has shown that an averaging procedure leads to an equivalence of the

Coulombic and Tresca boundary conditions which may be written respectively as follows; 2,

=Pow

10)

and 2,

= mTo

where m is known as the friction factor and 6, is the wall normal stress. Kudo suggested that, for cases where there is a distribution of wall normal stresses, it is possible to consider a mean value, 0,. associated with a mean coefficient of friction, p, thus;

where zo has been related to the uniaxial yield stress assuming that a von Mises yield criterion applies. It is worth noting that for the stick condition, that is m=l and hence from the above relationship the maximum value of p is 0.577 as was mentioned previously. In soil mechanics, the difficulties in deriving the constitutive equations that correctly predict multi-path loading cycles has led to the application of discrete computational methods of which the most successful is the distinct element method [19]. For a powder sliding against a relatively smooth wall it is possible to develop closed-form solutions for the friction from a knowledge of the geomeuy, material and frictional properties of a single particle [20]. In principle, this simple analytical approach should be applicable to soft solids by introducing elastohydrodynamic interaction laws at the particle-wall contacts. Unfortunately, soft solids tend to be composed of small and irregular shaped particles and, hence, it would be difficult to specify the interaction laws with any certainty. 5. CONCLUDING REMARKS

The experimental results presented in this paper demonstrate the existence and importance of a third body formation in any paste processing operation. The main interaction takes place at the

342 boundary between a rigid equipment wall and the material because this boundary acts as the interface for the energy dissipation from the equipment into the bulk of the material. In addition, the boundary also acts as the site for the heat uansfer either from or to, the bulk of the paste material. Any changes taking place at the wall will have a major influence upon the efficiency of the deformation process. Generally, external factors such as temperature, surface roughness and velocity affect paste processing through the formation of a third body in two respects; first by forming a lubricating layer which is relatively rich in the liquid phase concentration and second by reducing the viscosity of a thin layer of the paste in close contact with the wall. In summary, the boundary characteristics play a major role in the processing operations of any softsolid material. Hence, it is essential that the boundary conditions be characterised for optimisation and control of the process and where possible the characteristics of the corresponding third body be evaluated.

7.

ACKNOWLEDGEMENTS

15.

The authors wish to thank a MAFFDTI Link Scheme, UK for the financial support.

16.

8.

9. 10. 11. 12.

14.

17. REFERENCES

1. 2.

3. 4.

5.

6.

M. Godet, Wear, 1984, 100,437. Y. Berthier, M. Brendle and M. Godet, Proc. of the 14th Leeds-Lyon Symposium on Interface Dynamics in Tribology, Lyon 8-11 Sept. 1987. (eds. D. Dowson, C. M. Taylor, M. Godet and D. Berthe) 19. A. Ravikiran and B. N. Pramila Bai. Wear, 171 (1993) 33. K. Tanaka and Y.Uchiyama, in Advances in Polymer Friction and Wear", Polymer Science and Technology,Volume 5B (ed. L. H. Lee), Plenum Press, New York, 1974, p. 499. J. M. Georges, D. Mazuyer, A. Tonck and J. L. Loubet, J. Phys. Condens. Matter, 1990,2, SA399-SA403. C. Pooley and D. Tabor, Proc. Roy. Soc. London, 1972, A, 329,25 1.

18. 19. 20.

U. Yilmazer, U. and D. M. Kalyon,, J. Rheo., 1989, 33(8). p. 1197. M. J. Adams, B. J. Briscoe and S. K. Sinha, Proc. of the 20th Leeds-Lyon Symposium on Dissipative Process in Tribology, 1994 Elsevier Science ( 4 s . D. Dowson, C. M. Taylor, T. H. C. Childs, M. Godet and G. Dalmaz) 223. J. J. Benbow. S. H. Jazayeri and J. Bridgwater, Powder Tech. 65 (1991) 393. M. J. Adams, S. K. Biswas, B. J. Briscoe and M. Kamyab, Powder Tech. 65 (1991) 381. M. J. Adams, B. Edmundson, D. G. Caughy, R. Yayha, J. Non-Newtonian Fluid Mechanics, 51 (1994), 61. K. L. Johnson, in "Contact Mechanics", Cambridge Univ. Press, Cambridge 1985. 13. B. K. Aral and D. M. Kalyon, J. Rheol. 38(4) (1994) 957. M. J. Adams, B. J. Briscoe and S. K. Sinha, Roc. 27th Int. Society for the Adv. Mat. and Process Eng. (SAMPE) Tech. Conf., Oct 9-12, 1995, New Mexico, 877. J. Chakrabarty, in "Theory of Plasticity, McGraw Hill Book Co., NY. A. F. Bower, N . A. Fleck, A. Needleman and N. Ogbonna, Proc. R. Soc. Lond. A, 441 (1993) 97. M. J. Adams, B. J. Briscoe and S. K. Sinha, "Wedge indentation of a elasto-viscoplastic paste". Manuscript in preparation. H. Kudo, Int. J. Mech. Sci., Part I, 2, (1961) 102 and Part 11, 3, (1961) 91. C. Thornton, in Tribology in Particulate Technology, Adams Hilger, Bristol(1987) 292. M. J. Adams, B. J. Briscoe and L. Pope, in Tribology in Particulate Technology, Adams Hilger, Bristol(l987) 8.

DISCUSSIONS

J. Greenwood: Having been brought-up in Bowden and Tabor's laboratory, it is heresy to hear that heating the "Plasticine" will reduce the coefficient of friction:

p = SIP

343 where s and p are shear normal stresses respectively. Softening the body will reduce s and p by the same amount. How is "Plasticine"different?

M.J. Adam: In our work, the heated platens were in contact with the "Plasticine"for a relatively short time interval such that only a thin layer was heated. Consequently,the interfacial shear stress was reduced

without any effect on the normal stress. This is analogous to Tabor's study of nylon friction using a spherical steel slider. He found that, in the presence of water for short contact times, the friction coefficient was reduced due to plasticisation of the surface layer. As an additional point, for long contact times the friction increased due to an increase in contact area arising from bulk plasticisation . For a soft solid such as "Plasticine", this effect would not occur because the real area of contact is approximately equal to the apparent value.

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SESSION IX GRANULAR LUBRICATION Chairman :

Professor Brian Briscoe

Paper IX (i)

Numerical Experiments with Flows of Elongated Granules - Part II

Paper IX (ii)

Particulate and Granular Simulation of the Third Body Behaviour

Paper IX (iii)

Measurements and Modeling of Granular Flows in the Collisional Lubrication Regime

Paper IX (iv)

A Simple Model for Granular Lubrication; Influence of Boundaries

This Page Intentionally Left Blank

The Third Body Concept / D.Dowson et al. (Editors) 1996 Elsevier Science B.V.

347

N U M ~ ~ V ~ F U ) W S W R L O M X ” ~ - t A K I ” U W o l d G. Blrod, Old Saybrook, CT,USA This papa is an extension of earlier work with granular-flow simulations.The behavior of infinitely-wideflat sliders upon a granular carpet is calculated. Distributions of normal and tangential stress are determined by timaaveraging. In many respeds the granular conglomerateexhibits fluid behavior. Inclination of the slider is shown to generate lift Over considerableranges of the operating parameters the normal and tangential stresses at the slid@exit are shown to be of comparable magnitude

The purpose of this paper is to predict the flow behavior of weat and/or powder particles using numerical simulations of granule-granuleinteraction. The present investigation is an extension of work reported in an earlier article’. T here, for infinitelylong particles, the Couette-flow configuration was explored &tr a variety of interaction parameters. At the conclusion, some preliminary results were given for the “slider-beanng”configuration here to be studied’. Justification for certain aspects of the present tmtment cen be hund in the earlier paper. But it must be admitted that gross simplifications have been

mtrodwed in order to pursue the analysis. When such simplifications are success&l, they are said to show “insight”; when they hi1 they are deemed “naive.” Here we take that risk! The onus is lessened when we declare that we do not expect here to make accwate predxtions of granular flow. Rather, we expect that the results will suggest relations useful for the empirical reprasentation of expenmental results. With numerical calculations it is possible to “get inside” the flow -- a feature of assistance in the formulation of constitutive relations. In 1990 the writer presented an analysis of COW Oowl based on constitutive equations consistent with the theory of HafP. Th~swork was not pursued to publication because no way was seen

’ In this preliminary study, the intrinsic calculations were correct,but the total forces were

incorrectly summed, l d i n g to conclusions at variance with the v e n t findings.

logically to connect the pressures within a slot to those existing in the ambient. Quite independently, and more recently, Khonsari‘ and co-workers have extended a similar treatment to load-supporting configurations. At the bearing entrance they have imposed an impact pressure, and in place of an exitpressure boundary-condition they have imposed a center-of-pressure suggested by experiment‘. The agreementwith sxpeormentthen obtatned is encouraging, but clearly more knowledge concerningappropriate pressure boundary-conditions is desirable. An objective here is to add to this knowledge. For the sake of brevity, we shall give here only the absolute minimum of analysis necessaryto make the presentation self-contained.

Figure 1 shows the physical situation to be analyzed. An infinitely wide flat slider bearing slides over a carpet formed of granules. The lift and drag exerted on the slider are sought. The existence of rough walls is mimicked by the positioning of equis paced granules whose motion, or lack thereof, is specified. The slider is roughly half the length of the computational field. (See Figure 2). Granules are anayedwithin the carpetand become disanayed when encounteringthe slider. “Measurements”are made as indicated in the figure. The granules are represented by cylindrical Grce fields, with a cutoffat radius, a Figure 3 depicts the interaction oftwo similar granules with center-tocenter -on of distance, r. The normal force of repulsion, F,, is shown. The quantities ”G’ and “k” are material properhes. The choice of an exponential function is convenient. but arbitrary. The tangential force. F,, is given by a Coulombfiction expression. The efFaxs of pmcle distortion during collision rn

348 neglected, except that the “arm” for interchange of angular momentum is taken as rl2, rather than “a”. Multi-particlecollisions follow the same treatment

F,,with separation, a fi= F, with separation, 2a hF

Energy of approach 2 a to a KE of Moving-Plate Granule, 1 / 2 M w U ~

To characterize more conveniently the physical properties of the granules. we introduce two dimensionfree parameters, the “force ratio,” fr, and the “hardness ratio,” hr.The second of these parameters, hr, relates the granule hardness to the magnitude of the impact the gmule is likely to receive. It is important that the granule be soft enough for the computation properly to sample the collision process, but not so soft as to permit gross distortion. From the two defined parameters,6 and hi, we identify:

k = loge(fr)

The number of variables to be explored is greatly reduced by the use of dimensionlessvariables.

To render the equations dlmensionlessthe following ”

feasible, all calculations were performed with the following set of parameters, selected on the basis of the earlier study (Ref I ).

Hardness ratio, hr = 5 Force ratio, B = 3 Restitution factor, fac = 1 on approach fkc- 0.8 on retreat Time increment = O.W(a/U.) Wall particle spacing (center-to-center)= 1.33 dims Total dimensionlessrunning time: 1OOO Gaps ranged from 5 to 10 granule diameters Gaps H,, H,and H,were varied extansively The coding was in PowerBASIC 6, a compiled, k t,versatile form of BASIC, backwardlycompatible with most earlier BASICS. It incorporatm a built-in first sort routine. Running times on IBM clones with CPU’s 486 DX 66 and 33 ranged from 1 to 7 his.

DlscusslonQfResults All macroscopic results for the slider on granules must be statistical averages, in space or in time. In our numerical experiments,the shim oosition maintained Runs were started with the free granules randomly distributed. Because the coding reset exiting and wayward granules, results for the m e o v d l configuration usually tended to the same average values. But there was some evidence of irreproducibility which cannot yet be documented. Some ofthe ‘‘rogue” d t s were, no doubt, causal by entrapment of a “free” granule by wall granules.

w.

The configuration chosen for most of the illustrations has H1=10,H2=5, H3=4and a length of 37.5. Figures 7 and 8 show the load’ buildup as a function of computing time based on two averaging periods. After an elapsed time of about 300, the load tendsto fluctuateabout an average of 30.That is, after

units” were us&. length: a, in equations,; 2a, in figures. mass: M of free particle time: a/U,

All particles, free as well as wall-attaohod,were taken to be the same size. Again, to make the present study

1

In this paper, a dimensional stress is the force on a granule made dimensionless through division by h&U,’/a, and a dimensionless load is the sum of these individual stresses over all relevant wall granules.

349 about 2 passes of the plate past the slider, the load has reached its asymptotic behavior. The deviations from a timeaveragemean depend on the averaging period, and in any given system, their significance would depend on the inertia associated with the load. Figure 9 shows the normal stress and the shear stress on a slider riding on a catpet 4 granule diameters thick, with a gap ratio of 2:1 and a trailing gap of 5 diams. The carpet would just pass through this trailing gap if jostling of the particles did not occur. Because the slope of the slider is much greater than typical lubrication values, being I / I 5, there is a substantial component of lateral thrust (included as shear) upon the slider. The normal stress on the plate should be in substantial agreement with that on the slider, as shown in Figure 10. Corresponding velocity profiles are shown in Figure 1 1. These certainly resemble those found in the classical lubricating flow of a Newtonian liquid. Reverse flow is seen to occur on the slider-sideof the entrance. Slip occurs at the gap surfaces. Averaged freeparticle counts for the crossgap bins are shown in Figure 12. When the end-bin counts are increased by % to account for volume excluded by wall-fixed granules, the transverse distributions are seen to be relatively uniform. The corresponding longitudinal plot of the mean trsnsverse density (relative magnitudes, only) is shown in Figure 13. As might be expected, the relative density ISgrrater in regions of higher normal stress. Figure 14 explores the effect of inclination fix a fixed slider length of 37.5 diams. and carpets that would, without jostling,just fit through the slot exit. The maximum lift at HI /H2-2.5 is reminiscent of the result for the classical slider bearind. But behavior at the extreme thicknsss ratios is not. Note,in particular, that there is load capacity even without inclination.In 3

The finding of a significant effect due to inclination is at odds with an erroneous conclusion in ref. 1. In that earlier work, no distributionsof force were cal-culated,and an erroneous summation of forces was made.

ref 1 it WBS shown that there is a normal stress generated wen in Couette flow. Table I summarizes some of the results of the simulation runs. The results for the entrance normal stress on the slider w e obtained by spline least-squarecunre-fit extrapolations6om the interior pcluding & gnrrance node. The inlet normal stress is approximated by:

N1

=

2 8 7 E - 0.19H2 HI

The ratio on the slider of the exit tangential stress to the exit normal stress (a local friction d c i e n t ) is approximately:

N2 These approximations are tentatively suggested for use with continuum-theory approximationsof similar slider configurations.

It is a great pleasure to acknowledge the mcouragemont of David E. B m , who monitored this work, sponsored by the Army Research Laboratory under NASA Contract NCC3-29 I .

350

TABLE I TABULATION OF RUNS4 N1

N2

H1

H2 H3

10 10 10 10

5 5 5 5

3 4 7 9

37.5 37.5 37.5 37.5

0.212 0.25 0.77 1.54

0.295-0.23 20.61 0.502 1.07 0.96 1.22 1.13

10 3 10 4 10 5 10 7 10 9 1 0 10

2 3 4 6

37.5 37.5 37.5 37.5 37.5 37.5

0.11 0.28 0.15 0.423 0.53 0.564

0 . 9 n 9 T -7r72- 6 0.55 0.5 1.06 0.62 0.56 1.72 0,175 0.138 1 . 7 3 0.13 0.09 2.29 0.14 0.08 2.61

1.3 0.35 1.39 1.4 1.36

0.27 - 7 . h 5 . 3 1.0 0.625 0.88 1.25 0.76 1.08 0.75 0.47 1.41 0.25 0.125 1 . 5 8

a

9

LEN

5 4 3 7 5 5 3 2 7 5 5 3 3 5 6 5 4 3 5 6 5 5 4 5 6

1.

T2 Effect

FLO

of

t 1.59 1.96 2.15

%SOL

LIFT

SHEAR

.7 79 .1 91 .8 104

12.4 28.5 50.8 68.9

5.25 14.7 26.4 35.1

19.5 20.5 32.7 12.3 11.8 11.6

9.81 10.3 16.9 5.44 5.24 5.06

85.1 82.8 97.3 84.8 62.8

39.8 37.6 44.2 38.2 29.3

Effect of Inclin ation

5 . 5 71.5 82.7 65.6 63.9 64.5

Effect of Len th 85.5 107 101 85.1

Nwnericul Experiments with Flows of Elongated Gmules, Harold G Elrod and David E. Brew, Leeds-

Lyon Symposium,Lyon, France, Sept $6,1991 2. plleliminary ?%eoryfor Gmnule-Lubricated Bearings, H. G.Elrod. Meeting chaired by Prof D. Fuller, Wright Patterson Airbase, August 1990. 3.

Gmin How 0s a Fluid-MechanicolPhenomenon,P. K. Haff, Jnl. Fluid Mech. (I 983), vol. 134, pp. 401 -43

4. An Analysis of Powder Lubricated Slider Beurings, K.T.McKe~ague& M. M. Khonsari, to appear in the A S. M. E. Jnl. of Tribology. 5. 7%eQ u a m - H ~ m @ a m iMechanism c of Powder Lubrication: Part IT-Lubricant Film Pressure profile, Hooehang Hcshmat, Jnl. ofthe Soc.of Tribologists and Lubrication Engineera, vol. 48, no. 5, pp. 373-383.

6.

PowerBASIC, version 3.2, PowerBASIC, Inc., 235 Oak St - Suite 21, Brentwood, CA 94513. ~

' N1= n

~~~~

o d stress at entrance.N2 = n o d s-s

at exit T2 = tangential stress at exit.

35 1

Figure 5 oMu10 plaan Midway in Slidar Enbmcglo; Exit=s;Lmgth=37.s

&peP=l;

352

,

0

30

4m

am

nmt PI~UN 8 L A vs Time (luge at)

CUpsN.EatMcCrlO, Eat-5. Lslgth-37 5

353

l . . . I . . . l .

. . , . . . I . . .

I . . . , . . . ,

i

- JI --

1i

-1

1I

F i p m l2Vaioua TMIMMPUlideDimibutiona CupU= 4;Eatnnw = 10; Exit= 5-; = 37.5

354

Pi-

--

13 Rolrtive Dauity witbin clrp (Global %sotidm 80% ) Cupt- 4; Enbanm- 10, Exit- 5; La@ 37.5

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

355

Particulate and granular simulation of the third body behaviour A. Ghaouti, M. Cham, P. Dubujet and F. Sidoroff Laboratoire de Tribologie et Dynamique des Systemes, URA CNRS 855, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, B.P. 13 1 , F 6913 1 Ecully Cedex , France lntermedate between molecular dynamics and granular mechanics, particle mechanics is t ~ s e don a d r e c t numerical simulation of the quasi-static behaviour of a particulate aggregate with molecular type interaction laws. Two different types of simulations are presented with special emphasis on the post processing analysis. For application to friction and wear, these methods are exemplified on the two dmensional monotonous and cyclic shear behaviour of a n ;imorphous third body layer between crystalline first and second bodies. Influence of the third Iwdy thickness, normal load and loading condtions are discussed. 1. DISCRETE MECHANICS PARTICLE AGGREGATES

OF

1.1 Introduction

The third body which exists or is created in the contact of two rubbing solids often cbxhibits a granular or particulate structure. This may in fact occur a t Mferent levels : it IS of course well known that the creation, twhaviour and evolution of wear debris often plays an essential part in the friction and wear mechanisms 111. This particulate structure however may also appear a t a more microscopic level like for instance in colloidal lubrication where the interaction between colloid particles partially controls the action of the lubricant. From a more fundamental point of view iind in opposition with the bulk behaviour which can essentially be described a t a macroscopic and continuum level, a correct understanchng of surface phenomena I ~ s i c a l l y requires a description a t the microscopic molecular level which is responsible for such effects as surface tmergy, capillarity adhesion, etc. .. The discrete nature of materials and in particular of the third body must therefore be taken into account. Direct simulation and the wrrespondng numerical experiments it

provides appears as a natural tool for this understanding, complementary to the usual macroscopic mechanical analysis. Particulate mechanics is such an approach, in some sense intermedate between molecular dynamics and granular materials The purpose of the present work is to present this approach and the underlying assumptions and to exemplify its application to friction and wear problems. 1.2 Molecular dynamics The description of matter as a n assembly of interacting particles is a very old idea in physics. Omitting earlier attempts it is indeed the starting point of statistical physics. Naturally the development of computers allowed the d r e c t simulation of such a n assembly and resulted in the apparition and development of molecular dynamics. It is simply based on the integration of Newton’s equation of motion 2-

mi--d x i dt2

-

c F~~ j*i

for each particle under the interaction of all remaining ones.

356 Initially restricted to the description of the thermodynamic equilibrium of an isolated homogeneous system by using the energy conservative Verlet's algorithm and periodxity condltions, it has progressively extended its range and provided a deep insight in several fields, primarily in the physics of fluids [2l. More recently it has been applied to a variety of problems in tribology. A typical and historically interesting example is the molecular stick slip model developed by M. Robbins 131 where it was shown that some stick slip like behaviour can be obtained as resulting from the regular "liquefaction" of an otherwise solid like interfacial layer. This kind of approach has also given nice results about the velocity dependence of friction as well as about different friction regimes. The approach of U. Landmann [4] is more systematic, and probably more quantitatively realistic due to a sophisticated physical analysis of the interaction laws to be used. It has been applied to quite a variety of contact and friction problems with or without lubrication. The work of Belak [5] as applied to indentation is also worth mentioning. Initiated at a molecular level, these ideas can also be applied a t a more macroscopic level for the description of granular lubrication 161, the usual pair interaction law being then replaced by a more complex granular interaction including friction. A basic characteristic of all these new applications is the fact that they do not concern, as initially, a periodically simulated infinite system but a confined system at least in some directions i.e. in some sense a molecular or granular aggregate. 1.3 Granular mechanics

From a quite different point of view similar ideas have been developed in civil engineering for the description of granular materials like sand. A striking feature of these materials is the contrast between a very simple material structure - an assembly of rigid spheres with Coulomb friction is quite representative - and the resulting very

complex behaviour. Homogenization methods however imply u f i c u l t conceptual problems 171 and again numerical simulation appears as an appropriate method. Cundall's approach is quite typical of this trend IS]. Essentially it is again based on the integration of motion equations for all particles

with viscous damping and where the interaction is limited to adjacent grains with appropriate normal and tangential contact laws. Although quite similar to (l), this approach is quite different for it does not pretend to a precise physical description of microscopic dynamics and rather considers the particle mass and viscosity as numerical parameters to be chosen for a proper numerical behaviour of the integration algorithm used. The left hand side of (2) must rather be viewed as a numerical regularization for solving the quasi-static evolution problems. Somewhat different in its scope, J.J. Moreau's approach [9] is based on a more rigorous integration of the dynamical equations for rigid particles with contact interaction laws derived from convex analysis. In fact it is quite similar to the so called "hard sphere" model of molecular dynamics but with a different field of application - namely macroscopic granular materials. The dynamical equations are here properly treated but the interaction laws as well as the dynamic time scale involved cannot be directly applied to the mechanics of materials. 2. PARTICULATE MECHANICS

2.1 Basic framework and assumptions The simulation method which wlll be presented here is essentially intermedate

357 between the two main streams described above and in some sense parallel to d .J. Moreau's approach which uses molecular dynamics techniques for solving granular problems. Here we shall use the techniques of granular mechanics to solve molecular problems or more generally problems for which the interaction between particles is not of contact type but rather based on pair interaction. Its basic physics will be the "quasi static equation of motion (2) 'I

inappropriate for liquids but in case of solids subject to external loadmg the basic physics will remain, namely quasi equilibrium evolution with temporary instable transitions. A nice representative experimental framework is also provided by bubble raft models [ 10, 111. 2.2 Viscomechanical approach The numerical resolution of (3) of course requires some numerical regularization. The simplest algorithm will be defined by

(3) j#i

At

xi( t + At) = xi( t) + -Fi(t) Pi

where the force acting on each particle results from external sources to be discussed later and from the interaction with all the other particles with an interaction potential

The simulation which will be presented 1)eIow are often based on a Lennard-Jones potential

L

Alternatively this can be considered as the Euler integration scheme for the "viscomechanical" equation of motion

but this has no real physical meaning and must rather be considered as a numerical convenience for a) following the quasi-equilibrium evolution b) resolving the temporary instable transitions

J

with n1= 12 and n 2 = 6 . Here e,, the bondmg energy, and q,, the equilibrium separation are the basic physical characteristics. In particular it should be remembered in the following that the circles representing the particles are not material and may overlap. Contact between particles may be conventionally defined but it does not have an intrinsic physical meaning. With respect to molecular dynamics this model obviously ignores dynamics i.e. thermal fluctuations. It will therefore be

Fw' I

v

Figure 1. Particle wall interaction. In this approach the particulate aggregate is deformed and loaded by the motion of some "walls". A wall is a kinematical solid defined

358

t)y its interaction

law with all particles expressed in the wall coordmate system X, Y (Figure 1). This allows ddferent kinds of walls to be defined - smooth walls : linear, angular, circular,... -particulate wall consisting in a finite number of particles with fixed relative positions, -gravity force can also be simulated as a wall. The motion of these walls can be controlled under fixed velocity or force both in the X and Y hrection. The correspondmg software MI'ART has been developed in C++. It is limited to finite aggregates and do not allow periodicity conditions, 2.3 Cundall's approach Cundall's approach 181 is based on the "viscodynamical" equations (2) and it uses a central finite Uferent scheme

This algorithm was implemented by (hndall in the TRUBAL software (which in a more sophisticated and commercial version has now become FLAC) initially developed for simulating the behaviour of a (periodically simulated infinite) granular material. In order to use it for tribological problems it was necessary to CB m o M y the interaction law by introducing in addition to the existing linear elastic contact law accounting for the repulsive part of the interaction an attractive part which in the present version is taken as

with two parameters K and n which are adjusted in order to fit the experimental data obtained on bubble raft adhesion experiments

@develop a consistent treatment of a finite aggregate through the introduction of moving walls to control the loading process. I t must be noted also that this confinement may be restricted in some direction, while keeping periodicity condition in other dwections as frequently assumed in these problems [4][6]. 2.4 Data analysis and post processing The fundamental result of all these simulations is the position of all particles and their evolution, which for a standard test amounts to a large quantity of information. Post processing of these results is therefore essential to extract the physical information and insight which are expected from this kind of simulation. In addition to the motion and rearrangement of all particles, the global force displacement structural response is a dwect output. This response in general obviously results in rather jagged curves manifesting the disordered aspect of the particulate process. The other available treatments and visualisations are the following -a vectorial representsation of the velocities or hsplacements of each particle. revealing the localization process which frequently occurs at W e r e n t time levels. A local representation of the desequilibrium force on each particle is also available showing the hsorder repartition and evolution - a visualisation of the contact forces. This treatment is a basic result in Cundall's approach which includes contact as an essential concept. It is less natural in our molecular static problem where contact is purely conventional. - a local stress tensor may be defined on each particle by

359 which is the localized form of Weber's formula [7] giving the macroscopic stress in granular homogenization. It also corresponds in the quasi-static-limit with the virial expression used by U. Landmann 141. A similar relation can be defined for deformation but it still has to be implemented. - different kind of statistical treatment can also be realized following the usual treatment in molecular dynamics I121. More generally post processing is a critical step in these simulation and probably is. with the computation size, the major Miculty for the three dimensional extension which otherwise presents no conceptual ddficulty. All the simulations presented here will be two dimensional. They will be focussed also on global response. 3. APPLICATION TO FRICTION AND WEAR 3.1 The basic simulated experiment

Friction and wear will be simulated by the shearing of an amorphous layer (third body) between two crystalline bodies. One fundamental aspect of particulate materials indeed is the different behaviour for Crystalline materials (all particles have the same size) and amorphous materials (vonsisting in particles of different diameters). This difference appears as well in the global behaviour (crystalline material is stronger than amorphous material) as in the M e r e n t observed micromechanisms for deformation [lo][111. The basic experiment therefore will start from initial configurations obtained by locating an amorphous layer between two crystalhe substrate and then applying a fixed normal load to these substrates. The configurations wlll then be deformed by a monotonous or cyclic shearing motion imposed to the two substrates. Two different kinds of loadmg condtions will be considered - constant normal load F, (controlled force) - constant normal &placement z (controlled v docity)

while the shearing motion will be realized under constant velocity. Two u f e r e n t kinds of simulation has been performed 0 A set of simulations has been realized using the viscomechanical approach, on rather small configurations allowing a systematic analysis (influence of the layer thickness, of' the applied load, of the loadmg condtions). 0 A few simulations have been realized both in the viscomechanical and in Cundall's approach on a larger configuration. These simulations will be described later. 3.2 Other applications

Other simulations related to contact mechanics and tribology can be realized. Adhesion and the related instabilities (adhesive avalanche and rupture) can be simulated by the slow approach of two blocks followed by their separation. This corresponds to soap bubble experiments [ 111. Indentation of a half space by a crystalline punch also corresponds to bubble raft experiments. A description of these experiments will be found in I131 clearly showing qualitatively the very Mferent behaviours obtained for a crystalline and amorphous half-space. More details and examples of visualisation will be found in 1131.

4. SMALL SIZE SIMULATIONS 4.1 Analysed configurations The material consists in three kinds on particles with chameters 0.7, 1 and 1.4. A crystalline two dimensional material with 12-6 Lennard Jones interaction can be shown to obey the 2D Hooke's law with

G----

eo

n

E = 8Gl3

v=1/3

The interaction law have thus be chosen so that for the crystalline material G = 60 (the amorphous stiffness will of course be much

360 lower and cannot be predcted theoretically). Strictly speaking (10) determines the bonding cnergy e, only for the interaction law between identical particles. For different particles. there is no clear rule for choosing e,. Idere some averaging procedure have been used.

0.7 and 1.4 in a 4:1 ratio. These three configurations J, K and L respectively are shown in Figure 2. 4.2 Squeeze behaviour

Starting from a load-free configuration these three configurations have been squeezed. Figure 3 shows the corresponding response curve (relation between the normal force F, and displacement z) for these three configurations J, K, L. A regular monotonous behaviour is obtained except for some accidents. These accidents are obviously related to particle rearrangements. This is confirmed in Figure 3 by the fmax curve for the L configuration, where fmax is the desequilibrium, a measure of the local dsorder. These local irreversible transitions appear sooner for the thick layer L.

501 a

40

0 I

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Figure 2. Small size configurations. ,I (25 particles in the amorphous layer) K (50 particles) and L (75 particles). Only the amorphous third bodies have been presented for configurations K and L. Each crystalline substrate consists in particlcs of diameter 1 with more particles constituting the wall through which the system will be actuated. Three dflerent amorphous layers with thickness in ratio 1 :2:3 have been generated respectively consisting in 25, 50, 75 particles of hameters

0.1

0.2

0.3

0.4

Figure 3. Squeeze behaviour. Figure 4 shows the particle oz dlstribution, as defined in (9), obtained for the final state of the L configuration (white particles correspond to the tensile or low compressive values while black correspond to high compressive values. It follows from this diagram that most particles are in a compressive state but that the stress is non uniform with some tensile stressed particle near the boundary and even inside the amorphous body. In fact the compressive

36 1 force seems to be mainly transmitted along some particle lines, a well known fact in granular materials.

Figure 4. Stress distribution in the loaded L configuration.

test is related to a substantial vertical &sp lacemen t .

I

-20

0

For each configuration J, K and L, three initial configurations have been defined correspondmg to an applied normal F, force of 0, 18 and 36 (configuration 0, 1 and 2 respectively). Nine initial configurations are thus defined ,JO. J1, 52, KO... 4.3 Simple shear behaviour These configurations have been subjected to a simple shear motion of amplitude 8 which corresponds to a maximum shear of about 60% for the L configuration, slightly more for the others under two ddferent ioadmg condtions -- constant normal force ( F, =0, 18 or 36) (test JOGP, J 1GP, ...). -- fixed normal dsplacements (test JOGZ, ...) An example is given in Figure 6 which shows the response for the L l C Z test (initial cmfiguration L1, shearing with fixed hsplacement). They give the tangential F, i ~ n dnormal Fz force as a function of the A relative horizontal displacement. significant relaxation of the normal force F, is observed while the tangential friction ('urve is irregular but without significant change. The tangential force F, is also shown on Figure5 for the LlGP curve (shearing under constant normal load). This

I

I

I

1

2

3

. . ....

X

I

I

I

I

i

4

5

6

7

6

Figure 5. Simple shear. The other tests show similar tendencies. 4.4 Cyclic shear behaviour Cyclic shear of amplitude k 2 (k 14% for the L configuration) have been realized under the same loadmg condtions (fixed normal load or fixed normal hsplacement). Some of the obtained results are presented in Figures 6-9

30

-

20-

Fx

10-

0- 1 0-

-20-

-30 ! -3

X

I

-2

I

1

I

I

1

-1

0

1

2

3

Figure 6. First L1Z cycle (constant normal bplacemen t).

362 Figure6 represents the response for the first L1Z cycle : tangential force F, as a function of x. Again a quick relaxation of the normal force F, is obtained even leadmg to negative force (attraction) is the second half of the first cycle. Figure 7 represents the first three cycles of the same test with the same convention (dotted lines for F,). It shows no significant evolution of the cycles. The F, behaviour seems also quite disordered around a zero mean value. 301

constant z &placement because the normal load then quickly relaxes as shown above.

1:4j.N

-

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

12

.........

0.8+-g1

--

0.61

..........

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

-

..................... ........-

...

\

Oe4i 0.2 N

:

-0.2 -2

1

I

I

I

-1

0

1

2

I

I

I

1

-1

0

1

2

301

:

-30 -2

X I

I

I

I

i

-1

0

1

2

3

Figure 7. First three cycles L1Z. Figure8 shows the influence of the applied normal force. This is exemplified on the L configuration and for cycling under constant normal load: the LOP, L1P and L2P cycles correspond to the three applied normal forces 0, 18 and 36 respectively. The influence of this normal force on the tangential hysteresis curve is rather small. There may be a slight increase in the shear force level with the applied normal force. The essential effect however is on the vertical deformation which becomes much higher when the normal load increases. This is of course related to the high h/l value for the amorphous layer. In fact this effect still exists in the J and K configurations but it is much smaller. The influence of the initial state is of course not significant for the LOZ, L1Z and L2Z tests a t

X

-2

Figure 8. lnfluence of the normal load. Finally Figure9 shows the influence of the layer thickness. This is exemplified on the first cycle under constant normal displacement ( J l Z , K1Z and L1Z tests). The thick layer corresponds to a rather regular response, while irregularity is increased for thinner layers. It is however not clear whether this results from the layer intrinsic thinness or from the smaller h/l ratio. The first reason

363

seems more plausible but further simulations would be necessary.

-1

-2 -3 -40

Figure 10. Large size configuration

!

I

I

1

I

-2

- 1

0

1

2

Figure 9. Influence of the layer thickness 5. LARGE SIZE SIMULATION

5.1 Presentation A larger size

simulation has been developed involving two particle sizes and 1172 particles. The initial configuration is shown in Figure 10 for the MPART simulation. The corresponding TRUBAL simulation uses the same particles arrangement but with periodicity in the x dwection, which implies some differences in the wall geometry. The two simulations (MPART and 'I'RUBAL) have been performed on the same geometry. They are however not directly comparable @ the interaction laws are not the same Jones for MPART and (L,ennard superposition of a linear repulsive contact law and a power law attraction for 'I'RUBAL) . @ the lateral boundary conditions are not the same (free boundary for MPART, periodicity conditions for TRUBAL).

6.2 Shearing response

The TRUBAL cycle response is represented in Figure 11 for the five first cycles. The behaviour which is rather irregular in the first two cycles seems to regularize later, with no signdicant evolution of the mean behaviour.

F x / L(N/rn)

0.0151

-p---.

-0.010I

Y (96)

The corresponding MPART simulation is shown on Figure 12 both under fixed

364 &placement (F, and F, response) and fixed normal load (F, response) for the first loadmg (x = 50 corresponding to y 12%). The result is surprisingly different. One reason for this probably is the free boundary effects which leads to a very high compaction of the amorphous layer. Further analysis is required.

-

Fx-fixed Fz Fx-fixed z

........... R-fix4 z

(which is equal to 1 in the crystalline part). Evolution of this profile in the first 10 cycles is presented on Figure 13 showing a significant wear of the first crystalline layer. 6. CONCLUSION

More simulations are required in order to correctly understand the influence of all parameters. The presented results however show the physical insight which may be obtained for friction and wear by using these simulations.

REFERENCES

15

1. Y. Rerthier, L. Vincent

2. x

't

0

I

I

I

I

1

10

20

30

40

50

3.

Figure 12. Shear behaviour MPART. 5.3 Wear evolution

4.

-

Initial slate

% of small bubbles

Alter 10 cycles

5.

1.0-

0.9-

0.8-

0.7-

Wear of the crislalline layer

0.60.5 0.4

.h Rearrangement 01 bubbles in the amorphous layer

!

I

I

I

I

I

0

100

200

300

400

500

Thickness (lrubal

unil)

6. 7.

8.

Figure 13. Cyclic wear evolution The wear of the crystalline first and second bodies can be characterized by the z profile of the proportion of small particles

9.

and M. Godet. Fretting fatigue and fretting wear. Tribology International, E&t. Butterworth, 22 (1989) 235-242 J.P. Hansen and I.R. McDonald, Theory of simple liquids, Academic Press. London, 1986. P.A. Thomson and M.O. Robbins, Shcar flow near solids : Epitaxial order and fluid boundary conchtions, Phys. Rev. A, 4 1 ( 1990) 6830-6836. U. Landmann et al., Nanotribology and the stability of nanostructures, Jpn. J. Appl. Phys., 32 (1993) 1444-1462. J. Belak, D.B. Boercker and 1.F. Stowers. Simulations of nanometer scale deformation of metallic and ceramic surfaces, MRS Bulletin, May 1993. p.5560. A.A. Lubrecht and Y. Berthier, Granular lubrication : A simple model and trend, Leeds-Lyon '94. P. Dubujet, F. Emeriault, B. Cambou and F. Sidoroff, Ganular homogenization : the elastic case, European Journal of Mechanics, to be published (1995). P.A. Cundall and O.D.L. Strack, A chscrete numerical model for granular assemblies, Gbothechnique, 29 (1979) 4765. J.J. Moreau, Some numerical methods in multibody dynamics : application to granular materials, European Journal of

365

Mechanics /A, Special issue (2nd ESMC (fenoa) 13 (1994) 93- 114. 10. D. Mazuyer, J.M. Georges and B. Cambou, Shear behaviour of an amorphous film with bubble soap raft model, J. Phys., 49 (1989) 1057-1067 11, D. Mazuyer et al., De l'utilisation des bulles de savon. Film produit par Lipsis Production, CNRS, MESR, 1991. 12. A. Ghaouti, P. Dubujet and B. Cambou, Analyse statique d u n ensemble de grains bvaluation d'une en interaction : cohhion, Congrhs Franpis de Mbcanique, Lille, Septembre 1993. 19. B. Cambou, M. Chaze, P. Dubujet, A. Ghaouti, Y.M. Lamidon and F. Sidoroff, Discrete models €or contact problem, Proceedmgs of CMIS (Carry-leRouet, Septembre 1994), Ed. M. Raous and P. Chabrand, Plenum Press.

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The Third Body Concept / D. Dowson et al. (Editors) (0 1996 Elsevier Science B.V. All rights reserved.

367

Measurements and Modeling of Granular Flows in the Collisional Lubrication Regime Juin Kima, Chih-Ming Yua and John Tichyb a Graduate Students

b Professor and Associate Head Department of Mechanical Engineering, Aeronautical Engineering and Mechanics Rensselaer Polytechnic Institute Troy NY 12180-3590USA This paper concerns an annular flow sliding shear cell experimental apparatus in which we have observed a process we call granular collisional lubrication. There is a critical speed when the motion becomes smooth and the surface separation increases. Presumably, the particles are strongly agitated by the sliding surface and colliding with one another, rather than rubbing. This is the onset of granular collision lubrication. Among the key experimental findings are that for both sloping and parallel surfaces the normal (pressure) and shear stress are proportional t o the square of the shear rate. The primary feature of granular collisional lubrication is that significant load carrying forces are generated from the so-called "wedge effect" as in hydrodynamic lubrication, but equally from the collisions in simple parallel shear flow (the flat surface case). We present a constitutive equation which can exhibit a rheological normal stress in parallel flow and thus better model granular lubrication as a quasi-hydrodynamic process.

1. INTRODUCTION Over recent years there h a s been increasing interest in the possible use of granular or powder mixtures as a means of applying solid lubrication. Low heat rejection high temperature diesel engines with the potential for higher thermodynamic efficiency and reduced energy consumption have been a goal of energy planners since the energy crisis of the 1970's. The gas turbine industry and various US government agencies hope t o double engine thrust-to-weight ratios by increasing temperatures t o 800'C. At t e m p e r a t u r e s g r e a t e r t h a n 5OO0C, conventional liquid lubricants cannot be applied. Most lubrication schemes at these higher temperatures have centered on solid

lubricants: applied as coatings, generated as replenishing films, or introduced as flowing granules. In this study, the granular flow concept is studied. There are a large number of studies on various aspects of granular flows as applied to tribological conditions. Elrod [13 has reviewed existing literature to 1988. Most attention is paid to papers which model the mixture a s a continuum, and the particles are accounted for by concepts borrowed from the behavior of dense gases. The "granular temperature," proportional to the square of the velocity of particles relative to the mean flow, becomes a key variable. Papers cited by Elrod include those of Haff [23 (theoretical), Walton and Braun [31 ( m o l e c u l a r d y n a m i c s simulation), and Savage and Sayed [41

368 (experimental), etc. Since 1988, papers in the tribology literature have appeared by Dareing and Dayton [51, Heshmat and Walton [61, Heshmat [71, Heshmat [81, Dai and Khonsari [91, Dai and Khonsari [lo1 and Dai et al. [ l l l , etc.. Dareing and Dayton fit measured behavior of proposed lubricating slurries to known rheological equations such as the Bingham plastic fluid model. Heshmat has performed experiments on thick-film bearing test rigs with powders. Khonsari and co-authors apply more complex constitutive equations for mixtures. Often, underlying t h e constitutive equation or the solution method is the assumption of a small effect: dilute suspension, small particles, etc. Other theories available are due the work of Jenkins [121, Jenkins and Richman [131, Johnson and Jackson 1141 and Lun, et al. [151. The differences among the cited papers include different treatments of the boundary conditions (one cannot just set the particle velocity equal to the surface velocity), and different particle mechanics assumptions (elastic collisions, nearly elastic collisions, etc.) to arrive a t different constitutive relations for the momentum and energy fluxes. In this paper, a process called granular collisional lubrication i s studied, as observed in an annular shear cell apparatus. The shear cell consists of a lower circular cylinder slot in a rotor which is filled with spherical beads (granules). The rotor slides with respect to a stationary weighted upper circular cylinder which fills the slot and compresses the beads. At low speeds, the rotation is accompanied by vibration and grinding noises, apparently due to strong frictional forces between t h e highly compacted beads and the surfaces. At some increased critical speed, the machine suddenly quiets down, and the upper surface lifts off a s the beads become separated due to increased agitation. This is the transition t o granular collisional

lubrication. The former regime could be called granular frictional lubrication. The current study extends the annularshear-cell experiments performed in an earlier paper, Yu et al. [l61, and presented to a primarily rheology audience. In addition, a constitutive equation is proposed which seems to display key features of the process. A quadratic dependence of the stresses upon effective shear rate and the lubrication wedge effect are found. The present paper includes studies of the variations of the stress with solids fraction and the effects of the particle size and surface roughness on the shearing flow.

2.DESCRIPTION OF EXPEXUMENT The experimental apparatus is shown Figures. l a and lb. The present shear cell apparatus has been used in experiments on dry metal powders by Craig et al. [171 and [MI. A more detailed description of the apparatus can be found in these papers, as well as Ref. [lSI, and Yu's dissertation [191. The shear cell consists of two concentric horizontal aluminum disks t h a t are mounted on a rotating vertical stainless steel shaft. The bottom disk has an The annular channel 19 mm wide. channel is 19 mm deep with a mean radius of 68 mm. The shear area is 8117 mm2 and the channel mean length is 0.479 m. The granular material to be tested is contained in the channel. The top disk has an annular protrusion that fits into the channel of the bottom disk. The top disk is free to rotate in order t o measure the torque caused by the shearing action of the granular material, It also is free t o translate in the vertical direction, so as to allow for expansion or contraction of the granular material under shear. Thin ring-shaped pieces are fastened to the upper and lower surfaces of the channel. Depending on the transmission rings used, rough o r smooth shear surfaces are presented to the beads in the channel. The

369

Top Disk Assembly

Counterweight Tr

4

Bottom Disk

' I

I

m

Force Transducer Mounting

L

Flexible Coupling Gear Reduction Unit Motor

Speed Controller

1 1

/

I

I I

Figure l a - Sketch of the shear cell apparatus

370

U-

1

Figure 2. Flow channel schematic with inclined transmission surface translation and rotation of the upper shear surface is accomplished using a linearbearing, ball-bearing mounting. The annular protrusion of the top disk does not contact the side walls of the bottom disk channel. The beads used in the tests are soda lime glass (density pp= 2550 kg/m3). The upper and lower sieve sizes for small beads are 0.85 and 0.71 mm, for large beads are 1.70and 1.40 mm, giving the beads average diameters of 0.78 mm and 1.55 mm, respectively. New beads are used for each test run. The displacement of the upper surface assembly is measured using a dial indicator, which determines the average fractional solids content knowing the volume of beads in the channel. For these series of tests, the height of the channel is kept at about the depth of WD = 5.1 bead layers. The tested beads are placed in the channel and their density determines their volume, knowing their total mass. The volume of beads divided by the channel volume determines the solid volume

fraction v.

Four different values of v

(0.534, 0.546,0.558,0.570) are used for these

tests. At the high end, strong grinding occurs (frictional granular lubrication). The top disk is kept from rotating by a torque-arm that is connected to a force transducer which determines the shear stress. The rotation rate of the bottom disk is determined using a n optical tachometer. The rotational speeds are between 80 and 880 rpm, which results in linear speeds between U = 0.57 m/s and U = 6.29 m/s. Nominal shear rates (= U/H)fall between 72 and 1573 s-'. Forces are applied to the top disk using a system of weights and counterweights t o change the applied average normal stress. The normal forces used are between 23.0 and 45.5 N, resulting in average normal stresses between 2800 and 5550 Pa. To study the lubrication wedge effect, top transmission rings with a series of sloping regions are used, see Figure 2. The circumference is divided into alternating flat and inclined regions each of six pairs comprising 60' of circumference. The

37 1

1

r

top disk

coated with granular material. Spherical particles a r e bonded onto t w o thin aluminum a n n u l a r plates. A hightemperature epoxy is used to bond a dense monolayer of beads to each plate. The plates are then secured to the top and bottom of the channel by very thin, high-shearstrength, double-sided adhesive tape. Tests are performed with both smooth and rough coated stationary surfaces for all four slope configurations. The surface roughness of the smooth plates was not measured. However, they were polished before each test run are much smoother than the rough plates. The average size of the particles bonded on the annular plates is 0.78 mm. The thickness of the epoxy is about 25 mm.

3. EXPElUMENTALPROCEDURES

Figure lb. Schematic of the annular shear cell flow channel wedge regions match the flat height at one end, have a sudden step at the other end, and zero slope at both ends. The shape is a cubic polynomial. The sliding direction is such that the wedge leading edge to the flow is the flat edge, so the transition to the inclined region is smooth. There are three heights of the wedge: AH = 1.29, 1.90 and 2.34 mm. The average slopes a r e denoted by (dh/dx),, -AW(LI6) = 0.0, 0.0162, 0.0239, and 0.0293. In discussions below one refers to average normal stress (thrust force per area), because the stress varies locally as the slope changes along the trough. The top and bottom horizontal surfaces of the annular channel are the shear transmission ring surfaces. The top surface remains stationary while the bottom one is rotated about the vertical axis. The beads are driven into motion by contact with the moving surface and a shear flow results. The moving lower surface is

A typical experiment starts with a known quantity of granular material which is loaded into the trough in the lower disk and then capped by the upper disk. The torque arm of the upper disk is then connected by a horizontal string to the force transducer. Counterweights to balance the upper disk assembly are applied to the disk to develop specific normal stresses at the top of the granular material. After applying a known average normal stress, the material is prestressed and consolidated by shearing it for a few seconds. The initial at-rest vertical displacement reading is then recorded. Tests begin by starting the drive motor and slowly increasing the speed of rotation of the lower disk assembly to the desired level (the desired average solids fraction). The loading weights and rotation rates are increased in step-like fashion. With the addition of each weight increment, the material is initially compacted and the gap height decreases; the increased shear stresses increase the torque load on the drive motor and reduce the rotation rate. The drive motor speed and hence the shear-

372 cell rotation rate are then increased a t a constant normal load until the upper disk is raised t o its original level, thus maintaining the solids volume fraction. The gap height is indicated by the dial indicator reading. The normal load, torque and rotation rate corresponding to this particular test are then recorded. The motor speed is reduced to zero and the final at-rest vertical displacement reading recorded again. If this value deviates from the initial value, the average of the two is used in later calculations. Proceeding in this manner, data are obtained to produce curves of normal stress and shear stress versus nominal shear rate for constant values of mean solids fraction. The same sets of steps are repeated for the four different upper shear-transmission surfaces corresponding to the same gap height (the same solids fraction). The entire process is repeated for a variety of applied normal stresses and speeds. For each test run, the normal stresses and the associated speeds of rotation are changed without bringing the system to a halt. Each data point represents the average of 6 test runs, and each test run lasts for half an hour and is conducted at intervals of one hour. The ranges of particle sizes did not change significantly and still stayed within the sieve mesh sizes. There were no obvious changes of the particle shapes. 4. RESULTS AND DISCUSSION

Selected experimental results are shown in Figures 3-6. Figure 3 shows typical normal stress (averaged over the transmission ring surface) versus shear rate behavior for the smooth upper transmission rings. The slopes of the curves on log-log axes nearly equal two in all cases which we shall include in the analysis. Normal stress increases with increasing inclination of the upper surface. The "th" theory lines shown

correspond to a simple curve fitting method described in 1171. Shear stress, similarly averaged, for the smooth surface is shown on Figure 4. The same trends are i n evidence with respect t o the effect of inclination and the relation of the data t o the theory. Figure 5 shows the normal stress (averaged over the transmission ring surface) versus shear rate behavior for the rough upper transmission rings. Again, normal stress increases with increasing inclination of the upper surface. Figure 6 shows the variation of the dimensionless stresses with solids fraction for small beads (D = 0.78 mm), both rough and smooth drive surfaces with four different angles of inclination. The stresses are nondimensionalized using the scaling pp D2(U/HI2, as suggested by the theory below. The stresses are shown t o increase monotonically with increasing v. At a constant value of v, the stresses are also shown t o increase with increasing inclination of the drive surface, such trends also being predicted by the theory. During tests it was observed that the initially smooth, polished surface of new glass beads evolved into a rough, frosted surface just as what happened in the experiments of Savage and Sayed [41. In addition, there are large amounts of dustlike fine powder generated by the grinding of the beads found in the test trough after each test run. The powder may increase the surface friction and decrease t h e coefficient of restitution. 5. ANALYSIS

In constructing a granular collisional lubrication theory in the manner of conventional hydrodynamic lubrication theory, two key features must be included: (1) a collisional normal stress generated by interparticle collisions which occurs even in parallel flows, and (2) a lubrication normal stress due t o converging surfaces

373

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

o................................ 4 T ................................ -................................

4

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--.............................

--..............................

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100

Nominal shearrate U/H (s-l) Figure 3 - Variation of normal stress (averaged over the shear surface) with nominal shear rate,smooth stationary surface, solids volume fraction v = 0.595, film thickness W D = 5.10

-e-

*

6AH/L= 0.0 - exp 6AH/L= 0.0162 - exp 6AH/L= 0.0162 - th

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

. loo

... ... .

... ... .

Nominal shear rate U/H (i')

.. . .. .. ...

... ... .

.. . .. .. ...

.. . .. .. ...

... ... .

... ... . lo00

Figure 4 - Variation of shear stress (averaged over the shear surface) with nominal shear rate,smooth stationary surface, solids volume fraction v = 0.595, film thickness W D = 5.10

374

6AH/L = 0.0162 - th

16' ..............................

n

+6 A W = 0.0293 - exp

5 e v1

H

Br

.. .. . .

0

2

. .... ..

. .... ..

. .... ..

. .... ..

lo00 100

lo00

Nominal shear rate U/H (s-')

Figure 5 - Variation of normal stress (averaged over the shear surface) with nominal shear ratelrough stationary surface, solids volume fraction v = 0.595, film thickness HID = 5.10

+6AH/L = 0.0

0.5

0.51

0.52

0.53 0.54 0.55 Solids fraction v

0.56

0.57

0.58

Figure 6 - Variation of dimensionless normal stress with solids fraction, rough stationary surface, film thickness WD = 5.10, small beads D = 0.78 mm.

375 (the lubrication "wedge effect"). We propose a constitutive equation of the following form for the deviatoric stress: 7ij = ~p

D~ b( V) f ( 2 ) i j

(1)

Modifications to viscosity such as those proposed in Refs. [71-[91 will not work --they predict no load carrying in the absence of a wedge. In form, Eq. (1) is a second order fluid model (and t h u s is "admissible," in the formal rheology terminology of, say, Bird [ZOJ), where the linear term f i j and the quadratic term f i m f m j are omitted. The

where D/Dt i s t h e u s u a l m a t e r i a l derivative. The inertialess balance of force is,

O=-. dnmi

(5)

Am

For lubrication conditions, the following orders of magnitude apply: &=-

H L'

v,-u,

Vy-&U,

-E Z. $ Y h

(6)

The stresses become: 2

nyy = 2p, D 2 b ( 9 ) , n,

=0

,

term p p D2 b is the quadratic coefficient and b[T(v)] is a dimensionless function of the granular temperature which we assume can be found from energy considerations. Such a form may arise from continuum studies of Jenkins [[121-[131 or molecular dynamics studies of Lun and Bent [211 and Elrod and Brewe [223. The total stress is given by qj= psij

+ 7ij

(2)

where 6ij is the kroneker delta and p is the pressure. Note t h a t both pressure and deviatoric normal stress may contribute to load, not just pressure contributing as in classical hydrodynamic lubrication. Load is related to the (nyy- nn) stress difference and friction to zv.

The load is

the integral of the difference (nyy- pa) where Pa is ambient pressure, and at the edge of the film nn = p a . The rate of deformation tensor is found from: T duj f .v. (vu)u = -, (3) - (VU). tJ . + (vu)ij h i and the second order tensor is

and the equation of motion is,

o = E -d- +p& - + - .d z ,

d7xy

dx h dy Bagnold's seminal work in grain [231 shows the same p p D2 ( d u x / & ) 2 depend-

ence on normal stress as well as shear stress. However, Bagnold's model is not presented in the context of a n admissible constitutive equation. The above set of equations can, in principle, be solved as a boundary value problem, knowing b(v) and knowing a wall boundary condition, but in light of all the complexities a n d uncertainties i t is probably not worth the effort a t this point. Regardless of the solution details, load per area (both with and without a wedge) will be proportional to p p (D V / H ) 2 , and frictional force per a r e a is t h u s proportional to

(WHl2. Desirable features a r e t h e squared proportionality to apparent shear rate, and that there is load in the absence of a wedge. Undesirable i s t h e fact t h a t friction coefficient is proportional to E = HJL, and would equal zero in simple shear. EPp

376 6. CONCLUSIONS

3.

This study h a s presented annularshear-cell experimental results for the stress t h a t is generated in a simple shear flow of two different sizes of glass beads. We consider only the case of high solids fractions where t h e major s t r e s s contributions are collisional. The experi m e n t s were carried o u t at high concentrations. Upon examining t h e experimental d a t a , t h e following conclusions a r e obtained: (1) The larger t h e solids fraction, t h e higher the overall stress levels. (2) T h e friction coefficient decreases s l i g h t l y with i n c r e a s i n g solids fraction. (3) Increasing t h e roughness of t h e stationary drive surface increases the overall magnitude of the stresses. (4) Experiments have confirmed that the lubrication wedge effect exists. Larger mean slope produces larger load and lower friction coefficient. The d a t a seem to be well correlated with respect t o nominal shear rate (= U/H). (5) A constitutive equation h a s been proposed which exhibits proper normal stress and squared proportionality t o apparent shear rate Granular lubrication is an intriguing field which may have technological importance. I t is relatively easy to perform controlled low-tech experiments in which the basic physics seem straightforward. However, researchers are a long way from being able to predict experimental results from a fundamental perspective.

4. 5.

114120

6.

7.

8. 9. 10. 11.

12.

13. 14. 15. 16. 17. 18. 19. 20.

7. REFERENCES 21. 1.

2.

Elrod, H.G. Interface Dynamics, Elsevier (1988) 75-88. Haff, P.K., Jour. Fluid Mech., Vol. 134 (1983)401-430.

Walton, O., and R.L. Braun, Jour. Rheol., Vol. 30, 5 (1986) 949-980. Savage, S. and M. Sayed, Jour. Fluid Mech., Vol. 142 (1984) 9 1-430. Dareing, D. W., and Dayton, R. D., STLE Trib. Trans., Vol. 35, 1(1992)

22. 23.

Heshmat, H., and J.F. Walton, AZAA paper 90-2047,AlAAISAEIASME 26th Joint Propulsion Conference, Orlando FL (1990) Heshmat, H., STLE Trib. Trans., Vol. 34,3, (1991)433-449 Heshmat, H., Lubr. Eng., Vol. 48, (1992) 373-383. Dai, F., Khonsari, M. M., Znt'l. Jour. Eng. Sci., Vol. 29,9 (1991) 1019-1033 Dai, F., Khonsari, M. M., ASME Jour. Appl. Mech., Vol. 60, (1993) 48-58. Dai, F., Khonsari, M. M., and Lu, Z. Y.,STLE Trib. Trans., Vol. 37, 3 (1994) 5 16-524. Jenkins, J.,ASME Jour. Appl. Mech., VO~. 59 (1990) 120-127. Jenkins, J. and M.W. Richman, Phys. Fluids, Vol. 28 (1985) 3485-3495. Johnson, P.C., and Jackson, R., Jour. Fluid Mech. ,Vol. 176 (1987) 67-93. Lun, C.K.K., Savage, S.B., Jeffrey, D.J., and Chepurniy, N., Jour. Fluid Mech., Vol. 140 (1984) 223-256. Yu, C.-M., Craig, K., and Tichy, J., Jour. Rheol., Vol. 38, 4 (1994) 921-936. Craig, K., Buckholz, R. H., and Domoto, G., ASME Jour. Appl. Mech., VO~. 53, (1986) 935-942. Craig, K., Buckholz, R. H., and Domoto, G., Jour. Trib., Vol. 109 (19871,232-237. Yu, C.-M. , Ph.D. Thesis, Rensselaer Polytechnic Institute, 1995. Bird, R.B. et al. Wiley and Sons, New York, (1987) Lun, C.K.K. and Bent, A.A., J o u r . Fluid Mech. ,Vol. 258 (1994) 335-353. Elrod H.G.,and D. Brewe, NASA TM #105567, AVSCOM TR#91-C-6, (1992) Bagnold, R., Proc. Roy. Soc., Vol. A 225 ( 1954)49.

The Third Body Concept I D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

377

A SIMPLE MODEL FOR GRANULAR LUBRICATION; INFLUENCE OF BOUNDARIES .4. A . Lubrecht, C. Chan-Tien and Y . Berthiera “1,aI)oratoire de Mdcanique des Contacts, URA CNRS 856, INSA de Lyon, France. 111

this paper the influence of the boundary waviness on the behaviour of a simple numerical granular shear cell

is investigated. Both boundaries have a sinusoidal waviness of which the wavelength and amplitude are varied, h g e t her with t,he thickness of the separating granular film. The particle geometry and the particle-particle

iriteract,ion are kept as simple as possible, to limit the number of variables. However, in order to use a non-trivial particle geometry and to avoid regular packing, clusters of two rigidly connected spheres are used with a sphere radius containing a random component. From this very simple model problem, the tangential force (friction) hrtween the upper and lower surface is studied as a function of the waviness amplitude, wavelength and film t~hickriess.T h e frictional behaviour depends heavily on the thickness of the granular film u p to a certain thickness (thin film). From this value onwards the behaviour remains virtually constant (thick film). T h e transition from t.lrin film to thick film behaviour is studied, as well as the influence of the wall mass (under constant applied load) o t i the mean friction and the friction fluctuations.

1. INTRODUCTION

l’his paper tries to extend the simple nioclel for (.;ranular Lubrication (GL) [la], in order to explain a number of experimentally observed phenomena [2,4]. The complexity of these phenomena requires a modular theoretical representation i i i order to advance both research and application. The model is based on Molecular Dynamics (MD),which describes the positions, velocities and forces acting on the individual particles, or granules. A thorough overview of the literature is given by Elrod [6,7] and Campbell [3]. This dis(.let,(,approach was adopted instead of a. continuous one [5,9,15] because the discrete/tra.nsient character of the film was thought to be of pri11iary importance. The parameter which is most notably different froni other molecular dynamics applications, is t.he mean free path length between part,icle collisions. In GL this mean path length is effectively zcro, in other words, a particle interacts all of the tirnc. with at least one other particle, and it is likely to interact with more than one at t,he same I.imr. 111 other words: particles are i n a state of quasi-static equilibrium. This simple observation has iinportant consequences. As is explained for

instance by Jean and Moreau [11,13], the energy loss during a collision can no longer be described using a coefficient of force restitution. This has been explained in detail in [12]. As a consequence it is necessary to reformulate the laws of particle interaction. The continuous interaction leads to a second problem, caused specifically by the representation of the granules as identical cylinders or spheres. Any order in the boundaries will lead to a degree of ordering in the simulation which is unphysical, and causes strong anisotropy. To avoid this ordering, spherical particles with a certain size distribution are used. In order to creak particles with more complex geometries, two individual spheres are rigidly connected to form a cluster. A third problem is related to the computer time required to solve such an MD problem. A realistic model of GL would require one to study the motion of millions of granules (in three dimensions) and their interactions with the (nonsmooth) walls, over long periods of time. In order to reduce the computing time, the application of a more efficient numerical solut,ion technique is required. Presently, this problem is avoided by limiting the study to two dimensions and by the use of periodic boundary conditions.

378 ‘l’he forces between two particles are strictly normal; no tangential (friction) forces exist, in order to avoid the “introduction of friction, to explain friction”. I n particular this paper studies the tangential forces between two surfaces wit,li a sinusoidal waviness as a function of the gap (film) height, waviness amplitude and wavelength, for imposed wall speeds.

2. MODEL

1.1. N o t a t i o n

amplitude of wall waviness dimensionless amplitude, A = A / ? distance between the centres of i and j d 23. . - 1Pi - - P j I = Jc.2 - “ j 12 (Yi - Yj 12 film thickness dimensionless film thickness, H = h/7‘ coefficient of friction mean coefficient of friction force of particle j on particle i mass of particle i relative mass of wall particles average particle mass,

-

152

lower body (wall 2) wavelength of the surface feature dimensionless wavelength of surface feature, W = w / ? dimensionless time increment standard deviation of coefficient of friction orientation of cluster i

+

=< mi >= 47rpp3/3

dimensionless particle mass, M i = mi/ < m > number of clusters normal from i t o j , Sij = (nz,?zy) 1(P;. -&)/[$j -61 position of particle centre i , $i = ( i i , yi) dimensionless position of particle centre i , Fj = $a/? radius of particle i average particle radius, 1- =< ri > dimensionless particle radius, Ri = r i / ? reduced particle radius, 1/Rij = 1/Ri 1/Rj

+

h i e

dimensionless time, T = t u / ? velocity of lower surface velocity of particle i dimensionless velocity of particle i dimensionless relative velocity of + particle i to j , K j = vj - V, coordina.tes upper body (wall 1)

-

In the following sections the different “physical ’) aspects of the model are addressed, such as the geometry, the interaction forces, the characteristics of the wall and those of the total shear cell.

2.1. Granular g e o m e t r y The geometry most often used in Molecular Dynamics is that of a collection of identical perfect cylinders or spheres. This assumption has limited consequences when the particles interact only occasionally. However, when interaction becomes common, as in granular lubrication, the precise particle geometries start to play an important role. First of all, identical cylinders or spheres tend to arrange themselves into a regular packing [16]. This causes a near det,erministic behaviour with a very strong anisotropy. In order to avoid this regular packing, the particle size ri is given a random component R according to: ~i

= i;

+R A r

where R is a normally distributed random number between [-1,1] and i; is the average radius. Using A r / ? = 0.1 this regular arrangement is completely destroyed. This can be observed from the orientation of the granules formed by a particle pair, see below. In reality the particle geometry is very complex, it would therefore be of interest to perform the model calculations with particles of complex geometries. This results in various theoretical and numerical problems, such as the difficulty of calculating whether contact occurs between two particles and establishing the size and the direction of the resultant force. In order to avoid these

379 polilems, clusters consisting of several identical c-yliiidersor spheres can be used. Since the principarts have a trivial geometry, the above cited tasks become simple once again. On the other h a l i d , the fact that these clusters have a nontrivial geometry allows bridging and severely limits the rotational freedom of the particles. In this pqm, the clusters consist of two identical rigidly mnected spheres, see Figure 1. Extensions towards clusters consisting of more particles of different size are easily envisaged. One can also extend the complexity of the bond between the two spheres.

Figure 1 Coordinate system of two interacting clus-

a tangential force does not introduce an “uncontrolled” degree of freedom. All free clusters are subjected to a gravitational force. 2.3. Walls In order to limit the number of variables, the walls bounding and driving the granular flow are made up of clusters. These clusters have the same properties, except for their mass, as the free clusters. The centres of gravity of the clusters are aligned along a straight or sinusoidal line: d s i n ( 2 ~ X / W ) ,see Figure 2. The wall particle size is adjusted slightly, so as to fit the periodic interval exactly. Like their free counterparts, the clusters making up the walls have an identical size distribution; they are generated from the same random sequence, using the same parameters. The only difference with the free particles is that their mass is generally larger, and that wall particles can not move individually: their position and orientation with respect to their neighbours is fixed.

and I . The cluster geometry is 5ornpletely detrrmined by the position of its centre P,, its radius r , &nd Its orientation 0,. ters

2.2. Inter-particle forces Because t h e clusters are made up of spherical

particles, determining the contact forces between clusters, remains a simple task. The algorithm coniputes the forces on individual particles, and sunis them into the total force and moment around the centre of gravity of the cluster. Tot.al force and moment are then used to obtain the iiiot.ion of the cluster. l’he normal force between particles is modeled using a fully elastic Hertzian spring; the react.ion force is proportional to ‘(penetration” to the power 1.5, see [lo]. Energy dissipation during contact is accounted for by a viscous dash pot 18,141. No tangential forces are included in the iiiotlel, in order to avoid the introduction of a coefficient of friction in order to “measure” a coefficient of friction. Since rotation is limited by the cluster geometry, see Figure 1, this lack of

Figure 2a Wall waviness: A = 2, W = 20, H = 10.

Figure 2b Wall waviness: A = 2, W = 20, H = 20

2.4. S h e a r cell The number of clusters required for a full scale three dimensional model is so large that two different ways are employed to reduce this number.

3 80 First of all the third dimension is removed, clust.ers can only move in two dimensions, and the flow modeled has a thickness of only one particle. Even after this drastic reduction, the number of particles necessary in the direction of the velocit,y remains prohibitively large. To overcome this problem periodic boundary condit,ions in X are iiitroduced. Physically the model problem represents a shear cell, with a lower surface moving at a const,a.nt velocity in the X direction, while the upper surface is free t o move in the Y direction, in order t,o est,ablish an equilibrium between the applied force and the reaction forces of the clusters. The t,otal wall mass and the total applied force are not necessarily related through gravity. The tangential force on the upper wall is registered and divided by the normal load, thus it is expressed as a. coefficient of friction. 3. DIMENSIONLESS EQUATIONS

I I I order t,o simplify the calculat.ions, the equat.ioiis are made dimensionless using “natural” parameters. ‘l’he dimensionless particle radius is: Rj = r i / ? , where ? is the mean particle radius. ‘l’he dimensionless cluster position is: Pi = $i/?. The dimensionless particle mass is Mi = mi/riz, wit,Ii m = 47rpr3/3. The c_limens_ionlessforce on particle i by particle j is Fii = fij,/(~~g). 1Iie cliiiiensionless moment of inertia is Ij = l l / (I n ? ) .

-

r

l

Using t,liese parameters, the dimensionless gravitational force reads:

The dimensionless viscous dissipative force during collision reads:

The equation of motion of cluster i is given by:

and nisi,

E‘ I< = -

c

Gjj

j #i

since a cluster consists of 2 identical particles. 4. NUMERICAL SOLUTION

The equations of motion of t8heindividual particles and those of the upper body, are solved using the Verlet leapfrog algorithm [l], particle-particle interactions are identified wing a neighbourhood list [ 11. The numerical values of the parameters used in the calculations are listed in Table 1. The normal force on the upper wall is chosen such that a mean pressure of 1 kPa is generated. -

Ir Ar/F M,,,

I

1.0 x 10-4 I, [mi . , 0.1 [-I 1 . 0 x l o 2 I I-1

I

P

E’ AT Y

The dimensionless repulsive elastic force reads:

=

1.5 x 10” 2.0 x 10-5 0.1

INm-?

[-I

1-1

Table 1 numerical values used. The friction values shown in the following sections are averages over time intervals of 1. The values between T = 0 and T = 20 are discarded, to avoid start-up phenomena, and the other values are averaged to give a mean friction coefficient f and a standard deviation “ J .

38 1 5 . NUMERICAL TESTS I r i tlir following sections a number of tests are rrbported investigating the role of certain model I)itraiiieters/variables. This in order to identify iiumerical artifacts which could otherwise be intcqmted as real, physical effects.

5.1. Ensemble average A random sequence determines both the size of tlie particles (wall and free) as well as their initial positions and orientations. In order t,o study the iiiflucwce of the random sequence on the contact I)t~liaviour,five different seeds S were used. The rc~sultsfor these five different random sequences itre c,onipared in Table 2

S f

-1

-2

-3

-4

-5

0.186 fO.06

0.189 j10.07

0.201 h0.07

0.193 f0.07

0.194 f0.07

Table 2 f and uf as a function o f tlie seed S o f the r.,indoni sequence, A = 2, W = 10, H = ‘LO.

From this table it can be concluded t,liat, the wiriations in f and uf, between different ensemIdrs are limited. Furthermore, it call he conc.luclecl that the f value for S = -1 is rather low, cx)nipared to the average value over five ensembles of 0.193. 5.2. Time average ‘I’he general sampling time was chosen to be 50 iiiiits, after a “running in” time of 20 units, to i~liminatethe influence of initial events. Sampling t,imes of 100, 200 and 500 units were used as test i-asps, and the results are compared i n Table 3.

[

Ttt,t -

[ f

uj

11 11

11

50 0.186 f0.06

I I I

100 0.190 f0.07

I I

I

200

I

500

0.191 f0.07

I [

0.194 f0.08

1 I

Table 3 f and u j as a function o f the total simulation L ~ I I I C Tt,t, A = 2, W = 10, H = 20.

l+om t,his table it can be concluded that the cnsenible average of f = 0.193 (see sectmion5.1), ittltl t,he average over T = 500: f = 0.194, are very close. The ensemble and time avera.ge seem to cwnverge to the same value.

5.3. Influence of the gap height The number of clusters in between the two walls determines the gap height. Whenever this number is large, the addition or removal of one cluster should not alter the contact behaviour significantly. Consequently, simulations with 198, 199, 200, 201 and 202 clusters in the gap were performed, and the results are compared in Table 4. From this table it can be concluded that the variations in f and U J , for different numbers of clusters are limited to the variations obtained in section 5.1. Furthermore, it can be concluded that the mean friction value for 71, = 200 is rather low, compared to the average (see above). nc

198

199

200

f

0.192 f0.07

0.201 f0.07

0.186 f0.06

201

202

0.201

0.217

f0.08 f0.08

Table 4 f and

aj as a function o f tlie film thickness (number o f clusters nc in the gap), A = 2, W = 10, H N 20.

5.4. Influence of the viscous dissipation In order to see if the friction recorded is not influenced (or worse: generated) by the viscous dissiacting during collisions, the value pative force of the coefficient y was varied by several orders of magnitude. The results are presented in Table 5.

Fu

y

0.002

0.005

f of

0.206 f0.07

y

0.1

f

0.186 f0.06

0.192 0.196 f0.08 h0.07 0.2 0.5 0.190 0.201 f0.07 f0.06

uj

0.01

0.02

0.05

0.208

0.192

f0.08 f0.06 1 .o

2.0

0.197 k0.07

* *

Table 5 f and aj as a function o f the viscous damping coefficient 7, A = 2, W = 10, H = 20, * indicates that violent oscillations caused the program to terminate.

The variations in the mean coefficient of friction are of the same order as those observed in section 5.1, and no trend can be distinguished. The same conclusion holds for t,he friction variations aj. However, it was noticed that for even larger values y 2 2.0 the particles tended to stick

382 together, forming durable struts which increased the friction variations, and caused the program to terminate. The same behaviour was found for thinner films, for y 5 1 friction and friction variation are independent of y, and for even larger value, the program terminates. Therefore, it can be concluded that the resultant tangential force is neither generated nor strongly influenced by the viscous dissipation force, at least up to a certain limit value. This tangential force can possibly be explained by the small correlation length between the surface slopes on which action and reaction forces act. Hence, the average tangential component of the action force of the particles on the wall will lie opposite to the direction of wall motion, while the average tangential reaction force will be zero. Consequently, a net tangential force opposite t o the direction of motion results. 5.5. Influence of the time step In order to see if the time step A T influences the numerical results, tests were carried out with AT, A T / 2 , AT/4 and AT/10. The results are presented in Table 6a.

AT

-

f

of

2 x 10-~ 0.186 f0.06

1 x 10-~ 0.192 f0.06

5x

0.197 f0.07

2x 0.209 60.07

Table 6a f and uf as a function o f the time step AT, A = 2, W = 10,H = 20.

The mean coefficient of friction has a tendency AT. However the range of f values obtained is not different from the range observed in the previous sections.

t,o increase with decreasing

AT

f uf

2x 0.199 60.06

1x 0.194 f0.06

5 x

0.207 f0.07

2x 0.197 f0.07

From this table it can indeed be concluded that the time step A T does not seem to influence f. The value of uf does not vary with AT.

5.6. Influence of the periodic boundaries In order to study the influence of the position of the periodic boundaries, a specific case waa studied with a domain size L of eight waves, sixteen waves, thirty-two waves and sixty-four waves. The results are presented in Table 7.

I

8 1 16 I 32 I 64 f I1II 0.186 I 0.191 I 0.196 II 0.196 -~ u4 11 f 0 . 0 6 1 I f 0 . 0 4 5 1 f0.038 I f0.022

L

r

1

11

I I

1

Table 7 f and uf as a function o f the number o f waves in the shear cell L , A = 2, W = 10, H = 20.

The use of larger domains tends to induce the same convergence of the mean friction f,as observed in section 5.2 using increasing averaging times. However, a reduction of the variations in aj according to uj N 1/& is also obtained. This reduction in uj follows naturally from the application of the statistical laws of large ensembles. The values of f for large domains coincide with those for small domains and long time averages. This indicates that the position of the periodic boundary conditions in all domains used, has a negligible effect on the results. In order to obtain more realistic values for uj it is necessary t o replace the averages over 1 time unit by a more realistic model of a force transducer, involving the upper body mass, the transducer stiffness and the stiffness of its environment. 6. RESULTS

6.1. f ( H , d , W ) Table 7 lists f and uj as a function of the wall waviness amplitude A and wavelength W for dif-

383

gap height H 20

I[

5

I

10

0

11

0.140

I

0.140

I

$

11

0.177 f0.14 0.221 f0.19 0.241 fO.19 0.361 fO.80

I

0.185 f0.13 0.217 f0.24 0.229 f0.39

I

3

-

11

5

I

I

0.140

1

0.157 f0.08 0.209 f0.16 0.280 i0.37 gap height H 10 20 [

I

= 10 40

I

80

I

0.140

1

0.140

I

I 0.149 f0.08 0.184 f0.14 0.194 f0.30

= 20 40

0.152 f0.09 0.166 f0.13 0.181 h0.22

I

80

I

00

0.140 0.140 50.06 0.140 f0.06 0.140 f0.06 0.140 f0.06 co

much larger than the waviness amplitude, af is constant and independent of the wall waviness ( d , W ) . These films can be called thick films when H / d > 10. For thin films two different zones can be distinguished: a zone where the surface slope is important d / W > 0.1, and a zone where the slopes are small. In the last zone, f and of have values close to the “straight” wall value. In the high slope zone friction and friction variation increase dramatically for the H = 10 case. A mild increase in f can be noticed for H = 20 and H = 30, whereas af does hardly change. These observations can be explained in terms of the ability of the film to adjust to geometrical variations of its boundary. Whenever the film is relatively thick, it will be able to accommodate these variations with ease. As a consequence the parameter H / d seems a sensible choice to distinguish the different regimes. However, the slope of the waviness also plays a role, and perhaps a more complete parameter should combine both H , d and W . 6.2. Influence of film height In order to study the influence of the gap height in detail, calculations with gap heights of 7 mean radii, 8, 9, 10, 12, ..., 20 were carried out for one particular surface configuration. The results are plotted in Figure 3.

U, A=4, W=20

Oe5

m

0.4

Table 7 f and g f as a function o f the gap height 1-I. and as a function o f wavelength W (horizontal) and amplitude A (vertical). Please note that the (cases W = 00 and A = 0 are identical and serve as asymptotes.

0.3

0.2

0.1 0 -

0

2

4

6

8 10 12 14 16 18 20

H

Figure 3 Mean coefficient o f friction f and friction variation uf versus the film thickness H , A = 2, W = 10.

384 The thansition from thin to thick film behaviour seems to take place around H = 15, or at HIA N 8. Once again the thicker films have much smaller variations aj than the thinner ones; one can conclude that the thick granular film starts to behave as a continuum.

From this table it can be observed that the variations uj increase with increasing M,. The increase is very important for the gap height H = 10, and much more limited for H = 20. The influence on the mean friction value f is limited, most likely because of the linear forcedeformation relation employed.

6.3. Influence of wall mass ‘I’he wall inertia, and in more complex systems also the stiffness and damping, play a n important role in the behaviour of a transient system. As a consequence, the evo1ut)ion of the variables studied ($ and af)should depend on the charackristics of the mechanism applying the load and speed. In order to minimize the number of variables, only the influence of wall inertia is studied, stiffness and damping are taken to be zero. The inertia will limit the immediate response of the wall with respect to the force balance. The larger t,he wall inertia, the less the upper wall can follow small perturbations in the film. As a consequence, large forces are built up, resulting in large variations of the upper wall position. It can therefore be expected that when the system’s inertia is too large, the friction signal will tend to oscillate violently around a n average value. Whereas, with small inertia, these variations will be limited. The granular film itself will also play a role, the thicker the film, the better it, can accommodate geometrical variations, and thus the better it can damp force fluctuations. Table 8 shows f and af as a function of M,, the ratio of wall particle mass and free particle mass.

7. DISCUSSION A N D CONCLUSION

gap height H = 10 M , 11 100 I 200 I 500 I 1000 f 11 0.241 1 0.261 I 0.263 1 t I1

c ~ j

M,,, f uf

)I

II

I

f0.19

I

I

I &0.47 I f 0 . 6 3 I *

gap height H = 20 100 I 200 I 500 0.186 zt0.061

0.200 fO.10

0.201 lt0.23

1,

1000

I

0.205 lt0.25

I

Table 8 f and as a function o f the wall mass M,, A = 2, W = 10, H = 10/20. * indicates that violent oscillations caused the program to terminate.

This paper has analyzed i n detail the mean coefficient of friction and its variations “measured” in a shear cell with varying boundary waviness. When the film thickness is large with respect to the waviness amplitude, the mean friction and friction variation tend to be small. Thin films show two different regimes, depending on the slope of the boundary waviness. When this slope is smaller than 0.1, the values o f f and aj tend to their “straight” surface values. For values larger than 0.1, mean friction and its variation increase dramatically. The transition between thin and thick film behaviour is not gradual at all, on the contrary, it is very sudden. Therefore, this sharp transition cannot be explained in terms of adding another layer, and thereby increasing the accommodation capacity of the film a little. On top of this gradual behaviour, a more sudden change occurs. This might in effect be caused by the maximum length of the bridges (struts) between the two surfaces. Once this length is exceeded, their role will suddenly diminish. The transition is also influenced by the slope of the waviness, as has been shown before. As the model of a granular flow is inherently transient, the behaviour of the system depends to a great extent on the characteristics of the “mechanism” applying load and imposing the relative velocity. Even with the simple model studied, the mass of the wall bounding the flow, can significantly change the values of f and aj “measured”. For thin films an increase of the wall mass, under a constant applied load, causes a large increase in the friction fluctuations. For thicker films the increase in a! is only modest. Real world “mechanisms” are much more complex than the simple system studied here. Apart from

3 85 their mass they can be characterized in terms of stiffness and damping. However, this simple model already shows that the dynamic characteristics of the “mechanism” can influence the mean values “measured”. The granular model used in this paper is far from realistic. Although particle geometry is non trivial, it is far removed from the complex reality. The force-deformation relation is purely elastic, arid i n principle the entire contact load can be carried by a single particle. The introduction of B nonlinear plastic behaviour is one of the priorities. Such a nonlinear model would translate increasing variations in contact forces in increasing coefficients of friction. These variations should be interpreted both in a geometrical and in a temporal sense. An important role of a successful granular film seems therefore t o reduce force (pressure) variations, both in space -and time. Furthermore, a full three dimensional model is required to allow all degrees of freedom their role, and to obtain a more realistic transient behaviour. The contact should have an inlet and outlet, and be capable of building up a film with a certain thickness, depending on the operating conditions. Last but not least film thickness and friction are not the parameters of main interest. The evolution of the operating roughness as well as the wear rate should allow predictions concerning performance as a function of time, and thus the operating life, and are therefore the main but distant goals.

REFERENCES Allen, P.M., Tildesley, D.J., 1987, “Computer Simulations of Liquids,” Clarendon Press, Oxford. Berthier, Y . , Colombid, Ch., Vincent, L., and Godet, M., 1988, “Fretting Wear Mechanisms and their Effects on Fretting Fatigue,” A S M E J. of Trib.,110,pp. 517-524. Campbell, C.S., 1990, “Rapid Granular Flows,” Ann. Rev. Fluid Mech., 22, pp. 5792. Colombih, Ch., Berthier, Y . , Floquet, A., Vincent, L., and Godet, M., 1984, “Fretting: Load Carrying Capacity of Wear

Debris,” ASME J. of Trib., 106,pp. 194-201. 5. Dai, F., and Khonsari, M.M., 1993, “A Continuum Theory of a Lubrication Problem with Solid Particles,” ASME J. of Appl. Mech., 60,pp. 48-58. 6. Elrod, H.G., 1987, “Granular Flow as a Tribological Mechanism - A First Look,” LeedsLyon Symposium on Tribology, Elseviers, pp. 75-88. 7. Elrod, H.G., and Brewe, D.E., 1991, “Numerical Experiments with Flows of Elongated Granules,” Leeds-Lyon Symposium on Tribology, Elseviers, pp. 219-226. 8. Gallas, J.A.C., Herrmann, H.J., Sokolowski, S., 1992, “Convection Cells in Vibrating Granular Media,” Phys. Rev. Lett., 96, 9,pp. 1371-1374. 9. Heshmat, H., 1991, “The Rheology and Hydrodynamics of Dry Powder Lubrication,” Ttrb. Trans., 34, 3, pp. 433-439. 10. Johnson, K. L., .i985, “Contact Mechanics,” Cambridge University Press. 11. Jean, M., and Moreau, J.J., 1992, “Unilaterality and dry friction in the dynamics of rigid body Collections,” Proceedings Contact Mechanics International Symposium, ed. A. Curnier, Presses Polytechniques et Universitaires Romandes, Lausanne, pp. 3148. 12. Lubrecht, A.A., Berthier, Y . , 1994, “Granular Lubrication: a simple model and trends,” Proceedings of the 21st Leeds-Lyon Symposium on tribology. 13. Moreau, J.J., 1993, “New Computation methods in granular dynamics,” Powders and Grains 93, ed. C. Thornton, A.A. Balkema, Rotterdam, pp. 227-232. 14. Ristow, G.H., 1992, “Simulating Granular Flow with Molecular Dynamics,” J. Phys. I France, 2 , pp. 649-662. 15. Yu, Ch.-M., Craig, K., Tichy, J., “Granular Collision Lubrication,” J. Rheol., 38,4, pp. 921-936. 16. Zhang, Y . , and Campbell, C.S., 1992, “The Interface between Fluid like and Solid like Behaviour in two-dimensional Granular Flows,” J. Fluid Mech., 237, pp. 541-568.

This Page Intentionally Left Blank

SESSION X SOLID LUBRICANTS Chairman :

Professor John Tichy

Paper X (i)

Tribological Behaviour of Solid Lubricated Contacts in Air and High-Vacuum Environments

Paper X (ii)

Self-Lubricant "Mosaic" Surfaces of Type 316 Austenitic Stainless Steel

Paper X (iii)

Role of Third Body in Life Enhancement of MoS,

Paper X (iv)

Significance of Transfer Layers for Dry Frictional Applications

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

389

Triboiogical behaviour of solid lubricated contacts in air and high-vacuum environments C. Donnet, M. Belin, T. Le Mogne and J.M. Martin Iaboratoire de Tribologie et Dynamique des Systtmes- CNRS URA 855 b l e Centrale de Lyon, BP 163 - F-69 131 Ecully Cedex.

Advanced solid lubricants coatings for vacuum applications have been the subject of considerable development for many years, thanks to the use of the new coating techniques, such as physical andlor chemical vapor deposition processes. The present paper discusses and compares the friction behavior of two hnds of thin iilm solid lubricants (MoS2 and hydrogenated Diamond-Like Carbon - DLC) in ambient air and in vacuum down to Pa. We show how friction is dependent on the environment, and the analogy of the results for the two kinds of coating. The potentiality of DLC coatings used as solid lubricant for space applications is thus hghlighted. in comparison with the more extensively used MoS2 lubricant.

1. INTRODUCTION

Solid lubrication is generally used when conventional liquid lubrication does not fit the design requirements, due to particular situations with h g h pressures, reactive environments, high vacuum, very high or cryogenic temperatures, and i n micromechanisms. Solid lubricant coatings, allowing heavily-loaded counterfaces to roll orland slide over each other with minimum tangential resistance, have been the subject of considerable development for many years, thanks to the use of physical or chemical vapour deposition techniques [ 1-21. Thin film processing technology allows to elaborate various adherent coatings in a controlled and reproducible way. Much attention has been paid to the improvement of conventional solid lubricant coatings (lamellar structures, carbon-based layers, etc.) and the development of new coatings, such as niulticomponent, multilayered and doped systems. Coatings tribology is actually in a development stage. Finally it will allow tribologists to achieve the monitoring of friction and wear for specific applications, taking into account the diversity of experimental conditions of engineering devices. If studies of solid lubricant coatings have motivated

many research laboratories for 15 years, industry has not yet adopted its potentialities, due to many technical and economical reasons. From a technological point of view, there is a considerable dispersion of tribological results, due to the diversity of coatings, elaboration procedures and tribological parameters. In particular, the need for fully understanding the relationships between the nature of the lubricant coating and its tribological performances in relation to the nature of the environment during sliding has become more pressing for many applications enforcing extremely high reliability. The present paper discusses and compares the friction behaviour and mechanisms of two kinds of thin film solid lubricants (MoS2 and hydrogenated hamond-Like Carbon - DLC) in ambient air and in high vacuum condition, with particular emphasis on the role of the third body in terms of transfer film and friction-induced wear debris, depending on the environment. Present results, gathered with previous works through a literature survey will highlight the potentiality of DLC coatings used as solid lubricant for vacuum applications, in comparison with the more extensively used MoS2 lubricant.

2. LITERATURE SURVEY

2.1. MoS2 coatings One of the most common and studied materials used as a solid lubricant is molybdenum disulphide, which has a lamellar structure [3-91. Covalent bonds join sulphur and molybdenum atoms in planar arrays of hexagonal S-Mo-S “sandwiches”, whereas weak Van der Waals interactions between adjacent sulphur planes allow easy-shear, parallel to the sliding dmction. The most preferred MoS2 coatings are usually synthetized by RF magnetron sputtering and exhibit a friction behavior strongly depending on the environmental conditions. Ultra-low friction in high vacuum (friction coefficient less than 0.02) is attributed to low shear strength consequently to the formation of a transfer film. Ambient conditions lead to irreversible tribo-oxidation of MoS2 into molybdenum oxides, thus leading to the inhibition of the solid lubricant properties, with friction coefficient values higher than 0.20 and high wear rates leading to the destruction of the coating. 2.2. D L C coatings

Amorphous diamond-like coatings ( D L O , known primarily as a hard coating, provide some of the lowest friction coefficients ever measured in the widest range of environments, from high vacuum to ambient air, including dry environments [ 10-113. For many years, a considerable amount of works has been devoted to uibo-investigations of DLC coatings, with a noticeable dispersion of the friction and wear results. This is explained by the diversity of structures and compositions, depending on the elaboration procedure and parameters. Table 1 and Table 2 gives a summary of the friction behaviour of DLC thin films respectively in high vacuum (less than Pa) and in ambient air. Some of the references mentioned report also friction tests in other environments, such as dry air or dry inert atmospheres. One of the major interest of DLC is the deposition temperature, which can be lowered below 20O0C, thus making possible to deposit coatings on most relevant engineering materials, including polymers [ 11. Adhesion properties are generally improved by the use of intermediate layers, such as Tic, Sic, Ti or TiN/TiC couple, depending

On the nature of the substrate [ll]. The strong atmosphericdependence of friction and wear of DLC coatings appears in many studies. Sugimoto [ 191 and Kim [34] have studied the uibochemical reactions inside the contact, identified by infra-red spectroscopy microanalysis of the contacting surfaces, transfer film and particles, thus allowing the correct understanding of the uibological mechanisms in relation to the presence of specific reactive gases during friction. 2.3. Environmental sensitivity One of the motivations to optimize DLC coatings with low friction and wear in the widest range of environmental conditions is the need for reliable solid lubricants in technological fie\& demanding exueme reliability, for example magnetic storage devices or vacuum and space technologies. hi particular, space mechanisms are required to function in vacuum, but also during the assembly, test and storage phases, which are often performed in ambient atmosphere during the months preceding the launching. If MoS2 coatings systematically exhibit friction coefficients higher than 0.10 in ambient air, due to irreversible tribo-oxidation, many studies indicate the potentialities of DLC to slide with friction coefficient values less than 0.10 with low wear rates in atmospheric conditions. Nevertheless, few results from Tables 1 and 2 report uibological investigations of a given DLC coating in both vacuum and air conditions. Moreover no systematic correlation has been shown between the uibological mechanisms and the coating characteristics, in terms of hydrogen content, carbon hybridization ratio, addition element concentration and mechanical properties, such as the hardness and the intrinsic stresses. Further studies are encouraged to design DLC coating characteristics in relation to the synthesis process, more particularly to improve the solid lubricant properties in the widest range of environment and conditions.

39 1

3. EXPERIMENTAL PROCEDURE

4. RESULTS AND DISCUSSION

In an attempt to go further in this field, we have focused our attention on the role of the environment on friction of two typical solid lubricant coatings, hydrogenated DLC and pure MoS2 thin films. Experiments performed in high vacuum allow us to elucidate the friction mechanisms without any chemical effect due to reactive gas, whereas the progressive increase of the environmental pressure allows us to monitor tribochemical effects influencing the friction level and the associated wear mechanisms. Experiments have been carried out using an analytical ultra-high vacuum tribometer described elsewhere [49]. Since detailed results have been already published [22, 491, the following emphasizes on the comparison between the two kinds of coatings, with some highlights on running-in friction in UHV, and the effect of the environmental pressure on steady-state friction, from UHV to ambient air. Moreover, the role of the third body in terms of transfer film and friction-induced wear debris depending on the environment is considered. Table 3 summarizes the structure and intrinsic properties of the MoS2 and DLC coatings used in our tribological investigations. The nearly pure and stoichiometric MoS2 has been synthetized by RF magnetron sputtering in the UHV preparation chamber coupled with our uibometer. Hydrogenated DLC coatings have been synthetized by RF PECVD from acetylene. Details on the film synthesis and characterization and the friction tests performed on the various coatings have already been described elsewhere [22. 501. The thickness of the coating is ranging between 50 and 100 nm. For the uiboinvestigations, a given environmental pressure can be monitored from UHV Pa) to ambient 5 air (10 Pa, with a relative humidity of 40%). Selected ambient air pressures were used between these two extremes The tests were performed using a reciprocating pin-on-flat configuration, with sliding speed of 1-2 mm/s and mean hemian pressures in the 0.5- 1.O GPa range. The flat substrate is a silicon wafer and the counterface is an AISI 52100 steel ball.

4.1. Steady-state friction and shear strength Fig. 1 presents the evolution of the steady-state average friction coefficient of the pure MoS2 and hydrogenated DLC coatings, as a function of the environmental pressure during sliding. Friction in the millirange is observed for both films in an UHV pressure of Pa:fless than 0.002 for the MoS2 and less than 0.007 for the DLC.Ultra-low friction in the 0.01-0.02 range is recorded in a vacuum ranging from to lo-' Pa. A low friction increase till 0.10-0.15 is observed for environmental 5 pressures from 50 hPa, up to ambient pressure (10 Pa). These fr-iction results are in agreement with the geneml feature of the uibological behaviors depicted in Table 1 and Table 2. Taking into account the low thickness of the coatings (between 50 and 100 nm) and the low surface roughness of the contacting surfaces, the friction mechanism is entirely governed by the buildup of a transfer layer, ensuring easy-shear resrricted to the hertzian zone, without any ploughing term, as seen in Fig. 2 corresponding to the DLC wear mck 1 in UHV (Fig. 2.a), in a poor vacuum of 10 Pa (Fig. 2.b) and in ambient air (Fig. 2.c). This is a common feature for both MoS2 and DLC coatings. From this observation, the shear strength values depending on the environment can be calculated (Table 4). The low friction recorded in high vacuum is associated with shear strength values in the m g e of 1 MPa, whereas ambient conditions lead to shear strength values in the range of 100 MPa. 4.2. Running-in friction

The running-in period, preceding the steadystate friction regime is interesting to depict carefully, since it reveals some differences between the two types of tested coatings. In the case of MoS2 (Fig. 3.a). only a few friction cycles (N < 5) are necessary. These first cycles are necessary to remove the oxidized topcoats, since the coating was in ambient air before tribotesting in UHV.

392 As described in [22], the tribometer is connected

with a preparation chamber equipped with the sputtering device used to synthetize the MoS2 coating. When the coating is directly uibotested without any air exposure between the synthesis ad the tribological test, no running-in period is observed. Concerning the DLC coatings, the build-up of the transfer film occurs during an initial stage of about N = 50 cycles, with an initial increase of the friction coefficient up to 0.2-0.3, followed by a decrease to the stabilized low value of 0.006. Optical observations of the pin at different stages of the friction experiments (Fig. 3.b) indicate that the transfer film is not completely formed until the end of the running-in period. 4.3. The easy shear in ultra high vacuum As previously described, friction in the millirange, observed in both cases, is associated with weak Van der Waals interactions between DLC hydrocarbon chains [19, 511 and between oriented sulfur-rich basal planes of MoS2 [4-9,491. The steady-state low friction force is minimized thanks to Ihe combination of weak sulphur-sulphur interactions, associated with frictional anisotropy between superimposed MoS2 sandwiches, as identified by high resolution transmission microscopy performed on wear particles [52-531 ad shown in Fig. 4. Moire patterns in different areas are identified, with misfit angles between adjacent and superimposed sulfur planes measured by calculating the diffractopns of the digitized areas. These results confum the frictional anisotropy mechanism between easy-shear sulphur-rich basal planes, with a friction force depending on the misfit angle, as theoretically calculated by Sokoloff [54], Hirano ad Shinjo [ 5 5 ] . Steady-state friction of DLC coatings in UHV is c k t e r i z e d by extremely mild wear (wear 3 coefficient K less than mm .N.m-') and a very low production of wear particles. compared to MoS2 in the same test conditions. Low wear associated with a reduced formation of particles is a great advantage of the tested DLC coatings, since it directly influences the lifetime, and the wear particle formation is often responsible for friction noises and

instabilities. The low friction results in high vacuum, already observed by Sugimoto et al. [19] with amorphous C:H containing silicon, were explained by hydrocarbons transfer from the rubbed film to the ball surface and oriented along the sliding direction. Such a mechanism seems to be a common feature of hydrogenated DLC coatings in high vacuum. 4.4. The tribochemical interactions i n poor vacuum and in air For both types of coatings, higher gas pressures lead to a friction increase from less than 0.007 up to 0.10-0.15 (Fig. 1). Such a behavior is also in agreement with the most of already published results (Tables 1 and 2). involving oxygen and water uiboreactivity of MoS2 and DLC topcoats, when recovery times of friction-induced fresh surfaces (due to chemisorption effects) are of the same order of magnitude as the periods between two consecutive passes in a reciprocating or rotating sliding motion. In poor vacuum, the friction increase may be explained by the increase in bond strength from = 8 kllmol. (Van der Waals bonding between hydrocarbons -DLC- and sulfur-rich basal planes MoSz-) to = 20 M/mol. (hydrogen bonding at C=O sites by water molecules). As observed in Fig. 2.b, few wear particles are formed and only mild wear OCCUIS.

In ambient air, a strong increase of the frictioninduced wear debris is observed for both the DLC (Fig. 2.c) and MoS2 (not shown). The particles are located on the edge and on both extremities of the wear track on the plane, and around the henzian zone on the pin. They probably induce a modification of the easy-shear sliding mechanism and lead to an 3 increase of the wear rate higher than mm /N.m, which is the critical value recommended by Holmberg et al. [56] for most of the solid lubrication mechanisms. This appears to be a current strong limitation for both MoS2 and DLC coatings in space applications, when sliding sollicitations in air irreversibly inhibit the vacuum millirange friction properties during the storage and test procedures performed on earth before launching. Additional works are in progress to explore the DLC potentialities to overcome this limitation, since low

393 friction results in humid ambient air (fas low as 0.04) have been reported by many authors (see Table 2) for amorphous C:Si:H coatings.

5. CONCLUDING FUTURE TRENDS

REMARKS

AND

A general trend on solid lubrication properties of MoS2 and DLC coatings depending on the environment is identified on the basis of numerous published papers and some recent results obtained, although an extreme diversity of synthesis procedures exists, especially in the case of amorphous carbon compounds. Different points are highlighted: - the friction range from low values (near zero friction, less than 0.002) to higher values (between 0.10 and 0.15) when the environmental pressure increases from UHV to ambient air. For both types of coatings, the millirange friction behaviour is systematically and exclusively observed in an ultra high vacuum environment; - such a uibosystem offers to uibologists a remarkable model situation to elucidate fundamental aspects in solid lubrication (a "quite simple" chemical composition, a low thickness - less than 100 nm, the presence of a transfer layer reducing the influence of the conterface and a fully controlled environment); - the potentialities of DLC coatings as solid lubricant for vacuum applications have not been investigated as thoroughly as those of the wellknown MoS2 coatings. This is due to an extreme diversity of synthesis procedures and an insufficient correlation between coatings properties and uibological behaviors performed with slandardized uibotests in both air and vacuum environments. The high internal stresses and the friction dependence on water vapor or oxygen partial pressures are the two strongest problems of DLC coatings, with regards to the reliability and the tribological performances in a wide range of atmospheres.

ACKNOWLEDGEMENTS

The author is grateful to Dr A. Grill and V. Patel (IBM Watson Research Center, NY) for their collaboration on uibological investigations of DLC coatings in various atmospheres.

REFERENCES

1.

2. 3.

4. 5.

6. 7. 8. 9. 10. 11.

12. 13. 14. 15. 16. 17.

K. Holmberg, A. Mathews, Coatings Tribology, Tribology Series, 28, D. Dowson, ed. Elsevier, 1994. B. Bhushan, B.K. Gupta. Handbook of Tribology, Mc Graw Hill, 1991, 1.11 - 1.14. I.L. Singer, Fundamentals of Friction : Macroscopic and Microscopic Processes, I.L. Singer and H.M. Pollock, eds., Kluwer Academic Publishers, 1991,237. T. Spalvins, J. Vac. Sci. Tech., A5 (2) (1987) 121. P.D. Fleischauer, R. Bauer, Trib. Trans., 31 (2) (1988) 239. J.R. Lince, J. Mat. Res., 5 (1) (1990) 218 E.W. Roberts, Trib. Inter., 23 (2) (1990) 95. P.D. Ehni, I.L. Singer, Applied Surf. Sci., 59 (1992) 45. J. Moser, F. Levy, J. Mat. Res., 8 (1) (1993) 206. A. Grill, V. Patel, Diamond and Related Materials, 2( 1993) 597. K. Holmberg, J. Koskinen, H. Ronkainen, J . Vikersalo, J.P. Hirvonen and J. Likonen, Diamond Films and Tech., 4(2) 1994. K. Enke, H. Dimigen, H. Hiibsch, Appl. Phys. Lett., 26 (1980) 291. H. Dimigen, H. Hiibsch, Philips Tech. Rev., 41 (6) (1983/1984) 186. R. Memming, H.J. Tolle, P.E. Wierenga, Thin Solid Films, 143 (1986) 31 1. S. Miyake, S. Takahashi, I. Watanabe, H. Yoshihara, ASLE Trans., 20 (1987) 121. H. Dimigen, H. Hubsch, R. Memming, Appl. Phys. Lett., 50 (1987) 1056. K. Miyoshi, J.J. Pouch, S.A. Alterovitz, Mat. Sc. Forum, Trans. Tech. Publ. (Switzerland), Vol. 52/53 (1989) 645.

394 18. 1.1. Aksenov, V.E. Strel’nitskij, in “ First European Conference on Diamond and Diamond-Like Carbon Coatings ”, CransMontana, Switzerland, Sept. 17-19, 1990). 19. I. Sugimoto, S. Miyake, Appl. Phys. Lett.. 56 (19) (1990) 1868. 20. K.Deng, W.H. KO, Sensors and Actuators A, 35 ( 1992) 45. 21. M. Maillat, H.E. Hintermann, Surf. Coat. Tech., 68/69 (1994) 638. 22. C. Donnet, M. Belin, J.C. AugC, J.M. Martin, A. Grill and V. Patel, Surf. Coat. Tech., 68/69 (1994) 626. 23. D. Paulmier, H. Zaidi, T. Le Huu, H. Nery, A.M. Durand, Diamond Films and Tech., 4 (2) (1%). 24. Y. Kokaku, M. Kitoh, J. Vac. Sci. Tech., A7(3) (1989) 23 11. 25. K.Enke, Thin Solid Films 80 (1981) 227. 26. C. Weissmantel. K. Bewilogua. K.Breuer, D. Dietrich, U. Ebersbach. H.J. Erier and B. Rau, G. Reisse; Thin Solid Films, 96 (1982) 31. 27. K. Miyoshi, Surf. Coat. Tech, 43/44 (1990) 799. 28. M. Hilden, J. Lee, G. Ouano, V. Nayak, A. Wu. IEEE Tans. Magn, 26 (1990) 174. 29. J.P. Hirvonen. R. Lappalainen. J. Koskinen, A. Antilla, T.R. Jervis and M. Trkula, J. Mat. Res., 5 (1 1) (1990) 2524. 30. K. Oguri, T. Arai, J. Mat. Res. 5 (11) (1990) 2567. 31. F.M. Kustas, M.S. Misra. SPIE Vil. 1325, Diamond Optics 111 (1990) 116. 32. E.I. Tochitsky, A.V. Stanishevskii, V.V. Akulich, O.V. Selifanov and I.A. Kapustin, Surf. Coat. Tech., 47 (1991) 792. 33. J.P. Hirvonen. J. Koskinen, R. Lappalainen. A. Anttila and M. Trkula, J. Electron. Mat., 20(1991) 127. 34. D.S. Kim, T.E. Fischer, B. Gallois. Surf. Coat. Tech. 49 (1991) 537. 35. A. Grill, V. Patel, B.S. Meyerson, Surf. Coat. Tech., 49 (1991) 530. 36. B. Marchon, M.R. Khan, IEEE Trans. Magn., 27 (1991) 5067. 37. Y. Itoh, S. K b i , T. Hioki, J. Kawamoto, J. Mat. Res., 6 (1991) 871

38. K.Oguri, T. Arai, J. Mat. Res., 7-6 (1992) 1313. 39. S. Agarwal, E. Li, N. Haiman, IEEE Tans. Magn., 29 (1) (1993) 264. 40. I. Smeets. I. Meneve, R. Jacobs, L. Eersels and E. Dekempeneer, J. de Physique I V , Colloque C3, Vol. 3. Aoilt 1993,503. 41. H.J. Lee, R. Zubeck, G. Hollars, J.K. Lee, M. Smallen and A. Chao, J. Vac. Sci. Tech., A1 1 (6) (1993) 3007. 42. T.A. Yeh, C.L. Lin, J.M. Sivertsen. J.H. Judy, J. Magnetism and Magnetic Mat., 120 (1993)314. 43. G.D. Lempert, S. Bunker, Nucl. Inst. Meth., B80181 (1993) 1502. 44. X. He, W. Li, H. Li, Vacuum, 45 (9) (1994) 977. 45. M. Belin, C. Donnet, J.C. AugC, A. Grill and V. Patel, Diamond Films and Tech., 4 (1) (1994) 51. 46. B. Bhushan, J. Ruan. Surf. Coat. Tech., 68/69 (1994) 644. 47. K. Taube, M. Grischke, K. Bewilogua. Surf. Coat. Tech., 68/69 (1994) 662. 48. J. Meneve, E. Dekempeneer, J. S m e e t s , Diamond Films and Tech. 4 (1) (1994) 23. 49. C. Donnet. T. Le Mogne. J.M. Martin, Surf. Coat. Tech. 62 (1993) 406. 50. T. Le Mogne, C. Donnet, J.M. Martin, A. Tonck, N. Millard-F’inard, S. Fayeulle and N. Moncoffre. J. Vac. Sci. Tech., A12 (4) (1994) 1998. 51. T. Le Huu, H. zdidi. D. Paulmier, Wear 181183 (1995) 766. 52. J.M. Martin, C. Donnet, T. Le Mogne and T. Epicier, Phys. Rev. B, 48 (14) (1993) 10 583. 53. J.M. Martin, H. Pascal, C. Donnet. T. L e Mogne, J.L. Loubet and T. Epicier, Surf. Coat. Tech., 68/69 (1994) 427. 54. J.B. Sokoloff, Phys. Rev., B42 (1990) 760. 55. M. Hu-ano. K. Shinjo, Jap. J. of Trib., 36 ( 5 ) (1994) 497. 56. K. Holmberg, A. Mathews. Thin Solid Films, 253 (1994) 173.

395

Table 1 Literature survey on friction of DLC coatings in ulua high vacuum Friction coefficient

Type of DLC coating

Synthesisprocedure

Reference

0.01 to 0.02 0.01 to 0.02 0.02 0.01 to 0.3-0.4 0.02 to 0.25 0.30 0.01 to 0.14 0.007 0.04 c0.03 0.007 0.04

a-C:H a-CH a-C:H a-C:H a:C:H: me tal a:C:H a-C a:C:H:Si a-C:H Various coatings a-C:H a-C:H

PECVD / Acetylene PECVD / Ethylene PECVD / Toluene-Benzene-Acetylene PECVD / Acetylene or Ethylene Sputtering (Metal) + PECVD (Ethylene) PECVD / Hydn>carbongas Arcdischarge Electron Cycl. Res. / Ethylene-Silane PECVD / Hydrocarbon gas 7 commercial suppliers compared PECVD / Acetylene PECVD / Hydrocarbon gas

Table 3 Analytical characterizationof the pure MoS2 [50] and hydrogenated DLC [22] coatings Uibotested in the UHV tribometer. Coating (Elaboration) fiOpeflY Results Method DLC

(RF-PECVD)

MoS2 (PVD-Spu ttering)

Structure H concentration c sp3/c sp2

Hardness

Amorphous 40 at.% 40/60 17 GPa

Structure Composition 0 Impurity da Hardness Young modulus

Nanocrystalline (10 nm) MoS2.01f0.1 Less than 4 at.% 4.01 8 GPa 170 GPa

TEM NRS NMR 13C Nanoindentation

TEM XPS / RBS

NBS GXRD Nanoindentation Nanoindentation

Table 4 Shear strength values deduced from friction ecperiments (MPa) Ambient air

a-CH MoS2

88 56

Poor vacuum (10' Pa)

Ultta high vacuum

18 5

4

Pa) 1

396

Table 2 Litterature survey on friction of DLC coatings in ambient air. Friction coefficient Type of DLC coating 0.08 to 0.12 0.20 to 0.40 0.05 to 0.15 0.04 to 0.19 0.05 to 0.15 0.15 to 0.21 0.10 to 0.18 0.15 to 0.25 0.20 to 0.90 0.04 to 0.13 0.12 to 0.18 0.04 0.10 to 0.22 0.07 to 0.10 0.12 to 0.18 0.08 0.20 to 0.35 0.20 to 1.20 0.04 to 0.07 0.03 to 0.09 0.20 to 1.00 0.05 0.2 to 0.6 0.20 to 0.60 0.10 to 0.60 0.10 to 015 0.04 to > 0.30 0.15 0.10 to 0.20 0.20 to 0.60 0.05 to 0.08

a-C:H a-C:H a-C:H a-C:H a-C:H a:C:H:metal a-C:H a-C:H a-C a-C a:C a:C:H:Si a-C a-C a-C a-C:H a-C:H a-C:H a-C:H:Si a-C:H: Si a-C and a-C:H a:C:H:Si a-C:H a-C and a-C:N a-C a-C:H Various coatings a-C:H a-C a-C:H and a-C:W a-C:H:Si

Synthesis procedure PECVD I Acetylene PECVD I Benzene PECVD I Ethylene Ion plating / Benzene PECVD I Ethylene Sputtering (Metal) + PECVD (Ethylene) PECVD /Hydrocarbongas PECVD I Methane or Butane Sputtering Arc discharge Arc discharge PECVD I Methane + H2 + S i c 4 + Ar Ion beam Arc discharge Arc discharge PECVD I Methane + H2 PECVD I Acetylene Sputtering I H2 IBAD I Silicon oil PECVD I Sputtering I Hydrocarbon gas PECVD I Methane + Sic14 Sputtering I Hydrocarbon gas Sputtering I N2 Ion beam Dual ion beam sputtering I Methane 7 commercial suppliers compared PECVD I Acetylene Not mentionned PECVD or Sputtering /Acetylene PECVD / Methane + S i b

Reference

397

Figure 1. Steady-state friction coefficient values for pure MoS2 and hydrogenated DLC coatings, depending on the environmental air pressure during sliding experiments.Results from [22,49,52].

CI

c Q,

. I

0

* *

. I

Q,

0

0

c 0

. I

CI

0

Air pressure (Pa)

398

Figure 2. Optical micrographs of war scars on the DLC films, after 300 cycles. (a) in ambient air ( lO5Pa, RH= 40%); (b) in poor vacuum (lo1 Pa); (c) in UHV (10’ Pa). Results from [22,45].

70 pm

399

Figure 3. Average friction coefficient versus the number of cycles, as tested in UHV. (a) M o h coating; (b) DLC coating. Optical micrograph inset show the contact zone. The DLC transfer film is not complete until the friction has not reached the low steady-state value. Results from [22,53].

a

9

E 0.008 .-a

8 0.006 80 5 0.004

-

-

-

z 0

0

20

40 60 Number of cycles

80

100

400

Figure 4. Imaging of MoS2 wear particles: a general view and enlarged zones of localized frames ( 1 ) and (2). Inset diffractograms are displayed in reverse contrast for a better visibility. These results explain the frictional anisotropy and the possible near-zero friction obtained with MoS2. [52,53].

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

40 1

Self-lubricant"Mosaic"surfaces of type 316 austenitic stainless steel G. Zambelli, J-F. Carton, P. Chevallier and J-D. Wagnikre Department of Materials Engineering, Swiss Federal Institute of Technology, DMXLMPH Ecublens, CH- 1015 Lausanne, Switzerland. Mosaic coatings are composite surfaces tailored for specific tribological systems. This type of surface may be of great interest in improving the friction and wear behaviour of a base material. They may be manufactured by laser cladding of alternate lines of alloys of different composition [ l l . Laser surface treatment offers the unique advantage of creating a locally controlled microstructure with specific phases. The poor sliding contact behaviour of stainless steels against itself could beimproved by mosaic surfaces. I n this study, the material choice was limited to an austenitic stainless steel 316L. Using the mosaic concept, surfaces were modified by the deposition of lines of a n Epoxy+Graphite mixture. During sliding tests between a pin of the same type of stainless steel and the mosaic surfaces, a film transfer of Epoxy+Graphite mixture was observed outs the pin contact surface inducing a third body effect. The formation of a solid lubricant film was already effective for mosaic surfaces with 20% surface lines of a lubricating mixture Epoxy+Graphite 30%. From this microstructurale limit, the wear resistance increased for the mosaics surfaces, an increase associated with a decrease of friction coefficient. These types of mosaic surfaces equally delayed the seizure phenomena during contact with stainless steel 316L. Manufactured mosaic surface of alternate lines of lubricant mixture with different composition is a specific application of composite coatings. This type of coatings is able to induce an optimum tribologic behaviour during sliding contact by synergetic effect. The main interest in creating a self-lubricating contact is to avoid the use of oil lubrication. This development is important for h t u r e applications with respect to environmental considerations. 1. INTRODUCTION

Austenitic stainless steel is well known to give problems when subjected t o unlubricated friction and in particular to be sensitive to galling [2,31. As this material is commonly used in such various domains as nuclear, chemical and food engineering, it would be of a great interest to improve its superficial behaviour. A possible solution consists in creating a composite surface, known as a ''mosaic'' surface. The base material i s inlaid with another by laser cladding or alloying to produce a superficial structure with specific tribological properties. The poor sliding contact behaviour of austenitic stainless steels such as 316L against itself is due to easy prow formation and its high stacking fault energy. The deposition of lines of a hard alloy such as Stellite (Cobalt alloy) having a low stacking fault energy provide one way of preventing prow formation 141. Another way is by manufacturing a pattern of solid lubricant.

This mosaic lubricant network would be able t o induce a protective third body layer. In this study stainless steel was modified using a n Epoxy+Graphite mixture. A simple pattern consisting of alternate traces of the two materials was chosen. Two complementary aspects were studied; the production of mosaics and the mosaic tribological behaviour. An optimisation of the wear behaviour was studied by using different surface configurations. 2. EXPERIMENTAL

1.1. Manuhcturing The base material was a 316L austenitic stainless steel (16%Cr, lWoNi, 3%MO). Deposition of a n Epoxy+Graphite 30% volume powder was made by heated infiltration into grooves machined on 316L surfaces. The mosaic consisted of alternate lines of two materials. Different types of mosaic were manufactured, by varying the groove profile and the steel trace width.

402

Wear Depth Ah

Figure 1. Schematic description of TriboART C400.

1.2. Friction tests A specific sliding test developed for this project was used to characterize friction and wear behaviour (figure 1). It was a reciprocating sliding test TriboART by cylinder (pin)on planar contact. Motion was produced by a LVDT controlled electromagnetic linear motor. The moving pin was a 316L stainless steel cylinder of 16 mm radius and of either 2 mm, 4 mm or 6 mm thickness (figure 2). Cylinders were machined by spark erosion, giving a superficial roughness parameter of Ra = 1,5 pm. Flat samples were polished to a 1 p m diamond finish (Ra = 0,5 mm). The stroke length D was 10 mm. The sinusoidal variation of the linear velocity depended on the choice of frequency (between 1 and 5Hz). Tests were carried out a t 50% re1ative humidity.

Figure 2. Reciprocating sliding (TriboART),cylinder on plane contact.

test

403

Inox 316L / Inox 316L

0

10

20

30

50

40

L (m)

TriboArt / C400

Figure 3. Friction coefficient versus sliding distance of 316L/316L contact. F=23.5N, D=lOmm, b=6mm, R=16mm, velocityv=20.10-3mh, sliding length L=50m, temperature T=20°C, RH = 50%.

IInox 316L / Inox 316L I

Ah 40

30 20

10 0

-10

I

0

1

10

I

20

I

30

TriboArt / C400

I

40

I 50

L (m)

Fig, 4. Wear depth versus sliding distance for 316U316L alternative contact. F=23.5N, k 1 0 mm, b=6mm, FklGrnm, velocity ~=2O.lO-~mh, sliding length L=50m, temperature T=20°C, RH = 50%. The tangential load FT was measured, giving also the friction coefficient p. The vertical displacement Ah between samples surfaces in moving contact measured by laser beam gave a value of the total wear depth of both samples. General tribological testing conditions were : nominal pressure p= 90 MPa, velocity vh 20.10-3 d s , sliding length, temperature T= 20°C, relative humidity RH = 45 - 55%.

3. RESULTS

Stable friction coefficient measured for austenitic stainless steel 316L in self contact was p = 0,61 and wear Ah = 0,2 mm at L = 50 m (figure 3). After a short running period influenced by oxide interaction (m = 0.31, plastic deformation of asperities, adhesion and film transfer, prow formation and debris induce gouged scratch of wear The wear depth Ah was mainly

404

concentrated at 316L pin. After a running period, the wear rate increase until a stationary zone (figure 4). Study was made with a 316L pin on repetitive contact with mosaic CH1 surfaces (77% surface 316L + 23% surface EpoxyGraphitel33% mixture) Figure 5 gives the friction coefficient as a function a of total sliding distance L = 100 m. The average value of the friction coefficient is p = 0.4.

The wear depth Ah i s practically zero. This particular behaviour is due to the measurement of Ah depending of opposing effects: an increase of Ah associated with solid lubricant film compensated by a decrease of pin high. Friction coefficient p and wear depths A h for 316Lhosaic with surface percentage of Epoxy+Graphite mixture lines is shown i n figure 6.

Inox 316L / Inox mosaic CH1 ~~

0

20

40

60

-

~-~

100

80

L (m)

TriboArt I C400

Figure 5. Friction coefficient versus sliding distance for 316L/ mosaic CH1, alternative contact. ~ sliding length L=lOOm, F= 23.5N, D=lOmm, b=6mm, R=16mm, velocity v = ~ O . ~ O -m/s, temperature T= 2WC, RH= 50%.

1 ,

2

100

0.8

Q)

.I

gu

'

0.6

0)

0.4

.I

'f 0.2

. 1

&

0

20

40 60 Relative R+G

80

100

(Or,)

Figure 6. Variation of friction coefficient m and wear depth Dh for 316U mosaic alternative contact with relative surface percentage of Epoxy+Graphite mixture lines. p= 90 MPa, velocity v= 20.10-3 d s , sliding length L=100m, temperature T=20°C, relative humidity RH = 45 - 55%.

405

A film transfer of Epoxy/Graphite mixture was observed on pin contact surface inducing a third body, thereby decreasing the 316L friction and wear at the contact. The formation of this solid lubricant film was effective for mosaic surfaces with the friction coefficient decrease following approximately an inverse mixture law. A significant decrease in wear rate was also measured with an increase i n the surface fraction of lubricating mixture Epoxy+Graphte 30% and the lifetime was also increased.

lines and accumulated over the wear traces. The zero wear rate recorded was due to the measurement method depending on a compensation effect between negative wear depth of 316L zones and positive accumulation of lubricant residues inducing a lubricant coatings at the extremities of wear traces. This i s a specific effect of sliding test conditions.

4. DISCUSSION

Previous results have shown that mosaics surfaces induce some modification of stainless steel tribological behaviour. With regard to reciprocating friction, the friction coefficient of 316 steel on itself in the present test conditions was high (in the order of 0.6). Debris generated during the test on stainless steel was not kept in contact because of the low normal load and high stroke. Thus no third body layer was created which could have induced a change in the friction coefficient [51. A network of parallel lines, containing solid lubricant mixture of Epoxy+Graphite 30%, contributed to the improvement of tribological behaviour. For the same test conditions the friction coefficient was lowered (p = 0,4) and the wear loss was essentially observed at the pin surface contact. During alternative sliding, stainless steel debris was removed and mixed with solid lubricant extruded from the lubricant lines. A self lubricant behaviour was observed limiting the wear rate. Observation of mosaic wear surfaces contact gave very thin lubricant debris on 3 16L lines (figure 7). Only grooves and prow formation were observed. The same observation was made on wear surface contact of 316L pin. In both case the lubricant mixture was accumulated at the extremities of wear traces. The selflubrication effect is dependant on a very thin film of Epoxy+Graphite mixture renewed by lubricant mixture of mosaic

Figure 7. Wear surface contact of mosaic CH1(77% surface 316L /23% surface Epoxy + Graphite133% mixture). Sliding tests between 316L pin and mosaic surface of 30% lines of 316U 20% lines of Epoxy+Graphite 30%/ 50% lines of Stellite6 showed no effective synergetic effect for improving the tribological behaviour of the sliding contact. Burnished Epoxy+Graphite 30% volume coating (100% mixture) on 23% surface line grooves gave a friction coefficient of p= 0.4 and a wear depth Ah = 5 pn. The lifetime of this coating was long and the apparition of alternate lines of Epoxy-Graphite and 3 16L (mosaic 23% Epoxy-Graphite) was no effective for a sliding distance L > 1700 m. 5. CONCLUSIONS

During this study, austenitic stainless steel surfaces were modified to create surface composites. Mosaics with different amounts of complementary phase such as solid lubricant mixtures. Epoxy/Graphite 30%, were manufactured. A mosaic network of more than 20% of solid lubricantlines

406

reduced the 316L wear and the friction coefficient. Galling and seizure of 316L contact were delayed when both types of mosaic surfaces were used. Mosaics are of a great interest for the choice of an optimum behaviour of a material having poor tribological properties such as austenitic stainless steel. Depending of the application they are sufficient to diminish wear and friction locally to load carrying areas which are subjected to wear. An interesting solution i s given by a burnished lubricant mixture on surface line grooves with low depth.

Acknowledgements This study was supported by the Board of the Swiss Federal Institutes of Technology within the context of Priority Program on Materials Research.

REFERENCES 1. D. Lauper, D. Elliot and G. Zambelli, Friction and wear behaviour of mosaic surfaces formed by laser line remelting of cast iron, Wear, 162-164 (1993) 89. 2. A.F. Smith, The fiction and sliding wear of unlubricated 316 stainless steel at room temperature in air, Wear, 96 (1984) 301. 3. K.L. Hsu, T.M. Ahn and D.A. Rigney, Friction, wear and microstructure of unlubricated austenitic stainless steels, Wear, 60 (1980) 13. 4. J.F. Carton, J.D. Wagnihre and G.Zambelli, Friction and wear behaviour of "mosaic" surfaces", 8th International Conf. Surface Modification (1994), Technologies, Nice, Sept TMS.53. 5. M. Godet, The third-body approach a mechanical view of wear, Wear, 100 (1984) 437.

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Role of the Third Body in Life Enhancement of MoS2 K.J. WaN and I.L.Singer Code 6 170, US Naval Research Laboratory, Washington, DC 20375-5342 USA A lubrication replenishment process that accounts for the long life of MoSz coatings worn heavily early in sliding is described and quantified. Reciprocating sliding of a steel ball against MoSz coated flats was performed using a new test nietliodology called ‘stripe testing’ to monitor wear evolution. Worn surfaces were characterized with optical (Nomarski) and Michelson (interference) microscopy, as well as energy dispersive X-ray spectroscopy. Two important ‘third-bodies,’ the ball transfer films and compacted debris patches at track turnaround points, were identified. Material transfer between the track and ball surfaces acts as a reservoir of solid lubricant and plays an important role in sustaining lubricated sliding of MoSz. Dynamics of the process were inferred from measurements of third-body material loss and buildup on track and ball surfaces. 1. INTRODUCTION

2. EXPERIMENTAL

MoSz coatings, typically 51 pm in thickness, can provide ultra-low friction lubrication for sliding or rolling contact under moderate loads and extreme sliding conditions (e.g. vacuum, space). Interestingly, thin coatings of MoS2 can withstand hundreds of thousands of sliding cycles, having overall wear rates <
Thin, dense MoS2 coatings were deposited by the IBAD technique [6,7] to thicknesses from 285 to 1020 nni on hardened steel substrates. A thin (30-40 nm) TiN interlayer was present to act as a diffusion barrier during deposition [ti]. Six different MoS2 coatings were examined in this study; the results for one of these coatings (320 nm thick) are reported in detail in this paper. Reciprocating sliding experiments were performed at 3-4 m d s sliding speed in a dry air environment (RH<2%) with 6.4 mm diameter 52100 steel balls. The initial load was fixed at 9.8 N (mean Hertzian pressure of 0.92 GPa). Wear tests were performed using a reciprocating sliding test methodology, diagrammed in Figure I and hereafter referred to as “stripe testing.” In this methodology, a series of sliding tests were performed to various fractions of sliding life; a new ball was used for each successive track. Individual tracks were run a length of 5 mm for the first n = { 1, 3, 10, 30, 100, ...} cycles; then, the stroke length was shortened to 3 mm for an additional 2n cycles. Tests performed in this manner result in tracks containing three turnaround points (one at each end and one in the middle), and adjacent tracks had segments worn to duplicate sliding cycles. Friction coefficients were monitored throughout the tests, and failure (if reached) was

408

f

(/

than 100 cycles resulted in little or no measurable wear. By 3000 cycles, all of the coatings tested had substantial coating loss. A MoSz coating demonstrating typical wear behavior is shown in Figure 2 [ l l 1. The wear behavior can be divided into three distinct stages.

Figure 1. Schematic of reciprocating sliding 'stripe' testing series for this wear study. Arrow shows ball starting location, turnaround points are indicated by circles, and sliding cycles for the track segments are rluinbered.

defined as the number of sliding cycles attained before the average friction coefficient reached 0.2. After the sliding tests, wear tracks and ball transfer films were examined by optical (Noniarski) microscopy. Track depths were measured via Michelson interference (MI) microscopy and are reported as maximum track depths. Thickness of wear tracks, debris patches at turnaround points, and ball transfer films were estimated by energy dispersive X-ray spectroscopy (EDS) using a thin window Tracor Northern system. EDS spectra were acquired at beam energies of 10 and 20 keV, beam current of 2.0 nA and detector take-off angle of 25". At these energies, the sampling depths are 4 . 7 5 and 2.6 pm, respectively (see e.g. Ehni and Singer 19 I). Since the Mo L, and S K, X-ray peaks overlap around 2.3 keV, the combined X-ray signal intensity, I~o+s,was used to quantify MoS2 coating thickness. Area analysis was used to obtain average thickness values of worn surfaces. Conversion of IMcocsto thickness was acconiplished using a stepped thickness coating of MoS2 deposited on Si [see Appendix]; IhlO+swas approsiniately linear with coating thickness for thicknesses less than -500 nni at 20 keV and -120 nm at 10 keV. 3. RESULTS 3.1 Coating W e a r

Reciprocating sliding stripe tests were performed on 6 coatings that had better than average sliding endurance in rotating pin-on-disk tests [ 10 1. Friction coeflicients reniained low throughout testing (0.02-0.06) until late in sliding life. After testing, wear track depths were measured by MI. For all the MoS2 coatings, sliding for fewer

1

10

100

1000

10000

100000

Sliding Cycles

Figure 2. I B A D MoS2 coating wear track depths ttreasurecl by interference tnicroscopy.

For tlie first 100 cycles, there was no measurable wear (Stage I). A period of rapid wear follows (Stage II), where the coating is worn to nearly the full thickness by -1000 cycles. A long period of low average wear is then observed during the remaining -20000 cycles (Stage 111). 3.2 Third bodies -wear tracks

Figure 3 shows a montage of optical micrographs displaying the wear tracks between 100 cycles and failure. Before 100 cycles (not shown), the tracks had a lightly burnished appearance and a small amount of material deposited at the track ends. From 100 to 300 cycles, light scratches were visible on the track. Patches of compacted debris were visible at the track ends, and ejected debris particles were observed along the sides of the tracks and beyond the compacted debris at the track ends. Between 300 and 1000 cycles, larger patches of material were seen in the track and at tlie ends of the track, and scratches were more pronounced. By 3000 cycles, darker (brown) regions were observed in the track, suggesting that the coating was worn through to the TiN interlayer. Scratches remained pronounced over the entire

Figure 3. Montage of optical micrographs of wear tracks showing evolution of IBAD MoS2 wear track ntorphology behveen I00 cycles and failure.

track surface. Compacted and loose debris remained visible along the sides and at the ends of the track; debris patches at track ends were less pronounced. At failure, while some regions still appeared to have intact coating, long strips of the dark areas (TIN interlayer) as well as bright white areas were visible. In Figure 3, tracks worn to comparable sliding cycles are positioned adjacent (but offset diagonally) to each other. First, note the consistency of the morphologies exhibited in tlie two 300 cycle tracks, the 900 and 1000 cycle tracks, and the two 3000 cycle tracks. In this arrangement, it can be seen that the amount of compacted and loose debris deposited at the ends of the wear tracks increased with sliding cycle until 3000 cycles; after this, the compacted debris was depleted as sliding progressed. The loose debris ejected from the track is excluded from further participation in the sliding process. Several types of third bodies were identified from the optical microscopy of track surfaces; examples of these are pointed out in Figure 3. These included lumps of compacted debris on the wear track surface (A), large patches of debris at turnaround points (B), and small (
patches of inalerial observed at the ends of the tracks are directly under tlie turnaround points, and not beyond the turnaround points; the ball rests over these points during each cycle. Together, the individual third bodies make up the distinct morphologies associated with each identified stage of wear. (A more detailed examination of wear track morphology and chemistry will be published elsewhere). 3.3 Third bodies -transfer films on balls

Transfer films on ball surfaces were distributed in three distinct regions of the contact [12 1, and a number of third bodies were identified. The progression of third body formation on the ball surfaces was correlated to the 3 stages of wear; like tlie track surfaces, each stage had a distinct morphology. During the first few sliding cycles (Stage I, not shown), very thin films of MoS2 transferred to the center of the contact (determined by AES [ 1 I]). Thicker patches of compacted debris were observed around the perimeter of the contact zone. During Stage 11, the center of the contact zone acquired srnall lumps of debris (Figure 4a) and by Stage 111, tlie film had become a continuous, thick transfer pad (Figure 4b). Copious amounts of loose debris were observed around the contact zone on the

410

Figure 4. Optical inicrographs of ball transferJltns fortned during sliding against IBAD MoS2 coatings aJter (a) 90, and @) 9000 sliding cycles. ball surface by Stage 11, accumulating as sliding progressed. 3.4 Quantification of wear and third body evolution The buildup and depletion of material on track and ball surfaces were quantified using EDS and are shown in Figure 5 . As espected for dense coatings, material loss in the tracks is consistent with the optical interferometry results (Figure 2). On the balls, the average transfer film thickness in the center of the contact incrcased as sliding progressed. Thickness of ball transfer films at failure was not quantified due to oxygen incorporation, m
-

300

-0

200

t:

400

C

'

100

E

0

1

10

100

1000

10000

100000

Slldlng Cycles

Figure 5. Track, patches at turnaround points (end and midpoints), and ball trans,fer j h n thickness measured by EDS,

the outermost turnaround points in the wear tracks (Figure 5 , filled squares). From the plot, it can be seen that buildup occurred during the period of rapid coating loss from tracks in Stage 11. Depletion of the end patches to nearly zero thickness occurred during the long steady state (low wear) Stage 111. The patches at the center turnaround points, also shown in Figure 5 (open squares), were formed afler the stroke length was shortened; consequently, these patches were accumulated on previously worn track surfaces. During the period of rapid coating wear (Stage 11). these center patches were about the same thickness as those found at the outer endpoints. Conversely, the center patches in Stage Ill were thinner than the corresponding end patches. This is not unexpected, since the center patches were formed after the coating was substantially worn). However, these center patches are substantially thicker than the wear track on either side, therefore providing evidence that substantial lubricant redistribution to as well as fronr end patches continues after the high wear period. 4. DISCUSSION

The progression of third body wear morphology (Figures 3, 4), together with quantification of clianges in thickness (Figure 5 ) are interpreted as a lubricant transfer process (Figure 6). During Stage I, a film transfers from the coating to the ball surface, and some of the lubricant is deposited in patches at the turnaround points, either directly

41 1

Stage I

(a1

Polch

Stage II Ejected debris

Icl

Stage 111

Figure 6. Schematic of lubricant transfer processes between the coating wear track (coating), ball transfer film (ball xfer), and patch niaterial at turnaround points (patch)for (a) Stage I, (b) Stage 11, and (c) Stage III sliding. Solid arrows indicate observed material transfer directions, while dashed lines indicate other possible transfer routes.

(plowed) from the coating or indirectly (retransferred) from the ball transfer film (Figure 6a). In Stage I1 (Figure 6b), more of the lubricant removed from the track is transferred to the patches at turnaround points as well as onto the ball. The material deposited at the turnaround points and on the ball surface can act as reservoirs to replenish lubricant lost from the sliding contact. During Stage I11 (Figure 6c). the end patches become depleted as they replenish lubricant to the sliding interface. Throughout Stages I1 and 111, material is ejected (as loose debris) and lost to regions of the ball surface outside the contact zone as well as along the edges and beyond the ends of the tracks; this material is largely unrecoverable and is excluded from participation in the replenishment process. We note that previous investigations of MoSz sliding have documented the individual processes

described above. Transfer films are formed on the first pass [13,14,15], and MoS2 debris can be extruded through the sliding contact and exchanged between transfer film and track surfaces [ 16,171. Transfer film buildup has been correlated to lubricant loss in the track [4,13,14], and the importance of the transfer film for endurance of solid lubricants has long been noted by Lancaster

[W.

Our experiments suggest the endurance is not simply determined by the wear rate of the MoS2 coating, but rather by the dynamics of the replenishment process diagrammed in Figure 6. Together, the evolution of the thickness of transfer films, wear tracks, and end patches at turnaround points determine the net loss of material from the contact, not simply a coating wear rate. The amount of lubricant available to the contact is established by the dynamics of MoS2 coating wear and replenishment. The model diagrammed in Figure 6 can be reduced semi-quantitatively to a simple summation of material fluxes JV (between coating, ball, end patches, and ejected debris), as shown in Figure 7.

Figure 7. Senii-quantitative material transferflux.

The models in Figures 6 and 7 are consistent with the third-body processes described by M e t [ 19,201:1) debris detaches from the first-bodies, 2) the debris is trapped in the contact, and 3) debris is ejected from the contact. In the simplest sense, it is this lossflux (or ejected debris) which is relevant to overall wear, rather than the individual particle detachment mechanisms observed. It is recognized that the material transfer process is influenced by

412

particle entrapment in the contact, which in turn is influenced by such parameters as geometry, sliding configuration, and system vibration [20). In our Configuration (ballan-flat, bi-directional sliding) there are localized points on the track where lubricant material can build up. Unidirectional pinondisk and flat-on-flat test configurations would each have different entrapment geometries and rates. Interestingly, while the ability of MoS2 debris to build up and remain entrapped in the contact may be beneficial in some cases, it is detrimental in others (e.g. torque-bumps formed on MoSz coated bearing surfaces during dithering [2 1 I). Finally, little is known about the third-body materials properties controlling these tribological interactions: mechanical properties, chemistry (bulk and interfacial), structure/phase, and morphology can contribute. If no chemical degradation is involved, the effective wear can be controlled by limiting the loss flux ( J , A ) , e.g., reducing either debris loss or debris generation rates. More detailed understanding of transfer film properties (mechanics, chemistry, etc.), coupled with an understanding of the lubricant transfer dynamics, can be used to guide modifications of solid lubricant chemistry or structure to enhance wear life and bearing performance.

5. CONCLUSIONS A new methodology, ‘stripe testing,’ was used to study the wear behavior of thin, dense MoS2 coatings. It was found that IBAD MoS2 coatings wore rapidly during the first 5-10% of sliding life. Despite this early loss, lubrication of tlie sliding contact continued for tlie remaining 90% of sliding life. A dynamic transfer process was proposed, where third body lubricant reservoirs were formed, then emptied; this process provides replenishment by redistribution of lubricant between the track and ball surfaces. The dynamics of the process were inferred by coupling the stripe test methodology with quantitative measurement of material loss and buildup on the wear tracks and ball surfaces. 6. ACKNOWLEDGMENTS

The authors thank R.N. Bolster (Geo-Centers) for coating deposition, J.C. Wegand (Geo-Centers)

for some tribotesting, and L.E. Seitzman (NRL) for valuable discussions. REFERENCES I . T. Spalvins, Thin Solid Films 118 (1984) 375. . G.D. Gamulya, G.V. Dobrovol’skaya, I.L. Lebedeva and T.P. Yukhno, Wear 93 (1984). 3 . P.D. Fleischauer and R. Bauer, Tribol. Trans. 3 1 (1988) 239; M.R. Hilton, R. Bauer and P.D. Fleischauer, Thin Solid Films 188 (1990) 219. 4 . I.L. Singer, S. Fayeulle and P.D. Ehni, Wear, in press. 5 . G.B. Hopple, J.E. Keem, and S.H. Loewenthal, Wear 162-164 (1993) 919. 6 . R.N. Bolster, I.L. Singer, J.C. Wegand, S. Fayeulle, and C.R. Gossett. Surf. Coat. Technol. 46 2

(1991) 207. 7 . L.E. Seitzman, R.N. Bolster, I.L. Singer, and J.C. Wegand, Tribol. Trans. 38 (1995) 445. 8 . L.E. Seitzman, I.L. Singer, R.N. Bolster and C.R. Gossett, Surf. Coat. Technol. 5 1 (1992) 232. 9 . P.D. Ehni and I.L. Singer, Appl. Surf. Sci. 59 (1 992) 45. 10. K.J. Wahl, L.E. Seitzman, R.N. Bolster, and I.L. Singer, Surf. Coat. Technol. 73 (1995) 152. 11 . K.J. Wahl and I.L. Singer, Tribology Letters I (1995) 59. 1 2 , S. Fayeulle, P.D. Ehni and I.L. Singer, in Mechanics of Coatings, Leeds-Lyon 16, Tribology Series 17, eds. D. Dowson, C.M. Taylor and M. Godet, Elsevier, Amsterdam, 1990, p. 129. 1 3 . P.D. Fleiscliauer and R. Bauer, Tribol. Trans. 31 (1988) 239. 1 4 . M.R. Hilton, R. Bauer, and P.D. Fleischauer, Thin Solid Films 188.(1990) 219. 1 5 . P.D. Ehni and I.L.Singer, in New Materials

Approaches to Tribology: Theory and Applications, Materials Research Society Symp. Proc., Vol. 140, eds. L.E. Pope, L. Fehrenbacher and W.O. Winer (Pittsburgh, 1989) p.245. 16 . H.E. Sliney, ASLE Trans. 21 (1977) 109. 1 7 . R.L. Fusaro, ASLE Trans. 25 (1982) 141; R.L. Fusaro, NASA TP-1343 (Cleveland, OH, 1978). 18 . J. Lancaster, J. Tribol. 107 (1985) 437. 1 9 , M. Godet, Wear 100 (1984) 437. 20 . M. Godet, Wear 136 (1990) 29. 21 . R. Bauer and P.D. Fleischauer, Tribol. Trans. 38 (1995) 1.

413

APPENDIX A stepped-thickness coating of IBAD MoS2 on Si was used for calibration of the Mo La + S K, EDS signal. The thicknesses were measured optically by MI and were found to be 120, 235, 475, and 950 nm. The integrated peak area of the Mo+S signal vs. MoS2 thickness at 20 keV is plotted in Figure Al. The data were fit using a linear least squares algorithm. Good correlation was found for Uucknesses below 475 nm at 20 keV and 120 nm at 10 keV (not shown), with correlation coefficients 0.9995 and 0.995, respectively. Since the substrates and balls used in the present experiment are steel, four further data points were acquired (at 20 keV) using various MoSz coatings between 55 and 440 nm thick deposited on 440C and 52100 steel substrates. These values are also plotted in Figure Al. As can be seen from the plot, the integrated intensities observed for MoS2 on these steels are comparable to those observed for MoS2 on Si.

EDS Mo+S vs MoS2 Thickness

20000

-s

loo00

6Ooo 0

I 0

0 X

100

200

(Coating 4) Ni (Coating 4)

300

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600

Thickness (nm)

Figure A I . QuantiJcation of EDS Mo +S signal as a function of M0S2 coating thickness on Si substrate at 20 keV. Valuesfor 4 coatings on steel substrates at 20 keV and the MoS2 coating detailed in this study (on A450 and Ni substrates) are also shown.

The coating examined in this study was found by EDS to have a higher than average mass density given its measured thickness (see open squares in Figure Al). Additional data points for intermediate thicknesses were obtained using sputter craters measured by interferometry. Some enhancement of IM,,++s can be attributed to the presence of about 2 at.% Mo in the substrate, which was M50 steel. However, this can only account for approximately 2000 counts for bare M5O and 800 additional counts at 320 nm. This was confirmed by the examination of the same coating deposited on a Ni foil, which results in only a small drop in intensity of the order expected (shown by X in Figure Al). The higher IM*+S signal of this coating as compared to the other coatings examined for the calibration was believed due to its being Mo-rich (e.g. MoS24, which increases its effective density. This was consistent with the measured coating thickness vs. quartz crystal monitor mass data obtained during coating deposition. Although the mass density of the coating examined in this study deviated from the norm, the thickness was still within the regime that can be approximated by a linear relationship. Since the coating is thin (320 nm), a large fraction of the 20 keV EDS signal comes from the substrate elements. Calibration for the dense film was obtained by subtracting the contribution to the IMMS signal from the M50 steel; this was estimated by using the intensity ratio of Fe K, to Mo La obtained from uncoated M50 steel and monitoring IFs across the worn surfaces. A corrected linear fit for the coating was then obtained, and these values used for quantification of wear track thicknesses. EDS data from transfer films on the 52100 balls were obtained with 10 keV electrons because the films were too thin to be measured accurately using 20 keV electrons. At this lower beam energy, enhanced X-ray excitation cross-section allowed for better differentiation between small changes in thickness. Estimates of thicknesses were obtained by using the 10 keV calibration data from the MoS2 coating on Si, but it is recognized that this probably overestimates the thickness by up to 20%. Thus, the thickness estimates of transfer films (which may be fluffy or porous) are used simply for comparative purposes. However, the changes in the mass thickness observed in a given region are real.

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415

Significance of transfer layers for dry frictional applications RiSdiger Holinski

Department of research and development of DOW CORNING,Pelkovenstr. 152,80992 Munich, Gel.lllaIly

To improve tribological performance, solid lubricants have been added to many materials such as sinter metals, carbon brushes, brake linings and plastic materials. Solid lubricants were found to reduce wear of components to stabilize hction and to reduce vibrations. If composites are in sliding contact to metal surfaces initially no transfer of material occurs from one component to the other. Friction force increases and thereby interface temperature, whch leads to the formation of a friction layer at the composite surface and to transfer of material to the surface of the metal component. T h s results in a substantial reduction of friction and frictional temperature. After tribological experiments investigated were several plastic materials and carbon brushes containing Molybdenum Disulfide and combinations of solid lubricants. It was found that wear was low in cases where transfer films showed good adhesion to metal surfaces. Adhesion depended on chemistry of the transfer layer. Thin films were found to have a longer life than h c k films. Cohesion of solid particles within the film depended on the chemical composition of the film. Certain combinations of solid lubricants form extremely thin transfer films with excellent adhesion on the substrate resulting in extremely low wear rates. 1. Introduction

The slidmg mechanism of composites against metal surfaces has been investigated by many researchers. It has been found that during the initial running-in procedure no material is transfered from the composite to the metal surface.

During this initial period, fnction coefficient increases dramatically and thereby frictional temperature (1). Thereafter small quantities of composite material are transfered to the metal surface until a certain thickness is reached which does not change anymore. During trander of material friction coefficient decreases again, so does frictional temperature (figure 1).

416

t

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QUANTITY OF MATERIAL TRANSFER 2

TIME

FRICTI0 N COEFFICI E NT

1

TIME Figure 1. Friction coefficient during wear-in This phemomenon has been explained by the adhesion behaviour. When sliding is initiated between the surfaces of the polymer in contact with metal, shear takes place in the polymer and a polymer film is left on the metal surface. In other words, the interfacial bond formed between the polymer and the metal substrate is stronger than the cohesive bond within the polymer. Friction increase during the run-in period is explained by the formation of bonds between the polymer and the metal surface. Furthermore, cohesive bonds within the polymer are sheared of€, producing high friction and high-frictional temperature (2). Polymer surfaces at the area of frictional contact have been investigated and formation of a fiictionlayer was found. This friction-layer has a different structure and composition than the matrix-material. At the end of the running-in period, fricuon-layer is rubbing against the transfer-layer on the metal surface. The lifetime of transfer-layers depends on the adhesion of composite material to the metal substrate and on the cohesive bonds within the polymer layer. Bonding was found to depend substantially on the chemistry of the uansfer film (1).

In order to obtain more information on adhesion, transfer-layers from a number of dry-frictional applications have been investigated. 2. Experimental

Transfer-layers on metal surfaces were investigated by scanning electron microscopy and energy dispersive microprobe analysis. Frictional tests with polymers on metal rmrfaces have been investigated by the ring-block machine. 3. Discussion of results A steel shaft was running against a bearing shell, consisting of resins and molybdenum disulfide as a lubricating filler. Microprobe analysis revealed that the shaft surface was coated by a rather thick film of molybdenum disulfide (figure 2). In the scanning electron micrograph, a rather thick film on metal substrate can be seen. Analysis reveals that this film consists of molybdenum disulfide and has a thickness of several micrometers, since the iron content detected is comparably small.

417

3 F-fO

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Fe

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0 Mo

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8

10

Figure 2. SEM micrograph and microprobe analysis of surface of steel shaft (1000 x) Another plain beanng was running against a steel shaft in a different application. In this case, the resin was filled with a combination of solid lubricants including molybdenum disulfide. Again it was found that the metal shaft was coated by a transfer film. This film has a thickness of less than 1 pn, as can be seen from figure 3. The film seems to be very homogenous. The chemical analysis shows that dominating is the iron peak. The transfer-layer basically consists of the elements of the lubricants composition including molybdenum &sulfide. In practical applications it has been found that the plain bearing containing a filler of various solid lubricants have a much lower wear rate than the MoS? filled plain bearing. This explains that the transfer-layer being formed on the metal substrates is thinner for the combination of solids. Obviously, the adhesion of tlus lubricant's composition is better than that of molybdenum &sulfide, since the wear life of the plain bearing is much longer in comparison to the MoS7 containing bearing.

Figure 3. SEM micrograph (5000 x) microprobe analysis of steel shaft surface.

and

Special anthction bearings contain a dry composite consisting of a binder and solid lubricants. All the spacings of such a ball bearing are filled with the dry composite. During running of the anrhction bearing, a transfer film is formed on the moving parts of the bearings, such as balls and rings. Transfer-layers have been investigated on the balls and were found to consist of the composite material. It has been found that this transfer film reduces friction, frictional temperature and wear rate. During development of such a self-lubricating composite for anti-fiction beanngs, various solid lubricants and combinations thereof have been tested. It has been found that a certain combination of solids led to the best wear rate and best lifetime of the bearing. Again the combination of solid lubricants are responsible for the adhesion of the transfer-layer on the metal substrate and its lifetime. Transfer-layers are removed from the moving parts in the antifriction bearing by fatigue or abrasion. Thereafter, a new transfer film is being formed from the reservoir of the composite wearing off tventually the composite material.

418

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~~-

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. .-

____

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........

..

.. ~.

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Figure 4. SEM microgriiphs of ball surface before (left) and after (right) run with dry composite (5000 x) The kcy lo long life of such a dry lubricant is the adhesion of transfer films on moving parts of the b r i n g and thc cohesive bonds within the compositc matcrial (figure 4). In electric motors, carbon brushes are in sliding contact with a copper commutator. A carbon brush consists of a mixture of graphite and copper powder. Normally, such a composition contains 5 % of molybdenum disulfide in order to reduce carbon brush wear and reduce commutator wear. After tests of carbon brushes in electric motors, chemical analysis was performed of thc wear track of the carbon brush and the surface next to the wear track. From figure 5 it can be seen that the carbon brush contains a certain amount of molybdenum disulfide. In the wear track the molybdenum disulfide content is much higher. That means the area of frictional contact of the carbon brush is coated with molybdenum disulfide film. It was further noted that the copper commutator has been coated with a black layer. This layer seems to consist of a transfer of carbon brush material including molybdenum disulfide. The elements molybdenum and sulfur have been detected at the commutator surface.

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. . . . . . . .

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-

Figure 5. Microprobe analysis of an MoS2 containing carbon brush. Top: next to wear scar; bottom: in wear scar Carbon brush formulations have been filled with a combination of various solid lubricants in place of molybdenum disulfide. Wear experiments revealed that such combinations of solids resulted in a dramatic wear reduction of carbon brushes. Almost no wear had been detected on the copper commutator surface. Microprobe analysis revealed that extremely thin transfer-layers have been found on the copper surfaces. Obviously, these transferlayers showed extremely good adhesion on metal surfaces preventing wear of the copper substrate.

419 Because of the long life of these transfer-layers. no material had been required for formation of neu transfer-layers which resulted i n rather low carbon brush w a r . Such a transfer-layer has not the tendency to continue to grow. but stavs at a thickness of less than 0.2 pm (figure 5 ) . The surface roughness of wear scars have been determined on copper brush and commutator surface. It showed that the combination of solid lubricants resulted in much lower surface roughness in comparison to a carbon brush filled with molybdenum disulfide (figure 6).

Friction force passed through a maximum and came down to v e q low levels. Thc ring which has becn run in with a load of 3 kg came down to low friction after about one minute. The film wiuch has been run in with a load of 10.5 kg needed about 10 minutes to amve at the low friction force. This means that the cohesive forces are much higher for a film which has been run in with higher loads. The transfer of lubricating material to the metal surface rcquired niuch higher friction forces and took much longer. There was obviously a struggle between the cohesive forces within the composite and the adhesive bonds between the composite material and the metal surface (figure 7). At the tribological contact of the block sliding against the ring, a very thin film of molybdenum disulfide has been detected. At the end of the experiment. lubricating layer is sliding against the lubricating layer at very IOU friction coefficients. .. .

.

.

,

.

..

. . .

. ..

. . .. .

'I

Figure 6. Surface roughness of \\ear scar of carbon brushes. Left. Molybdenum Disulfide. right combination of solids Some more inforniation has been collected using the ring-block test machine. A composite film was applied to the ring surface. By loading up the block. such a composite film has been run in on the ring using 2 different loads. In a second experiment. the block test specimen was removed from the machine and another new block was put in its place. Tests were continued with the same load. From figure 7 it can be seen that initially friction increased to rather high friction forces.

I

L.OOr2

-.

L.: : -

>.

.

-*

:. *

"C

.

:.

.

. . ... ~ . . ;.. .. .. .

_i

""

. ""

.

.

., ..,,

Figure 7. Friction force of a composite film running :gainst li steel block. 'Top: run-in load: 3 kg: bottom. run-in load. 103 kg

420

4. Closure: To improve lubricating performance of composites in the past molybdenum disultide powder has been used as a filler. This actually resulted in reduction of friction and wear rate when composites have been in sliding contact against metal components. However, molybdenum disulfide had the tendency to transfer to metal substrate and form rather thick solid layers. M e r some time, these layers failed due to fatigue or abrasion. A new film had to be formed on the metal surface.

Certain combinations of solid lubricants also resulted in transfer of material to the surface of the metal counterpart. In general, it was found that these transfer-layers have been much thinner than those formed out of pure molybdenum &sulfide. Also adhesion was much improved since these films lasted much longer. This longer life reduced the wear rate of composite material substantially, because new transfer-layers needed only to be formed when the old one had failed. Quality of transfer-layers obviously depends on the bond strength of solids to metal substrates, the thickness of such films. and cohesive bonds within the transfrr-layer.

References 1. C. Langlade, S. Fayeulle, R. Olier; New insights into adhesion and lubricating properties of graphite-based transfer films, wear, 172 (1994), page 85 92 2. Bowden, Frank P.; and Tabor, D.;The Friction and Lubrication of Solids. Part 2, Oxford Clarendon Press &ondon), 1964

-

SESSION XI HYDRODYNAMIC LUBRICATION Chairman :

Professor Jean Frene

Paper XI (i)

Pressure Drop in a Hydrostatic Pocket. Experimental and Theoretical Results

Paper XI (ii)

Application of the Homogenization to Thin Film Gas Lubrication

Paper XI (iii)

Boundary Conditions for Reynolds Equation with Particular Reference to Piston Ring Lubrication

Paper XI (iv)

Effect of Compliance on the Extent of Optimum Compliant Air Thrust Bearing Operating Range

Paper XI (v)

Experimental Measuring of Velocity Profiles in Herringbone Grooved Journal Bearings

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

423

Pressure Drop In A Hydrostatic Pocket. Experimental and Theoretical Results M. Arghir, S.E. Attar, D. Nicolas Laboratoire de Mtcanique des Solides URA CNRS,Universitt de Poitiers 40, Avenue du Recteur Pincau, 86022 POITIERS CEDEX

-

This paper presents experimental 'and numerical results of the pressure drop in a hydrostatic pocket. The pure hydrostatic flow was investigated for laminar and turbulent regimes. The good agreement between experiment and theory obtained in the turbulent regime enables to propose a relation for the pressure drop coefficient. 1. INTRODUCTION

Geometric discontinuities cannot be handled by the Reynolds equations or by the film thickness averaged (bulk flow) equations. The hypothesis involved in deducing this equations (neglecting the transversal velocity, constant pressure across the filni thickness) exclude the existence of a flow pattern with recirculation zones. The effect of geometric discontinuities is introduced in the equations of the lubrication theory using concentrated pressure droplrise coefficients. This coefficients are usually deduced from experimental information. During the last years the force of the numerical methods offered an alternative tool for predicting unconventional flows in bearings. Because no approximations are made, the integration of the complete system of the flow governing equations may be considered as a riumerical experiment. This is true for the laminar flow regime, when no modelling assumptions are made and the only difficulty is the numerical integration of a non-linear system of differential equations. For the turbulent flow regime the nccessity to describe the turbulent behavioiir introduces modelling assumptions. Concentrated inertia effects act different if the flow is a shear driven or a pressure driven one. The pure shear driven flow correspoiids to the limiting case of a hydrostatic bearing working in centred position. As first shown by Constantinescu and Galetuse [4] the pressure may rise or may drop, depending on the surface Reynolds number and the ratio of the film heights. The pressure driven flow is the limiting case of a flow through an orifice. The fluid is accelerated in the land region and a pressure drop occiirs. For an inviscid flow or if the protruding corner would be

rounded the pressure drop is given by Bernoulli's formula. In real flows, the streamlines are curved after the inlet. A small recirculation zone may be located on the step wall after the contraction. This curvature reduces the flow section and so enhances the pressure drop. This effect may be quantified by a pressure drop coefficient.

5 = - AP2

pu, 2

Experimental investigation of this effect were done by Chaomleffel and Nicolas [3] and by Constantinescu [S] for the laminar and the turbulent flow regimes. Numerical studies were done by SanAndres and Velthuis 191 and by Braun and Dzodzo 121. Their results concerned only the laminar flows. In this paper we present experimental and numerical results obtained for a pressure driven flow in a step. The results are obtained for laminar and turbulent flow regimes up to Rep=12000. 1.1. Notations A, coefficient in (A3) CI , y, coefficients in (14) h, thickness k, k', turbulent kinetic energy, non-dimensional k,, k,, coefficients in (2) I,, mixing length p, pressure P, film thickness averaged pressure Q, flow rate Rep, Reynolds number of the Poiseuille flow R, Rp, local Reynolds numbers s, parameter defined by (22)

424

Figure 1 Experimental device To, reference temperature u, v, velocity components u,, friction velocity lit, yt. non-dimensional velocity and distance ii,,,, film thickness averaged vclocity s,y, Cartesian co-ordinates x, E, coeflicients in (22) h,reference dynamic viscosity p, coefficient in (4) E, E'. dissipation, non-dimensional @, general variable p, dynamic viscosity p,,u~l> pLsl~, turbulent and effective viscosity p, dcnsity T. slicar strcss 5. pressure drop coefliciciit

- pocket length

!,=o.o751n

- pocket depth - pocket pressure level - ineasured temperature

h,=2mm+hf or 5mm+hr Po=0.5.10SPa to 8.105Pa T=18"C to 30°C

A close circuit pump with a 1.2 m 3 reservoir is used to supply the fluid. The temperature of the fluid is not controlled so heating occurs during a measuring set. The average exit tempcrature is continuously measured by a thermocouple. The pressure is measured by a classical manometer. The flow rate Q is determined using a volumetric counter. 2.2. Bulk model of the flow

Three flow regions can be distinguished on figure 2a: I. the pocket region 11 the step region 111. the thin film region The theoretical pressure variation is presented on figure 2b. The flow in regions I and 111 is governed by the Reynolds equation presented by Frine et al. [6]

Re, I 1 0 0 0 1000
(3)

2. EXPERIMENTAL DEVICE AND RESULTS 2.1. Description o f the ex~ierimcntaldevice

The experimental device presented on tlie figure 1 is made of two plates separated by lateral sheets

which enable to eliminate the lateral flow and to control tlie height of tlie thin film The lower plate has ;I pocket and is provided at one edge with ten supply orifices in order to have a uniforni flow along the width L. The upper plate is flat and is provided with pressure measuring locations in its median plane. The characteristics are:

- axial width, - thin film length, - thin film thickness

L=O. 1In e =o. 1nl h,=O. lmin to 0.541niii f

The viscosity is considered to vary with the teinpcrature.

(4) In the region I the pressure PSI is calculated by linear extrapolation of the measured results.

425

bulk velocity in the thin film zone.

The pressure gradient in the region I is very small compared to the pressure gradient in the region I11 because the height ha is always much larger than the height hr. 2.3. Measurement accuracy An accurate evaluation of the pressure drop coefficient imposes that the surfaces should be parallel, the film thickness should be well known and the pressure and the flow rate measurements should be of known tolerances. A finite element calculation of the deformations produced by the film pressure shows that the plates should be thick enough. A 40 mm thickness of the aluminium plates was appropriate. The tightening of the screw-bolts is made using a torque wrench in order to ensure an uniform distribution of the stresses. The film thickness in the land region is not a priori known because the lateral sheets are squeezed ‘after the tightening of the screw-bolts. However we can estimate this thickness using the measured flow rate Q and pressure P4.

Figure 2a Flow geometry

Figure 2b Theoretical pressure distribution

and the flow rate is given by Q

11:

P3 -Po

I -

ll,

$.I

In the region 111 the pressure Pn2and the flow rate are: 1, P,, = P4 -

(7)

1,

C’,. = 1, -5.10-3m

@a> In the region 11, the pressure variation is modelled by the pressure drop coefficient 5 that relies the pressure variation due to the step to the

The accuracy of the flow rate measurements is estimated to 1%. The accuracy of the pressure measurement is in the order of 2% and it can attain 4% for small values. The accuracy of the temperature measurement is in the order of 2%. Taking into account this accuracy, the experimental uncertainty of the calculated film height is between 2% and 3%. That is experimentally validated because for the same test conditions, calculated film heights vary less than 2%. 2.4. Experimental results The pressure drop coefficient is given by

426

3

&* *

i

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

ha/hf : 4C

*

* I2

I0 A

0 0

0 0

15.3 9.7 9.3 65

4.8 4.5 2000

4000

6000

8000

10000 Rep

12000

Figure 3 Experimental pressure drop coefficient The experimental results are prcscnted on the figure 3 as function of the Reynolds number for different film thickncss ratio h./hr. Each symbol represents a different test, i.e. many supply prcssures are considered for the same geometry The dispersion of the results is rnoderatc. Because the measured pressure accuracy may attain 4% for small values, the dispersion is more important for low Reynolds numbers. So, for Reynolds numbers less than 2000, the accuracy of 5 may attain lo%, but it is around 6% for higher Reynolds numbers. At Reynolds numbers less than 1500, the pressure drop coefficient is very depcndcnt of this; it decreases rapidly with increasing Reynolds number. If the Reynolds number becomes high, the pressure drop coeflicient is around 1.5. Apparently the pressure drop coeflicient docs not depend on the film thickness ratio, its variation being less than the measurements accuracy.

3. THEORETICAL MODEL

3.1. Flow governing equations

The mathematical model consists of the time averaged Navier-Stokes equations. The equations are numerically integrated on a two-dimensional domain.

The turbulence model is the classical k-E turbulence model introduced by Launder and

427

Spalding IS]. For the coefficient C, intervening in the relation (13) an expression introduced by Rodi II3 I was used.

proportional velocity perturbation only in the same point. The convergence of the iterative process is controlled by the source terms of the pressure correction equation:

The same accuracy is used for the transport equations residues. This expression is better adapted for situations when the equilibrium between the kinetic turbulence energy generation, Gk, and the dissipation E is not satisfied. The form of the source terms So was presciited by many authors, e.g. in [ I ] . The equations are discretized using the finite volume method. The coupling between the pressure field and the velocity field is solved using the SIMPLE algorithm proposed by Patankar [ 111. The “power law” was used for discretizing the convective terms. The control volumes for the components of the velocity are staggercd from the grid points to avoid an unfavourable decoupling between the pressure and the velocity fields. The grid consists of variable spaced rectangles. Very line grid spacing in both directions were used in the vicinity of the protruding corner of the domain. The grid spacing varies like a geometric progression towards the entrance and the esit section and towards the upper wall. The computational domain do not covers all the length of the experimental device. The entrance and the exit sections are considered far away from the step zone in order lo have fully developed flow. The numerical algorithm has two steps: an iniplicit predictor step and an explicit corrector. At the beginning of the predictor step an estimation of the pressure field is used in the momentum equations which are implicitly solved. The new estimations of the velocity ficld are used to calculate the source term in the discretized pressure correction equation. This equation is also implicitly solved in the predictor step. The resolution of the linear systems is made using a line-by-line relaxation algorithm combined with a red-black columns numbering. In the corrector step. velocities and pressures are adjusted considering that the pressure perturbation in a point determines a

3.2. Boundary conditions In the inlet section we suppose that the flow is parallel to the walls:

laminar flow regime u(y) = 6 u mg 1 - i ) turbulent flow regime I

-

~ ( y ) = ~ u ~ [ 2 - m i n ( i , l - i ), ]n ~2 3 (18) The inlet average velocity, u,,,, is calculated from the Reynolds number given by (3a). A constant kinetic energy profile, corresponding to 15% turbulence degree level is considered in the inlet section. Even if the entrance boundary conditions are not very accurate, the distance from the inlet section to the step zone is large enough for having a fully developed flow before the contraction. The additive character of the pressure in an incompressible flow enables the selection of the exit section of the computational domain. The position of the exit section is selected analysing the pressure distribution in the land zone. In the vicinity of the exit section the effects due to the contraction are attenuated and the average pressure distribution must regain a linear variation. The boundary conditions for a fully developed flow are imposed in the exit section.

428

am

, @={u,v,~,E}

-=0

ax

The atmospheric pressure is considered as a reference value and is imposed in one of the control volumes near the exit section. The wall boundary conditions for the laminar flow regime are the typical no-slip conditions.

In turbulent flows numerical boundary conditions usually replace the no-slip conditions. These are obtained using the logarithmic law at the wall in the first grid point near the boundary, Schiestel [lo]. They are imposed as gradient type boundary conditions for the velocity component parallel to the walls. For the turbulent quantities k and F. the logarithmic law provides an estimation in the first grid point near tlie walls. 2

~ = 0 . 4 , E = 7.8 /

(224

\2

dr

= w.ll u, = -

U + =-

'

U

u,

y + = -f y u r

P

(22c)

=-ursign(up f 2 -uwRI,)

The logarithmic law is solved as a non-linear equation in the first grid point near the boundary. The solution sp and so u, is used to calculate the gradient of the velocity component parallel to the wall. The estimations of k and E in the first grid point near the wall are used as boundary conditions on a computational domain with shifted boundaries. The point P must always lie in the zone wlicre logarithmic law is valid, 11.5
Figure 4 Detail of the structured grid of the wall boundary conditions neglects the intermediate sublayer (1 1.5
429

0.25

5

0.20

4

g 0.15 c

5 z.

0.10

0.05

1

0.00

0

0

I0

20 x [inm]

30

40

Figure 5a. Pressure variation for laminar flow on figure 5 for laminar and turbulent flow regimes. Streamlines in the pocket are presented on figure 6. It can be seen that the pressure level in the pocket is constant. As expectcd, the pressure has a linear v'ariation in the land region. In turbulent flow the effect of the contraction is more pronounced and the development zone which follows after the step is longer. In estimating the pressure drop due to the contraction this development length is ignored and the linear pressure variation is extrapolated to the step wall. The difference is calculated between the pressure level in the pocket and the extrapolated land pressure.

The experimental and theoretical results are presented on figure 7. The laminar flow results are detailed on figure 8. The results were curve-fitted separately for the laminar regime and for the turbulent regime. The pressure drop coefficient is approached by the following relations: 7.78 , 300 < Re,, < 2000 Re:*

<=-

40 x Imml

60

80

Figure 5b. Pressure variation for turbulent flow 0.0051

E

t

0.004

0.003

Y

0.002 0.001

0'0000.021

0.023

0.025

0.027

0.029

Figure 6. Streamlines in the pocket 3.45

4. COMPARISONS AND DISCUSSIONS

20

0

Re, > 2000

A good agreement between theory and experiment is obtained for the turbulent regime. The results obtained for Rp>5000 are greater as the values measured by Chaomleffel [3]. His values are very close to 1. The pressure drop coefficient obtained from our numerical results can be approached by the relation: c n ic

5 = 1.96 + J U J J

Re b34

430 do not allow to appreciate the disagreement between the measured results and the calculated one. It seems that for very small Reynolds numbers (
5

r; 4

3

2 1 Rep O . O E + O 2.OE+3 4.OE+3 6.OE+3 8.OE+3 1.OE+4 1 . 2 E + 4

Figure 7 Pressure.drop coefficient - theoretical and experimental results

ACKNOWLEDGEMENTS This work was performed with the partial financial support of Rtgion Poitou-Charentes, Contract no. 94/RPC-B-6. The authors also express their gratitude to S. Brochet for his contribution.

Experiment

r

REFERENCES

5

4

1. Argliir,

3

2.

2 1 0

400

800

1200

1600 Rep2000

Figure 8 Pressure drop coefficient for small Reynolds numbers

3. 4.

As seen on figure 8, for Reynolds number between 300 and 1200 the theoretical results give a quasi-constant value of the pressure drop coefficient. Our theoretical results show the same behaviour as San Andres' and Velthuis 191 results but the values are somewhat greater. This differences could be due to different grid arrangements. The experimenkd variation of E, are less rapid than the theoretical ones.

5.

6. 7.

5. CONCLUSIONS

For the pure hydrostatic regime an abrupt ch,ange of the flow section entrains important pressure drops due to coupling between inertia and viscous effects. For laminar flow, the experimenkil uncertainties

8.

9.

M., Frene, J., "Determination des caractkristiques statiques et dynainiques des joints rainurks fonctionnmt en position centree", Rapport Final de Contrat, juin 1995. Braun, M. J., Dzodzo, M., "Effects of the Feedline and the Hydrostatic Pocket Depth on the Flow Pattern and Pressure Distribution", Paper No. 94-Trib-27, ASMEISTLE Tribology Conference, Maui, Hawaii, October 16-19, 1994. Chaomleffel, J.P., Nicolas, D., "Experimental Investigation of Hybrid Journal Bearings", Tribologv International, 19, 5, pp 253-259, 1985. Constantinescu, V., N., Galetuse, S., "Pressure Drop Due to Inertia Forces in Step Bearings", ASME Journal of Lubrication Technology, 98, pp 167-174, 1976. Constantinescu, V.N., "On conditions at the inlet edge of a lubricating film operating at large Reynolds numbers", (in Romanian) The 541 Conference on Friction, Lubrication and Wear, Bucharest, Sept. 1987. Frhe, J., Nicolas, D., Degueurce, R., Berthe, D., Godet, M.,"Lubrfication hydrodynamique. Paliers et Butbes",Editions Eyrolles, Paris, 1990. Hwang, Y.H., Liou, T.M., "Expressions €or k and E Near Walls", AIAA Journal, pp. 477479, March 1991. Launder, B.E., Spalding, D.B., "The Numerical Computation of Turbulent Flows", ComputerMethods in Applied Mechanics and Engineering, Vol. 3, pp. 269-289, 1974. San Andres, L.A., Velthuis, J.F.M., "Laminar Flow in a Recess of a Hydrostatic Bearing", Tribology Transactions,35,4, pp 738-744, 1992.

43 1 10. Schiestel, R.,

"Modc'lisation et sinrulation des c'coulemerrts turbulents",Hennes, Paris, 1993. I 1. Patankar, S., 1980, "Nunrerical Heat Trotisfir And Fluid Flow",Hemisphere Pub. Corp, 1980. 12.Patankar, S.V., Spalding, B., "Heatarid mass transfer in boundary layers. a general calculation procedure", Intertext Books, London, 1970. 13. Rodi, W., "A New Algebraic Relation For Calculating The Reynolds Stresses",U h M , 56, T2 19-22 I , 1976.

APPENDIX The approach used to reformulate the turbulent wall boundary conditions was suggested by Pak2nkar and Spalding [ 121. Practical relations for the velocity profiles can be obtained using van Driest's mixing length relation. Very close to the wall. the transport equations can be drastically simplified.

calculated.

Using relation (A5) which replaces the logarithmic law, the non-dimensional velocity up' is calculated and so the friction velocity ur and the wall shear stress are determined. Relation (A5) has the advantages of being continuous from the wall to the validity domain of the logarithmic law and do not necessitates the resolution of a non-linear equation. In Schiestel [lo] relation (A5) is approximated by a polynomial expression:

s=

(5)

= R-'

- 0.1561.R4.4J- 0.08723-R".' +

0.03713*R4"*, O < R < l o J (A7)

au

T I = jl-

aY

Thc approxiiliation given by this relation is not correct because it calculates negative values for s. We deduced a different approximation of the relation (A5)

g , (r), - 0.1704 < r < 3.2

(A3) Introducing the definitions of the shear stresses in equation (Al) and after integration one obtains the non-dimensional velocity profile: u+=

11'

+'C

Jo

2dq' 1+/1+4[1:(q')]2

The result of the numerical integration of (A4). = u+(y+), is putted in a form appropriate to be

used for calculations in the first grid point near the boundary. I = f ( y + u + )= f(R) 11'

This relation enables tlie direct calculation of uz without solving the non-linear relation of the logarithmic law in the first grid point P near the wall. The distance yp and the velocity up are known. and the local Reynolds number RP can then be

g2(r), 3.2 < r < 5.5

(A81

g3(r), 5.5 < r < 11.7947

r = ln(R)

(A84

g,(r)=0.00126646-0.50471.r +0.00242796.r2

(ASb)

g2(r)=-0.0131839-0.425012.r -0.0444457.8+0.0073206 1-r2

(A8c)

g3(r)=5.756S3-4.12612-r+0.838655.? -0.0881695.r3+0.00464523.r4 -9.75491.10-5.rS

(A84

The boundary conditions for k and E must take into account that the first grid point close to the wall might lie under the domain of the logarithmic law. Hwang and Liou [7] proposed the following relations.

432

k * = 3 [ (Ay+y'* - I 1 - 2 ,

and the profiles of k and E are: E*=-

(Ay')" + 1

k *'

a)y+ 2-7

XYi

k * = 3 [ 0.771S(y+ ) I 0.77 1S(y

6 ' 9

-l]1-2

+1

k" 0 . 4 +~ b)O
where

=-

k' = 0.0135(y')2 E+

and &=0.45 was determined from experimental data. The other two constants, A and a, are calculated imposing the continuity of k and E at y+=y:. For y=:7 one obtains: A=0.8748,

a,=O.OO 1353

(A 12)

= 0.09 +0.001353(y')2

Using the relations (A5), (A13) and (A14) do not offers to the presented k-E model the capability to handle very low Reynolds number flows. On the other hand, it is possible to treat flows with large separation or reattachment zones when the point P lies bellow the domain of the logarithmic law without increasing the computational effort.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

433

Application of the homogenization to thin film gas lubrication ( i . Bayada

''' and M. Jai "

"Mecanique des Contacts C.N.R.S. URA 856, lnstitut National des Sciences Appliqukes, Bat 1 13, 69621 Villeurbanne cedex, FRANCE "Mathematiques, C.N.R.S. URA 840, lnstitut National des Sciences Appliqukes, Bat 401, 6962 I Villeurbanne cedex, FRANCE

The objective of this work is to present some new approaches for the numerical solution of the compressible Reynolds equation and to give a rigorous determination of the averaged Reynolds equation modelling the flying characteristics of a magnetic head over a rough rigid-disk surface for any periodic roughness ( longitudinal, transversal and two-dimensional). This homogenization technique is based on the two-scale convergence and allows us not only to compute the leading average term but also the next term. SYMBOLS

A = gas bearing number 13 b/l I-, = bearing width (m) I i = Normalized film thickness h/h, h = local film thickness (m) h,, = minimum film thickness (m) I = bearing length (m) K Knudsen number h,/ho P = normalized pressure p/pa P,, = homogenized normalized pressure p = local pressure ( N m-' p;, = ambient film pressure ( N m-2 ) V = running surface velocity (m/s) W = normalized load carrying capacity w/(p,bl) MI = load carrying capacity ( grm ) X,,X2 = normalized coordinate system xJI, x,/b X , , X ? = coordinate system in the sliding and width directions, respectively (m) Y ,.Yz =local fast scale coordinate 11 = roughness frequency N, = Number of the discretization points along X ,-direction N, = Number of the discretization points along Xi-direction h, ha = mean free path of gas at pressure of airbearing and at ambient (m) A = normalized roughness amplitude 6 /ho 6 = roughness amplitude (m) E = I/n

6 -P U

P A

'

R=[O,l]x[O, I ] P I = [O,1 IXW, 11 I. INTRODUCTION

The study of ultra thin gas film bearings has become of great interest in recent years. The prime motivation has come from the computer magnetic disk recording industry where higher recording density and signal resolution can be achieved if the readlwrite element which is attached to the taper-flat slider can be maintained closer to the magnetic disk rotating at a high speed. The hard disk data storage surfaces of magnetic storage devices are artificially roughened in order to control the interfacial static force condition that exists between recording head and disk surface during rotational start-up. The flying height between head and disk continues to decrease in order to satisfy recording density requirements and is now approaching the 0.03 micron level, which is of the same order as the surface roughness height produced by texturing. There has been much discussion and

434

disagreement in the tribology literature related to tlie behaviour o f tlie pressure for solutions o f the Reynolds equation when the wave number is large. Mitsuya et al. [ S ] have proposed an averaged Reynolds equation extended to the slipflow regime without considering the tiniedependent terms. In a further work Mitsuya et al. [ b ] have proposed the same averaged equations extended with the time-dependent terms. We present in this paper a new averaged Reynolds equation. based on the two-scale convergence [3,7], in a more general way than the film thickness averaging. This formulation enables us to recover Christensen's results as a particular case.

The usual method to solve this equation i s to solve a sequence

{

P ~ + I ) ~ Ill=

0

for the initial guess

P" satisfying the boundary conditions. This i s done by defining P'"", for all m > 0, to be the solution o f the linear problem:

Numerical results are obtained using the L.P.D.E.M method [4.8] which gives greater nti m er ica I st abiIity than tlie fin ite d ifferen ce method especially when the wave number i s large.

2. BASIC FORMULATION

(3) cf

=A

NP""

I

)

for .Y = ( .Yl, ,Y2 )

2.1. T h e Model Lubrication Equation 'The characteristics o f lubricating film operating between the head and disk were assumed to be governed by tlie modified Reynolds equation taking the slip flow boundary conditions into account:

V . ( ( h 7 p+ 6Ac,p,1h')Vp) = bpV.V(ph) ( I ) which correctly predicts tlie performance o f the air bearing for classical operating conditions with 0 5 K 5 2.5. The air bearing pressure and clearance variables are given by p and h respectively. The ambient pressure and mean free path appear as pa and ha, while tlie disk velocity and fluid viscosity are expressed by V and i t . When the array o f variables given by (p,h,x,y) i s normalized with respect to (p,,hg,l,b), respectively, the resulting equation appears as:

This method, called fixed point algorithm in this paper, does not allow us to use a classical Reynolds code or tlie L.P.D.E.M approach. Moreover it seems difficult to improve the convergence by using another method as Newton-Raphson which i s available for the following approach by changing the unknown function.

2.2. Change of unknown function Let us introduce the new function

u = -1 p ? +-6 K p 2

ti

Then, the problem ( 3 ) becomes:

435

2.3.Some comparison

I '

0K /I

('=-/'I+-/

2

"

:j

= -

on the houndar?,

where: /)( .\.U)

=

-6K

+ J(6K)' + 2 H ' U

As the non-linearity appears only in the right hand side, we can now linearize (4) and introduce the Newton sequence u""' for

i

the initial guess U". For all m > 0, solution of the linear problem

I,,,_,,is the

W+l

As previously mentioned, equation (5) allows us to use not only standard finite difference or finite element methods but also the LPDEM scheme which can be described as a mixed finite difference method. Although more difficult to implement, the LPDEM scheme has the advantage to be a very stable method which requires less discretisation points than classical methods, especially when the gap is not smooth. The following figures summarize some aspects of the calculations performed with B=10, K=l.28 and A=8557. The "exact" load, we=6.85, has been computed using a very fine mesh (Nx=400, Ny=50). Figures I a and 1 b give the relative error

Iw - we1

for various meshes using both a

We

classical fixed point method to solve (3) and a Newton-LPDEM scheme to solve ( 5 ) . Figure la is related to a smooth gap while Figure Ib is related to a rough one with A = I and n=50. The superior stability of LPDEM scheme is demonstrated. Let us remark however that this stability has been achieved by a more time consuming procedure.

0.01

0 025

with /,'( . \ . l / " ' ) =

I

,-.

LPOEM-NEWTON F n h l PI**

0 02 al

r

*0015

B

& 0 01

OW5

-.- - .- -

~

0

To solve Equations (3)-(5) we restrict ourselves in this paper to finite difference approach using two methods. The first one is the classical finite difference method which is very simple to implement but a very fine mesh grid is needed for a precise solution. The second method is the LPDEM scheme [ 4,8 1.

50x25

10Or35

15Or35

2W.35

25Or15

Mox35

Figure 1 a: Smooth surface Relative error of the calculated load for various meshes

436

04

0 15

where k is a given periodic function of one or two variables.

01 o)O 25

z 3 0)

1

\

02

We introduce a fast scale variable Y defined by: \

a 1 5

x .

y = 2 1=1,2

01

c

0 05 0

50~25

100r15

150135

200x15

250x35

100rl5

k'igure I b Roughness case. A=I , n=50. Relative error of the calculated load for various meshes

3. ROUGHNESS 0 ESCRlPT 10N

AND

TWO

SCALE

so that H(X) becomes a function of X and Y which are first considered as independent. H ( X ,Y ) = H ( X )+

iqY)

Due to the I-periodicity of the function with respect to Y , the knowledge of R o n a roughness cell [Y]=[O,l]x[O, I] is sufficient to obtain the real gap anywhere.

3. I . Introduction

Let us consider the real pressure P with the following expansion :

A lot of methods have been introduced to take into account the numerical difficulties

P ( X ) = P " ( X ) + &<(X,Y) + E Z P 2 ( X , Y ) +...

induced by the roughness of the surfaces. Some o f these works are based upon a statistical represcntation of the surfaces, others are based upon a purely deterministic work [ I ] [2] to obtain an averaged equation. I n our approach, the discrimination between a slowly varying natural scale thickness a n d a local periodic highly varying roughness is introduced by a multiple scale double variable analysis. A formal expansion of the pressure using a small parameter is assumed, the searched solution being the first terni of the expansion. I-lowever the second term of the expansion can also be easily computed. This method has already been developed in many papers for the classical incompressible Reynolds equation [5,6] where a more detailed description can be found. 3.2. Homogenized system

Let us assume that the real gap is defined as an €-periodic function around an averagc value H( ,Y,, X,) by:

Now P , is function of X only and P, is function of both X and Y and is submitted to the following conditions: Y ) is an I-periodic For each fixed X, Y + P, (X, function. Introducing this expansion into the Reynolds equation ( 2 ) and using the differential rule

we obtain an expansion of differential operators with respect to E' , i > 0. An identification of the leading term gives:

437 By introducing PI in ( 6b ), we obtain the following problem with only one unknown PI, :

‘l‘lic second term is obtained after integration in llic Y- variable through [ Y ] in the following

tiwm: where the matrix A*(Po) and the vector @*(Po) are defined by (6b)

From equation (ba), we observe that for I>,, given, we can express P I as a function of PI, in thc following form:

where oi (i=1,2) and xI are I-periodic functions solution of the auxiliary problems in the Y variable (X i s fixed).

+6KH?)) i=1,2

cw with A , i s the operator defined by:

(7) Equation (8) is the ”averaged” Reynolds equation describing the average behaviour o f the fluid for small E. These results are valid for any roughness cell defined on [Y]. In the general case it is impossible to obtain an analytic expression o f

a,,0

in closed form and we

have to compute numerically the auxiliary problems (7) and then integrate their solutions to obtain the coefficients.

438 3.3. Transversal case

3 ,

28

in some cases, due to the particular shape of the roughness, it i s possible to obtain an analytical forinu lation for the

u,; and 0 * . This

is true in particular

for transversal (resp. longitudinal) roughness where:

26

5

?1 E

24 22

H< 128 g 16 14 12 1

0

k'or cxamplc. in the transversal case, the homogenized equation (8) reduced to :

011

011

021

041

051

061

071

0.41

091

Figure 2: Transversal roughness with n= I 0 0 Pressure at the center line 3 28

26

$

r

21 22

-EXACT --HOMOGENIZED

1- 1.4'

I

1

1 1 6 I 4

12

tv 0

0 133

0267

04

0531

0667

0.4

0913

Figure 3: Transversal roughness with n=300 Pressure at the center line on !J

4. NUMERICAL RESULTS Although equation ( 8 ) is valid for any periodic roughness, the following results are only related to longitudinal and transversal roughness. All numerical results are related to the following data: R = 10, K= 1.78, A=8557, A= I.

-. l.igures 7 to 5 show the convergence of the numerical solutions o f the Reynolds equation towards an " average'' solution for small E. One particular interest o f theses results is that they show that convergence is considerably faster for longitudinal that for transversal one. This fact has already been observed for incompressible tl ti ids.

Figure 4: Longitudinal roughness with n=20 Pressure at the center line

0

02

0 399

0 599

0 798

Figure 5 Longitudinal roughness with n= I 0 0 Pressure at the center line

x2 0 998

439

Figures 6 to 9 demonstrate the interest ol' computing not only the average pression Po

but also the following term PI. We can see how P,,+F:P, , the corrector, is close to the "exact" solution P by reintroducing small local oscillations. For moderate A, the corrector enables us to recover completely the exact solution. For greater value of A, the corrector is not so good for E =0.025 but becomes better for siiialler values of E.

O*u

02 u

0

om

0 741

Figure 8: Exact, Homogenized and Corrector pressure solutions at center line A = 8557.5, K=1.28, A=0.5, E = 0.025 N,=200, N,,=35

x1 0

0.411

0.-

0.n

0.111

I;igure 6: Exact, Homogenized and Corrector pressure solutions at center line A = 2139.4, K=0.64, A=0.5, E = 0.025 N,=200, N,=35

19

0

0127

0217

0372

04M

OW1

07Y)

087

1 . 0995

Figure 9: Exact, Homogenized and Corrector pressure solutions at center line A = 8557.5, K=1.28, A=0.5, E = 0.0125 N,=400, N,=35

I 1

5. CONCLUSIONS

I 5

E

1:: 09

07 0

0122

0247

0371

O m

0621

07e

On?

0995

Figure 7: Exact, Homogenized and Corrector pressure solutions at center line A = 2139.4, K=0.64, A=0.5, E = 0.0125 N,=400, N,=35

We demonstrate in this paper how to cope with any 3-D periodic roughness for compressible film flow.The averaged Reynolds equation obtained by homogenization can besolved by a new robust algorithm using both Newton Raphson method and LPDEM formulation. Moreover, we are able to reintroduce oscillations from the average solution to obtain a more precise approximation of the exact pressure. Further steps in that study could be the introduction of evolutive effects.

440 REFERENCES I. G . Bayada and J.B. Faure, ASME, Journal of Tribology, I I 1 ( 1 989) 323.

5. Y. Mitsuya, T. Ohkuto and H.Ota, ASME, Journal of Tribology, 1 11, No3. (1989) 495.

2. H.G. Elrod. Proceedings of the 4th LeedsLyon Symposium on surface roughness on lubrication, Institution of Mechanical Engineers IME, (1977) 1 1 .

6.Y. Mitsuya and H. Ota , ASME, Journal of Tribology, 113, No3. (1991) 819.

3. M. JAl , Model. Math. Anal. Num., 29, No 2 (1995) 199.

4 M. JAl, Preprint Equipe d' Analyse numdrique Lyon Saint Etienne, No I18 (1991).

7. Nguetseng G., SlAM J. Math. Anal., 20, No3 (1989) 780. 8. C.H.T. PAN, A. PERLMAN and W. LI, Proceedings of the 13th Leeds-Lyon, Symposium on Tribology, (1987) 8.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

441

Boundary Conditions for Reynolds Equation with Particular Reference to Piston Ring Lubrication M. Priest ', R.I. Taylor b, D. Dowson a and C.M. Taylor a

'

Department of Mechanical Engineering, The University of Leeds, Leeds, LS2 9JT,UK Shell Research Limited, Thornton Research Centre, P.O.Box 1, Chester, CHI 3SH, UK

This paper considers the lubrication of the interface between a piston ring and cylinder wall, as encountered in reciprocating internal combustion engines and pumps, with the specific aim of evaluating alternative boundary conditions that can be applied when solving Reynolds equation. It is shown that different boundary conditions result from assuming different models of lubricant film cavitation in the interface and that the choice of boundary conditions can have a sigruficant influence on the results of the analysis. Theoretical predictions of hydrodynamic pressure, lubricant film thickness and friction for the top piston ring of a singlecylinder diesel engine are presented for two alternative forms of cavitation which illustrate the sensitivity of the analysis to the choice of boundary conditions. In an attempt to gain an insight into the correct boundary conditions to use, a review is presented of available experimental data. This concludes that experimental data published to date fails to resolve clearly which boundary conditions are more appropriate or whether perhaps Merent boundary conditions are suited to different conditions of load, speed, temperature and degree of lubricant starvation. 1. INTRODUCTION

When solving Reynolds equation for the lubrication of a converging-dwergingwedge such as encountered with journal bearings and piston rings, the hydrodynamic pressure distribution in the lubricant can only be determined when boundary conditions are specified at the lubricant /environment interfaces. These boundary conditions are based in part on assumptions concerning the physical behaviour of the lubricant and in particular on the nature of cavitation in the diverging lubricant film. Apart from being of academic interest, the choice of boundary conditions can have a significant effect on the form of the hydrodynamic pressure profile and hence the load capacity of the contact and the predicted lubricant film thickness. Furthermore, a range of frictional power loss estimates can result depending on the boundary conditions assumed and whether or not friction contributions from cavitated regions of the contact are included. The standard assumption in piston ring lubrication [l] has been that the lubricant cavitates

according to the Reynolds criterion and then reforms to ensure that the lubricant pressure is equal to the gas pressure at the trailing edge of the ring. Recently, a different boundary condition based on the assumption that flow separation occurs from the piston ring rather than cavitation has been proposed [2,3]. This arose as a consequence of experimental observations of the oil film between piston rings and the cylinder wall using laser induced fluorescence &IF) techniques [2,3,4]. This paper has in fact partly been prompted by the recent resurgence of interest in the nature of cavitation in the piston ring / cylinder wall interface generated by the continued development of the LIF film thickness measurement technique and the quality of the results produced. The aim of the paper is to describe the various boundary conditions that can be applied when undertaking piston ring lubrication analysis, to show that the results obtained are sensitive to the choice of boundary conditions and to review the available experimental evidence in an attempt to gain an insight into the correct boundary conditions to use.

442 NOTATION total axial friction force per unit circumference due to hydrodynamic action and asperity contact lubricant film thickness lubricant film thickness at the cavitation/ separation boundary lubricant film thickness at the reformation

boundarv minimum lubricant film thickness on the ring profile asymptotic film thickness downstream of separation pressure gas pressure at the inlet of the lubricant film gas presswe at the outlet of the lubricant film pdw pressure in the cavitated region radial gas pressure relief force per unit circumference at the unwetted lower edge of the ring radial applied gas pressure force per unit circumference radial gas pressure relief force per unit circumference at the unwetted upper edge of the ring time radial force per unit circumference due to inherent ring elastic tension axial piston velocity radial force per unit circumference due to asperity contact radial component of hydrodynarmc force per unit circumference axial coordinate relative to centre of mass axial coordinate at the inlet axial coordinate at the cavitation/separation boundary axial coordinate at the reformation boundary axial coordinate at the outlet radial coordinate relative to centre of mass

f q

fraction of the clearance space width in the radial direction occupied by lubricant in the cavitated region dynanucviscosity

2. PISTON RING LUBRICATION MODEL

The lubrication model of the piston ring / cylinder wall interface used in this paper was developed for use in automotive company design and analysis departments taking as its starting point research studies undertaken at the University of Leeds over the last twenty five years. For the purposes of this paper it can be regarded as essentially the model of Dowson et a1 [l] with enhancements to account for mixed and boundary lubrication as suggested by Ruddy et a1 [ 5 ] . The piston ring / cylinder wall interface is considered to be axisymmetric such that we need only consider a section through the interface as shown in Figure 1. Piston

Combustion Chamber

Crankcase Figure 1: Piston Ring Model The piston ring is loaded against the cylinder wall by its inherent tension force T and the applied force due gas pressure acting on the inner diameter of the ring PR. The magnitude of this latter force

443

depends upon the gas pressures acting above and below the ring, p, and pz respe&vely, and whether the piston ring seals against the upper or lower flank of the piston groove. These applied forces are supported by the force generated by hydrodynamic action W,, the radial gas relief loads due to gas pressure acting on the unwetted regions of the ring face Pu and PL and, if the lubricant film thickness

modified the full Sommerfeld by proposing that the negative pressures should simply be neglected, i.e. set to zero, effectively producing a cavitated region. The resulting boundary condition is referred to as the Giimbel or half Sommerfeld condition.

U

is small, by the asperity contact force W,. It is in determining the hydrodynamic force W, that the Reynolds equation is solved. A one dimensional, incompressible form of the equation appropriate to this situation is

5(h3z)

= 6qCJZ+ dh 127-dh dt

I

I I

Double integration of equation (1) is required across the interface subject to appropriate boundary conditions to determine the hydrodynamic pressure profile and thereby the hydrodynamic force W,. It is these boundary conditions which are the focus of this paper. 3. ALTERNATIVE BOUNDARY CONDITIONS

Figure 2: HydrodynamicPressure Profile and Film Shape with Full Sommerfeld Boundary Conditions Osborne Reynolds appreciated the role of film rupture in his classic work on lubrication theory (81 leading later to the formulation of the Reynolds cavitation condition independently by Swift [9] and Steiber [lo]. The boundary conditions applied at the cavitation boundary are

The simplest solution of the Reynolds equation (1) is obtained by assuming that there is no

lubricant film rupture such that the only boundary conditions are the bounding gas pressures at inlet and outlet at x = x,, p = p, at x = x,, p = pz This is the solution proposed by Sommerfeld [6] which is generally referred to as the Full Sommerfeld condition. The resulting lubricant film shape and hydrodynamic pressure profile with the boundary conditions of equation (2) are shown in Figure 2. This very simple approach is, however, inadequate as it unrealistically requires the fluid to continuously sustain very large negative pressures and as a consequence under predicts hydrodynamic load capacity. GUmbel [7] recognised this and

(3)

Where the pressure in the gas cavities p,- is the saturation pressure of the dissolved gas which is often assumed to be atmospheric. The Reynolds condition is superior to the half Sommerfeld since it correctly accounts for oil flow continuity across the cavitation boundary. In applying this condition to piston ring lubrication, account must be taken of the large gas pressure that can exist at the outlet position. This results in the lubricant film reforming and the hydrodynamic pressure rising to the outlet gas pressure as shown in Figure 3. The pressure gradient at the reformation boundary can be determined from consideration of oil flow continuity across the cavitated region

444

yielding the following boundary conditions for the cavitation and reformation boundaries dP =O at x =x2, p =0, -

*

(4)

dx

at x =x,, p =0,

=67U(

4 -4

dx

This has been the most common solution in piston ring lubrication to date [ 11.

U

dP = 27u at x = x,, p = p 2 ,dx h2 The full fluid film condition is only approximate, however, since a full fluid film is assumed and no development of the lubricant/gas interface is considered [ l l ] . Coyne and Elrod [12,13] overcame this deficiency by developing a two-dimensional Newtonian analysis which defines the shape of the lubricant-gas interface and includes the effects of gravity, inertia and surface tension. In piston ring lubrication, gravity and inertia effects are negligible and the pressure and pressure gradient at the point of separation are given by at x =x,, p = p 2 , dp =-6 ' u ( l - 2 t ) dr h;

cavitated region Figure 3: Hydrodynamic Pressure Profile and Film Shape with Reynolds Cavitation and Reformation Boundary Conditions An alternative approach to Reynolds cavitation is to consider that flow separation occufs rather than cavitation in a similar manner to that proposed for journal bearings as discussed by Dowson and Taylor Ill]. The simplest flow separation condition, which is referred to as the full fluid film condition, may be derived from the Navier-Stokes equation. Flow separation takes place from the stationary surface of a bearing when the cross-film velocity gradient is zero. In the piston ring / cylinder wall interface the piston ring is the considered the stationary surface in terms of the hydrodynamic model and lubricant entrainment and thus the flow will separate from the piston ring at the outlet gas pressure subject to the pressure gradient condition derived from the Navier-Stokes equation

(6)

where h, is the asymptotic film thickness downstream of the separation point whose relationship with the film thickness at the point of separation 4 may be determined from tabulated data in [12,13] given the entraining velocity. the lubricant viscosity and the surface tension of the lubricant / gas interface. The form of hydrodynamic pressure and film shape resulting from the above separation boundary conditions is shown in Figure 4.

7

1

Figure 4: Hydrodynamic Pressure Profile and Film Shape with Flow Separation Boundary Conditions

445

The hydrodynamic pressure profile is characterid most signiticantly by a small subambient pressure loop upstream of the point of separation. It is interesting to note that no examples of either the full fluid film boundary condition of equation ( 5 ) or the Coyne and Elrod condition of equation (6) being applied to piston ring lubrication could be found in the literature. Other variations on the cavitation and separation conditions have, however, been adopted. Wakuri ef a1 [ 141 proposed that the lubricant cavitates according to the Reynolds cavitation pressure gradient condition as given in equation (3) but at the outlet gas pressure. The analyt~caljustification for this condition relies upon the saturation pressure of the dissolved gas in the lubricant being equal to the outlet gas pressure which seems unlikely given the large magnitude and variation of this pressure throughout the engine cycle. Recently Richardson and Borman [2] and Taylor ef a1 [3] have taken this one stage further by applying the Reynolds pressure gradient condition at the outlet gas pressure but treating the lubricant film rupture as flow separation rather than cavitation. This solution has little analytical justification but is based on experimental observation of the lubricant film between a piston ring and cylinder wall using laser induced fluorescence (LF)techniques. It will be referred to here as the modified Reynolds separation condition and is illustrated in Figure 5.

U

The boundary conditions for the modified Reynolds separation condition are at x =x,, p =p2, dP =O dr

(7)

It is apparent from this discussion of alternative boundary conditions and the various forms of lubricant film shape and hydrodynamic pressure profile that result, that there is the potential to obtain very different values of radial hydrodynamic force W, and consequently to predict differences in lubricant film thickness, axial friction force and therefore frictional power loss. The axial friction force F, as shown in Figure 1, is influenced directly by the lubricant film thickness and also by the axial extent of the lubricant film. In all the above boundary conditions, the friction force in the regions with full fluid films is obtained by integrating the hydrodymmc and asperity contact shear stresses axially across the region as discussed in [5]. In the cavitated region obtained with the Reynolds cavitation and reformation condition illustrated in Figure 3, it is assumed that a series of gas cavities with oil flowing around them is formed such that there is still a hydrodynamic friction force acting on the piston ring. This is computed using the approach proposed by Dowson and Higginson (151 where the full film shear stress is linearly scaled by a factor T which is the fraction of the radial clearance space between the piston ring and the cylinder wall occupied by lubricant which is given by

- =-k h

, ,

,

i’ I

Figure 5: HydrodynamicPressure Profile and Film Shape with Modified Reynolds Separation Boundary Conditions

With the separation solutions, the lubricant leaves the piston ring at the point of separation and there is no subsequent friction acting on the piston ring. Hence, the axial extent of the regions over which frictional shear stresses act may be very different with cavitation and separation boundary conditions, leading to greater differences in total friction force and power loss than would be expected on the basis of film thickness variation alone.

446 4. COMPUTATIONS Calculations have been undertaken for the top piston ring of a singlecylinder diesel engine using the Reynolds cavitation and reformation boundary conditions of equation (4) and the modified Reynolds separation boundary conditions of equation (7). The engine modelled was a CAT1Y73 singlecylinder diesel engine (130 mm bore; 165 mm stroke) running at a speed of 1200 rpm and 14 bar brake mean effective pressure (BMEP) load. Further details of this engine can be found in (3, 161. The axial profile of the piston ring was a symmetric parabola with a parabolic radius of curvature of 166 nun. For the purposes of this paper, it was assumed that there was a plentiful supply of lubricant such that the inlet was always flooded and that there was no torsional twisting of the piston ring such that the axial ring profile offered to the cylinder wall remained constant throughout the engine cycle. The viscosity characteristics of an S A E 30 lubricant were used with viscosity varying as a function of cylinder wall temperature from 4 mPa.s at top dead centre (TDC) to 13 mPa.s at bottom dead centre (BDC). The maximum sliding velocity was 10.8ds. Figure 6 shows the hydrodynamic pressure profiles superimposed on the ring profile for the two alternative boundary conditions at 20° of crank angle after TDC firing.

"i 60

3 N

2o

10 0

distance from inlet (mm)

p, Reynolds cavitation and reformation

-.....-.. p, modified Reynolds separation

Figure 6:Predicted Hydrodynamic Pressure Profiles at 20' Crank Angle after Top Dead Centre (TDC) Firing

The hydrodyrmuc pressure with the Reynolds cavitation and reformation solution rises from the bounding gas pressure at the inlet to a maximum just before the point of minimum film thickness and then falls to atmospheric pressure ( p =0) at the cavitation boundary soon into the diverging outlet region. As the gas pressure at the outlet, which is the combustion chamber pressure, is signrficant at this stage in the engine cycle, the lubricant film reforms and rises to the bounding gas pressure. The modified Reynolds separation solution exhibits similar behaviour in the inlet region but with a reduced maximum pressure and the flow separates from the piston ring soon into the outlet region. Between the separation point and the outlet edge of the ring there is a large region which is unwetted by lubricant and is exposed to the outlet gas pressure. This provides significant radial load relief at this stage in the engine cycle thus reducing the required hydrodynamic load which accounts for the reduced maximum hydrodynamic pressure in the inlet region.

o f . . . 0

.

im

. .

.

1

360

.

.

.

I

540

.

. .

1

7m

crank angle (degrees) Reynolds cavitation and reformation

.....-.--modified Reynolds separation Figure 7:Predicted Cyclic Variation of Minimum Film Thickness Figure 7 shows the predicted cyclic variation of minimum lubricant film thickness for the two boundary conditions with zero degrees of crank angle being TDC firing. Both solutions exhibit the expected characteristic shape of curve with small film thicknesses around the dead centre positions where the entrainment velocity is small and large film thicknesses at the mid-stroke positions where the entrainment velocity is large. Film thicknesses

447 on the power and exhaust strokes (0' to 360' crank angle) are generally smaller due to the higher gas loading on the rings and there is a step change in both w e s just after mid-stroke on the intake stroke (at approximately 470") which is associated with a ring lift event when the ring moves from one side of the piston groove to the other with a consequent change in gas loading on the inner diameter of the ring. Film thickness predictions away from the dead centres are larger with the modified Reynolds separation solution than with Reynolds cavitation and reformation especially on the power and exhaust strokes when gas pressures are higher. The main reason for this difference lies in what happens after lubricant film rupture with the two conditions as before this point the hydrodynamic pressure profiles are similar. With the Reynolds cavitation and reformation condition there is a cavitated region which may extend to the outlet if there is insuflicient gas pressure to require reformation. There is no contribution to radial load capacity from this region as the cavity pressure is assumed to be atmospheric. With the modified Reynolds separation condition, as noted above, the flow separates from the ring and the outlet gas pressure acts on the unwetted surface from the separation point to the outlet. The combined effect of hydrodynamic and gas relief load gives the modified Reynolds separation condition a generally superior radial load capacity than the Reynolds cavitation and reformation condition and hence larger film thicknesses. The predicted cyclic variation of axial friction force for the two alternative boundary conditions is shown in Figure 8. This friction force is the summation of the contributions from hydrodynamic and boundary friction. Hydrodynamic friction predominates in the mid-stroke regions where film thicknesses and sliding velocities are large as can be most clearly seen on the exhaust (180' to 360') and intake (360' to 540') strokes. Boundary friction occurs around the dead centre positions where the film thicknesses are small and appears as characteristic spikes as can be seen at M O O , 360' and 540". On the power stroke (0' to 180') and latter quarter of the compression stroke (675" to 720°), there is a more complicated mixture of the

two components due to the high radial gas pressure

loading on the ring.

-100

1

crank angle (degrees)

Reynolds cavitation and reformation .....-.--modified Reynolds separation Figure 8:Predicted Cyclic Variation of Friction Force The friction force is generally greater with the Reynolds cavitation and reformation solution than with modified Reynolds separation. This reflects both the differences in film thickness between the two solutions as shown in Figure 7 and the larger axial extent contributing hydrodynamic shear stress with Reynolds cavitation and reformation as noted previously. The overall frictional power loss derived from these predicted friction forces, expressed in terms of friction mean effective pressure (FMEP),is 6.8kPa for Reynolds cavitation and reformation and 4.5 kPa for modified Reynolds separation. This equates to a 34% lower FMEP prediction with modified Reynolds separation conditions compared with Reynolds cavitation and reformation. 5. EXPERIMENTALREVIEW

Experiments that are able to provide insight into cavitation phenomena in the piston ring / cylinder wall interface basically either measure hydrodynamic pressure or film thickness. The majority of piston ring lubricant film thickness observations have used capacitance transducers mounted flush in the cylinder wall. This technique was pioneered by Hamilton and Moore [ 171 and used by the same research group in several

448

subsequent studies [18,19,20,21] and also by other workers such as [22,23,24,25]. If the clearance between the piston ring and cylinder wall were M l of lubricant then the lubricant film trace measured with this technique would reproduce the ring profile passing the transducer. What Hamilton and Moore and other workers found, however, is that lubricant starvation affects the lubricant film trace in the inlet region and cavitation distorts the outlet region. Detailed analysis of the cavitated film was not possible, however, because the ~ o ~ evalue c t of the dielectric constant could not be precisely determined due to the unknown lubricant/air mixture. In recent years, a number of studies of piston ring lubricant film thickness have been undertaken using laser induced fluorescence @IF) techniques such as [2,4,16,26,27,28,29]. This method basically involves shining a laser light into the lubricant film between the piston ring and cylinder wall through a window or fibre optic mounted in the cylinder wall and measuring the intensity of the fluorescence produced in the lubricant film and passing back through the window or fibre optic. The intensity of the fluorescence is linearly related to the lubricant film thickness assuming the film is continuous. However, if cavitation occws or if attempts are made to measure the film thickness on the cylinder wall between the piston rings, where there may be lubricant on the cylinder wall and the piston land with an air space between, then this relationship does not hold and only a subjective estimate of an effectivefilm thickness can be made [16). Two examples of LIF film thickness measurements undertaken at Thornton Research Centre on a firing CAT-1Y73 singlecylinder diesel engine are given in Figure 9. The graph is based on the data reported by Brown et af [16] and shows measurements taken in the mid-stroke region on the power stroke for two Merent lubricants, an SAE 15W/30 universal diesel engine oil (UDEO)and an SAE 10W/30 super high performance diesel oil (SHPDO), with a cylinder wall temperature of approximately 120'C. The piston and ring pack, which are moving from right to left in the figure, are superimposed on the graph to show that the passage of the rings past the transducer can clearly be seen in the traces. There is insufficient detail, however, to shed any light on what form of

cavitation occurred in the outlet region especially given the recognised uncertainty of the measurement in this region. It is interesting to note, however, that there is no strong evidence of fluid film reformation in either of the traces.

Figure 9: LIF Measurements from a Fired CAT-1Y73 Single Cylinder Diesel Engine 6.00

-

6.00

\

I

C

4.00

0

'i

y5.00

I X P.OO 4 .r(

)1

1.00

........I.& .........R& .........5. X-kie

(mm)

Figure 10: Ring Profile Superimposed on an LIF Oil Film Measurement from a Cameron-Plint Reciproc-sting Tester (Figure 8 from Richardson and BoPI) Figure 10 is taken from Richardson and B o r n [2] and is an example of an LIF film thickness trace measured between a section of piston ring and cylinder liner in a Cameron-Plint reciprocating

449 tester. The measured ring profile is superimposed on the film thickness trace and shows starvation of the inlet on the left and what appears to be separation in the outlet region on the right. Richardson and Borman classify this as separation rather than Reynolds cavitation because there is no evidence of film reformation at the back of the ring [Z]. Given that this is a reciprocating test rig with atmospheric pressure at inlet and outlet, however, there would be no fluid film reformation according to the Reynolds cavitation and reformation conditions of equation (4) if one assumes that cavitation occurs at atmospheric pressure. It is therefore not possible to confidently identhe cavitation phenomenon in the outlet. In Figure 11, a similar form of output is shown b r the top ring of a motored diesel engine taken from Hoult et a1 [4] with (1) identifying the inlet and (2) the outlet. The lubricant apparently rises to meet the ring at the inlet although there is still a degree of starvation. In the outlet region the lubricant film is in close proximity to the ring profile to a point much further downstream than the data presented in Figure 10 but again it is not possible to discern the details of the cavitation process. wear

[30,31,32] being the most notable examples. Their work was conducted on the lower half of a Petter AVl diesel engine with the cylinder left open to atmosphere using a single piston ring mounted on a specially designed piston which eliminated piston tilt and ring twist. Hydrodynam~cpressure was measured by a small piezoelectric pressure transducer mounted in the cylinder wall between two capacitance film thickness transducers which measured the film profile and hence enabled the pressure profile across the ring face to be resolved. The lubricant used for the tests was a hydraulic oil which was used simply because it gave a convenient viscosity at room temperature. The work showed that in mid-stroke regions the Reynolds cavitation condition of equation (3) was, in general, satisfied although there was some evidence of small negative pressures in the outlet region. Near dead centres, however, large negative pressures were observed in the outlet region with a maximum of -0.78 MPa recorded just after TDC with a large radius, convex ring profile 1321.

0.4

-0.4

7"

-0.8

Figure 11: Top Ring Profile Superimposedon an LIF Oil Film Measurement from a Motored Diesel Engine (Figure 1 from Hoult et a1 [4]) Hydrodynamic pressure measurements between piston rings and cylinder walls are not so numerous in the literature with Brown and Hamilton

Figure 12: HydrodynamicPressure Measurements from a Piston Ring with a Double-Sloped Triangular Profile Running in a Motored Diesel Engine (Figure 4c and 4d from Brown and Hamilton [32]) Figure 12 is taken from Brown and Hamilton [32] and shows pressure profiles just after TDC

450

measured under a piston ring with a convergentdivergent symmetric triangular profile. The axial coordinate x is measured from the inlet and a is the axial ring width. The peak negative pressure recorded with this ring was -0.70 MPa at 7' after TDC. It appears from these experiments that for short periods of time, pressures far below the saturation pressure, at which cavitation would normally occur, can be sustained. However, as the authors themselves pointed out [32],it was possible that the pressure gauge itself was acting as a local disturbance of the cylinder wall and could have caused premature cavitation in the immediate vicinity of the pressure gauge leading to problems in interpreting the data. 6. DISCUSSION

It has been shown in this paper that a number of alternative boundary conditions are available when solving Reynolds equation for the piston ring / cylinder wall interface and that these boundary conditions are basically distinguished by the assumed nature of the cavitation occurring in the outlet region of the piston ring profile. Examples of the use of all thc boundary conditions proposed may be found in the literature except for the full fluid film separation condition of equation ( 5 ) and the Coyne and Elrod condition of equation (6). The computations presented for two alternative boundary conditions have highlighted the sensitivity of the analysis to the chosen boundary conditions but the review of available experimental data fails to resolve which are the correct boundary conditions. It could perhaps be that Werent boundary conditions are more appropriate to different conditions of load, speed, temperature and degree of lubricant starvation as proposed for journal bearings [Ill. Two important points which arise from the experimental review are the lack of strong evidence for lubricant film reformation at the outlet and the apparent existence of signrficant negative hydradynamic pressures, i.e. tensile stresses, in experimental studies on a motored test rig. This latter point suggests that under certain conditions the Coyne and Elrod separation solution of equation

(6) might be the most appropriate. Computations using Coyne and Elrod separation would therefore be a worthwhile undertaking in any further research in this area.

7. CONCLUSIONS (i) The boundary conditions applied when solving Reynolds equation for the piston ring / cylinder wall interface depend upon the assumed nature of the cavitation in the diverging lubricant film. (ii) The results of such an analysis are sensitive to the choice of boundary conditions. (iii) Available experimental data fails to resolve the situation although interestingly there is no strong evidence of lubricant film reformation. (iv) The apparent existence of sigruficant negative hydrodynamic pressures, i.e. tensile stresses, in experiments on a motored rig suggests calculations using Coyne and Elrod separation should be undertaken. 7. ACKNOWLEDGEMENTS

The authors would like to thank Shell Research Limited, Thornton Research Centre and the Industrial Unit of Tribology, University of Leeds for funding this research work and for permission to publish this paper. REFERENCES 1.

Dowson D., Economou P.N., Ruddy B.L., Strachan P.J. and Baker A.J.S., "Piston Ring Lubrication - Part 11, Theoretical analysis of a single ring and a complete ring pack", Energy Conservation Through Fluid Film Lubrication Technology: Frontiers in Research and Design, ed. S.M.Rohde, D.F. Wilcock and H.S.Cheng, ASME pub., pp.23-52 (1979)

45 1

Richardson D.E. and Borman G.L., "Theoretical and experimental investigations of oil films for application to piston ring lubrication", SAE Paper 922341 (1992) Taylor R.I., Brown M.A., Thompson D.M. and Bell J.C., "The influence of lubricant rheology on friction in the piston ring-pack", SAE Paper 941981 (1994) Hoult D.P., Wong V.W. and Azzola J.H., "Direct observation of the friction reduction of multigrade lubricants", SAE Paper 910742 (1991) Ruddy B.L., Dowson D., Economou P.N., "A review of studies of piston ring lubrication", Proc. 9th Leeds-Lyon Symp. on Tribology: Tribology of Reciprocating Engines, Paper V(i), pp.109-121 (1982) Sommerfeld A., "Zur hydrodynanuscien theorie der schmiermittehreibung", 2. Math. Phy., 50, pp.97-155 (1904) Giimbel L.K.R., "Vergleich der Ergebmse der rectinerischen Behandling des Lagerschmieran-gsproblem mit neueren Veisuchsergebmsen", Monatsbl. Berliner Bez. Ver. Dtsch. Ing., Sept, pp.125-128 (1921) 8.

9.

Reynolds O., "On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments, including an experimental determination of the viscosity of olive oil", Philos. Trans. R. Soc. London Ser. A 177, pp. 157-233 (1886) Swift H.W., "The stability of lubricating films in journal bearings", J. Inst. Civ. Eng., 233 (Pt. l), pp.267-288 (193 1)

10. Steiber W.,Das Schwimmlager., Berlin: Ver. Dtsch. Ing. (1933) 11. Dowson D. and Taylor C.M., "Cavitation in bearings", Ann. Rev. Fluid. Mech., 11, pp.3566 (1979)

12. C o p e J.C. and Elrod H.G., "Conditions for the rupture of a lubricating film. Part I: theoretical model", Jour. Lubrication Technology, Trans. ASME, July, pp.45 1-456 ( 1970) 13. Coyne J.C. and Elrod H.G., "Conditions for the rupture of a lubricating film - Part 11: new b o u n m conditions for Reynolds' equation", Jour. Lubrication Technology, Trans. ASME, J a n ~ ~pp.156-166 y, (1971) 14. Wakuri Y., Soejima M. and Taniguchi T., "On the oil film behaviour of piston rings (correction of effective pressure region of oil film)", Bull. JSME, Vol. 21, No. 152, pp.295302 (1978) 15. Dowson D. and Higginson G.R., Elastohydrodynarmc Lubrication, SI edition, Permagon Press, Oxford, England, pp.38-39 (1977) 16. Brown M.A., McCann H. and Thompson D.M., "Characterization of the oil film behaviour between the liner and piston of a heavyduty diesel engine", SAE Paper 932784 (1993) 17. Hamilton G.M. and Moore S.L., "The lubrication of piston rings, First paper, Measurement of the oil-film thickness between the piston rings and liner of a small diesel engine", Proc. Instn. Mech. Engrs., Vol. 188, 20/74, pp.253-261 (1974) 18. Hamilton G.M. and Moore S.L., "Measurement of piston ring profile during running-in", Piston Ring Scuffing, Instn. Mech. Engrs. Conference, Paper C69/75, pp.61-70 (1976) 19. Brown S.R. and Hamilton G.M., "The partially lubricated piston ring", Jour. Mech. Eng. Sci., Instn. Mech. Engrs., Vol. 19, N0.2, pp.81-89 (1977) 20. Moore S.L. and Hamilton G.M., "The starved lubrication of piston rings in a diesel engine",

452

Jour. Mech. Eng. Sci., Instn. Mech. Engrs., V01.20, N0.6, pp.345-352 (1978) 21. Moore S.L. and Hamilton G.M., "The piston ring at top dead centre", Proc. Instn. Mech. Engrs., Vol. 194, pp. 373-381 (1980) 22. Myers J.E., Bonnan G.L. and Myers P.S., "Measurements of oil film thickness and liner temperature at top ring reversal in a diesel engine", SAE Paper 900813 (1990) 23. Grice N., Shemngton I., Smith E.H., ODonnell S.G. and Stringfellow J.F., "A capacitance based system for high resolution measurement of lubricant film thicknesses", NORDTRTB '90,Proceedings of the 4th Nordic Symposium on Tribology, Lubrication, Friction and Wear,Jakobsen J., Klarskov M., Eis M. (Eds.), Lyngby, DNK, Technical University of Denmark, pp.349-361 ( 1990) 24. Clarke D.G., Shemngton I. and Smith E.H., "Simultaneous measurement of pistodpiston ring friction and oil film thickness in an IC engine", Experimental Methods in Engine Research and Development '91, Instn. Mech. Engrs. Seminar, HQ, December, pp.51-58 (1991) 25. Grice N. and Sherrington I., "An experimental investigation into the lubrication of piston rings in an internal combustion engine - oil film thickness trends, film stability and cavitation", SAE Paper 930688 (1993)

26. Lux J.P., Hoult D.P., Olechowski M.J., "Lubricant film thickness measuements in a diesel engine piston ring zone", Lubrication Engineering, May, Vol. 47, 5 , pp.353-364 (1991) 27. Richardson D.E., Borman G.L., "Using fiber optics and laser fluorescence for measuring thin oil films with application to engines". SAE Paper 912388 (1991) 28. Hoult D.P., Azzola J.H., "The possible role of surface tension in the reduction of top ring drag", SAE Paper 932781 (1993) 29. Phen R.V., Richardson D., Borman G., "Measurements of cylinder liner oil film thickness in a motored diesel engine", SAE Paper 932789 (1993) 30. Brown S.R. and Hamilton G.M., "Pressure measurements between the rings and cylinder liner of an engine", Piston Ring Scufllng, Instn. Mech. Engrs. Conf., Paper No. C72/75, pp.99-106 (1976) 31. Brown S.R and Hamilton G.M., "The partially lubricated piston ring", Jour. Mech. Eng. Sci., Instn. Mech. Engrs., Vol. 19, N0.2, pp.81-89 (1977) 32. Brown S.R and Hamilton G.M., "Negative pressures under a lubricated piston ring", Jour. Mech. Eng. Sci., Instn. Mech. Engrs., V01.20, N0.1, pp.49-57 (1978)

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

453

Effect of compliance on the extend of optimum compliant air thrust bearing operating range I.IordanofP, P.Hermelb and PStephanc

a Student at the PSabatier University b Engineer at ABGSEMCA c University Lecturer at PSabatier University

This work is about the influence of compliance on the extend of optimum operating range. It is shown that although compliance has t o be high enough because of the numerous advantages which have been presented in many papers, it has t o be limited in order to keep a n extended optimum operating range. A very simple method is presented which will help the designers in order to optimize a thrust bearing. A comparison with a complete calculation is made. 1.INTRODUCTION ABG SEMCA, specialized i n a i r conditioning systems has t o conceive small high speeds (30000 t o 80000 rpm) turbomachineries. Heshmat 111 has shown t h a t compliant bearings offer higher load capacity, lower power loss, and in [21, he has shown experimentally the good misalignment tolerance of such bearings. In [3], it has been found that the best profile for the air film was a leading converging profile followed by a parallel profile (figure 1). The governing equation for a compressible fluid in steady state conditions is the Reynolds' equation:

where t h e compressibility number A contains the operating conditions. It has been shown in [3] that for a given A, we can find the maximum load capacity with the relationship:

O,= 3Hl(Hl-l)/A

and [31 has confirmed the positive effect of compliance on misalignment tolerance. The aim of this work is to outline the negative effect of compliance on the extend of the so called optimum thrust bearing operating range (where the load is higher than 95% of the maximum load capacity). Thus, a simplified solution in order t o obtain t h e extend of optimum operating range versus A is developped. OR

ShLspeed

L1

leaf

1H2=1

transition angle 01

angular extend of pad 8s

Figure 1. Geometry of the thrust bearing.

454

2.OPTIMUM OPERATING RANGE: LINEAR STIFFNESS 2.1 Results for the rigid thrust bearing. In this paper, all the results will be given for the following geometry: 0 =40°

R, = 0.5 i t has been shown in [31 t h a t the maximum load capacity depends on the HI (entrance film thickness) and 0, (transition angle) values. Figures 2 and 3 show the evolution of Hlowa nd O,Op, (which optimize the load capacity) versus A.

9, H1

Then, it is interesting to know if a given thrust bearing (defined with fixed values of HI and 0,) is able t o develop high loads over a broad range ( in terms of A). For this purpose, the optimum operating range will be defined as followed : For a given A, thrust bearing profiles which develop a load capacity of 95% of the maximum load capacity are belonging t o the optimum operating range. Thus, the first study consists in an evaluation of the influence of HI and 0, on the operating range of a rigid sector : - For each A value, and with HI= HI*,, €)Inlax and elruin which give 95% of the maximum load capacity are researched (Ol,,lax> 810p,and ‘lnlin<

‘lop,)

each A value, and with 8,= clop,, Hlrllax and Hlnlinwhich give 95% of the maximum load capacity are researched (Hlnlax>Hlop,and - For

Hl,i”< HIOP,).

“t 200

0

400

rn

800

lo00

Figure 2. Hlq, versus A

28

6

01°

Results are given in figures 4 and 5 . For a 8, of 20°, the load is over 95% of the maximum load capacity from A=20 to more than 1000. This value will be chosen for the following studies. Figures 4 and 5 outline that a good choice of H, and 8, will give a very extended optimum operating range for a rigid bearing. hi Hlmax

12 11 10 9

a

7

l3! 0

I

200

I

400

II

600

figure 3. CllOp,versus A

I

I

800 lo00

0l

o

I A ~ 4 o o 6 o o a ~ i o o o

Figure 4. Optimum range : H1 versus A

455

rotor Dlane

34+

13 10

A

200

0

600

400

800

lo00

Figure 5. Optimum range 8, versus A 2.2.Optimum compliant thrust bearing operating range (0.R) :simplified solution. In t h i s p a r t , local compliance is considered (ed the deformation on each point only depends on the pressure applied on this point). Heshmat [ l l has presented a technology which structural behavior can be presented with local compliance (see figure

6).

.

..

.

.

. .

.

Stiffening elements

Slot in bump foil t o improve element independence

Figure 6. technology with local compliance behavior. The resulting deformation leads t o an entrance film thickness diminution versus maximum pressure on the sector ( see figure 7): HI = HIgeo-

s (pNax-0

where Hlgeo is the initial entrance film thickness and S is the local compliance.

III

deformed geometry initial geometry

0Pressure field Figure 7. H1 diminution versus load. Thus, as A increases, the load capacity on the sector increases and H I decreases. As Hlop,increases with A, the compliance will reduce the optimum operating range. For a fixed 8, value (20" for a 40" sector extend), the rigid study gives (see 2.1) Hlnlaxr(A) (and the maximum pressure associated PNaxl(A))and Hlminr(A) (and the maximum pressure associated Pnlarz(h)1. T h e n , t h e maximum (respectively minimum) initial entrance film thickness) for a compliant sector is given by:

Curves of figure 8 give the evolution of versus A for the tested geometry and with a local compliance of 3.65. The optimum operating range is much more extended for the rigid geometry than for the compliant one. For the compliant geometry, the larger the compressibility number is, the broader the operating range is (O.R,, > O.F$l). Hlmaxr, Hlminr, Hlgbornax' HlgCornin

456

Optimum operating range extend

~

mm.”

m

a Hlgeomax 0

HIgeomin HI maxr

0 HI minr

0

50

100

150

200

250

300

350

450

400

500

Figure 8. Optimum operating range graphic.

2.3..COmparhnwith the complete solution. The very simple previous study has now to be compared with the complete resolution of t h e elastoaerodynamic problem. The algorithm of figure 9 summarizes the resolution method described in [ll and [31.

For the calculation, the following values are chosen: = 8 (thrust bearing B1)

Hlgeo

= 11 (thrust bearing B2)

H1g60

Hlpeo = 15 (thrust bearing B3) 5

p a = 10 Pa

geometry and

H: film thickness field on the thrust

-5

pa= 1,85 10 P a s ro = 40 mm

bearing

h0=6pm

and thus A versus rotation speed o is obtained:

H=H+I -H2 calculation

2

6p r o

A=&=

2

-3

5.166 10

61 (61 in

rpm)

Pa%

Figure 9. Complete calculation : algorithm.

Figure 10 gives t h e evolution of t h e dimensionless load capacity versus A. Table 1 and 2 compare the extend of optimum operating range obtained by the simplified model and by the complete calculation. These tables outline t h e very good approximation given by the simplified study.

457

1800 1600 1400 1200 1000 800 600 400

WA= w/PaA Pa : external pressure A : thrust bearing surface

200 0 0

50

100

150

200

250

300

350

400

450

500

Figure 10. Load capacity versus compressibility number : complete calculation. ~~

~

B1

B2

0

140

250

140

250

500

0 aax 27100

27100

48400

48400

!36780

Amin Amax -in

I33

Tablel. simplified calculation (figure 8).

B1

I32

3.l.simplified solution The compliance is supposed t o change when H, reaches Hlmax,

HI= Hlgkomax- S1(Pmaxlo-l) = ~ l r n a n r o (after this point, a little decrease of H, is researched)

B3

hn

0

120

230

h a x m n

120

230

500

23200 44520

44520 96780

0 cr)max 23200

described in 2 t o the double stiffening elements case.

Rotor

ner 2:S2

Table2. Complete calculation (figure 10).

3.0PTIMUM OPERATING RANGE: NON LINEAR STIFFNESS. it has been shown the bad influence of compliance on the optimum operating range extend. Heshmat has experimentally shown [2] the good effect of double stiffeners on the optimum operating range (figure 11).This part will extend the simplified study

Piston. Figure 11. Double stiffening elements. This point is graphically defined (see figure 12) by the intersection of:

458

20

Optimum operating range

18 16 14 12

10 8 6

4 2

A

0

50

0

100

150

200

250

300

350

400

450

500

Figure 12. Optimum operating range graphic : double stiffening elements. and H=

Curves of figure 12 gives the optimum operating range for a thrust bearing (thrust bearing 2s) defined by:

Hlgeo

In this point, Pmaxlis written Pmax10and thus, the entrance film thickness after this point will be : HI=

~ l g t o sI(Prnaxl0-l) -

- SJP-PmaxlJ

with SI*S2 se -- -

SI

+

s2

The profile will be no more the optimum profile when H, = Hllllnr The corresponding point is defined graphically by the intersection o f H=

Hlmi&A)+

Sl(Pmaxl0-1)

+

and = Hlgto

se(pmax2(~)pmaxlJ

Hlgto= 11 (upper stiffener) Hlmaxd=5.58 (lower stiffener, see figure 8) S,=3.65 S,=l.29

This t h r u s t bearing h a s a broader operating range than the equivalent single stiffening element thrust bearings B2 and B4 : the optimum operating range is going from A=140 (as thrust bearing B2) t o A 4 2 0 (as thrust bearing B4).

3d.Complete solution. As in 2.3,the simplified solution will be now compared with the complete resolution of the problem. A n algorithm of the complete solution is presented figure 13. Figure 14 gives the evolution of the load capacity versus A for the thrust bearings B2, B4 and 2s.

459

800 600

0

50

100

150

200

250

300

350

400

450

500

Figure 14.Load capacity versus compressibility number : complete calculation. In this case, the simple model also gives a very good approximation of the double stiffening e l e m e n t s t h r u s t b e a r i n g operating range.

geometry and dHs: distance between the two stiffeners

initialization

Newton-Raphson

I I

I

deflexion calculation

IH2- 1I

H=H+ 1-H2

'igure 13.Complete double stiffeners thrust bearing calculation : algorithm.

As expected, thrust bearing 2 s works as well as thrust bearing B2 at low A and as well as thrust bearing B4 at high A.

4.CONCLUSION With the results of the complete study of the rigid case : - knowledge of

- knowledge of H,,,jA), H,fim(A), Prna&) and Prna&) and for a given local compliance S , a very simple method has been presented in order to rapidly obtained the optimum operating range of a thrust bearing. As a matter of fact, the presented diagrams are able t o precisely define the geometry which will able to develop a higher load capacity over a broad operating range. They also outline the negative effect of compliance on the extend of the optimum operating range. The solution proposed by Heshmat [21 (double stiffening elements) increases the stiffness when the load increases. This paper confirms theoretically the good effect of the double stiffeners configuration on the optimum operating range extend. In this case, a very simple model h a s been

460 presented. It also gives a very good approximation of the complete study. This work will thus allow a great win of time in the design and a better behavior comprehension of the compliant t h r u s t bearing.

REFERENCES. l:Heshmat.H, Walowit J.A., Pinkus O., "analysis of g a s lubricated t h r u s t bearings", ASME j o i n t lubrication conference, October 1982, pp 638-646 2:Heshmat.H, Shapiro W., "Advanced Development of Air-Lubricated Foil Thrust Bearings.", ASME j o i n t lubrication conference, October 1982. 3:Iordanoff I., Hermel P.,Stephan P., "Optimization of air compliant t h r u s t bearings", 21e Leeds-Lyon symposium, September 1994.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

461

EXPERIMENTAL MEASURING OF VELOCITY PROFILES IN HERRINGBONE GROOVED JOURNAL BEARINGS J. ABSI and D. BONNEAU Labomtoire de Mkanique des Solides, Universit6 de Poitiers Unit6 de recherche associ& au C.N.R.S. U.R.A. 861

1. INTRODUCTION The determination of the velocity field in a lubricant film is of great importance as it enables us to understand the behaviour of the fluid inside contacts and to appreciate other phenomena which occur in lubrication, such as formation and rupture of the film. Moreover, we note that when there is an abrupt change in the film section, for exemple near the grooves, it is essential to determine velocity fields from which curves can be established for each thickness of the film throughout the contact. These curves show the flow mode, and enable us to determine other parameters as, for example, the pressure distribution in contact.

In this paper, we present the measurements of fluid velocity field in the HGJB obtained by an optical method. The spatial resolution and the precison of this method is studied. We describe also the experimental apparatus (mechanical and optical elements), and finally we give and discuss some experimental results.

In recent years, Herringbone Grooved Journal Bearings -HGJB- (Fig-1) have been adopted for business machines and other applications for two reasons: 1- the stiffness, and therefore the stability of the

bearing in concentric or nearly concentric operating conditions are considerably better.

2- due to the grooves, a leakage-free journal bearing can be obtained.

Figure 1. Herringbone Grooved Journal Bearing

There are few experimental studies realised on this type of bearings; nevertheless, we can mention the works of Hirs in 1965[1] on the stability of the Herringbone Grooved Jounal Bearing (HGJB) and those of Bootsma in 1974(2] on the conditions of leakage. Bonneau in 1983[3] presented several methods of measurement of the fluid velocity field applied in the case of a plain journal bearing.

2. OPTICAL METHODS OF VISUALIZATION The measurement of the velocity field, must be performed without perturbing the flow in films less than lmm thick. According to the works of Bonneau et a1 in 1983, the optical methods are capable of measuring fluid velocity in small gaps while respecting the previous conditions.

Aluminium powder will be used from which the smallest particles will be obtained by decantation.

This measurement in one point of the flow can be realised through the observation of the movement of the fluid particle at the same point. These methods enable us to obtain the velocity field v by measuring the movement of a particle Ax

The size of the particles used will be less than 20pm. A narrow band of laser beam several micrometers thick, oriented in the direction of the flow, illuminates the lubricanting film in the cross section. The aluminium particles are illuminated as they cross the laser beam.

AX

during a period of time At. (V = -).

At

The choice of a method depends mostly on the specifications of the flow we have to study. A thin film flow presents a greater variation of speed in its thickness and thus requires a method with a greater spatial resolution.

A schematic representation of principle of the method is shown in figure-2

The optical method used requires a lighted surface covering the investigated field. This surface facing the point of observation must be as thin as possible to avoid superposition on the line of sight of the points which are going at about the same speed.

A method by visualization of solid tracers has been chosen because of its high qualities in spatial resolution, its precision, its easiness of use and also because the results given both qualitatively and quantitatively are easily exploitable.

In order not to mingle the movement of a particle in the lighted field thus creating a light trace, and the movement of a particle through the field we use a stroboscopic disc which transforms the light trace into a series of points.

The precision of the measurement will depend on the precision with which both the movements and the period of time will be measured. More details on the spatial resolution and on the precision of measurment have been developped by Bonneau in 1986.

The observation device -generally a camera- must be as reliable as possible with a depth of field more important than the thickness of the lighted surface. The camera fitted with a macro photographic lens of 105 mm focal length, is fixed in a transversal direction as shown in figure-2.

3. THE PRINCIPLE OF THE METHOD A small amount of lubricant with fine reflecting particles in suspension is fed in the gap of the bearing. The tracers have been chosen because of their light reflecting properties.

The velocities are calculatded from the distances between two succesive points and their corresponding time intervals deduced from the speeds of the stroboscopic disc. Stroboscopic disc ,

visualization surface

I

,D.camera

I

PC

the

monitor

Figure 2. Scheme of the optical method of visualization

463

...

* lubricant lens

lens

I Figure 3. A schematic representation of visualization system The period of observation must allow a distance of movement more important than the size of the object and limited to values giving movements equal to about ten times the spatial resolution.

4. EXPERIMENTAL APPARATUS The apparatus used is illustrated in figure4. It includes two plexiglass cylinders with a 1 mm radial gap and an inside diametre of 80 mm. Those cylinders can rotate in both directions independent from one another. They are driven by a tooth beltdrive system connected separately to two variable-speed motors. The rotating speeds of the cylinders can therefore be varied progressively in both directions, and these speeds are measured using electronic counters connected directly to the motor shafts. One of the surfaces of the bearing includes four herringbone grooves 1 mm deep and with a 30 degrees inclination. Liquid paraffin with a 0.03 Pa.s dynamic viscosity containing aluminium particles fills the gap between the cylinders.

The optical system is shown in figure-5. The lighting is a 35 mW He-Ne continuous laser beam. The beam is focused through the first lens in the position of the stroboscopic disc. The pulsated radiation thus obtained goes through a cylindrical lens and is transformed into a light strip.

The system incorporates a stroboscopic disc driven by a variable-speed motor, the rotation speed being measured by an electronic counter connected directly to a P.C. This stroboscopic disc transforms the continuous beam into pulsed light. The period of time between two pulsed lights is measured and memorized directly in the P.C. thanks to this system.

Iuljicating film

u-

Motor

b

counter

I

Figure 4. A shematic representation of the apparatus The observation device is a CCD camera (figure-2) with an electronic obturator. The camera is coupled to a computer including a Digital Image Processing code. After having fixed a picture, this code allows us to give the speed and direction of the flow in the considered point.

464

l

e

fl

f2

A

L1

L Figure 5. Lighting system

5. RESULTS

5.1. Characteristics of the flow A visualization with a continuous light enables us to clearly show a bidimensional flow in the neighbourhood of the smooth surface, which becomes a three-dimensional flow as we get closer to the grooves.

As we can see on the photo of figure-6 showing a mobile smooth surface, the lines traced by the particles become spots as we get closer to the grooves. If we allow the lighting surface to revolve a few degrees around its axis, we can visualize the three-dimensional flow pointing to the center of the bearing along the grooves. These results confirm the assumption that there is low axial leakage flow through the ends of the bearing. A whirling zone (figure-7) with an axial flow is observed near the groove edge. This zone follows the inclination of the herringbone grooves.

Figure 7. Whirl zone scheme

Figure 6. Visualization of the flow with a continuous light

465

5.2. Presentation of the speed distributions Figure-8 shows an example of visualization with a pulsated light. A regular succession of black spots in a given direction materializes the successive positions of the same particle in the lighting plan. Then we only have to calculate the average speed and the direction of this particle to infer the components of the speed of the fluid particle it replaces. This speed is given by a simple ratio of the distance between two successive spots and their corresponding time intervals.

Figure 9. flow of 0.1 mm thickness Figure-9 shows a flow of a very thin thickness (0.1 mm). The presence of' a succession of a black spots, confirmes the possibility of effectuing the mesures of speed in these hard conditions. This principle lets us develop a computational code which from a picture in pulsated light, mesures the speed vectors and accept, their representation in perspective geometry. Figure-10 represents the speed distribution before, along and after the groove step when the smooth member rotates and for eccentricities varying between 0 and 0.9.

Figure 8. Example of visualization with a pulsated light

After a projection of these results on the three planes of an orthonormal referential, we notice a parabolic distribution of the speed vectors, a three-dimensional character of the flow and finally the presence of a whirl zone and an axial flow at the place of the grooves.

466

-

80 mrnh

Id

Figure 10. Speed distributions

467 5. CONCLUSION Despite the problems created by the thinness of the flow lubricating (0.1 mm) and the three-dimensional character of the flow in a herringbone groove, the method by visualization of reflecting tracers allows us to describe this flow thanks to its easiness of realisation and to the optimisation of spatial resolution. The experimental results show a parabolic distribution of the speed fields. These results confirm the hypothesis adopted generally when we use the Reynolds equation and, in the same time, they lets us deduce the exitence of an axial flow at the place of the grooves turned towards the median plane. This latter result is on perfect agreement with Bootsmas' result and confirm the hypothesis of a low leakage in the case of an H.G.J.B.

REFERENCES 1. Hirs, G.G. ; "The Load Capacity and Stability

Characteristics of Hydrodynamic Grooved Journal Bearings," ASLE Paper No.64LC-24, Presented at the ASME-ASLE International Lubrication Conference in Washington, D.C.,October, (1964). 2. Bootsma, J. ; "The Gas-to-Liquid Interface of

Spiral-Groove Journal Bearings and its Effect on Stability," ASME Journal of Lubrication technology, Vol. 96, pp. 337-345 (1974). 3. Mutuli, S . Bonneau, D. et Fr&ne,J. ; "Velocity

Measurment in the Inlet Zone of a Hydrodynamic Contact," Proc. 10th LeedsLyon, Symp. Buttenvorth Ed., pp. 97114(1983). 4. Bonneau, D. ; "Formation du film lubrifiant

dans les contacts a alimentation non surabondante. Aspects Experimentaux et Theoriques," These de Doctorat es Sciences Physiques, Universite de Poitiers (1986).

This Page Intentionally Left Blank

SESSION XI1 COATINGS Chairman :

Professor Philippe Kapsa

Paper XI1 (i)

An Investigation into the Properties of a Thin Solid Coating Using an Optical Method

Paper XI1 (ii)

Tribological Analysis of Friction Damage on Coated Plastics Through the Third Body Concept

Paper XI1 (iii)

Friction and Wear Behaviour of Plasma-sprayed Cr203Coatings in Dry Sliding Against AlSl D2 Steel

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

47 1

An investigation into the properties of a thin solid coating using an optical method

A V Olver. P M Cann and J.-C. Loric Department of Mechanical Engineering, Imperial College. London. UK

The elastic modulus of a thin (3 pm) solid coating has been determined by pressing a coated wire against a diamond flat and measuring the contact width optically. The technique neither involves the use of ultra-low loads, nor of costly equipment. and provides results which are accurate enough to be useful in contact stress analysis.

1 INTRODUCTION

1.1 Need for measurements in coatings Thin solid coatings are now widely used in a variety of contact situations. The coatings usually have significantly different elastic properties from those of the substrate and there is increasing interest in methods for measuring them, primarily in order to analyse contact stresses. For example rough surface contact of coated bodies has been examined by Halling [l], Cole and Sayles [2.3] and Olver et al. [4] among many others. The need for this approach as an aid to surface engineering has been recognised [ 5 ] .

1.2 Difficulties with coatings However the usefulness of such analysis is often hampered by poor data on the coatings themselves, which may be anisotropic and even inhomogeneous. Some coatings have variable elastic properties which are amenable to manipulation by the process parameters 14, 61. Many coatings only exist as thin films or differ sigrufrcantly when manufactured in bulk, so that the standard methods of determining their elastic properties such as tensile testing or speed of sound measurements cannot easily be applied.

1.3 Other Methods: Other methods for measuring the elastic moduli of thin coatings include vibration methods

[7.8] and nano-indentation [6. 9-14], However. both these methods have significant disadvantages. The vibration method typically involves the measurement of a natural frequency of vibration of a slender beam. with. and without. a coating. The frequency measurement can easily be made with great accuracy and provided that the coating thickness is large enough and has been accurately determined, the method is potentially accurate for an isotropic coating. However. if any anisotropy is present. the error in finding the stiffness normal to the surface - what is required for a contact analysis - could be large. In the nano-indentation method. this difficulty is overcome because the elastic modulus is the result of a contact experiment. The elastic properties are derived from the relaxation upon unloading. However, if it is desired to eliminate substrate effects entirely. the load required is extremely small, making the control of the e,uperiment difficult and expensive. In addition, the indenters used are often designed for hardness (plastic) testing and hence inevitably cause some damage to the specimen. In this paper we describe a simple method for measuring the Young’s modulus of a thin coating which does not require ultra-low loads and enables the direct determination of the normal (contact) stiffness. precisely that quantity which we require for the theoretical analysis of contact stress.

472 2. PRINCIPLE ANALYSIS

AND

THEORETICAL

2.1 Optical method The method adopted consists of pressing a coated wire specimen against a transparent flat. The size of the area of contact and the positions of the fringes associated with the gap immediately outside the contact are then measured. This technique is similar to that used by Gohar [IS] and Foord et a/. [16] in the development of the optical film thickness technique. However in refining the method for thin coatings we have adopted the following:

2.1.1 Use of diamond Because we want the measured contact patch to be as responsive as possible to the coating properties, we need to select a counterface with a Young's modulus as high as possible. Such a material. which also has excellent optical properties, is provided by diamond (E = 1050 GPa, v = 0.20).

2.1.2 Use of line contact Ln order to minimise the effect of the substrate. we need to create and measure a contact dimension comparable to or smaller than the coating thickness. However. we do not want very low loads as they may be difficult to measure with sufficient accuracy. This problem was solved by using line contact between a wire and a flat diamond disc (Figure 1). 2.1.3 Use of zero order fringe. In the area of contact itself, the light wave reflected from the steel is n out of phase with that from the internal surface of the diamond, creating a minimum of reflected intensity. Immediately outside the contact, the intensity increases because of the phase difference created by the gap. Thus the region of the minimum intensity is that of the actual contact. This is in contrast to experiments carried out on partially reflective

metallic coatings, such as are commonly used for film thickness determination. In the latter case. a general phase change occurs which creates a .bright area of contact with a darker surround.

2.1.4 Use of higher fringes In addition, we may in principle use the higher order fringes, which occur when the gap between the diamond and the coated wire is equal to integral multiples of half the wavelength of the light. to determine the shape of the deflected surface. 2.2 Layered cylinder theory In this section the predictions of elastic theory for this situation are reviewed. As we are dealing with a single layer of known thickness and with line (two-dimensional) contact we may use the theory of Gupta and Walowit [I71 noting the corrections given by Cole and Sayles (21.

2.2.1 Contact width predictions The predicted half-width of the contact as a function of the layer modulus and thickness is given by Cole and Sayles in normalised form, for v = 0.3 [2]. The actual predictions of the theory for the particular parameters used in the e.xperiment of section 3 are shown in Figure 2 for a range of values for the Young's Modulus of the coating. 2.2.2 Effect of sensitivity of wire radius and layer thickness The effect of changing the wire radius on the sensitivity of the method for a 3 pm is shown in Figure 3. The lower wire radius creates a smaller contact patch whose size is less strongly influenced by the substrate and is therefore more sensitive to variations in the modulus of the coating itself. On the other hand the pressure is increased causing a greater likelihood of yielding and the absolute size of the contact to be measured is reduced.

473

Microscope

Figure 1. Principle of method. The contact between a diamond flat pressed against a coated steel wire is viewed through a microscope and the area of contact is determined.

.dls hal: width.

-

microns

max pressure, G Pa

100

200

300

400

500

600

Layer Modulus, GPa

Figure 2. Predictions of elastic theory [2] of the half'-width and maximum pressure for the contact of a coated cylinder on a flat. Substrate: E =169 GPa, v = 0.30, Counterface: (diamond), E = 1050 GPa, v = 0.2, Layer v = 0.25, 3pm thick,Load = 0.01515 MN/m, radius = 0.1232 mm

-

HalMdth, radius=O.fflmm, microns Max. Pressure, radius=O.fflmm, GPa

-If-

Max. Pressure, radius=O.Pmm, GPa

I 1

31

0 I00

---8t

200

300

400

Layer Modulus, GPa

500

I

Figure 3. As Figure 2 but with higher and lower values of the wire (cylinder) radius

414

40

7

Figure 4. The deformed geometry adjacent to the contact. The uppermost curve is the gap between the surfaces. The first dark fringe will occur at about 10 pm from the contact centre when the gap is equal to half the wavelength of light (about 290 nm). This is over three times the contact half-width and is thus very insensitive to the layer modulus. As for Figure 2, with Elaye,= 400 GPa. Dimensions are in pm.

2.2.3 Gap predictions The gap between the surfaces inmediately adjacent to the contact is shown in Figure 4. The fringe spacing is very weakly dependent upon the layer modulus because the wavelength of light is large compared to the deflections. 3. DEVELOPMENT OF METHOD AND RESULTS FOR TiN COATING 3.1 Loading device and optics The loading device used for the experimental work is shown in figure 5 . The diamond disc was 2 mm in diameter and was bonded to a steel frame. The load wdS applied using deadweights via a lever system. In order to ensure adequate alignment, the load was applied through a flat support resting on a steel ball. The contact was viewed through the diamond using a microscope. In later tests a video camera and a mioocomputer was used to obtain digitised images of the contact. 3.2 Choice of Wire Initially a guitar (music wire) stririg was used for the experiment because this choice appeared to offer a range of suitable rddii, low cost, high yield strength and good surface finish. However, it was found that most examples had longitudhal surface defects, probably arising from the drawing

operation, and polishing was found to be impractical. A commercially available hard drawn high alloy steel wire was therefore used. A tensile test gave a Young’s modulus of 166 GPa and a tensile strength of 1996 MPa. At this stress, the ratio of plastic to elastic strain was about 1/10. The wire was ferromagnetic indicating mainly martensitic microstructure. 3.2.I Determination of modulus As the tensile test gave a lower than expected value of the Young’s modulus, a more accurate measurement was carried out by the torsional pendulum method. A known inertia was suspended on the wire and the frequency of the torsional oscillations was measured. This gave a Young’s modulus of 169 GPa. This value was used for the subsequent calculations. 3.3 Image Analysis A typical view of the contact is shown in figure 6. Initial experiments using uncoated wires showed that the visible contact area exceeded the expectations of Hertzian theory. This has been noted by Gohar [15] and appears to be due to the optical illusion created by the intensity distribution at the edge of the contact area. As stated earlier, the true contact is bounded by the minimum intensity; any rise in intensity indicates that the contact has already been left.

415

Load

Figure 5. Schematic view of loading mechanism.

In addition, the inital gradient of intensity at the contact edge is zero because the surfaces are continuous. On the other hand, the eye tends to select the mean value between the dark and bright areas. leading to an overestimate of contact width. In order to overcome this problem, the image was digitised and processed so that the true minimum area was obtained. A typical result is shown in figure 7. The system settings are adjusted so that any increase in threshold causes the whole contact to disappear, eliminating the twilight zone at the contact periphery.

1,oad per unit length

Using this method, the modulus of the uncoated wire was determined as 177 GPa, in reasonable agreement with the mechanical measurements. 3.4 Results for TIN Coating A specimen of the wire was coated with titanium nitride using a commercial, reactive ion plating process. The coating thickness was measured by taper section and found to be 3.02 pm. Table I shows the results for three applied loads. Poisson’s ratios of 0.25 for the layer and 0.3 for the substrate were assumed throughout.

Layer Young’s Modulus GPa

Predicted p o GPa

Predicted a.

Measured a.

cvn

cvn

0.00535

400 500 600

1.94 2.09 2.2 I

1.75 1.62 IS O

1.70

438

0.01025

300 400 500

2.38 2.56 2.73

2.70 2.50 2.30

2.38

460

200 300 400 500

2.55 2.80 3.01

3.70 3.40 3.10 2.90

2.97

465

AN/m

0.01515

3.18

Interpolated Young’s Modulus GPa

Table 1. Results of Coated Wire Tests. Data as for Figure 2, except as shown.

476

Figure 6. Appearance of the loaded wire through the microscope. The fine grey area at the centre is the contact.

Figure 7. Processed image at the highest load (0.01515 MN/m). The contact width is 5.94M.30 pm (9 pixels).

477

The observed position of the first fringe was 9 pm from the centre of the contact under a load of 30.3 N. in approximate agreement with the predictions for the same elastic constants (Figure 4).

allow the determination of contact pressures to within *5%, for the present arrangement and to within %5% for a small (2D) asperity unaffected by the substrate. This is accurate enough to be useful.

4. DISCUSSION

4.2 Comparison with other methods

The technique described here provides a simple method of investigating the elastic properties of thin coatings which is simple in concept and requires a minmum of special equipment. It may therefore prove of value in a variety of non-specialist applications. 4.1 Precision of measurement

The following contribute to the errors in the measurement described in section 3 : Lack of precision in determination of the contact half width. (M.15 pm) Systematic error in location of the contact boundary. (M.05pm) Uncertainty in the elastic properties of the substrate and the diamond. (*15 GPa) Error in the measurement of coating thickness. (M.15 pm) Errors in local radius of curvature of the wire. (*2 pm)

In addition. the possibility of plastic deformation of the wire must be considered. Although at the highest load the stress was sufficient to satisfy yield, it does not seem likely that any significant plastic strain would occur at this stress level as inital yield would be confined to a small subsurface region - and from the tensile test evidence of section 3.3. For this reason the highest load was considered to be the most accurate measurement, despite the possibility of some plasticity. It is noted that the value of the modulus does not differ from those obtained at lower loads and that there was no evidence of a permanent impression. Using the calibration graphs (Figures 2 and 3) this would suggest a total error of *SO GPa (*17%) in the final measurement. Although this might not seem very accurate, this is comparable to the accuracy claimed by the nanoindentation method for this material [6] and would of course

It is clear that the method offers considerable advantages over the vibration and nanoindentation methods in low cost and that it is perhaps competitive in terms of speed of measurement. Nevertheless, some improvements are possible. Greater precision in the measurement of contact dimension could perhaps be obtained with higher magnification optics. In addition, using a thin metallic surface coating on the diamond might. by introducing a phase change, enhance the contrast at the contact periphery. In the present experiment. the location of the first dark fringe did not contribute significantly to the investigation of the layer properties. However, in principle. the gap could have been measured at any location, perhaps using the 'thin film' technique of Westlake and Cameron [ 181 which has been developed further recently [19]. This could contribute in the future to the more precise mesurement of contact stiffness, particularly for anisotropic or inhomogeneous layers

5. CONCLUSIONS

A simple method for the determination of the effective Young's modulus of a thin. solid coating has been described. The method consists of the optical measurement of the area of contact between a coated steel wire and a diamond flat. The use of line contact enables low contact dimensions to be obtained with moderate, and hence easily controlled, loads. Diamond provides a stiff, transparent counterface which makes the changes in contact size as sensitive as possible to the layer modulus. Measurement of a commercial sample of TiN, deposited on a high-alloy steel wire by reactive ion plating, gave a Young's modulus of 465k.80 GPa. This is comparable to other measurements [6] on this material.

418 ACKNOWLEDGEMENTS The authors are grateful to Tecvac Ltd of Stow cum Quy, Cambridge, England for the TIN coating.

REFERENCES [ 11 J. Halling, The Tribology of Surface Films,

Thin Solid Films, 108,( 1983) p 103.

[2] S J Cole, R S Sayles, A Numerical Model for the Contact of Layered Elastic Bodies with Real Rough Surfaces, Trans Am Soc Mech Engrs, Journal ofTribology, 114 (1991) p334. [3] S.J. Cole and R. S. Sayles, Stresses in and beneath a Surface Coating Due to a Rough Surface Contact, Microstructural Science, 20, (1991). [4] A V Olver, S J Cole and R S Sayles, Contact Stresses in Nitrided Steels, Leeds Lyon Symposium on Tribology, Leeds 1992. Published Elsevier 1993. (51 T Bell, Towards Designer Surfaces, Royal Society Lecture, London, December 1991.

[6] M. O'Hern, R. H. Panish, W. C. Oliver, Evaluation of the Mechanical Properties of TiN by Ultra-low Load Indentation, Thin Solid Films, 181, (1989) p357. [7] E Torok, A J Perry, L Chollet, and W D Sproul, Young's Modulus of TIN, Tic, ZrN and HfN,Thin Solid Films, 153 (1987) p37.

Stresses and hlechanical Properties I I 1 . B ( 1992) p319. [ 111 M F Doerner and W D N i x A Method for

Interpreting the Data from Depth-Sensing Indentation Instruments, J Mat. Research, L(4) ( 1986) p60 I . [ 121 L Chollet and C Biselli, Young's Modulus of TiN and T i c Coatings, Proceedings of 16th Leeds Lyon Symposium on Tribologv, 17 ( 1989) p2 17 [ 131 C T Rosemayer, F R Brotzen. and R J Gale. Mechanical Testing of Thin Films, Mat Res Soc Svmposium Proceedings: Thin Films: Stresses and Mechanical Properties,= ( 1989) p63.

[I41 W. C. Oliver, C. J. McHargue, Characterising the Hardness and Modulus of Thin Films Using a Mechanical Properties Microprobe, Thin Solid Films, 101,(1988) pl17. [ 151 R Gohar, Oil Films under Elastohydrodynamic Conditions, PhD Thesis, University of London, 1965. [ 161 C A F o o d L D Wedeven. F J Westlake, and A Cameron, Optical Elasto-hydrodynamics, Proc. Instn Mech. Engrs, 184 pt 1 ( 1969) p 1. [ 171 P K Gupta and J A Walowit. Contact Stresses between an Elastic Cylinder and a Layered Elastic Solid, Trans Am Soc Mech Engrs, J Lub Tech, (1974) p250. [ 181 F J Westlake, A Cameron, A Study of Ultra-

thin Lubricant Films Using an Optical Technique, , [8] J P Chambard, and M Nivoit, A Method for InSitu Determination of Young's Modulus of Deposits, Proceedings of 16th Leeds L.yon Svmposium on Tribology, (1989) p223.

191 E Vancoille, J P Celis, J R Roos, Mechanical Properties of TIN, Measured by Nano-Indentaion, Proceedings 0119th Leeds Lyon Symposium on Tribology,25 (1993) p3 11. [ 101 S P Baker, T W Bahee and W D Nix, TimeDependent Defomtion in Room-Temperature Indentation Experiments Using a Nano-Indenter, Mat Res Soc Symposium Proceedings: Thin Films:

Proc. Instn Mech. Engrs, 182 pt3G (1967) p75.

1191 G J Johnston, R W Wayte, & H A Spikes, The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts, ASLE Trans, 34, (1991), p 187.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

479

Tribological analysis of friction damage on coated plastics through the third body concept J. Denapeas P. Etienneb, J.-Y. Parisa, J. Phalippoub and R.Sempereb a Laboratoire de &nie de Production, Ecole Nationale dIng4nieurs de Tarbes Av. d h e r e i x , B.P. 1629, 65016 Tarbes Cedex - France Laboratoire de Science des Mat4riaux Vitreux, Universit4 de Montpellier I1 Place Eughne Bataillon, 34095 Montpellier Cedex 5 - France

Transparent plastics are promising materials for optical applications but they are unfortunately not scratch resistant. This damage leads to a loss of optical properties. Coating of these plastics by a hard material seems to be a means to overcome the observed disadvantages. This goal was achieved using both pdysilawrnes and colloidal particks of silica. Tribological experiments have been carried out to better understand the surface modifEations due to a sliding friction. The surface damage exhibits cracking and coating removal by abrasion, depending on the silica content of the film. With this respect, films prepared using a colloidal silica solution exhibit the best tribologic properties. With a low silica content the crack extension is severe. With t m high a silica content the film adhesion is not good enough and the coating may be removed by the friction. Three successive stages of su$ace degradation have been distinguished :(1) damage initiation by cracking, (2)particle detachment and (3) debris circulation (accumulation or elimination), in close agreement with the third body approach. The adhesion and the residual stresses of the coating play a mqjor role during the two first stages. The last stage of degradation is mainly related to the behaviour of the debris which acts as a protective screen or an abmsive body depending on the location of the debris in the contact zone.

1. PRESENTATION Transparent plastics are promising materials for optical applications. They are of low cost and their density is well below that of usual spectacles. Moreover plastic glasses do not break easily. Such qualities offer many industrial applications in the field of ophthalmic glasses. However, they are not scratch resistant enough and very quickly lose their optical properties due to surface damage Ell. Coating of these plastics by a hard material seems to be a means of overcoming these disadvantages. The goal was achieved using thin films (thicknesses between 2 and 7 pm) of both polysiloxanes and colloidal particles of silica E2, 31 deposited by dipping or spinning techniques 141.

In this paper, we investigate the tribologic properties of transparent plastics coated

with both systems (polysiloxane and colloidal silica). A coating is often required to achieve a low coefficient of friction [51, but coatings which reduce friction often increase wear [61. However, the tribologic behaviour of such materials can be successfully interpreted using the "third body approach" 173. Actually, the debris detached from the materials by friction and then moving through the contact zone, plays an important role by forming a dynamic screen. The accumulation of particles between the bodies in contact builds a bed of powder leading to sliding surface separation. This phenomenon involves a mechanism of load carrying capacity such as occurs in hydrodynamic lubrication and thereby reducing the wear. On the other hand, the elimination of debris from the contact zone enhances the interaction between the two solids and wear increases. Moreover, friction forces increase when the amount of particles in the contact

480

zone increases [81.Our work focuses mainly on damage and wear track and little attention will be paid to friction. The wear mechanisms can be analysed by a more localised approach where the response of the friction interfaces is described in terms of sites and modes of velocity accommodation 191. In our exemple, the sites should be the plastic substrate, the coating and the debris (third body) : respectively referred to as S1, 52 and S3. The modes cover the basic concepts of fracture mechanics and material behaviour i.e. elastic mode, fracture mode, shear mode and rolling mode : referred to as M1, M2, M 3 and M4. The combination of one site and one mode gives the velocity accommodation mechanism occuring on the observed spot of the friction track.

2. MATERIALSAND EXPERIMENTAL~THOD 2.1 Materiala The t r a n s p a r e n t plastic used as substrate for this study is a poly-diethyleneglycol-diallyl-bicarbonate.It is well known for i t s suitable optical properties. This substrate i s obtained through a low temperature polymerisation. The Young's modulus of such a substrate is 2.3 GPa and its flexural strength is 45 MPa. The solution which is deposited on the substrate in all cases, contains yglycidoxypropyltrimethoxy-silane, a chemical compound usually named "glymo". To this base compound is added an amount of silica. In this work, two ways of providing this addition have been used: a tetraethoxysilane (TEOS), and an alcoholic solution of colloidal silica. Dipping is performed in such a way that the sample thickness is close to 5 pm. The coatings using "glymo" and TEOS are labelled as the T series and those prepared using "glymo" and colloidal silica as the C series. The mechanical properties of the films depend on the nature of the silica reenforcement as well as the volume percent of the organic compound that undergoes the polymerisation reaction. The Young's modulus as well as the micro hardness of these films (obtained by a 3 point bending

151 or by nano indentation experiment 143)

are higher for coatings prepared with a polysiloxane compound. In addition, these properties increase with the silica content (table 1). The fracture strength remains constant at about 100MPa. As expected, there is not a straightforward relationship between the elastic properties or between the hardness and the scratch resistance. Table 1 Young's modulus and hardness of the tested coatings T and C series), the "glymo" and the substrate [4,51. coating

Silica Young's Hardcontent modulus ness (5%) (GPa)

"glymo" andTEOS (T series)

T 11% T23% T 31% T41%

3.2 4.5 6.1 9

50 100 140 230

"glymo" and C 10% colloidal silica C 30% (Cseries) C50%

3.8 4.6 5.5

20 40 80

"RlyTnO"

1.9

15

substrate

2.3

20

2.2 Experimental method The tribologic experiments are performed on a pin on disk rig associated with a computer recorder. It works with a linear reciprocating motion and use an hemispheric pin (12.5 m m radius of curvature) made of polished 100C6 steel (E 52100 steel in the SAE-AISI standard). The hardness of the pin is about 850 HV and its elastic modulus is 210 GPa. The displacement amplitude of the pin is 6.3 mm, the average speed is 0.05 m/s and the applied force is kept constant of 5N. In static condtion, the corresponding Hertz pressure reaches 35 MPa and the diameter of the contact area is 530 pm. The experiments are performed on a short time scale, the whole distance of abrasion never exceeding 15 m. All the experiments are performed in ambient air. The room air humidity is not controlled (it ranged between 45 and 60%) but the tested materials are not very sensitive to air humidity (they are

48 1

usually considered as hydrophobic). Stress corrosion effects may be ignored. The coeficient of friction is recorded continuously by measuring the friction force as a function of the time. The abrasion degree is evaluated by the volume of removed matter. Optical and SEM observations correlated with tridimensional profilometry measurements a r e used to examine the effects of the abrasion and the wear track. The radius of curvature of the profilometer stylus is 5 pm with a vertical resolution of about 0.1 pm. Cracks are detected on the samples but their real depth cannot be evaluated.

3. EXPERIMENTAL RESULTS 3.1 Friction and wear responses of the

uncoated plastic The friction response is quite sensitive to the sliding rig and the amount of debris trapped between the pin and the sample. The linear reciprocating tribometer gives high coefficients of friction (close to 11, while experiments performed using a rotating tribometer in the same conditions gives coefficients of friction in the range of 0.4. These apparently unexpected results are actually related to the track size which is far smaller with the reciprocating tribometer. Therefore, for the same sliding distance of the pin, the number of runs on the same point of the sample is greater than on the rotating rig. This effect induces very different modes of circulation of the wear particles for the two sliding devices. Debris is more easily recovered and trapped between the touching bodies in t h e l i n e a r reciprocating configuration. In such a case it plays the role of an abrasive material and in this role it induces a n increase of the coefficient of fkiction. The wear track has been observed after an experiment where the alternating cycles have intentionally been limited to five. The wear damage shows a lateral extent of about 800 pm. I t can be divided in two zones (figure la). The core of the track (400 pm ,,,ide) shows a surface which is a result of high particle removal and debris accumulation which sticks strongly to the wear surfaces (figure lb). Both sides of this

Figure 1 :Wear track on the uncoated substrate showing both abrasion and lateral cracking using the reciprocating linear tnbometer. (a) general view, (b) details ofthe central zone of contact and (c) detail of the crack pattern on the track sides.

482

central track exhibit an array of cracks (figure lc). This surface damage interacts with the visible incident light and then induces light diffusion. The goal of a film coating is obviously to hinder this diffusion effect. 3.2 Friction and wear experiments on coated substrate The coefficients of friction of the coated plastics are higher compared to the uncoated plastic (figure 2). This effect is clearly apparent for the low silica content coatings. However the coefficient of friction decreases as the silica content in the film increases.

0.9I 0

20 30 40 50 Silica content (in weigh percent) 10

I 60

Figure 2 :Variations of the coefficient of friction of the coated substrates as a function of the silica content for the T series ("glymo" and TEOS)and for the C series (''glymo" and colloidal silica). The wear of coated substrates is greatly reduced compared to that obtained with uncoated plastic. However, the wear tracks have almost the same lateral extent as those observed for the uncoated substrates but they show substantial differences depending to the type of coating and the silica content.

' Results

with coatings Prepared Using '&lymo"and TEOS (T series) matever the amount Of the of the cracking pattern on both sides of the wear track is less pronounced for the coated samples than for the uncoated plastic (figure 3a). These cracks propagate in both coating

Figure 3 : (a) General view ofthe wear track observed on the T coated substrate (40 weight percent) showing the coating removal, (b) details of the central zone of contact and (c) details of the track sides and the crack pattern affecting the coating and the substrate floor.

483 and substrate. The material removal affects the central area of the track (400pm wide) as previously mentioned (figure 3b). The lateral cracks have a higher density but they do not extent very far from the wear track (figure 3c). The surface damage is created by removal of the coating. On both sides of the track, the coating is broken into large pieces and a sharp step is seen at this location (Figure 4a). The step height is 5 pm which corresponds to the coating thickness. In the vicinity of the track sides, no wear occurs on the substrate after removal of the coating. Only cracks filled by debris are observed. However, in the middle of the track, the wear process affects also the substrate, and the debris now consists of a mixture of an organic compound with an organo-mineral compound which sticks strongly to the wear track. The free debris observed in the contact zone consists of a fine powder which fills up any cracks and accumulates against the

fkedebris trapped against the steps (protective screen by load canying effect)

lateral steps on both sides of the track. The initial size of the debris coming from the coating increases with the increase in silica content (i.e. when the "glymo" quantity decreases). This effect is related to coating adhesion which is expected to depend only upon the "glymo" compound. Furthermore initial removal of large particles of coating are not observed. A schematic picture of the wear effect can be drawn (Figure 4b) by following t h e analysis performed by tridimensional profilometry. Results with coatings prepared using 'klyrno"and colloidal silica (C series) The samples using C coatings show quite a different behaviour compared to the previous coatings. The coating damage seems very homogeneous with a higher wear resistance. In all cases, the contact pressure leads to plastic flow (creep) of both coating a n d substrate. The residual vertical deflexion is 3 pm after running (Figure 5). Cracking occurs whatever the silica content but significant material loss is only observed for the highest silica content.

debris gripped on the

abradedsubsaate (zone of highest p u r e of contact)

I

Y

Figure 5 : Deflexion of both coating and substrate under contact pressure (tridimensional profilometry, surface size : 1500x200 pm2). Wear affects only the lowest zone of the friction track (Ccoated substrate with 50 weight percent silica content). The samples having a low silica content (10 weight percent) clearly show a rather

Figure 4 : (a)Tridimensional view of the wear damage recorded b profilometry (surface size : 500x500 pm ) on the T coated substrate (40 weight percent) and (b) Schematic picture of the wear profile showing the coating damage.

I

high frequency of semicircular cracks and abrasive grooves all over the track (Figure 6a). The concave side of the curvature of the cracks indicates the direction of sliding. A tridimensional profile shows the morphology of the cracks and a very weak deflexion of the substrate below the coating (figure 6b). A good adhesion between the film and the

484

substrate is observed and crack interaction does not lead to large debris. The adhesive property is expected to be mainly linked to the percent of "glymo" compound of the coating. The colloidal particles do not play a role in coating adhesion at the substrate / film interface. When the silica content increases (30 weight percent) the wear track becomes more complex. Two crack patterns can be distinguished. The core of the track shows similar semicircular cracks as observed on samples with lower silica content. However, these cracks are not so visible as the previous ones and do not extend for long distances. On both sides of the core track, lateral cracks associated with small plastic grooves are observed. They are parallel and the space between two successive cracks is very small (figure 7a).

The samples having the highest silica content (50 weight percent) show the first significant removal of material in the central region of the track (Figure 8). The adhesion of the coating decreases and large particles of wear debris may be evident at the outset of the sliding (Figures 9a and 9b). The wear depth reaches 5 pm which as before corresponds to the coating thickness.

4. ANALYSIS OF FRICTION

DAMAGE The different damage patterns described above are representative of the same general wear mechanism taken at different stages of its progress. Three different stages can be discussed in term of debris behaviour in the contact zone [91 : (1) damage initiation without material loss, (2) particle detachment, and (3) debris circulation (accumulation and elimination) through the friction track. Each stage can be analysed through the activation of a specific velocity accommodation mechanism. T h e film substrate adhesion (function of the coating composition) and the residual stresses (due to the coating techniques) play an important role as they favour or delay the transition to the last stage of degradation dominated by the debris behaviour. 4.1 First stage : damage initiation by

cracking This first stage is well observed on the C coatings with a low silica content. No

Figure 6 :Aspect of the wear track observed on the C coated substrate having a low silica content (10 weight percent). (a) General view of the friction track showing the semicircular crack pattern and (b) details of the crack pattern recorded by tridimensional profilometry (surface size : 750x100 pm2).

significant material loss is occuring and only semi-circular cracks are observed. In fact, this stage of crack formation occurs on all the observed samples : it is also observed on both sides of the wear tracks (where the contact pressure is lower) on the T coatings, as well as on the uncoated substrates. The associated velocity accommodation mechanism involves fracture mode of both substrate and coating (mechanisms labelled as S1M2 and S2M2 according to the previous definitions), associated with a n elastic response of the sample. Crack formation occurs when the elastic energy stored in the material is transformed into surface energy which then allows stress

485

release. After the first crack appearance, the elastic energy increases again up to a level corresponding to the formation of a new crack. Hence, the semi-circular cracks involve an elastic response of the sample (Hertzian contact characterized by a large radius of curvature) and are usually found on brittle materials such glasses and ceramics [121. They originate from the stress distribution in the material which is induced by the pin displacement. In front of the contact area a

Figure 7 :Aspect of the wear track observed on the C coated substrate having an intermediate silica content (30weight percent) : (a) details of the lateral cracks associated with a plastic groove and (b) schematic view of the crack pattern along a local scratch inside the contact track.

compressive stress appears which is then balanced by a tension stress behind the pin [131. The cracks occur in the tension zone (mode I) behind the pin and show a semicircular shape whose concave curvature is oriented with the direction of the pin motion. With a reciprocating displacement of the pin, the net result is the interaction of two array of cracks oriented according to the two opposite sliding directions. The cracks a r e theoretically equally spaced. The space between two aGacent cracks is related to the coefficient of friction [141. It is small if the coefficient of friction is high. On the other hand, the length and the depth of the cracks are closely related to the mechanical properties of t h e material (hardness, Young's modulus and fracture toughness) [151. The second crack pattern is observed for coatings having an intermediate silica content. I t is usually encountered on brittle materials after the scratch tests 1163. I t refers t o a surface subjected t o a high local stresses which can involve a limited plastic flow from where cracking then occurs (as occurs with sharp indentors). The plastic deformation of the substrate favours such radial cracks by increasing the flexion of the coating. Such cracks are usually straight and parallel, symmetrical with regard to the central plastic groove and sloping backwards relative to t h e direction of the pin displacement [171. Local abrasion grooves are also observed on the coated samples and may be due to a material transfer adhering to the metallic pin. The cracks actually show relayed mechanisms : the two above patterns can be observed on a single crack. After crossing the groove flanks, the crack can have straight shape, perpendicular to the sample surface and directed backwards from the sliding movement. Then, when the stress field becomes purely elastic, the crack morphology changes and it continues by propagating as a semi-conical crack whose curvature is now open in the direction of sliding (figure 7b). 4.2 Second stage :particle emission

The second stage starts with the removal of large particles of coating as the result of an intensive prior cracking of the surface.

486

stage is clearly shown by the T series This stage is characterized by an increase of the coefficient of friction showing a higher sliding resistance because of great increase of particles between the sliding surfaces. The wear profile of the track has a U shape

Figure 8 :General view of the friction track showing crack patterns and coating removal of the wear track observed on the C coated substrate having the highest silica content (50 weight percent). The first particles are detached from the highest pressure spots being those in the middle of the friction track. T h e beginning of this second stage corresponds t o the C coatings with an intermediate silica content. The following runs widen the wear track until the contact pressure becomes low enough to avoid further damage. A poor adhesion between coating and substrate leads to a rapid destruction of the whole thickness of the coating. This behaviour is observed for the C coating with the highest silica content. The velocity accommodation mechanism involves shear mode of the interface substratehoating which can be labelled as (SYS2)M3. The detached debris is then finely ground inside the contact zone until the surface energy which may be created is balanced by the associated fracture energy [181. The accumulation of such moving and rolling fine particles builds a bed of powder which leads to the separation of the two bodies in contact [191. This protective screen of free debris allows the necessary velocity accommodation between the surfaces in contact due to its load carrying effect [201. 4.3 Third stage :debris circulation

The composition of the debris and its location in the contact zone plays a dominant part in the third stage of damage. this final

10.67 pm 100% 9.915 p 93 % 9.152 pn 86% 8.390 p 79% 7.627 pm 71% 6.864 pn 64% 6.102 pm 57% 5.339 pn 50%

4 . 5 7 6 ~ 43% 3 . 8 1 4 ~ 36% 3.051 pn 29% 2 . 2 8 8 ~ 21% 1.525 p 14% 0.763 p n ~ 7% 0.OOopm

0%

Figure 9 : Details of the coating damage observed on the C coated substrate having the highest silica content (50 weight percent) : (a) remaoval of a large particle detached by crack interactions (tridimensional profilometry, surface size : 600x400 pm2 and (b) level map of the previous profile.

487

where the depth corresponds to the coating thickness. The nature of debris evolves because, under the action of sliding friction, a chemical reaction may occur. Pure silica colloidal particles can react with atmospheric humidity giving rise to hydrated compounds [21]. Furthermore humidity stimulates the fracture of oxide ceramics [221 and contributes to achieving a very fine size of debris. Due to the hemispheric shape of the pin, the ground particles are drained off the borders of the wear track where the pressure is lower. A part is ejected out of the contact zone and no longer participates in the load carrying mechanism. The remaining part cannot escape and piles up against the steep sides and the external floor of the wear track where it acts as a protective screen. In the centre of the track where the pressure is the highest, the particles are not numerous enough to assume their role of screen. On the contrary, they are trapped in the track, they stick to the sliding surfaces and contribute to the wear damage by abrading the opposing material. This stage is characterized by a progressive increase of the wear depth in the centre of the track (aggressive role of the debris) while the external floor of the wear track remains flat and undergoes no further damage (protective role of the debris). The associated velocity accommodation mechanisms involve fracture, shear and rolling modes of the interfacial screen of debris S3(M2+M3+M4)on the lateral sides of the track and shear mode of the substrate S1M3 in the middle of the track. Hence, as expected, the wear behaviour of coated substrates is not straightforward by related to mechanical properties like the Young’s modulus and the hardness of the coating. As an example, coatings prepared from TEOS (T series) which exhibit the highest elastic moduli and hardness are more easily damaged than coatings prepared with colloidal silica filler. Further experiments must be done so as to evaluate the adhesion and the fracture toughness as a function of coating composition.

6. CONCLUSION The tribologic properties of optical polymers are improved by coating them with a modified silica film using a dipping technique. The surface exhibits damage by cracking and coating removal when abraded depending on the silica content of the coating film. With this respect, films prepared using a colloidal silica solution exhibit the best tribologic properties. Eve,n in this case, it appears necessary to optimise the film composition. With a low silica content the crack extension is severe. With too high a silica content the film adhesion to the substrate is not good enough and the coating may be removed by friction. The wear damage of such materials provides a particularly clear application of the third body approach and the velocity accommodation mechanisms. T h r e e successive stages of surface degradation have been distinguished : (1)damage initiation by cracking, (2) particle detachment and (3) debris circulation (accumulation and elimination) related t o specific accommodation mechanisms where relayed mechanisms occur. Furthermore, the adhesion of, and the residual stresses in, the coating play a mqjor role during the two first stages. The last stage of degradation is mainly related to debris behaviour. It acts as a protective screen or an abrasive body depending on the location of the debris in the contact zone.

REFERENCES

r 11

B.J. BRISCOE, D. TABOR, Brit. Polymer. J., 10 (1978) 54. r21 J. HENNIG, Kunststoffe, 71 (1981) 103. [31 K. GREIWE, W. GLAUBITT, S. AMBERG-SCHWAB, K. PIANA, Mat. Res. SOC.Symp. Proc., Vol. 271 (1992) 725. P. ETIENNE, Thesis, Universitb Montpellier I1 (1993). J. HALLING, Thin Solid Films, 108 (1983) 104. E. RABINOWICZ, ASLE Trans., 10 (1967) 1. M. GODET, Wear 136 (1990) 29.

488

[81 J. DENAPE and J. LAMON, J. Mat. Sci., 25 (1990)3592. [91 Y. BERTHIER, M. GODET and M. BRENDLE, Tribology Transactions 32 (l),(1989),490. [lo] Y. BERTHIER Mdcanismes et tribologie thesis n"88 ISAL 0050 (1988)Universiu C. Bernard - INSA Lyon. [113 P. ETIENNE, R. SEMPERE, J. PHALIPPOU, J. of Sol-Gel Sci and Techno 2 (1994)171. [12] D. TABOR, J. Lubri. Techn., 103 (1981)169. [131 B.R. LAWN and R.T. WILSHAW, J.M (at.Sci, 10 (1975)1049. [141 M.V. SWAIN Fracture Mechanims of Ceramics, 3, Ed. R.C. BRADT, D.P.H.

HASSELMAN, F.F. LANGE, Plenum Press (N.Y.) 3,(1978)257. [151 D.B. MARSHALL Progress in Nitrogen Ceramics , 65 , NATO AS1 serie E, Applied Sciences, (1983)635. [l61 J.C. CONWAY J r a n d H.P. KIRCHNER, J.Mat.Sci.,lB (1980)2879. [171 D.H. BURCKLEY and K MYIOSHI, Wear 100 (1984)333. [181 0.0 AJAYIO and K.C. LUDEMA, Wear 140 (1990)191. [191 M. GODET, Wear 100 (1984)437. 1203 Y. BERTHIER, Wear 139 (1990)77. [211 T.E. FISCHER, Ann. Rev. Mater. Sci., 18(1988) 303. 1223 T.A MICHALSKE and B.C. BUNKER, J. Appl. Phys., 56 (1984)2686.

The Third Body Concept / D. Dowson et al. (Editors) (D 1996 Elsevier Science B.V. All rights reserved.

489

Friction and wear behaviour of plasma-sprayed Cr2O3 coatings in dry sliding against AISI D2 steel J.E. Fernandez8, Yinglong Wan&', R. Tuchoa and A. Rinconb

aDept. of MechauGd and Civil Engineering. University of Oviedo, Ctra. de Castiello, sin, 33204 Gijon, Asturias, Spain b ~ ) ~ i y s i c o - ~ ~ i e~nstitute m i c a ~ of R O G ~ S O I CSIC, ~ ~ ~ , h/iadrid, Spain

This study investigates the influence of sliding speed and norind load on the friction and bvear of plasmasprayed Cr2O3 coatings, i n dry sliding against AISI D2 steel. Friction and wear tests were perfonned i n a wide speed range 0.125-8 i d s under different noniial loads using a block-on-ring tribometer. SEM and EDS were eniployed to identify the niechrulical and clienlical changcs on the woni surfaces. A tangential impact wear inotlcl was suggested to explain the steep rising of wear froin the nliilinimn-wear to the ~iiaximuni-wear.The results show that tlie wear of Cr2O3 coatings increases with the rising of load. Secondly, tliere exist a minimum-wear sliding speed (0.5 mls) and a niilyiiiiiun-wear sliding speed (3 m l s ) to a Cr2O3 coating in dry sliding. With the iricrease of speed, tlie wear of Cr2O3 coating declines in the range 0.125 - 0.5 m i s , then rises steeply froin 0.5 niis through 3 mls, followed by a decreasing. The large variation of wear value with respect to speed can be explained by stick-slip at low speeds, tangential impact effect at median speeds and softening effect of Ilasli temperature at high speeds. I n addition, the wear niechnrusnis of a Cr2O3 coating i n dry sliding versus AISI D2 steel are adhesion at low speeds, brittle fracture at median speeds and a nlisture of abrasion and brittle fracture at lugli speeds.

1. LNTRODUCI'ION

Ceramics have received mucli attention in friction aid wear appli~itionsin industry, such as i n ceriunic engines, due to their high hardness, high chemnic;?l st abi I i t y , high anti -oxidation at high temperatures , and heat isolation properties. The high cost i n production and brittle character. however, will restrict the application of bulk ceranics in industry to a certain extent. For this reason, ceramic coatings onto materials wllich are cheap and reliable i n shock, such as steel, are more widely employed. The ceranuc coating serves as an anti-wear layer and the steel substrate acts as a shock-resistant support. Main iniportnnt thermal spray processes for ceramic coatings are plasma-spray and detonation spray, since a coating of 0.3 nun tluck a i d with about 1%S'% porosity ~ i i ibe obtained. Thermally-sprayed ceramic coatings, such as Cr2O3, WC-Co, A1203, 'I'i02, etc. have been investigated tiibologicnlly at

room and high temperatures i n dry and lubricated sliding [ 1-41 Among them, a tlieriiially-sprayed Cr 203 coating gives the highest tvenr-resistance both i n dry and lubricated cases. .4dditivcs could significantly reduce the friction aid wear of plasmasprayed C q O 3 coating iJ-61, A plasma-sprnyetl Cr2O3 coating, could have failure mcclinnisms i n sliding, such as plastic defonnation, adhesion. and brittle fracture [ 11,7,8]. The speed and load ranges employed i n all tribological studics so far are liniited. Previous studies show that sliding speed a i d load have ;I strong influence on the wear behaviours of metals [9-1I ] aid sintered ceramics [12-141. The author's recent work reveals the substantial inlluence of sliding speed and norind load on tlie wear rate of plasma-sprayed A1203 coating [ 151. Therefore. tllis work aims at investigating friction and wear behaviour of the most important ceramic coating i n industry. Cr203 by plasma spraying, i n a wide range

490 of sliding velocity (0.125-8.0 m/s) under different loads, and trying to understand tlie relationship between friction, wear and the test conditions (speed, load. temperature) froin a new point of view.

2. EXPERIMENTAL DETAILS

2.1 Test Equipment Friction and wear tests were conducted on a self made block-on-ring friction aid wear tester as shown in Fig. 1. I t has a confoniid contact geoiiietry of thc specimens with a conformal contact area of 1 cm2. The ring speciinen is driven to rotate against the block specimen by a 4.3 kW DC motor. The speed of the ring can be varied from 0 rpm lo 3000 rpm (corresponding to a linear velocity r<mgeof 0 9.375 i d s at the outer circle of the ring). Tlie block specimen, coated with Cr2O3 by plasma-spraying, is pressed against the rotating ring specimen through a lever loading system. The noniial load on the block could bc up to 150 N in dry sliding. Friction forces could be measured by a strain sensor fixed on an elastic ann. The sensor is stressed by the friction force tluougli a lever system.

EDS systeni

2.2 Test Materials Tlie block specimens of steel AISI 1020 were coated with Cr2O3 by ambient plasma-spray using h4ETCO 9 ME3, 40 k W equipment and the spray parameters suggested by the manufacturer. The prolwrties of the coating are listed i n Table 1. The ring specimens were made of steel ( A N D2) hardened ,and tempered with hardness HRC 60. Table 1 Properties of used plasma-sprayed Cr2O3 coating Coniposition

99%: C q O 3 Balance: other oxides Trade inark of the powder METCO 106FH Powder size @in) 15-45 Melting point (OC) 2435 Tluchiess after polishing(mii) 0.3 fiwdness (Hv0.3) 1500 Porosity (%) 5 Rougluiess after polishing Ra ( p i n ) 0.3 Bond strength (MPa) 59-63 Density (g c111-~) 4.9

6.4 nun

*I P

B -

on Contact Sudace

Figure 1. The contact geometry of the used blockon-ring tribometer.

The wear was measured with a Mettler AE 200 Weigher with a precision of 0. I nig. The voluine loss is then obtained by dividing tlie weight loss by the density of the specimen milIerid. Woni surfaces were examined by a JEOL-6100 SEM and analysed chemically by a Link-ESLl000

2.3 Test Conditions The tests were conducted wit11 the conditions listed in Table 2. Tlie speciiiiens were cleaned with acetone in an ultrasonic bath for 10 minutes before testing. A average value of three tests was taken for each data point. Proper test durations were chosen to make sure that tests run in the steady-wear regime for a fairly long time.

3. TRIBOLOGICAL ANALYSIS RESULTS

TEST AND SEM

3.1 Friction and Wear Results 3.1. I Friction coefficients versus speed The dry friction coefficients of Cr2O3 / steel AISI D2 pair under a nonnal load 61.3 N are plotted versus sliding velocity from 7.8 x I O - ~to 8 nils and illustrnted in Fig. 2

49 1

Table 2 Test conditions Contact Materials Outer diameters of ring specimnen,mnni Apparent contact area,mm2 Normal loads, N Apparent contact pressures&Pa Sliding speeds, ni/s Test durations, m Lubricant Eiiviroiunent temperature,OC Environment hunidity ,?6 Nuniher of tests for each data point

f

dry 15 75

3

maximum and minimum friction coefficients was very large, indicating the existence of stick-slip phenomenon.

a.

I

Block-on-Ring,conformal Block: C q Q coating Ring: AISI D2 steel, HRC60 062 100 61.3-133 0.613 -1.33 0.125 - 8.0 7500

2

3.1.2 Curves of wear-sliding time Figure 3 gives the wear changes with sliding time of Cr2Q I steel AISI D2 in dry sliding at a velocity of 1 mls under a normal load of 88.5 N. The wear volunies of both Cr2O3 coating and steel AISI D2 rose with the increasing of time steadily in the testing period (4x103 cycles. 7500 in).

1 0.5

a

. CrZOWrteel AISI D2 Dry rlldlng 8 - Room Temperature

10 0- 0- 0-

Sliding Velocity (mls)

Figure 2. Dry friction coefficient of the (21203 I steel AISI D2 pair versus sliding speed under a nonnal load 61.3 N

The minimum and maximum friction values for each speed were obtained from a ten-minute friction test. It is noted that both the fluctuation and the average value of friction coefficient decreased withthe increasing of sliding velocity. In the speed rnnge 0.031 mls - 0.375 mls, the variation between

o^ 6 E

, I m/s

88.6

N

-

6-

0

10

20

30

a203

r t d AIYDZ

50

Slldlng Cycler (xl.E3)

Figure 3. Curve of wear-sliding time of the Cr2O3 / AISI D2 steel in dry sliding at a velocity 1 m/s under nornial load 88.5N.

492

3.1.3 Influence of load on wear The dry wear results of Cr203coating against normal load at velocities 1 mls and 3 inls are shown in Fig.4. As expected, the wear of Cr2O3 coating increases steadly with the rising of normal load.

*'

-t CrZ03,

Cr20W1tccl AlSI Dry illdlng Slldlng dlrtancc 7500 m

3 m/s

b2

AISI D2 steel (ring specimen) were much higher in the speed range 0.125 - 1 mls, but lower i n the speed range 2 - 8 mls. The reason that the wear of the Cr2O3 coating was even higher than that of steel at high speeds in dry sliding may be attributed LO the particle size of the used Cr2O3 powder (15-45 pm). A better iuitiwear perfonnaice of Cr2O3 coatings could be expected with powder size 5-25 pin (METCO 13GF). The minimum-wear speed and maximum-wear speed will be discussed i n the section "Disciission 'I.

-

z575zmirsl Dl Dry Wing

sh

--C

3

: Room

-C

0

60

80

100

120

140

1

W a r Of 0203, 133N Wsir of s t d A N 02. 133N

Wur ot 0203.61.3 N W w of s t d *Lu Dz, 61.3 N

rT 6 6

v

Normal Load

(N) I

Figure 4. The dry wear results of Cr2O3 coatings versus nonnal load at velocities I mls and 3 nils 0

3.1.4 Influence of speed on the wear of C q O 3 coating and AISI D2 steel Tlie iilfluence of speed on the dry wear values of the Cr203 I AISI D2 pair under iioniial loads 61.3 N and 133 N are presented in F i g 5 It is seen that there exists a nlirlirnuii wear speed (0.5 mls to both Cr2O3 coating and AISI D2 steel) and a niaxiniiini-wear speed (3 nils to CqO3 coating and I i d s to AISI D2 steel). To Cr2O3 coating (block specimen). wear declined with increasing of speed in the speed range 0.125 - 0.5 nils, and rose drastically with tlie risiiig of speed in the range 0.5 3 nils, a i d then decreased with the increasing of speed in the range 3 to 8 nils. To AISI D2 steel (ring specimen), the wear values were fairly high when speeds were lower thai the minimum-wear speed (0.5 m l s ) . With the increasing of speed from 0.5 m l s , the wear value increased from 0.5 m l s to 1 inls mid reached a maximum at 1 m l s , followed by a decleming from 1 inls to 4 ids, aid then remaining nearly constait. It was also noted that coiiipiied with the wear values of the Cr2O3 coating (block specimen), tlie corresponding wear values of the

1

2

3

4

5

6

7

8

Slidina Velocity (m/r)

Figure 5. The inlluence of speed on the dry wear values of the Cr2O3 (block) l AISI D2 steel (ring) pair under normal loads 6 1.3 N and 133 N

3.2 SEM (Scanning Electron Microscope) and EDS (Energy Dispersive Spectrum) Analysis Results As a refereiice, the surfirce of a pliisma-sprayed Cr2O3 coating after griiidiiig before wear test is demostrated in Fig.6 The surface i n Fig 6 posseses nucropores and iiucro fractures froiii the grinding. The worn surface of a Cr2O3 coating i n dry slidiiig against AISI D2 steel under 133 N normal load at speed of 0.25 inls (wear results see Fig.5) is given in Fig. 7. Figure 7 indicates the existence of a rather thick surface layer. Tlie element percentage of EDS in Fig. 7 (Fe, 77%; Cr, 21% in weight) reveals that there existed severe steel transfer. On the other hand,

493 adhesion damages were also observed. Therefore the wear mechanism in this case was adhesion damage to the CqO3 coating arid material transfer from steel to Cr2O3 coating.

The worn surface of a plasma-sprayed Cr2O3 coating in dry sliding versus AISI D2 steel under 133 N nornial load at sliding velocity of 0.5 mls (wear data shown in Fig.5) is illustrated i n Fig.8. The coverage of the transfer film of steel in Fig8 is relatively less comparated with that in Fig.7. The elements weight percentage (64%Fe, 35%Cr) i n Fig.8 from EDS verified t h s observed results. No severe adhesion damages were observed. This was the surface where a minimum-wear value was achieved. The wear mecharism in this condition was also adhesion

Iigure 6. The surface of ~1 plasma-sprayed C q 0 3 coatiag after grinding bcfore wcar lest

Figure 8. The woni surface of plasma-sprayed Cr2O3 coating in dry sliding versus AISI D2 steel under a 133 N normal load at sliding velocity 0.5 m/s (minimum wear shown in Fig.5).

~

Figure 7. The worn surface of a C q O 3 coating in dry sliding against AISI D2 steel under a 133 N riorinal load at speed 0.25 m/s (wear results see Fig.5).

Figure 9 shows the worn surface of a plasmasprayed Cr2O3 coating in dry sliding against AISI D2 steel under 133 N noriiial load at sliding velocity 3 m/s, under which a maximum-wear appeared (see Fig.5). The whole surface was full of micro brittle fractures. which was quite different froin the worn surfaces at speeds of 0.25 and 0.5 inls as shown in Figs.7 and 8. The EDS element weight in Fig.9 ( 13%Fe, 86%Cr) suggested a considerably declined transfer of steel compared with the cases at speeds

494

0.25, 0.5 and 1 mls. It is noted that the dominated wear mechanism at speed 3 mls (maximum-wear speed) appeared to be brittle fracture.

Fig.10. The worn surface of plasma-sprayed 0 2 0 3 coating in dry sliding against AISI D2 steel under 133 N normal load at sliding speed 5 mls. Figure 9. The worn surface of plasma-sprayed Cr2O3 coating in dry sliding against AISI D2 steel under 133 N normal load at sliding velocity 3 mls, under which a maximum-wear appeared (see Fig.5). The worn surface of a plasma-sprayed Cr2O3 coating in dry sliding against AISI D2 steel under 133 N normal load at a sliding speed 5 mls is shown in Fig10 (wear data given in Fig.5). The EDS element percentage of Fig. 10 is 14%Fe,85TKr. Fairly large brittle fractures and abrasive tracks were clearly observed. The dominating wear niechanisms were brittlc fracture and abrasion (possibly due to the detached C r 2 0 3 debris particles). The element weight percentage on the worn surface of plasma-sprayed Cr2O3 coatings plotted versus sliding speed is given in Fig.11. It is seen that the transfer qimatity of steel was very high at speed 0.25 m l s (77%Fe), and declined considerably with the rising of speed to 13%Fe at speed 3 mls, then remained sinall at speeds higher than3 mls.

e

h

loo,

I

ED9 Analyala Reaulta on Surfacer of Cr203 B l a b Condltlona: Dry rlMlng aplnat ltecl A191 133 N load

-

Fe element Cr element

I

r

l

Figure 11. Elemental weight percentage on the worn surface of plasma-sprayed Cr2O3 coatings in dry sliding versus AISI D2 steel under 133 N load at different sliding speeds.

4. DISCUSSION

There exists a minimum-wear speed (0.5 nils for both Cr2O3 coating and steel) and a niaximun-wear

495

speed (1 mls for steel and 3 m l s for Cr203 coating) i n Fig.5 for both 133 N and 61.3 N normal loads. A minimum-wear velocity 0.5 mls was observed with Yelf-niated sintered ceramics SiAION, A1203 PSZ and SSC (sintered silicon carbide) [12] and with ruckel on nickel [lo]. A minimum-wear velocity 1 mis was reported with brass on steel [9], copper on copper mid gold on gold [lo]. By changing the stiffness in the apparatus, Soda et al. [lo] found that the high wear at speeds lower than the minimumwear speed came from the stick-slip friction process and decreased to the same value as that at the minimum-wear velocity when a much higher stiffness was employed in the apparatus. The large variation of friction coefficient in the speed range 0 03 - 0.5 mls shown in Fig. 12 verified the existence of stick-slip processes. The magnitude of the variation decreased with the rising of speed. Corresponding to the stick-slip process was and irdliesive wear mechanism with material transfer (mainly from steel surface to the Cr2O3 coating). The amount of iron transferred to Cr2O3 surface declined considerably with the increasing of speed HS can be seen in Fig.11 was consistent to the 11uctuation of friction coefficient at low speed. It is iinderstadable that higher lluctuation in friction will lead to hgher wear value. In the speed range 0.5 - 3 mls, the wear of a Cr203 coatings increased sharply with the rising of speed as demonstrated in Fig.5. The failure type of brittle fractures at speed 3 mls as shown in Fig.9 xtivates tlie authors proposing a tangentid impact wear model to explain the wear increasing from 0.5 mis through 3 nils. The suggested tangential impact near model is illustrated i n Fig. 12(a,b,c,d). When tlie two moving surface are loaded, interception in the sliding direction may happen between tlie asperities of tlie two surfaces. as demonstrated in Fig.l2(a). It should be pointed out that tlie sliding of the two surfaces is actually a discontinuous process and the moment before the IWO asperities m,&e contact is shown i n Fig. 12h). After the two asperities make contact, two lunds of results could appear depending on the speed: (1) in cxse of low speed, plastic flow may take place and no brittle fracture happening to the asperity as indicated i n Fig.l2(c), as verified by SEM

photograph in Fig.8at speed 0.5 m/s; (2)when the speed is high, the tangential impact effect will produce a brief extremely high stress inside the asperity and the asperity will be fractured as a wear debris as shown in Fig.l2(d), as supported by the brittle fractures of the worn Cr203 surface at speed 3 nils (see Fig.9).

-

Moving velocity V

w

Moving velocity V

I

-

Low velocity VI

-

High velocity

Vh

Figure 12(a,b,c,d). Tangential impact wear model: (a) idealised asperity contact under load, showing interception in the direction of moving between asperities; (b) one moving asperity and one fixed asperity before contact; (c) after contact with low speed; (d) tangential impact contact with high speed

The impact stress inside the asperity and consequently the fracture rate (wear rate) of the asperity will be proportional to the sliding speed. The gradient of the wear rising with increasing of speed from mini mum - w ear to maxi mum - wear depends on the fracture tougluiess of the material. A lower fracture toughness will result in a higher gradient of wear rising. The reason that beyond speed 3 mls the wear value decreased with tlie rising of speed (see Fig.5) may be attributed to the effect of the flash

496 temperature. A high flash temperature will soften the asperities i n contact and ease the tangential impact effect. Tlie softening effect will be eillianced with tlie rising of flash temperature (namely with the increasing of speed). When a flash temperature is sufficiently high. the hardness declining and eventually plastic deformation will become a coinparable factor to tlie tangential impact effect. As a result, the wear will reduce with the increasing of speed. The plastic flow shown in Fig.10 (speed 5 ids) support tllis argument. When a flash temperature will commence to play an important role i n reducing the wear w i t h increased speed depends on the inel ling-point of the material. Since tlie melting point of steel (about 1500 OC) is lower than that of Cr2O3 coating (2435 OC), a flash temperature at speed 1 m l s might start influencing tlie wear-reducing process of steel instead of at speed 3 m l s as was tlie case for Cr203 coating (see Fig.S).

5. CONCLUSIONS The results presented above ca~ibe siiiiuiinrised as roiiows: 1) The wear of a plasma-sprayed Cr2O3 coating increases w i 111 increasing load. 2) There exist a miilimum-wear sliding speed (0.5 nils) and a maximum-wear sliding speed (3 m l s ) to the wear of a plasma-sprayed Cr2O3 coating in dry sliding against AISI D2 steel. With the increasing of speed, the wear of Cr2O3 coating declines in the range 0.125 - 0.5 mls, then rises steeply from 0.5 i d s through 3 m l s , followed by a decreasing. 3)The severe fluctuations of dry friction coefficient at speeds lower than 0.5 nils for CqO3 /steel pair, which conies from a stick-slip process, causes higher wear to Cr2O3 and steel than the minimum-wear. 4) The proposed tangential impact wear model could explain the steep rising of wear of Cr2O3 coating from 0.5 to 3 nils. The decreasing of Cr2O3 wear beyond 3 iiils may be attributed to softening effect of the llasli temperature. 5) Tlie wear mechallisins of Cr2O3 coatings i n dry sliding versus AISI D2 steel are adhesion at low

speeds (typically 0.25 mls), brittle fracture at median speeds (typically 3 m i s ) and a mixture of abrasion and brittle fracture at high speeds (typically 5-7 mls).

ACKNOWLEDGEMENT We are deeply grateful to the financial support by FICYT in Spain under the auspices of Principado de Asturias: "Tribological behaviours of plasmasprayed ceramic materials, thennoplastics and antifriction inaterials in meclirulical systems."

REFERENCES 1 Wang Y ,, Jin Y. and Wen S. The analysis of the friction mid wear mcchruliaiis of plasma-sprayed coatings at 450 OC. Wear 1988, 128.265-276 2 Wang Y .. Jin Y. and Wen S. Tlie analysis of the chemical structure a i d properties of ceramic surface films i n friction using SEM, AES and Micro-region X-ray Diffraction. Wear 1988, 128,277-2'90 3 W'ang Y.. Jin Y . and Wen S. l'he inspection of sliding surface and subsurface of plasma-sprayed using Scanning Acoustic Microscopy. Wear 1989,134,399-41 1 4 Wang Y. Friction arid wear beliaviours of plasma and detonation-sprayed ceramic and cerniet hard coatings in dry sliding. Wear 1993, 161,69-78 Wei J. 'and Xue Q. Effects of additives o n friction arid wear behaviour of Cr2O3 coatings. Wear 1993.160.6 1-65 Wei J. and h e Q. Effects of surfactants on the tribological properties of a Cr2O3 coating. Wear 1993,162-1&14,229-233 Vijande-Diaz R.. Belzunce J., Feniaidez E. , Rincon A. and PCrez M.C. Wear and microstructure i n fine ceramic coatings.Wear 1991,148J31-233 Hitsunai H., Hokkirigawa K.,'l'sumaki N . Transitions of microscopic wear mechanism for Cr2O3 ceramic coatings during repeated sliding observed i n a scanning electron microscope tribosystem. Wear 1991. 151,279-289

497

9. llirst W. and Laicaster J.K. Proc Roy SOCA 1960,259,228 10. Soda N. ,I(imura Y .aid T a d i a A.Wear of some F.C.C. iiietals during unlubricxted sliding Part I: effects of load, velocity and atmospheric pressure on wear. Wear 1975.33.1-16 11. Saka N.. Eleiche A . M.ruid Sdi N. P. Wear of metals at high speed. Wear 1977.44,l09-125 12. Ilenape J. and .Laxnon J. Sliding friction of ceranlics: mechrulical action of the wear debris. Jotinid of h4aterials Science 1990, 25359236W

13. Waig Y.S. ,Hsu S. M. and h4unro R.G. Ceramic wear maps : Alunlina. Jounial of the Society of Tribologists aid Lubrication Eiigiiieers I99 I , 47.1.63-69 14. Ravikirrui A.and Prrunila B.N. High speed sliding of A1203 pins against an En-% steel disc. Wear 1993, 162-164. 296-3M 15. Feniandez J.E., Rodriguez R., Wang Y ., Vijande R a i d Riiicon A. Sliding wear of a plasmasprayed A1203 coating. Wear 1995, 181-183, 417425

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SESSION Xlll DYNAMIC E.H.L. Chairman :

Professor Thomas H.C. Childs

Paper Xlll (i)

Kinematics of Roughness in E.H.L.

Paper Xlll (ii)

Influence of the Sliding Speed on the Elastohydrodynamically Lubricated Film Thickness Shape of Wavy Contacts

Paper Xlll (iii)

Surface Roughness Modelling for Piston ring Lubrication : Solving the Problems

Paper Xlll (iv)

Numerical Solution for Elastohydrodynamic Analysis of High Pressure Sleeve Seal

Paper Xlll (v)

The Evaluation of the Minimum Film Thickness in Ball-Plane Impact Experiments

This Page Intentionally Left Blank

T h e Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

50 1

Kinematics of Rougliness iu EHL G .E .M or ales-Espejel , J .A .C; r t w i wood * an (-1 .I .I,. M elgar O . “Insl,it,uto ‘I’ecnologico cle Monterrey, I T E S M , Mont,errey, Mexico DUniversity of Chrnhridge, Eng. Department, Chmhridge, 1 l . K .

III this paper, by considering only t h e central zone of t,he EHL cont>act,a n d by following t h e ideas of (;rrrnwood and Morales-Espe.jel 1994 [ti] that t,he viscosity is so high that. it disappears f r o m t h e eqiiations a n d t h e lubricant I)eronies i n effect just an elastic ‘t,hird hody’, a n d that, t h e roughness arriving at. t h e end of t,he inlet. produces a pumping effrct,, delivering a variable supply of oil which m u s t hr accommodated I)y t h e contact,, it? is shown t8tiat the pressure a n d film thickness variations in both; o w and two-sided roughness, can he described analytically simiilating t h e physical process. T h e results show t h e dancing around of t,he pressure ripples and t h e roughness during their passage through t h e contact, j u s t as in t h e experimental and numerical ohservations.

1

INTRODUCTION

Thr importance of t h e physical underst>andingof the role of roughness in lubrication is clear ; it certainly appears t h a t scuffing and pitting a r c directly influenced by it. G r e a t effort hn3 been devoted to this topic in t h e recent years. Steady stat,e analysis (stationary roughness) have been carried out, by several authors to invrst igatr t h e deformation of waviness a n d real roughness when passing through an EIiL cont,act (e.g. Lee and Cheng 1973 [l], C h a n g rt al. 1989 [2], Venner et al. 1991 [3], Greenwood a n d Johnson 1992 [4], (ireenwood a n d Morales-Espqjel 1993 [ 5 ] ,e t c ) a11 of t h e m concluding t h a t t h e roughness cert.ainly did not pass through unchanged. ‘I’he physical understanding of the kinematic hcliaviour of surface features in E H L is j u s t beginning to emerge. lt has recently been observed experimentally ( K a n e t a et al 1992 [i’]) t h a t stirfaces witlh transversely orient>ated humps passiiig through a n EHL contact under rolling/sliding conditions produce variations in t h e film thickness, which m a y travel with velocities differing from those of t h e b u m p s which produce t,heni. Venner 1991 [8] has shown hy numerical simulation t h a t t h e pressure ripples generated in these cases, or with wavy surfaces, travel with t h e VPlocity of t h e rough surface a n d t h a t t h e film thick-

ness disturbances travel wit,h t h e average velocity of the Iiil)ricant,. Lubrecht a n d Veniier 1993 [9] have shown t h e (lancing around of pressures of a t w e s i d e d surface waviness in an EHL contact. using a sophistlicated multigrid model. Greenwood and Morales-Espqjel 1994 [ti], 1993 [lo] argued that, t h e transient. solution is m a d e of two separate parts: tjhe st,eady statmesolution (particular integral) and a complementary funct,ion tlur to the inlet, modulation of film a n d pressures. Their analysis is b a w d on t,he assrimpt,ion t h a t the contact geomet,ry in EHL can be represent,ed by that, of a n infinit,ely long c o n h c t with sinusoidal roughness, a n d a given nominal film thickness a n d mean pressure. T h e y also showed that, for typical EHL pressures viscosity effects are negligible, so t h e Reynolds equation c a n be linearized a n d solved analytically. T h e almost undeformed roughness at t h e inlet produces a pumping of the oil, giving a variable delivery much as in a standard gear-pump, which generates an excitation function of unknown a m p l i t u d e b u t with a frequency determined by t h e velocity of t h e rough surface. In tAhis paper t h e ideas of Greenwood a n d Morales-Espejel are applied to one-sided a n d twosided waviness, t o demonstrate how with a simple analytical model it is possible to show t h e dancing around of pressures a n d film thickness in time.

502 The results are compared with sophisticated numerical solutions and good agreement, is ohtained.

The one-dimensional Reynolds equation for compressihle Newtlonian fluids is:

i'

(Ph3

aX

")

12qaT

- a(Ph) - u8X

at

(1)

Following t h e arguments of Venner [8], for typical EHL contacts the term w 0 and therefore, the solution of equation ( I ) reduces t80 Ir x h(z - a t ) therefore, for one-sided roughness t,he film thickness variations seem to travel with the average velocity of the surfaces u and the pressure variations with the velocity of the rough surface. According to the arguments of Greenwood and Morales-Espejel [6] this is just a particular case of a more general situation, where the transient solution is made of the combination of two pari,s, some times one of bhem is dominat. For the general case of two-sided roughness, following Greenwood and Morales-Espejel one has:

2.1

Particular Integral

With non-dependence on time the Reynolds equation (1) hecoinrs dp

12111

_ -dz -(I112

p'h* - -)

Ph

where p' and h' represent the values of density and film thickness at pressure maximum. For sufficiently high mean pressures, this reduces to ph = p* h"

+

-hh = -PP = 1 - C a ( p - P o )

ANALYSIS

2

+

with C = (71 - P l ) / a , PI = P / ( l Q p o ) and = y/( 1 ypo). Therefore, the Reynolds equation (2) for high mean viscosities is reduced to

y1

(3)

For a n infinitely long contact and sinusoidal undeformed roughness it can be shown that p* and h' may be approximated by the mean values p = p ( p o ) and h = h(p,,). The densiby ratio (Dowson and Higginson equation) can be linearized as

(5)

For a moving two-sided sinusoidal roughness with velocity 141 for the lower surface and velocity u2 for the upper one, the film thickness ratio H = h / h is assumed to be

If = I

2r + Hasin[-(x x - ult)]+

Hbsin[-(x 2r

- u2t)]

x According to (ireenwood and Johnson [4] sinusoidal film thickness variations produce nearly sinusoidal pressure variations, so 2r A P = ~ ( - pp o ) = Pasin[-(2

x

2r Pbsin[-(z

x

-uzf)]

- tilt)]+

(7)

by substituting equations (4) and (7) into the reduced Reynolds equation ( 5 ) it is possible to obtain the pressure amplit8udes

Having found t,he pressures, the corresponding elastic displacements v are found, from elastic theory and the assumption that the contact can be treated as an infinite wavy surface, then

V= vb

-h V

2r = Vasin[-(x

x

- uli)]+

2r sin[ -( x - uzt)]

x

with Va

= APa ,

vb

= APb

(10)

where A = 2X/(rE'ah) The film thirkneRs is the combination of the tindeformed roughness t and the elastic displacements t ~ that , is, measuring both roughness and

503

'Table 1: Complete input, data for t,he examples.

Example One-sided roughness Venner and Luhrecht, [ 1 I] 'Two-sided roughness h b r e c h t and Venner [9]

h

fY

R

f711flJ'

x

pin

(;Pa-'

E' GPa

110

(;Pa

Ins-'

Pa s

m

inin

pn

inm

0.54

0.4

22

117

0.048

1.22

0.0127

0.184

0.12

0.058

2.0

(0.354)

22

220

0.97

0.04

0.014

0.5

0 25

0.125

Po

?I

rlw values of zmoI reprrsent the amplitiide of the sinusoidal rimghurss, for the I'lir value in parentheses ( ) represents an estimate from graphs

displacement, a i ~positive outward from the cent.rr,line of the lubricant film,

2.2

Complementary Function

Equation (1) is not, linear, t)herefore its exact solirtion cannot be found by adding a particdar integral and a complementary function. However, one can extend the linearization used in the particular integral for this cwc. If again the viscosity is high, equation (1) is reduced to

The oil flow r = ( p h , ) / ( p h ) is approximated by

of two-sided roughness the amplitudes are equr

neglecting higher order ternis. This can he writ,t,tw as

r=I

Once the amplitudes H, and Hb are k n o w n , t,he pressures can he calculated from eqirat,ions (8) and (7).

cmc

TE

+

21r + Z, sin[-(r x

TT

-~1t)]+

=

l + Z + ( A + ( ' ) [ A r ~ + ( A P n ~ + A P b ~ )(16) ] For the st,eady stmate solution, 2, = - ( A C')AP, and zb = - ( A t#hrreforeequation ( 16) reduces to

+

TIT

rE

+ r2T = ( A + (J)[APIT+ APzT]

= 1,

+ (I)hfb,

(17)

with PIT and rgT as the components for the surfaces 1 and 2 . Taking

it is easy to calculate the transient pressure ampli t.utles --TflT

-rbT

A P n= ~ - , APwr = A', + C A', + C

504

= 2X1,2/(7rmhEt)based on XI = Xu/irl with and A 2 = XU/uz. ‘rhus, the comp1et.e solution is

4.5

:-

4

3.5

E

4

32.5.

21.5 1 0.5

;

2

3

4 r

5

6

;

I

Figure 2 : Film thickness and pressures as a fiinct8ionof ttime, for S = 0.

2n sin[-(x A\+C Xi raT

4.5

- at)]-

4

0x 3.5

-E

2

3.

2.5 -

21.5

4.5

4

1

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

0.5

T

2.5

Figure 3: Film thickness and pressures as a function of time, for S = -1.

sin[-(r 27r

x

T

Figure I: Film thickness and pressures as a function of time, for S = 1. Note that for one-sided roughness, say 2 , = 0 these equations retain only two sinusoidal t8erins

- uzt)] , sin[-(2n xu2 : X

u

- uzt)]

for both, the coefficient of 1 is 112, and one can expect. periodic variation in 1 but, not4in E . Again as in [6] the amplitudes of r,T and P)T

cannot, he determined without analyzing the inlet. Here arbitrary values were set to reproduce the examples chosen from literature.

505

3

RESULTS

l’wo cases from literature have been chosen for sohitmion(one-sided and t,wo-sided roughness): t,he data are given in Table 1. The arbitrary amplit.iltles chosen for the complement,ary function are r c 3=~ 0.0, rbT = 0.06, for the one-sided roughness example and r , = ~ 0.025, T b T = 0.1, for t.he t,wositlrd roughness one. For conipa.rison, what, may I ) t x described as the ‘gear-pump’ values, f ( p = ( ’ ) z 4 , b rh are 0.55 for each surface. It. will he clear t,hat, however oseful t,he gearpump analogy may he in explaining 7uh.y there should he an ’excitation’, quant,it8at,ivelyit, is of lit,t.levalue. Of course, t,he pressures and viscosity arc’ relatively low at. the end of t,he inlet,, and t h e cont.rihution to t,he flow of the pressure-gradient t,t,rm need not he negligible: it woiild seem t,hat it. largely cancels the shear-flow t,erm, so that, t,lie vxcit,ation is much smaller t,han t,tie gear-pump ;Lnalogy would suggest,. ‘I‘he first set. of data (one-sided roughness) are taktw from a point rontact. example, however, tirre khey are used in a line contact, solut,ion.

3.1

One-sided Roughness

’l%ree rolling-sliding conditions are analyzed 1 3712

= (S = I ) , u1 = 112 = ti (S = 0) and = 3712 (S = - I ) , where S is the slide t,o roll rai.io, S = (u2 - u l ) / V . Figures 1, 2 and 3 show the variation o f film t.hickness and pressures with time, for the three sli(le to roll ratios S = 1, S = 0 and 5’ = -1 at, a fixed point in z / b = 0.1875. In these figures t.hr%dimensionless time and pressures are tlefined as 7’ = ( C l ) / b and P = p / p o , in accord wit,h the rrf’erence. It is clear that, t,he wave1engt.h of / I and 1’ increases as the value of S, is reduced, which is (Jut, to the reduction in t.he rough surface velocity: i t must he emphasised that the wave1engt.h of the roughnr.w is the same in the t,hree cast’s. Venner and Luhrecht [ I l l show very similar resitlts for the cases S = 0 and S = -1, however, i t ] t,lwir plot for S = 1 trtiey report an increase of t,he nwan film thickness h., as the rough surface ent,ers i 1 i t . o the cont.act. It) seems that the vrlocit,y o f khe roiigh surface is so high that, the ‘ext,ra’ pttmped 111

711

lubricant can no longer h e accommodated in the volume released by deforming tht. roughness. Figure 4 shows the variat,ion of pressures ant1 film thickness along 3: for different, times and S = I ( u 1 = $ 1 4 2 ) . It, displays t2he progression of the roughness in a complete cycle. Since t,he velocit,y of t.he upper surface ( ~ 2 is ) larger than the srnoot811surface velocity, t,he d e c t , of t.he excitation funct,ion is important8arid the deformed roughness clearly shows a. coinhination of waves, sirn ilarly t.he pressiires. Figure 5 displays the wavinrss result,s for t,he case of pure rolling, ,Y = 0 (11, = 112) i n different. t.imes of a complet,e cycle. For piire rolling, since XI = A 2 = X the coniplement8aryfunct,ion has t,he same wavelrngt,li as t.he particltlar integral and the deformed roughness keeps its siiiusoidal shape and t.he pressures t,oo. Figure 6 shows the results for S = -1 (u1 = 3u.2) i n a complete cycle. In t,his case the rough surface is irioving with the lower velocit,y, again the complementary function is modifying tlhe wavelength of t,he deformed roughness and pressures. I n t,he figure, the effect of t,he two waves is clear.

3.2

Two-sided Roughness

Here the analyzed rolling-sliding conditions are = 0, 112 = 211 (s = a), U,1 = 762 = 6 (s = 0 ) and 111 = 3112 (S= - I ) . Figures 7, 8 and 9 show the variations of pressures and film thickness along time, for a fixed value of z / b = 0.1875 and t,he t,tiree rolling-sliding cases. For tJhe first, case (S = 2) and this particular point,, the pressures remain lower or equal to t.he overall mean value p o at all times. For S = 0, the pressures are sinitsoidal ant1 since t,he waviness of the two surfaces rcniain i n phase, only the completnrnt,ary function prcwures show up. The last, case (S = - I ) is the only one solved by the reference giving very good agreerrient, wit,h Figure 9. Figure 10 displays pressures and shapes along z / b for a complete cycle i n t8ime when S = 2. Again t,he left, hand side shapes i n the graph represent, the original undeforrned roughness and its ph a.se. 211

506

2

i

I

O'

.0:2

.0:1

1

0

0.1

x Imnl

0.2

0.3

T = 0.0000

T = 0.0426 1

1 1.B 1.6 &

1.4

1.2 1 -0.8

5

I

= 0.6 0.4

O'

-0:2

-0:1

x lml

0:1

0:2

T = 0.1280

?' = 0.0853

21

1.8

1

O'

-of2

-011

0 x IW

0.1

T = 0.1706 Figiirr 4: Pressures and film thickn~ssas a function of

0.2

;P

1 0.3

for different times and S = 1.

013

507

2r--T--l

I

1

1.8

1.a

1.6

1.6

a 1.4

,1.4

1.2

1.2

1

1

-0.8

-5

-0.8

= 0.6

= 0.6

0.4

0.4

5

I

-0.2

-0.1

0 x IW

0.1

0.2

0.3

O

-0.2

T = 0.0000

-0.1

0 x [ml

0.1

0.2

0.3

T = 0.0640

2r--T---

2 1 " 1 " 1 I

1.8t

1.8

1.6 ,1.4

1.2 1

-0.8

-5

0.6

0.4

-0:2

.0:1

o.2L-l---

I

I O'

0 x IW

0.1

0.2

O

0.3

-0.2

-0.1

0

0.1

0.2

x1 m

T = 0.1280

T = 0.1920

2r-l--l

1.8

-0.2

-0.1

0

X Iml

0.2

0.1

T = 0.2560 Figure 5: Pressures and film thickness as a function of

T

0.3

for different times and

S = 0.

3

508

1.6

1.6 ,1.4

.1.4

1.2

1.2

1

1

-0.8

-0.8 E

E. '0.6

2

I

'0.6

0.4 0.4

0.4 0.2

0.2 I

I

O'

-0:2

-0:1

0 x [ml

0.1

0.2

1

1

O'

0.3

-0:2

-0:1 x

0

0.1

0.2

T = 0.1280

T = 0.0000 2

1

1 .8t

I

I

O'

-0:2

.0:1

0

x lml

0.3

0.1

0.2

1

1

O'

0.3

-0:2

.0:1

0

x lmnl

0.1

0.2

T = 0.3840

T = 0.2560

-0:2

-0:l

x lml

0:l

0:2

013

17' = 0.5120 Figure 6: Pressures and film thickness as a funcbion of t for different. times and S = -1.

0.3

509

2.41

2

;

:

.

21.8

?!

i

1.5

1 a

0.5

I

O;

I I

0.5

1

1.5

T

2 T

Figure 7: Film thickness a n d pressures as a fiinction of time, for S = 2 a n d two-sided rough ness.

Figure 9: Film thickness a n d pressures as a firnct,ion of t i m e , for S = - I a n d two-sided roughness. Figure 11 shows t h e results for t h e case of pure rolling S = 0, where the waviness of both surfaces remains in phase along t h e whole cycle. T h e pressures are only due to t h e complementary function and t,he shapes remain almost undeformed. All the waves keep t,tieir origiiial sinusoidal shapes. Figure 12 displays t,he res~rlt~s for t h e case when u1 = 3112 ( 5 ’ = -1)) since the two surfaces are moving with different, velocities, for 7 = 0, it IS easy t o observe t,hat t,he pressure variations, which are only due to the inlet excitation, are t h e addition of t>he contributions of each surface t o the complementary functioii.

2.2 2

8 $1.8

0.5

1

1.5

1

2

T

Figure 8: Film thickness and pressures as a fuiict.ion of time, for S = 0 and t,wo-sided roughness. At. t,he heginning of t h e cycle T = 0.0 only t h r complementary function pressures show up, since I I , = 0 it,s short wavelerigt,h is d u e to t8he velocity 112 a n d t h e shapes a p p e a r almost, undeformed. Along t h e cycle, t h e amplitude of t h e pressures increases a n d then decreases again, t h e waviness is deformed loosing its original sinrrsoidal shape.

4

CONCLUSIONS

Following Greenwood a n d Morales-Espejel [6], the transient micro-EHL solution consists of t,wo parts; a particular integral, which represents t h e st,eady s t a t e solution (with stationary roughness) moving wit,h the surface velocity, a n d a complementary function, produced by t,he inlet p u m p i n g effect from t
510

o'2r-- o'2r---r-0.15.

m

0 i? 0.1 -

Roughas

0.05. 1

0-

-0.0 -0'07.5

.1

0.5

-0.5

1

-5.5

1.5

-1

0.5

0

-0.5

1

5

Xkl

T = 0.0000

r r

= 0.0250

1

o'21--

0.15-

0

s!

-

0.1.

0.1.

1

I

0-

0-

-0.0

-8.5

-1

0.5

-0.5

0.5

1

1

I

7' = 0.0750

T = 0.0500

I

0-

5

T = 0.1000 Figure 10: Pressures and film thickness as a function of

3:

for different times and 5' = 2.

1.5

51 1

o'2-To'zm 0.15-

0.1 5 .

0

0

fi

E

0.1 -

0.1 -

0.05.

hitill R O U Q ~ S S

I

I

0-

0.

T = 0.0500

T = 0.0000

o'2--7--o ' 2 1 l 0.15-

0.15-

5!

4

E

0.1.

0.1 .

I

I

0.

0-

-0'07.5

-1

T = 0.1000

-0.5

0

x*

0.5

1

T = 0.1500

0.15 o2'/ 5!

a 0.1 -

I

0-

T = 0.2000 Figure 11: Pressures a n d film t,hirkness as a funct.ion of

I

for different, times a n d S = 0.

5 12

0.1 5 . 0 r

0

-0.0 -5.5

-1

0

-0.5

0.5

Yh

1

1.5

T = 0.0000

o'2r-- o'2r-t

0.15

O.I5

I

I

L

-"05,5

-

0-

0-

-1

0.5

-0.5

-0'01.5

1

-1

-0.5

0.5

1

l' = 0.3000

T = 0.2000

0.15P 0.1 .

0.05.

MRoupms

I

0-

1.5 Kb

T = 0.4000 Figure 12: Pressures and film thickness as a function of

2

for different, times and S

= -1.

1.5

513 In this way the Reynolds equation is linearized and therefore the two separate solutions (for either the pressures or the film thickness) can he superposed. Both terms, the partlicular integral and t.he complementary function, can be found separat,ely by considering only an infinitely long heavily loaded contact, with known mean film t.hicknew h and mean pressure p,. Of course, since t h r inlet is not been considered, it is not possible 1.0 determine the amplitude of the excitation function and values have been arbitrarily chosen. The scheme is applied in tlwo examples from t,hv literature, with one and t,wo-sided waviness; t.hrrc. rolling-sliding conditions are studied. For t h c a first, example (one-sided rooghness), Figures 4,s and 6, it is clearly shown that, in the presenw of sliding, pressures and deformed shape are niade of a cornbinat,ion of several wavw and the shape h a s not entirely lost, its original wavelength, thv steady state roughness h a s not, disappeared and the amplitude of the complementary function is riot completely dominant, just. as predicted in G . E . Morales-Espejel [lo]. The results agree well witah Venner and Lubrecht [ l l ] . T h e second example (two-sided waviness), Figures 10, 1 I and 12 show well t8hedancing around of pressures and s h apes. When sliding is present, one can observe how the roughness is deformed to avoid coalition with the one on the other surface, and the pressures increase. For the pure rolling case, since the waviness remains in phase, only the complement,ary function in the pressures is seen. The result,^ agree well with Lribrecht, and Venner [9].

References Kwan Lee and H.S. Cheng. Effects of surface asperity on elastohydrodynamic lubrication, NASA report no. CR-2195,1973. L. Chang, C:. Cusano, T . F . Conry. Effects of lubricant rheology and kinemat,ic conditions on micro-elastohydrodynamic lubricattion, ASME J . of Trib. 111, 1989.

C.H. Venner, A.A. Lubrecht, W.E. ten Napel. Numerical simulation of overrolling

of a surface featsure in a n EHL line contract8,

ASME .I. of Trih. 113,1991. [4] .J.A. Greenwood and K.L. Johnson. T h e

behaviour of transverse roughness i n sliding elastohydrodynamic lubricated cont,acts. Wear, 153,page 107, 1992.

[5] J.A. Greenwood and G.E. Morales-Espqjel. The behaviour of real transverse roughness in a sliding EHL contact. Proc. 19th LeedsLyon Symp. on Trib. (1992), Elsevier Science, p p . 227-236, 1993. [6] J.A. Greenwood and G . E . Morales-Espejel. The behaviour of transverse roughness in EHL contacts. Proc. Instn. Mech. Engrs. 208, Part .I, J . of Eng. Trih., pp. 121-132, 1994. [7] M. Kaneta, T. Sakai, and H. Nishikawa. Optical interferometric observations of the effects of a b u m p on point contact EHL, ASME, J . o f T r i b . 114,pp. 779-784, 1992. [8] C.H. Venner. Multilevel solution of the EHL line and point contact problems. Ph.D. t8hesis, University of Twente, Enschede, T h e Netherlands, ISBN 90-9003974-0,1991.

[Y] A.A. Luhrecht. and C.H. Venner. Aspects of twmsided surface waviness in an EHL contact. Proc. 19th Leeds-Lyon Symp. on Trib. (1992), Elsevier Science, pp. 205-214, 1993.

[lo] G.E. Morales Espejel. Elastohydrodynamic lubrication of smooth and rough surfaces. Ph.D. thesis, Engineering Department, IJniversit,y of (:ambridge, 1993. [ll] C.H. Venner and A.A. Lubrecht. Numerical simulation of waviness in a circular EHL contact, under rolling / sliding. Proc 21st. Leeds-Lyon Sym. on Trib. (1994).

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

515

Influence of the Sliding Speed on the Elastohydrodynamically Lubricated Film Thickness Shape of Wavy Contacts F. Couhier ', A . A . Lubrecht ', D. Nblias", L. Flamanda "Laboratoire de MCcanique des Contacts, URA CNRS 856, INSA de Lyon, France A one dimensional analysis of the elastohydrodynamically lubricated contact between a simple wavy surface and a smooth one is presented. The solution of the discretized equations, Reynolds, film thickness and force balance is obtained using a multilevel algorithm. It is shown that the lubrication of wavy or rough surface involves the solution of a time dependent problem. The influence on the lubricating conditions, pressure and film geometry, is studied as a function of the sliding ratio. A local analysis of the evolution of the surface deformations is performed. Attention is focused on the evolution of the film thickness shape for symmetrical kinematic conditions around the pure rolling case. An asymptotic analysis of the lubricating mechanisms for the lightly and heavily loaded zone of the contact hopefully allows a better understanding of the evolution of the film thickness wavelength in the hertzian area. The modification of the film thickness shape is explained using parameters such as the distance between the rollers during the entrance of the waviness in the hertzian area. The analysis of the geometrical configuration of [.he waviness in the inlet of the contact, depending on time and direction of the sliding speed, leads to an improved comprehension of the different film thickness shapes observed.

1. Introduction

would rather like to:

Since 1966, when Dowson and Higginson [6] published the solution of the line contact problem, and 1976, when Hamrock and Dowson [9] published four articles concerning the resolution of the elliptical contact, the solution of the smooth elastohydrodynamically lubricated contact has become well understood. Further studies were carried out by Prakash and Christensen [20], Houpert and Hamrock [ll],Lubrecht et al. [15], ("hittenden et al. [3] and Hamrock et al. [lo]. However, these studies are not suitable for the prediction or the explanation of the time life limitation generally observed. Because real surfaces are rough, and as a result of wear mechanisms (adhesion, abrasion, corrosion plastic deformation, micro-cracking or fretting), break-down in lubricated conjunctures may occur. Of course, in many cases, it is possible to avoid the tribological failures by over-sizing the machine element. This is generaly an expensive solution. A5 a result of economical reasons, the industry

Decrease the material volume: A lighter structure, with its associated smaller inertia, is obtained. Money is saved on both material and energy. Increase the contact severity: As a result of the constant improvement in material quality, bearings can be down-sized, increasing- the contact severity. Decrease the manufacturing costs: The smooth surfaces which are required for a good operation of the lubricated contact require an expensive super-finishing of the contacting surfaces. The objective is then to try d o estimate the effects of contact roughness. Increase the reliabilitv of the machines.

~

In order to fulfill these contradicting goals, it is necessary t o understand how the elastohydrodynamic rough contact behaves. This work tries to supply part of the answer by means of a numerical analysis of the rough E.H.D. contact. In order to account for the effect of roughness, two methods are identified.

516

The first one is based on the work of Christensen [5] published in 1970. In that analysis, a stochastic approach of the roughness is considered. Several authors have worked o n that analysis. Among them Chow and Cheng [4], Patir and Cheng [19], Majumdar et al. [17], Prakash and Czichos I201 and Sadeghi and Sui [21] for the line contact . The recent development of computing power has enabled the possibility of numerically taking into account the effect of roughness using a deterministic method. Because the longitudinal rough contact is stationary, and consumes less time computing, a first review of the published work can be established. It refers to the work of Goglia et al. [7,8], Kweh et al. [12,13], Lubrecht [14], Lubrecht et al. [16] and Venner [22]. The transverse solution of the contact problem was studied next, using the line contact problem, which is of interest here. The investigators were Chang and Webster [2], Chang [l],Osborn and Sadeghi [18], Venner et al. [25], Lubrecht [14], Venner [22], Venner and Lubrecht [24,23].

-

T = u2tfa

TJct " = ("I

+ u2)/2

"1 "2

U = qo'ii f (R'E') W

W = w/(R'E')

a

-t)

t) = Il/t)o

VO

x Q C

-P

P = PIP0 PO

c = ("1 - zL2)/11

2. Nomenclature

W

w2

Half-width of hertzian contact Waviness amplitude of the .42 ondulation of surface 2 E' Elasticity modulus of body 2 G = aE' Dimensionless material parameter (Dowson) h Film thickness H = hR'/a2 Dimensionless film thickness Dimensionless film thickness Hcen at X c e n Dimensionless minimum film Hmtn thickness Dimensionless integration constant Hoo L = ~ ( 2 u ) ~ l ~Dimensionless material parameter (Moes) M = W ( 2 U ) - ' / 2 Dimensionless load parameter (Moes) Pressure P Dimensionless pressure p = PfPHertz Maximum hertzian pressure PHertr Maximum elastohydrodynamic Pmaz pressure Dimensionless pressure spike Ppeak R' Curvature radius of body 2 R Dimensionless roughness t Time T = iitfa Dimensionless time a

Dimensionless time Operating temperature Contact mean velocity Velocity of surface 1 Velocity of surface 2 Dimensionless speed parameter (Dowson) Applied load per length unit Dimensionless load parameter (Dowson) Abscissa Dimensionless abscissa Dimensionless left boundary of fit Dimensionless location of Pmaz Dimensionless location of the inflexion of pressure Dimensionless Location of Hmin Dimensionless location of Ppeak Dimensionless right boundary of % Pressure viscosity Roelands index Pressure viscosity Barus index viscosity Dimensionless lubricant viscosity Reference viscosity Hydrodynamic parameter Dimensionless calculation area Density Dimensionless lubricant density Reference density Sliding ratio wavelength of the generated ondulations Wavelength of the ondulation of the surface 2

3. Modelisation Solving the one dimensional lubrication problem (elastohydrodynamic contact between a rough elastic cylinder and a smooth rigid plane) consists of the numerical determination of the pressure and the film thickness distribution in the contact area, for all time steps. Supposing that, for the lubricant flow: the film thickness is much smaller than the other dimensions of the contact, the lubricant has a Newtonian behavior, the lubricant pow is laminar, the inertia and mass forces are small in comparison with the forces due to viscosity, the density and the viscosity are constant over the film thickness, no sliding occurs at the lubricant/body interface. For the deformation of the bodies the assumptions are that: the contact dimensions are much smaller than the dimension of the bodies, the

517 A2 and w2 are the caracteristics of the modeled waviness. Force balance equation:

VT, / % P ( X , T ) d X = 17 2

(4)

Boundary conditions:

Figure 1. Geometrical configuration

stresses are proportzonal to the strazns, the bodzes art homogeneous and zsot ropzc, the deform at zon due t o the pressure as zero at an certazn dzstance. The pressure and film thickness distribution are linked through the Reynolds equation 1, the film thickness equation 2 and the force balance equation 4. These different equations are presented below, using dimensionless variables. The boundary conditions are also presented:

Revnolds eauation:

Z ( P H 3 a P )

as

7 x

ax

a

=ax (PHI +

a (-P W

z.

with:

x

RJ2770 = 6 (211 + u 2 )-a3 PH

Film thickness eauation:

The roughness is modeled in this work according to a cosine law. The lower surface (rigid plane numbered 1) is supposed to be smooth, the upper one (elastic parabola) is wavy. The expression of the waviness as a function of space and time is given using dimensionless parameters: !I? ( X ,T ) = A2 sin

(z

(X - $T))

VT, P ( X , , T ) = ( X , , T ) = 0 (5) Hoo ( T ) is a constant depending on time only. Its value is chosen so that the force balance equation is verified at each time step. It is a characteristic of the distance between the rigid plane and the center of the upper rough cylinder. For the numerical solution of the problem, the equation has been discretized using a second order accurate finite difference method. The transient aspect of the problem has led to the development of a time dependent solution scheme. As a result, for all time steps T , the pressure distribution P ( X ,T) and the film thickness H ( X ,T ) have to be computed. The method accounts for the transient effects of the wavy surface is the following way: The smooth solution is first computed on a calculaThus, a fast solver has been built tion area in order to solve this problem, it uses multilevel techniques (see Lubrecht [14] and Venner [22]). The discretization used in X and T is of second order accuracy. The smooth EHD problem is stationary and can be used as initial condition for the time-step algorithm. Considering a time increment of one time step, and due to the velocity of the wavy surface, the waviness enters in the calculation area and the transient effects should be accounted for. The multilevel techniques (see Lubrecht et al. [16], Venner [22] and Venner et al. [24]) are very helpful for the resolution of the time-dependent problem. This process is repeated until the final time is reached. It takes of course a running in time until the effects of the entrance of the waviness are completely taken into account. The Reynolds equation (1) is time dependent. However, for smooth surfaces, at each time step, the geometry is the same. This means that the smooth solution problem is stationary.

(3)

518 4. Operating conditions

'The data used for the numerical simulation are preseiikd, first consider the geometrical aspect.

I

(z

Geometrical data

I Parameter I

Value

I Unit II

IJ2

0.339 166

pni

I

I

Table 1 Outline of t,he geometry data used for the numerical simulations

Parameter E'

Value

Unit

226000

MPc Pr s

4.0 lo-' 0.68

IlO 2

M L

I

-

The operating conditions are outlined in table 3 . Operating conditions Parameter Value I Unit

I

Tf,t

100

'rable 3 Operating conditions for Lhe numerical simulation

The different dimensional and non-dimensional parameters which characterize the severity of the contact are outlined in the following table. They concern the elastohydrodynamic parameters, the Moes dimensionless parameters A4 and L and t,hose according to Dowson W , and G.

139 9.520

MPc-'

-

Table 4 Elastohydrodynamic parameters for the numerical solution Around the rolling speed, which is maintained constant, several sliding conditions were chosen. For the Newtonian elastohydrodynamic analysis, only the mean rolling speed is an important parameter. This means that, to obtain the same lubrication condition, an infinite number of speeds for the surfaces 1 and 2 can be considered. Using the sliding ratio C, the surface speed can be written according to: u1

u2

Table 2 Outline of the material and lubricant characteristics

2.237 lo-'

= (1+E/2)E = (l-C/2)E

5. Results 5.1. Smooth surface results 5.1.1. Pressure and film thickness For the Newtonian elastohydrodynamic contact, and for smooth surfaces, no transient effects occur. As a result, some general characteristics can be presented (Table 5). 5.1.2. Precision The verification of the precision of the chosen mesh-size can be established by comparing the value obtained for H,,, for different values of the number of points. Figure 2 presents this comparison for the central and minimum film thickness. The calculation area is a domain between X, = -2.5 and X, = 1.5. The plot shows that N = 513 presents a reasonable cost/quality compromise. The corresponding mesh-size induces an absolute error of 3.2 %

n,

519

p

[-I

1

0.8 0.6 0.4 0.2

0 -1

Xmln hmln Xpeak Pneak

H

-

0.9844 0.1414 0.9609 0.749

-

[PI

0.16

-

0.12 -

o

o

o

o

o

0

-

-+

O.08l0 100

.

'

. . . . . . I

1000

J

10000

N Figure 2. Influence of the number of discretization points on the central and minimum film thickness value

for the minimum film thickness plot and of 3.1 % for the central film thickness plot. For the following calculations, this number of

nodal points will be used. The dimensionless time step has been chosen equal to the dimensionless space step. 5.1.3. Smooth solution

IJsing

1

[-I

0.02 0

_________________-_________________ -1

-0.5

0

0.5

1

x [-I

Figure 3. Dimensionless solution of the smooth elastohydrodynamic lubricated contact

implied in each zone of the EHL contact :

.t

0.14 0.1

1

I

-

0.5

0.06

GPc

Outline of the main parameters referring to the smooth surface EHL lubricated contact

0.18

0

pm

Table 5

0.24 I

-0.5

dimension-

less variables, Figure 3 presents the pressure and

the film thickness distributions for the operation conditions defined before. An interpretation of that solution should lead to an understanding of the different phenomena

The inlet: Due to the convergent, a pressure generation occurs. Because of the piezoviscosity of the lubricant, the viscosity increases enormously. As the pressure is still small, the deformation remains small. The inlet is characterized by hydrodynamic phenomena. The central zone: Because of the continuity of the lubricant flow and because of the very high viscosity, the lubricant crosses the central zone deforming the elastic body, as the lubricant "stiffness" is much bigger than that of the solids. The viscosity is high and the lubricant moves like a solid through the central zone at the mean velocity. No more hydrodynamic effects occur. The outlet: Because of hydrodynamic effects, the pressure decreases very rapidly and cavitation phenomena appear. As a result, a high film thickness gradient occurs, the corresponding pressure peak appears, as well as the outlet constriction which reduces the lubricant flow out.

520

5.2. T h e o r e t i c a l items w i t h regard to tran-

s i e n t effects The previous analysis has shown that two low pressure zones are identified (inlet and outlet.), where hydrodynamic pressure generation and cavitation are the physical phenomena which dominate the problem, and one high pressure one (central area) which only concerns the flow of a very stiff lubricant with the mean contact velocity. Using that result, and considering the high pressure zone only, an asymptotic description of the Reynolds equation can be presented. As no more hydrodynamic effects occur, the Reynolds equation becomes, using dimensional variables :

As a consequence the film thickness shape in the high pressure zone is :

The shape of the 3-function, and precisely its amplitude, depends on the operating conditions, and more precisely on the configuration in the inlet (near X = -1). A parametrical study of that function with regard to sliding is of interest. As T is periodic, and because the evolution of its period is now well known, a Fourier transform analysis may help the understanding of the effect of the sliding (for a constant mean velocity). The first step is to evaluate the influence of the sliding ratio C on the wavelength modulation w / w 2 .

The solution of such an equation is :

h(3:,t)=F z-(

+ "'9

2

(7) 3

From t,liat one can conclude that,:

I

I

1

,

W./ll..

Front the smooth surface analysas results, the churactenstac uelocaty an the central zone as the liibracant one ii (because of the huge value of the rliscosaty). Let us associate the central zone waveltiigth w . The frequency as 7 = w / i i . As a result, the generated wavelength an the liagh pressure zone can be determaned as a function of the wavelength of the wavy surface and of the characterastacs velocataes. 'I'his nicans that.

A s a result,, F is a periodic funrtion, its main wavelcirgtfli is given by :

@I

(b ----...... -

I

1 -

I

(4-

,

,,J' __I'

0 -

__....

...-___...

-2 -1

-3

I

I

I

,

'

I

,

I

Figure 4 . Influence of sliding on the wavelength modulation in the high pressure zone

A plot of this influence is presented in Figure 4 and was generated using a constant rolling speed. By changing one of the surface speeds, for constant mean velocity, the speeds of the second is calculated and the E/2 ratio allows the calculation of w / w ~ . Three parts are identified in this plot: (a) : -

(9)

I

I

:

2 -

What ever the chosen posataori an the contact, the frequency f of the roughness as the same. Because the characterastac uelocaty an the low p r r s s u r ~zone as the wavy stirface one 112, und the assocaated Wavelength as w2, the frequency as f 2 =

I

u1

< 0, u2 > 0

The surfaces 1 and 2 move in different directions,

52 1

--

Because the mean speed is non-zero, the pressure generation is possible, The waviness is generated from the inlet.

(6): -

-

-

~1

-

~2

>0

Both surfaces move in the rolling direction, This is the most common operating condition with regard to sliding, For the particular value of C/2 = 0 (pure rolling), the wavelength generated has W / W Z ,= 1.

(c): u1 -

> 0,

> 0,

u2

<0

5.3. Numerical simulation After a certain time, a periodic solution is obtained. The F-function, which mathematically represents the shape of the film thickness can be considered as function of one variable only. It has actually been noticed that both are linked. Because the X-range (high pressure zone) is relatively small, F is studied as a function of T .

The surfaces 1 and 2 move in different directions, Because the speed of the wavy surface is negative, the wavy surface enters the central zone through the outlet,

- The same range of waviness generation

is obtained as in cases ( a ) et ( b ) , but their wave generation w/w2 is negative. The means that the waviness in the central zone is generated in the other direction as the surface displacement, that is, in the rolling direction one. From this analysis, we deduce that this waviness generation will occur as the roughness comes in the inlet after crossing the central zone. From these observations : 0

to one are difficult to obtain. A great number of oscillations are generated in the central zone, and a great number of mesh points is necessary to represent correctly the film thickness shape (see discretization error). For that reason, only a sliding range of C/2 = -1 to C/2 = 1 has been considered.

For one mean speed of the lubricant, it is possible to find two sliding ratios which generate the same wavelength in the central zone.

C/2 = 1 corresponds to a stationary case, where d H / d T = 0, the rough surface is stationary, the roughness should be completely flattened, or in other words, the generated wavelength is infinite ( W / W Z = fco). From a numerical point of view, results concerning solutions with a low w/w2 value relative

314 112

114 112

514 312

314 112

(d) (e)

Table 6 Definition of the surface velocities used

Five sliding ratios were considered for the numerical simulations. One of them, C/2 = 0 corresponds to the pure rolling case and the four others where chosen so that a symmetrical waviness ratio w/w2 occurs around the pure rolling case (see Figure 4). Table 6 summarizes the surfaces velocities and the generated wavelength for the five sliding ratios considered. The corresponding labels used on the different plots are defined. The associated plots (Figure 5, Figure 6 and Figure 7) respectively present the film thickness considering the space variable (for a given time), considering the time variable (for the geometric central position) and the results of a Fourier analysis of the time dependent film thickness geometry. A second set of results are obtained using the pure sliding stationary contact. Different positions of the waviness (see Table 7) were considered to evaluate the influence of the modification of the inlet geometrical condition on the gener-

522 ated central film thickness. For the stationary rough EHL contact, the waviness in the central zone are completely flattened so that the central film thickness is constant in the hertzian zone (see Figure 8). As a result, a t each phase which is accounted for, the associated central film thickness can be identified.

0.1

,

0'

H

1

I

I

'

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

[-I0.1

x [-I

0.08 0.06

0.04 0.02

0

H Table 7 Outline of the different phase angles used for the stationary simulations

Because the surface has been chosen wavy, two items are characteristic of the film thickness generated in the high pressure area.

I

I

I

I

1

I

0.06

0.04 0.02 n

0.1

0.08 0.06 0.04

0.02 0

H

6. Discussion

x [-I

0.08

The corresponding local pressure distribution is also presented on Figure 8. A particular abscissa is identified on the latter plot. This is the point a t which an inflexion occurs in the pressure distribution. From a physical point of view, that point gives an image of the regime change bet,ween t,he inlet and the central zone. The inlet is characterized by hydrodynamic effects (pressure generation) whereas the central zone is characterized by the lubricant piezoviscosity and body elasticity (pressure transportation).

These particular values are summarized in Table 7 with the corresponding central film thickness. Figure 9 presents the plot obtained when linking the pressure inflexion abscissa and the generated central film thickness.

[-I0.1

[-I0.1

"

I

I

'

-1

-0.5

0

0.5

1

x [-I

Figure 5 . Film thickness for the rough elastohydrodynamic lubricated contact for different value of the sliding ratio

523

0.03 I

0.015 0.01 0.005

i

1

0.03 I

1

0.025 0.015 0.01

0.005 nl

1

0

5

10

5

10

F T ( H ) [-I

- 0.03 I

15

-2

w = 1/T 7-1

1

0.025 0.015

0.002

0.01

0.001

0.005 1

n l

n 0

F T ( H ) [-I 0.03 I

15

w

-20

[-I

= 1/T

1

0.025 0.015 0.01 0.005

1

0

H

0.2

0.4

0.6

0.8

-1 T

[-I

0.03 I

[-I

1

0.025 0.015 0.01 0.001

0.005 0

0.2

0.4

0.6

0.8

-

T \-I

Figure 6 . Film thickness for the rough elastohydrodynamic lubricated contact for different value of the sliding ratio

"

0

5

10

15

2

w = 1/T

7-1

Figure 7. Fourier Transform of the film thickness for the rough elastohydrodynamic lubricated contact for different value of the sliding ratio

524

0.9

,

The first one concerns the wavelength. The main wavelength was already characterized using a theoretical point of view. The second one is the corresponding amplitude for each identified wavelength.

I

0.8

0.7 0.6

0.5 0.4 0.3

0.2 0.1

0 -1.1

H

-1.05

-1

-0.95

-0.9

-0.85

x [-I

[-I 0.07 I

I

0.06 0.05 0.04 0.03 0.02

0.01

I

0’ -1.1

-1.05

-1

-0.95

-0.9

-0.85

x [-I

Figure 8. Solution for the stationary wavy surface contact, for different shifting of the waviness position Hcen

[-I

0.018

,

I

I

0.016 0.014

-

0.012 0.01 -

0.008 -

0.004 -

1

0.006

0.002 01

a

-1.05

-1

-0.95

-0.9

I

-0.85

Xinj

[-I

Figure 9. Generated central film thickness versus the first inflexion abscissa of pressure for stationary wavy surface

6.1. About wavelength w2 was chosen such that six full waves occur in the hertzian zone ( 2 a ) . Figure 5 presents the film thickness shape as a function of the space variable, for different sliding ratios. It shows that, as predicted by Figure 4 , the wavelength remains unchanged in the pure rolling case ( c ) . The shape seems to be close to a sine-function. An increase [or decrease] of the sliding ratio (increase of the rigid plane velocity [or decrease of the rigid plane velocity]) induces a modification of the generated wavelength in the high pressure zone. The number of waves present in the high pressure zone can be directly coupled to the sliding ratio. This analysis fits well with the plot of figure 4 or Table 6. A modification of the rolling/sliding condition also results in a modification of the film thickness shape (from the one obtained in the pure rolling case). This shape is referred to as the T-function. 6.2. About amplitude and shape Figure 6 presents the T-function for the dimensionless time variable. The reference time used has been chosen so that the same number of waves occur in a dimensionless time laps of one. Using this signal in Fourier transform analysis, Figure 7 presents the amplitude of each frequency in the contact. Whatever the rolling/sliding condition is, two frequencies seem to emerge from those plots. The first one corresponds to the generated wavelength ( w ) and the second one t o its double. High values of the sliding seem to lead to a development of the second wavelength. In the analysis, the second wave is associated to the non-linearity of the lubrication problem. An asymptotic model was used to predict the film thickness behavior in the high pressure zone. Considering the complete problem, a transition zone has to be considered between the two asymptotic models. The effect of this zone is t o gener-

525 ate non-linearities in the film thickness generation which are then transported trough the high pressure zone. Consequently, it seems important to underst,and the behavior of the contact in this zone. For that, let us assume that transient effects can be neglected in the inlet and become predominant i n the central zone. The following analysis is presented: The different positions of the waviness in this transient zone modifies the lubrication condition in the inlet. As a result, a global modification of the film thickness is obtained in the inlet before being transported through the central zone.

In order to evaluate this effect, steady state calculations were performed with a shift of the waviness with respect to the contact. The resolution of the problem for different phases leads to the generation of different central film thicknesses. The results corresponding to the different phase are presented on Figure 8 for the pressure and the film thickness. Plotting together central film thickness versus pressure inflexion abscissa for each phase angle, Figure 9 is obtained. The jump observed in this figure is associated with the entrance of a new wave in the transition zone (-1.05, -0.9). This jump involves an important decrease of the generated central film thickness. The new wave which occurs on the left part of the transition zone creates a sudden pressure increase at that point, which limits the lubricant entrance in the central zone. As a result, the generated film thickness is much less important that the one generated when the pressure perturbation occurs on the right side of the transition zone. If now one considers to introduce time effects by "jumping" from one state to the other, one generates film thickness variation close to those of Figure 5 (e). Since transient effects are neglected in this analysis, it should work best for small values of u2 (u2 << 21). Although the shape can thus be explained, the "dynamic" amplitude is twice the "static" one.

It seems most likely that the transient effects causes this difference. 7. Conclusion

Using a time dependent simulator, the film thickness in the high pressure zone has been studied for several values of the rolling/sliding ratio. For the given geometrical configuration and operating conditions, an asymptotic analysis has led to a better understanding of the waviness modification as a function of the sliding ratio in the central zone. The analysis of the shape and amplitude of the film thickness has led to a partial understanding of their evolution. Numerical simulations using more extreme values of the parameters (see Figure 4) than the one used in this work, might lead to clearer phenomena that facilitate a better understanding. 8. Acknowledgment

The authors are very greatfull to Dr J. A. Greenwood and Dr C. H. Venner for the number of interesting discussions which emerged around this research theme. The numerical simulations involved in that work were performed in the frame of the BRITE EURAM Contract Nb BRE2.CT92.0209.

REFERENCES 1. L. Chang. Traction in thermal elastohydrodynamic lubrication of rough surfaces. Transactions of the ASME: Journal of Tribology, 114(1):186191, 1992. 2. L. Chang and M. N. Webster. A study of elastohydrodynamic lubrication of rough surfaces. Transactions of the A S M E : Journal of Tribology,

113(1):llO-115, 1991. 3. R. J. Chittenden, D. Dowson, N. P. Sheldrake, and C. M. Taylor. The use of multi-level adaptive techniques for e.h.1.line contact analysis. In Fluid Film Lubrication Osborne Reynolds Centenary, Proceedings of the 13'h Leeds-Lyon Symposium on Tribology, September 8-12, 1987. 4. L. S. H. Chow and H. S. Cheng. The effect of surface roughness between lubricated rollers.

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Transactions of the ASME: Journal of Lubrication Technology, 98(1):117-124, 1976. 5. H. Christensen. Stochiastic models for hydrodynamic lubrication of rough surfaces. In Institution of Mechnical Engineers, volume 5 5 , pages 10131022, 1970. 6 . D. Dowson and G. R. Higginson. ElastoHydrodynamic Lubrication. S.I., Oxford : Pergamon Press Ltd, 1966. 7. P. R. Goglia, T. F. Conry, and C. Cusano. The effects of surface irregularities on the elastohydrodynamic lubrication on sliding line contacts. Part I - Single irregularities. Transactions of the ASME: Journal of Tribology, 106(1):104-112, 1984. 8. P. R. Goglia, T. F. Conry, and C. Cusano. The effects of surface irregularities on the elastohydrodynamic lubrication on sliding line contacts. Part 11 - Wavy surfaces. Transactions of the ASME: Journal of Tribology, 106(1):113-119, 1984. 9. B. J. Hamrock and D. Dowson. Isothermal elastohydrodynamic lubrication of point contacts, Part I - Theoretical formulation. Transactions of the ASME: Journal of Lubrication Technology, 98(2):223-229, 1976. 10. B. J . Hamrock, R. T. Lee, and L. G. Houpert. Parametric study of performance in elastohydrodynamic lubricated line contacts. In Fluid Film Lubrication Osborne Reynolds Centenary, Proceedings of the l S t h Leeds-Lyon Symposium on Tribology, pages 199-206, September 8-12, 1987. 11. L. G. Houpert and B. J . Hamrock. Fast approach for calculating film thichnesses and pressures in elastohydrodynamically lubricated contacts at high loads. Transactions of the ASME: Journal of Tribology, 108(3):411-420, 1986. 12. C. C. Kweh, R. W. Evans, and R. W. Snidle. Micro-elastohydrodynamic lubrication of an elliptical contact with transverse and tree-dimensional roughness. Transactions of the ASME: Journal of Tribology, 11~ 5 7 7 - 5 8 3 ,1992. 13. C. C. Kweh, M. J. Patching, H. P. Evans, and R. W. Snidle. Simulation of elastohydrodynamic contacts between rough surfaces. Transactions of the ASME: Journal of Tribology, 114(3):412-419, 1992. 14. A. A. Lubrecht. The Numerical Solution of the Elastohydrodynamically Lubricated Line- abd Point Contact Problem Using Multigrid Techniques. PhD thesis, University of ENSCHEDE (N. L.), 1987. 219 p. 15. A. A. Lubrecht, Napel W. E. Ten, and

-

R. Bosma. Multigrid, an alternative method of two-dimensional elastohydrodynamically lubricated point contact calculations. Transactions of the ASME: Journal of Tribology, 109(3):437-443, 1987. 16. A. A. Lubrecht, Napel W. E. Ten, and R. Bosma. The influence of longitudilal and transverse roughnes on the elastohydrodynamic lubrication of circular contacts. Transactions of the ASME: Journal of Tribology, 110(3):421-426, 1988. 17. B. C. Majurndar and B. J. Hamrock. Effect of surface roughness on elastohydrodynamic line contact. Transactions of the ASME: Journal of Lubrication Technology, 104(3):401-409, 1982. Time de18. K. F. Osborn and F. Sadeghi. pendent line ehd lubrication using the multigrid/muItilevel technique. Transactions of the ASME: Journal of Tribology, 114( 1):68-74, 1992. 19. N. Patir and H. S. Cheng. An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication. Transactions of the ASME: Journal of Lubrication Technology, 100(1):12-17, 1978. 20. J. Prakash and H. Czichos. lnfluence of surface roughness and its orientation on partial elastohydrodynamic lubrication of rollers. Transactions of the ASME: Journal of Lubrication Technology, 105(4):591-597, 1983. 21. F. Sadeghi and P. C. Sui. Compressible elastohydrodynamic lubrication of rough surfaces. Transactions of the ASME: Journal of Tribology, 111(1):56-62, 1989. 22. C. H. Venner. Multilevel Solution of the EHL Line and Point Contact Problems. PhD thesis, University of ENSCHEDE (N. L.), 1991. 318 p. 23. C. H. Venner and A. A. Lubrecht. Numerical simulation of a transverse ridge in a circular ehl Transactions of contact under rolling/sliding. the ASME: Journal of Tribology, 116(4):751-761, 1994. 24. C. H. Venner and A. A. Lubrecht. Transient analysis of surface features in an ehl line contact in the case of sliding. Transactions of the ASME: Journal of Tribology, 116(2):186-196, 1994. 25. C. H. Venner, A. A. Lubrecht, and W. E. ten Napel. Numerical simulation of the overrolling of a surface feature in an ehl line and point contact. Transactions of the ASME: Journal of Tribology, 113:777-783, 1991.

The Third Body Concept / D. Dowson et al. (Editors) Q 1996 Elsevier Science B.V. All rights reserved.

527

Surface Roughness Modelling for Piston Ring Lubrication: Solving the Problems M Visscher, D Dowson and C M Taylor Institute of Tribology, Department of Mechanical Engineering, The University of Leeds, Leeds LS2 9JT UK Friction models for piston rings and other machine elements often incorporate the Greenwood and Tripp contact model and the Patir and Cheng average flow model for the mixed lubrication regime. Problems arise, however, from the non-Gaussian roughness height distributions of cylinder liners and from the non-stationarity of the surface roughness parameters used in these models. This paper shows how these problems can be solved. It is concluded that the upper part of the liner’s roughness height profile shows a Gaussian dstribution and this is used to assess the proper roughness height for use in the friction model. The non-stationarity is solved using the plasticity criterion proposed by T R Thomas. This idea has not received much attention in the literature and it still lacks experimental support. In this paper, experimental validation is made available and it is concluded that both the use of the proposed solution for the non-Gaussian liner roughness and application of the Thomas plasticity criterion yield accurate predrction of piston ring friction. 1. INTRODUCTION

Piston rings generally account for 25 to 50 percent of the frictional losses in combustion engines. Therefore, reduction of piston ring friction can contribute significantly towards improving the engine’s he1 economy. On the other hand, emission legislation requires more and more reduction of engine oil consumption, thus demandmg decreasing oil flow through and lubricant film thickness in the rindliner contact. Piston rings therefore operate in the mixed lubrication regime to a significant extent. In the past decades researchers have developed models for lubrication and friction analysis of piston rings and a number of these models account for mixed lubrication. Rohde (1981) proposed a mixed lubrication model combining the Greenwood and Tripp (1971) contact model with the Patir and Cheng (1978, 1979) average flow model. The same approach has been adopted by researchers from the University of Leeds, e.g. Ruddy et al. (1981) and Edwards (1992), and will be used for the calculations in this paper. The Greenwood and Trim (GT) contact model aims at predcting the real area of contact and the asperity contact load for a given separation (or nominal film thickness) between two contacting rough surfaces, while the Patir and Cheng (PC) average flow model aims at predicting the

hydrodynamic bearing capacity, average lubricant flow and average shear stress in the lubricated contact of rough surfaces. In combining these two models, the film thickness where the GT asperity contact force plus the PC hydrodynamic bearing capacity equals the applied contact load is sought. To predict the total friction in the lubricated contact, boundary friction in the real contacts predicted by the GT model is assumed, and added to the hydrodynamic friction obtained from the PC average shear stress. In practice, the application of these models is not straightforward. Considering the GT and other contact models, serious problems arise from the fact that the roughness parameters adopted are nonstationary (Thomas and Sayles, 1978), i.e. their values depend on the long- and the shortwavelength cutsffs applied in the roughness measurement. Hence any desired result can be obtained by manipulating these cutsffs, i.e. the scanning length and the sampling interval or the instrument’s resolving power. These problems have been widely discussed in the literature and several solutions have been proposed, but the problems still exist (Greenwood, 1992). Another problem, although not fundamental yet practical, is the fact that the GT and almost all other contact models as well as the PC average flow model are at present restricted to surfaces with

528 (near) Gaussian peak and roughness height distributions. Application of these models to piston ring analysis is therefore questionable, since the cylinder liner normally shows relatively deep grooves and relatively low but flat summits, yielding significantly skewed nowGaussian height distributions. In this paper, the aforementioned problems are dealt with in a practical way. The idea of ‘hnctional filtering’ proposed by Thomas and Sayles ( 1978) will be used to cope with the non-stationarity of the roughness parameters. Further, a statistical approach will be applied to the liner roughness to derive an ‘equivalent height distribution’ which is (more or less) Gaussian and can be used with confidence instead of the observed skewed distribution. This approach will be validated by comparing computed friction results with measured results reported by Radcliffe (1993). 2. FRICTION MODEL

The mixed lubrication model used in the calculations for this paper is based on both the Greenwood and Tripp contact model and the Patir and Cheng average flow model. In the Greenwood and Tripp (1971) contact model, the surface roughness is described by parabolic asperities. A Gaussian distribution for the peak heights is assumed and the standard deviation cr (i.e. the Root Mean Square value or R,) is used as a measure for the height. The model hrther assumes an equal top radius p for all asperities and finally uses the asperity density q. Given a nominal separation of the contacting surfaces, the model predicts the real area of contact A, and the asperity contact load WA. In this paper, the threepoint analysis is used to find the peaks. This means that 2D measurements are performed and in a measured profile, a point is considered a peak when both adjoining points are lower. The ra&us of such a peak is derived from a parabola drawn through these three points. Patir and Cheng (1978) derived an average Reynolds equation in which flow factors were introduced to account for the roughness influence on the lubricant flow and the nominal film thickness h. In a second paper Patir and Cheng (1979) also introduced shear stress factors to account for the roughness influence on the viscous shear. These flow and

shear stress factors have been evaluated numerically for surfaces with a Gaussian height distribution. They depend on two parameters: the lambda ratio: A = h / q and a texture parameter 3: which is an indication of possible orientation in the roughness texture. The average flow model does not account for asperity deformation. In the case of contact the local film thickness is simply set to zero, i.e. the contacting asperities are truncated. In calculating the shear stress factors the friction in these contacts is neglected, as only viscous shear is considered. In the mixed lubrication model proposed by Rohde (1981), an initial film thickness is assumed. From this film thickness, the lambda-ratio is derived and the GT asperity contact load WA and the PC average hydrodynamic bearing capacity are evaluated. Together, these must equal the applied contact load and the film thckness is readjusted until equilibrium is reached. Then the friction force can be calculated. The asperity contacts, derived from the GT contact model, yield the boundary friction F b :

while the hydrodynamic friction F h is calculated by integration of the PC average viscous shear stress 7h over the apparent contact area. In accordance to the PC average flow model, q, is zero in the real asperity contacts. Furthermore, Rohde applied the following maximum to the viscous shear stress:

(70

=

shear strength and

a b

is the coefficient of

boundary friction, pay= average pressure.) 3. PROBLEMS WITH SURFACE ROUGHNESS

In applying the GT model and the PC average flow model, a number of problems are encountered. The following factors will be &scussed: the nonGaussian height distribution of the liner roughness, the influence of the long-wavelength cutsff, i.e. the scan length, and the influence of the shortwavelength cutsff, i e . the sampling interval or the instrument’s resolving power. Proposals will be

529 made to solve the problems practically and applied to the roughness measurements on a cylinder liner of the same make as the one used by Radcliffe (1993) and Radcliffe and Dowson (1995) for friction measurements on piston rings. In section 4, computed friction results are compared with the measured results by Radcliffe to validate the approach of this section. The roughness parameters presented below are all derived from 2D measurements in the axial dlrection of the liner at varying positions around the circumference. A Form Talysurf was used with 2 vm tip radlus of the stylus. The measured data has not been filtered, but the mean line was found by parabolic curve fitting. The differences between results from axial and circumferential measurements appear to be small, as will be dlscussed in section 4.4.

f

5 0.6 o'8

3.1. Non-Gaussian height distribution Fig. l a shows a typical roughness height dlstribution for the cylinder liner, as well as a Gaussian distribution with the same standard deviation. Clearly, the liner roughness height dlstribution is far from Gaussian, owing to the relatively deep valleys in the honed surface, which is also indicated by the values of the skewness (-3.58) and the kurtosis (23. l), which are by definition 0 and 3 respectively for a Gaussian drstribution. Therefore, in principle it is necessary to account for non-Gaussian height distributions in our models. McCool (1992) introduced a contact model based on a Weibull rather than a Gaussian height distribution and studied the influence of the skewness. This model, however, is still too simple for our liner, as the skewness and kurtosis of a Weibull distribution are limited to about -1.14 and 5.4

E

0.6

,g 0.4 E

0.2

'8 cn 0.0

I -20

-15

-10 -5 Roughness Height brn]

0

5

a. Whole profile ('total height' case)

--

0.0

0.5 1.0 1.5 Roughness Height [rm]

2.0

2.5

b. Excluding deeper valleys ('reduced height' case, omitting lower 2 1 percent of points)

1.0 r

1

-0.2 -0.5

f

0.8 0.6

g

0.4

3

0.2

0

0.0 -0.2

.-

:

8

:B K S-distance

-

-20

"

-I5

-10

'

I

,

"

'

-5

Roughness height [pm]

c. Cumulative Distribution of a

Cylinder liner

I

0

'

I

"

'

5

-0.2 " " " " " " " " " " " " " " " ' -0.5 0.0 0.5 1.0

1.5

Roughness Height [run]

d. Cumulative Distribution of b

Gaussian, with equal standard deviation as liner

Figure 1. Roughness Height Distribution

2.0

2.5

530 respectively. In fact it does not seem easy to find a mathematical model to fit the liner’s height dlstribution with such extreme values for the skewness and the kurtosis. Instead a different approach will be applied, enabling the use of present models based on Gaussian distributions. It appears that the part of the curve for the higher points in Fig. la, with a roughness height larger than about -0.4 pm, can be described by a Gaussian distribution as shown in Fig. lb. Thus the valleys are truncated and the roughness analysis includes the higher points only. The skewness and kurtosis of this truncated distribution are 0.103 and 2.85 respectively, being close to the values for a Gaussian distribution, while the standard deviation is reduced from 1.49 pm to 0.41 pm. T h s reduced value can be used in the contact and friction analysis, as the deeper valleys have no significant influence. To decide at what level to truncate the valleys of the profile, the Kolmogorov-Smirnov test (e.g. Daniel, 1978) has been applied. In this test, two dlstributions are compared by means of their respective cumulative probability curves as shown in Fig. lc for the observed and the Gaussian curve of Fig. la. The maximum vertical distance between the two curves, here called the ‘KS-dlstance’, is a measure from which it can be judged whether the distributions can be regarded the same. In our case, however, we use it to find the level of truncation for which the KS-distance is the smallest, i.e. for which the observed curve is closest to a Gaussian. The smallest KS-distance is found for the case of Fig. lb, and the cumulative probability curve is shown in Fig. Id. The KS-distance appears to be reduced from 0.22 to 0.018, compared with the case of Fig. lc. 3.2. Influence of the scan length

Fig. 2 shows the influence of the scan length on the standard deviation of the roughness height and of the peak height distributions. Two cases are shown. In one case, all data points are taken into account (‘total height’) while in the other case the deeper valleys are omitted to obtain a Gaussian dlstribution as explained in section 3.1 above (‘reduced height’). In the ‘total height’ case, the standard deviation increases with scan length, as is commonly observed, due to more wavelengths becoming involved, each contributing to the standard deviation. At scan

lengths larger than say 3 mm, the scan length influence clearly diminishes and becomes negligible. Further, the curves for the roughness height and for the peak height are quite separate, due to the small number of local peaks present within the deeper valleys. The ‘reduced height’ curves show a dlfferent behaviour. First of all, the curves for the roughness and the peak height almost coincide since the deeper valleys are omitted. More striking is the fact that for scan lengths between 0.5 mm and 3.0 mm the standard deviation increases rather then decreases with decreasing scan length. This is due to influence of single deep valleys, which cause the fitted mean line at small scanning lengths to become significantly skewed. As a result, the ‘main body’ of the distribution curve, which is regarded as the Gaussian part, becomes relatively wide compared with the overall distribution curve and the standard deviation for the ‘reduced height’ case is significantly increased. It is necessary to consider the standard deviation to use in the analysis. Thomas and Sayles (1978) suggested ‘functional filtering’, i.e. to set the longand the short-wavelength cut-offs to include the wavelengths important for the problem investigated. For the long-wavelength cut-off, this would mean taking the scan length equal to the dimension of the contact. There are two dimensions: the axial contact

2.0 c I

0’5 0.0

L A -

0

L

2

U

P

I

-

L

4

.

L

~

L U A U

_

6

8

10

Scan Length [mm]

Roughness height:

‘total height’ case ‘reduced height’ case - - - - - - - - ‘total height’ case ‘reduced height’ case ~-

Peak height:

Influence of Scan Length on the Standard Deviation r s of the Roughness and Peak Height Distributions.

Figure 2. I

53 1 width, which is roughly the piston ring width, and the circumferential contact length. i.e. the liner circumference. The former is between say 0.5 mm for oil-control rings and 2 nim for compression rings, while the other is for example 280 mm. As it appears that the standard deviation is more or less constant for scan lengths larger than 3 mm, it seems reasonable to derive the standard deviation from measurements with a scan length larger than 3 mm. As the roughness and the peak height Qstributions hardly differ for the 'reduced height' case, the standard deviation of the roughness height distribution will be assumed to be equal to the standard deviation of the peak height distribution in the rest of this paper. 3.3. Influence of the sampling interval Fig. 3 shows the influence of the sampling intervals on the roughness parameters used in the mixed lubrication model. These graphs are all for the 'reduced height' case and 10 mm scan length. The results for the dlfferent sampling intervals were derived from the same scans at a basic sampling interval of 0.5 pm by omitting intermdate data points as appropriate. For example, every 4 in 5 points were omitted in the evaluation for a 2.5 pm sampling interval, which thus only included the first. sixth, eleventh, ... data points. This ensures that differences in results are due only to differences in sampling interval rather than hfferences between scans at almost, but not exactly the same position. The standard deviation q,of the peak height Qstribution appears to be quite scattered between the different circumferential positions (Fig. 3a). The sampling interval also contributes to the scattered appearance of the graph, due to some relatively high peaks present in the unworn profile. which may or may not be seen at a particular sampling interval. Nevertheless, the overall appearance is that the sampling interval hardly influences the standard deviation of the height dlstribution. This is confirmed by the curve fit:

0.6

I

tp 0.2

1

0.1

1

0 ' 0. I

'

""'-

'

"""'

-Yl "

I

10 Sampling Interval [pm]

loo

a. Standard deviation a, of the peak height distribution

i 0.1

1

10

100

Sampling Interval (ccm]

b. Mean peak radius

0.1

1

10

100

Sampling Interval [rm]

c. Peak density

0

observed curve fit

Figure 3 Influence of Sampling Interval interval (Fig. 3b, c). The following curve fits are derived:

in which the sampling interval 6and Dare in pm. The mean peak radius p and the peak density q are known to be strongly dependent on the sampling

532 in which p i s in pm and 17 in pn2. Now the mean peak radlus and the peak density do not appear independently in the GT contact model, but in the form of (alp,and (rlpo>. The following curve fits for these combined parameters were derived directly from the roughness scans:

These curve fits are slightly Werent those derived from the fits (31, (4) and ( 5 ) . owing to stochastic interdependence of the parameters. If for example the mean peak radius is relatively small for one scan and at a particular sampling interval, then the correspondmg peak density tends to be relatively large. Note that (tlpo> is often assumed to be independent of the sampling interval, which does not hold in this case. The sampling interval especially causes big problems in the application of contact models. Considering the peak radius and peak density, in principle any value can be obtained. This problem is well addressed in the literature and a review has been given by Greenwood (1992). At present, fractal models are proposed for describing the roughness profile, as they account for the non-stationarity of the texture: The parameters of fractal models are in principle scale (i.e. sampling interval) independent. In practice, however, the fractal parameters are still instrument and scale dependent (Hendriks, 1993; Ganti and Bhushan, 1995; Bhushan, 1995). A more straightforward approach is the use of a ‘plasticity criterion’ as proposed by Thomas (1982). He considered that small scale asperities would deform plastically during the first stages of runningin and therefore diminish. The sampling interval in the evaluation of the model parameters must then be chosen to include those asperities that are just not deformed plastically. This can be achieved using the so-called plasticity index proposed w by Greenwood and Williamson (1966), which reads:

in which E’ is the composite modulus of elasticity and H,, the micro-hardness. When w is larger than unity, the deformation is regarded to be entirely

plastic, while the deformation is entirely elastic for smaller than 0.6. The plasticity criterion of Thomas then says that the sampling interval must be chosen so as to yield a plasticity index of 0.6. For piston rings and cylinder liner, the composite modulus of elasticity is about 115 GPa. The hardness of the liner used by Radcliffe (1993, 1995) was about 2 GPa and assuming the micro-hardness to be three times the bulk hardness (see e.g. Tabor, 1951, Gane, 1970), the plasticity index w is 0.6 for a (d/?)-value of 10”. According to equation (6), the proper sampling interval is then about 10 pm and equation (7) yields an (17Paj-value of about 0.07. 4. EXPERIMENTAL VALIDATION

Measured friction results for a three-piece oilcontrol ring, reported by Radcliffe (1993), have been used for the experimental validation. Predctions for the oilcontrol ring friction were obtained using the piston-ring lubrication code 2853pg9, version 3.2, developed and owned by the Industrial Unit of Tribology in the University of Leeds. The experimental and numerical procedures will be outlined before presenting the comparison of predicted and observed results. 4.1. Experimental procedures Details of the motored test rig have been Qscussed by Radcliffe (1993). The liner, piston and piston rings were from a Jaguar V12 5.3 1. engine. The bore was 90 mm, the stroke 71 mm and the connecting rod length 131 mm. The piston rings were of the three-piece type, consisting of two narrow rails which were radially and axially loaded by a spring. Both rails were 0.66 mm in height and had a fitted tension of 1.037N/mmz in total. The ring profiles were measured before and after the tests and parabolic curve fits were derived. The top ring profile had a radius of 11.O mm and an offset (with respect to the rail’s mid-height) of 0.1 mm towards the crank case. The lower profile extended between 0.17 m m below the rail mid-height (crank case side) and 0.13 mm above mid-height. The bottom rail profile had a radius of 3.5 mm, an offset of 0.03 mm towards the cylinder head and extended from 0.17 mm below to 0.18 mm above the rail’s midheight. The standard deviation of the profiles’

533 surface roughness height was less than 0.05pm after running in. A floating liner assembly was used for the friction measurements. The liner was heated by water circulating through a heater and subsequently through a water jacket surrounding the liner. The lubricant was provided from a heated tank at the same temperature. The liner temperature was monitored using several thermocouples mounted about 1 mm below the liner surface. Four temperatures were used in the measurements: 25, 50, 75 and 100 “C. The lubricant was a Mobil Delvac Special 10W/30 with a dynamic viscosity of 0.124, 0.038, 0.016 and 0.0079Pa.s at the respective temperatures. The speed was varied between 300 and 3000rpm in steps of 300 rpm. The results used in this paper were derived from measurements on the piston and the oil-control ring only, i.e. omitting both compression rings. Measurements on the piston only, omitting all rings, were used to estimate the friction of the oil-control rings only.

4.2. Numerical procedures The numerical procedures were similar to those reported by Rohde (1981). The ring profiles were assumed to be rigd and parabolic, i.e. barrel shaped, with a possibility of an off-set. Ring twist was neglected and therefore the axial spring tension was not taken into account. Th~senabled the use of common procedures for compression ring analysis to be used for the three-piece oil-control ring rails, provided that the radial spring tension was included in the total ring tension. The mixed lubrication model, outlined in section 2, was implemented in the code. Bore distortion was neglected, as well as ring inertia and radial friction between the rails and groove and between the rails and spring. Further assumptions were, that there were no gas pressures acting on the rails, and that both rails were fully flooded on both the u p and the downstroke. The lubricant temperature was assumed to be equal to the liner temperature and piezoviscous effects were neglected, yielding constant viscosity over the stroke as the liner temperature was homogeneous during the experiments. A full transient result was obtained by seeking radial equilibrium and convergence of both the squeeze velocity and the film thickness at every crank angle, as well as con-

vergence of the film thickness over an engne cycle. After convergence had been achieved, the friction was evaluated as outlined in section 2. 4.3. Friction results Fig. 4 shows both the measured oil-control ring friction results reported by Radcliffe (1993) and the predicted results. Along the horizontal axis, viscosity and crank speed are combined in one parameter to incorporate the results at Merent liner temperatures in one graph. Although the curve looks like a Stribeck curve, it must be born in mind that it is derived for transient conditions. The friction shown is averaged over the engne’s cycle. The reported friction is for both rails together. The predxted results are obtained for the fitted rail profiles as mentioned in section 4.1 under the assumptions gven in section 4.2. In addition, the roughness of the rail profiles was neglected, as its contribution to the composite roughness was negligible. Further assumptions were a coefficient of boundary friction ui, of 0.12 and a shear strength g of 2 MPa. Four cases were analysed to test the validity of the approach to derive the roughness parameters presented in section 3. The solid line was obtained for the values derived in section 3 (0=0.41 p i ; O/p = and qPa= 0.07). The p r d c t e d mean friction compares well with the observed values. To investigate the significance of the roughness parameters,

z

loo

[

1

\

10

100

1000

Dynamic Viscosity x Crank Speed [Pa.s.rpm]

measured predicted: up=0.41p;qFq,=0.07; udj= - - - - - - - - up= 0.85 p;llpap= 0.07; udP= 10” - ..- . . - ..- .. up= 0.41 pn; rlpap= 0.05; udp= 10’’ - .- . - .-. - . . up= 0.41 pm; rlpap= 0.07; udp= 0

Figure 4 Comparison of measured and predicted oil-control ring friction. (ui, = 0.12; r0 = 2 Mpa)

534 three fiirtlier sets of predictions have been produced. In each set one of the three roughness values Qffered from the proposed values while the other two values remained the same. None of these series compare as well with the measured results as those for the proposed values (solid line in Fig. 4). Fig. S shows a comparison of predicted and measured friction over an engine stroke. The latter has been filtered to enable interpolation to be adopted in the subtraction of piston-only friction from the measured friction on a complete piston and oil-control ring assembly. Further, the data filtering eliminated to some estent the noise from engine vibration.

-60 Crank Angle [degrees]

~~

~

~

strength t-0 were assumed. The shear strength was taken to be 2 MPa as often reported in the literature. AccorQng to Briscoe and Tabor (1978), its value is normally in the range between 1 and 10 MPa for boundary films. Within this range, variations in the shear strength hardly affect the mean friction which is 46.20 N at 1 MPa and 48.39 N at 10 MPa shear strength (for IT = 0.41 km; d&l= llpa = 0.07; ffb = 0.12). Similar results were reported by Rohdc (1981). Therefore the assumption made for the lubricant’s shear strength docs not yield unreliable results. The assumed value of the coefficient of boundary friction was based on the results, so that the solid line in Fig. 4 compared best with the measured friction at the lower values of the viscosity-speed parameter. Radcliffe (1993) found the same value in a similar way, but using a different, simpler mixed friction model. As the roughness testure of the honed cylinder liner is in principle anisotropic, the GT-parameters might be different between different dlrections of measurement. Therefore a replica has been made from the liner surface to allow for measurements in all directions. The folowing curve fits for the GTparameters were derived in circumferential dlrection:

measured friction predicted friction

Figure 5 Comparison of measured (Radcliffe. 1993) and predicted oil-control ring friction. (engine speed = IS00 rpm; dynamic viscosity = 0.0079 Pas: ffb = 0.12; q, = 2 Mpa: q,= 0.41 p i ; qpr+ = 0.07; ody= 1 d )

4.4. Discussion Firstly. attention will be paid to the assumptions niade for the shear strength and the coefficient of boundary friction. Secondly the Qfferences bctween roughness parameters derived from axial and circumferential 2D measurements will be discussed. Thirdly we will focus on the significance of accurate assessnient of the roughness parameters (as outlined in section 3) and finally. some remarks will be made on the remaining Qfferences between predcted and observed friction values. As stated in section 4.3, the values for the coefficient of boundary friction crt, and for the shear

Using the Thomas plasticity criterion. the proper qpo-value is again about 0.07. Measuring in a &rection of 45 degrees with respect to the axial dlrection yielded the following curve fits:

and the proper value for (i&j is about 0.08. which is slightly higher. In general, the GT-parameters appear to be fairly constant. regardless of the scanning direction. The approach presented in section 3 appears to be quite significant, as the mean friction results are influenced by variation of the three roughness parameters a (alp, and ([email protected] is very clear for the standard deviation a, but also for the other two. For

535

example. (@) is often reported to be in the range between 0.03 and 0.05, although proof is laclang in the literature. Using a value of 0.05 instead of the derived 0.07, would yield an underestimate in the boundary friction of 20 percent, while the value of 0.07 would yield a very accurate prediction. Similar for (alp, which is generally reckoned to be somewhere between and lo-'. Using a value of underestimates the predicted boundary friction by about 40 percent, while the derived value of again yields a good prediction. Apart from the values reported or assumed in the literature, a large range of values can be derived from surface roughness scans, depending on the sampling interval, as shown in Fig. 3. It is thus very important to derive the roughness parameters logically and carefully. Considering the results shown in Fig. 4, it appears that the predcted friction is somewhat smaller than the measured friction in the midregion of the parameter viscosityxspeed (between 10 and 100 Pa.s.rpm). A probable cause is the way in which the oil-control ring friction is determined experimentally (see section 4.1). It is very likely that the friction of the piston alone is smaller than the piston friction when the oilcontrol ring is mounted, as the oil-control ring prevents lubricant flow to the upper part of the piston and the piston appears to operate in the mixed lubrication regime. Therefore, it is likely that the piston friction, subtracted from the (piston + oil-control ring)friction, is too small and thus the determined experimental ring-only friction is too large. This effect can be quite significant as the friction of the piston alone in this regon is 8 to 15 N, compared to a p r d c t e d oilcontrol ring friction in the range between 12 and 26 N. In the right hand side part of Fig. 4 (viscosity x speed > 200 Pa.s.rpm), the predcted friction slightly exceeds the observed friction. This could be due to viscous heating in the contact area, as the mode of lubrication is predominantly hydrodynamic. This would yeld a lower viscosity than expected, and thus the points of observed friction should be moved further to the left Considering the extreme value at 3000 rpm; 25 OC, the mid-stroke velocity is 11.2 m/s and the mid-stroke minimum film thickness is predicted to be 0.9 pm for the top rail and 4.0 pm for the bottom rail. This could yield a flash temperature of about 7OC, according to

Blok's theory (see van Heijningen, 1986). yieldmg a contact temperature of 32 "C.The average contact temperature, however, will be somewhat lowcr. as the flash temperature evaluation was based on the minimum film thickness rather than the average. and because the contact inlet region is cooler than the exit region. For an average contact temperature of 29 "C, the lubricant viscosity would be 0.100 Pa.s rather than the assumed 0.124 P a x This brings the measured points close to the predicted line, as the real (viscosity x speed) parameter declines from 372 to 300 Pa.s.rpm.

5. CONCLUSIONS Basic problems concerning surface roughness characterization in mixed lubrication analysis have been addressed. These problems and their solutions are as follows: The liner roughness height dstribution is principally non-Gaussian, whle the mixed lubrication modelling assumes Gaussian distributions. It appeared that the upper part of the height distribution, omitting the deeper valleys, is close to Gaussian and the Kolmogorov-Smirnov test could be applied to derive the proper roughness height as input for the friction calculations. Surface roughness parameters depend on the scan length. However, considering that the scan length should in principle be similar to the contact size, it appeared that this dependence is negligible for the contact dmensions typical for piston rings. Surface roughness parameters also depend very much on the sampling interval. T h s problem could be solved by considering the physics involved in the contact and the mixed lubrication problem. The Thomas plasticity criterion was applied and appeared to be useful. This criterion assesses the sampling interval such that the plastically deforming, and therefore diminishing, asperities are just not included in the profile measurement. Furthermore, the roughness parameters, as derived in the way mentioned above, appeared to be more or

536 less independent of the direction in 2D scanning, although the liner roughness is non-isotropic. Experimental validation was possible by comparing predcted friction with measured friction for an oil-control ring from a motored engine test performed by Radclrffe (1993). It appeared that the proposed approach to determine the surface roughness parameters yielded very good results. This is the first time that experimental evidence is gven for the correctness of the Thomas plasticity criterion to assess the short-wavelength cut-off. The same approach will be applied to the analysis of piston ring wear and ring profile development during the engine’s life cycle.

Edwards, S P, 1992, “The Contribution of Piston Ring Packs and Cylinder Bore Distortion to Engine Friction ”. Ph.D. Thesis, The University of Leeds, UK Cane, N, 1970, “The Direct Measurement of the Strength of Metals on a Sub-Micrometer Scale”, Proc. Rqyal Soc. London, Vol. A3 17, pp, 367-391 Ganti, S, and Bhushan, B. 1995, “Generalized Fractal Analysis and its Applications to Engneering Surfaces”, Wear, Vol. 180, pp. 17-34 Greenwood, J A, 1992, “Problems with Surface Roughness”, Fundamentals of Friction: hilacroscopic and ibficroscopic Processes (Proc. NATO A f v . Study Inst. on Fundarnentals of Friction),

NATO AS1 Series E: Applied Sciences, Vol. 220, pp. 57-76

ACKNOWLEDGEMENT This research was sponsored by the Engineering and Physical Sciences Research Council. The authors would like to thank Mr. M. Priest from the University of Leeds Industrial Unit of Tribology for providng the piston ring software and for his assistance, and also Dr. C.D. Radcliffe for providng the cylinder liner for the roughness measurements and the computer data from his friction measurements.

REFERENCES Bhushan, B, 1995, discussion on paper “A Fractal Theory of the Temperature Distribution at Elastic Contacts of Fast Slidmg Surfaces”, by S. Wang and K. Komvopoulos, J. Trih., Vol. 117, No. 2, pp. 2 14215 Bhushan, B. and Majumdar, A, 1992. “ElasticPlastic Contact Model for Bifractal Surfaces”, Wear. Vol. 153, pp. 53-64 Briscoe, B J, and Tabor, D, 1978, “Shear Properties of Thin Polymeric Films”, J. Adhesion, Vol. 9, p. 145 Daniel, W. 1978, ‘L4pplied Nonpararnetric Statistics ”. Houghton Mifflin Company, Boston, ISBN 0-395-25795-6

Greenwood, J A, and Tripp, J H, 1971. “The Contact of Two Nominally Flat Rough Surfaces”, Proc. IAIechE, Vol. 185, pp. 625-633 Greenwood, J A, and Williamson, J P B, 1966, “Contact of Nominally Flat Surfaces”, Proc. Royal Soc. London, Vol. A295. pp. 300-319 Heijningen, G J J van, 1986, “De Bepaling van de Teinperatuur- en Warmtestroorriverdelingin h4achines of Ailachine-Onderdelen (The Assessment of the Temperature and the Heat Flow Distribution in Machines or Machine Elements) (in Dutch), Syllabus Delft University of Technology, The Netherlands ”

Hendriks, C P, 1993, “Meting van de Vervormde Ruwheid van Elastomeren onder Statische Kontaktbelasting - Dee1 2: hfetingen en Confrontatie met hlodellen (Measurement of the Deformed Elastomer Roughness at Static Contact Pressure - Part 11: Measurements and Comparison with Theoretical Models) (in Dutch), M.Sc. Thesis Eindhoven University of Technology, report no. T&M S93.04 ”

McCool, J I, 1992, “Non-Gaussian Effects in Microcontact”, Int. J. Mach. Tools ManuJ, Vol. 32, NO. 1/2, pp. 115-123 Patir, N. and Cheng, H S, 1978. “An Average Flow Model for Determining Effects of ThreeDimensional Roughness on Partial Hydrodynamic Lubrication”, J. Lubr. Technology, Vol. 100, No. 1, pp. 12-17

537 Patir, N, and Cheng, H S, 1979, “Application of Average Flow Model to Lubrication between Rough Sliding Surfaces”, J. Lubr. Technologv, Vol. 101. pp, 220-230 Radcliffe, C D, 1993, “An Experimental and Analytical Study of a Piston Ring Pack”, Ph.D. Thesis, The University of L e d , UK Radcliffe, C D, and Dowson, D, 1995, “Analysis of Friction in a Modern Automotive Plston Ring Pack”, Lubricants and Lubrication (Proc. 21st. Leeds-Lyon Symposi um on Tribologv) Rohde, S M, 1981, “A Mixed Friction Model for Dynamically Loaded Contacts with Application to Piston Ring Lubrication”, Friction and Traction (Proc. 7th. Leeds-L.yon Symp. Trih.). pp. 262-278

Ruddy, B L, Dowson, D, and Economou, P N, 1981, “A Theoretical Analysis of the Twin-Land Type of Oil-Control Plston Ring”. J . hlech. Eng. Sc. (IhfechE), Vol. 23, pp. 51-62 Tabor, D, 1951, “The Hardness of hletals”, Oxford University Press, Oxford Thomas, T R. and Sayles, R S, 1978, “Some Problems in the Tribology of Rough Surfaces”, Trib. Int., Vol. 11. No. 3, pp, 163-168 Thomas, T R. 1982, “Defining the Microtopography of Surfaces in Thermal Contact”, Wear, Vol. 79, pp. 73-82

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

539

Numerical Solution for Elastohydrodynamic Analysis of High Pressure Sleeve Seal H. Xua, P.L. Won8 and Z. Zhangb 'City University of Hong Kong, Department of Manufacturing Engineering, Kowloon, Hong Kong bShanghai University, Department of Mechanical Engineering, Shanghai, P.R. China With the use of a closely fitting sleeve between a moving shaft and a pressure vessel, the sealing effect can be enhanced. The leakage through the clearance space is reduced due to the elastic deformation of the sleeve. This paper presents an elastohydrodynamic analysis for a common type of high pressure sleeve seal. The effect of parameters such as seal geometry, initial clearance and working pressure on leakage rate are examined. 1. INTRODUCTION

Success in many modern manufacturing processes such as isostatic pressing, water jet cutting, crystal synthesis and powder compaction rely largely on the advancement in high pressure technology. Machines that generate high pressures face the sealing problem for moving parts such as rotating shafts and reciprocating rams. Basically, the magnitude of clearance between the moving shaft and the pressure vessel is linearly related to the working pressure. The higher the pressure, the clearance will be larger. Thus, the leakage rate will be increased. In order to reduce the amount of leakage, it seems that the increase in clearance due to the increase in pressure has to be somehow compensated by elastic deformation of certain components involved. One of the common high pressure seal is the sleeve type which adopts a thin elastic sleeve closely fitted between the housing and the moving shaft. The elastic deformation of the sleeve is to improve the volumetric efficiency of the seal. The study of the elastic deformation of seal housing and plunger started with Kamal [l]in 1968. He analysed a simple plunger cylinder type high pressure seal. The deformation of components was assumed to vary linearly in axial direction. The fluid was assumed to be incompressible and a simple linear relation of

viscosity with pressure was adopted. A subsequent paper by Wang and Kamal [2] provided a more general analysis for the same problem. The compressibility of the fluid was considered and its viscosity was assumed to have an exponential dependence on the pressure. Harris [3] studied the sleeve type high pressure seal in 1972. "he leakage and torque of the seal were discussed in consideration of deformation of both sleeve and plunger. However, not much data were presented. In 1994, Gibseon et al [4] analysed a plungerbarrel system of unit injector up to 140 MPa. Pressure and clearance distribution were calculated with the assumption of isoviscous and incompressible fluid. Xu et al [5] have recently developed a new type high pressure seal based on elastohydrodynamic concept, which is so-called all metal viscoelastic moving seal. A simple analysis [6] was performed and results indicated that the seal is able to maintain a full oil f ilm at very high pressure with a high volume efficiency and low friction coefficient. The magnitude of elastic deformation of components under high working pressures is greater than that of the initial seal clearance. This is, in fact, a heavily loaded conformal EHD problem. Hitherto, full numerical solution is scarce. This paper analyses the elastohydrodynamic characteristics of the common sleeve type high pressure seal.

540

\ \

\

Sleeve

\

\

Seconciaryseals

'Y

Po

\

t 4

\

\

/

/

/

/

/

/

/

/

Fig. Structure scheme of high pressure sleeve seal

2. MODELLING

A typical high pressure sleeve seal is shown in fig.l. A plunger is able to pass in and out of a high pressure cylinder through a closely fitting elastic sleeve. The fluid between the cylinder and the sleeve is sealed by a set of secondary (stationary) seals. Because of the viscous effect, the pressure will decrease from p , at x=O to the initial pressure pi at x =L. The outer surface of the sleeve is under the constant working pressure p , while the inner surface is under a pressure distribution which is in the range of p o > p > p i . The difference in pressures acting on inner and outer surfaces leads to a fact that the expansion of clearance due to the high pressure between the plunger and sleeve will greatly be controlled. The axial speed of the fluid, u, at any points in the clearance can be expressed by

where q = dynamic viscosity of the fluid, p = pressure along the clearance, h = fluid film thickness, and Uo= axial speed of plunger.

The first term is the squeeze flow term and the second one is a shear flow term. Since Wo is small in high pressure sealing, the second term c a n be neglected and Equation (1) can be rewritten as

By integrating Equation (2), it gives the axial mass flow rate as Q=---npDh'dp

12q dr

(3)

where h denotes the clearance between the sleeve and plunger and can be written as

h = C(x)(l

+ ECOS~)

(4)

where e and I) are the dimensionless eccentricity and angular position respectively. C(x) includes the original thickness and the elastic deformation of plunger and sleeve. By using Lame's formula for thick-walled cylinder, the thickness can be obtained as

54 1

xD~oc'p0 for mass ledage. me 127,L governing equations in dimensionless form can be written as

-

and

where C, is the initial clearance. p , is the working pressure. k, and k, are effect coefficients and can be derived as

where E is the Young's modulus and Do is the outer diameter of the sleeve. The boundary conditions are PZ.0

=

In this analysis, the eccentricity of plunger is not considered, such that E = 0. Hence the dimensionless leakage c a n be simplified as

(7)

Po

where

-where the initial pressure pi can be atmospheric pressure or any other values. The pressure-viscosity relation of working fluids is given by Barus equation

C(x) = 1 +

q-kg,

(9)

q = qoeaP

The pressure-density relation is given by Dowson-Higginson formula

P

=

Po(l

+

(13)

(15)

0.6P ) 1~1.7~

Equations (3) to (10) constitute the isothermal governing equations of high pressure sleeve seal.

3. NUMERICAL SOLUTION Calculations are done in dimensionless form. Dimensionless variables are expressed with an overline. The relative units are, D for diameters, L for axial dimensions, C, for clearance thickness, p , for pressures and Young's modulus, q, for viscosity, p, for density, Up, for pressure-viscosity coefficient

-p =

l +

O.6JjP0 1 + 1.7%,

All equations above are fully dimensionless except Equation (18) which contains the system pressure, p , and with unit GPa. The parameters CJI and DJI are very significant. The former determines the initial clearance and the later describes the sleeve structure.

542 When p,, p,, ii, E , C P and D f l are given, the solution of high pressure sleeve seal can be obtained by ordinary difference method. The calculation procedure is as follows: 1. 0 is assumed; __ - 2. C(X), q , p are set up; 3. i is calculated by solving the Equation (12); 4. ?, are calculated and then substituted back to Equation (12); 5 . The new pressure distribution j is then calculated and compared to the previous j.If the difference does not satisfy the convergence criteria, the values of c(i),6, j are revised and the program returns to step 3 to recalculate until the convergence criteria is satisfied. 6. The boundary conditions of j are checked. If they are not satisfied, 0 is adjusted and the program returns to step 2 until the final solutions are obtained.

1 Po 2 Po 3 Po 4 Po 5 Po

-- 50 --

1 MPa

MPa

100 MPa 150 MPa 200 MPa

c(i),

0.4 -

0.2 -

-X

Fig.2 Pressure distribution in dearanca

4. RESULTS AND DISCUSSION

The pressure distribution along the longitudinal direction under different system pressures p , is shown in Fig.2. When p , is small, the pressure distribution is similar to that of a simple plunger sealing, where the pressure at the high pressure end declines linearly to that at the low pressure end. As the system pressures increased, the pressure distribution no longer be a straight line. The rate of pressure drop is faster in the entry region than that in the exit. However, when the system pressure is further increased. The mode of pressure distribution is changed. The pressure declines relatively mildly at first and then sharply near the exit. Fig.3 shows the clearance distribution along the longitudinal direction under different system pressures. When the system pressure is low, the clearance distribution is with a wedge shape. For p , is 100 MPa, the

-

1Po-1MPa 2Po-50MPa 3Po-100MPa 4 Po 150 MPa 5Po-200MPa

.

Dq(D- 1.2

'

.

o.5

5

-

d 0.25 0.5 0.75

0.3 0

-

X Fig. 3 Clearance distribution

543

1

curve declines sharply at first and its gradient is gradually diminished until the low pressure end. For high system pressure cases, the clearance drops rapidly near the exit due to the large pressure gradient. Fig.4 shows the variation of dimensionless leakage rate with system pressure under different clearance ratio. The larger the clearance, the greater the leakage will be. The effect of clearance on leakage rate is the greatest when the system pressure is about 50 MPa. When under higher system pressures, the differences in leakage rate with different clearance ratio is much smaller. The dimensionless leakage rate is the leakage rate normalised with a term,

--

1 cqc 0.002 2 cqc 0.003 3cq(c-O.005 4 co/C 0.007

0.75

‘8.5

025

100

150

-

20(

Po lMPal 4 . 4 Leakage vs system pressure uker dHferenl clearance

-

1 ctyc 0.002 2ctyc-0.003 3 CCJC 0.005

20-

50

100

Po (MPa)

150

I

200

Fg.5 Relative leakege rate vs system pressure

“Dpoc’po. In order to have a better view on 12rlL how the leakage rate varies with system pressures, all curves of Fig.4, Q, were multiplied by p , and plotted against with p , in Fig.5. The y-axis of Fig.5 only illustrates relative values and has no physical meanings. Leakage curves of Fig.5 are all similar in shape. With increasing pressures, leakage rates increase sharply at first, then level off to a peak and finally, gradually decrease again. There is a shift in the pressure at which the leakage reaches its maximum with the increase in clearance ratio. The maximum leakage pressures are in the range from 30 to 50 MPa for these four cases. There are two significant geometrical parameters CJD and DJD, which greatly affect the performance of a seal. The effects of them on leakage rate are shown in Fig. 6 and 7 respectively. Fig.6 depicts that the larger the clearance, the leakage rate is greater. The increasing rate drops gradually with the increase in clearance ratio. It can be seen that for values of CJD larger than 0.005, the curves approach to their limiting values. Fig.7 shares a similar shape of Fig.6. The curves increase drastically for DJD is small. Their gradient deceases gradually as DJD increases. For DJD is large, the curves approach to limiting values which are leakage rates of a simple plunger sealing when under the same

544

-

1 Po-50MPa 2 Po 100 MPa

2Po-100MPa

0.4

t

-

CdC 0.005 ,,,.

~

............ . -..'.

1

2

.

.

_.

-

0.1

3

E

Rg.6 Relation of leakage with dearance raUo

conditions. In Fig.7,the limiting values of the three curves are shown with solid lines near the end of x-axis.Points having the half value of limiting leakage rates are joined with a solid line in the figure as a reference. It can be seen that for D D greater than 1.2, the volumetric efficiency of the seal is quite poor.

ACKNOWLEDGMENT The authors would like to express their appreciation to the City University of Hong Kong for financial support to the project.

.

-

Odo

Rg.7 Relation of leakage with sleeve thickness ratio

REFERENCES 1. M.M. Kamal, J. of Lub., ASME Trans., (1968),90(2),412. 2. N.M. Wang and M.M. Kamal, J. of Lub., ASME Trans., (1970),92(2), 310. 3. H.D. Harris, J. of Lub., ASME Trans., (1972).94(4), 335. 4. D.H.Gibson, P.J. Dionne and A.K. Singhal, J. of Tribo., ASME Trans., (1994),116(3), 116. 5. H.Xu, T. Lei, Y. Zhao and C. Wang, China Patent No. 91108440.1,(1994). 6. H. Xu and T. Lei, STLE Trans., (1994), 37(4),767.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

545

T h e evaluation of the minimum film thickness in ball-plane impact experiments I.Muw',

T. Morosanub, E.N.Diaconescu'

'Mechanical Departament, University "Stefan cel Mare" Suceava l-University Street, 5800-Suceava, Romania bElectrical Departament, University "Stefan cel Mare" Suceava 1-University Street, 5800-Suceava, Romania During the impact between metallic surfaces, respectively a ball and a lubricated plane, the two contacting surfaces are separated by a thin film. The estimation of film shear and rate of shear needs an accurate evaluation of real film thickness in contacts. In this paper, the authors suggest the use of an experimental capacitance method to evaluate the minimum film thickness in the contacts subjected to impact. Some remarks concerning the response of the lubricant under the pressure pulses are also presented. 1. INTRODUCTION

The shear response of EHD contact is governed mainly by rheological behaviour of lubricant. During the time of transit trough the contact (of lo4 seconds order) the lubricant is compressed at a few gigapascals and a shear stress depending of tangential speeds of surfaces and film thickness occurs. The evaluation of lubricant characteristics under different conditions of shear can be made by classical traction experiments or by other experiments such us impact experiments [ l ] ( 2 ) . The evaluation of shear and shear rate can be performed only if the film thickness and surface speeds are determined. Within the known classical methods of film thickness evaluation, there could be used only those based on the evaluation of a physical parameter evolving the same speed as the observed phenomenon. Such parameters are the optical and the electrical ones. The electrical resistance measurements of film thickness in ball-plane experiment of impact was made by Jacobson [ I ] . His results are informative and confirm the presence of the film in contact with a thickness of the order of a few micrometers (1-5pm). This evaluation is not sufficient for assesement of shear and shear rate. Lewicki [3] considered in detail the electrical resistance method and concluded that it would not allow satisfactory measurement of film thickness to be made.

The interference method gives information concerning the configuration and the thickness of the film for the entire contact, but it has the disadvantage that it can not be used on real contacts. It also requires that one of the pieces to be transparent. The metal to metal time of impact is of order of tens of microseconds [ l ] [4]. The investigation of the evolution of the metal to metal impact by interference method requires the recording of the interference fringes at the speed of the evolution of the phenomenon. The capacitance method [ 5 ] uses electrical parameters to observe the development of the film thickness . These parameters are very easy to observe and record, but they not give much information regarding the configuration of the film. That is why this method was preferred to determine the minimal thickness of film between the ball and the flat surface. 2. THE MEASURING SYSTEM

The main elements of the measuring system are the steel ball and the steel disc. The ball falls free, without spinning, and hits the plane surface of the disc. To get a tangential speed component of the centre of ball, the flat surface can be positioned at a known angle versus horizontal position. The ball and the plane are connected to an electrical system, figure 1, with screened leads. This system contains an adjustable frequency source and an oscilloscope

546 4. EXPERIMENTAL TECHNIQUE

-@,

oscilloscope

I Figure 1 Test rig. with ability to store the evolution of observed parameters. During the experiment, the flat surface of the disc is lubricated. A transducer system measures the falling time of the ball over a known distance, and so the final speed can be deduced. An electric pulse of known level and frequency is sent to the disc. As long as the distance between the ball and the disc is relatively large (minimum several centimetres) the oscilloscope indicates only the parasite signal (attenuated by resistor R); when the ball falls and approaches the disc surface, a quick pulse increment is detected. At contact, the oscilloscope gives the value of the source signal. The size of the recorded pulse increases with the reduction of the distance between the two elements and the relative ball-disc speed. The value of amplitude is strongly affected by variations of film thickness within micrometers. This sensitivity gives a high fidelity to the system. 3. TEST LUBRICANT

The lubricant used for this investigation was the Romanian oil TBOEP2, usually destined for lubricating concentrated contacts such as gears, ball-bearings etc. The properties of this lubricant, precisely determined in the laboratory, are presented in Table I.

,.

Figure 2. A typical oscilloscope trace.

The oscilloscope is set " on" in trigger position. The amplitude level of start is selected by trial and error. The flat surface is positioned in a determined angular position from horizontal, in order to obtain the needed tangential and normal speeds. The horizontal positioning of the disc can be done as it follows: the ball falls free from 0.5 m and the impact point is considered the centre of a 20 mm diameter circle; if the next four impacts take place within this circle, the adjusting is considered accomplished. This position of the disc is used as reference for the following angular positioning. An example of oscilloscope trace record during impact experiment is presented in figure 2. The data were transferred and stored into a computer memory.Under given experimental conditions, the test was repeated until the oscilloscope record five trace of close values. The average value of the maximum amplitudes was used in the analytical step of the method. The next step was to establish the dependence between the maximum value of the recorded pulse and the maximum capacitance in contact. The assembly ball and disc, was replaced by capacitance elements with precisely determined values (keeping the other elements of the system the same in order to maintain the similar influence over the global capacitance). The capacitance corresponding to maximal amplitude of signal recorded for each ball-plane impact experiment can be determined by using the correlation diagram (Figure 3).

5. INTERPRETATION CAPACITANCE READINGS

OF

THE

A numerical model was developed to evaluation minimum film thickness corresponding to contact capacitance. The model, from Chittenden [ 51 considers: a) the effect of curved lines of electric flux; b) the effect of elastic deformation of the bodies; c) the effect of increased pressure on the dielectric constant of the lubricant; d) the effect of air upon global contact capacity. The real flux lines are curved, Figure 4a, and this leads to a difficult and complex model; the

541

0

0

0 0

0 0.00

o m ' 0.w

,

I 10.00

,

I l0.W

I

I 10.00

,

I 40.00

,

40.00 (10.00 disbls MI-pln.

120.00

I J0.W

Capadl.ncd

Figure 3. Correlation diagram of the capacitance with the maximum amplitude signal. assumption that the flux lines are parallel, Figure 4b, simplifies the mathematical model. The simplified model introduces an error which has to be compensated introducing an additional constant of correction in the capacitance formula:

where:

cMEA: experimentally measured value of capacitance; cMODvalue of capacitance predicted by parallel flux model; cFLu-constant to account for curvature of lines of flux; The value of cFLU was determined using an experimental rig; this allows the control

Fig. 4 Realistic (a) and assumed lines (b) of magnetic flux.

Figure 5. The capacitance static measurements of the ball-flat surface system (a) compared with calculated values (b). of the approach of the ball to the flat surface. As in impact experiments, the flat surface was lubricated with a thin film of the same oil. The distance between the ball and the disc has been established with a precision of iO.5 pm and was modified in the 2i100 pm range, The results of static capacitance measurement in comparison with the calculated values are presented in Figure 5 . The used formulas for calculation of ball plane impact parameters are presented in Appendix 1. The modified dielectric constants of the lubricant were calculated using the Clausius Mosotti formula: E-

1

( E + 2)P

= constant.

(2)

This relation shows that the permittivity of mineral oil increases as its density increases. The change of density with pressure was taken into account by experimental compressibility tests (Appendix 2). The effect of elastic deformations of the elements was determined according to the elastic Hertzian contact theory (Appendix 3) considering the maximum pressure value in contact which corresponds to minimum value of the film thickness. Because the lubricant film is thin (being levelled using a blade with an aperture h=0.3

548

Table 1 T90EP2 oil properties

UM I Density at atmosphenc pressure, po 2

Kdm

865

Relative permittivlty at atmosphenc pressure, E 3,27

d)

mm), the capacity of the ball-plane system has two terms: a) one for the central zone, filled with oil; b) the second one, for the annular zone having both oil (hu=0.3mm) and air as dielectric. For the second zone the composite dielectric coefficient was represented by the relationship:

The expenmental results are presented in Table 3 and Table 3 The vanation of film thickness is presented in Figures 6 and 7 The flow chart of the computer program to interpret the measured capacitance is presented in Figure 8 7. CONCLUSIONS

~ r c o m-

&roil * foil + Erair . fair

(3)

where fo,l- separation percentage of oil

fo,l

(x, Y) =

~

h“ h( x, Y)

.

(4)

’

fair- separation percentage of air

The calculation of disc-plane capacitance was made by dividing of the zones into a large number of concentric annuli. Assuming that the concentric annuli are flat, the total capacitance results by adding the capacitance of even annuli. A detailed description of the this is presented in Appendix 3 6. EXPEIUMENTAL RESULTS

The maximum values of signals recorded by the oscilloscope were determined for: a) constant normal speed and variable tangential speed of the ball centre; b) constant tangential speed and variable normal speed of the ball centre;

The results reveal that the film thickness are placed towards the inferior limit of the values presented by Jacobson. It can be assumed that this is caused by the size of the balls ( 1 1. I I mm diameter used in our experiment against SO mm used by Jacobson). The oil compressibility was determinated up to 1.4 GPa and the range of aplicability was extended to 5 GPa according to Ramesh’s formula. As a result of this method, the effect of oil compressibility isn’t very well determined. The errors can be diminished by a better relationship between pressure and density The charts reveal that the film thickness depends on both normal and tangential speeds. The film thickness decreases faster for low tangential speeds. As the tangential speed increases, the decrease of film thickness is slowing down Increasing the tangential speed and keeping the normal speed at a constant value, a significant film thickness decrease is observed. When there is only normal speed, the values of the film thickness are higher and tend towards an asymptote. This tendency is assumed to be a consequence of the changes in the lubricant behaviour. At increased pressure, when the lubricant is considered quasi-solid, the variation of the density with pressure becomes insignificant. REFERENCES 1. B.O. Jacobson, Rheology and Elastohydrodynamic Lubrication. Elsevier ( 1991) 383.

549

rw1

lwl 35

1.5

d

T

1.4

T*

3 t 1.3

* + * ****

1.2

' 0.5

AVt=O.5

4 0

u,u

I

1

2

3

0

4

Figure 6. Correlation of minimum film thickness with normal speed. 2 . B Paffoni, J. Frene, R. Gras, J. Blouet, Une nouvelle machine dessais pour I'etude du comportement des lubrifiants en reyme transitoire. Eurotrib 1985 (in French). 3. W. Lewiclu, Some physical aspects of lubncation in rolling bearings and gears. Engr. Lond. (1985) 200 176-178 and 212-215. 4. I Musca, Theoretical and experimental aspects of ball-plane impact phenomenon. Analele Universitgtii "Stefan cel Mare" Suceava, Romania, Mechanical Section (1995) No. 7-12 75-29 (in Romanian). 5 R.J. Chittenden, D. Dowson, C.M. Taylor, in Elastohydrodynamic film thickness concentrated contacts. Part 1 . Experimental investigation for lubricant entrainment aligned with the major axis of the contact ellipse. Proc. Instn. Mech. Engrs. Vol. 300 No. C3 207-225. 6. K.L. Johnson, Contact Mechanics. Cambridge University Press ( 1985) 452 7 K.T. Ramesh, The Short-Time Compressibility of Elastohydrodynamic Lubricants. Journal of Tribology (1991) Vol. I13 361-371. 8. I . Musca E.N. Diaconescu 1.M.Ciornei G. Slevoaca V. Buduroi and E. Flandofer, Essais de compressibilite pour des huiles roumaines. 6-Th Conference on EHD Lubrication and Traction, Suceava, Romania, 1992, p. 9- 12, (in French).

[mis]

. 0.2

0.8

0,6

0.4

1

Figure 7. Correlation of minimum film thickness with tangential speed. Input:

Geometry Load Matenals ro rbes Cenval inial thickness Signal arnplltude

Fm

I Calculate the value of capacitance according to the oscilloscope results

I

I

Calculate the Hertzian parameters of the contact

1

Calculate the annuli areas and associated values of the dielectric constant

I Calculate the separation of each annulus

I

I

X L Calculate the theoretical capacrtance C

CMEn=CMOD+CFLUNo

I

Record value of central film thickness

Adjust the central separabon

I

Figure 8. The flow chart of the computer program.

550

Table 3 Expenmental results at different normal speeds No Vn [m/s] Vt [m/s] 1 1 I 40 0 13 1.98 0 1.3 3.42 I .4 2.80 I .5 3.13 I .6 3.43 1.7 3.70 0 0 1.8 3.96 0.35 1.1 1.35 33 1.94 0 35 3.3 2.4 0 35 3.4 2.78 0 35 3.5 3.95 0 35 3.6 3.1 I 0 35 0 35 3.7 3.36 3.8 3.41 0 35 3.9 3 55 0 35 0 35 3. 10 3.69 3II 3 94 0 35 3 1 I30 05 32 I .9l 0.5 3.3 3 37 0.5 34 3 75 05 05 35 3 09 05 36 3 39 05 37 3 67 05 38 3 93 ~

Umax [V] I 72 2 05 2 33 2 64 1 85 3 11 3 25 3 43 1 98 2 48 278 39 3 13 3 27 3 40 3 55 3 69 3 85 3 98 188 3.48 3.73 3 00 3 42 3 72 3 96 4 08

Table 3 Experimental results at different tangential speeds of the ball centre No Vn [m/s] Vt [m/s] Umax [V] 1 1 3 43 0 03 387 13 3 12 0 15 3 95 I3 3 42. 0 33 3 00 14 2 12 0 43 3 00 15 3 13 0 56 3 01 16 3 43 0 62 3 03 17 3 42 0 69 3 04 I8 3 43 0 76 3 10 31 3 13 0 03 3 65 3.80 3 13 0. I9 3.3 0.43 3.90 33 3 13 34 3 13 0 55 4 00 35 3 13 0 72 4 00 26 3 13 0 80 4 00 4.10 0 89 27 3 13 4.15 38 3 13 0 98

c [PFI 8 90 I 09 1.92 5.00 6.36 8.14 9.04 20 19 10 55 13 91 15 90 I6 69 18 14 19 13 30 00 30 98 31 90 23.96 23.82 9 96 13 91 15.50 17 35 10 I:! 2210 13 69 34 48

c [PFI 16 53 17 03 17 35 17 35 17 41 17 51 17 64 18 01 31 64 22.63 23 29 23 95 33 95 33 95 24 61 24.61

ho [rim] 3 45 365 337 I 93 I83 I 69 I .67 I61 33 I 65 I55 I 53 150

I 45 I38 I34 131

I37 I36 3 46 64 59 50 31 35 31

19

h,, [pm] I45 140 137 I37 I34 I33 I31 127 1 19 I 13 1 07 1 03 103 10; 0 99 0 99

55 1

APPENDIX 1. Formulae for calculation of impact parameters

(9)

According to impact theory of spherical bodies with radius R I , Rz , mases m l , m2 the maximum pressure in the centre of the contact can be wnte as [ 6 ] :

[

4E*)'5

y , =- 3 0

2n 3R3I4

.(:

-mV- , ) ' I 5

P ( f ) = +-3 { F . f ) ]

m

8

where P represents maximum interaction force correlated with maximum approach The contact time, T,, is calculated by

1

m, m,

1 1 -=-+-,

1

R,

R,

1

-=-

E'

(10)

(6)

were

1 1 -=-+-,

or by [4]:

1-v;

El

Radius of hertzian area corresponding to P

+-I - v :

* IS

Pressure vanation inside of the contact area was considered by parabolic

E2

When the second spherical body is fixed and the first falls free in gravitationalfield from a height H. the ball speed at the begining of the impact is

V = $ p

(7)

APPENDIX 2 Evaluation of oil density Maximum approach of the centres of the bodies IS

Ramesh [7] using Kolsky bar. propose for describe the behaviour of lubricant in compression, at pressure to approximately 5 GPa, the correlation:

o= During the impact the variation of the force of interaction, P, can be approximated by [ 6 ] :

KE

(1 - 06)'

'

were K is the longitudinal modulus (in a linear approximation), a is a constant (which essentially identifies the slope of a shock speed versus particle velocity plot for a given material) and considered by

552 Ramesh and in this works a=l, & is the uniaxial lonptudinal strain and cs is normal stress. assimilated in this work wth the normal pressure Expenmental research in compressibility for T90EP3 oil was reported [8] at pressure until I 4 GPa Using the experimental value of the compressibility (determined at the highest pressure of the quasistatic compressibility expenment) in Ramesh's formulae. a value of longitudinal modulus, K=6 5 GPa was calculated The corresponding density was obtatned as

radius of compuIabon=radiua of the ball

ball

I

'Q1

Figure 8. The division of the surface of the bodies into concentric annuli. for the ball and

p=- P 0

Iplmw= - 6 .

I+&

+u-

with APPENDIX 3. Evaluation of surfaces deflection .A ball plane contact generate a circular

hertzian area. The elastic deflections in normal direction of the surfaces can be writen as [5] [ 6 ] .

14.

1 - v3 np,, I:' 40

-,-:)

= -- (-03

for r l a (16)

and

S, = u:(o).

(32)

APPENDLX 4. Theoretical evaluation of ballplane system capacitance.

The bodies are theoretical divided in the hertzian contact zone and the non hertzian contact surface zone of the bodies. Each zone of surfaces is divided in circular sectors, Figure 8 . Theoretical capacitance of the i-th sector can be written as

(33)

The indexes 1 and 3 are significant the considered body The ongin of axes system is considered in the centre of the contact area with z axis along normal direction to tangential plane (xoy) oriented towards the sphencal body The deformation in z direction modifies the geometry of the bodies The new co-ordinate z of the considered point of bodies can be wnten as

A,, - area of the i-th sector. S,-medium distance between surfaces in the considered sector zone, q)-permittivlty of free space, E, -relative permittiwty Global theoretical capacitance of the contact is obtained by cumulating the elementary capacitances C, in the hertzian ( h ) and non hertzian (e) zone

I

i

SESSION XIV INVITED LECTURES

Chairman :

Professor Kenneth Ludema

Paper XIV (i)

How Lubricants Behave in E.H.L. Contacts

Paper XIV (ii)

Elastohydrodynamic Films with Emulsions

Paper XIV (iii)

Understanding Grease Lubrication

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

555

How Lubricants Behave in EHL Contacts B. Jacobson

SKF Engineering & Research Centre B.V. Postbus 2350, 3430 DT Nieuwegein, The Netherlands When more and more realistic models for the lubricant rheology in heavily loaded rough EHL contacts are used, some new insight is gained. For a long time it was assumed that if the calculated oil film thickness was larger than a few times the R, value of the surfaces, the lubrication could be expected to be successful. There was never any explanation why the highest tops in the surface structure did not break through the oil film despite the fact that they were higher than the oil film thickness. In some applications in the early ~ O ’ S ,where squeeze motion and sliding motion were superimposed on the rolling motion of an EHL contact, the old rule of thumb suddenly no longer worked. The oil film thickness to roughness ratio had to be larger than expected to avoid smearing damage which was caused by direct metallic interaction through the oil film. The surfaces behaved as if they were rougher when sliding was superimposed. In modem very smooth bearings, the opposite is clearly seen. The calculated mean oil film thickness needed to separate the bearing surfaces is much smaller than the composite surface roughness of the surfaces. This leads to the conclusion that the surface structure is to a higher or lower degree elastically deformed by the pressure variations in the oil film and thus that the lubricant rheology and shear stress will determine the behaviour of the asperities and whether the lubrication is successful or not.

1

INTRODUCTION

Different mathematical models for the lubricant behaviour in bearings have been proposed in order to explain why lubricant films can decrease the friction and wear of lubricated surfaces. The first mathematical model, proposed by Newton [ I ] in 1686, had a linear relationship between shear stress and shear rate, and the ratio was called the viscosity of the liquid. This model worked extremely well for lightly-loaded lubricated contacts such as journal bearings, and was already being used successfully in 1883 by Petrov [2] for the prediction of bearing friction. The Newtonian lubricant model also predicted the pressure build-up and the oil film thickness-load-speed relationships in a correct way. When Martin 131 published his calculation of the oil film thickness between gear teeth in 1916, his results predicted such a thin film that it was clear that the gears would not be able to work without wear having the roughness they had. In 1941, Meldahl [4] included the elastic deformationscaused by the oil film

pressure in the calculation model, but still the predicted film thickness was too low compared to engineering surface roughnesses to explain successful lubrication. When in 1949 Ertel [5] and Grubin [6] also included the pressure-viscosity effect on the oil film thickness, the calculated film thickness in a smooth elastohydrodynamic contact became about as large as the mean surface roughness heights. Later, this led engineers to use theoretical calculations of oil film thicknesses for smooth surfaces, also when predicting the lubrication of rough surfaces. The standard assumption was that the calculated oil film thickness had to be larger than a few times the R, value of the surfaces (Hamrock and Dowson [7] and Harris [8]) to make the lubrication successful. No detailed explanation was given of the phenomenon of full film lubrication (no metallic contact through the oil film) despite the fact that the highest peaks in the roughness distribution were often many times higher than the thickness of the lubricant film.

556 Already in 1958-59 F.W. Smith [9] had found that a Newtonian lubricant model could not describe the traction forces measured in combined rolling and sliding motion for heavily-loaded contacts. His measurements showed that the Newtonian model could only describe the tractional behaviour at very low sliding speeds, and when the sliding speed increased the shear stress reached a maximum and could even fall at higher sliding speeds. He concluded that lubricants had a shear strength which gave the maximum shear stress possible to transmit through the oil film. The concept of a limited shear strength and solid-like behaviour was used by Jacobson ( 101in 1970 in his calculation of oil film thickness for a point contact, see Figure 1. In the figure the oil film thickness and pressure distribution are shown and the region with solidified oil is indicated by a broken line in the pressure distribution. In the same report, shear strength measurementsfor oils solidified under pressure were recorded using the high pressure chamber shown in Figure 2. Later, measurements at higher pressures and temperatures (111, made in a new high pressure chamber, see Figure 3, revealed that the shear strength increased linearly with an increase in pressure: also, the pressure increase needed to retain the oil in the solid state at a higher temperature exactly matched the compression of the oil with the thermal expansion due to the increase in tempenture. The oil converted to a solid at a constant density, indpendent of temperature.

2

ROUGH SURFACES

As the mean lubricant film thickness in a rough, lubricated EHL contact seems mainly to be determined by the inlet zone, except for contacts at high sliding speeds when the lubricant is in a glassy state, the calculated film thickness could predict lubrication behaviour quite well for typical engineering surfaces in beatings and gears, despite the fact that the roughness peaks ought to have penetrated the oil film if their form was maintained in the EHL contact. The first indications that the simple EHL theory for smooth surfaces could not fully predict the behaviour of rough surfaces were noticed about 20 years ago when lubricated surfaces in combined rolling and sliding needed a thicker calculated oil film than predicted for pure rolling, in order not to damage the surfaces. It

could also be seen on gears where some running in took place. The simple EHL theory failed to provide an adequate description of solid contact through the oil film. As the elastohydrodynamic calculations assumed linear Newtonian behaviour [I] for the lubricant, one possible way to explain the oil film collapse was by assuming the lubricant to be no longer Newtonian. If the oil was non-Newtonian, an increase in shear strain rate would no longer give a shear stress increase proportional to the shear strain rate increase. This permitted enhanced pressure flow peqendicular to the relative sliding velocity of the bearing surfaces compared to that expected for the Newtonian case. Indeed, if this side flow was large enough, the whole macro-Hertzian contact would collapse within the contact time. For shorter times, it was still possible for an individual, compressed asperity to re-emerge from the surface. It was only necessary that, by virtue of a slightly higher pressure compared to the surrounding ambient level, the side flow was sufficient to empty the micro-contact. As the local asperity pressure fluctuations are functions of the heights and slopes of the asperities, the film collapse is governed by these as well as by the surface velocities. The steeper the pressure fluctuation, the faster the collapse of the oil film under the asperity, Asperities with low slopes will be elastically flattened by the pressure variations in the oil film while sharp and steep asperities will maintain their form until they touch the opposite surface, see Figure 4. Asperities with intermediate slopes will be elastically flattened at the inlet of the EHL contact but will slowly re-emerge into the oil film due to the elastic spring-back of the asperity, see Figure 5. Depending on how fast the asperities reemerge compared with the time available for the transport through the contact (typically lC3 to lo4 s), the asperities can touch through the oil film at the outlet or not. This phenomenon was experimentally shown by superimposing a sliding speed on normal squeeze motion between a polished steel ball and a flat lubricated surface using the test rig shown in Figure 6 (111. Oil film breakthrough was indicated by electric contact between the balls and the plate. Polished surfaces (R, = 0.008 pm) needed only 5 cSt viscosity to avoid metallic contact during the

557

impact time when the sliding speed was zero. A sliding speed of 0.14 m/s made it necessary to increase the viscosity to 26 cSt in order to avoid metal to metal contact. For a rough surface, R, = 0.18 pm, in contact with the polished ball, the viscosity needed to be much higher, 68 cSt at pure impact and between 7000 and 16300 cSt for a total sliding distance of 29 pm during the impact time. It was thus necessary to have a viscosity more than 100 times higher to keep the surfaces sepmted by an oil film when a sliding distance of 2.5 percent of the Hertzian contact width took place during impact. That sliding distance is of the m e order as the surface roughness wave length. The non-Newtonian behaviour of the lubricant allowed oil film breakthrough which could not be predicted by a Newtonian lubricant model.

3

SMOOTH SURFACES ASPERITY LUBRICATION

AND

In recent years the opposite effect has also been seen. For extremely smooth surfaces the asperity pressure gradients are not able to displace the lubricant sideways and cause an oil film collapse at the asperity level so that the lubricated contact behaves as if it was mathematically smooth [12]. This leads to oil film collapse only at very high sliding speeds and high loads when the whole Hertzian contact collapses. Depending on how far up on the shear stress-shear strain rate curve the lubricant stress point is situated, different behaviour will be experienced by the asperities. If the lubricant stress is far below its local shear strength, an increase of the shear rate will increase the shear stress and thereby build up steeper local pressure gradients. This leads to build-up of steep pressure spikes, both in pure rolling situations and in combined rolling and sliding. These pressure spikes above the high points of the surface structure flatten the surfaces locally and give them a lower effective roughness. This is probably one of the main reasons why well run-in surfaces can work without metallic contact through the oil film, even when the asperity heights are considerably larger than the calculated mean oil film thickness. The rule of thumb for choice of oil film thickness compared to the composite surface roughness of the lubricated surfaces can thus be explained if the roughness is about halved inside the

EHL contacts for good surfaces compared to the roughness outside the contact. The smoother the mating surfaces, the more important this phenomenon because both the local pressure gradients and the heights of the local pressure spikes go down. The decrease in the local pressure gradients decreases the risk of pushing out the oil from under the asperities for any given shear strength of the oil. At the m e time the lower asperity pressures will maintain the lubricant in the Newtonian state at the asperity tops and thus allow some sliding speed between the surfaces before the stress in the oil reaches the shear strength and gives the oil a much smaller effective shear strength in a direction perpendicular to the sliding direction. and thus can be pushed out from the asperity contact. The higher the sliding speed and the higher the local viscosity at the asperity tops, the further into the non-Newtonian behaviour regime the lubricant will come, and the earlier the asperity tops will break through the oil film.

4

CONCLUSIONS

The above leads to the conclusion that rough surfaces lubricated with oils having a high a-value (pressure viscosity coefficient) need a much thicker mean oil film compared to the surface roughness than smooth surfaces lubricated with low a-value I ubricants. Thus, the ratio between the mean oil film thickness and the surface roughness height needed for good lubrication steeply decreases when surfaces get smoother and the lubricants remain Newtonian in the EHL contact.

REFERENCES 1. 2.

3.

Newton, I. (1686), "Philosophiae Natumles Principia Mathematica". Imprimature S . Pepys, Reg. Soc. Praeses. 5 Julii, Londini. Petrov, N.P. (1883), "Friction in Machines and the Effect of the Lubricant", Inzh. Zh., St. Peterb.: 1.71-140; 2.227-279; 3.377-436; 4. 535-564. Martin, H.M.(1916), "Lubrication of Gear Teeth", Engineering (London), 102, 199.

558 4.

5.

6.

7.

Meldahl, A. (194I), "Contribution to Theory of Lubrication of Gears and of Stressing of Lubricated Flanks of Gear Teeth", Brown Boveri Rev., Vol. 28,No. 11, pp. 374-382. Ertel, A.M., "Hydrodynamic Lubrication Based on New Principles", Akad. Nauk SSSR, hikdnaya Malhematica i Mechanika, 3,2,4152. Grubin, A.N. and Vinogmdova, I.E. (1949), "Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces", Investigation of the Contact Machine Components, Kh. F. Ketova, ed.. Translation of Russian bdok No. 30,Central Scientific Institute for Technology and Mechanical Engineering, Chapter 2. Hamrock, BJ. and Dowson, D. (1977). "Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 111- Fully Flooded Results", J. Lubr. Technology, Vol. 99,No. 2,264-276.

Figure 1

Harris, T.A. (1991). "Rolling Bearing Analysis", Third Edition, John Wiley & Sons, Inc. 9. Smith, F.W. (1958-59)."Lubricant Behimiour in Concentrated Contact Systems - The Castor Oil-Steel System", Wear, Vol. 2, 250-263. 10. Jacobson, Bo (1970), "On the Lubrication of Heavily Loaded Spherical Surfaces Considering Surface Deformations and Solidification of the Lubricant". Acta Polytechnica Scandinavica, Mech. Eng. Series No. 54,Stockholm. 11. Jacobson, Bo (1991). "Rheology and Elastohydrodynamic Lubrication", Tribology Series 19,Elsevier. 12. Cann, P. et al. (1994), "The Lambda Ratio A Critical Reexamination", Wear, 175, 177188. 8.

Theoretical height function and pressure field The broken line surrounds the solidified region.

559

Figure 2

Photograph of the fust high pressure chamber.

Figure 3

Photograph of the second high pressure chamber.

-

560

EHk contact

Mo

micro-EHL

Figure 4

EHL contact with asperities of different slope.

Figure 5

Asperities flattened and reemerging during the transport through the contact.

56 1

View A-A Figure 6

Drawing of the test apparatus.

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

563

Elastohydrodynamic films with emulsions Yoshitsugu Kimura, Kazumi Okada and Wenyi Liu Institute of In dustrial Science, University of Tokyo 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

Emulsions, when u sed as the lubricant, form ehl films having a minimum thickness different from the prediction from their bulk viscosity. This behavior originates from the much larger particle diameter of the dispersed phase than the ehl film thickness they form. The present paper undertakes to present a unified view about the behavior of O N and W/O emulsions by analysis employing a two-phase hydrodynamic film model accompanied with a theory of trapping of oil particles by the lipophilic surfaces with O/W emulsions.

1. INTRODUCTION

Emulsions often exist as the third body between metal surfaces in contact. Oil-in-water ( O W )emulsions are widely used as the lubricant in plastic forming or as the hydraulic fluid in oil-hydraulic systems. Waterin-oil (W/O) emulsions are also used as the hydraulic fluid on one hand, while they are unintentionally formed when lubricants are contaminated with water on the other. In rolling contact, it has been noted that emulsions form ehl films having a minimum thickness much different from the prediction based on their bulk viscosity. Oil-in-water emulsions of several percent in oil concentration have a viscosity which is not so much higher than that of water, but they often form thick ehl films almost comparable with those formed with oil alone, i.e. neat oil, at least over a certain rolling speed range [ 1-81. Inclusion of water as the dispersed phase in W/O emulsions increases the viscosity of oils. However, results of measurements of ehl film thicknesses with W/O emulsions have been confusing; in some experiments they formed thicker films, and in others they formed thinner films than neat oil [9-131.

The primary reason for this apparent contradiction can be found in the size of the dispersed particles relative to the thickness of ehl film they form. In many applications, emulsions having a mean particle diameter of several micrometers are used to form ehl films with a central film thickness of some tenths of micrometer. In those cases, an ehl film can no longer be considered as a single-phase continuum to be characterized by its bulk viscosity, but should be considered as a two-phase film in which the viscosity of the two phases must be treated individually. With O/W emulsions, analysis was made by Kimura and Okada based 011 their 'trapping' model [3-41. That is, when an oil particle was introduced to an inlet region, it clogged the clearance at a point where the film thickness was equal to the particle diameter. If the solid surfaces were lipophilic, the particle was trapped there and, on approaching the center of the conjunction, hydrophobicity of the surfaces excluded the water from the film with the decrease in its thickness, resulting in an increase of the oil concentration. Only the mean particle diameter was used for the calculation, and the point where the oil concentration became unity was taken as the inlet pressure boundary by simply ignoring the viscosity of

564

water. Then the film thickness was predicted by the use of a starved ehl theory. This concept was later employed by Wilson et al. [14-161 in their dynamic concentration model. With W/O emulsions, Liu, Dong, Kirnura and Okada proposed a two-phase hydrodynamic film model [ 131. It claimed that large water particles introduced between solid surfaces formed water patches in which local viscosity was represented by that of water. The remainder of the film was composed of oil as the continuous phase which still carried small water particles. These two parts of an ehl film possess their own viscosities and, through the use of a concept of 'equivalent viscosity', analysis was made of the film thickness. The present paper summarizes these analyses and presents a model with which unified analysis is possible of ehl film thickness with O W and W/O emulsions in pure rolling line contact.

2. TWO-PHASE HYDRODYNAMIC FILM MODEL

W/O emulsion. Then a certain part of the film is occupied by 'large' particles, which form 'patches', and its remaining part is an emulsion composed of the continuous phase suspending 'small' particles. Local viscosity at any point q,(x.Z) in the film takes either of the two values: the bulk viscosity of the dispersed phase in the patches, or that of the emulsion containing the small particles outside the patches. A number of formulae have been proposed for the bulk viscosity of emulsions. Many of them are based on an assumption that the particles of the dispersed phase are approximated by rigid spheres. This causes the viscosity to increase with the concentration of the dispersed phase, but in different manners depending on the formulae. In what follows, the formula proposed by Brinkman [ 171

11

qc

=

(1 -

will be used, which showed reasonable agreement with experimental determination [In]. In eqn.(l),

Figure 1 gives a concept of an ehl film with an emulsion in line contact, in which the x-axis is taken in the direction of rolling and the z-axis parallel to the rolling axis. The diameters of the particles of the dispersed phase have a certain distribution, as illustrated in Fig.2 for a

r is the

- approximation by eqn.(7) 0

.I

3 0.6 o'8

experimental data

t

f

Patch

c X

7 Particle

1

Ehi film

Fig. I . Concept of two-phase hydrodynamic film.

10

100

Diameter of particles, pm Fig. 2. The distribution function for particle diameter of a W/O emulsion.

565

viscosity of an emulsion, q c the viscosity of the continuous phase and 4 the volume concentration of the dispersed phase, 4 being that of the small particles outside the patches in the present context. It should be noted here that inclusion of oil in O/W emulsions increases the viscosity of the film, no matter whether it forms patches or is suspended in water outside the patches. On t h e contrary, in W/O emulsions, the presence of water as the 'large' particles tends to reduce the viscosity of the film, while the suspended 'small' particles of water increases it. Let us examine the local viscosity more quantitatively. First, the atmospheric viscosity in the patches can be assumed constant being given by that of the dispersed phase if the insignificant effect of interface tension is ignored. However, the viscosity outside the patches needs analysis. The fraction that the patches occupy in a unit area of a film is determined by the emulsion concentration and the distribution of particle diameters. However, the critical diameter to classify the 'large' and 'small' particles is, hypothetically, given by the local film thickness and, since the film thickness varies in an ehl film typically in its inlet region, it is a function of x. Then the fractional area of the patches and therefore the concentration of the 'small' particles outside the patches become a function of x , and so does the local atmospheric viscosity outside the patches as well. This means that the change in the viscosity with film thickness, in addition to that with pressure, has to be taken into account in an ehl calculation.

Continuous phase

Patch

Z

hi

Fig. 3. An element of ehl film.

viscosity. A calculation would become much simpler if an equivalent viscosity

v,

is defined a s a

d e t e r m i n i s t i c f u n c t i o n of t h e c o o r d i n a t e x . Determination of the equivalent viscosity is then made by the use of the average flow concept after Patir and Cheng [ 181. As Fig.3 shows, a small element of an ehl film d r k is considered, which is large enough to assume a number of patches in it, but is small enough to assume a constant film thickness h as well as a constant film composition over it. Properties of the emulsion, i.e. the viscosity of the dispersed and continuous phases, the volume concentration of the dispersed phase and distribution of its particle diameter, and film thickness are assumed for the element. Then the patches are randomly arranged in the element, and two values of the local viscosities are given in and outside the patches. The element is covered with a grid, and either of the two values of rl,is assigned to each nodal point. The Reynolds equation for a constant film thickness

3. EQUIVALENT VISCOSITY

In principle, a full ehl calculation could be made by the use of the local viscosity q,. However, it should be noted that the position of the patches in an ehl film is a random, time-varying variable, and so is the local

is rewritten in a finite difference form. In eqn.(2),p is the pressure.

566 As the boundary conditions, a small pressure

difference is assumed across the element in the xdirection, and dp/dZ= 0 is assumed at the sides parallel to the x-axis. Then the Reynolds equation is numerically solved t o determine the pressure distribution within the element, an example of which is shown in Fig.4. The average flow rate in the x-direction for a unit width is given by the left-hand side of the equation,

(3)

For larger fractional areas of the patches, it becomes difficult to locate them in an element. In those cases, calculation can be made by inverting ‘figure’ and ‘matrix’, since it has been found that results are not affected by the configuration of the patches if kept isotropic. The numerical procedure so far described is repeated by randomly relocating the patches in the element in a Monte-Carlo principle to obtain a reliable value for the equivalent viscosity in each case. Figure 5(a) shows an example with O/W emulsions of the equivalent viscosity relative to the atmospheric viscosity of neat oil plotted against 4 and <; total volume fraction of the oil phase and

4 is the

5 the partial

volume fraction of the oil phase in the small particles If on the right-hand side is the average pressure in the element, ’I, represents the equivalent viscosity, which gives the same average flow rate in the x direction through a hypothetical single-phase film element having the same geometry under the same boundary conditions with respect to the pressure.

PI

4.00

2.00

1 .00

Fig. 4. Example of the pressure distribution in an element. The ratio of viscosity of the emulsion outside the patches to that of the patches is 60:l.

Fig. 5. Relative viscosity versus concentration of dispersed phase 4 and volume fraction of small particles 5 (viscosity of base oil = 1.0). (a) O W emulsions, (b) W/O emulsions.

567

suspended in the water phase outside the patches. The equivalent viscosity increases with the increase in $, almost independent of

5 at least in the range of the

volume concentration of oil from 0.1 to 0.4. With W/ O emulsions, Fig.S(b), the equivalent viscosity decreases for lower

<

5 values, while it increases for

higher values with the increase in the volume fraction ol water

4. The limiting case

<=1.0 gives the bulk

viscosity of the emulsion following eqn.(l).

4. CONCENTRATION OF OIL PHASE IN O/W

EMULSION

In the presence of most commercial non-ionic emulsifying agents, steel surfaces tend to be lipophilic and hydrophobic, or equally lipophilic and hydrophilic. In the former case, selective entrainment of oil occurs at the inlet region leading to an increase in the concentration of oil above its initial value. With O N emulsions,this phenomenon was analyzed in a couple of earlier papers [3-41 as the process of 'trapping' of oil particles as briefly described in Section 1. The two-phase hydrodynamic film model makes it possible to describe the concentration process in more detail and the building up of the pressure more accurately. In the context of the two-phase hydrodynamic film model, the trapping means that the patches are, once they are formed, fixed between the solid surfaces. Since the distribution of the particle diameter is taken into account, the position, or thex-coordinate, at which the trapping takes place is not uniquely defined any more. The trapping occurs one particle after another; in an inlet region, a larger particle is trapped earlier, or farther from the center of a conjunction, and a smaller particle is trapped later, or closer to the center. On approaching the center of the conjunction the film

thickness decreases. Then the continuity of flow requires exclusion of a part of the film from the clearance between the solid surfaces in the form of a reverse flow. As !he result of the trapping, the patches cannot move relative to the surfaces, and therefore the continuous phase must be excluded. In the earlier theory [3-41, what is excluded was assumed to be water, but the continuous phase to be excluded is an emulsion in the present model. Further, since the trapping is progressively occurring with particles of gradually decreasing sizes, the volume fraction of oil in the continuous phase changes along the x-coordinate. Figure 6 gives a change in the composition of a film in the inlet region with a small decrease in the film thickness from h to h-dh. Let us assume the volume fraction of the trapped oil patches is v l , that of small oil particles suspended in the continuous phase is V3 and that of water is v, . A decrease in the film thickness by dh excludes an emulsion with the volume fraction

. "

Vs + Vw

, while causes a part of the suspended oil

particles,

to be newly trapped. From the continuity,

we have

I,

Fig. 6. Change in the composition of a film with a decrease in the film thickness from h to h-ph.. Volume fractions, vl, v l : oil pa!ches, v,, v x , vs: oil in the continuous phase, v,,, v,,, v,,: water.

568

w

,

v,

.

1.2

v,.

- v -~ -

v*

+

I

(4)

B

"I A

If we denote the volume fractions of oil and water in the film by dh)and W(h)=l-dh),respectively, and the volume fraction of the small particles in the oil phase by f,(h)=#(h)t;(h), all being a function of the film thickness h, eqn.(4) is rewritten as

oil 40 vol.% oil 20 vol.% oil 10 vol.% oil 5 vol.%

0.5

0.0

1.0

Dimensionless film thickness, Fig. 7. Changes in volume fraction of oil with film thickness in O W emulsions. Dimensionless mean The dimensionless particle diameter is 0.504 X particlc diameters are the ratios to the reduced radius of the rollers.

(5)

On rearranging, we have a differential equation,

where the prime indicates the derivative with respect to h, and dh)is the distribution function of the particle diameter. Further, if dh) is approximated by a Weibull function,

Numerical integration of eqn.(8) gives the change in the total volume fraction of the oil phase in an ehl film with decreasing film thickness; examples are shown in Fig.7 where the film thickness is given as the ratio to the reduced radius of the rollers. With W/O emulsions, exclusion of the dispersed water seems less likely than with O/W emulsions because of the higher viscosity of the surrounding oil phase. Some effect can be seen in a comparison with the experimental data, but detailed analysis is yet to be made.

5 . FULL ELASTOHYDRODYNAMICSOLUTIONS 5.1 Viscosity

where A and E are numerical constants to be determined experimentally,eqn.(6) is reduced to

The particular feature of the present theory consists in the inclusion of the variation of the equivalent viscosity due to the change in the composition of twophase films, in addition to the change caused by the increase in pressure as in the usual cases. To cope with this additional complexity, nuinerical calculation

569 is conducted by using a multigrid technique [19-211. Eight levels of grids are employed to cover an ehl conjunction. The first level has 26 nodes; the number of the grid mesh is doubled on each successive level and, on the eighth level, the number of the nodes becomes 3201. With O W emulsions, the equivalent viscosity is little affected by as shown in Fig.S(a), and those values for c=O are used for the present calculation. On the other hand, only limited data are available for their viscosity-pressure coefficient. A measurement of highpressure viscosity of O W emulsions on a rollingsphere viscometer gave viscosity -pressure coefficients which continuously increased from almost nil for water to a value for pure oil [22]. However, the same viscosity-pressure coefficient as that of oil is tentatively employed for the convenience of calculation, because contribution of the continuous phase to the pressure build-up can be practically ignored. With W/O emulsions, the effect of lipophilic surfaces to exclude water phase is ignored, and the equivalent atmospheric viscosity is calculated for a constant water concentration 4 throughout a conjunction. The values of the relative viscosity obtained by the numerical calculation for a constant 4 can be approximated with sufficient accuracy by a quadratic function, q , = a t 2 + bl; + c

under which experiments were made (3-4,6, 131. Ehl films are made between steel rollers of 40 mm in diameter at a pure rolling speed of 3.14 ms-' under a mean Hertzian pressure of 0.9 GPa. The oil is paraffinic mineral oil with atmospheric viscosity of Pa s and viscosity-pressure coefficient of 49.3 x

17.7 GPa-l at 40 "C. All emulsions are prepared with non-ionic surfactants as the emulsifier. 5.3 Results

Figure 8 shows an example of the results for an O/ W emulsion, in which changes in the dimensionless pressure, the dimensionless film thickness, the concentration of oil phase and the equivalent viscosity are plotted against the x-coordinate. The change in the concentration of the oil phase, and that in the equivalent viscosity, are found taking place over a rather confined zone in the inlet region, and the pressure starts to increase just before the concentration is completed. In some cases, the concentration of the oil phase levels off at a certain value less than unity, and the effective viscosity also remains less than unity.

(9)

Measurement of high-pressure viscosity of W/O emulsions up to 0.2 GPa was made by the present authors on the rolling-sphere viscometer, which showed that the viscosity-pressure coefficient of W/O emulsions was little different from that of oil [ 131. Thus a viscosity-pressure coefficient of oil is used for the calculation for W/O emulsions. 5.2 Conditions Calculation is conducted for the following conditions

-6

-4

-2

2

0

Dimensionless coordinate

x

Fig. 8. An example of the calculated results for O/W emulsions. Dimensionless quantity: X=x/b, H=(lz/R)(x/8w),P=(p/E)(2x/~)'~ where b is the half Hertzian contact length, R the reduced radius of the rollers, w the load on unit width, and E the effective elastic modulus. Dimensionless mean particle diameter (ratio to R) is 0.504X 10".

570 0.6

-prediction by the present theory expermental data -prediction with bulk viscosity

E 5

m

vl

0.4

/

Y

-

.-uc

-

-E c E 0.2

2

.-CC .2

in the small particles suspended in the oil phase outside the patches and the equivalent viscosity against the xcoordinate. Also with W/O emulsions, the general shapes of the pressure and film thickness profiles seem much alike to those with neat oil. However, decrease in the fraction of the small particles due to successive formation of the patches is clearly shown in the inlet region, and is accompanying decrease in the equivalent viscosity as well. Figure 11 compares the minimum film thickness for W/O emulsions with different water concentrations between experimental data, a prediction by the present theory and a prediction based on the bulk viscosity of the emulsions. With the increase in the bulk viscosity with the water concentration, the prediction based on it increases. Making a contrast, the experimental results and the prediction by the present theory agree reasonably in showing a slight decrease in the film thickness with increasing water concentration.

h

0

1

10

50

Initial oil concentration, vol.% Fig. 9. The minimum ehl film thickness with O/W emulsions. Mean particle diameter is 5.04 pm. They must change further at the exit constriction of the film, but this effect is ignored here. The general features of the pressure and film thickness profiles are common to those with neat oil. A change in the minimum film thickness with the initial oil concentration of O/W emulsions is compared in Fig.9 between experimental data [3-41, a result of the present theory and a prediction based on the bulk viscosity of the emulsion. It is evident that the data fall close to the curve for the present theory, which gives much larger film thickness than the prediction based on the bulk viscosity. It should be mentioned that Fig.!, represents a case in which perfect 'trapping' takes place. With different emulsifying agents, experimental data can fall on a curve which is the curve for the present theory horizontally shifted to the right. Since the abscissa is plotted on a logarithmic scale, this means that the emulsions behaved as if their bulk concentrations were reduced by a certain factor. In other words, oil particles were trapped with a certain probability, termed 'trapping probability' [3-4,6]. With W/Oemulsions, plotted in Fig.10 are changes in the dimensionless pressure, the dimensionless film thickness, the partial volume fraction of the water phase

6. CONCLUSIONS

The present paper undertakes to present a unified 3

0

2

r' 0:

5 n -6

-4

-2

0

2

Dimensionless coordinate X

Fig. 10. An example of the calculated results for

W/O emulsions. Definitions of the dimensionless quantities X, H and P are common to Fig.8. Dimensionless mean particle diameter (ratio to R) is 2.30 X 10'.

57 1

1.5

prediction of ehl film thickness close to experimental results.

- prediction with bulk viscosity

E

5 0

expermental data

v)

2 1.0 Y .-u

REFERENCES

s E c

1. T. A. DOW,CASA SME Technical Paper, MS77-

2 0.5

.-E .-c

r: 0.01 0

'

, I . , . . I , . , . I . . . , l 10

20

30

40

Water concentration, vol.% Fig. 11. The minimum ehl film thickness with W/O emulsions. Mean particle diameter is 2.30-19.6 vm.

view about the behavior of O/W and W/O emulsions as the third body by analysis employing a two-phase

hydrodynamic film model, which is accompanied with a theory of trapping of oil particles by lipophilic surfaces with O N emulsions. Taking the distribution of the particle diameter into account, this model assumes that the particles having diameters larger than the local film thickness occupy some part of a film by themselves forming the patches, while the remaining part of the film is emulsion composed of the continuous phase with suspended particles of the dispersed phase having diameters less than the local film thickness. The local viscosity in the film is assumed to take either of the two values: that of the dispersed phase in the patches, or that of the emulsions containing small particles outside the patches. Numerical solution of the Reynolds equation for a small element in which the patches are randomly arranged gives an equivalent viscosity so that a hypothetical single-phase element with that equivalent viscosity results in the same flow across the element. The full elastohydrodynamic solution using this equivalent viscosity, while also considering the trapping of oil particles with O/W emulsions, leads to

339 (1977). 2. Y. Sakaguchi and W. R. D. Wilson, Proc. 5th Conf. on Plastic Working (1984) 457 (in Japanese). 3. Y. Kimura and K. Okada, Proc. JSLE Intern. Tribol. Conf., Tokyo (1985) 937. 4. Y. Kimura and K. Okada, Proc. IMechE,Tribology Friction, Lubrication and Wear Fifty Years On (1987) 85. 5. T. Nakahara, T. Makino and K. Kyogoku, ASME J. Tribol., 110 (1988) 348. 6. Y. Kimura and K. Okada, Tribol. Trans., 32 (1989) 524. 7. D. C. Barker, G. J. Johnston and H. A. Spikes, Proc. 18th Leeds-Lyon Symp. Tribol. (1992) 493. 8. D. Zhu, G. Biresaw, S. J. Clark and T. J. Kasun, ASME J. Tribol., 116 (1994) 310. 9. H. Hamaguchi, H. A. Spikes and A. Cameron, Wear, 43 (1977) 17. 10. G. Dalmaz and M. Godet, Trans. ASME J. Lub. Tech., 100 (1978) 304. 11. G. Dalmaz, Proc. 7th Leeds-Lyon Symp. Tribol. (1981) 231. 12. G. T. Y. Wang, P. Kenny and H. A. Spikes, Tribol. Int., 17, (1984) 309. 13. W. Liu, D. Dong, Y. Kimura and K. Okada, Wear, 179 (1994) 17. 14. W. R. D. Wilson, Y. Sakaguchi and S. R. Schmid, Wear, 161(1993) 207. 15. S. R. Schmid and W. R. D. Wilson, Tribol. Trans., 38 (1995) 452. 16. S. R. Schmid and W. R. D. Wilson, STLE Prep. 95-AM-8D-2 (1 995). 17. H. C. Brinkman, J. Chem. Phys., 20 (1952) 571.

572

18. N. Palir and Cheng, H. S., ASME J. Lub. Tech., 100 (1978) 12. 19. C. H. Venner, Ph.D. Thesis, University of Twente (1991). 20. C. H. Venner, W. E. ten Nape1 and R. Bosma, ASME J. Tribol., 112 (1990) 426.

21. S. Natsumeda, J. JAST, 39 (1994) 951 (in Japanese); to be published in Jpn. J. Tribol, 39, in

English. 22. S. Asanabe, Y . Tozaki, S. Matsumoto and M. Fukutomi, Prep. JSLE National Meeting, Nagoya (1986) 337 (in Japanese).

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

573

Understanding grease lubrication P.M.E. Cann,

Tribology Section, Department of Mechanical Engineering Imperial College of Science, Technology & Medicine, London SW7 2BX, UK. Grease lubrication remains a scientifically neglected area of tribology as, in contrast, to fluid film lubrication there has been little progress in our understanding in recent years. At present we know little of the mechanisms of film formation, and loss, and the nature of the separating film formed. There is no satisfactory model for greases and thus it is impossible to predict performance, or service life, from simple bulk rheological properties. The aim of this paper is to clarify the mechanisms of film formation by greases in rolling elastohydrodynamic (EHD) contacts. Thus existing lubrication models are reviewed and compared to experimental fmdings and, in the light of this, more recent work being carried out in the Tribology Section is reported. These studies have concentrated on fundamental aspects of grease behaviour in a model bearing contact and have sought to explain the lubrication mechanisms and nature of the film formed. The different film formation mechanisms observed in this work are discussed. Evidence of both hydrodynamic and boundary layer formation is presented and the implications of the Merent mechanisms of load carrying considered. 1. INTRODUCTION

The last thirty years have seen considerable advances in many areas of tribology. One exception to this is grease lubrication; a maverick in an otherwise well ordered tribology world. In comparison to fluid film lubrication, we have no detailed knowledge of the mechanisms of film formation or loss and their relationship to bulk grease properties. The lack of a satisfactory model means that it is impossible to predict lubricating performance accurately for any given application. There are general rules of thumb accumulated over the years, the NLGI gtade, thickener type, base oil viscosity and type, but these can only provide a rough guide to grease performance. Almost, inevitably, the only real way of detenniniq? grease suitability is by application testing, which is a costly and lengthy business. This is particularly true for rolling element bearings where over 90% are grease lubricated, yet there is still no simple method for screening grease performance apart from full bearing tests.

The question of grease performance in bearings is an important one as their premature failure is often attributed to lubrication breakdown. With the current drive towards "infiite" bearing life it becomes increasingly important that grease performance should match that of the engineering components or, at least, to be able to include lubrication performance, accurately, in the life prediction models. We need to understand the physical mechanisms controlling grease film formation before we can begin to develop predictive models. The problem is a complex one. Greases are two-phase lubricants composed of a thickener which is physically dispersed in a base oil. The thickener is usually soap or polymer fibres, which may vary in size from 1 to 100 microns, or dispersions of small (- micron) particles. Greases therefore have a matrix structure; the scale of which can vary from simple particle interaction to the formation of extended fibre networks.

574

Thus, neither the structure nor the chemical composition are uniform when compared to the scale of an EHD contact. The theological properties of greases are also complex and dependent on both the shear rate and the duration of shearing (1). At low shear rates grease behaves as a plastic solid and does not flow until a critical yield stress has been reached. This has significant implications for the ability of the grease to flow mund and, hence, replenish the rolling track. As a result the EHD contact is often starved of bulk lubricant. Whilst at high shear rates grease suffers irreversible viscosity loss due to the breakdown of the physical matrix. The complex theology and local variations in the composition of greases means that it is difficult to develop a model to describe their behaviour in an EHD contact. At present it is impossible to specify the viscosity or composition of the lubricant entering the contact, nor define the supply condition; thus it is impossible to predict the nature or thickness of the ensuing lubricating film. The aim of this paper is to clarify our current understanding of grease lubrication mechanisms and the nature of the film formed. Earlier work, both experimental and theoretical, is reviewed and, in the light of this, new results are presented. Grease behaviour and film formation in a starved contact has been studied visually using a modified form of optical interferometry. The images taken of the grease EHD films are transformed into film thickness maps showing the distribution in the contact. Evidence of both hydrodynamic and boundary layer formation is presented and the implications of the Merent mechanisms of load carrying discussed. 2. GREASE LUBRICATION OF EHD CONTACTS

Fundamental studies of grease lubrication have been mainly concerned with the measurement of film thickness or traction in model bearing contacts (3)-(13)(16)(21)-(23) and the development of empirical descriptions of grease theology (1)(14). The results from this work have been used to develop, and verify, the existing EHD grease models (16)-(20).

2.1. Experimental Studies of Grease Behaviour It is the work from the model bearing contacts, usually twin disc (3)(4)(5) or ball-on-plate devices (2)(6), that provides us with the most direct information on the EHD behaviour of greases. In the latter configuration a steel ball is loaded, and rolled, against a glass disc. Optical interferometry (2)(4)(6)-(12) is used to measure EHD film thickness and, simultaneously, to observe grease flow close to the contact (11). This work has shown that, initially, the EHD films are much thicker than for the base oil. This is due to fresh grease being entrained into the contact and very large thickener clumps have been observed (13) during the fvst few seconds of rolling, These structures locally distort the film and are thought produce local pressure variations in the contact (13). As the test proceeds grease is pushed aside by the ovemlling of the ball and does not readily flow back to replenish the track (5)(10). This can result in progressive bulk starvation of the inlet, and a significant drop in film thickness (8)(10)(22), unless the supply is maintained by an external mechanism. If replenishment is externally maintained then film thickness depends on the effective grease viscosity in the inlet and degree of starvation (12). In a bearing there is no such mechanism to continually force grease into the rolling track. It is the supply and film formation mechanisms which occur, therefore, in the absence of external redistribution of the grease which are important. In experiments where the grease supply is not maintained the film thickness is both time (8)(22) and test condition dependent (21)(23). With continued rolling, at constant speed, the film thickness drops as the inlet is progressively starved. After extended running an equilibrium film thickness is usually reached (4)(21). This would suggest that a flow balance, of lubricant lost from the rolling track and locally resupplied from the grease reservoir, has been achieved. At low temperatures the film thickness is often much less than that given by the base oil under equivalent test conditions (4)(23). At higher temperatures the grease film can greatly exceed that of the base oil (23) suggesting that the resupply is more effkient and that both base oil and thickener are contributing to film formation. One of the problems in this work is that the grease films formed under bulk starved conditions

575

are usually very thin, often less than 80 nm (8)(23), and this has proved difficult to study experimentally. As yet we have little information on the composition of such films. The experimental work has demonstrated the complexity of the grease lubrication problem, even in a simple model contact. It has signified the importance of the inlet supply condition, which results from the operating conditions and grease rheological properties, in controlling film thickness. If grease flow into the contact is maintained a thick film composed of base oil and thickener is formed. Under bulk starved conditions the films are much thinner. There is also little direct evidence as to the nature and properties of the lubricating films and the way in which these depend on the formation mechanisms. 2.2. Models of Grease Lubrication in Rolling

Contacts It has proved difficult to incorporate such observations into a generic model for grease lubrication. Several film formation mechanisms have been offered for greases in both model and bearing contacts. The problem remains one of defining the supply mechanisms and the nature of the lubricant. Models have been suggested which encompass both the ‘continued flow’ and ‘starved’ behaviour observed in the experimental work. At present the only predictive models that have been developed are based upon fully flooded EHD theory. One of the first papers to formulate such a model was published by Kauzlarich and Greenwood (16). This approach has subsequently been refrned by other workers (17)(20). Generally a classical fluid film EHD analysis is used combined with an empirical grease flow equation. The model assumes that both thickener and base oil flow into the contact (16)(17) and that the grease rheology can be described by a bulk flow curve. The rheological model is based on Herschel-Bulkley (15)(16)(17)(18)(20), Bauer (19) or Bingham (20). The models generally yield an expression relating grease film thickness to the rheological parameters (16). In its simplest form grease film thickness can be related to that of the base oil. Jonkisz and heminski-Freda (18) predict that grease films should be 1.5 times greater than that of the base oil for the fully flooded condition. In the

starved condition a value of 0.7 times is given. Dong and Qian (19) obtain values of between 1 and 2 in their analysis. The results from these models have been compared to experimental film thickness measurements with limited success (15)(16). There are problems, however, in the accuracy of the experimental measurements as the limited sensitivity of the techniques used makes exact comparison difficult. The ‘full flow’ approach does not, explicitly, offer a physical mechanism for grease lubrication however the assumptions inherent to the model have implications for the supply condition and the nature of the film formed. There are two main assumptions in these models; firsty that ‘whole’ grease, containing both thickener and base oil, flows into the inlet. Thus the grease behaviour in the inlet can be predicted from a bulk flow equation. The grease is therefore considered to be a continuum, on all scales, when compared to the EHD contact. There is, however, evidence that large thickener structures survive the inlet and pass into the contact (13). It is therefore not possible to take an average bulk viscosity for a grease and use this as representative of lubricant consistency in the inlet. This assumption also has implications for the nature of the film formed. The grease structure will be partially degraded by passage through the inlet. Within the contact the very high local stresses will continue to break the structure down to form particles dispersed in the base oil. In the EHD grease models only bulk viscosity and hence hydrodynamic film formation is considered and thus ignoring any solid film contribution from the thickener. The second assumption is that the inlet is continually supplied with grease, thus the model is not valid for the heavily starved condition. In later papers (19)(20) starvation parameters have also been included in the models. Although the degree of starvation assumed is not very severe. The “full flow” approach is the only tool available at present for the prediction of grease film thickness in rolling contacts. However there are other physical models describing mechanisms of film formation where there is reduced, or negligible grease flow, into the contact.. Perhaps the most widely accepted view of grease behaviour in a bearing is that it acts as a

576 reservoir releasing oil into the rolled track (25). Thus the ability of a grease to bleed oil is often taken as a guide to lubricating performance (26). This model implies that the lubricant film is composed of base oil alone and that its thickness is determined by the base oil properties and the efficiency of supply. There is little direct evidence, however, for the 'oil bleed' mechanism and Scarlett (27) in his review prefers an alternate mechanism of a high viscosity layer retained within the rolling track. The lubricant film is formed of highly degraded grease which is deposited in the fust few minutes of operation. Excess grease is pushed away from the rolling track and forms a close fitting seal to prevent lubricant loss. The dominant factor controlling grease film formation, is the mechanism of lubricant supply to the contact. The nature of the material supplied and the efficiency of the process will determine the thickness and composition of the film formed. It is these aspects which have been studied further in the experimental work reported below. 3. EXPERIMENTAL WORK & RESULTS

Grease lubrication in a rolling contact has been studied through the observation of inlet supply mechanisms and measurement of the resulting film thickness and distribution within the contact. The grease is applied as a single charge to the rolling track and there is no attempt to push fresh grease into the track. This represents, perhaps, the most severe condition for assessing grease lubrication of the contact. Flow of lubricant, and hence film formation, is now a spontaneous response due to primary contact conditions (speed, temperature, geometry) and grease rheological properties. The model contact is formed by a steel ball loaded and rolling against a glass disc. A video camera is mounted on a microscope which is positioned above the contact and this records grease flow and EHD film thickness. Film thickness is measured by a modified optical interferometry technique that is described in reference (24). A silica spacer layer is used, in conjunction with the chromium, to give enhanced visualisation and measurement of films within the contact. It provides a map of film thickness variation within

the contact with a resolution of 5 nm. This sensitivity is necessary to measure the very thin films formed by a grease under starved flow conditions. The spatial resolution is 3pm. Using this technique, therefore, it is possible to observe the contact supply condition and map the resulting EHD film formed. 3.1 Grease Behaviour in Rolling Contacts

Figures 1-4 show images taken from a grease lubricated contact with the inlet on the right. The colour variations within the contact show differences in film thickness. The grease used was a commercial lithium hydroxystearate with a mineral base oil (viscosity 46 cSt (@ 40°C). Figure 1 is an image taken from a slow speed flooded contact, the bulk grease meniscus can be seen in the inlet. This was taken at the start of the test when fresh grease is still being ovemlled in the track. A very thick film (200-300 nm)is formed in the contact. The local colour variations c o n f i i that this is not a 'classical' fluid EHD film and that it is comprised of thickener and oil. Large thickener clumps can thus survive passage through the inlet region and enter the contact. The high shear stresses within the contact break these structures down depositing them in the track which is seen in the exit region. At higher speeds, or as the test proceeds, the bulk grease moves away from the track and the contact is severely starved. Figures 2-4 show a series of images taken from a test carried out at 0.1 m/s. These images correspond to the start, 10 and 20 minutes running time. The corresponding film thickness profiles are plotted along the centre line, parallel and transverse to the rolling direction, in Figures 5 and 6 respectively. Figure 2 was taken just after the start of the test, after the fmt few revolutions. The bulk of the grease has already moved to the side of the rolling track and the contact is effectively starved. As the test proceeds the film within the contact continues to breakdown (colour changes from yellow to blue) and the distribution changes. The supply condition also changes as the test proceeds (Figure 3). There is more free oil available close to the contact (23). The consistency of the grease also changes as the structure breaks down due to repeated ovemlling. Thus there is evidence of improved lubricant availability (Figure 4) to the sides of the contact at

577

the end of the test. Here the film in the centre of the contact is very thin, typically 15-25 nm. At the edge however there is local flow of lubricant into the contact as indicated by the &/oil meniscus. This supply is intermittent and appears to be determined by the amount of lubricant locally available. One observation from these tests is that when rolling is stopped liquid lubricant gathers around the contact reforming a meniscus in the rolled track (11)(23). IR analysis (22) has established that this is mainly base oil very little thickener is present. It is possible that this provides a second, continual, replenishment mechanism; that of flow of oil into the track due to local capillary forces around the contact (11).

film formed during the test. An example is shown in Figure 7 where the static profile is compared to the film formed during rolling. The results confirm that most of the film in the centre of the contact is a solid deposited layer which maintains separation even when static. To the sides of the contact this is augmented by hydrodynamic film formation. Further evidence as to the nature of the film is provided by optical microscopic examination of the track and surrounding grease at the end of the test (22). For the grease used in these tests the film appears as finely divided particles or droplets 2-3 pm in diameter. The grease to the side of the track is heavily worked by the repeated passage of the ball and its large scale structure is degraded.

3.2. EHD Film Thickness Profiles The corresponding film thickness profiles are shown in Figures 5 and 6. Profile b corresponds to Figure 2, c: Figure 3 and d: Figure 4. The film profile for the fully flooded base oil case is also shown in profile a. In Figure 5 the profiles are taken along the centre line (x, y = 0) parallel to the direction of rolling. The inlet is again on the right hand side. Profile 5b, although heavily starved, has the features of a high viscosity EHD film with a pronounced exit restriction. This can also be seen in the side lobe formation in the corresponding transverse profile (6b). The film thickness is significantly larger than that of the base oil 5a and 6a. As the test proceeds this high viscosity film breaks down and the film shape approaches that of the static Hertzian contact. The load carrying is primarily by residual film of deposited thickener which is seen as a green band through the contact in Figure 3. Af€er 20 minutes running this localised band has broken down to give a fairly constant film of -20 nm over most of the contact. There is, however, evidence of localised EHD film formation to the side of the contact which is due to improved flow of lubricant from the grease (see Figure 4 and Figure 6d). This effect; the localised formation of an EHD film as a result of the inlet supply condition has also been observed in heavily starved fluid film contacts (30). Film profdes were also taken from the grease contact at the end of the test when rolling is stopped. These provide a measure of the residual

4. MECHANISMS OF GREASE LUBRICATION IN ROLLING CONTACTS

-

The results presented have demonstrated the complexity of the grease lubrication problem. Depending on the conditions; the mechanism of lubricant supply, the thickness and the composition of the resulting film, will all change throughout the test. It is interesting to compare these observations with the models offered by earlier workers. The current work shows that all three film formation mechanisms; full flow, high viscosity layer and oil bleed, can occur depending on the test duration and conditions. This is shown in a simple physical model in Figure 8. Initial overrolling of fresh grease entrains large thickener structures into the contact where they are physically degraded and deposited in the rolling track (Figure 8 top). Atter the fmt few passes the bulk inlet flow ceases. The separating film is now formed by a high viscosity layer that breaks down with successive overrolling. The thickener structures are thus further degraded releasing base oil, which is squeezed from the track leaving deposited thickener particles (22) (Figure 8 middle). Both the ‘full flow’ condition and the resulting high viscosity layer are only observed at the start of the test. As the test proceeds the film continues to break down reducing to a solid layer (Figure 8 bottom). The dominant lubricant supply is now from the sides of the contact. Two distinct supply mechanisms are suggested (23) under these conditions:

578

Figure 1 View of a Wly noodedgrease contact

Figure 5 Grease film thickness (x, y 4 ) : a: base oil, b: 1 minute, c: 10 minutes, d: 20 minutes

m

8

4

Figure 2 Starved grease film after running for 1 minute (b)

Contact position (pm)

Figure 6 Grease film thickness (x=O, y):a: base oil, b: 1 minute, c: 10 minutes, d: 20 minutes

Figure 3 After 10 minutes running (c)

Contact position (p)

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

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

~~

Figure 4 After 20 minutes running (d)

Figure 7 Comparison of rolling and static grease films (x=o, y)

579

high viscosity layer deposited in track

-

gellant lumps broken down by overrolling

residual film in centre of contact

bulk grcasc displaccd /to sidc of contact grease overrolled in track structure shear degraded released oil displaced from contact

I

\central film mainly gellant particles grcase worked by overrolling releases basc oil 1

’

,improved oil supply givcs hydrodynamic film Figure 8 Grease lubrication in a model bearing contact. (i) Intermittent flow of shear degraded grease driven by the overrolling action of the ball.

(ii) Continued flow of base oil from the grease into the track due to capillary action. The amount of oil available increases as test proceeds (23) due to progressive breakdown of the grease close to the track. Both these mechanisms are facilitated by shear degradation of the grease and increased operating temperatures (23). The improved lubricant availability contributes to the developing hydrodynamic film. The capillary mechanism highlights one aspect of grease lubrication that is often ignored; that of the surface chemistry. If replenishment is dependent on reflow of base oil close to the contact then this will be controlled by capillary and surface forces. Thus the surface properties of the bearing materials and the physical chemistry of the lubricant need to be considered. The grease lubricating film is therefore a residual layer of degraded thickener particles and, superimposed on this, a hydrodynamic film generated from fluid either supplied from the reservoir or retained in the track. Load canying is thus apportioned between the hydrodynamic film, at

the sides of the contact, and the residual surface film in the centre. Thus the problem of formation and maintenance of grease lubricating films is essentially one of flow balance. The prevailing loss and supply mechanisms can change with test condition and grease properties. Observation of grease behaviour in the glass disc experiments suggest that the important processes occur close to the contact. The scale of these effects therefore needs to considered and thus it is improbable that the oil flow, to the contact, occurs throughout the bulk grease. The role of the thickener in film formation is often disregarded. This work suggests that the thickener is deposited on the surfaces and plays an important role in load canying. There is supporting evidence for this observation from earlier work where soap thickeners have also been shown to have boundary lubrication properties in sliding (28) and journal bearing contacts (29). Polyurea greases also deposit thick films of transformed thickener in rolling contacts (31). Little is known of these deposited films; optical examination in this study suggests that they are composed of small particles with associated droplets of fluid. It is also possible that such films have another function apart from load canying and that is to help retain base oil in

580

the track which would otherwise be squeezed out during overrolling. The role of grease rheology in this model is difficult to quantify. Lubricant supply appears to be govcrned by the breakdown of the grease close to the track by repeated overrolling with the ball. The lubrication models assume that it is grease behaviour at the high shear rate conditions present in thc inlet which is important. This work would suggest that it is the grease structural breakdown at the relatively low shear stress levels to the side of the contact that determines lubricant replenishment. 5. CONCLUSIONS

This paper has sought to consolidate our existing knowledge of grcase lubrication mechanisms and to provide a framework for future studies. The main conclusions can be summarised as follows:

(i) Scale effects are important when considering grease supply mechanisms. The important processes occur close to the contact. The total film thickness is the result of a flow balance of lubricant. (ii) Two supply mechanisms havc been identified: (a) intermittent supply of grease pushed into the contact by the overrolling action of the ball (b) continued flow of oil into the track due to local capillary action (iii) Grease lubricating films have hydrodynamic and deposited thickener components. Load carrying in the ccntre is mainly due to the solid film which is augmented by the hydrodynamic film at the sides. (iv) The main oil supply is to the side of the contact where it generates the thickest EHD films in a similar way to starved fluid film lubrication (30). This has important implications for the lubrication of elliptical and near-line contacts.

This paper has been concerned with grease mechanisms in a model bearing contact. It remains to be seen if such ideas are valid for the more complex problem of grease lubrication in rolling element bearings.

REFERENCES Bauer, W.H., Finkelstein, A.P. & Wiberly, S.E.,“Flow Properties of Lithium StearateOil Model Greases as Functions of Soap Concentration and Temperature”,ASLE Trans., 3, pp 215-224, (1960). Wedeven, L., “Optical Measurements in Elastohydrodynamic Rolling-Contact Bearings.” PhD Thesis University of London, (1970). Kageyama, H., Machidori, W. & Moriuchi, T., “Grease lubrication in elastohydrodynamic contacts.”, NLGI Spokesman, June, pp 72-81, (1984). Poon, S.Y., “An Fxperimental Study of Grease in Elastohydrodynamic Lubrication.”,ASME Trans. J. Lub. Tech, 94F, pp 27-34, (1972). Aihara, S. and Dowson, D., “A Study of Film Thickness in Grease Lubricated Elastohydrodynamic Contacts.‘I, Proc. of the 5th LeedsLyon Symposium on Tribology, Paper 111 (v), pp 104-115, (1978). Palacios, J.M., Cameron, A. and Arizmendi, L., “Film thickness of Grease in Rolling Contacts.”,ASLE Trans., 24, pp 474-478, (1981). Kageyama, W., Machidori, W. and Moriuchi, T., “Grease Lubrication in Elastohydrodynamic Contacts.”NLGI Spokesman, 9,pp 72-80, (1984). Rasteger, F. and Winer, W.O., “On the Traction and Film Thickness Behavior of Grease in Concentrated Contact ”, NLGI Spokesman, 50, pp 162-174, (1986). Bordenet, L., Vergne, F., Chaomleffel, J-P. & Dalmaz, G., “A Study of Grease Film Thicknessesin Elastorheodynamic Rolling Point Contacts.”,Proc. 5th Int. Conf. Tribolom Ewtrib, 4, pp 133-137, (1992) Astr&im, H, Ostenson, J.O. & HOglund, E., “LubricatingGrease Replenishment in an Elastohydro-dynamic Point Contact ”,Paper 92-Trib-9. Astr&im,H.,Isaksson, 0. andHC)glund,E., “Video Recordings of an EHD Point Contact Lubricated With Grease.” Trib. Int., 24, pp 179-184, (1991).

58 1

Williamson, B.P., “An Optical Study of Grease Rheology in an Elastohydrodynamic Point Contact under Fully Flooded and Starvation Conditions.”, Proc. I.Mec. Eng. J. Eng. Trib. Part J, 209, pp 63-74, (1995). WstrOm, H.,. & Venner, C.H., “Soap thickener induced local pressure fluctuations in a grease lubricated EHD point contact”, Proc. I.Mec. Eng., J. Eng. Trib. Part J., 208, pp 19 1-1 98, (1 994) Bair, S., “TheHigh Pressure Rheology of a Soap-Thickened Grease.”,Trib. Trans . STLE,37, pp 646-650, (1994). Zhu, W.S. & Neng, Y.T., “A Theoretical and Fxperimental Study of EHL Lubricated With Grease.”,J. Tribol. ASME Trans., IJ, pp 38-43, (1988). Kauzlarich, J.J. & Greenwood, J.A., “ElastohydrodynamicLubrication with Herschel-BulkleyModel Greases”, ASLE Trans., l5,~ ~ 2 6 9 - 2 7(1972). 7, Jonkiss, W. & Krzeminski-Freda, H., “PressureDistribution and Shape of an Elastohydrodynamic Grease Film.”, Wear, 55, pp 81-89, (1979). Jonkiss, W. & Krzeminski-Freda, H., “The Properties of Elastohydrodynamic Grease Films.”, Wear,77,pp 277-285, (1982). Dong, M & Qian, X., “Theoryof EHD Grease Lubricated Line Contact Based on a Rejined Rheological Model.”, Trib. Int., pp 261-267, (1988). Cheng, J., “ElastohydrodynamicGrease Lubrication Theory and Numerical Solution in Line Contact.”, STLE Trib. Trans., 37, pp 71 1-718, (1994). Cann, P.M. and Spikes, H.A., “Film Thickness Measurements of Greases Under

a,

Normally Starved Conditions.”,NLGI Spokesman, 56, pp 2 1-3 1, ( 1992). Cann,P., “The Influence of 7emperature on the Lubrication Rehaviour of a Lithium Hydroxystearate Grease., Eurogrease, Jan/Feb, pp 25-32, (1995). Cann, P.M., “Starvationand Reflow in Grease Lubricated Elastohydrodynamic Contacts.” acccpted for publication Trib. Trans. STLE. Cann, P.M., Hutchinson, J. & Spikes, H.A. “The Development of a Spacer Layer Imaging Method (SLIM for Mapping Elastohydrodynamic Contacts”, accepted for presentation ASME/STLE Joint Conference Oct. (1 995). Booser, E.R.& Wilcock, D.F., Lub. Eng.,2, pp 140-143, 156-158, (1953). Baker, A.E., “GreaseBleeding - A Factor in Ball Bearing Performance.“,NLGI Spokesman, 22, pp 27 1-279, ( 1958). Scarlett, N.A., “[Jseof Grease in Rolling Bearings.“,Proc. IMecE. Part 3A,&l pp 167-171, (1967). Godfrey, D., “Friction of Grease and Grease Components during Boundary Lubrication”, J. Lub. ASLE Trans., pp 24-3 1, (1964). Horth, A.C., Sproule, L.W. & Pattendon, pp 155-161, W.C., NLGI Spokesman, 2, (1 968). Chevalier, F. C., Lubrecht, A.A., Cann, P.M.E., Colin, F. & Dalmaz, G., “Starvation phenomena in EHL point contacts: Influence of inletjlow distribution” Presented at the 22nd Leeds-Lyon Symposium, (1 995). Endo, T., “Recent Developments in Diurea Greases.”,NLGI Spokesman, 57, pp 532541, (1993).

z,

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SESSION XV SURFACE DEGRADATIONS

Chairman :

Professor Y 0shitsugu Kimura

Paper XV (i)

Smoothing Effect of the Third Body Compaction on Alumina Surface in Sliding Contact

Paper XV (ii)

Friction in Abrasion of Alumina Fibre and Silicon Carbide Particle Reinforced Aluminium

Paper XV (iii)

Adhered Film Formation on Steel Surface by Impingement of Hard Particles

Paper XV (iv)

The Wear Mechanism of Ductile Metals by Slurries : Fatigue or Ratchetting ?

Paper XV (v)

Surface Degradation and Third Body Formation in Tribocorrosion Systems

Paper XV (vi)

Modelling Fluid Interactions in Magnetic Fluid Grinding

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

585

Smoothing effect of the third body compaction on alumina surface in sliding contact K. Adachi a, K. Kato a and R. Takizawa a

a Laboratory of Tribology, School of Mechanical Engineering, Tohoku University, Sendai 980-77,Japan The effect of fine wear particles as the third body on surface smoothing of alumina is investigated in sliding contact against itself under different normal load, sliding velocity and temperature. Smooth surface formed as a result of wear is composed of the part of original grains and that of agglomerated wear particles. Hardness of the part of agglomerated wear particles distributes widely up to 2,000 kgf/mm2 according to the frictional conditions. The smooth surface geometry is depended on the characteristics of agglomerated wear particles. In unlubricated sliding of alumina against itself at 900°C,mirror like smooth surface of the maximum surface roughness in the order of 0.01pm is generated as a result of sintering of wear particles on wear surface. 1. INTRODUCTION It is well known that very fine wear particles are often produced in wear of ceramics and they are trapped within the contact area ( l ) ~ ( ~It)is. the reason why wear particles are called as the third body (3). Furthermore, many researchers observed surface layer agglomerated those fine wear particles, which was called as uibo-film (4), ( 5 ) , transfer film (@* inter layer agglomerate film (*), debris film (9), particle layer (lo), surface layer of compacted materials ( I ] ) , layer of compacted wear particles ( I 2 ) , film-like substance(13) or border layer (I4) on the basis of [heir structure, formation mechanism and so on. It has been also reported in these investigations that this kind of agglomerated wear particles controls friction and wear. Therefore, the behavior of the wear particles is recognized to be very important in order to understand the wear mechanism and design high wear resistant material or optimum operating condition. On the other hand, it is well known that wear surface becomes smooth as a result of wear under some frictional conditions ( I 2 ) , (15). This is an interesting phenomenon for surface finishing technology. The smoothing mechanism is discussed from the view points of chemical reaction between bulk material and water ('*), and dissolution of binder at grain boundaries (15). Furthermore, the rule of the fine wear articles for such smoothing process is pointed out (18. It is likely that the wear particles affect on wear surface if they are trapped within the contact area. (7)9

The purpose of this paper is to clarify the effect of the wear particles as the third body on smooth surface formation, For this purpose, it is shown experimentally that agglomeration and sintering of wear particles at the contact interface produce hard and mirror like smooth surface.

2. EXPERIMENTAL PROCEDURE Sliding test of alumina against itself was carried out with pin on disk test rig under three different experimental conditions as shown in Table 1. In test "A", normal load and sliding velocity were changed in the wide range under unlubricated condition at room temperature. In test "B", normal load and atmospheric temperature were changed in the wide range under unlubricated condition. And in test "C" , normal load was changed under water lubricated condition. After the wear test, wear surfaces were analyzed by a surface profilometer and observed with the scanning electron microscope (SEM). Pin and disk specimens were made of sintered alumina. The tip of pin specimen was finished spherically with radius of 2mm. Initial surfaces were prepared by grinding and their maximum surface roughnesses were about 3-5pm. Mechanical properties of the used alumina are shown in Table 2.

586

Table 1. Experimental conditions.

Table 2. Mechanical properties of alumina. Vickers hardness HV, GPa

16.5

Fracture toughness Klc, MPamln

3.5

I

20

20-1000

20

II

Young8 modulus E, GPa Poisson's ratio n

390 0.24

~

I

Load(N)

I

3-100

I

2-20

I

3-100

0.2

I

0.1

I1 I

I

Thermal conductivity I , W(mK)

. I

29.3

*wL

0.2mm

0.04mm (a) (b) Fig. 1. SEM photographs and surface profiles of representative wear surfaces ; rough surface (a) and smooth surface (b). The arrow indicates the sliding direction of pin.

3. EXPERIMENTAL RESULTS 3.1. Wear surfaces of alumina In all experiments initial surfaces became smoother or rougher as a result of wear in sliding contact. In this study, surface of the maximum surface roughness of less than Ipm is defined as a smooth surface. SEM photographs and surface profiles of such representative wear surfaces are shown in Figs. 1 (a) and (b). The different roughness of these wear surfaces is quite clear. Figure 2 shows one example of their surface roughness changes with number of friction cycles. In the case of smoother surface, the maximum surface roughness decreases drastically at the initial stage of sliding to the value of less than 1pm. Figure 3 (a) shows regions of smooth surface

1S

2

4

6

0

10

12

Number of cycles N, xl@ cycles

Fig. 2. One example of the change of surface roughness with number of cycles.

587

(a) (b) Fig. 3. Region of smooth surface formation and rough surface formation in test "A" (a) and test"B" (b). formation and rough surface formation in relation to normal load and sliding velocity. Figure 3 (b) shows these regions in relation to normal load and temperature. It is clear that smooth surface can be formed under various frictional conditions. The critical conditions between smooth surface formation and rough surface formation are influenced by normal load, sliding velocity and temperature . It is very important to clarify these critical conditions in order to understand macroscopic wear behavior, however, we may leave the details to another paper (I7) since this is out of the scope of this study. In this study, we focus on the smooth surface formation, especially on the effect of the wear particles on the smooth surface formation. 3.2. The effect of wear particles on smoothing process with wear Figures 4 (a)-(d) show the SEM photographs of wear surfaces formed by smoothing process and schematic surface profiles of initial and final wear surface. It can be seen that surface smoothing proceeds by wear of highest point of alumina grains. Furthermore, removal of fine particles of less than original grain size can be regarded as a main wear mechanism by comparing the change of surface profile with mean grain size of 3-5pm. Here, we shall concentrate on the position of smooth wear surface (Fig. 4 (d)). It is mentioned point that smooth surface is formed at the middle level between top and bottom of initial surface profile. Here, in order to clarify the smoothing mechanism of alumina in sliding contact, we introduce following two parameters.

(I) Relative area of smooth surface. It is defined as the ratio of the smooth surface area to the contact area. This parameter has almost the same meaning as the profile bearing length ratio of Abbott curve.

(2) Relative wear deprh. It is defined as the ratio of the wear depth from the top of asperity to the maximum surface roughness. This parameter has almost the same meaning as the profile section level of Abbott curve. Fig. 5 shows the relationship between introduced relative area of smooth surface and relative wear depth in smooth surfaces obtained in unlubricated sliding contact at 900°C.The region under or above the observed values corresponds to area of smooth surface or that of surface hollows, respectively. The Abbott curve of initial surface is also shown in the same graph. It can be seen that relative area of smooth surface increases with increasing of relative wear depth. Especially, almost whole wear surface becomes smooth when relative wear depth reaches to 50% in this experimental condition. This correlation represents the progress of smoothing with wear. This figure also suggests that area of smooth surface is composed of the flat surface of worn alumina grains (Fig. 6 (a)) and that of agglomerated wear particles ( ' 6 ) (Fig. 6 (b)). Because the region under the Abbott curve means that of existence of alumina when the material is cut at a certain level corresponds to wear depth. Figure 7 shows the SEM photograph (taken under low angle of 30') of smooth surface area without surface hollows obtained as a result of wear in water

588

(d)

(C)

Fig. 4. SEM photographs (at@)and schematic surface profiles (d) of wear surface by smoothing process. The arrow indicates the sliding direction of pin. under condition of 50N of normal load, 0.1 m / s of sliding velocity and 20'C of atmospheric temperature. Some convex polygons can be seen on the smooth surface. By consideration of alumina grain size and shape, we can be fairly certain that each convex polygon is the part of original alumina grain. On the basis of detailed observation as shown in Figs. 5 and 7, the schematic diagram of general smooth surface can be summarized as shown in Fig. 8. It was clear in this section that smooth surface formed as a result of wear has the part of original alumina grains and that of agglomerated wear particles. In other words, it can be considered that the agglomeration of wear particles accelerates the surface smoothing.

-- Temperature :900°C

0

10

20 30 40 Relative wear depth, YO

50

60

Fig. 5 . Relation ship between relative area of smooth surface and relative wear depth in smooth surface obtained in dry sliding condition at 900'C.

589

(a) (b) Fig. 6. Smoothing surface of two underlying regions ;(a) region of original alumina grains, (b) region of agglomerated wear particles.

wear partlcles

Fig. 7. SEM photographs (taken under low angle of 30") of smooth wear surface obtained under condition of 50N normal load, 0. I d s sliding velocity, 20°C temperature and in water.

Fig. 8 Schematic diagram of general appearance of smooth surface.

3.3. The effect of wear particles on smooth surface geometry Figures 9 (a)-(c) show the SEM photographs and surface profiles of smooth surfaces obtained under three different sliding conditions. It can be seen that smooth surfaces obtained under each conditions are difference from the view point of their appearance and surface roughness. The wear surface obtained in unlubricated sliding wear at 9W°C(Fig. 9 (c)) is the smoothest with maximum surface roughness reduced to the order of 0.0I pm. We shall now look more carefully into the surface roughness of smooth surface and discuss the difference of each surface roughness as shown in Figs. 9. It can be seen in Figs. 7 and 8 that surface

roughness is produced by the difference in level between the flat part of worn original alumina grains and that of agglomerated wear particles. Assuming that wear rate of alumina grain is smaller than one of agglomerated wear particles, we can explain such difference in level on smooth surface. Figure 10 shows the SEM photograph (taken under low angle of 30") of smooth surface area obtained as a result of unlubricated sliding wear under conditions of 3N of normal load, 0.1 m/s of sliding velocity and 20'C of atmospheric temperature. From comparison of this figure and Fig. 7, surface roughness obtained under dry sliding condition as shown in Fig. 10 is produced by the same mechanism as one of smooth surface as shown

590

Fig. 9. SEM photographs and surface profiles of wear surfaces obtained under three different sliding conditions : in dry,W=3N, v=O.lm/s, T=20°C (a), in water, W=50N, v=O.lm/s, T=20"C(b) and in dry,W=30N, v=0.2m/s, T=9W°C (c). The m o w indicates the sliding direction of pin. Profiles are masured in the vertical direction of sliding.

59 1

Fig. 10. SEM photograph (taken under low angle of 30') of smooth wear surface obtained under condition of 3N normal load, O.lm/s sliding velocity, 20°Ctemperature and in dry. The arrow indicates direction of pin motion.

in Fig. 7 and scratch marks formed on the part of agglomerated wear particles. Assuming that the part of agglomerated wear particles is relatively soft, we can explain such formation of scratch mark on smooth surface. These results suggest that the value of surface roughness is depended on characteristics of the part of agglomerated wear particles. Furthermore, it may be suggested that if the part of agglomerated wear particles becomes harder, more smooth surface is produced by prevention of the scratch and by decrease of difference in wear rate of two parts of original grains and agglomerated wear particles. It was observed in this section that characteristics of agglomerated wear particles dominate the smooth surface geometry such as appearance and surface roughness.

Fig. 11. Vickers hardness distribution on smooth wear surface obtained under three different sliding conditions : in dry, W=3N, v=O.lm/s, T=20'C (a), in water, W=50N, v=O.lm/s, T=2OoC (b), and in dry, W=30N, v=0.2m/s, T=900°C (c).

592

Fig. 12. SEM photographs of thermally etched smooth wear surface obtained under two different sliding conditions : in dry,W=3N, v=O.lm/s, T=20'C (a), (b) ,and in dry,W=30N, v=0.2m/s, T=900°C (c), (d).

3.4. Characteristics of the part of agglomerated wear particles Figures 11 (a)-(c) show Vickers hardness distribution on the smooth surface obtained under three different experimental conditions correspond to the Figs. 9 (a)-(c). The hardness distribution of original alumina also shown in the same graph. Indentation load was log, which was the smallest possible load for the used equipment. In the case of hard material with Vickers hardness of 1,000 kgf/mm2, the size of indentation mark with log load is equivalent to one grain size of alumina used in this experiment. Therefore, measured hardnesses include the value of grain and one of agglomerated wear particles. Furthermore, it is obvious that smaller value than one of original alumina means hardness of the part of agglomerated wear particles.

It can be seen in these figures that the hardness distributions on smooth surface obtained under three different conditions differ from one surface to another. From these figures and Figs. 9 (a)-(c), surface roughness seems to decrease with increasing of hardness of the part of agglomerated wear particles. In Figs. 11 (a) and (b), almost of the values of hardness distribute below that of the original alumina . From this result one may say that thin layer formed by agglomeration of the wear particles cover whole smooth surface even if we can see some convex polygons as flat surface of worn alumina grains as shown in Figs. 7 and 10. In Fig. 11 (c), even the part of agglomerated wear particles have high hardness (600-2,200 kgf/mm2). At least, we can be fairly certain that the wear particles produce hard surface of more than 600 kgf/mm2 by agglomeration under unlubricated sliding condition at 900°C.

593 Figures 12 (a)-(d) show the SEM photographs of thermally etched (1.5504C,exposure time : 1 hour) smooth surface obtained under two different frictional conditions corresponds to Fig. 9 (a) and (c). It can be seen in these figures that two kinds of grains with different scale of several microns and less than 1pm distribute on these surfaces. It is obvious that each grain size corresponds to the one of original alumina grain or wear particles, respectively. In Figs. 12 (a) and (b), we can see many delaminations of the part of agglomerated wear particles that can not be seen in Figs. 12 (c) and (d). We shall now look more carefully into behavior of the wear particles on smooth surface as shown in Fig. 12 (d). It is likely that the wear particles with size of less than lpm are sintered at the center area surrounded by original grains. It was observed in this section that the wear particles produce smooth surface with various hardnesses according to the frictional condition , especially, in unlubricated sliding at 9OO0C,the hardness of smooth surface generated by agglomeration of the wear particles reaches to more than 600 kgf/mm2 as a result of sintering of the wear particles. Furthermore, it follows from what has been said that increase of hardness of the part of agglomerated wear particles leads surface roughness of wear surface to quite small value. 4. DISCUSSIONS

Pin and disk specimens were the same alumina as mentioned before. a -alumina fine particles with sub-microns were used as fine wear particles . These particles were selected as the same crystal structure and same size as observed fine wear particles. Figure 14 (a) shows a schematic diagram of agglomerated layer formed by sliding in alumina particles trapped between pin and disk, and Fig. 14 (b) shows its SEM image observed after ultrasonic cleaning in acetone. It is clear that fine particles form the agglomerated layer by friction. Here, we focus on the surface of aggregated layer formed by fine particles. Figures 15 (a) and (b) show SEM photographs of the surface formed under two different normal loads. It can be seen that appearance of this surface change from porous (Fig. 15 (a)) to smooth (Fig. 15 (b)) with increasing normal load. The same change of surface appearance with temperature was also observed. Figures 16 and 17 show the effect of normal load and friction cycles on Vickers hardness of agglomerated layer under Vickers test load of log. It can be seen in these figures that harder agglomerated layer is generated by increasing of n o d load and friction cycles. Furthermore, it is clear in these figures and detailed observation of smooth surface that fine particles produce the hard surface with Vickers hardness of more than 1.000 kgf/mm2 as a result of sintering. The result of this simulating test, it was confirmed that the sub-micron alumina particles produce smoother and harder surface by rubbing

It was found in previous chapter that the behavior of the wear particles dominates the properties of smooth surface such as surface profile and hardness. Let us now discuss the behavior of fine particles as the third body from following two points of view in this chapter. 4.1. The effect of frictional condition on surface properties of agglomerated fine particles In order to clarify the effect of frictional condition applied to fine particles on surface properties generated by them (Section 4.1), and to discuss the possibility of sintering of fine particles (Section 4.2), simplified model experiments were carried out under well-controlled conditions of normal load and temperature with pin on disk rig as shown in Fig. 13. Fine particles of alumina were supplied into the contact interface (I8), and friction force was applied under various loads (0.5-13N) and temperature (20-85O'C). The behavior of wear particles at the contact interface could be simulated by this method.

%'

nfrared lamp

Load

I

I

Fig. 13. Schematic diagram of apparatus for simplified model experiment.

594

Fig. 14. Schematic diagram of agglomerated layer formed by sliding in alumina powder supplied between alumina pin and disk (a) and its SEM photograph observed after ultrasonic cleaning in acetone (b). The mow indicates the sliding direction of pin.

(a) (b) Fig. 15. SEM photographs of the surface of agglomerated layer formed under two different normal load at 850'C : 5N (a) and 13N (b). The arrow indicates the sliding direction of pin.

595

1200 1

500

A1203 pin f A1203 powder / A1203 dirk

E

Temperature :850'C Frlctlon cyclr : 1 CyClO Vlckrrr teat load : 10s

300 v) v)

g

200

U

/

E

=:

5

lo00

: >

800

/f

I

$

600

aI C

1 400 E

f 0

T

-

3 5

.. ... ..

0 t3* " 0 5

N

Fig. 16. Effect of normal load on Vickers hardness of agglomerate layer under Vickers test load of log.

I .

10

...I

15

20

a

m

.

3

25

.. 30 ....35 1

Number of friction cycles N, cycler

Fig. 17. Effect of number of friction cycles on Vickers hardness of agglomerate layer under Vickers test load of log.

under the high contact pressure and high temperature.

4.2. The possibility of sintering of f i e particles at the contact interface by friction It is well known that the combination between pressure applied to fine particles, temperature and exposure time is important to sinter the fine particles. However, it is difficult to estimate real contact pressure applied to fine particles at the contact interface in mentioned sliding test. We can calculate the contact pressure based on Hertzian theory, however, it is impossible to apply such calculated macroscopic value to that applied to fine particles at surface hollows with size of several micrometers. On the other hand, in simplified model experiments total normal load is supported with only fine particles. Therefore, assuming that total normal load apply to the circle area with the diameter corresponds to the width of agglomerated layer, we can estimate contact pressure applied to the fine particles. Figure 18 shows the comparison between experimental condition, which is shown as combination of the calculated contact pressure and atmospheric temperature in this model experiment, and general sintering conditions. The sintering conditions for commercial roduct of ceramics and that reported by Yu. et al are also shown in same graph as a general sintering conditions..

Tempemturr : 850°C Normal lord during frlctlon : 13N Vlckera 1.rt load : lOg

200

10

Normal load during friction W,

1

cy

10'0 10

.......".... ....- ...........

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

"

i

2 100 ' a al

5

10

2 a

100

u) u)

.... ... ........ .... .........."..-.... "."..., ""

5

"

L

...................c,..,..,.....

............... ""..,.,

10 I

Fig. 18. Comparison between experimental condition and sintering conditions for commercial product ceramics and for alumina ceramics produced by high pressure sintering (I9). It can be seen that temperature or pressure in our experimental condition is smaller or higher than that in commercial product, respectively. However, they are close to a sintering condition used by Yu. et al. who report fabrication of alumina ceramics by high pressure sintering. This result proves the possibility of sintering of fine particles at the contact interface by rubbing at high temperature.

596

5. CONCLUSIONS Smoothing of alumina wear surface in sliding against itself was observed experimentally and its mechanism was analyzed. Obtained conclusions are as follows; (1) Wear surface of the maximum surface roughness in the order of 0.01pm is generated at the normal load of 30N and the temperature of 900'C. (2) Smooth wear surface has the part of original grains and that of agglomerated wear particles. (3) The roughness of wear surface decreases with the increase in hardness of wear surface. (4) The hardness of wear surface increases up to 2,000 kgf/mm2 as a result of sintering of agglomerated wear particles.

ACKNOWLEDGMENT This research was supported in part by Grant-inAid for Scientific Research of The Ministry of Education, Science and Culture. We wish to thank Mr. K. Fukurai and Mr. K. Kunimitsu for their support in these experiments.

REFERENCES J. Denape : Wear Debris Action in Sliding Friction of Ceramics, Proc. of the 18th LeedsLyon Symposium on Tribology, (1992) 453462. J. K. Lancaster, Y. A. Mashal and A. G. Atkins : Particle Detachment Processes in the Dry and Lubricated Wear, Proc. of the 18th Leeds-Lyon Symposium on Tribology, (1992) 237-246. M. Godet, The Third-Body Approach : A Mechanical View of Wear, Wear, 100 (1984) 437-452. A. Blomberg, M.Olsson, J. Bratth, H. Engstrm and S . Hogmark : Sliding Wear Behavior of Al2O3, Sic and Sialon Face Seals, Proc. Jpn. Int. Trib. Conf. Nagoya, (1990) 1371-1376. K. Komvopoulus and H. Li : The Effect of Tribofilm Formation and Humidity on the Friction and Wear Properties of Ceramic Materials, Trans. ASME, J, Trib., 114 (1992) 131-140. 0.0.Ajayi and K. C. Ludema : Mechanism of Transfer Film Formation during Repeat Pass Sliding of Ceramic Materials, Wear, 140 (1990) 191-206.

(7) A . P. Sernenov and A. A. Katsura : Investigation of Friction and Wear of Corundum Ceramics at Temperatures to 15OO0C,Proc. Wear of Materials-1979 (1979) 551-555.

(8) E. Zanoria and S. Danyluk : Ball-on-Flat Reciprocating Sliding Wear of Single-Crystal, Semiconductor Silicon at Room Temperature, Wear, 162-164 (1993) 332-338. (9) J. Denape and J. Lamon : Sliding Friction of Ceramics : Mechanical Action of Wear Debris, J. of Materials Science, 25 (1990) 3592-3604. (10) P. J. Blau : Friction Microprobe Investigation of Particle Layer Effects on Sliding Friction, Wear, 162-164 (1993) 102-109. (11) M. G. Gee and D. Butterfield : The Combined Effect of Speed and Humidity on the Wear and Friction of Silicon Nitride, Wear, 162-164 (1993) 234-245. (12) T. E. Fischer and H. Tomizawa : Interaction of Tribochemistry and Microfracture in the Friction and Wear of Silicon Nitride, Wear, 105 (1985) 29-45. (13) R. S. Gates, S. M. Hsu and E. E. Klaus : Tribochemical Mechanism of Alumina with Water, Trib. Trans., STLE, 32 (1989) 357-363. (14) N. M. Alexeyev : The Structure of Border Layer in Deformed Bodies under Friction, ROC. Ewotrib '89, 1 (1989) 117-122. (15) X. Dong, S. Jahanmir and S . M. Hsu : Tribological Characteristics of a-Alumina at Elevated Temperatures, J. Am. Ceram. SOC.,74 (1991) 1036-1044. (16) M. G . Gee : The formation of aluminium hydroxide in the sliding wear of alumina, Wear, 153 (1992) 201-227. (17) K. Adachi and K. Kato : Transition Mechanism from Mild Wear to Severe Wear of Alumina Ceramics in Sliding Contact, Proc. of JAST Tribology Conference, Tokyo, ( 1995) 59 1-594. (18) A. Iwabuchi, K. Hori and H. Kubosawa : The Effect of Oxide Particles Supplied at the Interface before Sliding on the Severe-Mild Wear Transition, Wear, 128 (1988) 123-137. (19) Y. Ishitobi, M. Shimada and M. Koizumi, Fabrication of Translucent A 1203 by High Pressure Sintering, American Ceramic Society Bulletin, 56.6 (1977) 556-558.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

597

Friction in abrasion of alumina fibre and silicon carbide particle reinforced aluminium N. A x h

Department of Materials Science and Metallurgy, University of Cambridge Pembroke Street, CB2 342, Cambridge, UK

ABSTRACT

Two types of metal matrix composites have been tested regarding their friction properties in abrasion. Firstly, composites consisting of 10 or 30 vol.% silicon carbide particles in an AlSi7Mg aluminium matrix and secondly composites with 10 or 30 vol.% alumina fibres in AlSilMgMn aluminium have been evaluated. Also the unreinforced aluminium alloys were evaluated as reference. Silicon carbide and flint abrasives of different grit sizes were used in a pin-on-drum wear and friction tests set-up. The influence of applied load and matrix hardness was also systematically investigated. Special attention has been paid to how the coefficient of friction is changed in abrasion due to the reinforcement and the matrix hardness. It is shown that both fibre and particle reinforcements reduce the coefficient of friction in abrasion. The reduction of the friction is strongly dependent on the testing parameters. Generally, the coefficient of friction is reduced with increased amounts of reinforcements and with higher matrix hardnesses, but almost independent of the applied load and the type of abrasive, The reasons for the reduction in friction caused by the reinforcementsand the correlation between the reduction in friction and wear rate caused by the reinforcement are discussed. It is believed that the load distribution over the phases in the contact zone is a crucial parameter which decides which phase will dominate the overall friction.

1.

INTRODUCTION

Materials used in situations where good wear and friction properties are desired, are very often of multiphase type. Traditional multiphase materials often used in tribological applications include tool steels, cast irons and cemented carbides. Composites form a sub-group of multiphase materials, and can be described as artificially manufactured multiphase materials containing phases from different material groups. A variety of composites of different types, e.g. light metal and polymer matrix composites, are available and often used in uibological applications. The understanding of how different phases in composites and multiphase materials contribute to the tribological properties is therefore an important task in tribology. Metal matrix composites of the type studied in this work have had a reputation of combining an excellent wear resistance with a low weight. It is true that they have shown better wear resistance compared to unreinforced alloys in some contact situations, however in other situations the effect of

reinforcements is rather low [ 1-31. Generally, and especially for fibre reinforced composites. the contact situation has been shown to be of crucial importance to the wear performance [4]. A large number of papers have also been published

on the frictional properties of composites [I, 5-71. Both polymer matrix composites [8], carbon fibre reinforced glass matrices [9] and light metal matrix composites with ceramic reinforcements [ 10-121as well as ceramic composites [13] have been extensively studied. The sliding friction of composites has been more systematically studied than friction associated with abrasion. Nevertheless, friction in abrasion is an important feature, e.g. in grinding and for applications such as brake disc materials. The kinetic friction force is the tangential force necessary to slide one body over the surface of another. The friction force is sometimesdescribed as the sum of two contributions: one caused by surface asperities deforming the counter surface and the other due to the shearing of adhesive contacts. This view was largely developed by Bowden and Tabor

598

in their work on friction in the 1950s [14]. Since then numerous papers have been published on the origin of friction in terms of the interaction between surface asperities in sliding contact. Good over-view articles are provided in i15.161. 250 0 Heat trcatment: A

a>

200

cn

150

modes were defined. It was shown that the EP and EW modes describe load disrribution limits above or below which, respectively, the pressure distribution Cannot fall. Different types of surface interactions can fulfil the EP and EW modes. It is believed that the load distribution concept can be used also for friction.

'f! B

100

&

4

50

n 0

15 30 Amount of alumina fibres, vol.%

(a>

10

250

3a 50

0 (b)

0 10 30 Amount of SIC particles, vol.%

Fig. 1. Vickers hardness of both the unreinforced matrix materials and the composites as depending on amount of reinforcerncnt and heat treatment for the alumina fibre reinforced composites (a) and the silicon carbide particle composites (b). Recent works by Axen, et a1 have shown how the load carried by each phase in a multiphase material subjected to abrasion depends on the wear resistance and area fractions of the phases [17, 181. The load on each phase was described in terms of load distribution modes. Equal pressure (EP), equal wear (EW) and intermediate (I) pressure distribution

Fig. 2. Scanning electron micrographs of a fibre reinforced (a) and a silicon carbide reinforced (b) composite with 30 or 10 vol.% reinforcement, respectively, both polished and etched (Keller's). The present study investigates the friction properties in abrasion of an Al-SilMgMn alloy reinforced with alumina fibres and an AlSi7Mg reinforced with silicon carbide particles. The influence of type and amount of reinforcement, abrasive particle type and

599

size, applied load, and heat treatment of the composites have been investigated.

75 pm Sic (a) and flint (b) abrasives as a function of the applied load.

2

The S i c particles were of irregular shape and an average diameter of 20 pm. The &alumina fibres were of 3-5 p m diameter and 500 pm length (ICI Saffil RF-grade fibre). The fibre composites were manufactured at the Department of Production and Materials Engineering, University of Lund, Sweden with a vibration excited hot liquid infiltration technique, using a preform with the fibres randomly oriented. The particle composites were made by SINTEF Produktionsteknikk, Norway using a rheocasting technique. The fibre composites are described in detail in [ l , 191.

MATERIALS AND EXPERIMENTAL METHODS

2.1. Materials and heat treatments

Two metal matrix composites based on hardenable aluminium alloys were studied in this work: The hypoeutectic AlSi7Mg (ISO;7% Si, 0.3% Mg) reinforced with 10 or 30 vol.% silicon carbide particles and the AlSilMgMn (ISO; 0.9% Mn, 0.7% Mg, 1.0% Si) with 10 or 30 vol.% alumina fibres. 1.2 3.

g

1.0

'3

0.4

5

0

10

(a>

20

15

Load, N

1.2

,

I

, ' , '

I Abrisive: 75 d m flint 4 I

I

I

,

,

,

,

,

,

I

Heat treatment: Q 0 O%fibres 0 30%

2.2. Abrasive wear and friction tests

k

2 C

0.8

.P

u8

0.6

0.4

0 0 a I

0

0)

,

,

5

1

1

1

10

15

Both the pure and the reinforced alloys were heat treated to three different hardnesses, in this work referred to as A (annealed), Q (quenched) or 4 2 and Q1 for the particle and the fibre composites, respectively. (quenched and aged for 2 or 1h). All specimens were first soft annealed at 400'C for 1h and slowly cooled in the furnace to room temperature (A). Some specimens were hardened by solution treatment at 540 'C (AlSilMgMn) or 520 'C (AISi7Mg) for 20 min and quickly quenched in cool water (Q). Ageing for one hour at 175 'C (AlSilMgMn) or two hours at 160 'C (AlSi7Mg) resulted in optimal hardness, see Fig. 1. The micro structures of the materials in the annealed condition are presented in Fig. 2. The distribution of the reinforcements is even, but single pores in the matrix can be found. Also a pure hot-sintered Sic was tested as reference.

20

Load, N

Fig. 3. Coefficient of friction for the unreinforced AlSilMgMn alloy and the composites with 30 ~01.96 alumina fibres after heat treatment Q tested against

A pin-on-drum abrasion machine was used to evaluate wear resistance and friction force of the materials. A rotating drum of diameter 200 mm was covered with either silicon carbide (2500 HV) of mesh grades 80, 220 or 400 corresponding to 200, 75 or 20 pn grit sizes, or flint (900 HV) abrasive papers of 220 mesh (75 pm). The S i c abrasives were harder than the aluminium alloy matrices and harder than the alumina fibres but equally hard as the SIC reinforcements. The flint abrasives are softer than both the reinforcements but harder than the matrices. The pin specimens were about 25 mm long before testing and had a square cross-section of 5x5 mm. The specimens were pressed against the cenue of the drum with forces ranging from 0.9 to 39 N. corresponding to nominal surface pressures of 0.04 to 1.56 MPa. The pins were continuously moved

600 parallel to the axis of rotation of the drum, to form a helical wear track, so that the samples were always tested against fresh abrasives. The sliding speed was chosen as 0.08 ms-l. The friction and the wear rate were continuously measured during 10 revolutions corresponding to 6.3 m sliding distance using a strain gauge and a LVDT displacement transducer, respectively. Before each test the pins were run-in using the actual load and abrasives, i.e. the initial wear was not considered. Friction results presented are averages of at least two measurements. The uncertainty is estimated to be better than 5 % of the quoted coefficientsof friction. 1.2

1

1

1

1

1

1

I

1

I

I

I

1

I

1

1

75 pm flint (b) abrasives as a function of the applied load. 3.

1.2

1

Adrasive: 7 5 ' p Sic Heat treatment: Q 0 Puresic 0 O%particles 0 30%

6

& u-4 Y

10

(a>

g

1.0

'3 0

&

."6)

48 V

30

20 Load, N

40

PmTT

F

00

0% particles

1 o1

0 0 1

0.4

0 (b)

0.8

10

1

1

20

1

I

I

I

I

1

30

1

I

I

I

I

I

1

40

Load, N Fig. 4. Coefficient of friction for the unreinforced AlSi7Mg alloy and the composites with 30 vol.% SIC parucles after heat treatment Q as well as for a pure sintcred SIC tested against 75 pm Sic (a) and

8

3

0.6 400 o

0.4 0

I

-0

C

0 . 0 0

Ile2

1.0

3

0

0.4

I

3.

0

0

RESULTS

'

l

l

I

I

I

I

,

,

I

,

Abrasivd: 200 )un Heat treatment Q 1 0 PureSiC 0 OZparticles a 30%

0-0

. e 0 0

i i i l l l l l i l i l i i l l l i i

0 0

e

601

decreased from about 0.8 to 0.6 for loads above ca. 10 N, similar to for the fibre reinforcements. 1.5

In the figures 6 to 10 relative changes in the coefficient of friction are shown. The friction reduction is compared to the unreinforced matrix material (Fig. 6 and 7), or compared to the largest abrasives (Fig. 9) or the softest matrix (Fig. 10). respectively.

Abrasive: 75 pn Sic heat UeatmenC Q 0 0% fibres

5

'g 1.3

rw w

30%

0

5

for the particulate composites when tested against flint abrasives (Fig. 4b).

5

'9 1.0

1.5

k 8u

,

,

0.8

I

I

5

I

S 1.3 rw

4

0

,

1

1

1

1

I

l

l

1

Ab:asive: 75 Sic 1 Heat treatment: 0 O 0

1

OQpartiiles 10%

U

C

.P

0.5

0

5

10

20

15

Load, N

(a)

2 8

1.0

$ *a 0.8

3

1.5 C

Heat treatment: Q

0

2 t

,

.0a

0

.$ 2

I

0.5

1.3

ru

(a)

30%

0

h

r\

U

U

1.5

5

'30

-

I

I

I

I

I

1.3

-

1.0

c=;c G I-

%

0

U

I

I

1

I

1

1

1

1

1

1

1

Ab/asive: 75 flint 1 Heat treatment: Q 0 0% particles 0 10% 4 30%

C

.P

s

0

(3)

0

5

10

15

20

Load, N

Fig. 6. Coefficient of friction relative to the unreinforced alloy for the unreinforced AlSil MgMn alloy and the composites with 10 or 30 vol.% alumina fibres after heat treatment Q tested against 75 pm Sic (a) and flint (b) abrasives as a function of the applied load. With the coarse 200 p abrasives the reduction in friction caused by the reinforcements is much lower, as seen from comparing Fig. 4 and 5. In fact, the reinforcement hardly reduces the friction at all in mts with the largest abrasives (Fig. 5). As for the fibre reinforced composites the friction is lower against flint than against Sic abrasives; the friction reduction, however, goes only from about 0.7 to 0.6

n

w

n

3,

w

4

8

0

.$ 2

0.8

M

t

I

0.5

0

10

20

30

40

(b)

Load, N Fig. 7. Coefficient of friction relative to the unreinforced alloy for the unreinforced AlSi7Mg alloy and the composites with 10 or 30 vol.% silicon carbide particles after heat treatment Q tested against 75 pm Sic (a) or 75 p flint (b) abrasives as a function of the applied load. It is seen in Fig. 6 and 7 that the relative reduction caused by the fibre and particle reinforcements is

602 higher at loads below some 10 N. Only for the largest (200 pm) abrasives is the friction reduction low (about 95% of the matrix value) for all the tested loads (Fig. 8). For the fibre reinforced composites the friction reduction is greater in the tests against flint (Fig. 7b). This was, however, not confirmed in the tests with S i c abrasives. The coefficient of friction is lower for 30 ~01.96 reinforcement in all tests except against the coarse 200 pm S i c abrasives where their is hardly any difference between 10 and 30 vol.% of reinforcement (Fig. 8b). The coefficient of friction was lower for smaller abrasives for both the unreinforced alloys and the composites (Fig. 9). However, the composites are more sensitive to the abrasive grit size than the unreinforced alloy (Fig. 9b). For the composites smaller abrasives also leads to lower friction at low loads, unlike the results from the unreinforced alloy. The hardened (Q or 42) AlSi7Mg alloy both gave friction values being some 90% of the soft annealed matrix material with very little difference between the heat treatment Q and 42, as seen in Fig. 10. In fact, the difference between the two heat treatments was not great for the composite materials either (Fig. lob). As above, the tendency towards a larger friction reduction at low loads is only distinguishable for the composites and not for the unreinforced materials.

against 200 p n Sic abrasives as a function of the applied load.

DISCUSSION

4.

Traditional friction theory states that in abrasion the friction is the sum of the adhesive friction and the friction caused by ploughing. The ploughing component should be the quotient of the ploughing front area to the load carrying area of the individual abrasives. Thus, for a homogeneous material the ploughing friction term depends mainly on the shape and size of the abrasives. 1.5

8

3

'3

1.3

10

0

1

C

73

S

1.3

lu

1

1

1

1

1

1

1

130%Sic

Heat treatment: Q 0 O%particles

0

30

20 Load, N

b

1

I

I

I

1

1

200Lsic 7 5 p 2 0 p

0

-

I

40

4

1

1 -

30%

0

CI

e

n

n v

n v

3

0.5 0

10

20 Load, N

30

40

Fig. 8. Coefficient of friction relative to the unreinforced alloy for the unreinforced AlSi7Mg alloy and the composites with 10 or 30 vo1.Q silicon carbide particles after heat treatment Q tested

20 30 40 Load, N Fig. 9. Coefficientof friction relative to the results with 200 p m abrasives for the unreinforced AlSi7Mg alloy (a) and the com sites with 30 ~01.96 silicon carbide particles (b) a ter heat treatment Q 0

10

F"

603 for tests with 75 or 20 p m Sic abrasives as a function of the applied load.

The type of reinforcements used in this work improve the abrasion resistance in mild wear but lead to almost no improvement in tough wear [l]. A relatively low penetration of the abrasives can also explain a lower friction, since the ploughing part of the friction is reduced. This can explain the relatively lower friction at low loads. Also the friction reduction with increasing reinforcement content and decreasing grit size can be explained by a reduced ploughing friction.

For a composite or multiphase material the situation becomes more complicated. It has been shown that the wear resistance of composites depend to a large extent on the ability of the reinforcements to prevent penetration of the surface. Mild wear result in little digging out or cracking of the reinforcements. Instead the abrasives or asperities slide over the reinforcementswhich prevent penetration.

8

Reinforcement 0%

'3

u

S 1.3 Qd

0

42

d

s

.P

g

1.0

8u -3 0.8

3 &

0.5

-

0

10

30

40

Load,N

(a)

s

-3

20

Reinforcement 30% Sic 1.3

0.5 20 30 40 (b) Load, N Fig. 10. Coefficient of friction relative to the results for the annealed AlSI7Mg alloy and its composites for the unreinforced AlSi7Mg alloy (a) and the composites with 30 vol.% silicon carbide particles (b) after heat treatments Q and Q2 for tests with 75 Sic abrasives as a function of the applied load.

0

10

Recently, AxCn et a1 reported on a wear resistance model for abrasion which is based on the load distribution over the phases of a composite or multiphase material. From measured values of the wear resistances of individual phase materials, the upper and lower limits for the wear resistance of a composite built up from those phases can be estimated. The model was based on the idea that the more wear resistant a phase the larger part of the applied load must that phase carry for the overall wear rate to be the same, which is a necessary steady-staterequirement. As a consequence the most wear resistant phase dominates the wear resistance. Since the friction force is ideally proportional to the applied load each phase should contribute to the overall friction according to the load it carries. However, the load distribution is not always the same but depends on all the tribosystem parameters. In the model this is described in terms of load distribution modes. Generally, tough abrasion leading to large abrasive grooves result in the wear resistant phase taking a relatively smaller part of the load, whereas in mild wear or small grooves the wear resistance is dominated by the most wear resistant phase [17. 181. It follows that also the friction of a composite should depend on the load distribution in the same way. This fits well to the results presented in this work, since the friction is most reduced in milder wear,but hardly at all for coarse wear, e.g. with the largest abrasives. 5.

CONCLUSIONS

The coefficient of friction in abrasion of aluminium alloys can be strongly reduced by adding ceramic reinforcements which do also in most cases improve the abrasive wear resistance. In this work the friction coefficient of alumina fibre or silicon carbide particle reinforced aluminium alloys was reduced from being about half that of the unreinforced alloy

604 in some cases to being only a few per cent lower in other cases.

The reduction in coefficient of friction depended was strongly related to the conditions under which the tests were performed. Often the reduction was slightly higher at loads below some 10 N (0.4 MPa) compared to higher loads. Smaller abrasive particles result in greater friction reduction. The largest Sic abrasives tested (200 pm) gave a coefficient of friction for the particle reinforced composites being only about 5% lower than for the unreinforced alloy, whereas the smallest abrasives (20 p)gave only half the friction for the 30 vol.% particle composites compared to the unreinforced alloy. Also, the friction reduction is generally higher for harder matrices. The highest amount of reinforcement used in this test series, 30 vol.%, gave lower friction coefficients than only 10 vol.% for both fibre and particle reinforcements. Generally, the reduction in friction achieved by adding ceramic reinforcements to an aluminium alloy seem to be more pronounced the milder the wear. Large abrasive grooves, caused by coarse abrasives, high loads or soft matrices, gave a relatively lower friction reduction, whereas milder wear gave the best friction reduction. It is believed that a crucial parameter for the friction of composites is the pressure distribution over the phases. If a phase carries a higher load, it will also contribute more to the overall friction, as it will also dominate the wear resistance. ACKNOWLEDGEMENTS The composites were fabricated and supplied by Lars-Olof Pennander at the Department of Production and Materials Engineering at the University of Lund, Sweden. The work has been supported by the Human Capital and Mobility Programme of the EC. Also the Swedish Institute is acknowledged for their financial support to N. AxCn. REFERENCES N. AxCn, A. Alahelisten and S. Jacobson, 1. Weat 1994,173,95104. A. Alahelisten, F. Bergman, M. Olsson, S. 2 Hogmark, Wear, 165 (1993) 221-226.

N. AxCn and K. H. Zum Gahr, Mat. -wiss. u. 3. Werkstofftech. 23,360-367 (1992).

4. I. M. Hutchings, Materials Science and Technology 1994.10.513-517. 5. N. H. Sung and N. P. Suh, Wear 1979, 53, 129- 141. N. Saka and D. P. Karalekas, Proc. Int. Conf. 6. on Wear of Materials, Vancouver (1985) 784-793.

7. N. AxCn, I. M. Hutchings and S. Jacobson, 1995 Tribology International,Submitted. 8. K.-H. Zum Gahr, Z. Werkstofftech. 1985, 16, 296-305.

E. Minford and K. Prewo, Wear 1985, 102 9. 253-264. 10. A. G. Wang and I. M Hutchings,Materials Science and Technology, January 1989, Vol. 5, pp. 7 1-76. 11. M. K. Surappa, S. V. Prasad and P. K. Rohatgi, Wear, 77 (1982) 295-302.

12. S. V. Prasad, C. S. Naredranath and P. K. Rohatgi, Proc. Int. Conf. on Aluminium AlloysPhysical and Mechanical Properties. University of Virginia (1986) 1067-1079. 13. H. Liu, M. E. Fine, H. S. Cheng and A. L. Geiger, Journal of the American Ceramic Society 1993.76 [l], 105-121. 14. F. P. Bowden and D. Tabor, The friction and lubrication of solids, Clarendon Press, Oxford, 1950. 15. J. Larsen-Basse, ASM Handbook, Friction, Lubrication and Wear Technology, Volume 18, ASM International, USA, 1992,25-38. 16. I. L. Singer and H. M. Pollock (ed.), Fundamentals of friction: Macroscopic and Microscopic Processes, Proceedings of the NATO ASI, Braunlage, Han, Germany,l991. 17. N. Axtn and S. Jacobson, Wear 1994, 174, 187-199. 18. N. AxCn and B. Lundberg, Tribology International 1995, accepted for publication. 19. L.-0. Pennander et. al., Proc. of the eighth international conf. on composite materials (ICCMB), Honolulu, Hawaii, USA, July 1991.

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

605

Adhered film formation on steel surface by impingement of hard particles Noriyuki Hayashi", Yoshimi Kagimoto" and Hiroshi Akiyamab "Nagasaki Research and Development Center, Mitsubishi Heavy Industries, Ltd., 1-1Akunouramachi, Nagasaki, Japan bNagasaki Shipyard and Machinery Works, Mitsubishi Heavy Industries, Ltd.

At the particle erosion test under high temperature condition, the instance that the adhesion of impinging particles made films on the worn surface of stainless steel was found. By the analysis of SEM and XMA, it was observed that the thickness of film was about from 5 to 15 pm and it was smaller than the average diameter of particles. Under 500°C condition stainless steel which covered with adhered film had almost equal wear resistance with cermet coating which was about five times as hard as stainless steel. Using the result of this test, the condition of the film formation was discussed. As a consequence, it was found that the state of the film formation under high temperature condition was concerned with the contact area between the particle and the test piece formed at the impingement.

1. INTRODUCTION

At coal-fired power plant there are problems of t h e solid particle erosion u n d e r high temperature condition, and many studies were made until now [l-51.The wear resistance of materials depends on its hardness [6,71, so the application of hard materials to t h e parts exposed to the particle erosion is very effective. The hardness of materials, however, tends to decrease as the temperature elevates. The self lining, for example, is other means to improve the wear resistance. Authors found t h a t the formation of thin film made from impinging particles decreases the wear rate of material and changes the index n if the wear rate is proportional to the n t h power of the particle impingement velocity [81. About the particle erosion wear, some theories and mechanisms of wear have been proposed. For example, t h e theories of relationship between the particle impingement angle and the wear rate were proposed by Finnie [91 and Bitter [10,111. Bitter referred to the model of the deformation wear [lo] and the cutting wear [ 111, too. Recently the wear mode maps about

the particle erosion of brittle materials were shown by Hutchings [121. The discussion about the mechanism of particle adhesion, however, has not been enough, so the improvement of wear resistance by film formation h a s not applied to the parts of machinery. I n t h i s paper t h e instance of t h e film formation in the high temperature erosion test will be shown, and the model of the particle adhesion will be discussed. 2. EXPERIMENTAL PROCEDURES

To investigate the state of adhesion and the influence of a d h e r e d film on t h e wear resistance, t h e erosion t e s t s u n d e r high temperature condition were performed. 2.1 Experimental apparatus The experimental apparatus used in the high temperature erosion test was the nozzle-type erosion tester. The apparatus is shown schematically in figure 1. Gas is circulated in the apparatus by blower, and is heated before flowing into the

606

Rotating direction

Particles

Test piece holder

Figure 2. Location of test pieces, test piece holder and nozzle Collector Cyclone Filter

Figure 1. Schematic diagram of t h e high temperature erosion tester merging part. Particles a r e supplied from hopper by feeder at settled rate, and merged with gas in the merging part. The gas carrying the particles flows through nozzle into furnace. Test pieces are fixed to holder in the furnace, and the furnace is heated up to t h e t e s t temperature. The temperature of the furnace is measured by thermocouple and monitored through the test. The test piece holder can be rotated by motor. The test pieces are exposed to the gas flow and worn by particle erosion. The particles carried by gas are collected by collector, cyclone and filter, and only gas is circulated. 2.2 Test pieces The test piece is cylindrical, with 20mm diameter and 50mm height. The location of the nozzle and the test piece holder fixing test pieces is shown in figure 2. The test piece holder was rotating through the test and all test pieces were exposed to the gas flow equally. The merit of using the cylindrical test piece is that since the particle impingement angle is different in one test piece the relationship between the impingement angle and the wear rate can be obtained from only one test piece. The method

Table 1 Chemical components and hardness of test piece materials Stainless steel Cermet coating' 75%Cr C,Chemical 24.5%Cr-20%Ni- 25%Nikr components O.OG%C-Fe (NiCr:80%Ni20%Cr) Process HVOF" Hardness HV a t RT 180 630 a t 500°C 120 580 110 a t 650°C

* Provided to 600°C test ** High velocity oxygen fuel flame spray to obtain the relationship will be described later in detail. The test piece materials are shown in table 1. Two kinds of material were provided to the test, one was austenitic stainless steel and the other was Cr,C,-NiCr cermet coating material. In table 1 the components and hardness of each materials are shown. Cermet is about five times as hard as stainless steel at 500°C. 2.3 Test conditions Table 2 shows t h e t e s t conditions. To investigate the influence of test condition, the t e s t s were performed under different temperature and velocity conditions and using different particles. The temperature of the tests

607

Table 2 Test conditions Test 1' Test 2' Test 3" Test 4" Test 5" Test 6" RT 650 650 500 650 Temperature (T) , "C 500 Impinging particle Fly ash Fly ash Fly ash Fly ash Fly ash Fly ash 35 13 Average diameter of particles (ds0), pm 13 35 13 35 100 40 100 100 50 Particle impingement velocity (v) , m/s 100 Atmosphere and carrying gas Air Air Air Air Air Air 39 135 39 135 270 98 Particle contents in carrying gas, g/m3 18 24 45 26 45 26 Experiment time, hour * Wear measurement and analysis of worn surface ** Analysis of worn surface

1

Table 3 Chemical components and density of particles Fly ash Fly ash (d,,:13pm) (d5,:35pm) Chemical components,% Si0,

qo, Fu,O, CaO Density, kg/m3

63.6 23.3 3.2 2.6

63.6 17.6 3.7 2.1

2.2x103

2.1~103

were room temperature (RT), 500°C and 650°C. And two kinds of fly ash, which have different average diameter, were provided to the tests a s impinging particles. The impingement velocity were 40, 50 a n d 1 0 0 m / s , a n d atmosphere and carrying gas were air. The analysis of worn surface was carried out on all test pieces, and measurement of wear was performed on the test pieces under 500°C condition (test 1 and 2 of table 2). The chemical components and density of the fly ashes are shown in table 3. The fly ashes contains mainly SiO, and Al,O,. 2.4 Measuring method of wear Roundness measuring instrument was used for measurement of wear. Figure 3 is the example of the contour of the worn test piece. The contour of the test piece before the test is reproduced by using the contour of not worn side. And the wear depth a t each position of

Direction of particle impingement

Figure 3. The example of the contour of the worn t e s t piece measuered by roundness measuring instrument (stainless steel provided to test 1) the test piece is obtained from the change of the contour. The wear depth is not constant at each position because of t h e difference of particle impingement angle. So, as mentioned above, it is possible to obtain the relationship between the impingement angle and the wear depth at the measurement of only one test piece. 3. RESULTS 3.1 Analysis of worn surface To investigate the state of particle adhesion t h e worn surfaces were analyzed by X-ray

608

500 1

500

Stainless steel

Le(

400

hP+

f:

300

cm

*

!.

A

200

A

G m 100 0

0

A

"

0 0

50 100 Particle impingement velocity, d s

Figure 4. Relationship between particle impingement velocity and contents of Si and Al, which is main components of particles, on worn surface of stainless steel obtained by XMA analysis (particle impingement angle: 45") microanalyzer (XMA). Figure 4 shows t h e relationship between the particle impingement velocity and the contents of Si and All which are the main components of particles, on the worn surfaces of stainless steel. The contents of particle components tend to increase as increase of velocity and particle diameter. Figure 5 shows the relationship between the test piece material and the contents of particle components on the worn surface provided to 500°C condition test. The contents of particle components on stainless steel is greater than on cermet coating. And the adhesion of particle is especially severe a t impingement of 35pm particles. Figure 6 a n d 7 a r e t h e images of SEM (scanning electron microscope) and results of XMA analysis on the cross section of the worn surface of stainless steel provided to 500°C tests. On the worn surface by 13pm diameter particles, shown in figure 6, adhered film is not observed. On the other hand, on t h e worn surface by 35pm diameter particles, shown in figure 7, the continuous thin film, which contain the components of particles, Si and Al, were formed on the worn surface. The thickness of the film is about from 5 to 15pm, which is smaller than average diameter of impinging particles. 3.2 Measurement of wear

Test 1 (d50: 13pm)

Test 2 (ds0: 35pm)

Figure 5. Contents of Si and Al on worn surface of stainless steel and cermet coating provided to test 1 and 2 obtained by XMA analysis (T: 500"C,v: lOOm/s, particle impingement angle: 45")

The influence of film formation on wear rates (wear depth per unit time) was appeared. Figure 8 shows the wear rate a t each position of the test pieces under 500°C condition. As supplying rate of particles were different at each test, the wear rate presented in figure 8 were converted into the value in the case that t h e particle contents were 50g/m9, by t h e assumption that the wear rate is proportional to the particle contents in the carrying gas. The wear r a t e of stainless steel decreases as increase of particle diameter, especially at the position where the particle impingement angle is about from 30" to 45'. On the other hand the wear rate of cermet coating does not depend on the particle diameter. This results suggest that the adhered film formation decreases the wear rate of stainless steel. The relationship between the test conditions and the maximum wear rates of each material are shown in figure 9. At the test supplied the small particles, which did not form the adhered film on worn surface, stainless steel was worn three times as great as cermet. But the wear rate is almost equal at each material when the large particles, which adhered on worn surface of stainless steel and formed thin film, were used. Authors led the equations describing the relationship between the particle impingement angle and the wear rate [131.The wear rate E is represented by following expressions.

609

Figure 6. Cross section of stainless steel surface worn by small, average diameter is 13pm, fly ash

(T:500"C,v: lOOm/s, particle impingement angle: 45")

Figure 7. Cross section of stainless steel surface worn by large, average diameter is 35pm, fly ash

(T:5OO0C,v: lOOm/s, particle impingement angle: 45")

610

Direction of particle impingement

3 5

$ 5

j4

j4

3

c,

?3

t 3

E 2

E 2

$ 1

3 1

SO

3 0 -90

-180

0

0

90

180

0

90

180

a, dcg

a, dcg

(a)Test 1 (d, : 13pm) stainless seeel

(b) Test 1 (ds0;13pm) cermet coating

3 5

$ 5

j4

s4

c Q ,

3

1 3

Test piece

-90

-180

?3

E2

E2

3 1

2 1

BO -180

0

-90

90

180

-90

-180

a, deg

0

90

180

a, deg

(c) Test 2 (dso:35pm) stainless steel

(d) Test 2 (d,o; 35pm) cermet coating

Figure 8. Wear rate of each position of test pieces ( T: 5OO0C,v: 1OOm/s 1 Table 4 Ec and Ed of each test piece (T: 5OO0C,v: lOOm/s) E", wnhour

Stainless steel

Test 1(d5,:13pm) Stainless steel Cermet coating Test 1 (dS0:13pm)

Test 2 (ds0:35pm) Stainless steel Cermet coating

Test 2 (d50:35pm)

E,. umhour

4.0

1.0

1.4 1.5

1.3 0.8

0.9 1.6

Figure 9. Maximum wear rate of each material (T: 5OO0C,v: lOOm/s) E=

where Ec=cutting wear rate Ed= deformation wear rate 8 = particle impingement angle

{$

Eccos2e+Edsin28 sine

when tane>l/3

(1)

E= { ~ E c ( s i n 2 e - 3 s i n 2 e when t a n 0 4 3

(2)

Applying the results of the test to equations (1) and (21,E, and Ed were obtained. Table 4 shows E, and Ed at each material and test condition. It is noticeable that E, of stainless steel decrease when adhered film was formed.

61 1

4. DISCUSSION

From the results of the test the formation of thin adhered film improves the wear resistance of s t a i n l e s s steel. And t h e a d h e r e d film thickness is smaller than the average diameter of impinging particles. It suggests that the film is not formed by the adhering of the whole particle, but by the adhesion and fracture of particle to leave a part on the worn surface. It is expected that, if the contact area formed between the particle and the test piece by the impingement increases, the adhering force increases, too. In this section the contact area formed by impingement will be derived and the relationship between the contact area and the state of adhesion will be discussed. It is supposed that the particle is spherical and plastic deformation is occurred a t the test piece only. If the contact between the test piece and the particle is elastic, the maximum normal force F,,,u and the radius of the contact area re are described next equations [lo].

(5)

If the contact pressure reaches the elastic load limit of the test piece y , the plastic deformation of the test piece surface begins. The particle velocity a t which t h e elastic limit is j u s t reached, u ' ~,,is expressed in following equation

[lo].

Putting the properties of steel and the particle into equation (6), the value of ule,becomes about I d s . As the velocity discussed in this paper is much higher than ule,, the influence of plastic deformation is not ignored. Bitter led the equation on the contact area by plastic deformation [lo]: mp

(3)

(4) in which p= density of particle R= radius of particle El= equivalent Young's modulus

E,,E,= Young's modulus of particle and test piece, respectively v,,v,= Poisson's ratio of particle and test piece, respectively v'= particle velocity to the normal direction of impinged surface

=2nRHmax

(7)

where rpmax= the maximum radius ofprojection of the plastic deformation area in the impingement H,,,= depth of indentation after impingement. And the total contact area in the case of the plastic-elastic contact A, is:

where remax= the radius of contact area when plastic deformation begins. The formation of the permanent indentation requires an amount of energy Qp equal to [lo]:

From equations (3) and (41, the contact area at elastic deformation m,Z is derived: where re=the radius of the plastic deformation area

612

3 100

~

0

and the relationship between velocity is:

QP

and particle

rn A

A

is represented in following equation.

(10)

where m= mass of the particle. From equations (7)and (91,the area subjected to plastic deformation, nrp,,lar2, is described in next equation. (11)

Putting equation (10) in ( l l ) ,nrp

is:

(12)

Putting equation (6)to (51, the contact area subjected to only elastic deformation when plastic deformation occurs, w enllu2, is:

Putting the property of the test piece and the particle into equation (141, the total contact area is derived. Comparing the contact area A, and the results of the tests on stainless steel, figure 10 is obtained. Figure 10 shows t h a t contents of particle components on worn surface tend to increase as increase of the contact area between particle and test piece. The case using cermet as the test piece is not mentioned here, because cermet has high Young's modulus a n d hardness, a n d it is necessary to consider t h e effect of particle deformation. Since cermet does not deformed as easily as steel, it is supposed that the contact area at the impingement on cermet is smaller t h a n on steel, and t h e amount of particle adhesion to cermet is smaller than to steel. 5. CONCLUSIONS

(13)

Putting equations (6),(12) and (13) into (81,the total contact area in plastic-elastic impact, A,,

At the particle erosion test under the elevated temperature condition the instance that the thin film which contains the components of impinging particles was formed on the worn surface was found. As a result of the film

613 formation, under 500°C condition the wear rate of stainless steel is almost as same as of Cr,C,-

NiCr cermet coating which is about five times as hard a s stainless steel. And the thickness of film is about from 5 to 15pm, which is smaller t h a n t h e average diameter of impinging particles. By the discussion on the contact area between particle and test piece at the impingement, it was found that the state of particle adhesion is concerned with the contact area under high temperature condition.

REFERENCE 1. Y. Shida a n d H. Fujikawa, Wear, 103

(19851281. 2. A. V. Levy, J. Yan and J. Patterson, Wear, 108 (1986) 43.

3. A. J. Ninham, I. M. Hutchings and J. A. Little, Corrosion 89, (1989) 544. 4. P. M. Rogers, I. M. Hutchings and J. A. Little, Surface Engineering, 8 (1992) 48. 5.B. Q. Wang, G. Q. Gengand A. V. Levy,Wear, 159 (1992) 233 6. W. A. Stauffer, Metal Progress, 69 (1956) 102 7. E. Rabinowicz, JSLE-ASLE International Lubrication Conf. Text, Tokyo, (1975) 54 8. Y. Kagimoto, S. Matsumoto and Y. Arakawa, Proc. JSLE 34th Conf. (Toyama), (1989) 563 (in Japanese) 9. I. Finnie, Wear, 3 (1960) 87 10. J. G. A. Bitter, Wear, 6 (1963) 5 11. J. G. A. Bitter, Wear, 6 (1963) 169 12. I. M. Hutchings, J. Phys. D: Appl. Phys., 25 (1992) A212 13. N. Hayashi, Y. Kagimoto, A. Notomi, Y. Takeda and H. Akiyama, Proc. JSME Conf. in Kitakyushu, (1994) 266 (in Japanese)

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The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

615

The wear mechanism of ductile metals by slurries: fatigue or ratchetting? A A.Torrance, Y.Yang Blake and B. Crosby

Department of Mechanical and Manufacturing Engineering, Trinity College, Dublin 2, IRELAND. There have recently been proposed two mechanisms for the formation of wear particles from ductile materials: low-cycle fatigue, and ratchetting. The two mechanisms are briefly discussed, and the results of a test designed to measure the "wear ductility" of metals are shown to be consistent with low-cycle fatigue. However, the wear ductilities measured in these tests can also be used to correlate the results of 3-body abrasive wear tests assuming a ratchetting mechanism.

1. INTRODUCTION

To predict the wear rate of metals from their mechanical properties would be very useful, but in practice, it is often a tantalizingly elusive goal. Empirical correlations are of limited value, and a full physical understanding of mechanical wear is still some way off. However, in recent years, several authors have suggested that the mechanical wear rates of metals could be related to the plastic strains induced in their surfaces as they slide (1 -4). It is assumed that one of the sliding surfaces is harder than the other, and that both surfaces are of rigid-plastic materials. If plane strain is also assumed, calculations of the surface stresses and strains can be made using the slip-line field of figure 1, where an asperity on the hard surface is represented as a rigid wedge which deforms the softer surface as it slides All investigators agree about the calculation of the stresses and forces on the wedge. The relevant equations are for the forces per unit width (2): F, F,

(A.sina + cos(2&-a)).ED.kS = (A.cosa + ~in(2c-a)JED.k~ =

(1,) (2)

(3) where: A = I + d 2 +2&+21)-2a, k, = shear yield strength of soft material, 2&= arccosfjl,

Figure 1. Slip-line field and hodograph for stress and strain calculations. z f= where z is the shear strength of ED. k'

The experiments of various workers have shown that these equations will predict p well both for sliding wedge experiments (1,2) and for real surfaces (3). There has, however, been some hsagreement about the way strains should be calculated, and how the plastic strain should relate to wear rates. As the wedge slides across the soft material it raises a wave (AED) before it and produces a strained layer of thickness h behind it (cf. fig. I). Challen et al. (1) suggested that the number of wave passes (N) to cause the strained layer to break free from the surface would be related to the global plastic strain in each pass, ye, by a Coffin-Manson low cycle fatigue relation:

616

N=($)D

(4)

C and D are'material constants which must be found experimentally, whilst ye can be found from energy considerations. If a wedge of unit width moves through unit distance at velocity U, the external work done is F,. This is dissipated in shearing a volume of metal h and shearing the surface layer on ED. The work done on ED is:

k,

p U

which vields:

(ye.h +{%)ks

=F,

(5)

allowing ye to be calculated from the geometry of figure 1. Full details of how the wear coefficient can be calculated from these considerations have been given elsewhere (1,2,5,6). Experimental wear results can be fitted to this model by choosing appropriate values of C and D, but it is only recently that a test has been developed to measure these quantities independently (5,6). An alternative to this simple approach has been suggested by Kapoor (4). He pointed out that the strain can be divided into two components: a fully reversing axial strain, E,, which acts parallel to the surface; and a "ratchetting" shear strain, y, which accumulates at each passage of a wave across the soft surface. He proposed that this would lead to two competing failure mechamsms: low cycle fatigue, with the equation:

N=

(&)

and obtained some results, whch could be interpreted as ratchetting provided unrealistically high values of C were used. However, further aaalysis of these results, coupled with some extra experiments (6) showed fairly conclusively that the results for aluminium and brass fitted the earlier model of Challen and Oxley (1,2) much better, with values of D close to 2, and values of C close to those estimated by metallography (2,5). Those for copper were not well enough controlled to be used. As the special wear test had been successful in measuring C and D for aluminium and brass, it was decided to repeat the test for copper in a better controlled way, and then to see whether the values of these material constants could be used to predict wear rates in more complex contact conditions. This paper describes these tests and their results: the application of the measured material constants to the prediction of wear by abrasive slurries. 2. EXPERIMENTS.

2.1 Wedge tests. The experimental set-up used for the special wear tests is shown in figure 2. Three non-ferrous materials were chosen for testing which had similar hdnesses but widely differing ductilities (see table 1). One end of a non-ferrous bar having a Loading bolt.

~-

,Load arm.

2

(6)

and ratchetting with the equation:

N=@)

(7)

Kapoor (4) argued that whichever mechanism gave the lower value of N would be the one to occur. He felt that in most cases this would lead to ratchetting. Yang and Torrance ( 5 ) attempted to verify his ideas experimentally for aluminium alloy, brass and copper with a specially developed wear test,

DYNAMOMETER

LATHE SADDLE Figure 2. Wedge wear test on lathe

617

diameter of 34 mm, was held in the chuck of a lathe whilst the other end was supported on a running centre. One end of a hard steel tool was ground and polished to a blunt wedge of the desired attack angle. It was either 3.3mm or 4.5 mm in width and was mounted in the loading arm,being held against the bar by tightening the loading bolt. Alignment with the axis of the bar was ensured by mounting the loading assembly on trunnions. These in turn were mounted on a 3-axis Kistler dynamometer fixed to the saddle of the lathe whch allowed normal and tangential forces to be recorded throughout a test on a chart recorder. Lubrication was provided by engine oil (Elf ISW/40 competition S) which was fed onto the surface of the bar through a wick. Tests were run with a variety of attack angles between 2.5' and 25'. First the lathe was set rotating at 35 rev/min with a very light load applied to the wedge. The loading bolt was then tightened to apply the test load. The first set of tests was allowed to run for about 2 minutes, giving around 70 passes of the wedge over each point of the bar's surface. However, for some of the lower wedge angles, extra tests were run for up to 3 hours to allow a larger number of strain cycles to be applied to the testpiece. Normal loads of 400N and 500N were used for each wedge angle. The wear of the testpieces was measured in all cases by weight loss, determined by weighing them on a balance accurate to 0.1 mg. . The ratio of normal to tangential force (p) was calculated from the dynamometer readmgs. Full details of the tests on aluminium and brass are given in references 5 and 6. For a test to be valid, it was necessary for sufficient strain cycles to be applied to remove a depth of material greater than the thickness of the strained surface layer. Most of the tests on aluminium and brass fulfilled this criterion (5,6). However almost all of the tests performed on copper were too short. Also, there was evidence that the high ductility of copper had allowed considerable departures from plane strain. The tests on copper were therefore repeated for this paper. Before each test, a rectangular groove of the same width as the wedge, and 1 mm in depth, was machined in the copper bar. The test was started

TABLE 1, Properties of testpieces, A. Aluminium alloy (5083) C. O.F.H.C. Copper B. cdp Brass (60:40) Matl. Hv A. 125 B. 170 C. 116

H,, oy( m a ) o,,, (MPa) R.A.

E,

151 265 408 50% 0.69 217 398 480 19% 0.21 165 204 379 87% 2.04 Note: cr = -log,(l-R.A./lOO) Hv measured at 20 kgf load; H,at 0.01 kgfload o,,, = Hvx9.81/3;a,,is O.I%proof stress.

with the wedge pressing on the base of the groove. In this way, sideways flow of the copper was restricted, and conditions approached plane strain much more closely than in previous work (5,6). The results from these tests were used to calculate C and D for the three materials as described in the next section. These values were then used to interpret their abrasive wear rates which were measured using a modified Struers Wear Test (7) as described below.

I I

II

LOAD

I

Figure 3. Modified Struers Abrasive Wear Test. 2.2 Abrasion tests.

The apparatus, which is shown in figure 3, is a modified metallographic polishng machme. The polishing disc is replaced with a circumferentially grooved cast iron lap. A piece of the material to be tested, 12.5 mm in diameter, is mounted in resin,

618 and after being weighed to an accuracy of 0.1 mg, it is placed in a holder which allows it to be loaded against the lap by a dead weight. The lap itself was covered with an abrasive (see table 2) which was mixed with sufficient water to produce a smooth slurry. Loads of between 10 and 50N were applied to the specimens, and tests were run for 1 to 5 minutes at a speed of 125 rev/min with the specimen running on a pitch circle 130 mm in diameter. After each test, the specimen was carefully cleaned, dried and re-weighed to allow the volume of metal removed to be calculated. Each material was tested against three different abrasives and each test was repeated 3 - 6 times;

TABLE2. Me! 1. 2. 3.

Abrasives used Material Size ransand 212 - 300 sand 75- 150 glass beads 100- 200

the mean value is reported here. It was decided to report the results of the tests as non-dimensional wear coefficients, K, defined thus, where b is the width of the wedge:

K=

related to ductility. Since each metal will suffer much the same strain when an abrasive grit passes over it, we may expect to find a relationship between K, and C measured in the wedge test. If wear takes place by low-cycle fatigue, as seems to be the case in the wedge tests (6), then we should get the relationship:

whereas if wear is by ratchetting, we should get:

where 2 is a geometrical constant depending on the characteristics of the abrasive slurry.

3. RESULTS The results of the wedge wear tests have already been discussed in detail elsewhere (5,6), so only the graphs which allow the values of C and D to be calculated are given here. The results for aluminium and brass are those previously published (5,6), but for copper, fresh results were obtained using the extra precautions described above.

W.Hu~9.81 3~Fn.b.s

W is the volume of material worn away in the test, and s is the total sliding distance. K is normalized, not by the bulk hardness of the material as suggested by Archard (8), but by the microhardness of the worn surface as recommended by other workers (9,10,1 l), which they found gave better correlation with abrasive wear resistance. In our work, the surface microhardness was measured with a Vickers indentor at 10 gf load on small lands polished on the asperities of the worn surface. A similar method was used by Mutton and Watson ( 1 1).

Although the absolute wear rate of the materials tested will depend on their hardness, K should not be affected. However, if the wear in the Struers test is related to the plastic strain which the abrasive imposes on the metal, then K may be

N revolutions

Figure 4. Developing a wear equation. The raw results from these tests are the forces, the attack angle of the wedge and the weight loss of the specimen. From the lirst two, it is possible to calculate the strain per cycle, and the thxkness h of

619

the worn layer from equation (5) as described previously (5,6). N can be found from the weight loss as follows. Suppose that there are R revolutions of the testpiece in a test, and a depth t is worn away. The total distance slid, s, is given by:

1.4

I Y 72.614 - 0.473X

1.2 1

s = nDR

(11)

3 0.8

30.6

and the wear volume W by: W

=

nD. t. b 0.4

where b is the width of the wedge. Using:

k, =

0.2

Hv~9.8 1 2

3 6

3

4

3.5

4.5

5

5.5

WN) Figure 5 . h(N) v. Ln('yJ for copper

It follows from equation (7) that:

- t ks K = t.b.dI.Hv~9.81 3~Fn.b.R.xD R ' F ,

6

(13) 1

Since the number of revolutions N to remove a thickness h is related to R by:

R-N

I

0.5

s

_t - _h

$

v

0

E 4

we can substitute N for R and h for t in equation (13). Combining this with equation (2), and finding from figure 1 that the ratio MED = (sin& - sin@ we anive at the result:

J7(sin &-Sin N=

2.5

a

1

-0.5

-I -1.5

)

K[A cos a+sin [ 2 & 4

(1 4)

wluch allows N to be found from the measured value of K.It is then possible to plot on a log scale N against 'ye for a series of different wedge angles and so obtain values of C and D. These results for the three test materials are given in figures 5 to 7., which show experimental points and a line fitted by least squares for each material. The equation of the line is also shown in the form:

t'

I

1.5

2

2.5

1

3

3.5

4

1

1

4.5

5

5.5

LnO

Figure 6. Ln(N) v. Ln(yJ for brass

Y=a-mX so that: C = e" and D =I/m. The values are given in table 3, where it can be

620

2

5 -

4 -

.13

-

2 -

1

-0.5

1

2

3

4

5

6

I

K = 0.0214K + 0.00038 K = O.O048,3/C- 0.00007

0 ' 0

0.05

0. I

0.15

0.2

WN)

1/c

Figure 7. Ln(N) v. Ln(y,) for aluminium

Figure 8. "Ratchetting" graphs for the abrasion tests: 1/C v. K for each abrasive (cf. table 2).

TABLE 3. Values o f C and D-for the three matenah Mat1. A1 5083 Brass 60/40 CuOFHC

a 2.39 1.88 2.614

C 10.9 6.6 13.7

m

D

0.555 0.548 0.473

1.80 1.73 2.11

seen that the behaviour previously found with aluminium and brass is also shown by copper. The wear coefficients, K , from the abrasive wear tests were then plotted. It was found that for all three abrasives, they could be fitted best by equation (lo), as shown in figure 8. The fit is quite good, suggesting that a ratchetting wear mechanism is operating in these tests, rather than the low cycle fatigue occurring in the wedge tests. The actual values of the wear coefficient are lower for the finer sand than for the coarse sand, and lower still for the glass beads as might be expected. 4. DISCUSSION

From the results presented above, it appears that both low-cycle fatigue and ratchetting can occur in practice during the wear of ductile metals. However, it is not immediately clear what

determines which mechanism occurs. Kapoor (4) believed that ratchetting should be the dominant mechanism, as he thought that accumulating strain would be more damaging than reversing strain. He gave a method of calculating when each mechanism might be expected. When it was applied to wedge tests, it indicated that only materials of very low ductility should wear by low-cycle fatigue (5). However, Oxley et al. (6) questioned Kapoork assumptions of the damaging effects of different components of plastic strain. They felt that he had underestimated the damage caused by the reversing part of the strain cycle in a wedge test and showed that low-cycle fatigue was the most likely mechanism in this case. Ratchetting was also considered by Kapoor and Johnson (12) to be an explanation of other types of wear. They designed an experiment to model the formation of thin wear platelets which had been observed by several authors (13-15). Under the influence of local stresses, small slivers of metal could be extruded from asperity tips, either sideways for ridges parallel to the direction of motion, or in the direction of sliding. At each asperity contact, the slivers would extrude a little further until they became long enough to break free

62 1 as wear particles. The process was essentially one of repeated small increments of strain in the same direction, or ratchetting. A full mathematical treatment of the process was given which explained well the experimental observations. It was shown that for the extrusion of thm wear flakes by ratchetting an asperity with a reasonably sharp change of slope (an 'ledge") was needed. The stress concentration there would then ensure that plastic flow would result in some of the asperity tip being extruded each time it was stressed. It was pointed out that this mechamsm could also explain erosion of metals, blasted by particles. Pummelling of a ductile material by random impacts would lead to the extrusion of small slivers in the much same way, and t h s could be used to explain the erosion experiments of Cousens and Huchings (1 6). The contact stresses in the abrasive wear tests reported here will lie somewhere between these erosion experiments, where there is zero friction, and the sliding wear experiments studied by Kapoor and Johnson (12). Most of the abrasive particles should roll over the surface of the metal (7) with little sliding, and this was confirmed by microscopy. The correlation of these wear results with a ratchetting equation can thus be explained. However, it is still not clear when ratchetting would give way to low-cycle fatigue, and how such a transition could be predicted. Oxley ( I ) has argued that the relationslup between hction and wear rate commonly observed in experiments on metallic wear is much more consistent with a low-cycle fatigue law than with ratchetting.; but against tlus must be set the results discussed by Kapoor and Johnson (12) which seem to be clear cases of ratchetting. The contribution of the work reported here to this discussion is to show that a "wear ductility I' C measured in a wedge wear test, assuming a low-cycle fatigue wear law can be used to correlate the wear rates of three ductile metals by some simple abrasive slurries. This suggests that there are common material properties underlying the two mechanisms, and that it could be profitable to put some effort into developing ways of measuring them. The wedge wear test used here has some

defects which have been dmussed more l l l y elsewhere (5,6): experimentally it is difficult to set the attack angle of the wedge, 01, accurately enough to ensure accurate strain calculations; and also it can be difficult to get a good enough approximation to plane strain; as regards the analysis, work hardening is ignored, which leads to some errors in the estimates of strain. However, within the limitations of the technique, these initial results are quite encouraging.

5. CONCLUSIONS A special wedge wear test has been developed to measure the "wear ductility" C of ductile metals. The wear mechanism operating in this test appears to be a form of low-cycle fatigue. However, in some simple wear tests against abrasive slurries C can be used to correlate the wear rates provided a ratchetting mechanism is assumed. Th~s is consistent with the findmgs of Kapoor and Johnson (12) and , as regards the wedge wear tests, with those of Oxley (2,6).

ACKNOWLEDGEMENTS The authors are most gratefit1 to Professor P.L.B. Oxley and Dr. A. Kapoor for helpful discussions about t h s work.

REFERENCES 1. Challen, J.M., Kopalinsky,E.M. & Oxley, P.L.B.

"An asperity deformation model for relating the coefficients of friction and wear in sliding metal friction," in "Tribology - Friction, Lubrication and Wear fifty years on, Vol 11," I.Mech E., London (1987) Paper C156/87. 2. Black, A.J., Kopalinsky, E.M. & Oxley, P.L.B. "Asperity deformation models for explaining the mechanisms involved in friction and wear - a review" Proc. I. Mech. E., 207 (1993), 335-353. 3. Lacey, P. & Torrance, A.A. T h e calculation of wear coefficients for plastic contacts, Wear, 145 (1991) 367-383.

622 4. Kapoor, A., "A re-evaluation of the life to

rupture of ductile metals by cyclic plastic strain." Fatigue Fract. Engng. Mater. Struct., 17 (1994) 20 1-2 19.

5. Yanyi Yang and Torrance A.A. "Wear by plastic ratchetting: an experimental evaluation." To be published in Wear (1995). 6. Yanyi Yang, Torrance A.A. and Oxley P.L.B. "Modelling mechanical wear processes in metallic sliding friction" Submitted to J. Phys. D (1995).

7 . Fundal E. Private communication (1991). 8. Archard, J.F., "Contact and rubbing of flat surfaces", J.Appl. Phys, 24 (1953) 981-989. 9. Richardson R. C. D., "The wear of metals by hard abrasives", Wear, I 0 (1967) 291.

10. Richardson R. C. D., "The maximum hardness of strained surfaces and the abrasive wear of metals and alloys", Wear, 10 (1 967) 353. 1 I . Mutton, P.J. and Watson, J.D. "Some effects of microstructure on the abrasion resistance of metals" Wear, 48, (1978) 385.

12. Kapoor. A. and Johnson, K.L. "Plastic ratchetting as a mechanism of metallic wear", Proc. I?. Soc. Lond A 445 (1994) 367-381. 13. Akagalu, T. and Kato, K. "Plastic flow processes of surface layers in flow wear under boundary lubricated conditions" Wear 11 7 (1 987) 179.

14. Reda, A.A. Bowen, R. and Westcott, V.C. "Characteristics of particles generated at the interface of sliding steel surfaces" Wear 34, (1975) 26 1-273.

15, Kuo, S.M. and Rigney, D.A. "Sliding behaviour of aluminium" Muter. Sci Engng A 157 (1992) I3 1- 143.

16. Cousens, A.K. and Huchings, I.M. "A critical study of the erosion of an aluminium alloy by solid spherical particles at normal impact" Wear, X X (1983) 335-348.

NOMENCLATURE. Points in stress field (see fig. I ) . 5 f lrJ4+&-ff-q. Constant in least squares fit. Width of wedge. Wear ductility. Exponent in L.C.F. equation. Tresca's factor (J'= C O S ~ E ) . Tangential force per unit width Normal force per unit width. Depth of strained surface layer. Vickers hardness. Microhardness of worn surface. Archard's wear coefficient. Shear yield strength of soft metal. Gradient of least squares fit. Revolutions to remove h. Total revolutions in test. Total sliding distance in test. Total wear depth in test. Sliding speed in test. Velocity of metal along ED. Variables in least squares fit . Geometrical constant of abrasive. Angles defined in figure I .

Equivalent plastic strain in cycle. Ratchetting strain in cycle. Reversing strain in cycle. Coefficient of fnction. Tensile yield stress 9.8 1xHv/3. Shear strength of ED (see fig I ) .

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

623

Surface degradation and third body formation in tribocorrosion systems S. Mischler, S . Debaud, E.A. Rosset, D. Landolt Materials Department, Ecole Polytechnique FCdCrale de Lausanne, 1015 Lausanne, Switzerland

The tribocorrosion behaviour under sliding conditions of a 316L grade stainless steel in 0.5 M H,SO, has been studied at two applied potentials in the passive range and in the cathodic range. It was found that the wear and frictional behaviour depends critically ion the applied potentials. The observed results can be interpretated by using the third body approach proposed by Godet et al [ 11. At the passive potential no third body is formed and surface degradation occurs by two mechanisms: particle detachment and metal dissolution. At the cathodic potential no corrosion occurs and the presence of a third body reduces significantly the rate of particle detachment. 1. INTRODUCTION

The third body concept is a very useful theoretical tool allowing one to establish relations between microscopic mechanisms and the macroscopic properties such as wear, friction and load carrying capacity of tribological systems. From Lhe point of view of surface degradation,the wear process under dry rubbing condition is considered a!! a particle flow including material detachment (by different possible mechanisms such as adhesion, abrasion, fatigue, oxidation) from the first bodies leading to the formation of third body particles with their possible elimination from the contact as wear particles [ 11. For the description of tribological systems operating in corrosive liquid environments (tribocorrosion systems) the third body concept should be extended in order to consider the interaction of mechanical (wear) and chemical (corrosion) degradation mechanisms. For example, in tribocorrosion systems surface degradation i n the contact occurs not only by particle detachment (as in thecase of dry rubbing) but also by corrosion, i.e. the transformation (by transfer of n electrons e ) of a solid metal M in metal ions Mn+ dissolved in the corrosive solution

according to the following electrochemical reaction. M(so1id) = M"+(dissolved)+ ne-

(1)

The consequences of surface degradation by corrosion on the wear and frictional behaviour differs fundamentally from the degradation by particle detachment. In effect, since dissolved metal ions have no load carrying properties, corrosion cannot be considered as a source of third body. In addition particle detachment and the behaviour of the third body may depend on surface effects determined by the corrosion conditions. Changes of frictional coefficient with the applied potential observed on irodiron rubbing contacts exposed to salt solutions have already been related to electrostatic repulsion forces and the formation of FeOOH and iron(I1) carboxylate at the metal surface [2]. The present study was initiated with the aim to investigatethe influence of corrosion phenomena on the surface degradation and third body formation of a model tribocorrosion system. For this purpose a wear test rig equipped with an electrochemical setup was used in order to deter-

624

mine the influence of the applied potential on the wear and frictional behaviour of an alumina pin (chosen for its inertness) sliding against a 316L stainlesssteel plate immersed in a0.5 M sulphuric acid solution. By applying either a cathodic potential of -1.2 V or a passive potential of 0.3 V (all the potentials are given here with reference to the MSE standard mercurosulphate electrode),it was possible to impose different corrosion conditions to the stainless steel during rubbing. At the passive potential a thin metal oxide film (2-5 nm thick) forms on the stainless steel surface. This film represents a barrier separating the metal from the solution and therefore, it protects the underlying metal against corrosion. Under rubbing conditionshowever, mechanical abrasion may interfere with the formation of the passive film so that significant metal dissolution may take place. By measuring the current passed at the passive potential it is possible, according to Faraday's law, to determine the amount of dissolved metal and therefore the contribution of corrosion to the steel surface degradation. At the selected cathodic potential, the driving force for reaction (1) becomes small, so that practically no metal ions are formed and therefore the corrosion rate remains negligible(below 0.001 mm penetration per year [3]). At the cathodic potential rubbing is not supposed to affect the corrosion rate. For a more details concerning the application of electrochemical techniques to tribocorrosion tests the reader is referred to the literature [4,5]

(10 mm diameter). The hardness of the steel was 225 HV 10and its compositionmeasured by atomic absorptionis giveninTable 1. Theoscillating pins were prepared by machining the ends of alumina rods of technical purity (4 mm diameter) in the shape of truncated cones (120" included angle). The diameter of the flat end was 0.5 mm giving an apparent contact area of 0.2 mm2.Prior to the wear test, discs and pins were cleaned in a an ultrasonic ethanol bath. Wear tests: Frictional test were carried out in a slightly modified version of the reciprocating pin-on-plate rig described in more details elsewhere [4,5].The modification consisted in replacing the Briiel& Kjaer vibration exciter with a linear motor (developed by ETEL SA, Mbtier) allowing for precise displacement control of the pin. During the test the frictional and the normal forces as well as the electrochemical parameters (current and potential) were continuously monitored using a Macintosh computer. The coefficient of friction was determined by dividing the frictional and the normal forces measured when the pin was in the middle of the wear scar. The pin was oscillating at a frequency of 5 Hz. The linear motor was driven in order to maintain the pin motionless for 20 ms at the end of each stroke. In this way the stroke length of 5 mm corresponded to a sliding speed of 62 d s . The applied load was 5N resulting in a nominal contact pressure of 25 MPa. The electrochemical tests conditions involved cathodic polarization at - 1.2 V MSE during 5 minutes to reduce residual surface oxide films followed by polarization at the selected potential. After 20 minutes polarization the rubbing was started. The rubbing time for all experiments was 1800s correspondingto 18000strokes.

2. EXPERIMENTAL Testmaterials: Sliding wear conditions were established by rubbing an alumina pin against an

quench annealed 316L grade stainless steel disc Table 1 Chemical comwsition of the 3 16L steel Cr Ni Element Weight 9% 17.2 12.5

Mo 1.13

Mn 1.46

Fe 67.2

625 At the end of the test the plates and the pins were removed from the solution and rinsed with distilled water. All experiments were carried out at room temperature (2 1-22°C). For each condition the experiments were repeated twice in order to check for reproducibility. The wear scar volume was determined by optical profilometry using an UBM laser system. For this the average cross section surface of five profiles measured across each wear scar was determined and multiplied by the stroke length. The morphology of the wear tracks and on the flat ends of the alumina pins were investigated using a JEOL 6300F scanning electron microscope.

(Fig. 2a). The scratches and grooves observed in the center of the wear scar (Fig. 2b) indicate that

3. RESULTS Wear andfriction: The measured value of

the coefficient of friction as well as the measured wear rate on the stainless steel discs are listed in Table 2. The listed coefficient of friction correspond to the average value observed during the rubbing time for each experiment. Generally the deviation fiom the average value was within the range of +/- 10%. SEM images of the wear track formed at the cathodic potential are shown in Fig. 1. The formation of a third body bed is clearly visible in Fig. l a. This bed covers the whole track surface and is probably formed by plastic deformation and compaction of particles detached from the steel disc (Fig. lb). NO such third body bed was visible in the SEM on the disc rubbed at the passive potential

Figure 1. SEMimagesofthe wear trackformedon the steel disc at the cathodic potential ploughing took place on the stainless s t e l SIXface. Since no wear particles were found either in the solution or around the contact area one may

Table 2 Wear tests results Potential

Coeff,of friction

Wear scar volume on the disc [nun31

0.01 - 0.02 0.15 - 0.26 (datafor two samples tested under identical conditionsat each potential)

cathodic

passive

0.37 - 0.44 0.32 - 0.30

Third body

particles bed none

626 conclude that two body abrasion contributed to the material degradation at the passive potential.

not interfere with the chemical reaction occurring at the steel electrode, i.e. the reduction of H+ to molecular hydrogen.

I .E+01

--+

rubbing .

1.kt00

$

..

1.G-01

u Y

c

tiI4 3

I li-02

u 1 .1<-03

1.11-04

500

0

so0 1000 1.500 2000 2500

Time [s] Figure 3 . Evolution of the current at the passive potential.

Figure 2. Evolution of the current at the passive potential. The geometry of the pins as observed by optical microscopy as well as Lhcir s u r l c e morphology characterised by SEM did not change during the experiment. Under thc conditions o f this study alumina was therefore not subject to wear or corrosion. Few wear debris were found by SEM analysis accumulating a1 theedgcs of'the flat end of the pins rubbed at the cathodic potenrial. Electrochemical behnviour. The current was not significantly affected by the rubbing at the cathodic potential. This show that rubbing does

A quite opposite behaviour was found at the passive potential. Here the beginning of the rubbing was characterised by a sharp and significant increase in current from 0.007 mA to about 1 mA (Fig. 3). When rubbing was stopped the current decreased again to the value observed before ru bbi ng . B y assuming that the current flowing at the passive potential is determined by reaction (1) only and flows mainly through the rubbed area, one can determine the average corrosion rate and the metal volume removed by corrosion in the wear track using Faraday's law. According to this the corrosion rate expressed as penetration Rcor per year is obtained using (2):

627

Rco, = 3.15 lo5 x iNbx M,,, / (F x n3,6 x r ) (2)

where Fis the Faraday's constant (96500 C/ mole), M,,, the average atomic mass of the 3 16 steel (M,,, =), r its density (7.95 g/cm3) and n the average valence of dissolution. The current density under rubbing conditions irub can be estimated by dividing the average current observed during rubbing by the wear track area (0.025 cm2). The average values M,,, and n3,6 were estimated by a mixture rule corresponding to X = 0.172XCr + 0.125XNi + 0.703XFe.where X is either the atomic mass (Cr=52, Ni 58.7, Fe 55.8, M,,, = 55.5 @mole)or the valence of dissolution (Cr=3, Ni=2, Fe=2,n3,,=2.2).The metal volume removed by corrosion in the wear track can be obtained by integrating the corrosion rate over the rubbing time (1800 s) and the wear track area (0.025 cm2). The obtained current densities and the corresponding corrosion rates are listed in Table 3. The corrosion rate experienced by the passive metal surface outside the track can be determined by dividing the current observed before rubbing by the disc area (0.79 cm2) and integrating it according to (2). In this way one obtains a current density of 9 10-4 mNcm2 and a corrosion rate of 7 10-3 &year. The significant difference by more of 4 orders of magnitude in corrosion rate found at the

passive potential between surface inside and outside the wear track indicates that under rubbing conditions the passive film is periodically removed by abrasion thus exposing native metal to the corrosive environment. Since the surface is kept at a constant passive potential the passive film is spontaneously re-built. However the film formation requires a finite time, during which the metal dissolves at a very high rate determined by the applied potential. The variation of current and of pin horizontal position recorded during a stroke (Fig. 4) lends

*.O

7

1.5 -

7 E

u C

1.0.

2 h

a 0.5

-

0.0

4 0

100

200

300

Time [ms] Figure 4. Variation of current and horizontal pin position during sliding.

Table 3 Current densities, corrosion rates and volume removed by corrosion from the wear track at the passive potential Sample 2 Sample 1 Current density [mNcm*] 37 43 Corrosion rate [mdyearl 380 450 0.055 0.063 Volume removed by corrosion [mm3]

628

Table 4 Contribution to wear scar volume on the steel disc bv Darticle detachment and corrosion Wear in mm3 by: Cathodic potential PassivePotentid parricle detachment 0.01 - 0.02 0.09 - 0.20 corrosion none 0.06 - 0.06 total wear (sum) 0.01 - 0.02 0.15 - 0.26 (data for two samples tested under identical conditions at each potential) support to this mechanism. At the end of each stroke, when the direction of motion changes, the pin remains motionless for 20 ms. During this dead time the current drops to about 10% of its maximum value. Such a relation between current and pin displacement has been quantitatively related to the continuous passive oxide removal during the displacement with the subsequent repassivationof the worn area at thedead time [4]. 4) DISCUSSION Systems: The difference i n applied

electrochemicalpotential of the two tribocorrosion systems investigated here result in a significant difference in wear and frictional behaviour of the 3 16L stainless steel. At the cathodic potential the material loss is more than one order of magnitude less that at the passive potential whilst the coefficient of friction is slightly higher. Such a difference in wear and friction can be related to the different mechanisms of first body surface degradation and third body formation. Sugace degradation of the first bodies: Despite the fact that under static conditions the corrosion rate of passive stainless steel is negligible, extremely high corrosion rates up to 450 mml year (nearly 1 pmlminute) are observed in the wear track during rubbing due to the interference of abrasion with the formation of a corrosion protective passive film. However corrosion alone cannot account for the total material loss observed at the passive potential. The comparison of the wear data of Table 2 and the volumes removed by corrosion given in Table 3 leads to the conclusion

that corrosion is responsible of roughly 1/3 of the overall material loss at the passivepotential whilst particle detachment due to mechanical interactions is responsiblefor the remaining material loss (see Table 4). At the cathodic potential surface degradation is due to particle detachment only since no corrosion occurs at this potential. Note however that the rate of particle detachment is significantly more important at the passive potential than at the cathodic. Such a difference can be explained by the formations of a third body on the cathodic sample. Third body: The compact particle bed found at the cathodic potential can be considered as a third body separating the metal from the alumina (first bodies). By accommodating most of the difference in velocity between the two first bodies, this particle bed protects the metal surface from further particle detachment and reduces in this way the extent of wear. The energy dissipation resulting in friction is probably determined by the phenomena taking place in the third body, i.e. plastic deformation of the detached particles, compaction of the particles and rheology of the particle bed. At the passive potential no particle bed can be observed and therefore the metal surface undergoes abrasion either by the asperities of the aluminapinor by singleparticlespossiblytrapped in the contact. The abraded particles do not form a protective bed but are eliminated from the wear track. In this way relatively severe abrasive conditions are maintained on the rubbing area. The absence of a third body bed on the

629 passivesamplecan beexplained by assumingthat detached particles either dissolve very quickly or cannot become compacted enough to form a load carrying bed. In the case of small particles, it is possible that diffusion controlled reactions, like the metal dissolution trough a passsive film, can be accelerated by the unfavourable surface to volume ratio. In this way detached particles in suspension in the solution could dissolve before they can agglomerate. A possible reason for the lack on compaction can be related to controlled repulsion forces acting between detached particles atthe passive potential but not at the cathodic. Another possible explanation is that the passive oxide film covering the particles surface renders difficult the compactation of the particles by reducing the adhesion strength between particles. The mechanisms determining the formation or not of a third body remain however unclear and further understanding of particle rheology and surface physical-chemistry is needed. 5) CONCLUSIONS This work has shown that the third body concept can be conveniently used in order to describe the dependence on corrosion conditions of the wear and frictional behaviour of the investigated tribocorrosion system. Two relevant mechanisms contribute to the surface degradation of 316L stainless steel rubbing against alumina: particle detachment and metal dissolution (corrosion). The latter mechanisms contribute significantly to surface degradation in the contact even when the metal outside the contact is protected efficiently against corrosion by the passive film. The formation or not of a third body depends critically on the surface state and determines the extent of surface degradation.

ACKNOWLEDGEMENT The authors thank M. P. Mettraux for the SEM analysis. REFERENCES [l]M. Godet, Y. Berthier, J. Lancaster, Wear modelling: using fundamental understanding or practical experience?, Wear, 149 (1991), 325-340. Y .Y. Zhu, G.H. Kelsall and H.A: Spikes, The influence of electrochemical potential on the friction and wear of iron, Tribology Trans. 37 (1994), 81 1-819.

[3]W. Baeckmann, W. Schwenk and W. Prim, Handbuch des kathodischen Korrosionschutzes, VCH Editor, Weinheim (1989), Chapter 2. [4]S. Mischler, E. Rosset, D. Landolt, Effect of Corrosionon the WearBehaviour of Passivating Metals in Aqueous Solution, Thin Films in Tribology, D. Dowson, C.M. Taylor, T.H.C. Childs, M. Godet and G. Dalmaz Editors, Tribology Series 25, Elsevier Amsterdam (1993), 245-253. [5]S. Mischler, Ph. Jemmely, E. A. Rosset, D.

Landolt,Tribocorrosionin aqueous lubricants, Proc. of the 1stSwiss Conference on Materials Research for Engineering Systems,B.Ilschner, M. Hofmann and F. Meyer-Olbersleben Edtors, Technische Rundschau (1994).

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

63 I

Modelling fluid interactions in magnetic fluid grinding T. H. C. Childs and F. Y.Chang Department of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK

Magnetic fluid grinding is a recently developed process that has been used to finish grind ceramic ball bearings much more quickly than can be achieved by lapping. It has been established that grinding is by two body abrasion and that the process is quick because large sliding speeds are set up between the balls and a drive shaft that acts as the abrasive surface. A mechanical model has been set up to predict the amount of sliding: it predicts less sliding than is observed. This paper reports initial experimental studies aimed at improving understanding of the process mechanics, eventually to improve the process modelling.

1. INTRODUCTION

This paper concerns the application of tribology as well as more general fluid mechanics to analysing the operation of a manufacturing process, magnetic fluid grinding. The conclusion is that the 'third body of knowledge' of fluid mechanics is more complicated in this instance than is the tribology. Magnetic fluid grinding is a new process, under development to replace lapping for the finish manufacturing of ceramic ball bearings. Half the cost of manufacture of ceramic balls is in their finishing; much of this stems from the slow surface removal rate achieved in lapping. Magnetic fluid grinding is much faster but is not yet developed to the quality and reliability of lapping [ 1-81. Figure 1 shows the elements of a magnetic fluid grinding cell. Balls to be finished are placed in a cylindrical container filled with magnetic fluid and grinding grits. The container is placed on a bed of permanent magnets. The divergent magnetic field generated in the fluid causes a flotation force to act on the balls and grits. A cylindrical disc in the fluid, placed close to the magnets (and labelled 'float' in figure 1) increases the upward force on the balls. When a shaft is pressed down on the balls and rotated, the balls are driven round the cell and material is removed. A removal rate of 5pm / min by diameter has regularly been achieved with 10 mm diameter silicon nitride balls, compared with a

Figure 1. A magnetic fluid grinding cell.

typical figure for lapping of 0.2 pm / min. A typical ball / shaft contact load is OSN, compared to a ball contact load in lapping of 10N. The linear speed of the shaft where it contacts a ball is typically 10 m/s, compared to a lap surface speed of 1 m/s. In lapping, fluids are present to lubricate the contact; they exert little viscous drag on ball motion. Previous work [5,7] has established that in the low load, high speed, high fluid viscous drag conditions (compared to lapping) of magnetic fluid grinding, high sliding speeds ( speeds up to 8 m/s have been estimated) can be created at the shaft / ball contacts. Further, grits become embedded in the contact surfaces. The high removal rate obtained with magnetic fluid grinding occurs by two body

632 abrasion when high sliding velocities occur. In lapping, only rolling with spin occurs. Previous work [6] has also started to model the process mechanics, to predict the sliding speed. This is reviewed and extended in this paper. It is difficult to observe ball and float motions in a grinding cell: the walls are opaque and the magnetic fluid is black. For this reason and also further to study motions experimentally, an analogue model has been built - figure 2.

shaft, ball circulation and float angular velocities; the ball's spin angular speed is and its spin axis direction is p; and the contact sliding (or creep) velocities at the shaft, container and float are V,, V, and Vp It also defines the cell geometry by four radii R,, Rf, R, and Rb and the slope 8 of the conical ended drive shaft. It has been shown kinematically [ 5 ] that V, = R,R, - R,o, sin p V, = R,R, - R,U, - R,U

V,

-

c

Float

Iil I

Shaft

Figure 2. A model cell to study ball and float motions.

The ball / shaft / container geometry is the same as in figure 1 but inverted. A load ring placed above the balls replaces the float to create a ball load by gravity. Experiments and theory to predict observations in this rig are also reported, to build up background understanding that will eventually be fed back to improve the modelling of the real grinding process.

,COS( p - e)

(1)

RfRb-R,o, C O S ~ - R , U ,

For a given geometry and shaft speed, these are 3 equations in 7 unknowns. For a given ball load, 6 equilibrium equations introduce 1 1 more unknowns. Figure 3b introduces the problem force and moment variables. At each of the contacts of the ball with the shaft, container and float there is a contact load, a friction sliding force and a friction spin moment (any one load, for example Wf, may be regarded as the given load). The ball is acted on by a fluid drag force Db and a drag torque Qb. It also experiences a gravitational and a centri-fugal force. The float is acted on by the ball contact forces and moments and also by a fluid drag torque Qp Equations 2, from [ 6 ] ,are respectively two moment, two in-plane force and one out-of plane force ball equilibrium equations; and one float moment equilibrium equation (where N is the number of balls in the cell). Qbcosp+ M, - M,sin8 - R b ( F, c o d + Ff) = 0 Qbsinp + M, W,

+ M, cos0-

R b ( F, sine+ F,) = 0

=(w, -mg)/cose

W, = ( W, - mg) tan 8 + mR,Ri

F, = F,

(2)

+ F, + D,

2. THEORY

N(RfFf-Mf)=Qf

It is required to find the dependence of sliding speeds at the ball contacts on the shaft speed, ball loading, cell geometry, contact friction and fluid viscosity.

The remaining 9 equations relate forces and motions through contact friction laws and fluid drag laws. Contact friction is characterised at each contact by the Hertzian radius of contact a (it is assumed here that the contacts are near enough circular), the spin pole offset e, the spin parameter x and the limiting sliding friction coefficient p, where

2.1. Real grinding tests Figure 3a introduces the motion variables of the process: a,, Rb and Rf are respectively the

633

a = (0.75WR, / E)”’

kh

e = V/ws x = 2%/(ClW,)

CI L

(3) \

I

I

1

E* is the contact effective Youngs modulus and the spin and rolling angular velocities w s and orcan be derived from the ball motions - figure 3. It is shown in [6] that the growth of traction forces and moments through microslip to full sliding conditions can be fitted to the following equations: F

__ = tanh(0.6xe/a)

(4)

PW

[s]+[

1

),”

0.56( tanh( 0 . 3 ~ ) ’

Expressions for the fluid drag forces on the balls and float are not so well defined, partly because the fluid motion is not well understood. The following assumptions have been made. The ball drag torque Qb. The torque on the ball is as if the ball were rotating in a still fluid of infinite extent, of density p and viscosity q. Then, for Reynolds numbers < 100 [6] Q,, = 3.5R:(03qp)

112

r w c Fc

M,-

The float drag torque Qf Interaction between the float and the bottom of the cell acts as a brake on float rotation, while interaction with the fluid above drive it forward [6]: Qr = Qn- Q,

(b)

where

Qn = 1.57qRfR:/z, Qfu

CIL

= 4,41Of[ ~ ( n - Q, ~ ) / P ] Z ” ( ~ R ~ )(6) ~

and zg is the gap between the float and the bottom of the cell and f is a factor = 1. Qflis obtained from a fluid laminar shear analysis. Q& is an empirical expression for the fluid drag in a ball race [9], supposing the geometry of float and balls to be similar to a thrust race. Ikball draP force Dh.The drag force is

Figure 3. (a) motion and (b) force / moment variables.

taken to be of Stokes origin: Db

=cd(nRi)(pv:/2)

(7)

where Cd is a drag coefficient and Vr is the relative velocity between the ball and the fluid:

634

c d has been taken as for motion through an infinite fluid - nearby wall interactions have been ignored. The size of Vfluid has been a major question. In this paper, a range of options is considered, all supposing that the fluid is dragged round by the shaft:

where N is an integer allowed to vary from 1 to a large number. The 18 equations 1 through 9 (some are multiple equations) may be reduced by eliminations and rearrangements to 4 equations for the unknowns V,, V,, Vf and Rf , dependant on the cell geometry, shaft speed, float load Wf, contact elastic moduli and friction coefficients and the fluid viscosity and density. These equations have been solved numerically by a minimisation of residuals technique.

2.2. Model motion tests The theory of section 2.1 has been adapted to the geometry and conditions of the analogue model studies, figure 2. The inversion of the rig leads to a change of sign of the gravitational force terms mg in equations 2. Other changes relate to the fluid drag terms. It is possible to run the rig dry (in air): in this case fluid drags on the ball are set to zero. Whether the rig is used dry or flooded by fluid, the float is out of (above) the fluid. The drag Qf arises from the ball thrust race through which the load is applied. Then equation 6 becomes simply (9)

Figure 4 shows schematically the cell built to measure the viscosity of magnetic fluids. The torque on a rotating disc in magnetised fluid was measured using a commercial viscometer but only at disc speeds up to 100 rev/min. Torque was calibrated to a viscosity by observing the torques caused by a series of standard oils of known viscosity placed in the cell. The viscosity of a water based magnetic fluid used in the grinding tests was measured, with grinding grits added at concentrations from 0 to around 30% by volume. Two size ranges of grits were used: 10 to 25 and 20 to 60 pm. When the fluid was supplied, its neat viscosity had been measured as 0.024 Pas at 22°C. A pin on disc machine was used to measure friction coefficients. It was built for the load range typical of magnetic fluid grinding: 0.1 to 2 N. 3.2. Real grinding tests No new grinding test results are reported in this paper. The ball motion observations compared with theoretical estimates in section 4 were obtained with approximately 10 mm diameter silicon nitride balls driven round a 40 mm diameter cell in which there was a water based fluid containing 7% by volume of grits. The drive shaft, with a conical end of slope 8 = 30" was an austenitic stainless steel and the float and container wall was an aluminium alloy. 3.3. Model motion tests Model motion tests to determine the dependence of ball and float circulation rate on shaft speed were carried out both with no fluid (air) and p7

Qf = f,NW,R, +4,410f,[q~,/p]Z"(2R,)3(10) where the first term is a bearing contact friction loss term and the second is a viscous loss, with q/p referring to the lubricant of the thrust race.

3. EXPERIMENTATION

3.1. Material property characterisation The theory of section 2 needs values for fluid viscosity (and density) and also for the sliding friction coefficients at the contacts in a cell.

I

1

Figure 4. Magnetic fluid viscosity measurement cell.

635 with water (q = 0.001 Pas) in the cell. Cell dimensions were similar to those of the real grinding cell. Ball materials were varied: steel, alumina and glass were used to study the effects of ball density. The shaft was kept as steel but container and float surfaces were varied from aluminium alloy to perspex (transparent) to an elastomer, to study the effects of different contacts on motion.

the dry model tests p from 0.56 to 0.21 depending on materials and for the tests in water from 0.75 to 0.19. Table 1 . . riction coefficients of ceramic balls. Environment 1

1 6 Perspex 0.2 11 0.19/ 0.26 Elastomer 0.29/ 0.3110.25 1. Notation is: without grit in system / with grit

4. RESULTS

4.1. Material properties.

Figure 5 shows the measured viscosity of the fluids that are the subject of the real grinding test studies. Below 15% by volume of grits, viscosity varies only slowly with grit concentration, as expected theoretically [lo]. For larger concentrations, the behaviour depends on grit size. As the grinding tests were carried out with 7% by volume of grits, the viscosity in the real grinding tests may be taken as approximately the same as that of the fluid without grits.

I

0

I

I

I

I

5

10

15

20

Volume

o/o

o f grits

Figure 5. Magnetic fluid viscosities with 10 to 25 p m (x,+) and 20 to 60 pm (o,.) size grits.

4.2. Real grinding tests.

Figure 6 shows the ball circulation rates measured at different shaft speeds for three different loads Wf. The solid line is the expectation in the absence of sliding at the ball / shaft contact. Sliding is deduced for shaft speeds over 1000 rev I min, the greater the smaller is the load. Figure 7 gathers the theoretical predictions of the circulation rates. The group labelled (i) are the predictions when the viscosity (0.04 Pas) and friction coefficient (0.16) recorded in section 4.1 are used in the model of section 2. I ; in addition N = 3 is used in equation 9 to determine the relative velocity of a ball through the fluid, equation 8. This choice of N is made on the basis that the fluid may have the average velocity of the shaft, container and float: the container is stationary and the float almost so. It is seen that the group (i) predictions do not accord with the results of figure 6. The group (ii) results are obtained by arbitrarily increasing N to 20, which is equivalent to supposing that the fluid is almost stationary in the cell. Ball circulation rates are less than for group (i) but still greater than measured. It is only (group (iii)) by increasing the viscosity to 0.2 Pas and reducing the friction coefficient to 0.05 (a wider variation of these properties is thought to be unlikely), as well as increasing N to 20, that results close to experiment are predicted. There is clearly a quantitative short coming in the modelling. 4.3. Model motion tests.

Friction coefficient results are listed in Table 1. Some results are strange, for example the higher coefficients in water than dry. However they give a range of values for use in the theoretical calculations: for the real grinding tests p = 0.16; for

The measured dependence of ball and float circulation rate on shaft speed is shown in figure 8 for three different balls driven in dry conditions, for a load Wf = 0.36 N. The ball circulation rates are consistent with no sliding. The float rotation rate is

636

I5O0 1000

r 7 - l 30 +

%.

revlmin

revlmin

500

1000

I/’

0 2000

4000 R,, rev lmin

0

6000

1000

500 Qr , revlmir, 0 Qb,

revlmi n

t

-500

@a*/-

j/

+

1

0

joo0

0

-I.

Figure 6. Ball circulation rates in real grinding tests, Wf= 0.2(*), 0.5 (0)and 0.8(+)N.

2000

4000 RS, rev lmin

6000

Figure 8. Model motion tests in dry conditions with steel (*), alumina (+) and glass (0)balls, conditions described in text. Solid lines are predicted results.

4000 Q,, revlmin

2000

6000

Figure 7. Predicted ball circulation rates, see text.

very dependent on ball type (i.e. on ball density). The figure also shows theoretical predictions. The cell wall was perspex, the float had an elastomer

layer; the friction coefficients used in the calculations were therefore (from Table 1) 0.56 on the drive shaft, 0.21 on the cell wall and 0.29 on the float contact. The particular form of equation 10, after substituting for cell dimensions and bearing drag factors was Qf= 1.2~10-~NWf+4.6~105 213

(11)

637 A good agreement between experiment and theory is seen, giving confidence in the contact mechanics modelling. Figure 9 shows the measured motions of alumina balls when the cell was flooded with water. Whereas, in dry conditions, float rotation was in the opposite direction to the shaft rotation at low shaft speeds, in water float rotation was always positive.

3000 +

2000 Qb. revlmin

i

1000

0 1000

500 Qf, revlmin 0

-500 0

Similar results were obtained with the steel and glass balls. Figure 9 also shows predicted motions. Friction coefficients relevant to water (Table 1) were used, and equation 11 for float torque was unchanged. Viscous resistance terms were included, equations 7 to 9. The predicted results were very dependent on the value of N in equation 9; best agreement with experiment was obtained with N = 3, a very different size to the best fit value in the real grinding tests.

5. DISCUSSION AND CONCLUSION An initial mechanical model to predict ball motions in magnetic fluid grinding can be made to predict sliding between the balls and drive shaft as observed, but only by selecting fluid viscosities and sliding friction coefficients that differ from values measured by a factor of 3 to 5 (figure 7); further, an arbitrary choice has to be made (N = 20 in equation 9) of the fluid velocity in the grinding cell. The mechanical model has been adapted to describe model motion tests in dry conditions, when there is no fluid drag on the balls. A good agreement between theory and experiment is observed. This gives confidence that the solid contact aspects of the modelling are good enough. The mechanical model has also been used to describe the model motion tests in water-flooded conditions, in which fluid drag forces do act. A value of N = 3 must be used to obtain good agreement with the experiments. Attention is focussed on the currently inadequate nature of the drag modelling. Work is continuing with the model motion tests to develop better theoretical models of drag.

ACKNOWLEDGEMENTS

2000

4000 Rs, revlmin

6000

Figure 9. Model motion tests in water with alumina (+)balls, conditions described in text. Solid lines are predicted results with varying N.

This work is being carried out supported by the Control, Design and Production Group of the UK Engineering and Physical Sciences Research Council; and by SKF and T & N Technology Ltd.

638 REFERENCES I . S. A. Horton, Third European Symposium on Engineering Ceramics, F. L. Riley, Ed, Elsevier, London, 1991,35-50. 2. N. Umehara and K. Kato, Trans. Jap. SOC.Mech. Engrs., 54 (1988) 1599-1604. 3. N. Umehara and K. Kato, Appl. Electromagnetics in Mater., 1 (1990) 37-43. 4. T. H. C. Childs and H. J. Yoon, Ann. CIRP, 41 Pt.1 (1992) 343-346. 5 . T. H. C. Childs, S . Mahmood and H. J. Yoon, Proc. Inst. Mech. Engrs., 208 Pt. B (1994) 47-59.

6. T. H. C. Childs, D. A. Jones, S. Mahmood, B. Zhang, K. Kato and N. Umehara, Wear, 175 ( 1 994) 189-198. 7. T. H. C. Childs, S. Mahmood and H. J. Yoon, Tribology International, in press, 1995. 8. T.H.C. Childs, S. Mahmood and H. J. Yoon, Proc. Int. Symp. Advanced Ceramics for Structural and Tribological Applicns. Vancouver 1995, pp.377388, CIM, Montreal, 1995 9. T. A. Harris, Rolling Bearing Analysis, Ch. 13, Wiley, London, 1966. 10. R. Roscoe, J. Appl. Phys., 3 (1952) 267-269.

SESSION XVI FRICTION Chairman :

Professor Chris M. Taylor

Paper XVI (i)

A Justification of Friction Laws

Paper XVI (ii)

Friction of Sliding Surfaces Carrying Adsorbed Lubricant Layers

Paper XVI (iii)

Effects of Thin Layer on Friction and Wear of Cast Iron Under Severe Sliding Conditions

Paper XVI (iv)

An Elastic-Plastic Model with Adhesion for the Sphere-Flat Contact

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The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

641

A justification of friction laws J .-F. Ganghoffer", A. Brillardb and J. Schultza "CNRS-ICSI, 15 Rue Jean Starcky, B.P. 2478, 68057 Mulhouse, France bFacultC des Sciences et Techniques, 4 Rue des FrBres LumiBre, 68093 Mulhouse, France The contact problem between two bodies is revisited, considering the existence of a third body having a small thickness and separating the two solids. The contact problem is now posed over a three-body system, with an intermediate layer -called interphase-, which is imparted a specific constitutive law. The case of a viscoplastic interphase is considered with a special emphasis. The cases of an interphase built with a nonlinear incompressible elastic material or a thin incompressible fluid film are also considered. Starting from the variational formulation of the problem, a perturbative method is applied in order to derive successive problems, obtained when identifying the different powers of the small parameter associated to the thickness of the interphase. The first order problem describes the limit situation of an interphase having a vanishing thickness. It is thus shown that the general contact laws with or without friction can be deduced, instead of being postulated and their expression essentially depends on the constitutive behaviour of the interphase. For example, in the case of a thin fluid film obeying Stokes equation, one recovers Coulomb's friction law. Finally, the convergence of the solution of the initial problem to the solution of this first order problem is established, using epi-convergence arguments.

1. Introduction Although the origin of friction as a science can be attributed to early studies (e.g. Coulomb in the 18th century), the formulation of the theoretical framework describing the general behaviour of frictional systems is quite recent. Contact mechanics has borrowed ideas from the classical plasticity theory and from the theory of variational inequalities. There exists an extensive literature concerning unilateral frictionless and frictional contact problems (see, for example, the papers by Klarbring [l] and Telega [2] and the references therein). The general formulation of Signorini's problem with friction is Find a displacement field u ( x ) in a body 52 such that uij,j

+ fi

u =0,

onS,

~ , j N =j t i , UN

50

in 52,

= 0,

;

UN

on St

50

;

UN

-UT E aIK(o,)(UT),

UN

= 0,

on

sc

on S,

(1)

(2)

where u = u ( u ) is defined through a constitutive law and the boundary of R is divided in the three

complementary parts : 852 = S, U St U S,. N denotes the outer normal to the boundary and we define UN

= N.u.N ; UT = u.N -a".

Displacements (resp. tractions) are prescribed on S, (resp. S,), while S, represents the contact surface. (1) are the unilaterality conditions and (2) is the sliding rule involving the subdifferential of the indicator function of some convex K ( u N )at U N . This subdifferential sliding rule is associated when the convex is the same as the one defining the friction condition. A simple and well-known friction law is that of Coulomb UT = 0, I UT I< c1 I O N I I UT I= c1 I bN I a 'kT=

UT,

where X is the nonnegative friction coefficient, which is constant in Coulomb's model. Physical considerations, such as the nature and the topography of the surfaces in contact, the material properties of the sliding bodies, the history of sliding, the role of adhesion on friction are very important in both the understanding of friction phenomena and the modelling of friction. Nevertheless, they are insufficient for the study of boundary or initial value problems. As a consequence, friction laws or sliding conditions can-

642 not be deduced from such considerations and thus have to be postulated. In this work, we present a deductive approach of friction laws, considering that the contact between two bodies involves a third thin layer of an intermediate material. Such an assumption is pertinent for a lubricated contact. Considering that this layer is very thin compared to the dimensions of the two other bodies, a small parameter E can be defined as the ratio of the layer thickness to the characteristic length of one contacting body. The original problem formulated in the three-body system then depends on this small parameter E. The solution can be expanded in a series of powers of E (see, for example, [3], [4] for quite similar situations). The first order term represents the limit when E goes t o 0 and is associated t o a layer having a vanishing thickness. Different possible materials will be considered for the layer. The corresponding contact laws will be derived through this perturbative method. Finally, the convergence of the solution of the original problem t o the solution of the first order problem will be proved, using an epi-convergence argument. 2. Contact problem with friction : the case of a thin viscoplastic interphase

We consider two bodies Rf and R i , which will be called solids, bonded together by a thin viscoplastic layer a: of thickness 2 ~ .This layer, which will be called third body or interphase, is supposed to be a cylinder : R: = w x ( - - E , E ) . The lateral boundary of this third body is S: = 7 x (-E,E). The contact surfaces between the solids and the layer are Sf = w x { E } and S$ = w x {-&}, see Figure 1 below. The whole boundary bR' of $2' = Rf U RL,U R: is assumed to be lipschitz continuous. Body forces f are applied to the three bodies, surface tractions t are applied to S: and to a part SftUS;, of the boundary aRfUaRt, of the solids. The solids are held fixed on the remaining (non void) part S~,US~, of their boundary. The layer is given a viscoplastic Norton-Hoff law. More precisely, we consider the generalized Norton-Hoff law introduced by Friaa [5], which associates to every perfect plasticity criterion a viscoplastic law.

Figure 1. The adhesive joint problem.

The time derivative of the strain rate is related to the stress tensor through

where X is positive, q is greater than 1, ad denotes the deviatoric part of u defined as

ad. = uij - I 3 (ckk)6ij '3

6 i j representing the symbol of Kronecker, and the norm of a second order symmetric tensor u is Von Mises norm defined by

1.1

= (4

0;

0 ; ) 112

.

This law (3) describes the behaviour of incompressible viscoplastic materials such as some glasses, steel at a high temperature, polymers above the glass transition temperature ..., corresponding to secondary creep (the inelastic strain linearly varies with time), with no elasticity domain and no hardening effects (see Lernaitre, Chaboche [S]). The contacting solids are supposed to be linear elastic materials, with a possible anisotropic and non homogeneous behaviour, expressed in rate form by the following constitutive relation

a13, .= A i.j L. 1

ekl(u)r

(4)

643

which can be inverted eij(u)

= aijkl

ffkl,

where u denotes the time derivative of u. The coefficients q j k l and A i j k l verify the usual conditions of symmetry and ellipticity. We assume that these coefficients do not depend on the third variable 2 3 . In this paper, the summation convention is assumed, latin indices take their values in {1,2,3}, while greek indices take their values in {1,2}. 'The problem is now stated in a mixed Ilellinger-Reissner variational principle in rate form Find ( u ' , u ' ) in the space CE x V' of admissible stresses and velocity fields, which will be described later on, such that

+

A C ( u C , 7 ) B'(T,u') = 0, RC(u',v) = L'(v),

Vs

E E'

v v E V',

(5) (6)

2.1. Asymptotic expansion of the solution In order to expand the solution of these equivalent problems (5)-(6) or (7) in powers of E , we first consider a unidirectional zoom in the thickness direction 2 3 , associated to the change of variables Y = ( Y l , Y Z , Y 3 ) € 00 Y = (Yl,YZ,Y3) E

0 1

-

2

= (Yl,YZ,EY3) €

Q.,

- ~ = ( Y I , Y Z , Y ~ - ~ + E ) E Q ~(8) Y = (Yl,YZ,Y3) €

0 2

-

-X=(Y1,Yz,Y3+1-&)€Rtz.

Using this change of variables (8), we can transform the functions of the 2 variable into functions of the y variable according to

4.) = T(Yh (we will write with upper bars the coefficients or functions of the variable y). Trivially, one has

,s,

41.

ss,

4 . 1 W z ) = E s,

v,a(.)

dx = E sn, T(Y> dY T(Y) d 4 Y )

= T,a(Y) ; v,3(.) = &-lT,3(Y). Using these properties, (5)-(6) lead t o the

IIellinger-Reissner variational principle now written in a fixed domain Cl = 01 U $22 U 0, as These variational equations (5)-(6) are equivalent to the following differential equations governing the equilibrium of the three-body system, including the conditions of continuity of the velocity arid traction vectors on the two contact surfaces

Aoi ( 3 , T )

+ E A A ~ ZF)( +~ ,Bo(F,?)+ v 5: € 3

+EB1(T,TP) = 0,

(9)

B O ( Z , T +) & B l ( 3 , T ) = = Lo@) + E L I @ ) ,

r)

vT ET

(10)

where E' (resp. is the new space of admissible stresses (resp. velocity fields) and

-

-. c

A o l ( 3 , T ) = Jnluna a i j k l oij Tkl dY

A o z ( 3 , T )= Jn, 1 6 lq-'

B0(?,T) = C T C . ~ .

'1 1

=ti,

on SftUS& U Sz = S:,

where n is the unit outward normal to the boundary of R' and [v] denotes the jump of v on the contact surface, that is the difference between the two traces v+ (from above) and v- (from below) of v on this surface.

q j Fij

dy

sn,unaTi, e , j ( T ) dy- Jn,

B1(5:,T) = - Jn, Tia ei,(E) dy

7i3

ei3(T) dy

644

In this work, we consider the situation where the interphase has thickness-dependent properties. This means that the coefficient X in NortonIIoff law depends on E in the following way X = XOEQ

(11)

where Xo is a positive constant and a is a constant. We now expand ii" and iF i n series of powers of & u - u-0 + & T 1 + & ~ F 2 + . . .

-E

- u--o + & T i 1 + & 2 i 7 2 + . . . u -

-c

and because of the power in front of the bilinear form Ao2, we are led to different situations according to the position of a with respect to -1. 2.2. Model for a = -1

2.2.1. Description and s t u d y of the first order problem

We are in the case where the viscoplastic strain rate is proportional to the inverse to the thickness. The adhesive becomes softer as the thickness decreases. In this case, the first order problem of (9)-( 10) is Aol(Fo,?)

+Aoa(F,7)t +Bo(7,UO)= 0,

Bo(bo,E) = Lo(F),

V 5E

which can be written as

v,

v 7 € Ec'

(12)

(13)

A,

1 5 0

p-2

Tg

=

in Ro.

--O

Because of the incompressibility condition, the trace of the stress Pdis equal to 0 in R,. Hence, one derives that 3; is equal to 0 in R,. This implies that the relative normal displacement of the two interfaces is constant in the layer thickness. Finally, one deduces from (12) X~

1

lq-'

3; = E : , ~ ,

in

a,, V a E {1,2}.

qt,3

(13) implies that is equal to 0, which means that the stress tensor is constant through the layer thickness. Hence, iio linearly varies through the layer, with no normal relative displacement. The first order model above obtained is one in which the mechanical fields do not depend on the thickness coordinate. Thus, the interphase can be treated as a material surface. Considering the kinematics of the interphase, this first order problem shows that the deformation modes ukdominates over all other modes. Furthermore, it is shown that the stresses in the interphase have the same order as the ones of the contacting solids. Moreover, the previous relation between the components of %d and the derivatives of iit relates the jump [PT] of the tangential velocity to the tangential stress PT according to

A0

1-0

U

I

q-2 PTd

= [GI,

(14)

which can be thought of as a friction law with a stress dependent coefficient. Because the normal velocity has no jump, we get PN [PN]= 0, in a very strong sense, which associated to the conditions PN 0 and [Tik] 5 0 implies that unilaterality is satisfied. 2.2.2. Mathematical study of the conver-

gence We want t o describe the asymptotic behaviour of the three-body system, when the parameter E goes to 0 (and not the evolution of this system along the time). Hence, we also assume that both the solids and the layer are not deformed during the evolution process. This can be regarded as an approximation of the real phenomena for small times. In the paper [7]by Licht and the references

645

t,herein, one can find a mathematical study of the evolution process in a quite similar configuration. Because we want to express (7) only in terms of the velocity field u', we have to derive the local equations of (7) in Qf U 05 and the boundary t,raction conditions on 8R; U8Q2;,with respect to time, in order to obtain

We first observe Lemma 1. T h e velocity field uE is the solution of the minimization problem g v d+-

J',, h v d u ( z ) }(15) t

where the m i n i m u m is taken over the v's belonging t o (H1(Q1))3x (H1(Q2))3and F' is defined b y F'(V)

Then we introduce the functions g and h defined by 9 = f,

in Rf UQ5 ; g = f,

h =t,

on Sit U S& ; h = t ,

Y = (Yl,YZ,Y3) E

-

otherwise.

Proof: immediate.

on Sz.

13y the way, we can transform QE u QE, in a fixed domain R1 U R 2 by a change of coordinates similar to the one introduced in (8)

A j k I eij(v) e k l ( v ) dX+

FE(v)= +co,

in 0;

'Through this paper, we will assume that g belongs to L w ( 0 , T ; ( L w ( R ' ) ) 3 ) and h belongs to L"(O,T;(Lw(Sf, U Sit U S;))3). Because of the structure of the preceding local equations, the problem under consideration can be treated at each time as a "stationary problem".

= f In;"*;

0

Then we establish the following estimates Lemma 2 1 ) The solution u" of (15) satisfies

2) The stress tensor u' satisfies

Q1

-z=(Y1,Yz,Y3+E)ERf

Y = (Yl,

Y2, Y3)

E

where the C t e does not depend on

0 2

Proof. See [8].

z=(yl,y2,!/3-&)EQ;,

hut, in order to simplify the notations, we will never make use of this transformation. Furthermore, we notice that (3) can be inverted as uc. '1 =

I e(u') l ~ e i-j ( u~' ) ,

in Q:,

where p is the conjugate exponent of q , defined f = 1. by

+

The mathematical definition of the admissible stresses and velocity fields can now be written as

C' = { U

I uij = uji

; ~ l n :E (Lq(R:))'

;

E.

0

We are now in a position to apply the epiconvergence arguments (see the appendix for the definition and the main properties of this variational convergence). Noticing that the functional s

v

-sn.

g u dx ; v w

ss, h v du(z)

are continuous for the weak topology of ( ~ ' ( n , )x)(H1(R2))3, ~ we can apply Proposition A.3 of the appendix and thus focus on the epiconvergence of the sequence ( F')', in this weak topology. Our main result in this section is

646 Theorem 3. (F')c epi-converges in the weak topology o ~ ( H ' ( Q , ) )x ~(H1(Rz))3t o the functional Fo defined on this space by

+

F " ( v ) = f JnlUnaA j k I e i j ( v ) w ( v ) dz

+ pJUXlO) I . [ 1

We first choose a smooth function v in

Von(c2((nl))3x (C2((Ra))3and define the test function vco satisfying (El) in the following way -

if

I 2 3 12 2~ : wco(2)= w(z),

ifv E V",

IP d2'1d2'2,

otherwise .

F " ( v ) = $00,

where the space V" of (limit) admissible velocity fields is defined by

V " = {. E ( H ' ( R I ) ) ~ x ( H (Q2 N3 I [ 4 l W X { O I E (LP(w x { 0 } ) ) 3 ; div([v]) = 0 on w x (0) ; V I S , , ~ S ~= , 0 ; [w] = 0 on w x ( 0 ) ) . Before giving the main ideas of the proof of this result, let us establish the following immediate consequence for the convergence of the velocity field u' , through Theorem 3 and Theorem A.2

(VC0)3(4

=

= -;il;(z3)2{gy21,22,4

Corollary 4. (u')' converges i n the weak topology of (H1(R1))3x (H1(Q2))3t o the solution 11" of the minimization problem

- 2(21,22,-E)

+~(21,2ZIE)

- $(2'1,22,-E))

- 3 g 5 2 1 , 2 2 , E )

+ $(f1,22,-4

+2(21,22,E)

+f ( v 3 ( 2 1 ,

M i n { F " ( v ) - JnIun, g v dx -

+

22, E)

&(z1,22,-E)}+

+ v 3 ( 2 1 , 2 2 , -&)).

Then, in the strips {z E L?i U

I E 5 1231 5

2 ~ )we , connect these two values of v E oin an affine way with respect to where the m i n i m u m is taken over all v's belonging t o V". Hence uo is the solution of

VC"(2)

Jnluna A

v'"(2)

j k /

+

1

eij (u")e t / ( v ) dz+ JWXI0)

- J&na 9 v

I [uO1lp-2 bO1 [I.

dx+J~lrUSah r

vd 4 X L

E V".

Moreover, ( F ' ( U ' ) ) ~converges t o F"(u").

Ideas of the proof of Theorem 3 We have to verify the two assertions (El) and (E2) for the epi-convergence of (F')' to F" (see Definition A . l ) .

(23

x

= -f

-E)

v'"(21,22, E )

vC0(21,22,2~),

+ f (2E if

E

( 2 3 + & ) V'O(Z1,22,-&)+$

v'" is trivially divergence free in

z3)

5 13 5 2 ~ ,

x v c o ( ~ 1 , ~ ~ l - 2 ~ if) l- 2 ~5

d21dzz =

v

=$

23

(2E+X3) 23

5

-E.

a:.

coincides with v for I 2 3 1 2 2 ~ , is bounded, as one can easily verify, (vCo), converges to v in the weak topology of ( H ~ ( R ~ ) ) ~ X ( H ~ ( ROne ~ ) )can ~ . prove after some long computations (see [S]) Because v'"

())~"'11~.)~

lim F C ( v c o = ) F"(v).

c-0

First step : verification of (El), which reads in the present case as

Second step : verification of ( E 2 ) , which reads as

vv

v v € V",V 21,

E V " , 3 21'"

E

vclv'o

4

v :

limsup FC(v'")5 F " ( v ) , c-0

where the convergence of (wco), to u takes place in the weak topology of V " .

€

VC,V, +v

:

liminf F c ( u c )2 F " ( v ) c-?O

where the convergence of ( v C ) , to v takes place in the weak topology of V " .

647 Let us first choose a smooth function v in V o (v E (C2(n,))3 x (C'(G>)"). The verification of (EL)in this case is based on a subdifferential inequality involving the functional F' and the testfunction v'" previously defined (see [S] for the details). 0

Lemma 5. uo is the solution in V o of

hi,,,

+ fi= 0,

in =$

~1

u,j,j

+ f , = 0, 072 w

in

~

xo-

on w x (0).

Proposition 8. Assume that the solution u" of the limit problem (16) is smooth, that i s u"

belongs to

x (0).

= A o )Aijkl eij(u0)12-qAij31 e i j ( u o ) , 0

Let us now precise the convergence of the stress tensor u'.

Lemma 6. One has the following properties

(C2((n,))3 x (C2(&))3. Then

lim Jn;un; Aijk, eij (u' - uo) ekl(uc - u o ) dx = 0.

'-0

Proof Because u" is smooth, we can define the test function (u0)'O, associated to uo by (17). Using an integration by parts and a subdifferential inequality, one can prove 1

J&n;

dx

Aijkr

eij(U' -

e k / ( ~ '-

(u0)'O)

(u0)'O)

5

I $Jn;un; Aijkl e i j ( ( u o ) c o ~) H

1) ((~')ln;~n;). converges to u" defined b y

d ~ +

( ( ~ O ) ~ O )

+ 5s,, I e((uO)'O)IP d x -

=Aijk/ e i j ( u O ) , in the weak topology of(L2(R:

on w x (0).

[u"],

Because [uO]is divergence-free in w x (0) , we then recover (14).

R 1u R 2

Proof This is an immediate consequence of Corollary 4 , using the fact that for every v in V o , [ V Q ] = 0, on w x (0). This implies [21"]1

uT0 1 1 [uO]lp-'

Let us conclude this study, giving a "rate of convergence" of (u')' to uo

u 02

A i , ~ le , j ( u o ) = A I [u"] lP-2 [uO],,on w x {0}, x:-1 Aijkl eij(uo) nk =il,

since [uol3 = 0, on w x (0). This implies that

u at,))',

- ~1 J n ; ~ nAijtr ; eij(u') e k ~ ( ~dx+ ')

2) lim Jn. ufj e i j ( v c o )dx = '-0

0

1 -F S W X { 0 ) I bO1 Ip-2 bO1 [I. dU(X),

-

f o r every smooth function v in V o n ( C 2 ( G ) )x3 (C2(G))3, where vCo is associated to v through (1 7). Proof. The first assertion is a consequence of Theorem 3. The second one is a consequence of 0 Theorem 3 and Lemma 5. See [8].

Remark 7 Lemmas 5 and 6 justify the asymptotic limit relations previously obtained in section 2.2.1.,between the stress tensor ro and the velocity field ti". Indeed, as in [9], we obtain uo.N= 1 I [ti0] I P - ~ [u"], AZ-1 which implies on w x {0}, u& = 0,

on w x {0},

- ss;,us;,"s:

h (u' - (U")'"

du(t).

The conclusion is then obtained, using the first step of the proof of Theorem 3 and the compact embeddings of H'(R) into L2(R) and into

L'(dR).

0

Remark 9 The case of a layer made of an incompressible fluid obeying Stokes equation eij(u') = &uf:, where p is the viscosity coefficient of the fluid, is a special case of the preceding one, obtained for p = q = 2. Then, the friction law can be written as

[E;]= f

6;

= Ta3

;

[%la

= E&.

648

#

-1 2.3.1. Mathematical study Let us denote by F'" the functional corresponding to the case where X is defined by ( l l ) , that is 2.3. Model for a

F'"(v) =

f Jntun; A i j k i

e i j ( v ) e k i ( v ) dz+

F ' Q ( v ) = $00,

otherwise.

From the properties of the epi-convergence (Proposition A.5), one deduces

Proposition 10

1) Suppose that a < -1. T h e n (F'O), epiconverges i n the weak topology of (H1(S21))3x (H1(S22))3t o the functional F"- defined by

F " - ( v ) = f JnIUn2A i j k i e i j ( v ) e k i ( v ) d z , if v E V"-

F " - ( v ) = +oo,

otherwise,

where I/"- = {v E (H1(R1))3 x (H1(fi2))3I div([v]) = 0 on w x (0) ; v ~ s , =~ 0 ~; [v3] s ~= 0~ on w x (0)).

2) Suppose that 0 2 a > -1. T h e n ( P a ) < epz-converges i n the weak topology O ~ ( H ' ( Q x~ ) ) ~ (H1(R,))3 to the functional F"+ defined by F o + ( v ) = f Jnlun2A i j k i e i j ( v ) e k ~ ( v dx, ) i f v E V"+ F"+(V)

= +oo,

otherwise

where V"+ = { v E V" I [v]= 0 on w x (0)).

c-0

= A, lim

&'to = +oo.

p and for every

v in

V" Aijkl

e i j ( v ) e k / ( v )dc+

+ &Jn:

I e ( v ) IP dx.

Thanks to Proposition 8 . 5 and Theorem 3, one deduces from the preceding inequality that the satisfies epi-limite F"- of the sequence

< -1

This corresponds t o a layer which becomes softer when the thickness decreases. T h e first order problem in (9)-( 10) is Ao2(Fo,T) = 0,

V7E

B,(P,,5) = L,(S),

Ec

V5E

F,

which means that the stress deviator is equal to 0, so that the only force that the interphase can sustain is a pressure. T h e second above equation implies that q3,3 is equal t o 0, so that the traction vector is constant through the thickness. But inplane stresses can vary through the layer. 2.3.3. First order problem for a

> -1

Notice that the case a 2 0 corresponds to a situation where the layer becomes stiffer when the thickness decreases. T h e first order problem in (9)-(10) is then

+ Bo(T,Eo)= 0,

B,(P,S) = L,(S),

, '-0 Hence, for every positive

F'"(v) 5 f Jn;un;

2.3.2. First order problem for a

A,l(iP,T)

Proof 1) We notice that

Iim

Hence, one takes the infimum over all positive p's, in this inequality. This proves a first inequality between F"- and the given expression. Notice that the constraint " [v]E (LP(w x { 0 } ) 3 " disappears in the limit functional. T h e reverse inequality is easily obtained, building, for every function v in V " - , the test function presented in (17), that is in the first step of the proof of Theorem 3. The second case is proved in a quite similar way, using the subdifferential inequality used in the second 0 step of the proof of Theorem 3 (see [S ]).

VTE

Ec

v 5 E F.

The first equation implies that is equal t o 0, hence the velocity field is constant through the thickness direction. T h e second equation implies that q3,3 is equal to 0, which implies that the traction vector is constant through the layer. No additional information concerning other stress components can be obtained. This means that there exists a competition between the stiffening effect due to the geometry (the thin layer becomes stiffer, when its thickness decreases) and the softening implied by the scaling of the constitutive law of the layer.

649

3. A s y m p t o t i c model of contact without

friction We consider here the more simple situation where the two solids are bonded by a thin elastic layer, having mechanical properties one order smaller than the ones of the contacting bodies. The derivation of the first order contact law from the asymptotic method then follows the same steps as exposed in section 2, except that a nonlinear elastic behaviour of the interphase is iiow involved. This problem has been studied by Klarbring [lo]. Considering that the interphase is niuch softer than the two solids, the tensile modulus E scales as E = €I<, where I( has the same order of magnitude as the solids modulus. Under this assumption, the contact law is

iT&

=q 3

K ( 1- v) (1 + ' v ) ( l - v)'

The stress tensor i 7 ' is constant through the interphase thickness and the displacement 'i linearly varies through the adhesive thickness, i.e.

-0-u tL -

[u --o ] + f ( n o + +

'izo-).

These results show that the solution of the first order problem does not involve any dependence of the field variables in the thickness coordinate. Therefore, the interphase can be treated as a matcrial surface, letting the mechanical fields within the interphase only depend on their boundary values on this surface. From (18)-(19), we then deduce

4. Conclusion

A deductive contact theory between two solids has been established, assuming the existence of an intermediate thin layer. Considering different constitutive laws of this layer, different contact laws have been derived, which can be regarded as friction laws in which the friction coefficient is related to both the stress history within the layer and to its mechanical properties. The present approach is relevant as a mathematical process through which one seeks the limit behaviour of a layer having a vanishing thickness. A p p e n d i x : Definition and properties of the epi-convergence Definition A . l ([12], Definition 1.9) Let (X,r)be a metric space, ( F c ) c and F,, be functionals defined o n X with values in R U {+m} . (F',), epi-converges to Fo in the topology T if and only if the two following assertions are satisfied :

v I E x,3I; E

x,I,"

--*

I :

limsup F,(I,") 5 F,,(I)

(El)

r-0

VxEX,Vx, E X , t , + x : liminf F C ( z E2) F,,(I),

(E2)

c-0

the sequences ( I , " ) , and the topology r.

(tc),converging

20

I

in

This epi-convergence is a special case of the rconvergence introduced in [13]. It is well-fitted t o the asymptotic analysis of sequences of minimization problems, since one has the fundamental result

Theorem A.2 ([12], Theorem 1.10) Suppose that with

(20) implies that unilaterality is satisfied, when the thickness of the interphase goes to 0. N o relation linking the relative tangential displacement to the tangential stress is obtained from this model. Hence the friction law must be added as a postulate. Finally, notice that the convergence of uc to the solution of the corresponding limit problem has been proved in [ll].

1) F, admits a m i n i m i z e r Fc on X , 2) The sequence (f,), is r-relatively compact, 3) T h e sequence (F,),epi-converges t o a functional F,,, in this topology r. Then every limit point f of the sequence (fECr is a m i n i m i z e r of F, on X and lim Fc~(Ecl) = E'-+O

F,,(Z), if (5?E,)c~denotes the subsequence of (Zc)c which converges t o f. Notice the following stability result of the epiconvergence

650 Proposition A.3 ([12], page 40) Suppose that ( F c ) , epi-converges l o Fo in the topology r and that G is r-conlinuous. T h e n ( F , + G), epi-converges to F + G in the topology r . In the verification of ( E l ) or (E2), we usually need the following diagonalization result L e m m a A4 ([12], Corollary 1.16 and Lemma 1.15) Let ( Q ” , ~ ) ” , ~be a double indexed sequence of elements i n Ru{+w}. 1 ) There exists a function u I-+ p ( u ) increasing t o +m, such that

limsup

5 limsup limsup a,,p.

v-too

p-+m

2) There exists a function u to +a, such that

lim inf v-+a,

-

v-+w

p ( u ) increasing

> lim inf lim inf p + t m v-r+m

Proposition A.5 A s s u m e that (F,), epi-converges t o F i n the topology T , ( G c ) cepi-converges t o G i n this topology T and F, 5 G c ,f o r every E . Then F 5 G.

REFERENCES

[l] A. KLARBRING, General contact boundary conditions and the analysis of frictional systems. Int. J . Solids Structures, 22,12 (1986) 1377-1398. [2] J . TELEGA, Topics on unilateral contact problems of elasticity and inelasticity. Nonsmooth Mechanics and Applications. CISM Courses and Lectures 302, Springer-Verlag, Berlin, Heidelberg, 1988. [3] P.G. CIARLET, Plates and junctions in elastic multi-structures. Masson, Paris and Springer Verlag, Berlin, Heidelberg, 1990. [4] P.G. CIARLET & E. SANCHEZ-PALENCIA, Applications of multiple scalings in mechanics. Masson, Paris, 1987. [5] A. FFUAA, La loi de Norton-Hoff g6nCralisCe en plasticit6 et viscoplasticitd. ThBse, UniversitC P. et M. Curie, Paris, 1979. [6] J . LEMAITRE & J.L. CHABOCHE , MBcaniquz des matkriaux solides. Bordas, Paris, 1985. [7] C. LICHT, Comporternent asymptotique d’une bande dissipative mince de faible rigidit6. C.R.A.S. Skrie I, 317 (1993), 429-433.

[8] A. BRILLARD, Mathematical behaviour of thin layers in nonlinear mechanics. Preprint UniversitC de Haute-Alsace, 1995. [9] P. SUQUET, Discontinuities and plasticity. Non-smooth Mechanics and Applications. CISM Courses and Lectures 302, Springer-Verlag, Berlin, Heidelberg, 1988. [lo] A. KLARBRING, Derivation of a model of adhesively bonded joints by the asymptotic method. Int. J . Engin. Sci. 29,4 (1991) 493-512. [ll] J.F. GANGHOFFER, A. BRILLARD, J. SCHULTZ, paper submitted for publication, 1995. [12] H. ATTOUCH, Variational convergence for functions and operators. Pitrnan, London, 1984. [13] E. DE GIORGI, Convergence problems for functions and operators. Proceedings International Congress on ”Recent Methods in Nonlinear Analysis” Rome 1978. De Giorgi, Magenes, Mosco Eds. Pitagora Editrice, Bologna, 1979.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

65 1

Friction of sliding surfaces carrying adsorbed lubricant layers J A Williamsa and Y Xieb a Cambridge University Engineering Department, Trumpington Street, Cambridge, UK,

Department of Mechanical Engineering, Ohio State University, Columbus, Ohio, USA.

In concentrated contacts the behaviour of lubricants is much modified by the high local pressures: changes can arise both from molecular ordering within the very thin film lubricant layers present at the interface as well as from the deposition on the component surfaces of more solid-like polymeric boundary layers. These ‘third bodies’ separating the solid surfaces may have rheological or mechanical properties very different from those observed in the bulk. Classical elasto-hydrodynamic theory considers the entrapped lubricant to exhibit a piezo-viscous behaviour while the conventional picture of more solid boundary lubricant layers views their shear strength z a s being linearly dependent on local pressure p , so that 7 = zo + a p where z0 and a are constants. If z0 is relatively small, then the coefficient of friction p = z l p I= a and so Amonton’s laws are recovered. However, the properties of adsorbed or deposited surface films, or indeed other third bodies such as debris layers, may be more complex than this. A preliminary study h a s looked quantitatively at the influence of the pressure dependence of the shear strength of any surface layer on the overall friction coefficient of a contact which is made up of a n array of asperities whose height varies in a Gaussian manner. Individual contact points may be elastic or plastic. The analysis results in plots of coefficient of friction versus the service or load parameter PIHsNRa where P is the nominal pressure on the contact, H the hardness of the deforming surface, N the asperity density, R the mean radius of curvature ofthe asperities, and o is the standard deviation of their height distribution. In principle, any variation of z withp can be incorporated into the model; however, in this initial study we have used data on colloidal suspensions from the group at the Ecole Centrale de Lyon as well as examining the effect of functional relationships of somewhat greater complexity than a simple linear form. Results of the analysis indicate that variations in p are possible as the load is varied which depend on the statistical spread of behaviour at individual asperity contacts. The value of this analysis is that i t attempts to combine the behaviour of films on the molecular scale with the topography of real engineering surfaces and so give an indication of the effects at the full-size or macro-scale that can be achieved by chemical or molecular surface engineering.

652

Notation asperity contact spot radius mean separation of opposing surfaces D constant associated with maximum asperity height elastic modulus E con tact modulus E* tangential or friction force F surface hardness HS material flow stress in shear k asperity density N mean contact pressure P nominal contact pressure P P1,P2 lubricant con stan ts asperity shakedown pressure Ps asperity radius R asperity height z a,a1,a2,a3 lubricant constants lubricant constants interference or overlap between profiles friction or traction coefficient Poisson's ratio Root Mean Square roughness asperity height distribution function a d

1. Intraduction

Additives are used extensively in lubricants to improve their lubricating proprieties. One of their roles is to enhance the effective viscosity of the a lubricant and h e n c e t h r o u g h t h e m e c h a n i s m of hydrodynamics to increase t h e resulting protective l u b r i c a n t film thickness. However, another important function of an additive may be t h e formation o r enhancement, by either chemical or physical activity, of a boundary layer on the opposing surfaces: this acts both to protect the surfaces from degradation and, most importantly, to

reduce the shear or frictional force required to slide them over one another. Some of the earliest systematic work into this phenomena was that of Bowden and Leben [ll who used the technique developed by Blodgett a n d Langmuir [21 to deposit single and multiple close-packed oriented molecular layers of dry boundary lubricants, classically organic fatty acids, on suitable substrates a n d investigated their frictional behaviour. Even single molecular layers provided reductions in friction which were retained for a number of passes of the slider although much more lasting protection could be achieved with multiple layers - as is illustrated by the data of Fig Ua), from Bowden and Tabor 131. It was postulated that if condensed, solid films could be produced in real contact situations then corresponding useful friction reductions might be achieved. Boundary lubricants of this sort are classically thought of as weak solid layers, typically less than a micron in thickness, a n d considerable experimental effort in later years h a s gone into t h e investigation of their mechanical properties. Practical frictional measurements on real engineering surfaces a r e difficult to translate into measurements of film shear strength chiefly because of the uncertainty in estimating with sufficient accuracy the real area of contact undergoing shear. The more usual experimental approach is to use very smooth geometrically simple surfaces, nearly always in the configuration of a sphere against a flat, and to calculate the area of contact by elastic continuum mechanics. Typical data for a variety of solid organic films investigated in this way are shown in Fig. l(b), taken from Briscoe and Smith [41, plotted as shear strength 7against the mean contact pressure p . I t is clear t h a t the behaviour of these layers can be described by the equation 7 =

70 + ap,

(1)

where TO and a are constants. If the first term 70 is relatively small compared to the second (which will often be the case in loaded contacts in which p is large) then the

653

20

10

Number of NIIS

30 .10 over the same mck

50

Figure l(a) Friction of stearic acid films deposited on a stainless steel surface (from reference [31). 0

local coefficient of friction p equal to z l p will be numerically close to the value of a,i.e. to t h e slope of t h e curves in Fig. l(b). Amonton's law is thus recovered. In the case of two engineering surfaces in true contact at a number of asperities, if conditions are such t h a t p is constant at each micro-scopic contact, then it follows that it will also have the same value for the overall macro-scopic contact.

50

100

150

200

0

mean pressure p / MPa

Figure l(b) Interfacial shear stress T as a function of the contact pressure p for a range of organic polymeric films at 20°C.Very similar data be obtained for many organic materials (from reference C4I).

more liquid

4

I

Oil. additives plus dcpradalion products

't?

1000 nm

V

Figure 2 Schematic representation of a layered ZDTP anti-wear film structure (from reference 153).

654

However, in real engineering contacts, perhaps particularly on steels l u b r i c a t e d by mi n e r a l oils whose performance is enhanced by boundary additives, this simple picture of well-oriented mono-molecular layers sliding over one another is hardly credible. When dispersed in neutral oils active boundary lubricants are likely to produce rather thicker ‘mushy’ layers whose nature varies from t h a t of relatively strong inorganic oxides and sulphides close to the metallic substrate to a much weaker and more liquid like region at the outer surface - this range of structure and thus properties for the particular case of a ZDTP additive layer is illustrated in Fig 2, taken from Coy et a1 [51.

the molecular paraffinic chains are no longer randomly oriented b u t become aligned with the shear direction. Their subsequent resistance to shear will thus, as in the case of boundary films, be influenced by the local asperity pressures.

As a consequence of this more complex morphology ranging from the solidlike to the liquid-like i t is unlikely that the behaviour of the film can be adequately described by a simple linear relation; it is certainly reasonable to suppose that the shear strength remains a function of pressure but t h a t i t is likely t o be more complex than suggested by the form of equation (1). It is well established that the pressures at individual asperity contact between two engineering surfaces are very much greater than the nominal contact pressure. Even when this is well within the elastic limit, individual asperity pressures may be close t o the material yield stress, so of the order of GPa. At these sorts of pressures the rheological behaviour of paraffinic hydrocarbons is very different from that observed at lower containment pressures, all lubricants exhibit some degree of piezoviscosity: this is of course a key element in the development of elasto-hydrodynamic theory and a number of functional relations between the effective viscosity and the local pressure have been proposed 161. Experiment and recently reported molecular dynamic simulations suggest t h a t a t under these conditions a layering, or ordering, of the lubricant may become established in which

Figure 3 Schematic representations of the sphere-flat interface lubricated by a colloidal suspension of calcium carbonate in dodecane at different pressures. (a) At low pressures, p<2 MPa, the colloidal solution can flow continuously in the the interface. (b) At intermediate pressures 2qx-200 MPa the colloidal solution becomes compacted and sliding takes place between the plane and the film. (c) At pressures greater than ca. 200 MPa the sphere-plane contact is elastically deformed as is the colloid. The protective shell around individual particles is destroyed and sliding involves dodecane itself. (from reference “71).

655

Georges and Mazuyer [7, 81 have investigated this effect using a sphere on flat geometry lubricated by a colloidal suspension of calcium carbonate in n dodecane. The individual particles of the colloid a r e larger than t h a t of common molecules, being of the order of 10 nm, but are still very much less than 1 pm; additives in commercial grades of mineral oils a n d greases are often of a similar size. These authors found t h a t the behaviour of the suspension and the resulting traction stress is very dependent on the applied pressure. The various regimes of operation a r e illustrated in Fig. 3. At low pressures, in this case if p is less than approximately 2 MPa the liquid dodecane can flow relatively freely in the interface gap so that the interfacial friction results largely from viscous flow; the data on shear stress versus pressure indicated in Fig 4 suggests that within this range equation (1) applies with a value of TO effectively zero. Pressures of this magnitude are not large enough t o lead t o significant changes in geometry of the hard metallic o r ceramic substrate surfaces. A t somewhat higher pressures, within the range 2cpc200 MPa, the shear strength of the junction becomes a much weaker function of p r e s s u r e . Compaction of the colloidal film h a s taken place, illustrated in Fig. 3(b), and this effective slab of material appears to slide at its interface with the solid substrates which remain coated with dodecane molecules at a shear stress which is close to being constant, here the effective value of TO is greater than qv. At greater pressures, p>200 MPa the data once again can be fitted by a functional relationship of the form of equation (1) with TO = 0 but now with a different value of the pressure coefficient a. At pressures of this magnitude i t seems t h a t the shell of sulphonates surrounding the colloid is destroyed and sliding is of effectively solid dodecane against itself; slip involves C H 2 : C H 2 interactions as described by the

'crankshaft' model of Tabor [91 and the value of a and thus of p is similar t o that obtained by Bridgman [lo] for paraffins viz in the range 0.04 to 0.055.

mean contact pressure p r: w/xo2( Pa

Figure 4 Pressure dependence of the shear strength ?of a film of calcium carbonate at 20°C. Sliding speeds are of the order of 1 nm s-l to 1 cm s-l. Regions (a), (b) and (c) correspond to those illustrated in Fig. 3. Pressures p 1 and p2 are referred to in the text (from reference [71).

The aim of this paper is to model the frictional o r traction behaviour of two realistically rough surfaces whose interacting asperities are separated by a such a lubricant or boundary film which has a more complex behaviour than equation (1) would suggest. In particular we have examined the case of surfaces with elastic and plastic properties representative of metals and have allowed for interaction which may be either elastic (perhaps after the intervention of t h e phenomenon of shakedown) o r plastic s o leading t o continuous deformation of the softer surface. We examine both the specific lubricant rheological behaviour alluded to above from the work of Georges e t al. as well as extending the simulation t o more general shear/pressure relations.

656

2. Modelling boundary lubricated friction in repeated slidingbetweena sphm and a plane

Consider the contact between a sphere of radius R and a plane. When 6, the interference or overlap between t h e two profiles, is small then the stresses developed in both surfaces will be entirely elastic and we can use the Hertzian expressions to relate t h e mean contact p r e s s u r e p to the interference 6 and the contact modulus of the materials E*. Then p

=‘“qj 37c

I

where E* = ( l - v ~ ) ~ / E+i (1-v2I2/E2 and E and v are oung‘s modulus and oisson’s ratio respectively for t h e two materials designated 1 and 2. The maximum value of the mean contact pressure which can be sustained in repeated sliding of the sphere across the plane is the shakedown load for this geometry: this can be significantly greater than the mean value of pressure which can be sustained elastically on the first application of the load by virtue of the protective residual stresses that are generated in the early passes of t h e indenter. This s h a k e d o w n p r e s s u r e p s is directly proportional to k the yield stress in shear of the softer surface and is also influenced by p the traction or friction coefficient between the two surfaces; this dependence i s shown in Fig. 5 . For the case of frictionless, i.e. very well lubricated sliding, a mean asperity pressure equal to zk can be sustained by a purely elastic stress field; if the friction coefficient increases to 0.3 the allowable ratio ofpdk falls to about 2 [ l l l .

d

The shakedown pressure p s corresponds to t h e maximum allowable interference between the surfaces for purely elastic contact a n d we designate this particular value of 6 by 6e. If the contact is purely elastic then frictional resistance arises because of ‘adhesional’ effects at the

interface, there is no contribution to the overall value of p from terms associated with deformation of t h e underlying metallic substrates since we have taken these to be perfectly elastic. On t h e other hand, if the interference exceeds 6e and there is some relative sliding, a groove will be produced in t h e softer surface as it is deformed plastically. Under these circumstances the mean contact pressure p can be approximated by the hardness H s of the softer surface, so that p = -w= - - Hs (3) m2 2 where W is the normal load and a the radius of the contact spot: in such a case there will now be a n additional ‘deformation’ o r ploughing contribution to the overall value of the traction or friction coefficient p.

We have seen that, if z, the shear strength of the lubricating film or interface at this asperity contact, is proportional to the contact pressure p then t h e resulting coefficient of friction will be a constant for all such contact spots a n d t h u s for t h e macroscopic contact as a whole. However, if the strength of the interface is not directly proportional to p then the local interfacial coefficient of friction p a , arising from the effects of adhesion rather than deformation, will be a function of the interference 6 over the range 0<&6e, i.e. we could write that

p6 = -z = function(& P

(4)

When 6 i s greater than 6 e t h e local coefficient of friction will become constant because t h e local asperity pressure h a s saturated at a value of Hs/2. In order to proceed further, we require some information of t h e way in which z varies with p . The experimental work of George et al, referred to in Section 1, suggests t h a t for the system they examined the z l p relation has three distinct regions; these can

657

be modelled in a number of ways but for simplicity we write these as

where the values of the constants a1, a2, a3, p and y can be read off the data in Fig. 4. A variety of s h e a r s t r e s s - p r e s s u r e characteristics can be generated from equation ( 5 ) by varying the appropriate parameters. Figure. 6 shows the 7-p relation using values of a1, ap, as, /3 and y taken from Fig. 4; viz a1 = 0.6, a2 = 0.0273,a3 = 0.033,/3 = 1.15 and y = 0. 4

I

I

I

surtace and sub surface tlow

~

5

flow __

3

&

shakedown

I.OE-Ol],;*”

,

I

,

,

I.OE*oo

I.OE+OI

1.08402

I.OE403

,

I.OE-02

I.OE-O1

I.OE44

Figure 6 Curves fitted to the data of Fig. 4. Combining equations (4) and (5) we can now write

I

‘-

r x

I

u)

C

I

-0, E 2

I

y’

-0

.

-m0

1

- - - - elastic limit I -- - elastieperfectly plastic shakedown limit-

-

kinematic hardening shakedawll limit

0.1

0.2

0.3

0.4

0.5

friction coefficient D

Figure 5 A shakedown map for a sphere sliding on repeatedly on a flat. If the operating point which is located by coordinates representing the normalised mean operating pressure p lk and the traction or friction coefficient p lies beneath the curve then the contact will shakedown t o purely elastic conditions. If the operating point lies above the curve each pass will introduce a further element of plastic deformation. (from reference [151).

where 61 and 62 a r e the interferences corresponding to the pressures p 1 and p 2 respectively. If the asperity interference exceeds & then there is some plastic ploughing or grooving deformation of the softer surface and so the local coefficient of friction will consist of two contributions; a n ‘adhesion’ term of the sort described above and a ‘deformation’ term associated with this plastic deformation. If all the material displaced by the passage of the indenter is ploughed into side ridges then this additional contribution leads to the result [12,131that

658

where C is a constant whose value depends on the precise geometry of the indenter but is of the order of unity.

0

3. Contact of nominally fiat rough surfaces In practice, friction between surfaces is the result of many interactions between individual asperities of different heights and shapes which a r e distributed, perhaps randomly, on the two nominally flat surfaces. To estimate the overall coefficient of friction the separate effects of all these individual contact spots must be combined. In what follows, a s is conventional, we transfer all the roughness to one surface and assume that the contact between the two real surfaces is equivalent to contact between a surface carrying the combined roughness and a flat plane; we also suppose that each asperity acts independently of its neighbours. The asperities are further idealised as being each tipped by a spherical cap of characteristic radius R and t o have peak which follow a Gaussian heights z distribution @(z)between the limits hmin and hmax:

normal load

1

where o is the standard deviation of the distribution which is also equal in magnitude t o the Root Mean Square roughness value and D is a constant associated with the maximum allowed peak height on the surface, uiz

h max hmin

Measurements on various surfaces suggest that this cut-off value of peak height hm, can be sensibly set a t a value of 3 0 [14,151. Figure 7 illustrates the contact conditions envisaged in this idealised model. The harder surface carries the array of spherically capped asperities whose heights z vary from h m i n to h m a x in a Gaussian fashion.

hmin

profile tieight distribution

hard surface _-

soft surface

f

Figure 7 Contact conditions between a hard rough surface and a flat smooth counterface. The peak heights z of the roughness are distributed randomly hmin
659

Dimension d is the mean separation of the surfaces and 6 which is equal to z - d is the interference, o r depth of penetration, of a representative asperity into t h e softer surface. If the hard surface h a s N asperities per unit area then the number of asperities per unit area with a height between z and z + dz will be N@(z)dz and the contribution d P made by these to the total load supported will be given by

Thus, we can write from (lo), (12)and (13) that P , the nominal pressure is given by d+6e

hmax

nHsN j z - d ) (2R+d-z) exp 2fioD. To calculate t h e load per unit area o r nominal pressure p this equation must be integrated with the limits z = d to z = h m a x . Thus, allowing for the fact t h a t those asperities with values of d < Se will be elastic and those with d>ae will be plastic, we may write

{g}

dz 414)

The first term on the right hand side of this equation represents t h e fraction of the nominal pressure carried by those contacts deforming elastically while t h e second represents t h e contribution from plastic contacts.

4. Overall coefficient of friction

where 6e is the maximum interference for elastic contact. Within this region the radius a of each circular contact patch is given by

The overall coefficient of friction between the two sliding surfaces is equal to the ratio of F the total tangential force per unit area to the nominal pressure P ,

(11)

a==

a n d the contact pressure p is given by equation (2). Thus the load supported by an individual asperity is equal t o

-

_4 E*R1l2(z- d)3/2. (12)

- 3

When the deformation mode is plastic p H s / 2 and a can be expressed a s

=

Once again, the first term of this expression represents the contribution made by elastic asperity contacts a n d the second those in which plasticity h a s been imitated. In an elastic contact, the tangential force arises solely from t h e s h e a r strength of the interfacial boundary lubricant. Thus, the incremental tangential force dF due t o those asperities with heights between z and z+ dz can be written a s

660

When S > d+&, so that there is some plastic ploughing or deformation work t h e corresponding expression for dF becomes

so that, combining equations (14), (151,(16) and (17)

P =

22

exp(--)2 3 dz

Equation (18) can be solved numerically for a particular case in which t h e lubricant constants a1, a2, as,0, y, and the transition

pressures p 1 and p 2 are known. We also require a knowledge of t h e material and topographical surface constants H s , E*, Q and R,

66 1 5. Results and Discussion I).I

To illustrate the results and potential significance of this analysis we adopt two approaches. In the first we use the experimental data of Georges et a1 on the properties of colloidal calcium carbonate layers which can be satisfactorily fitted by the equations illustrated in Fig. 6:

0.6~ (p 1 2 Mpa) 0.02733, 0.033~

+

/ i s = 2SK) MPa E*ilis = 60

d R = 0.0014

0.05

1.146 (2 I p I 200 MPa) (19) (200 MPa I p )

If this information is combined with the material data Hs = 2500 MPa and E X= 150 GPa (so t h a t E*IHs = 60) and values of surface roughness o l R = 0.0014 (these figures are taken from the work of Samuels and Richards I161 and correspond to a ground engineering surface of a quenched and tempered martensitic AISI-4340 steel) then the resultant overall coefficient of friction can be sensibly plotted as a function of the load or service parameter P I H a R to give the data plotted as square plotting symbols in Figure 8. The vertical line is the shakedown limit - loads above this will generate some element of plastic deformation on each application o r pass and so lead t o higher values of p. Loads below the shakedown limit generate only elastic stresses. The shakedown limit is the rational design criterion for repeatedly loaded con tacts: for optimum use of materials, the tribological operating point of the device should be near but not above the shakedown limit. If these particular material and geometric parameters are adopted, then as the load or nominal pressure P increases within the elastic regime the coefficient of friction stays sensibly constant at the value 0.033; this is because virtually all the asperity contacts are operating at interface pressures above 200 MPa i.e. in the upper or regime (c) of Fig. 4. If the shear stress-pressure characteristic of

0

service parameter P/W,NRo

Figure 8 Coefficient of friction 1.1 versus the contact service parameter PIH,NRa for a material and surface with the parameters shown. The upper curve, square points, has been computed using the curves fitted to the data of Fig. 4. Up to shakedown the coefficient of friction is constant and equal t o 0.033. The lower curve, circles, corresponds to a lubricant film that saturates at a limiting shear stress of 6.6 MPa. The interval between plotted points represents an increment of approach of 0. lo.

the interface were t o saturate a t some specified level of stress, then at those asperity contacts operating within this regime the coefficient of friction, now having pressure p in the denominator would fall. This can be demonstrated by modifying the lubricant behaviour so that a t pressures above p 2 the shear strength of the interlayer is imagined

662 to remain constant at the maximum value generated within the central regime: this behaviour is shown as the fine dotted line in Fig. 6. The resulting values of p are plotted as the circles in Fig. 8: the fall in the friction coefficient is evident. The interval between adjacent plotted points represents an increment of approach of the two solid surfaces equal t o 10% of their mean RMS roughness. The simulation has been repeated with the same geometric data and ratio of E*IHs but with the value of Hs set at 500 MPa, instead of 2500 MPa, to give the data plotted in Fig. 9. It is clear that here, when loads are in the acceptable shakedown or elastic regime, because the asperity pressures are now all within the mid-range of the lubricant characteristic plotted in Figs. 4 and 6, limiting the lubricant shear stress has no effect on the resulting overall value of p.

The examples so far have used the specific numerical data on the colloidal suspension examined by Georges et al. Other lubricant or indeed debris or third body layers may have different shear-pressure properties. Figure 10 shows some of idealised forms of these; in this plot both shear strength z and normal pressure p have been normalised by the material hardness of the softer substrate Hs.

T

-

ap

Y' L-

H, = 5 0 0 M p a P l H , = 60 d R = 0.0014

Figure 10 Four model lubricant or surface film film behaviours. Curve 1 is that of a 'conventional' boundary lubricant in which z = czp with the coefficient a having the value of 0.1.

N

wx

8

s

8

service parameter PIH,NRu

Figure 9 Conditions as in previous figure except that H s = 500 MPa (20% of the value of that in Fig. 8. Now the great proportion of the asperity contacts operate within region (b) of Fig. 4 and so as preload increases so the coefficient of friction falls.

Curve 1 is for the 'standard' boundary lubricant for which 7 = ap, with the particular value of a = 0.1; materials 2, 3 and 4 all have shear strengths greater than material 1at low pressures but strengths which fall away in one way o r another a t higher values of pressure. They can all be modelled by appropriate choices of the parameters a,3./ and yin equations (5). Figure 11 shows the effect that interfaces with these properties have on the form of the overall coefficient of friction of the two surfaces in contact. As must be the case characteristic 1 generates a constant coefficient equal t o 0.1. Materials 2, 3 and 4 all generate higher coefficients of friction a t

663 low values of the service parameter but, most significantly, as the value of the load group PIHSNR gets closer t o the shakedown limit so the values of p associated with all three fall below the curve for 1. This indicates that lubricant additives which produce under some circumstances interface layers with higher friction or traction can actually lead to reductions in overall friction values when the statistics of the surface are taken into account. 0.2

E7Hs 60 u / R E 0.0014

predictions of the effect on the macroscale of fluid or boundary-film properties generated on the microscale.

6. Conclusions Predictions can be made of the overall coefficient of friction between two loaded rough surfaces in sliding contact from a knowledge of their surface topography and the rheological properties of the lubricant boundary layers. If the shear strength of the boundary layer is linearly dependent on the local hydrostatic pressure then, at all pressures no greater than that associated with shakedown, the surfaces will show a constant coefficient of friction. Above shakedown there is a small additional contribution t o friction from plastic deformation.

service parameter

P YNRO

Figure 11 The resulting plots of coeficient of friction p versus the service parameter P l H P R a for the four characteristic of Fig. 10. The analysis presented above is not of course restricted either t o the shear properties of particular layers o r necessarily t o those with variations of the forms illustrated in Fig. 10. The software will accept any relationship between 7 and p and we have examined several others, for example a series of power law relations in which 7 is proportional to p raised to some index n. The value of the analysis is that it brings together lubricant rheological properties on the microscale, whether these have been obtained from experiment o r perhaps numerical molecular simulation, with the realistic topography of engineering surfaces t o make

In circumstances in which the shear strength of the boundary layer is a more complex function of pressure the overall coefficient of friction will not be constant. In particular, it is possible - because of the statistical nature of the contact between rough surfaces - for the coefficient of friction to be reduced by a surface film which has an enhanced shear strength under a range of hydrostatic pressures. In assessing the value of potential lubricant boundary layer additives, whether by experiment o r by molecular dynamics simulation, rheology of the lubricant must be combined with a sensible contact model of asperity interaction.

Acknowledgements We are grateful t o the Thornton Research centre of Shell Research Ltd for financial support t o one of us (Y.X.)which enabled this work t o be undertaken.

664 References 1 Bowden, F. P. and Leben, L. The friction of l u b r i c a t e d m e t a l s . Philosophical Transactions of the Royal Society. A239 (1939) ppl-27.

2 Blodgett, K B. and Langmuir, I. Built-up films of barium stearate and their optical properties. Phys. Rev. 51 (1937) pp964-982. 3 Bowden, F. P. and Tabor, D. (1950) The friction and lubrication of solids. Clarendon Press, Oxford. p187.

4 Briscoe, B. J. and Smith, A. C.The shear properties of thin inorganic films. Reviews of the Deformation Behaviour of Materials 3(3)(1980) ~ ~ 1 5 1 - 1 9 1 . 5 Coy, R. C., Kirsch, L. J., Bates, T. W. and Burnett, P. J . Automotive Lubrication Studies. Proceedings of International Tribology Conference Austrib 94, Perth, December 1994. pp751-759. 6 Williams, J . A. (1994) E n g i n e e r i n g Tribology. Oxford University Press, Oxford. p326. 7 Georges, J - M . and Mazuyer, D. M., Tonck, A. and Loubet, J-L. Lubrication with a thin colloidal layer. Journal of Physics of Condensed Matter 2 (1990) ppSA399-403. 8 Georges, J-M. and Mazuyer, D. M. Pressure effects on the shearing of a colloidal thin film. Journal of Physics of Condensed Matter 3 (1991) pp9545-9550.

9 Tabor, D. (1982) The role of surface and i n t e r m o l e c u l a r forces i n t h i n film lubrication. in Microscopic A s p e c t s of Adhesion and Lubrication (Tribology series No 7) ed Georges, J-M. Elsevier, Amsterdam. ~~651-679. 10 Bridgman, P. W. Shearing phenomena at high pressures in inorganic compounds. Proceedings American Academy of Arts and Sciences 71 (1936) pp 387-460. 11 Johnson, K. L. T h e application of shakedown principles in rolling and sliding contact. European Journal of Mechanics NSolids 11(1992) pp375-394.

l2 Sin, H., S a k a , N. a n d S u h , N. P. Abrasive wear mechanisms and the grit size effect. Wear 55 (1979) pp163-190. 13 Xie, Y. PhD Thesis, (1994) University of Cambridge. 14 Halling, J. and Nuri, K. A. The elastic contact of rough surfaces and its importance in the reduction of wear. Proc. Instn. Mech. Engs.199 (C2) (1985) pp139-144.

15 Kapoor, A . , J o h n s o n , K. L. a n d Williams, J. A. The steady state sliding of rough surfaces. Wear 175 (1994) pp81-92. 16 Samuels, B. and Richards, M. N. The transition between mild and severe wear for boundary-lubricated steels. J o u r n a l of Tribology 113 (1991) pp65-72.

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V. All rights reserved.

665

Effects of thin layer on friction and wear of cast iron under severe sliding conditions K. Hayashi, K. Hirasata, K. Yamamoto* and K. Sugita**

* Department of Mechanical Engineering, Osaka Sangyo University, 3- 1-1 Nakagaito, Daito-shi, Osaka, Japan

** Mitsubishi Electric Corporation, Inazawa Works, 1 Hishi-machi, Inazawa, Japan

The wear tests using a pin-on-disk type test rig were carried out in order to clarify the dry friction and wear characteristics of cast iron under severe sliding conditions (high sliding speed and high contact pressure), and the frictional force, the wear rate and the temperature rise of cast iron pin were measured. Moreover, the crystalline structure of cast iron pin after sliding test was observed by microscope. Then, the relations among them were investigated. For a while from starting when the temperature of sliding surface of cast iron pin is not so high, the wear of cast iron pin was small (the mild wear), but its wear rate remarkably increases when the temperature rise becomes high enough to soften the cast iron pin near the sliding surface (the severe wear or so-called thermal wear). In the condition of thermal wear, the coefficient of friction is independent of the contact pressure but decreases with the increment of sliding speed. On the other hand, the wear rate of cast iron pin is little influenced with the sliding speed but proportionally increases with the increment of contact pressure. From the microscopic observations of the crystalline structure of cast iron pin after sliding test, it was seen that the crystallines near the sliding surface became soft because of the severe temperature rise and flew to the sliding direction. And the thickness of the layer in which the crystallines of cast iron pin flew increased with the increment of sliding speed but was not so influenced with the contact pressure. The way how the thickness of this thin layer changes with the sliding speed and the contact pressure is deeply related with the friction and wear characteristics.

1. INTRODUCTION

A cast iron is widely used as brake shoe material and many investigations have been carried out on its friction and wear characteristics. (')-(') Most of them, however, have treated the phenomena under relatively mild sliding conditions, and the investigations on the friction and wear characteristics of cast iron under the severe conditions of high sliding speed and high contact pressure as seen in some kinds of emergency brakes have been not so many r ~ p r t e d , ( ~and ) ~ many ( ~ ) things

to be clarified are still remained. Under the sliding conditions of high speed and high contact pressure, the temperature rises of sliding materials by friction are very large and the changes of properties of sliding materials by the temperature rise give the strong influences to the friction and wear characteristics. The dry friction and wear characteristics of cast iron under the conditions of high sliding speed and high contact pressure in room temperature, especially those in so-called thermal wear condition in which the temperature rise by friction becomes high enough to

666

Fig. I Experimental apparatus soften a cast iron are experimentally investigated here. For this purpose, the pin-on-disk type test rig with high rigidity is built up, and the wear tests using a cast iron pin and a mild steel disk are camed out. The frictional force, the wear amount, the wear rate and the temperature rise of cast iron pin are measured and the relations among them are clarified. Moreover, the crystalline structure of cast iron pin after sliding test is observed by microscope and its relation to the friction and wear characteristics are discussed.

I

Sliding direction

10 1

I

2. APPARATUS AND PROCEDURES OF EXPERIMENTS The pin-on-disk type test rig for this investigation is shown in Fig. 1. A cast iron pin with 6mm x 3.2Smm rectangular section is fixed on the load cell and is pressed against the surface of the rotating disk by means of air cylinder. The flywheel with sufficiently large moment of inertia and the electric motor with sufficiently luge torque are used in order to keep the rotating speed of disk constant during a test. The contact force and the frictional force can be simultaneously measured by a load cell fixing a cast iron pin. The dimensions and the chemical components

I-

(a) disk Fig.2 Dimensions of pin and disk ‘Table I Chemical components of pin and disk

I

I material

components

(wt%)

pin cast iron (FC250) C=3.270 Si=2.710 Mn=0.6 10 P=O.O60 s=o.o10

I

disk

1

mild steel (SS400)

c=o.1 1 1 Si=0.229 Mn=0.616 P=O.O I 8 S=O.O 16

667 of test pieces used here are shown in Fig.2 and Table I. All the tests were carried out under the conditions of room temperature and dry friction. Before starting the test, the cast iron pin and the mild steel disk were cleaned up with acetone. Then, the disk was rotated with a certain constant speed and the cast iron pin was pressed against the rotating disk with some contact force by means of air cylinder. When the cast iron pin slided on the mild steel disk for some distance and its wear amount (wear length) reached to a certain value (3rnm in this test), the pin was pulled apart from the rotating disk and the test was finished. The contact force and the frictional force between the pin and the disk were simultaneously measured by the load cell fixing the pin and the wear length of tested pin was measured by laser displacement meter.The temperature rise of cast iron pin was measured by the infrared imaging system and the thermocouples. Moreover, the crystalline structure in the section of pin was observed by microscope in order to investigate the relation to the friction and wear characteristics. The experiments were carried out in the ranges of contact pressure P = 29.4 196.0 MPa and sliding speed V = 1 .O-20.0 m/s.

-

Fig.3 Variations of frictional force and wear amount one from points B to C the severe wear region. The point B is called the transient point. A little more detail discussions about the transition from the mild wear region to the severe one will be done in the following. The temperature rise of the cast iron pin, H,measured by thermocouple, at the point I .2mm apart from sliding surface, corresponding to the transient point B is shown in Fig.4. The ratio of the temperature rise H to the friction power Np, Bp (=H/Np), at the transient point B is also shown in Fig.4. I t is seen from this result

500 3. EXPERIMENTAL RESULTS 3.1. Variations of friction and wear with sliding distance An example of experimental results how the frictional force and the wear amount of cast iron pin varied with sliding distance (sliding time) is shown in Fig.3. The wear of cast iron pin is very small in the region from point A (starting point of sliding) to point B, but its wear rate remarkably increased after passing point B and this condition continues to point C (finishing point of test). The region extending from points A to B is named as the mild wear region and the

V

z-100 10

c

I

I

I

10

100

500

5

P

-

a

1

m

0.1

1

P V , MPamIs Fig.4 Estimation of transient point

668 that, regardless of PeV value, the way of wear moves from the mild wear to the severe one when the temperature rise of cast iron pin reaches to a certain degree. And the ratio of the temperature rise to the friction power at the transient point, Bp, decreases with the increment of P*V value. Moreover, it was known from the measurements of temperature by the infrared imaging system that the temperature of cast iron pin near the sliding surface rose near to 400°C at this time. Meanwhile, the hardness test was carried out for the purpose of clarifying the reduction of hardness of tested pin with the temperature rise. The result of hardness test is shown in Fig.S. The hardness of cast iron pin does not so change up to about 200°C but it remarkably falls down at near 400°C. From the aforementioned results, it is thought that the temperature of cast iron pin was rising with sliding distance and the wear rate was small in the region extending from points A to B in Fig.3 but, when reached to point B, the temperature of cast iron pin near the sliding surface rose high enough to soften the pin and the thermal wear started and the wear rate remarkably increased. From the experimental results

-0-

mean value

I

I

for the various conditions of sliding speeds and contact pressures, it is known that the thermal wear of cast iron pin starts when the temperature of pin near the sliding surface reaches to about 400°C.

3.2. Coefficient of friction The friction characteristics will be discussed with the coefficient of friction. The coefficient of friction was calculated as the ratio of the frictional force to the contact force measured in the sliding tests. The relations between the coefficient of friction p and the sliding distance L are shown i n Fig6 and Fig.7 as examples. For both cases of sliding speeds, the coefficient of friction varies with the sliding distance

in different manners according to each contact pressures in the region in which the sliding distance is short and the way of wear still remains in the mild wear condition or does not reach to the complete thermal wear condition. As the sliding distance increases and the condition of wear moves to the thermal wear, the coefficient of friction converges to a certain value regardless of the contact pressures. The experimental results for P = I 17.6-l%.O MPa in these figures correspond to the cases in which the mild wear region were notably short, and the coefficient of frictions in these cases are equal to the aforementioned converged value. Adopting the coefficient of friction at 3mm wear length of cast iron pin, p, as its representative value i n the thermal wear region, the relations of poversus the sliding speed V for the various contact pressures are arranged as shown in Fig.8. It is seen from this figure that the coefficient of friction in the complete thermal wear condition is independent of the contact pressure but is strongly influenced with the sliding speed and reduces with its increment. The solid line in Fig.8 was drawn with applying the method of least squares to the experimental data and the coefficient of friction po is expressed with the following mathematical formula;

669

I V=5.0m/s

0 P-29.4MPa

0 H

A

C

QE

0

49.0MPa 68.6MPa 98.0MPa 117.6MPa 156.8MPa 196.0MPa

0

A

v

3

* 0

-. .

I

10

50

Sliding speed V , m/s

0

20

5 10 15 Sliding distance L , m

Fig.6 Variation of coefficient of friction with sliding distance

V40.0 mls 0 P= 29.4 MPa 0 49.0 MPa 68.6 MPa 98.0 MPa A 117.6 MPa A 156.8 MPa v 196.0 MPa

E

6

Fig.8 Relation between coefficient of friction and sliding speed in thermal wear condition

3.3. Wear rate The specific wear amount is usually used for the purpose of estimations of the wear characteristics. The conventional specific wear amount, W, is defined by the following expression; W = v / (F L)

0.4

(2)

where v is a wear amount in volume, F is a contact force and L is a sliding distance. Since v = A* I and F = A* P in the present case, Eq. (2) can be rewritten with I

0

I

I

I

10 15 5 Sliding distance L , m

1

w = I / (P'

L)

20

fig.7 Variation of coefficient of friction with sliding distance

where a = 0.55. f3 = - 0.43 and V is a sliding speed [mls].

(3)

where I is a wear length of pin and A is a sectional area of pin. This conventional wear amount, however, is not suitable in order to apply to the estimations and discussions of the wear characteristics For the severe sliding conditions such as accompanied with the thermal wear treated here. Then, a new physical value defined by Eq. (4). Wm, is introduced; Wm=dv/(F*dL)

(4)

670 where dv is a increase of wear amount corresponding to that of sliding distance dL. This newly defined physical value, Wm, has the same dimension as the aforementioned conventional specific wear amount and is named as "modified specific wear amount". Rewriting Eq. (4), the following expression can be obtained;

where t is a time and 1 is a wear rate in length. So, it is seen that the modified specific wear amount introduced here is a ratio of wear rate in length to P V value. Fig.9 shows an example of the relation of this modified specific wear amount, Wm, versus sliding distance, L. Though the values of modified specific wear amount in the mild wear region and the severe one are quite different from each other, the value in each region is almost constant irrespectiveof the sliding distance, and the modified specific wear amount in the thermal wear condition decreases with the increment of sliding speed, V. The experimental results for the other contact pressures also showed the same tendencies. Therefore, it may say that the usage of modified specific wear amount defined here instead of the conventional specific wear amount is more useful to discuss the characteristics of thermal wear. Then, calculating the modified specific wear amount in the thermal wear condition, Wmo. as the mean value of Wm in the severe wear region and arranging it into the relation to the sliding speed, V, the result as shown i n Fig.10 is obtained. It is seen from this result that the modified specific wear amount in the thermal wear condition is strongly affected with the sliding speed and reduces with its increment, but it is independent of the contact pressure. The solid line in this figure was drawn with applying the method of least squares to the experimental data and the mathematical expression for this line is as follows;

0

10 20 30 Sliding distance L , m

Fig.9 Variation of modified specific wear amount with

sliding distance Wmo = a V b [mm2/N]

(6)

b = - 0.93 and V is a sliding

where a = 5.6 x

speed [mls]. From Eqs. (5) and (6).the wear rate in length of cast iron pin in the thermal wear condtion, 1 ,is given by

i = 0.056

P

'

v 007

[mmls]

(7)

5.00E4

I .WE4

I .00E-5

I .00E-6 I

10

Sliding speed V

,d s

Fig.10 Relation of modified specific wear amount versus sliding speed in thermal wear condition

671

'fable 2 Temperature of cast iron pin near sliding surface in thermal wear condition 1 %MPa

3.5. Microscopic observations I n order to clarify the friction and wear characteristics in more detail, the observations of the section of cast iron pin by microscope were carried out after finishing the sliding test. The examples of microscopic observationsof crystalline structureof cast iron pin after the sliding test are shown in Fig. 1 1. The crystalline structure of cast iron pin in the inlet, the central and the outlet regions of the sliding direction are shown for the various sliding conditions. In these results, the thin layer in which the crystallines of cast iron pin flew to the sliding direction was seen near the sliding surface. This thin layer was formed as a result of the reduction of hardness of cast iron pin by the severe temperature rise and the flow by frictional force, and it is named here as "fluidity layer". Arranging the microscopic observation results, it is seen that the thickness of this fluidity layer varied with the sliding conditions as shown in Table 3. The thickness of fluidity layer in the thermal wear condition varied within the range from several tens to two hundred micrometers. Moreover, it is seen that the thickness o$ fluidity layer remarkably increased with the increment of sliding speed but reversely decreased with the increase of contact pressure. I t may be thought that these results are based on the following reasons. The increment of contact pressure generated the proportional increase of the wear of cast iron pin as previously mentioned and some parts of fluidity layer continuously disappeared as the wear particles. On the other hand, the increase of sliding speed was not accompanied with the increment of the wear of cast iron pin as mentioned in the previous section. So, the increment of heat generated by the increased sliding speed directly contributed to the increase of thickness of fluidity layer.

! Sm/s

4SO-SSo"C

4OO-SoO"C

20m/s

688-784°C

688 -7 15°C

where P is a contact pressure IMPal and V is a sliding speed I d s I . Therefore, it may say that, in the thermal wear condition, the wear rate of cast iron pin proportionally increases with the increment of contact pressure but is little affected with the sliding speed.

3.4. Temperature rise The temperature rise of cast iron pin near the sliding surface during test was measured by infrared imaging system. From this measurement, it was seen that the temperature of cast iron pin near the sliding surface increased more and more from the inlet to the outlet regions of sliding direction. The temperature of cast iron pin near the sliding surface in the thermal wear condition (at the point when the cast iron pin weared 2 -3mm in length) measured for the various sliding conditions are arranged in Table 2. The reason why the temperatures are shown with some widths is based on the fact that the temperature of cast iron pin near the sliding surface varied in the sliding direction as mentioned above. The values shown i n Table 2 correspond to the lowest and the highest temperatures in the sliding direction, respectively.

Table 3 Thickness of fluidity layer 196MPa <20pm 50pm

672

Fig. 1 1 Crystalline structure of cast iron pin after sliding test

4. DISCUSSIONS

The dry friction and wear characteristicsof cast iron under the conditions of high sliding speed and high contact pressure are discussed on the basis of the experimental results obtained in the previous chapter. The temperature rise of test pieces generated by the friction gives the notable effects on the friction and wear characteristics under such severe sliding

200pm

conditions. For a while after starting of slide, the hardness of cast iron pin does not reduce and the wear rate is small (the mild wear) because the tcmperaturc rise of cast iron pin is not so much. The wear of cast iron pin, however, remarkably increases when the temperature rise increases with the increment of sliding distance and reaches to a certain degree (the severe wear). The transient temperature moving from the mild wear region to the severe one for the cast iron tested here was about 400°C and this temperature corresponds

673 well to that at which the hardness of cast iron pin remarkably reduces. That is to say. when the temperature of cast iron pin near the sliding surface has reached to about 400°C, the condition of wear changes from the mild wear condition to the severe one. This wear in the severe wear region is the one accompanied with the reduction of hardness of cast iron pin by the severe temperature rise and is called the thermal wear. In this thermal wear condition, the cast iron pin near the sliding surface becomes soft because of the severe temperature rise and the thin layer, named as the fluidity layer, having the low plastic flow resistance is formed. The thickness of fluidity layer has strong connection with the friction and wear characteristics. The thickness of fluidity layer oughts to increase with the increment of friction work, namely with the increment of sliding distance. When the contact pressure increases, however, the frictional force hecomes larger and some parts of fluidity layer continuously disappear together with heat as the wear parlicles (the increase of wear rate). So, the thickness of fluidity layer does not increase with the increment of contact pressure and the temperature of cast iron pin near the sliding surface does not vary so much. As a result, the coefficient of friction in the thermal wear condition is not affected with the contact pressure. On the other hand, the increase of sliding speed is not accompanied with the change of the wear rate of cast iron pin. So, as the sliding speed increases, the temperature rise of cast iron pin becomes severer and the fluidity layer becomes thicker. As a result, the coefficient of friction in the thermal wear condition decreases with the increment of sliding speed.

investigated. From the experimental results obtained here, the following conclusions are derived. ( I ) The temperature rise of cast iron pin generated by friction gives the strong effects on the friction and wear characteristics. (2) When the temperature of cast iron pin near the sliding surface has reached to a certain degree, the condition of wear moves from the mild wear to the severe one (the so-called thermal wear). This transient temperature is about 400°C. (3)In the thermal wear condition, the thin layer named as the fluidity layer in which the hardness is remarkably reduced by the severe temperature rise is formed near the sliding surface of cast iron pin, and its thickness increases with the increment of sliding speed but not with the increment of contact pressure. The thickness of this thin layer has strong relations with the friction and wear characteristics. (4) To discuss the wear characteristics in the severe sliding conditions as treated here, the modified specific wear amount defined in this paper is more useful than the conventional specific wear amount. ( 5 ) The modified specific wear amount in the thermal wear condition is independent of the contact pressure but decreases with the increase of sliding speed. (6) The coefficient of friction in the thermal wear condition is independent of the contact pressure but decreases with the increment of sliding speed. (7) The wear rate of cast iron pin in the thermal wear condition is proportional to the contact pressure but is little influenced with the sliding speed.

6. ACKNOWLEDGEMENTS

5. CONCLUSIONS The dry friction and wear characteristics of cast iron under the severe sliding conditions of high speeds and high contact pressures were experimentally

The authors wish to special thanks to the members of Elevator Mechanical Development Section of lnazawa Works, Mitsubishi Electric Corporation for their helps and supports.

674 REFERENCES ( I ) K. Idemura, "Brake for Railway Rolling Stock",

J. of Japan Society of Lubrication Engineers, 21 -3( 1976), 133, (in Japanese) (2) R. Narutaki, K. Iwata, J. Aihari and K. Owa, "Friction and Adhesion of Grossly Deformed Metals at High Pressures and Temperatures", Trans. of Japan Society of Mechanical Engineers, 26-281 (1970),134,(in Japanese) (3) T. Teshima and Y. Komurd, "Unlubricated Sliding Friction and Wear Characteristics at High Speed", J. of Japan Society of Lubrication Engineers, 20-2( 1975),83, (in Japanese) (4) T.Sasada,"Friction and Wear under High Speed Condition", J. of The Japan Society of Mechanical Engineers, 76-650(1973),226, (in Japanese)

(5)K. Okada, T. Yoshida and A. Hijikata, "Friction and Wear Characteristicsof Gray Cast Iron under High Sliding Speed and High Contact Pressure", J. of Japan Society of Lubrication Engineers, 24-I( 1979), 27(in Japanese) (6) K. Okada, "Thermal Wear of Cast Iron under High Bearing Pressure", J. of Japan Society of Lubrication Engineers, 30-10(1983,733, (in Japanese) (7) K. Takasawa, T. l'sujimura and S. Yuri, "Friction and Wear Characteristics of Several Cast Irons", J. of Japan Foundrymen's Society, 57-8( 1985), 5 16, (in Japanese) (8)T. Tsujimura and S. Manabe,"High Speed Frictional Performance of Several Cast Irons and Cast Claddings", J. of Japan Foundrymen's Society,

59-7( 1987),421, (in Japanese)

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

675

AN ELASTIC-PLASTIC MODEL WITH ADHESION FOR THE

SPHERE-FLAT CONTACT A. Tudor and L. Seiciu Department of Machine Elements and Tribology "POLITEHNICA" University of Bucharest 31 3, Independenjei Spl., Bucharest, ROMANIA

Abstract For the elastic sphere-flat contact the radius of circular contact and the normal displacements of the loaded circle are determined considering the surface energy. For a variable static friction coefficient we determined the tangential displacement within the central stick circle, the relative slip and the energy dissipated per cycle. The nondimensional mechanical work is dependent on the shear and adhesion coefficient, thc molecular-mechanical friction coefficient and the elastic-plastic properties of the materials. Ke-ywords: Fricrion sratic and kineric; Adhesive force: Energy dissipated; Mechanical work.

I . INTRODUCTION

2. IDEALIZED ELASTIC-ADHESION MODEL

An elastic model for the behaviour of convex contacts between solid surfaces subjected to oscillatory tangential relative displacements of low aniplitude has been developed by Cattaneo, Midlin. Johnson [l]. An elastic model for the contact conditions in frettiug and the frequency effects was developed by Odfalk and Vingsbo 121, Vingsbo and Schon [3, 41. The measurements of the amount of energy dissipated per fretting cycle indicated a larger energy loss than predicted for the elastic model. The elastic model was found to be in good agreement with experiments on hardened steel for low normal contact pressures and the elastic-plastic model agreed well for soft materials. In the present paper the previous models are extended to include elastic and plastic deformation in the slip direction with a varying friction coefficient. Considering the molecular-mechanical theory of friction, we determine the energy dissipation in each cycle.

We assume that the sphere has an elastic (Young's) modulus El and Poisson's ratio v 1 and the flat has an elastic modulus E, and Poisson's ratio v 2 . It is further assumed that the bodies are made of ideally elastic material and that the contacting surfaces are perfectly smooth. From Hertzian theory it is known that the contact area will then be circular, of radius (1)

an = (3Fp14E')'I3

where F, is the applied normal load, R is the radius of curvature of the sphere, i / ~ = (* 1 - v : ) / ~ , + ( i - v : )/ E ~ , E* - the equivalent elastic modulus. The normal pressure distribution over the contact area is given by 21n/(2xa;) p(r) = 3Fz(1-r 2/an)

=

(2)

=p,(l - r 2 / u p ; p 0 = 2u#*/(srR) where r is the distance from the center of the

676 contact surface and p o is the maximum n o d hertzian pressure. To study the effect of adhesive forces in the absence of surface roughness we shall consider the Johnson theory [l], [S]. The n o d elastic displacement (Fz, and rz,)in the contact circle produced by the normal traction must satisfy the boundary conditions

Cd + Cs = 6 - rZ/2R,

(3)

where b = 6, + 8 2 is the total compression of two solids. This condition is satisfied by a pressure distribution of the form p(r) = p,(l -rZ/uZ)'R + pL(1 -rz/uZ)-'R

(4)

For equilibrium, the overall relative displacement of the two bodies 6 is constant. In this m e the surface energy per unit area of each surface (Us= - 2 x y a 2 ) and the elastic strain energy stored in the two bodies, a

The normal displacements of the loaded circle ( r s a )are (7)

C~= -(a2/2R>(2-r2/u2)+ X P ~ / E

The n o d displacements of the points in outsrde the loaded circle ( r > a )are

-

u, = -@d2a~)@u' -r2)sin-'(u/r +t2(u/r)(l-u'/r2'3 +

+(2pLa~)sin-'a/t (8)

rZ,=(rz/a) (,??/pol, r / a = F

If is noted

= pL/po, equations (7)and (8) become

-1

x/4)(2 -7- 4 i 3 for u, = (1/2)(2-7sin-1(1/+(1/2)Fiy

-2pdsin4(1/3

7s1 -l/Fy-

for

(7')

F"1

The analysis of normal displacements enables the determination a ring With radius r,, which has null . w displacements

-

(9)

ro = rJr = (2-4Fjm

UE= 2njp(uJ+uJ)dr,

and

0

For

normal forces, (16/9)F,sFF,s(64/9)F,, the normal displacements are given by the compression and the stretching. -

was satisfied by

the

small

%.

and p : = -2 ( y E ' / n a ) lI2, where y = y1 + y 2 - A y is the surface energy of each newly created free surface for body 1 (y,), body ( y 2 ) and the energy of the interface (Ay);yl and yz are the specific surface energies of the two solids. Equation (4) is p(r) = ( ~ E * / x R ) (-r2/u2)'PI -2(y~'/xa)m(1-r2/uz)-ln

(4')

The contact area will then be circular of radius u = uJl+k,,)m = a&,. kr=(l+ki,)m

(6)

where klr= 2. ( F , / F z ) [1+( l + F , I F , ) lI21 and F, = 3 x y -~ the "force of adhesion" 111, [ 5 ] .

-1s

'-1s

Figure 1

I -I

4;

0

as

I

1s

r

For example, in Fig. 1 are shown, the dimensional normal diq)iacements, r.,,versus 7 and 3.

677 ELASTIC TANGENTIAL TRACTION A simultaneously applied tangential force F, will nerate a tangential traction q(3 in the contact :a. The tangential traction has the same direction erywhere and the points of equal traction are 2ated on a circle. A tangential force whose ignitude is less than the force of limiting friction ie maximum static friction), when applied to two !dies pressed into contact with a normal force and adhesive force, will not give rise to a sliding .>tion (incipient gross slip). A first assumption that no slip occurs anywhere in : contact area, requires that the traction stribution Ill, 161, [71 is:

m which qo= F,/ ( 2 x a 2 ) . The relative elastic tangential displacement in the '0 bodies UI

= (aJa)(E*/pJ = (n/6)(1+E'/G')F,

(11)

iere G' = 2G, G2/ (G,+ G 2 ) - the equivalent elastic car modulus and F=F,/F, - the dimensional ngential traction. The tangential traction necessary for no slip rises a theoretically infinite value at the periphery of :: contact circle so that some micro-slip is evitable at the edge of contact. However, it may be sumed that the tangential component of the oduct of the friction coefficient p and the normal ntact pressure, i.e.

(35 PP(3 = 4'(fi

9

(12)

has a singularity at outer boundary of the contact ). This implies that slip will occur at some area ( F=I parts of the contact surface. The requirement of equilibrium in the tangential direction and continuity of the tangential traction component are satisfied by a friction distribution

(a

For the loaded points of the sphere and the flat where q(3 < q'(3 it is "stick" and for qCl') i t is "slip". The traction q(3/q'(3 isamonotonicallyincreasing function I ,forF=o andhasminimumvalue, qo/ (to+pp,+pp,) and maximum value, qo/ (ro+Pp;), for F=i. The conditions of normal and tangential loading (F,, F,) and the mechanical properties of the materials (to, P ,y , E, , 2 , v ,, ) define the incipient gross slip. There are possibly the subsequent limit conditions:

<

1. For F/
2. For F;? 6pi?$2+3P+3i0 (where To=to/po) slip occurs in every point of the loaded circle. The surface displacements within the loaded circle (Fsl),which are determinated by the tangential traction component q' ( 3 , are calculated by

qa= (i$z)(E'/pJ -

:iere q' ( 3 is the tangential friction traction. :cause the static coefficient of friction ( p ) is not Instant, we considered the molecular-mechanical eory 181 to be valid, '

= r,/p(r)

+

P

9

(13)

here to is the shear tension of a molecular nding; p - the piezocoefficient of the molecular lmponent of friction. the parameters t o and p are Insidered as properties of the material couple and ey are determined by experimental methods. F m @om (10) and (12) it can be Seen thatq(3

= (4/x)

E($ +

+ (nP/l6)(4(1 +E*/G')+(1+3E'/G8)~} -

(I5)

(x/2)PFi(l+E*/G'),

where E ( 3 is the complete elliptic integral of second kind with modulus.

3. For 6 P < / 2 s F<6P
678 (equation 11) corresponds to slip, and the total displacement may be decomposed into two components according to bra

The nondiniensional tangential displacement within that circle is

ii;; = (i+)@*/pJ= -((4/x)(P/2)rOE(qFj+ + -

(~P/16)(F/2)[4(1+E*/G') + (1 +3E'/G')P/F] (nP/2)FL(l+E'/G )c /a 1 8

7

-

1

(17)

For the loaded circle of radius I , it is considered the equation (14) used for the tangential traction. The resultant displacenients in the circle, F.5, are given by adding equations (15) and (17), with the result

Bra

-/

-11

= u,+u,

= (L,/u)(E'/po)= (4/n)TO[E(fi-

-C'LE(qa] + (nfl/4)(1+E'/G*)(1-2)(1-2F$= (18) = (x~/4)(1+E'/G*)(l-c?)(1-2~~)

first term, ( 4 / x ) T 0[ ~ ( r -7 -?E(F//c7 1 , because it is very small. Thus the stick region is the circle of radius C whose value can be found from the magnitude of the tangential force: neglecting

the

1

F, = \2xa4/(fi&0 =

C

$2acq"((fi&= 0

(19)

pF$a( 1 -3)

where k, is the "shear and adiesion coefficient",

k, = 3rJ(2P) + 1 - Fa -1/2

(20)

At each point the difFemre 6 rd (equation 22) art6Bd

=a '

+

'sa

(23)

where 6 is the (reversible)elastic component and 6 sa is the (irreversible) slip component. The slip component depends on the load distribution of the contact. The relative slip at any point in the annulus is determined by the tangential traction cf ( r 1 , which acts for F<1 and q N( 3, which acts outside the loaded circle ( F s F<1)with slip, s* = (sla)(E'/p,) = =(~p/16)((1 + E'/G*)[42(1-2FL)+(l+3E'/G')PJ) - ( x p / 2 ) p l (l+E'/G') + (4/5()2sin-'C7fi- (4/7t)ioC'Lr[(t7F)-lIE(3fi -(qE)(1 -P/P)K($fi+ + (PF/2[(2-P/2sin-'(~~+(r7Fj(l -FyP)'nI (24)

where K ( F / F ) is the complete elliptic integral of the first kind with niodulus (F,/r7 .

4. ENERGY DISSIPATED PER ELASTICADHESION CYCLE When the tangential force is increased from zero, microslip starts at the rim of the contact circle (F=l), and penetrates inwards into a circle with radius C, given by equation (21). When the tangential force F, = p F z , ( F = p ) , the radius c is zero, and this is the condition for incipient gross slip for each point. Because the sliding kinetic friction coefficient ( pk) is smaller than the static friction coefficient ( p), after the first cycle of the loading with traction, F=p , the tangential force decreases to F=pk. In this case if the sliding of one surface is continuous, the other moves in stick-slip motion. In the macroslip ("gross slip") period, the tangential traction F, is ensured by the difference between the elastic force which has opposite sign and the kinetic friction force. For the simple case when (lk is constant, it is possible to determine the energy dissipated per cycle (A W )for the sliding with constant direction and sense (Fig. 2).

679

w =W0h + wAB+ Wm/,

(25)

iere wOA/, W, WBOtrare the mechanical work of A, AB, BO' curve respectively. - I

Because the curve O'ABA is continuous, it results in the condition, (P/p&1-2F3

1 4 1- P k J I p

(29)

9

for the incipient "gross" slip with the kinetic friction coefficient. During the "gross" slip penod, the elastic component of the displacement is retrieved ( l j e a ) , which is determined by equation ( I l ) , s u b s t i t u t i n g F=F,/F,=Pk,, gives be, = ( n / 6 1 Pk, ( l + E ' / G ' ) . At the end of "gross" slip the friction coefficient increasing from pk (kinetic friction coefficient) top (static friction coefficient), the displacement of point B is 6,=6'

The tangential displacement during loading (OA) found using equation (22) and the tangential iction is = pk, 11 -(1- 6 r J m ) 3 ] ,

=

(26)

-6co=(~/12)P(1+E*/G*)(3-2ka-6j73 (30)

The nondimensional mechanical work stabilized cycle,

VoA = /Fd6,a = pka(6* - (2/5) m I1-(1-6 '/m)'"])

=

Pkd[6,-(2m/5)(1 -b&) srz 1. (31)

61

The nondhensional mechanical work WAB. 61

-

W M = /mara

b'

for

b'

Wo9 = /F&,

here m = ( n / 4 ) P ( 1 - 2 3 ) ( l + E ' / G ' ) . The nondimensional mechanical work W,,, for e first cycle is

w0jA

= -(Pka-2pk)b,-

8.

(32)

-(4n/5>([a */(2n)+b15n-[a$(2n) +bj5n)

0

(27) For

F=pk, (incipient 'gross" slip), 6 * = mand

VoA = (315)P ka6 '

(27')

and W,,/ = 0. The area inside the loop of Fig. 2 represents the energy, dissipated per the stick-slip period of motion, A W = W0lA + W,, This energy contributes to generating "the third body", which has an oscillating motion with the relative period

7- 71Tz = 6 c g J ( 2 E ' ) , where T is the period of stick-slip motion and T , the penod of sliding contact ( T z = a / v , v is the sliding continuous velocity). The energy dissipated per cycle contributes to tht. fatigue of materials and to the formation of wear particles. For the elastic-adhesion model, this euergy is constant if the friction conditions are identical.

680 5.AN ELASTIC-PLASTIC-ADHESION MODEL An elastic-plastic model for the contact of sphere and flat can be based on the elastic-adhesion model described previously, if the sphere and flat are not assumed to be ideally elastic. In agreement with the assumption 121. it is considered that there is a plastic r e 1 a t i v e d i s p 1 a c e ni e n t c o m p o n e n t , =a, ( b p / a )( E ' / P , ) , bTP= bea + 6 ,

+

(33)

8,.

friction load p,F,s Fy, the tangential displacenieiit is elastic and plastic. The point B (Fig. 3) on tlie unloading curve (A'B) may be situated in tlie plastic (B,) or elastic zone (B2). The tangential traction during unloading (OB) is determined by equation (28') and the effect of -hardening, for F> Fy,

F = F ' + 2 p ~ ~ , d ( 2 n ) + b ~ 3 1 2 - 2 ~ t + ( F (35) 0-~~/~~ If the Baunschinger effect is considered, the plasticity coefficient k;
T =TJT, = (6' - bB,,)pJ(2E')

Figure 3

The plastic beliaviour of the sliding contact is illustrated by tlie sclieniatic loop (AA'BB') of Fig. 3, in wliicli represents the yields tangential traction ( F , = F,/F,). This traction ( Fy)depends on the geometry of the contact ( R ) and the material( o y , E and v ). For a linear work hardening with a plasticity coefficient kp,the tangential traction during loading (OAA') is given by equation (26) adding the effect of hardeiung -for F>Fy

5

(34) At point A', F=pk,,gross slip begins with the kinetic friction coefficient p k . The gross slip appears only when the elastic load is greater than the kinetic friction force (tangential traction). During the loading period. the riiaxinial elastic load is deterniiiied by equation ( I ) for Fy7 6 , , = ( n / 6 ) ( 1+ E ' / G ' )

5.

<

7

I f the kinetic friction load pkF,> F y 9the Ctngential displacenient is always plastically. If the kinetic

(36)

where 6; is tangential plastic displacenient which may be determined by equation (34), 6; = art. for -F = F * = P k , , and b , , , , may be deterniiiied by equation ( 3 3 , b , , , , = a, for F = p k and F' = pk,.

6. CONCLUSIONS The suggested model is based on the surface energy and the variation of the friction coefficient with the normal pressure in loading zone. The tangential traction, normal loading arid mechanical properties of the materials define the incipient gross slip. There are possibly three h i i t conditions. which are functions of the material and the static and kinetic friction coefficients. They determine the energy dissipated per elasticadhesion cycle and the relative period of oscillating motion for tlie elastic and elastic and/or plastic bodies in the contact area.

REFERENCES 1 . K.L. J O ~ I L W I I ,Contact nirchanics. Cariibridgr University Press, 1985. 2. M . Odfalk, 0. Vingsbo. Ail elastic-plastic niodel for fretting contact, Wear. 157(1992), 435-441.

68 1

3. 0. Vigsbo, J. Schon, Gross slip criteria in fretting, Wear, 162-164 (1993) 377-356. 4. 0. Vingsbo, J. Schon, Friction coefficient in vibrational sliding. Proceedings 6th International Congress on tribology "EUROTRIB '93 " Budapest, vol. 5, p. 174-177. 5 . M.D. Pashley, J.B. Pethica and D. Tabor, Adhesion and micromecanical properties of metal surfaces. Wear, 100 (1984) 7-31. 6. S. Adibnazari, W.D. Hoeppner, Characteristics of the fretting fatigue damage threshold. Wear, 159 (1992) 43-46. 7. D.A. Hills, Mechanics of fretting fatigue. Wear, 175(1994) 107-113. 8. A. Tudor, Real contact in friction surfaces. Bucharest, Edit. Academiei Romine, 1990 (in roumanian).

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SESSION XVll MIXED / BOUNDARY LUBRICATION

Chairman :

Dr Joseph Tevaarwerk

Paper XVll (i)

An Examination of Additive Debris to Give Insight into Boundary Lubrication

Paper XVll (ii)

The Influence of Slide/Roll Ratio on the Film Thickness of an E.H.D. Contact Operating Within the Mixed Lubrication Regime

Paper XVll (iii)

The Influence of Plastic Bulk Deformation on Surface Roughness and Frictional Behaviour During Deep Drawing Processes

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 1996 Elsevier Science B.V.

685

An examination of additive debris to give insight into boundary lubrication J S Sheasby", T.A. Caughlin", S. Terranovaaand A. Cohcnb

"University of Western Ontario, London, Ontario. Canada. N6A SB9

''RAFAEL.P.O. Box 2250, Haifa, Israel. The antiwear action of S, P. S/P and Zn/S/P a d d h x blends was investigated by examining the generated debris. To mayimisc the ratio of add~tivedebris to wear debris the 4-ball test parameters were chosen to optimisc the performanceof each additive. Debris was taken from the oil by filteringand by centrifuging. and from around the wear scar. The debris was particulate and very fine, ranging in size from 10 nni to 3 pm with the larger particles apparently compacted smaller ones. It was proposed that the finer particles formed by the add~tiveshad the structure and chemistry of the film responsible for wear protection.

1. INTRODUCTION

Wear debris has long been recognised as an important &agnostic means in wear analysis. However, unlike most previous work. this paper is concerned with debris associated with the action of antiwear additives, rather than the wear process per se;though the two may wcll be related. To maximise the amount of "additive debris", and minimisc the amount of "wear debris", carc was taken to s e l d wearing conditions in whch the additives were clearly effkctive. Wear protection in boundary lubrication is traditionally considemi to result from the lubricants, or additives in the lubricant, reacting with the surfaces to forni a load bearing film. Shear occurs withm the film thereby minimising damage to the structural surfaces. However. it can reasonably be stated that only with ~JncdialkyldIUuophosphate additives has clear evidence for the operation of such films becn Sccn [ 1-41. More typically surfaces that were performing satisfactorily appear to be barc, or the quantity of film does not correlate with the performance. An alternate view of boundary lubrication has bcen developed by the laboratory of Dr. J. M. Gaxges 151. Georges' group describes how oxides, adsorbed lubricant, additives, etc., are picked up and mixed in thc convergent inlet of contacts. and thcn transformed into a colloidal paste by friction within the contact. Depending upon thc specific rheological properties of

-

the mix, the paste can cause abrasive wear, be a protective layer, or be transformed by rubbing into adherent films. The present authors have observed such a paste-like material in a Direct Observation Wear Machne O W M ) constructed by them (2.6,7]. The DOWM allows wearing samples to be viewed through the countersurface while under test at conditions matching those in the 44x111. The origin and sigruficance of features on wearing surfaces is thereby greatly clarified. In partJadar, the paste was observed to deposit in a halo around scars. Similar halos form around scars in the 44x111, and were found in this study to be a convenient source of addtive debris. 2. EXPERIMENTAL PROCEDZJRES

The tests from which debris was collected were performed in a Shell 4Wl lubricant lesting machine, basically following the practise of ASTM D4172-82, 1987. Tests were starled with the load on, and stopped with the load off. Padlel tests were also performed in our DOWM to give qualitative insights into the additives action. Standard AISl E-52100 grade EP, 1/2" diameter steel balls were used in both machines. The base oil was Solvent 150 N (kinematic viscosity 28.31 Cst @) 40°C) refined from Wcstern Canadian cnde.

686 Coinmcrcial additives were used to make blends containing: 1.5 -1% 2nd ZDDP (ZDDP), 2.0 ~ 1 % sulphudphosphorous (W). 1.O wtY0 amine phosphate (AP). 1 .O wt% amine monotluophosphate (MTP), I .O wto/o amine monothiocarbamate (MTC). and 2.0 wtY0 tricresyl phosphate (TCP). For brevity the blends will be rcferred to by the letters in the brackets. The oil was filtered through 0.2 pn Mdlipore filters just before use when debris was to be collected from the bulk oil, i.e. techniques 1-3 below. The resulting wear scars were scanned perpendicular to the direction of sliding by a Dektak profilometer. Wear volumes were calculated by revolving the traces through 180' (estimated accuracy +/- 3000 p3). The wear constants. K in pm3/N.m given in h s paper are defined by the equation: K = (wear volume)/(0.408s load x distance), where the load was that applied to all three balls.

3. RESULTS 3.1 Debris on worn halls

When the additives wcre performing optimally the appearance of wear scars by optical microscopy could be classified into thrcc groups. Figures 1-3. All the scars were surrounded by a halo of coloured material that was readily removed by a light wipe. ZDDP and TCP formed h c k colourcd films as in Figure 1. The scars formed in SP and MTC additives were essentially bare with patches of thick film, Figure 2. The AP and MTP additives were also essentially bare with variable amounts of tlunner film, Figure 3.

Debris was collected by: 1) continuously circulating the oil through a filter circuit before and during runs.The oil pot of the 4-ball tester was modified so that oil above the normal height was pulled through a 0.2 )un Millipore "Isopore" filter by a ceramic piston pump, and returned to the ball pot. Filters were changed every 30 minutes for 2 hours before a mn started, and at selected intervals throughout the run. 2) after tests were finished the oil and hesane rinsing of the pot were filtered through a 0.2 pn filter. 3) after tests were finished the oil and h e m e rinsing of the pot were centrifuged at 10,OOO g for times up to 6 hours. 4) debris was lifted from the scar area using a conducting C based adhesive (Catalogue No. CI 1200 Soquelec Ltd). 5 ) debris was Wed from the scar area by sputtering with gold and removing the gold film with epoxy resin glue.

In addition the scars and debris were examined directly by SEM and Scanning Auger. The intent of techmques 4 and 5, was to ensure that if iron was detected on analysis, that it was part of the debris, and not from the substrate. The only solvent used on the debris samples was HPLC grade h e m e . In all micrographs of wear scars the leading edge of the contact is on the left of the picture. -

Figure 1. Scar formed in TCP after wearing at IOOOC, 1200 rpm with 15 kg load for I hour. Scar diameter 237 pm. Wear constant 0. I I pm3/Nm. The scar is coated by a thick adherent film (Figure $), whereas the surrounding halo of friction material is readily wiped away.

Figure 2. Scar formed in the SP additive by wearing at 10OoC, 1200 rpm with 15 kg load for Ihour. Scar diameter 224 pm. Wear constant 0.33 pm'/Nm.

687 coatcd by a patchy thin film. as in the backgrounds of Figures S and 6. Many of the patches appeared to bc loose. and about to form into thin debris particles smaller than 0.2 pm diameter.

Figure 3. Scar formed in MTP after wearing at 100°C, 180 rpm with 15 kg load for 402 minutcs. Scar diameter 370pni.Wear constant 2.32 pm3/Nni. 3.1.1 Thick films

As has becn dcscribcd previously [ 2 4 . the lhick films formed on scars in oils containing ZDDP. and now TCP, were of irregular thickness. forming into pads 10-50 pm in diameter. In the DOWM the pads were seen to grow and break down continuously. This process is compatible with the appearance of the film in the SEM. as in Figure 4. where the pads can be seen to bc disintegrating around their edges, with many free particles present or about to be releasod.

Figure 4. Antiwear pads in the centre of the scar shown in Figure 1. 3.1.2 Bare metal

The "bare" metal in scars was seen by high resolution low voltage SEM to be in fact subslantially

Figure 5 . Debris in the centre of the scar shown in Figure 2. The larger particles are accretions of particles similar in site to the thin patchy film on the metal.

Figure 6. Debris near the centre of a scar formed in MTC atlcr wearing at 25°C. 1200 rpm with 15 kg load for 72 minutes. Wear constant 4.3pm3/Nm. The scar is well coated by a tlun film though individual SO nm particles are being released on the right hand side. The 1 Fm long particle at the bottom centre is an aggregate of much smaller particles in friction material.

688 3.1.3 Patchy films

The debris patches that could be Seen by optical microscopy on nominally bare scars had in fact a wide range of structures that rquired high nlagnifications to resolve. One type, (MTP ,and AP). was the same as in Figure 4, but covered only a fraction of the scar. More commonly, the material was clearly compacted from much smaller particles and only lightly attached to the scar. as in Figure 5. (one of the smaller central patches in Figure 1). Another type of film was based upon an amorphous organic material, wluch. because its similarity to material analysed and so named by Stinton et al., 181, will be termed "friction material". Friction material was present infrequently as Uun smears on scars as in Figure 7. and, also infrequently, as the matrix of thicker agpgates that were loaded with liner solid debris, as in Figure 6.

Figure 9 , Previously. the authors have referred to all of the halo film as "friction material" [24,7.91. This is now considered to be incorrect, as most of the halos were particulate in natw. with only a small fraction amorphous. Oil containing MTC formed voluminous amounts of a distinctively different type of halo material. Figure 10. The material was coniposed of 40 nm particles fused into a lacy network.

Figure 8. Particles in a thin part of the debris halo on a scar formed in MTP worn at IOO°C. 1200 rpm with IS kg load for 3 0 minutes. Wear constant 3.5 pm3/Nm. Scratches on the ball surface can be seen under the debris.

Figure 7. Central part of a scar formed by wearing in SP blend at 100"C, 200 rpm with 15 kg load for 60 minutes. Wear constant 3.9 pm3/Nm. The dark film is termed friction material ". '&

3.1.4 Debris around scam

The coloured halos around scars were typically made from fine separate debris particles as in Figure 8. Infrequently, friction materials of the types described in 3.1.3, were observed in association with the separate particles at the leading edge of scars,as in

Figure 9. Friction material and individual particles in the leading edge of the debris halo of the scar shown in Figure 2.

689

Figurc 10. Part of the debris halo around a scar formed in MTC after wear at 2S°C,550 rpm with 10 kg load for 2 minutes. Wear constant 7.4 pm3/Nm.

Figure 11. Debris collected by filtering oil with ZDDP after wearing at 100°C. 1200 rpm with 15 kg load for 60 minutes. Wear constant 0.07 pm3/Nm. The larger particles appear to be essentially monolithic at 80 000 X.

3.2 Debris retrieval

3.2.1 Continuous filtering The filter loop hnctioned in that the last prerun filters reported essentially clean, and debris was recovered from filters used during the run.However the goal of recovering initial and steady state debris for separate analysis could not be achieved when it was determined that much of the debris was finer than 0.2 pn. This approach was therefore abandoned in favour of single post-run collection techniques.

3.2.2 Post run filtering Examples of filters used after wear in several oils are given in Figures 11-14. Even the biggest particles are small compared to those reported in studies of wear debris. Further in most instances the bigger particles were clearly composed of compacted smaller particles. Particles smaller than the pore size of 0.2 pm were only retained by chance, but clearly most small particles were lost. 3.2.2 Post run centrifuging Centrifugrng the used oil was attempted to collect all the debris. including the smaller particles that

Figure 12. Debris collected by filtering oil containing S/P after wearing at 100°C, 1200 rpm with 1.5 kg load for 65 minutes. Wear constant 0.33 pm”Mm. The larger particles appear to be accretions of 80 nm sized particles.

would pass through thc porcs in the filters. In practice the collected debris was similar to that found on the filters. It could not be determined whether the smaller particles were lost in the rinsing procedures, or whether the centrihging was inadequate.

690

Tabic I Additive Debris Measurcrnents Typical small debris nm Film on scar Typical large dehris pm 2nd ZDDP thick 0 . 5 p i 3 x 2 (composite) SO TCP thick 0.2 piii 0.S (few. composite) 120 Amine phosphate thin* 0 . 5 (composite) 300 Aminc monothiophosthin 0 . 5 (flakes) 200 phatc S/P thin 0 . S (composite) 80 Thiocarba mate thin gel 30 Base oil thin 2 (compositc) I0 * thin means primarily bare by optical microscopy but typically with scattering of thick patches of film.

-

Figure 13. Debris collected by filtering oil containing MTP after w a r at 100°C, I200 rpm with IS kg load for 60 minutes. Wcar constant 1.71 pni'/Nm. The debris particles appcarcd to be monolithic at higher magnification.

Figure 14. Debris collected by filtering base oil after wearing at lOO"C, 1200 rpni with IS kg load for 60 minutes. Wear constant 64 pni3/Nm. The larger particles were accretions of I 0 nm s i z d particles.

Tablc 2 Analyses follouing wear in oil containing aminc phosphate Samples worn at lOO"C, 1200 rpm. IS kg load for the indicated times Sample Analyses Location On ball (6 mins ) Auger Scar Film on scar Gold extraction replica (6 S Auger Debris ahead of scar mins ) Carbon adhesive rcplica SEM / EDX (6 S mins ) Centnfuge (30 mins ) SEM / EDX Filter (60 mins ) SEM / EDX

C O P F e I 1 42 10 34 6 S2 15 24 31 44 8 17 63

24

86 75

12 22

2

13

07 05 1 01

69 1

Analyses following wear in oil containing dithiocarbamate. Wear Conditions Sample Analyses On ball Auger 100°C, 1200 rpni, IS kg.. 6 mins. 25OC. 548 rpm, 10 kg . 64 mins. 2 5 ° C 1200 rpni. 15 kg.. 72 mins. I00"C. SSO rpm, 10

On ball

Auger

Location

On scar. Dark debris ahead of scar. On scar. Thin dark filni Thick dark film.

C O S F e 51 13 13 20 81 4 6 10

38 28

Filter

SEM I EDX

17 87

Centrihge

SEM / EDX

68

21 8 32 27 16 28 40 12 32 12 0.3 0 . 2

21

5

2.8

3.2.3 Debris taken from worn balls

3.1 Chemical Analysis

The C based,and An collection tcchniques. in addition to renio\ing the iron background. had thc advantage of presening thc location of debris relative to Uic scar so that somethmg of the histoty of the particles was retained. Both techniques collected little from the scars themselves, and about I12 of that froni around the scars.The adhesive C bascd nt?terial was cheaper and faster to usc than the gold. However it was micro-rough nlalong it dificult to resolve parlicles in the SEM. and also the C content interfered with C andysis of the debris.

Analysis of thc debris was attempted using an SEM/EDX gatem and scanning Auger. Simple dcfinitive analyses wcre not obtained. with thc Auger in particular giting different values for a c h degrec of sputtering. Tqpical analyses for scvernl oils are given in Tables 2-5. lnspite of the Wiculdcs several pints can be made:

3.3 Summary of debris sbx

Best estint7tes of typical particle sizes Scen for the oils averaged over all the techniques are given in Table 1.

1. ZDDP antiwar film and its debris docs not nccessarily contain Fe

2. antiwmr film and its debris from all thc other additives contains Fe in sdlicicnt qimtity that it could be in stoichiometric proportion with for inslance P or S. 3. in P containing additives the P was in the phosphatc form, not phosphide. 1.all analyses rcported a significant C content.

Table 4 Analyses following wear in oil containing TCP. Samples worn at 100°C, 1200 rpm, with 15 kg. load for the indicated times of wear. Sample Analyses Location C O P S F e On ball (60 mins.) Auger On thick film. 31 41 II I2 Debris ahead of scar. 71 13 6 I0 Gold extraction replica Auger Debris ahead of scar. 17 30 1 (2) 17 (30 mins.) Debris behind scar. 75 II 2 (1) 8 Carbon adhesive replica SEM I EDX Debris ahead of scar. 70 23 5 2 (60 mins.) Debris behind scar. 66 27 6 I Debris to side of scar. 64 28 6 2 52 29 14 ( I ) 2.5 Centrihge (60 mins.) SEM / EDX

692

Table 5 Analyses following wear in oil with commercial S/P additivc. Samples worn at I O O O C , 1200 rpm, with IS kg. load for 60 niins. Sample

On ball

Gold estraction replica Carbon adhesive replica Filter

Analyses

Auger -

SEM / EDX

Location

Typical scar. Filni 011 scar. Dark debris ahead of scar. Debris ahead of scar. Debris behind scar.

SEM / EDX SEM / EDX

4. DISCUSSION

The intent of this study was to eqlore the use of additive debris in used oil as a diagnostic tool to further understand the mode of action of antiwear additives. In the execution of this project it became necessary to examine the material on and around wear scars more critically than hitherto. Two types of debris were found; particulate, and material that is probably primarily organic, i.e. friction material. Only the particulate material was recovered from the used oils. The particulate debris was fine, and as it also ranged in size from 10 nm to S pn, it could not be collected by any one technique. This prevented comparisons between the total amounts generated by the different additives, or by dilferent wearing conditions; and severely restricted the accuracy of estimates of parttcle s i x distribution. On the other hand, the debris from a particular wear test appeared to be very similar, whether taken from the oil, removed From the ball, or still on the ball. The particulate debris From each additive was also insensitive to the duration of the wear test, or whether the wear test was performed under optimal or less optimal condtions (Though, as mentioned below, more friction material was formed in the latter circumstance). Further as the bigger particles appear to be compacted smaller ones, the collection procedure can be matched to the needs of the analysis without loss of generality. The debris from the blend containing ZDDP was exceptional in not requiring the presence of iron for its formation. This has been noted previously. The zinc phosphate glass was able to compact singularly well into thick antiwear pads. In the DOWM [2]. the pads can be seen to build, and to disintegrate slowly into

C

O

24 23 60

44 48 21

47

30 11 26 23

7s 58

59

P

S 10

F

12

0 0

6

I

1

1.5

2 7 4

4 2 1

c 22 17 8

17 8 7 8

micron sized particles, whilst rebuilding elsewhere. It is not clear how metal is lost from the ball when this additive is working optimally. The other aatives appeared to function by reacting with the metal surface to form a thin film that was lost on rubbing as particles tens of nanometres across by a few nanometres thick. The basic mode of metal loss was therefore corrosive wear. These primary debris particles were circulated in the oil and compacted to varying degrees into thick films on the wear scar. The ability of the additives to form thick films was in the order TCP>MTP>AP>S/P>MTC. Observations in the DOWM would indicate that only the TCP, and possibly the MTP, films contribute significanlly to wear resistance. That is, the patches of film in the scars of Figures 2 and 3, would not have remained in the scar long enough to be of value. The role of friction material in the action of the additives was not resolved. It has been suggested that friction material is antiwear by being a precursor of film material, and indeed the quantity of friction material has been observed to depend upon the identity of the additives in the oil [7]. On the other hand, fiiction material has been observed lo be pro-wear [7]. both directly by removing film from scars when large masses go through a contac?, and indirectly by blocking the leading edge, thereby starving the contact of additive. Friction material was not found in the bulk used oil in this work, either on the filters or by centrifuge. However it was noted that more fiction material of the iype shown in Figure 7 was present on scars formed in the oils SIP, AP, and MTP, when the wear conditions c a d relatively high wear rates, than when the wear conditions for each additive were optimum. Hence it

693

bc inferred that too much friction nlaterial is harmful. It is therefore probable that the finer debris particles formed by all the additives have the structure ,and chemistry of the film materials responsible for wear protcdon. The dimensions of the parlicles makes them ideal for full characterisation by analytical E M .The kisk of transferring the particles to a TEM grid should bc easier than transferring the filins themselves. c;ui

2. J.S. ShGisby and T.A. Caughlin. "Thc dircct observation of the anti-wear action of ZDDP.. 27th Lccds-Lyon Symposium on Tribology. Leeds. UK. 199.1, in press.

3. J.S. Shwsby and T.A. Caughlin. "The Boundaries of ZDDP lubrication". 25th Leeds-Lyon Symp. on Tribology. D. Dowson el al. ( a t o r s ) 1993 Elsaier Sciencc Publishers B.V.. pp 277-286.

5. CONCLUSIONS

It was possible to select wear conditions for mch of the 6 antiwear additives studied so that the debris generated was the result of the additives action nthcr than processes of wear. The debris collected from the used oil was very tine ranging in size fiom 10 nm to 3 pm. with the larger particles almost certainly being composed of compacted smaller ones. It was proposed that the finer debris particles formed by all the additives had the structure and chemistry of the film materials responsible for wear protection.

4. J.S. Shcasby and Z. Nisenholz, "Antiwear characteristics of a commercial secondiry ZDDP adhtive",Trib. Trans.. 36, (1993) 30940.1.

5. J. M. Gcorges, "Colloidal Behaviour of Films in

Boundary Lubrication". Tribol. Series 7 ( 1982) 729761.

6.

J.S. Sheasby. T.A. Caughlin and J.J. Habeeb. "Observation of the antiwear acthity of ZDDP additives", Wear 150 (1991) 247-257.

7.

J.S. S h a d y and T.A. Caughlin, "Direct Observation of the Boundaq Lubrication of Ceramics". 34th Annual Conference of Metallurgists, Aug 19-24. 1905. to be published in Proceedings of Symposium "Chaklader: Advanced Ceramics".

6. ACKNOWLEDGEMENTS

l'hs work was funded by the Ontario Centre for Materials Research (OCMR). and by the National Science and Engineering Council of Canada (NSERC). The authors would also like to acknowledge the assistance of Mr. J.A. Jekl with the wear experiments, and Mr RD. Davidson of Surface Science Western for his skill with the FI-SEM.

8. H.C. Stinton, H.A. Spikes and A. Cameron, "A

REFERENCES I . H.A. Spikes, "Boundary Lubrication and Boundary Film'', 2Sth Leeds-Lyon Symposium on Tribology, D. Dowson et al. Eds.,Elsevier Science Publishers B.V., 1993,277-286.

Study of Friction Polymer Formation" T ~ s .2s, (1981)35s-360.

. ASLE

9. J.S. Sheasby. T.A. Caughlin, and W.A. Mackwood. "A comparison ofthe boundary lubrication of 52 100

stcel, 'JTZ and SijNj by S, P, SP, and ZDDP adhtives". submitted to Wear.

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The Third Body Concept / D. Dowson et al. (Editors) Q 1996 Elsevier Science B.V. All rights reserved.

695

The Influence of Slide/Roll Ratio on the Film Thickness of an EED Contact Operating Within the Mixed Lubrication Regime M. Smeeth and H.A. Spikes

Tribology Section, Department of Mechanical Engmeering, Imperial College of Science, Technology and Medicine, London, SW7 2BX, United Kingdom

Ultra-thin film interferometry is used to measure the film thickness of an elastohydrodynamic point contact under mixed sliding and rolling conditions in the thin film regime. By maintaining a fixed entrainment speed and varying only the slide/roll ratio, the precise influence of the sliding speed on the lubricant film thickness can be determined. The results clearly show that the film thickness falls under high amounts of sliding. A degree of asymmetry is observed in film thickness versus slideholl ratio plots, which is tentatively attributed to the different materials used in the contact. A number of different possible explanations for this behaviour are suggested and discussed.

1. INTRODUCTION

The lubricant film thickness is considered to be one of the most important parameters in elastohydrodynamic systems, since it dictates the extent to which asperity interaction will occur and hence plays a large part in determining failure modes such as pitting and scuffing. The prediction of film thickness using computationally obtained regression equations has now become a firmly established design tool (1) and there is close agreement between experimental results obtained under moderate speeds and those predicted by theory. Under high rolling speeds and/or high slidmg rates however, isothermal predictions become inaccurate since the effect of inlet shear heating is neglected. Film formation at high rolling speeds been extensively studied and the effect of inlet shear heating on the lubricant viscosity in the inlet and hence on film thickness is now predictable for such systems. Under mixed sliding and rolling conditions however, such as found in cams and gears, there appears to be a shortage of experimental work, particularly in the low film

thickness, high sliding speed area. According to most of the film thickness equations available, the film thickness is considered to depend on the mean entrainment speed and to be independent of the degree of sliding. Although some equations do introduce thermal correction factors for the effect of rolling and sliding speed, these are usually dominated by the effect of the rolling speed, the sliding speed having a small effect.

In the current study, modified optical interferometry is used to measure the film thickness under various degrees of sliding whilst maintaining a fixed entrainment speed and varying the slide roll ratio. Using this technique the influence of sliding speed on EHD film thickness is explored.

2. BACKGROUND

Since the development of the first usefil elastohydrodynamic film thickness equations over fifty years ago, it has been recognised that the film generated within the contact is dependent almost entirely upon the rheologcal behaviour of the

696 lubricant in the conjunction inlet and hardly at all upon its behaviour within the central zone itself. This recognition that the inlet could be essentially decoupled form the Hertzian flat regon enabled analytical solutions to be developed, by assuming an independent, constant film thickness plateau regon within the contact. Most EHD film thickness solutions such as the ubiquitous Dowson and Hamrock equation (1) have been produced assuming isothermal conditions. This gves excellent agreement with the majority of experimental work in rolling contacts. However the agreement is less satisfactory at high rolling speeds where the effect of inlet shear and compression heating under high rolling speeds produces deviations from isothermal predictions at relatively high speeds (2). Thermal effects in EHD contacts were investigated by Crook (3) who calculated a maximum temperature rise in the inlet of 1°C and only 4°C within the contact itself under pure rolling conditions. Under mixed sliding and rolling conditions however, where the majority of the thermal energy is generated by the relative sliding within the Hertzian contact, thermal effects increase with increasing sliding speeds. Although a temperature rise of 200°C within the contact was reported, this did not effect the inlet conditions significantly. Crook concluded that conduction of heat across the lubricant into the solid surfaces was the primary source of heat dissipation and that the temperature rise within the conjunction did not significantly affect the EHD film thickness in either sliding or rolling. Cheng ( 4 3 ) developed full solutions to the EHD problem which incorporated both viscous heating and heat transfer (through both the lubricant and the solid surfaces). He found that viscous heating i n the inlet zone could cause a reduction in the film thickness in the inlet zone, but only at very high speeds. Later Greenwood (6) considered the effects of inlet shear heating on more viscous oils at various speeds. Under rolling conditions, when the entrainment speed is greater than about 2m/s, inlet shear heating is sufficient to cause a reduction in the film thickness. Comparison with experimental work (7) showed that the deviation from the isothermal theory measured at high

speeds is primarily caused by inlet shear heating. He concluded that inlet shear heating could cause a significant decrease in the film thickness, at lower speeds than had previously been predicted. The techniques used by Greenwood were developed by Murch and Wilson (8) to calculate the reduction in film thickness when inlet shear heating is incorporated into the analysis. Their results were, however, based on the assumption that both the speeds and temperatures of the two surfaces in the inlet were equal, since Wilson (9) had showed that the sliding speed did not have a large effect on the film thickness in a system similar to that of an EHD contact inlet zone. The solution was therefore considered to be general for any slide/roll ratio. Experimental work later confirmed the findings of the analytical solution for pure rolling conditions ( 10). The thermal effects of sliding were considered by Agganval and Wilson ( 1 1) whose approach was used to produce semi-empirical correction equations for situations where different degrees of sliding were present (12). A thermal reduction factor was developed which incorporated a term for the sliding speed. The correction factor was, however, still dominated by the rolling speed. Previous experimental work carried out under mixed sliding and rolling conditions appears to be contradictory. Johnson ( 1 3) used optical interferometry to measure the film thickness of mineral oil at a temperature of 75°C over a range of slideholl ratios up to 100%. He found there to be no significant change in film thickness within the accuracy of the experimental technique, i.e. the film thickness was a function of the mean rolling speed and independent of the degree of sliding. lsaksson (14). also using conventional optical interferometry, reported a decrease in central film thickness of 21% at a slide/roll ratio of about 65%, but scarcely any decrease in the minimum film thickness. Dalmaz (1 5,16) measured the film thickness of small elliptical and point contacts using optical interferometry. He reported a decrease in both central and minimum film thickness of about 30% from the pure rolling value. The maximum

697 slide/roll ratio used in his work was also about 65%, but with a much higher entrainment speed

greatly enhanced. The system employed is fully described in reference ,

(3.5m/S).

The discrepancies between the above work may partly be due to the fact that the changes in the film thickness resulting from sliding are quite small and are at the limit of resolution of the measurement system. Because optical interferometry can only measure discrete separations, comparisons of film thicknesses at the sanie entrainment speed but with different slide roll ratios require considerable interpolation of the results.

To

Spectometer and Frame Grabber

4

The current paper uses a technique which can nieasure values of film thickness over a continuous range very accurately, thus enabling any effect due to sliding to be easily detected.

3. EXPERIMENTAL TECHNIQUE A point contact is formed by loading a 19.05 mm diameter steel ball agamst the flat surface of a glass disc coated with a semi-reflecting, chromium layer and a silica spacer layer. The ball and disc are driven by separate DC servo controlled motors, enabling a wide range of slide/roll ratios to accurately attained. A schematic diagram of the test rig is shown in figure 1,

The film thickness between the glass and disc is measured using ultra-thin film interferometry, a development of conventional optical interferometry. Although conventional interferometry has been used for a great deal of experimental work (17) and has proved a valuable technique, it suffers from a number of limitations, particularly in the thin film regon. The first is that i t relies on the visual observation of colours at discrete separations. It is therefore only possible to obtain film thickness measurements at a finite number of specific values. Under pure rolling and relatively thick film conditions this does not present any particular problem. However it poses a considerable difficulties in studying mixed sliding and rolling since it cannot resolve small changes i n film thickness. The ultra-thin film technique uses a spectrometer to detect the variation in colour so that the resolution of the system is

Disc Drive Shaft Rotation Figure 1. Schematic diagram of test rig

A second limitation of conventional interferometry is that it has a lower limit of about 120 nm (a quarter of the wavelength of light). In ultrathin film interferometry, this problem is overcome by using a transparent spacer layer, usually silica approximately 500 nm thick, which in effect acts like a solid layer of oil. The thickness of the spacer layer is measured prior to the test and the thickness subtracted from subsequent readings to g v e the true oil film thickness in the contact. The durability of the spacer layer is drastically reduced if more than a small degree of sliding is introduced within the thin film regme. During the current study, however, it was found that by using a thicker spacer layer than normal, (approximately 1 micron), the silica is far less vulnerable to damage by the sliding action of the ball within the mixed regime.

The ultra-thin film technique is customarily used to measure the central film thickness in a point

698 contact. However the method has been extended during these tests to enable a profiles of the contact to be made in either direction. The results of this study were all obtained in the thin film regon using a disc with a thicker than normal spacer layer as discussed above. The composite surface roughness of the ball and disc was measured as 15 nm, using a cut off length of approximately twice the Hertzian contact diameter, based on the findings of Nagaraj and Winer (1 9). All the tests were carried out at with a load of 20N (0.52 GPa Hertzian pressure) and at a temperature of 30°C unless otherwise stated.

mineral oil varies with slide/roll ratio at constant entrainment speed. The slide/roll ratio in this paper is defined as : SRR =

2(111- 112) ((71

+ 112)

x100%

where U1 is the speed of the disc and U2 is the speed of the ball. Therefore 200% represents pure sliding and a negative slide/roll ratio indicates that the ball surface speed is faster than that of the disc.

4. TEST LUBRICANTS

Two additive-free lubricants were tested, a traction fluid Santotrac 40 and a solvent refined mineral oil 100-SN. The properties of the two at the test temperature of 30°C are listed in table 1.

Pressure-Viscosity Coeff. (GPa-') 15 Mineral Oil 28 Santotrac 40

Viscosity (mPas) 24.9 32.5

Table 1 Lubricant properties at 30°C.

5. RESULTS Both lubricants were initially tested under pure rolling conditions over the speed range of 10 mm/s to 3 r d ~Both . showed Newtonian behaviour with a relationship between film thickness and speed very close to that predicted by the Dowson and Hamrock equation (1): h a(lI,~)~'~~ c

where a is the pressure viscosity coefficient and q is the dynamic viscosity at atmospheric pressure. Tests were then carried out in order to determine the sensitivity of film thickness to sliding speed. Figure 2 shows how the film thickness of the

-200

-100 0 100 SlideRoll Ratio (%)

m

Figure 2. Variation of film thickness with slide/roll at different mean entrainment speeds.

Figure 2 clearly shows that there is a decrease in the central film thickness at high sliding speeds compared to the film thickness measured at the same mean entrainment speed under pure rolling. At slide/roll ratios of less than 100% the film thickness is largely independent of the degree of sliding. For many systems this would be considered to be very high sliding. At above 100% slide/roll ratio in both directions, the film thickness decreases. This decrease appears to occur even in the very thin film regme. The influence of slide/roll ratio depends upon whether the ball or the disc is the faster moving surface. At positive slide/roll ratios, i.e. with the glass disc moving faster than the steel ball, the film thickness remains fairly constant up to about 150% sliding and only drops at sliddroll ratios

699 above this. However with negative slide/roll ratios, the film thickness starts to fall below the pure rolling case at about -50% slide/roll ratio (or even less for thin films).

one perpendicular to the rolling direction. The first pair is measured under pure rolling and the second set with a slide/roll ratio of +175% (i.e. a disc speed of 1.875 m / s and a ball speed of 0.125ds).

Figure 3 compares the film thickness for the mineral oil at 30°C and an entrainment speed of 1 25mh with that of Santotrac 40 at the same temperature but a lower entrainment speed of 0 75m/s.

Y

+

1

1

0 Santotrac 40 0 . 7 5 d s

Base Oil 1ooN 1.25 mls

--

A

100

r 0

-200

-100

0

loo

200

-

AI

-

A

-

10 Load (N)

0

u

Ah

1

-

7

1

4

4

20

30

Figure 4. Variation of film thickness with load under pure rolling and sliding condltions. Santotrac 40. 30°C

Slide/Rolt Ratio (%)

-175% SlidelRoll Ratio

Figure 3. Variation of film thickness with slide/roll ratio for two fluids 30°C.

-Rolling

The two fluids gwe results similar in form although there is an intriguing slight increase in film thickness displayed by Santotrac 40 at moderate, positive slide/roll ratios, compared to the pure rolling case. Figure 4 shows how film thickness varies with load for both pure rolling and mixed slidlngl rolling condltions for Santotrac 40 at 30°C. These results span the Hertzian pressure range from 0.323 GPa at 5N load to 0.566 GPa at 30 N load. It can be seen that the condition where film thickness is most sensitive to load is that of high positive slide/roll ratio, i.e. with the dlsc travelling faster than the ball. Figure 5 shows measured film thickness profiles of the mineral oil across the contact. Two pairs of profiles are shown, both measured at 3OoC and at an entrainment speed of I d s . Each pair consists of one profile taken in the direction of rolling and

50 -150

-50

50

150

Distance From Contact centre (Mcrons)

Figure 5 . Profiles across the contact. Mineral oil 3OoC, 1m / s mean entrainment speed.

Under pure rolling condltions, the minimum film thickness occurs in the side lobes of the contact and the ratio between the minimum and central film tluckness is about 0.65, which is very close to that predicted by the Dowson/Hamrock equations (1).

700 Under high sliding speeds both the minimum and central film thickness decrease by the same proportion. The constriction at the rear of the contact becomes gradually smaller with increasing sliding, approaching that of the side lobes at high sliding speeds.

6. DISCUSSION

These results show that central film thickness decreases at high slide/roll ratio. Interestingly this decrease is asymmetrical with respect to whether the ball or disc surface is moving faster. The reasons for this are not yet clear. One possibility relates to a finding by Kaneta who reported that different film shapes are seen in EHD contacts formed between bodies of different elastic inoduli in the case where the body of lower modulus has a faster surface velocity than that of the higher modulus (20). Kaneta ascribes this effect to the formation of an entrapment within the central region of the contact. However the film profiles shown in figure 5 reveal no inQcation of such an effect, even though the low modulus glass disc is moving faster than the steel ball. It is possible, however, that the slight rise in film thickness observed at positive slide roll ratios for Santotrac may be due to this effect. A more conventional explanation of the origtns of the influence of slide/roll ratio of film thickness and also of its asymmetry is in terms of a thermal effect in the inlet.

Wilson and Sheu (12) have derived an approximate thermal correction factor, defined as the ratio of the calculated thermal film thickness to that predicted by isothermal theory. The correction factor is a function of the slide/roll ratio and the thermal loading parameter, defined as: PU2V

I. = k

(3)

where j3 is temperature viscosity coefficient and k the thermal conductivity of the lubricant.

If L is small (< 0.1) then thermal effects are said to be negligible. The precise value of the thermal conductivity of the mineral oil used is not known, but values of k =O. 1 17 W/mKand p=0.026 K ' are reasonable approximations. Because of the moderate speeds and low viscosity used in the current study, the value of L is about 0.005, far too low to explain the measured decrease in film thickness. The correction factor proposed by Wilson and Sheu is, however, primarily concerned with inlet shear heating. An alternative explanation for the observed dependence of film thickness on slide/roll ratio may be based on the bulk heating of the two bodies. This effect has recently been incorporated into flash temperature analysis by Olver (21) who suggests that it can play an important role in determining film thickness, by contributing to the temperature of the lubricant in the inlet. Table 2 lists the temperature rises needed to be experienced by the lubricant in the inlet to account for the observed reduction in film thickness at high slide/roll ratio, calculated using the Dowson and Hamrock equation (1 ). The required rise in temperature is relatively modest.

1 Lubricant

I

-175%

I +175%

SRR

I

Mineral oil Santotrac 40

1

+lO"C +12"C

I

SRR +6"C +8"C

I

Table 2. Temperature rise at contact inlet required to give measured film thickness at high slide/roll ratios.

According to the flash temperature theory (22), most of the heat generated within the contact will pass into the faster moving body. Using the thermal properties listed in table 3, the dependence of heat partition on slide/roll ratio was calculated. The result of this calculation is shown in figure 6.

701 Thermal

Specific heat

of frictional or tractional heat generation due to sliding is given by: q = pWAU

Steel

(4)

420

Table 3. Thermal properties of materials.

-Heat htering Glass Disc

-Heat htering Steel Ball

-200+-100

0

Ball Faster, Disc Slower

l00__+Mo

Ball Slower, Dsc Faster

Slide Roll Ratio ( O h )

Figure 6. Heat partition for steel ball on glass drsc contact.

It can be seen that for very high negative sliding speeds, 95% of the heat generated within the contact enters the steel ball, whereas with very high positive sliding speeds, the heat generated is dissipated in about equal proportions into both bodies. This means that at high negative slide roll ratios the ball will be receiving more heat than the converse. Since the ball is relatively small and well-insulated compared to the disc, this is likely to result in the ball surface out-of-contact temperature becoming quite high, leading to a decrease in inlet viscosity. Attempts made to measure the bulk ball temperature failed because it was difficult to locate the thermocouple precisely on the ball surface. Figure 3 compares the effect of slide/roll ratio on film thickness for the two test lubricants. The rate

where p is the coefficient of friction or traction, W is the applied load and A U is the sliding speed The limiting traction coefficients for the mineral oil and Santotrac 40 were measured at 3OoC as 0.06 and 0.11 respectively. Therefore the two tests resulted in approximately the same rate of heat generation, since the mineral oil test was carried out at a faster speed. On this basis, it can be seen that the film thickness of Santotrac 40 is more sensitive to high sliding than that of mineral oil. If the observed behaviour is controlled by bulk heating of the contacting bodies, then the enhanced sensitivity of the film thickness of the traction fluid to sliding may result because the viscosity of this fluid is more sensitive to temperature than the mineral oil. The explanation for the dependence of film thickness on slide/roll ratio outlined above is based upon inlet heating of the lubricant which results in less oil being entrained into the contact than in the pure rolling case. A third possible mechanism for the observed dependence of EHD film thickness on slide/roll ratio has been suggested (23), based upon thermal effects within the contact coupled with continuity of flow. It is assumed that the effect of sliding on inlet heating is negligble, so that the same amount of lubricant is entrained into the contact for all sliding conditions at a given entrainment speed. However, when sliding is present, a slip plane will develop withm the fluid. This will, in effect, divide the lubricant film in the contact into two layers, one travelling through the contact at the speed of the upper surface and the other at the speed of the lower surface. The mean velocity of the lubricant passing through the contact will then become:

urnm=

yu1 + ( l-y)U2

(5)

where y is the fractional distance of the slip plane from surface 1.

702

If the same amount of lubricant is entrained under all sliding conditions then, by continuity of flow, the film thickness, h will be gwen by:

approaches the value of the absolute contact minimum at high sliding speeds.

REFERENCES where h R and UR are the film thickness and mean rolling speed in the pure rolling case. If the slip plane is mid-way between the surfaces and thus the film thickness will be the same as in the pure rolling case. However, in a contact with high sliding, the slip plane should approach the hotter of the two surfaces because the limiting shear stress of lubricants decline with temperature. Its position can be determined from flash temperature theory. Preliminary calculations using this model show quite good agreement with the results in figures 2, and 3, including the small increase in film thickness at moderate, positive slideholl ratios. so that y = 0.5, then clearly , U

6. CONCLUSIONS

1. Hamrock, B.T and Dowson, D., "Lsothermal Elastohydrodynamic Lubrication oJ' Point Contacts Part Ill. Fully Flooded Results", ASME J.Lub.Tech., pp. 264-276, (1977). 2. Koye, K.A. and Winer, W.O. "An Experimental Evaluation ofthe Hamrock and Dowson Minimum Film Thickness Equation jor Fully Flooded EIID Point Contacts". ASM E J.Lub.Tech. 103, pp. 284-294, (1981). 3. Crook, A. W. "The Lubrication ofRollers111. A Theoretical Discussion of Friction and Temperature in the Oil Film". Phil. Trans. Roy. Soc.,Lond. A254, pp. 237-258, (1961) 4. Cheng, H.S. ' A Rejned Solution to the Thermal EHL of Rolling and Sliding Cylinders". Trans. ASLE 8 , pp. 397-410 (1965). 5 . Cheng,H.S. Tsothermal Elastohydrodynamic Lubrication Theory in the Full Range oj' Pressure Viscosity Coefficients. Trans. ASME. J. Lub. Tech., 94, pp. 35-43 (1972). 6. Greenwood, J.A. and Kauzlarich J..J., "Inlet Shear Heating Elastohydrodynamic Lubrication". Trans. ASME. J. Lub. Tech. 95, pp. 41 7-426 (1 973). 7. Dyson, A., Naylor, H. and Wilson, A.R. "The Measurement of Oil Film Thickness in Elastohydrodynamic Contacts" . Roc. I.Mech.E., 180, Part 3B, pp. 119-134 (1966). 8. Murch, L.E. and Wilson, W.R.D., !4' Thermal Elastohydrodynamic Inlet Zone Analysis ASME. J. Lub. Tech. 96, pp. 605-610 (1974). Y4 9. Wilson , W.R.D. and Mahdavian, S.M., Thermal Reynolds Equation and its Application to the Analysis of Plastohydrodynamic Inlet Zones" Trans. ASME, J. Lub. Tech. 96, pp. 572-577 (1974). 10. Wilson, A.R. , ' I n Experimental Thermal Correction for Oil Film Thickness in EftL'', Proc. Sixth Leeds-Lyon Symposium , Mechanical Engmeering Publications., London (1980). I'

From the results presented and discussed the following conclusions can be drawn: (a) At high sliding speeds and constant mean entrainment speed, the film thickness falls from the value measured under pure rolling conditions by up to 20%. This fall is greater than predicted by thermal reduction factors, which were developed using the concept of inlet shear heating.

'I.

(b) The slide/roll ratio wrist film thickness plot shows a degree of asymmetry. One possible explanation for this is due to greater bulk heating of the steel ball when it slides faster than the disc. A second possibility is based on the concept of the position of a slip plane in the fluid controlling the rate of flow of lubricant through the contact.

(c) Both the minimum and the central film thickness fall by the same proportion under increased sliding speeds. The minimum constriction at the rear of the contact

,

703

I I . Aggarwal, B.B. and Wilson, W.R.D., “Improved Thermal Reynolds Equations” . Roc. Sixth Leeds-Lyon Symposium, Mechanical Engmeering Publications., London ( 1 980). 12. Wilson, W.R.D. and Sheu, S., “EEffect of Inlet Shear Heating Due to Sliding On Elastohydrodynamic Film Thickness“ . ASME, J. Lub. Tech. 105, pp. 187-188 (1983). 13. Johnson, G.J.“A Studv of the Lubricating I+.ilmsGenerated by Organo-Phosphorus AntiWear Additives”. PhD Thesis, University of London ( 1990). 14. Isaksson, O., “Measurement of the Influence of Sliding Velocity on Oil Film Thickness in an I?‘lastohydrodynamicPoint Contact,” Proc. Eurotrib, 2, pp. 403-408, (1989). 15. Dalmaz, G. “Film Thickness and Traction Measurements in Small Elastohydrodynamic Elliptical Contacts ”. Roc. Fifth Leeds-Lyon Symposium , Mechanical Engineering Publications., London (1978). 16. Dalmaz, G . and Chaomleffel, J.P., “Elastohydrodynamic Lubrication of Point Contactsfor C’arious Lubricants”. Roc.13th Leeds-Lyon Symposium ,Mechanical Engineering Publications, London (1986).

17. Gohar, R. and Cameron, A. “The Mapping of Elastohydrodynamic contacts. ASLE Trans. 10, pp. 2 15-225 ( 1967). 18. Johnston, G.J., Wayte, R. and Spikes, H.A. “The Measurement and Study of Vevy Thin Lubricated Films In Concentrated Contacts.” Trib. Trans. 34, pp. 187-194 (1 991). 19. Nagaraj, H.S., Sanborn, D.M. and Winer, W.0 “The Effect of Surjace Roughness on Surface Temperature Fluctuations in END Contacts”. Proc.Fourth Leeds-Lyon Symposium, Mechanical Engmeering Publications., London (1978). 20. Kaneta, M., Nishikawa, H., Kameishi, K., S h , T. and Ohno, N. “EJkct ofElastic Moduli of Contact Surfaces in Elastohydrodynamic Lubrication”, ASME, J. of Trib. 114, pp. 75-80, (1992). 2 1. Olver, A. V. “Testing Transmission Lubricants; the Importance of Thermal Response”, Proc.Inst. Mech. Engrs., J. Aero. Eng. G205, pp. 205, (1 991). 22. Jaeger, J.C., “Moving Surfaces of Heat and Temperature at Sliding Contacts ”,Proc.Roy. Soc.New. S. Wales 76, pp. 203-224 (1942). 23. Olver A.V. Private Communication. ”

This Page Intentionally Left Blank

The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.

705

The Influence of Plastic Bulk Deformation on Surface Roughness and Frictional Behavior during Deep Drawing Processes H. Lubbinge, R. ter Haar and D.J. Schipper a aUniversity of Twente, Tribology group, Enschede, The Netherlands In Sheet Metal Forming (SMF) processes, friction does play an important role. This with respect to the increase of product quality demands and the ability of predicting these processes by for instance finite element simulations. The existing simulation models do not contain an adequate friction model. In SMF processes different contact situations can be distinguished. As a result different coefficients of friction are locally present, which influences the forming process. Experiments are performed on a testing device by which it is possible to simulate the operational conditions as present in SMF processes. This test rig is a combination of a tensile tester and a friction measuring device, by which it is possible to measure the coefficient of friction as a function of the operational conditions (velocity and contact pressure) and deformation (elastic or plastic) in a well controlled way. Friction is presented in a generalized Stribeck-curve in which the different lubrication regimes can be distinguished, i.e. Boundary Lubrication (BL) and Mixed Lubrication (ML), which are also occurring during SMF processes. In SMF processes the sheet material deforms elastically and plastically and therefore the surface roughness will change and as a consequence will influence the frictional behavior between sheet and tool. In this paper, the influence of plastic deformation on A) the surface microgeometry and B) as a consequence of that on the frictional behavior of the sheet-tool system is studied. With the aid of a 3D-surface interference microscope, the microgeometry of the deformed material has been analyzed. The result of this investigation is that the CLAroughness due to the deformation first decreases and then increases with increasing deformation. Furthermore, friction is hardly influenced due to the change in surface roughness. No change in the shape and the level of the generalized Stribeck curve is found.

1 . Introduction

The industry is very interested in simulating sheet metal forming (SMF) processes like deep drawing and bending. This to reduce the costs for the design of a new product and tools. It is also desirable that the chance a process fails is minimized in the pre-production phase of a new product. To achieve this objective, computer simulations of the process are performed. The interest of these simulations is to govern the forces acting on the tool and the stresses in the sheet material. At the University of Twente such a simulation package, called DiekA (HuBtink 1986), is under development. Still too frequently simulations do not give the proper results. One important cause for this is the friction model used which describes the frictional behavior of the sheet/tool contact. At present a Coulomb friction model is often used. In this case

a constant coefficient of friction is supposed for the different contact areas. However, depending on the deep drawing conditions, different zones of contact between sheet and tool, with locally different coefficients of friction, can be distinguished, (Schipper 1988). This article deals with the influence of plastic deformation on the surface microgeometry of the sheet material. In literature many deformation experiments have been performed, e.g., von Stebut, Roizard & Paintendre (1989), Schey (1983) and Osakada & Oyane (1971), but the effect on the surface microgeometry, expressed by different surface parameters, is not quite clear. For this research a large number of specimen have been subjected t o free plastic deformation with different strain values. This means deformation without contact of a mating surface. This is a real situation which also occurs during deep drawing

706

-Blank

holder

Symmetry axis

-I

Table 1 Mechanical properties. 90 = perpendicular to rolling direction 45 = 45 degrees rotated compared to rolling direction 0 = parallel to rolling direction mean = (XO 2x45 xgo)/4 90 153 R, [MPa] 45 151 (60.2) 0 149 151 mean 90 308 R, [MPa] 45 306 (ffB) 0 312 mean 308 90 2.6 r-value 45 2.2 0 1.7 mean 2.2 90 0.222 n-value 45 0.229 0 0.230 mean 0.228

I

+

Figure 1. Schematic drawing of a deep drawing process, with different lubrication conditions.

processes, as can be seen in figure 1, adapted from Vegter (1991). There is no contact between sheet material and tool (blank holder and die) in the areas where lubricant is located. Next to the surface microgeometry measurements, friction measurements have been performed. This to study the effect of plastic deformation on the frictional behavior between sheet and tool. For this purpose a new developed friction tester has been used.

2.2. Experimental procedure The test specimen used have been punched out of the sheet material. The test specimen geometry is shown in figure 2. The deformation of the specimen is realized by using a tensile tester. The specimen have been punched in such a way, that the rolling direction is oriented perpendicular to t he deformation direction. A grid size of 2.5 mm x 2.5 mm is applied for measuring the local deformation of the specimen after testing. The plastic deformation is expressed by the natural strain E , defined as:

2. Plastic deformation of surface textures 2.1. Material properties The sheet material used for this investigation is an uncoated cold rolled steel with a thickness of 0.7 mm. It is a standard deep drawing steel used in the automotive industry. Table 1 shows the mechanical properties of this material. The r-value is defined as the ratio between € 2 and ~ 3 which are the transverse strains when performing a tensile test on a strip. These strains are equal only if the strip is isotropic, which in general is not the case. The n-value is the constant from the relation of Ludwik-Nadai, defined as ff = C . E n .

+

(

3

~ = l n1 + ,

where 10 is the original length and A1 the increase of length. The specimen have been deformed with different strains of 0, 0.03, 0.06, 0.09, 0.12, 0.15 and 0.18. The strain velocity i was about 0.001 s-', so quasi-static.

707

1.2 -

-

0)

The deformed surfaces of the specimen have been analyzed by using an interference microscope. The scanning area for the surface measurements was 766 pm x 597 pm. The cut-off length of the profile measurements was 0.8 mm. Before analyzing the test specimen with the interference microscope, they were rinsed in an ultrasonic cleaner. The roughness measurements were performed on the side of the specimen without the grid. So any influence of the grid 011 the surface texture has been avoided. 2.3. Results 2.3.1. The influence of free deformation on the R, parameter The results of the profile measurements (2D) are analyzed and presented in figure 3. The values of the profile measurements are mean values of 9 measurements. The results show a large standard deviation on the mean values. The roughness values overlap, so no significant differences can be observed. The surface measurements (3D) on the other hand show significant differences, presented in figure 4. The standard deviation is smaller, in spite of the fact that the values are mean values of 5 measurements instead of 9 measurements in case of the profile measurements. Measurements on surfaces with natural strains of 0.2 and 0.24 are

Figure 3. R, roughness profile measurements in the direction of deformation (perpendicular to rolling direction) as a function of the natural strain.

also performed. For small natural strains (until 0.06), the surface roughness parameter R, decreases. For larger strains the surface becomes rougher with larger strains.

2.3.2. The influence of free deformation on the average slope The average slope parameter is a so called hybrid microgeometry parameter. It incorporates both height and spacing information. In literature some investigators have found this type of parameter useful in friction and wear descriptions, (Whitehouse 1994). For sheet metal forming processes they are of interest as well, because of the influence of the rolling on the height distribution of the surface texture and the influence of the bulk deformation on the horizontal spacing. The average slope (A,) is defined as:

708

I

110 : e,

t3 2

0.068 :

105 1.00 -

c

Figure 4. R, roughness surface measurement as a function of the natural strain.

Figure 5. A, slope parallel to deformation direction (perpendicular to rolling direction) as a function of the natural strain.

dt

where - is the instantaneous slope of the profile. dx The measurement equipment calculates the mean slope of a large number of profile measurements next to each other of the measured 3D surface area. Figure 5 shows the slope parallel to the deformation direction as a function of the natural strain. The presented mean values are derived from 5 measurements. The figure shows a significant influence of the deformation on the average slope, corresponding with the R, roughness parameter. The values of the average slope decrease for low strains until 0.06, for larger deformations the slope parameters show also higher values. Next to the surface R, roughness parameter, also the slope parameter demonstrates t o be a good parameter to represent the influence of plastic deformation on the microgeomet ry. An unexpected trend of the different parameter values is the decrease for low strains. A possible explanation for this behavior could be the loss of the initial orientation of the microgeometry, originated during the rolling process, due to light distortions of the grains. For larger strains the

grains distort more en more and turn out of the surface, which causes roughening of the surface microgeometry. 3. Friction measurements

3.1. Friction tester As indicated in the introduction, friction measurements have been performed to study the effect of deformation on friction. ter Haar, Schipper, de Vries, Vegter & Broekhof (1994) reviewed a number of test rigs used to study friction in SMF processes known from literature and concluded that most of them do have important disadvantages. Therefore, a new testing device has been developed. In figure 6 the test rig is schematically presented. This test rig is a combination of a tensile tester and a friction measuring device. With this device it is possible to measure the coefficient of friction as a function of the operational conditions, velocity and contact pressure in combination with deformation (elastic or plastic) in a well controlled way. The deformation (elastic and plastic) of the sheet material is controlled by

709

tensile tester

Figure 6. New developed friction tester, (ter Haar et al. 1994). the tensile tester, whereas the friction measuring device measures the normal force acting on the contact and the friction force between the sliding tool and the sheet by means of piezo-electric force transducers.

3.2. Experimental procedure and results The coefficient of friction is presented as a function of the operational parameters, combined in a dimensionless lubrication number L . This dimensionless lubrication number L is expressed

by:

L=

Vinl

. 'h u m

p . R,*

(3)

where qinl is the inlet viscosity of the lubricant, vaumthe sum velocity of the interacting surfaces, in this case the sliding speed, p the mean contact pressure and R,' the combined centerline average (CLA) surface roughness, defined by:

-4

R,* =

(4)

The friction experiments were performed by keeping temperature, and therefore the inlet vis-

710

0.16

I

I

,

I

1

1

1

1

I

,

1

1

1

1

1

1

I

1

1

1

1

,

o

BL 0.14

P

0.12

-

0.10

-

0.080.06 -

0.02 0.04

.-

0.00

Without pre-deformation Curve fit of the data without pre-deformation With pre-deformation ( E = 0.17)

0

A

I

I

I

,

1

1

1e-5

1

l

18-4

1e-3

1e-2

Figure 7. Generalized Stribeck curve. cosity, as well as the contact pressure constant and changing the sliding velocity. Values of these parameters are listed in table 2.

Table 2 Operational parameters. [Pa4 1.2 Tzoo [MPaI 71.5 17 [m.s-l] 0.0125-0.5 v,,,

The tests were performed with the direction of sliding perpendicular to the rolling direction of the sheet material.

In figure 7 the results of the friction measurements are shown. In this figure the generalized Stribeck curve is shown for undeformed strips (continuous line). From this curve, two different lubrication regimes can be distinguished, Boundary Lubrication (BL) and Mixed Lubrication (ML). Next to these experiments with undeformed strips, a number of tests have been performed with pre-deformed strips. Before these friction measurements were carried out, the strips were deformed quasi-statically until a natural strain of E = 0.17. These measurements are reflected by the A-symbols. Here the L parameter has been corrected for the changed surface roughness as a result of the plastic deformation of the strips. The R, roughness for the undeformed

71 1

strips was 0.89 pm, for the deformed strips R,, = 0.95. From figure 7 it is clear that predriformation hardly influences the coefficients of friction for both the BL regime and the ML regime if the generalized Stribeck curve, i.e. p i~sa function of L, is used. 4. Conclusions

From the presented results, the following can bc concluded: 0

0

0

0

3D surface measurements show significant differences in the surface parameter R, whereas the 2D profile measurements did not show this. The slope is a good parameter to represent the influence of plastic deformation on the mi crogeomet ry.

For small deformations, a decrease of the slope and roughness parameters is measured, for larger deformations, the roughness and slope parameters increase with increasing deformation. Bulk deformation of the sheet material hardly influences the frictional behavior between sheet and tool. The generalized Stribeck curve ( p as a function of L ) remains the same.

5. Acknowledgements

The authors acknowledge Dr. H. Vegter of Hoogovens groep B.V. and Dr. N.L.J.M. Broekhof of Quaker Chemicals B.V. for their financial support and the supply of materials for this project.

REFERENCES Huetink, H. (1986), On the simulation of thermomechanical forming processes, PhD thesis, University of Twente. Osakada, K. & Oyane, M. (1971), ‘On the roughening of free surface in deformation processes’, Bulletin of JSME 14, 171-177. Schey, J. A. (1983), TTibology in metalworking, American Society for Metals.

Schipper, D. J. (1988), Transitions in the lubrication of concentrated contacts, PhD thesis, University of Twente. ter Haar, R., Schipper, D. J., de Vries, E. G., Vegter, H. & Broekhof, N. L. J . M. (1994), Friction measurements under sheet metal forming conditions, in G. Stachowiak, ed., ‘Conference Proceedings of Austrib 1994’, Perth, Australia. Vegter, H. (1991), On the plastic behaviour of steel during sheet forming, PhD thesis, University of Twente. von Stebut, J., Roizard, X. & Paintendre, B. (1989), The influence of bulk plastic deformation on diefsheet friction during strip drawing of hot dip galvanized sheets, in ‘IDDRG WGMeeting’, Budapest, Hungary. Whitehouse, D. J. (1994), Handbook of surface metrology, Institute of Physics Publishing Bristol and Philadelphia.

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W RlTTEN DISCUSS10N

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Written Discussion Contributions DISCUSSION

SESSTON TI - INVITED LECTURES PaDerII(i)(ii) ‘Stress Waves in a Sliding Contact’ by S Barbarin @MA, CNRS, Marseille, France), J A C Martins (Institute Sup Tech, Lisbon, Portugal), B Villechaise and T Zeghloul (Labs Mdcanique des Solides, Universite de Poitiers, France) Dr J A Greenwood, (Cambridge University, UK). In a Hertzian contact between a stationary rubber sphere and a moving glass block, it is well known that “sliding” can be a complete misnomer: the velocity accommodation takes place by “waves of detachment” or “Schallamach waves” which sweep across the contact. The conditions where this occurs have been studied by Schallamach and, for example, Briggs and Briscoe: but the mechanism of the instability has never been adequately explained. Can your program for studying instabilities in the solution for a uniformly stressed block be estended to study their formation in a more complex Hertzian stress field?

Renlv by Dr M Raous, (LMA, CNRS, Marseille, France). We are effectively interested in modelling Schallamach waves using our model. The present work is not specific to the simple geometry of the block and can be extended to complex cases because we use a finite element discretization. We are actually writing in our computer code a convenient rubber behaviour so as to work on the Schallamach waves with the various criteria. Professor F E Kennedy, (Dartmouth College, Hanover, NH, USA). You showed in your numerical simulations that sliding instabilities can occur even if the friction coefficient is constant. It seemed that those instabilities originated at a location near the edge of the contact. Does the location of the instability move if a different stability criterion is used or if a variable friction coefficient is assumed?

Why did instability originate in the centre of the contact in these experiments? Reillv bv Dr M Raous &MA, CNRS,Marseille, France). Using a variable friction coefficient (in section 2), the wave occurs more or less in the center of the contact zone but the wave remains much smaller than that observed experimentally. When using instability criteria (in section 3). a constant coefficient is assumed. The shape of the wave obtained as the deformation given by the eigenvector (as the one presented on Figure 10) is associated only to the energetic criterion. No comparisons could be actually be done with dynamic criteria. We are actually trying to show that the unstable solutions starting near the corner are evanescent and that the solutions originating near the center propagate along the contact because they are more powerful (the prescribed displacement is larger). Pailer I1 (iii) ‘Third Bodv Effect in Fretting’ by Mr Wei Jun, Mr S Fouvry, Professor P Kapsa and Professor L Vincent (ECL, Dept MMP, France) Dr A V Olver, (Imperial College, London, UK). Why do higher frequencies cause more rapid rejection of debris from the contact? Is this a general result?

Reillv bv Professor L Vincent (ECL, Dept. of MMP, France). The effect of frequency can be explained considering several aspects: 0

0

0

0

The exposure time of the wear scar surface of the flat is modified. The surface reactions between the surface and the environment are then less important at high frequencies. The surface temperature can be increased at high frequency. Mechanical properties of sliding bodies can be modified by the frequency but this effect occurs only for very high frequencies. The motion of debris in the interface can be modified by the velocity.

716 Concerning the last point, it is often observed during fretting tests that the debris are more easily ejected from the interface at high frequencies due to an increase of the momentum of debris.

P a l m I1 (iv) ‘Elsstic-Plastic Microcontact Motlcllinr Using Dislocations’ by I Polonsky and Professor L M Kerr, (Northwestern University, USA)

Professor J S Sheasbv (University of Western Ontario, Canada). Your pictures show a ring of wear around the contact. Can you explain this enhanced wear?

Professor F Sidoroff (ECL, LTDS, France). Did you try to relate the results you obtained for large values of (ah)to some kind of continuum approach?

Renlv bv Professor L Vincent (ECL, Dept, MMP, France). The typical W shape of the wear scars on the flat is surprising for a gross slip condition in fretting where the sliding occurs in the whole contact area. Of course this shape can be easily explained in the case of partial slip conditions where the sliding concerns only an external part of the contact. In our tests, this shape is created by the presence of debris adherent in the external part of the contact on the ball. Then aftcr some cycles, the pressure distribution in the contact is modified from a classical Hertzian type to a distortion where the pressure is low in the central part of thc contact and high in an esternal corona where dcbris arc adherent on the ball.

Rei~lvbv I A Polonslw and Professor L M Keer (Northwestern University, USA). We have not attempted a quantitative comparison of our results for large microcontacts (large values of ah) with results of continuum approaches. Such a comparison is not quite straightforward. It is first necessary to establish an elastic-plastic constitutive law approximating the material behaviour in our dislocation-based model and incorporate this law into a continuum computation scheme (such as a finite element code). Then, asperity contacts with the same asperity geometries and loading histories as in our dislocation-based simulations should be analyscd. It is hoped that such work may bc performed in the future.

Dr I L Sinper, (Naval Research Laboratory, USA). How do we distinguish cause and effect of third body on the friction coellicient?

Howevcr, some qualirative features of our results (e.g.junction growth effect and the nature of stress distributions bclow the contact) were compared to existing prcdictions (based on continuum plasticity) in a papcr submitted elsewhere by these authors.

That is, does friction create debris size/shape or does sizehhape of debris control friction? The example in thc talk was At& vs TIN at a relative humidity of 5%, p I 1 and debris are small, whereas at a relative humidity of 98%. p I0.2 and debris are plate-like.

Rei~lvbv Professor L Vincent (ECL,Dept. M?vlF’, France). In our opinion, friction creates debris with shape and size depending on the external loading conditions (normal force. shearing, humidity, temperature, ...). Often the presence of humidity, for low speed friction conditions, leads to dcbris compacted in the interface to form a smooth layer while dry conditions lead to powdcr like debris layer. The friction coellicicnt is then a consequence of the debris characteristics.

Certainly, the most important difference between our results and continuum elastic-plastic contact analyses is that the scale effects of the type described in the present work cannot appear in purely continuum models, as such models lack any characteristic length other than the contact size.

Professor T H C Cliilds (Institute of Tribololy. The University of Lecds, UK). Thank you for a vcry stimulating papcr: the size range betwecn continuum nicchanics and niolecular dynamic; simulation of contact problems is indeed of great interest. I am concerncd to know, however, in your calculation of the trajectory of a ploughing rigid 2-D asperity. whcre does the material displaced from the half-space go to?

717

In plane-strain rigid plastic calculations of the ploughing of a rigid wedge over a plastic flat. the tip of the wedge ends up at zero indentation depth, and the wedge moves forward supported by a plastic wave. In your case, the tip of the wedge stays below the surface and the material displaced from the path of the wedge seems to disappear. Maybe the answer is that it is accommodated by residual elastic compressive stresses: if this is the case, I would be interested to know how large are the residual stresses and what is the depth scale over which the volume is taken up? How might the calculated results differ for a second traverse over the same surface?

Renlv bv I A Polonskv and Professor 1 M Kerr (Northwestern University. USA). The discusser is quite correct that the area of elastic-plastic halfplane deformed by a rigid asperity should be preserved. This condition is satisfied in our model (to computation error). Indeed, the surface profile change is computed by summing up incremental displacements produced by individual dislocations, and it is well known from elasticity theory that the total volume change associated with the elastic field of a dislocation is zero. As a result, the ‘negative’ area of residual indent is compensated by the ‘positive’ area of a surface uplifting existing material around it. This may not be apparent from our figures because in the cases shown the indent depth is much greater than the maximum height of the uplifting. However, the horizontal estent of uplifting is much greater than the indent length (or the plastic zone size); theoretically, the uplifting estends to infinity, decaying with the distance from the indent. The fact that the area is actually preserved can be appreciated if surface profiles are plotted over a very broad horizontal range. However, the indent shape becomes difficult to see in this case, which is why a relatively narrow range was used in the figures in our paper. The above argument remains valid regardlcss of the detail of contact plastic deformation, i.e. whether the uplifting is ‘plastic’ (most of the displaced material actually flows upwards, forming well-defined pile-ups) or ‘elastic’ (most of the displaced material is forced downwards, which is compensated by a long-range elastic uplifting of the surface). In fact, on the scale of individual

dislocations elastic and plastic deformation are difficult to separate in a meaningful way. Of course, all this may not be true for materials capable of inelastic deformation by mechanisms other than dislocation slip (e.g. glasses exhibiting compaction under contact load), but our work does not deal with such materials. As regards repeated elastic-plastic contacts, we have not attempted to perform simulations of this kind as yet, mainly due to computation time limitations. This is certainly a very interesting problem, which we hope to address in our fbture studies.

SESSION 111 - THlRD BODIES Pill)er I11 (ii) ‘Third Bodv Formation and Friction Reduction on Mo/SiC Sliding in Reactive Gases’ by Dr I L Singer (Naval Research Lab, USA) Th Le Mogne, Dr C Donnet and Dr JM Martin (ECL. LTDS, Ecully, France) Dr S Mischler (EPFL - DMX - LMCH, Tribology Group, Lausanne, Switzerland). I have two questions related to esperiniental details of some relevance for the thermodynamic interpretation of the very interesting results you showed; (i) What was the temperature in the contact? (ii) Was it possible to measure the formation of gaseous reaction products (CO, COz,Hz?) by residual gas analysis or other techniques?

Reelv bv Dr I L Singer (Naval Res Lab,USA) (i) We have no way of measuring the temperature in the contact. However, at a sliding speed of 0.5 mnds, we do not expect sliding friction coefficients around 0.1 or less to raise the temperature more than a few degrees. (ii) Yes. Recently, we attached a differentiallypumped RGA tube to the chamber and sampled the gases within lcm of the sliding contact during tests with H2S gas. Unfortunately, interpretation of the

718 spectra was dificult. H2S (mass 31) was the strongest peak. But other peaks, such as mass 76 (likely CS2) appeared, and the usual gas products, CO (mass 28) and H2 (mass 2) increased with time. The important question to answer is: did these species exist at the contact or were they breakdown products of gases in the vicinity of the ionizer? Paner 111 (iii) 'From the Phenomenoloev to the Concents which Flow from the Third Bodv' by

Mrs P Jacquemard, Dr M-H Meurisse and Dr Y Berthier (INSA, LMC, France) Professor F E Kennedy @artmouth College, Hannover, New Hampshire, USA). Can you comment on the transient behaviour of the third bodies in your seal experiments?

In tests of face seals in our laboratory, we found that third body particles (primarily carbon debris) built up on the contact interface over a period of sliding until there was a nearly complete film of compacted wear debris. Frictioii also increased as the third body film became more complete. Then there was a sudden period of rapid elimination of third body particles from the contact interface, accompanied by some leakage of scaled fluid. Aftcr that, the friction decreased. Renlv bv Dr Y Berthier. Mrs P Jacauemard and Dr M H Mueiirisse (INSA, Lyon, France). The sealing function of a radial face seal has been studied in the case of I" bodies made respectively of carbon-graphite and nitrided stainless steel. For all the tests carried out, the average friction torque at the beginning of the test was equal to 0.4 Nm with neither measurable leakage flow nor instabilities. After a running time ranging from 5 minutes to 25 hours, the average torque increased while instabilities appeared with a maximal amplitude of 0.2 Nm and a period below one second. The 1" bodies made of carbon-graphite were examined in the case of two tests interruptcd after 60 running minutes with instabilities during respectively the 15 and 55 last minutes of the test. For the shorter unsteady running time, a greater amount of natural 3rd body remained trapped at the periphery of the smoothed annular zone. On its inner circumference the structure of the carbon-

graphite has been revealed. Following an unsteady running time of 55 minutes, the smoothed zone has a width of 2 mm compared to 1.5 mm on the other 1" body, and is also much more shiny as the result of the removal of almost all the natural 3rd body towards the outer circumference of the 1'' bodies. The 1" bodies have also been damaged near their outer circumference : grooves, scratches, pulling out ... The morphological evaluations of the 1" and 3rdbodies enable us to correlate the increase in the average torque to the radial flow of the natural 3rd body (Figure 8, Zone 2). As the inner circumference of the carbon-graphitic 1'' body is almost perfectly smoothed with not enough trapping sites, the natural 3rd body is carried away by the artificial 3rd body. After running 180 hours, we periodically observe an ejection flow of the composite 3rd body which corresponds with a torque drop. After 280 hours running, the ejection flow of the composite 3rd body is continuous corresponding with low values of the torque. During all the stages of the contact's life, the friction torque variations are correlated to the flows of the 3rd bodies. Dr J A Williirms (University of Cambridge, UK). I think it is true to say that the underlying

mechanisms of film formation and load support in radial face mechanical seals are still not fully established. Seal manufacturers tend to specify " P V values. Could you comment on your experimental values of this parameter? Are they similar to conimercial values? In the mixed lubrication regime, can you estimate the contribution to load support from hydrodynamics? Rei)lv bv Dr Y Berthier, Mrs P Jacauemard and Dr M H Muerisse (INSA, Lyon, France). In

mcchanical seal technology, there are two definitions of the " P . V parameter, depending on P value which is either the contact pressure or the pressure drop across the seal. The first "P V' parameter is used by the manufacturers to evaluate the rubbing conditions between the contact faces when conditions for film formation are bad. On our test apparatus the " P . V parameter ranges from 5 b . n h to 25 b.m/s. The second " P . V parameter is used to evaluate the sealing capability of the seal. In our case. this maximal ''P.V' parameter is equal to 51 b.m/s. The two definitions of "P.V'

719 are in use and this leads to wide variations in commercially quoted values. These factors do not take into account the effects of misalignment, vibration and the nature of the 3rd body. Furthermore the phenomena involved with a specific "P.V' value are quite different whether they are observed at low P and high V or at high P and low V. Consider the many parameters involved in the contact which interact to build the contact's life, the " P . V parameter must be cautiously employed because it includes too many different phenomena. The interpretation of the tests based on the Reynolds' model indicates that more than 90% of the load applied to the 1'' bodies is supported by hydrodynamic lift. The surface defects and the deformations affect elementary volumes of I*' bodies between them the thickness of artificial 3rd body is of the magnitude of a few tenths of a micrometer and where natural 3rd body is produced. On the scale of this volume. the stresses in the 1" body result either from interactions between 1" bodies, or from interactions between 1" and 3rdbodies. In the rest of the contact's life, the I" bodies are separated by the composite 3rd body made of the mixture of the artificial and natural 3rd bodies. For lack of information on the rheology of the 3rdbodies at each stage of the contact's life, the different ways the applied load is supported are studied using visualisation tests.

SESSION 1V EHL

- THTRD BODIES

IN

Paaer IV(i) 'Direct Ohsewation of Particle Entrv and Deformation in a Rolling EHD Contact' by Dr P M E Cann, J C Hamer, Dr R S Sayles, Dr H A Spikes and E Ioannides (Imperial

College, London, UK)

R I Taslor (Shell Research Limited, Chester, UK). How thin do the plastically deformed platelets have to be before they enter the EHD contact? Dr

Reidv hv Dr P M E Cann (Imperial College, London, UK). Earlier work by Wan & Spikes (Trans. ASLE, 31, 12-21, 1987) has shown that very large particles, many times the size of the film thickness. are entrained and pass through rolling contacts. The deformed particles in this study were certainly much greater than 10 nm thick. Dr J L Teuaanverk (Emerson Motor Technology Center, St. Louis, Missouri, USA).

1. What about conditions of large sliding velocities (U?= O)? 2. Does wear increase or reduce with PTFE? 3. Does the PTFE leave permanent dents in the surface?

Reidv hv Dr P M E Cann (Imperial College, London. UK). We have not looked at PTFE behaviour at high sliding speeds. There is evidence however that in pure sliding the large PTFE particles are trapped in the inlet and can starve the contact of lubricant particles are trapped in the inlet and can stanz the contact of lubricant. The reciprocating rig results showed that the PTFE particles in a simple basestock reduced friction and wear compared to the basestock alone. The commercial misture however had little effect when compared to the commercial basestock.

No - there is no evidence of this type of damage in the rolling tests. Professor J S Sheashy (University of Western Ontario, Canada). Doesn't the stiffness of the glass limit the pressure that can be achieved?

Renlv hv Dr P M E Cann (Imperial College, London, UK). The use of glass limits the masiniuni Hertzian pressure (- 0.5 GPa) that can be achieved in this esperiment. However it does seem able to cope with the very high local pressures generated by the particles. To go to higher, EHD contact pressures (- 3 GPa) it is necessary to use sapphire.

720 Paaer IV (ii) ‘The Entrainment of Solid Particles into Rolling Elastohvdrodvnamic Contacts’ by Dr R S Dwyer-Joyce and J Haymer (University of Shefield, UK) M r D S Mehenny (Institute of Tribology, The University of Leeds, UK). Was the load adjusted to maintain minimum film thickness at various speeds? Would smaller particles be able to pass through the contact at higher speeds without denting the surfaces? If the (a)values are adjusted for some debris size to film thickness ratio, would the differences for debris sizes be reduced? Renlv bv Dr R S Dwver-Jovce (University of Shefield, UK). No, the load was maintained constant throughout the testing. As the contact rolling speed was increased the film thickness increased, thus allowing more oil/particle misture to enter the contact. This was one reason for expressing the results as a particle entry ratio. The maximum lubricant film thickness achieved during these tests was 0.8 vm. The smallest particle size used was 1-2 pin. It is therefore expected that all particles will cause some indentation. Some further tests, not reported in this paper, were performed using particles sized 00.5 pm. The results were inconsistent because, for this size range, particles did seem to be passing through without causing indents. Larger particles become trapped further from the contact. In this region the fluid volume is great and so many particles become entrained. This is one reason why large particles are many times more likely to become entrained. One could adjust the entry ratio to account for this feature by multiplying the volume of lubricant in the contact (equation 2) by d/h. This gives a measure of the actual volume of lubricant from which particles were drawn. This would indeed reduce the dependence of entry ratio on particle size, but does not hlly explain it. Professor J J Kalker (Technical University of

Delft, The Netherlands). During your presentation you showed a number of slides on which results are

shown of a remarkable accuracy. Such an accuracy asks for more: 1. Could you increase the accuracy with the present method? 2. Could you devise another method to increase the present accuracy? 3. Do you consider it worthwhile to do either ( I ) or (2)?

Reijlv hv Dr R S Divver-Jovce (University of Shefield, UK). The results typically show scatter of the order of 30%. My belief is that the variability stems largely from two sources; firstly the difficulty in maintaining a consistent particle suspension. and secondly from the wide size distribution in each batch of diamond test particles. Reducing the errors from either of these two sources is difficult. Keeping test durations to a minimum and continuous mising helps to maintain a constant concentration. Sieving particles to improve the size distribution would be one option, however with micron sized particles this is a time consuiniiig process.

Interestingly, in the author’s earlier studies on abrasive wear (51 errors are of the same order. Perhaps it is the variability of the particle entry process which leads to irrepeatability in this kind of three body wear tcst. Dr J A Greenwood (University of Cambridge, UK). I wonder if your entrainment ratio is the best parameter? If we consider a dust suspension in air being entrained between two rollers with no gap between them, surely we shall still get dust going through? Would it be better, perhaps, to use the area ratio of the whole disk to the contact? This would still not focus on the vital place, the inlet to the contact. but might be closer. Reelv by Dr R S Divver-Jovce (University of Shefield, UK). Indeed, in the limiting case of zero film thickness the particle entry ratio would rise to infinity. The entry ratio parameter is meaningless when considering the suspension in air. Expressing the data in terms of an entrainment area of fluid rather than a volume would not show this disadvantage. However, as the speed increases the volume of oil entrained per unit area of disk

721

rises. The volume based ratio normalises this. whilst an area based ratio would not. Perhaps no one parameter will suitably express these results.

prner IV (v). ‘A Ball-in Si)here Aiwaratus for the Test of Hin Joint Prosthesis. Influence of the Third Bodv on the Friction and Wear Behrviour’ by Mr F Bernard, Miss C Annarelli, Professor J Bert, Dr J Dupuy-Philon (UCB, Dept Physique), R Cohen (Univ Lyon I, Fac Pharmacie), J L Besse, B Moyen and J L Lerat (HBpital Edouard Herriot, Lyon, France) Professor D Dowson (Institute of Tribology. The University of Lecds, UK). I.

You showed results in which the friction falls during the swing; are your recorded values the mean coefficients of friction, or the values at the mid-point of the swing?

2. You showed evidence of grain removal. Was the wear debris of grain size or sub-grain dimensions?

Renlv hv F Bernard et al (VCB Dept. Physique, France). 1. The results recorded during the tribological

test are the mean coefficients of friction measured during four cycles. One cycle is shown in picture 6. 2.

According to the optical magnifications, it seems that the average w a r debris size is more than 5 pm in diameter for both tests 1 and 2. This dimension in larger than the average size of the alumina grains (< 4 pm).

SESSION V - N A N 0 TRIBOLOGY Paner V (i) ‘Nanometre Scale Mechanical Pronerties of Trihochcmical Films’ by Dr S Bec and Dr A Tonck (Ecole Centrale de Lyon, LTDS. France)

Professor Koii Kato (Tohoku University, Sendai, Japan). For the measurement of thin film hardness on a hard substrate, how did you choose the optimum angle of indentor tip which will minimize the effect of pile-up on hardness. Reelv hv Dr S Bec (Ecole Centrale de Lyon, LTDS, Lyon, France). In this paper, we do not want to minimise the effect of pile-up. We take it into account and try to quantify it (assuming that the pile-up has the same properties as the tested material). The presence of pile-up, its geometrical shape and its size may be of great interest to know more about the bchaviour of the tested material.

Professor R C Cov (Shell Research Ltd, Thornton Research Centre, Chester, UK). You indicate that the properties of the ZDTP film varies with depih, that it is hetrogeneous, however, in your model you assume that it is homogeneous. Is there any evidence that the contact pressure affects the value of elastic modulus? Rei)lv hv Dr S Bec (Ecole Centrale de Lyon, LTDS, France). Yes, indeed, our simple model is constructed with the assumption that the film is homogeneous. But, the boundary conditions used in the modcl are taken in order to give correct values for very small penetration depths, for which we do not need any model whatever the nature of the substrate may be. Then, for the larger penetration depths and in the case of homogeneous film, the modcl is constructed to give a constant value for the elastic modulus of the film. If we do not find a constant value, it means that the film is not homogeneous. But because it is a global measurement including structure effects, the model does not give, in this case, the actual value for the elastic modulus, but only an average estimation. A more complex modelling would be needed to compute the actual values. We expect that the contact pressure does not affect the elastic modulus value very much, because the volume of material involved in the elastic measurements is much larger than the plastic zone where the pressure is high. So, most of the elastic information comes from the material submitted to a low pressure.

722 P a i w V (ii). ‘In-situ Measurement of the ViscoElastic Pronerties of a Sliding Lubricated Contact’ by Dr A Tonck, Dr D Mazuyer and Professor J-M Georges (Ecole Centrale de Lyon, LTDS, Lyon, France) Professor R C Cov (Shell Research Ltd, Thornton Research Centre, Chester, UK). With reference to your last figure, when you stopped sliding, there seemed to be a relaxation process taking place where both elasticity and film thickness were varying. Is this due to re-ordering of the adsorbcd stearic acid molecules? Rei)lv by Dr D Mazuver (Ecole Centrale de Lyon. LTDS, Lyon, France). Our interpretation of thc relaxation process of both tangential force and elasticity, considers that there is some re-ordering and local motions of the interdigitating molecules inside the shear plane. The shear plane is regarded as an interpenetration zone between the two adsorbed stearic acid monolayers. This interpenetration zone where molecules can interdigitate is certainly very thin (not more than 0.1 nm).

Dr J L Tevaanverk (Emerson Motor Technology Center, St Louis, MO, USA). Are transient effccts relevant in the modulus determination? Rei)lv bv Dr D Mazuver (Ecole Ccntralc de Lyon, LTDS, Lyon, France). The esperimental conditions used for the continuous determination of the elastic tangential modulus, especially the amplitude and the frequency of the superimposed sinusoidal vibration in the sliding direction are chosen to minimize transient effects. Actually, the damping component of the mechanical tangential transfer function is measured and is found to be negligible relative to the elastic part from which the modulus is determincd.

Dr J A Williams (University of Cambridge. UK). We heard this morning from Professor Briscoc that the shear strength of a boundary layer is linearly dependent upon the local hydrostatic pressure ( T = z o + ap). Are your observations on the mechanical properties of these monolayers of stearic acid in accord with this relation?

Rei~lvhv Dr D Mazuvcr (Ecole Centrale de Lyon, LTDS, Lyon. France). In our experiments in the range of pressure 5MPa-SOMPa, we find that the friction cocficicnt is independent of the contact pressure (see figure 4 of the paper) and is equal for this type of monolayer to 0.007. This means that the shear strength is in this case proportional to the hydrostatic pressure. This experimental point is in agreement with the relation found by Professor Briscoe for boundary layers and we find, in this rangeof pressure; a = 0.007 and T ,, = 0.

Professor Yoshi Kimura (University of Tokyo, Tokyo, Japan). How did you prepare the stearic acid films? Were they retracted from solution, or formed by a L-B method? Secondly. when the tangential force was applied, did the thickncss of the films change or not?

Renlv b s Dr D Mazuver (Ecole Centrale de Lyon, Lyon, Francc). The stearic acid monolayers are self-assembly layers prepared from a solution of dodecane with stearic acid (0.2% weight) and thc measurements arc made after twenty four hours of adsorption.

The answer to the second question is yes, at the bcginning of the sliding, a slight decrease in thickness (about 0.001nm) is observed. Some variations in the thickness are also observed aftcr change in speed, stopping and reversal of sliding.

P i w r V(iii) ‘Nanorheoloeical Behavior of Confined Liauid Lavers for Normal Contact’ by Mr F Auslendeer and Professor F Siddoroff (Ecole Centrale de Lyon, Lyon, France) Dr B Bou-SiIid (INSA, Lyon, France). Please state the boundary conditions used in your model to provide a significant physical interpretation. R e ~ l vIN Professor F Sidoroff (Ecole Centrale de Lyon, LTDS, Lyon, France). The boundary conditions, as specificd in (6) and (7), are based on the usual no-slip assumption. Frictional boundary conditions could probably have been treated in the same way. but they do not appear as physically relevant for the investigated application, namely

723 the mechanical interpretation of the surface force apparatus experiments as described in [2],[3], and the identification of the elastic property of the confined solid layer. This application, using the oedometric thin film model derived in Section 5 is now being developed.

Paner Wiv) ‘How to Achieve Contact Recording with a Low Stiction Force’ by Mr L Tosi and Dr B Bou-Said (INSA, LMC, France) M r P Marchand (Institut Francais due Petrole, France). I would request details about the existence of contacts and when thcy occur.

Renlv hv M r L Tosi (INSA. Lyon. France). The flying height measurement tests were perfornied on a super smooth glass disk and tlie FH is the distance between the top of the disk and the slidcr. The magnetic disks are not super smooth, like tlie glass disk. The roughnesses are sometimes higher than the FH. The contacts appear at this time.

SESSTON VI

- STARVED EHL

Paner VI(1) ‘Starvation Phenomena in E H L Point Contacts: Influence of Inlet Flaw Distrihution’ by Mr F Chevalier, Professor A A Lubrecht (INSA, LMC, France), Dr P M E Cann (Imperial College, London. U.K.), Dr F Colin and Professor G Dalmaz (INSA, LMC, France) Professor C M Tavlor (University of Leeds, U.K.). What is tlie evidence that the polynomial representation of inlet film thickness is realistic? Is this true for a wide range of machine elements such as gears, cams/followers. rolling elcnient bearings etc?

Rei)lv bv Professor T Luhrecht (INSA, LMC. France). What is more realistic in this approach is not the polynomial representation of the inlet film thickness itself. Many experiments show that the shape of the meniscus at the inlet of the contact moves to a concave shape when the velocity increases or when oil is removed from the

contacting surfaces. This phenomenon can only be explained if we considcr a loss of lubricant in the central region of the contact due to side flow generated by the pressure field. The inlet film thickness is perturbed and less lubricant is observed in the central part of the contact than in the well known sidc reservoirs. Our model can take such phcnonicna into account. Moreover, this depleted lubricant inlet distribution with a sharp gradient on the sides leads to good correlations between numerical and experimental results. It makes us think that it is one of the phenomena which could esplain the experimental observations. This phenomenon has been observed in test machines whcre a ball is continuously overrolling the same track. It is likely to happen in rolling eleniciit bcarings but it is dificult to estrapolate to other machine elements like gears or cams/followcrs bccause the lubricant is not rccirculating. Anyway, it is very difficult to predict this lubricant Icvcl which depends on many paramctcrs such as surface tension, gravity, inertia effects or centrihgal forces and on the repartition of the lubricant at tlie rupture boundary over tlie two surfaces. Dr J A Williams (University of Cambridge, U.K.). Could you commcnt on the physical significance of tlie non-dimensional paraiiietcrs (L) and (M) for example. do thcy readily relate to the Dowson and Higginson or Johnson variablcs? Do the particular numerical values 291, 328 have special significance or are thcy chosen to give a best fit Ivith experimental data‘?

-

Rcidv hv Professor T Luhrecht (INSA, LMC, France). (L) and (M) are thc dimensionless Moes parameters: (L) is tlie matcrial parameter and (M) the load paranicter. They are related to the dimensionless paramcters of Dowson arid Higginson U.G.W in the following way: L = G(2U)’l4 . M = W (xJ)‘”~ . So, like the parameters (U,G.W) the parameters (L,M) corrcspond to a given operating condition. The valucs L=3.28: M=291 are dctcrmined by the esperimental conditions: equivalent radius of curvature of thc surfaces, Young’s modulus, rolling speed, load, viscosity law. The only parameter which has been chosen to obtain a good correlation

724 with experimental results is the inlet lubricant distribution.

Dr B Bou-Said (MSA, LMC, France). What is the validity of the Newtonian state? What is the validity of the continuum state? Renlv by Professor T Luhrecht (INSA, LMC, France). In this paper, only starvation effects on the film thicknesses are studied. It is well known that non Newtonian effects play an important role on the friction forces but hardly affect the film thicknesses. Moreover, the experimental case treated operates at low speed which leads to a reasonable strain rate. The good agreement between experiments and theory seems to justify the hypothesis of the Newtonian state. Concerning the continuum equations, the minimum film thickness obtained is about 30nm: it leads to the superposition of many niolecular layers, if these molecules have a reasonable size. It has been shown that down to a few niolecular layers, a fluid behaves like a continuous medium

FZG gear test rig. The tests were performed for an oil temperature of 90’ C and a running time of 20 hrs. Measurements 111 show that, depending on the type of polymer, the decrease of viscosity during the first 20 hrs is significant for the shear stability. Table 1 shows the results. The dynamic viscosity q was measured in a rotary viscometer at a temperature of 100”C. Table 1 Results of Shear Stability Test

(q

MI00

Oil

PMAl PMA2 OCP

SBC

= 9,29n1pa) qtlrw

rim

relative

shear

before

after

stability

test

test

viscosity loss Aq

[mPas]

[inPas]

18,6 56.7 13.8 17.0

17,5 30.7 12.1 13.5

[YO] 63 45.8 12.4 20.4

index SSl[%]

12,5 54,s 38,2 45.0

Ill. I11 - J.M. Georges, S. Millot, J L Loubot. A Tonck, “Drainage of thin liquid films between relatively smooth surfaces”, J Chem Phys, 98. (9), 1993, pp 7345-7360.

Paner VIcii) ‘Merssrcmcnt of Oil Film Thickness in Elastohvdrodvnnmic Contact. Influence of Various Base Oils and VI Imiwovers’ by Mr B R Hohn, Mr K Michaelis and Dr-Ing U Mann (FZG,Munich. Germany). Dr J L Tevranverk (Energy Motor Technology Center, St Louis, Missouri, U S A . ) Is there a time dependence of the VI effect? Hence if you use the oil for 1-10 hours, do you still get a benefit from PMAZ? Renly by Dr-Ing Ulrich Mann (FZG,Munich, Germany). The presented results for the polymer containing oils are mainly affected by a temporary viscosity loss. Depending on the shear stability, a permanent viscosity loss can also be observed. Therefore, the polymer containing oils were tested in the CEC L-37-T-85 shear stability test with a

While the relative viscosity loss Aq indicates the absolute viscosity loss referring to the unused oil, the shear stability indes SSI shows the loss of the thickening effect of the polymer. It can be stated, that especially for the oil PMA2 (molecular weight Mw = 220.000, less shear stable) a relatively high (50%) viscosity loss was determined. This is a result of the degradation of the molecular weight by high shear rate and temperature in the EHD contact between the gear teeth. The viscosity loss for the oil PMAl (shear stable, M, = 20.000) is low. This type of polymer is usually used in gear application. For the middleweight polymers (SBC and OCP) the SSI is appros 40%, but the absolute viscosity loss Aq is relatively low. Because of the molecular weight (M, = 120.000) the shear stability is only slightly lower than for the PMA2. On the other hand the concentration of both polymers in the base oil is pretty low. thus, the effect on the absolute viscosity is also low. With the sheared oils PMAl and PMA2 film thickness nieasurements were performed. The results are shown in Fig 1. For a better

725

comparison the results of the unslieared oils PMA I and PMA2 are indicated as dotted areas.

Mr M Kalin and F Vodopirec (University of Ljublijana, Slovenia). Prafcssor A A Torrance (Trinity College, Dublin,

o’030

40

50

60 70 80 bulk temperature 1 9 ~

’c

100

F i g 1: Relative F i l m Thickncss of Slicarcd Oils

For the oils PMA1, sheared and PMAI. unshearcd no significant difference of film thickness and thus of effective viscosity can be observed. This result is not amazing because of the low viscosity loss of the oil PMAl after permanent shear. The measured film thickness of oil PMA2, sheared is considerably lower than for the unsheared oil. The effect of rolling velocity v,on relative film thickness also disappears. This means that after a certain running time the effective viscosity of oil PMA2, sheared is comparable to the oil PMA1, unsheared . The temporaiy viscosity loss C ~ I I S C Sa decrease of film thickness during the life time of polymer containing oils. In terms of polymer containing oils it is necessary to investigate the film thickness after a certain running time. References [ 11 Winter, H; Michaelis K; O’Connor, B: Pruhng

der Scherstabilitat von Mehrbereichsolen fur Kraftfahrzeuggetriebe. Mineraloltcchnik H 8, August 1986, pp 1-18.

SESSION VTI -THERMAL EFFECTS Paner VlW) ‘Three-Body Contact Temnerature in Fretting Conditions’ by J

Pezdirnik, Mr B Podgornick, Professor J Vizintin,

Ireland). White layers may form in steels without large temperature rises due to the large plastic strains which may be produced under conditions of high hydrostatic pressure such as those in sliding contacts. Have the authors considered this possibility and have they examined the microstructures they observe at high resolution in TEM to discover whether this niight be the case? Rcfcrcncc Morgan. J E; Stokes, R J and Torrance,

A A ‘Deformation in Heavily Loaded Rolling Contacts’, Proceedings of the 8th Leeds-Lyon Symposium in Tribology, The Running-in Process in Tribolog, Buttenvorths 1982, pp 184-191. Rcalv hv Mr B Potlgarnik (University of Ljubljana. Slovenia). We examined the initial niicrostruclurc of used steel and microstructure of the while phase. Secondary carbide particles, which are one of the two components of the initial steel microstructure dissolve in austenite, according to published data above 1000°C. No such particles were found in the white phase independently of its shape and size. It does not seem possible that high strain could cause the solution of secondary carbide particles, therefore it is concluded that in areas of white phase the steel was heated to a temperature above 1000°C. On the other hand the microstructure in the vicinity of the white phase indicates clearly to a tempering of steel up to the AC, temperature appr. 750°C for the I%C and 1.5% Cr steel. White phase shows a microstructure with a homogeneous matris with a dispersion of carbide precipitates of size below 0.05 p m . The microstructure of particles manufactured by water atomisation of steel of the same type as that used in fretting tests was also esamined. In powder particles of linear size appr. 50 p m it consisted of martensite and a significant quantity of a white phase, which was identified by X rays diffraction as retained austenitic. In this phase homogeneous matris and precipitates of size below 0.05 p m were found. that is a microstructure very similar to

726 that in some areas of the white phase on specimens tested in fretting tests. The shape of the white phase areas on the investigated specimens shows that in the initial stage of fretting the white phase started to form on several isolated points. With increasing amplitude and test time single islands of a few p m2 did grow by coalescence to the large single area. Actually the white phase is being investigated by TEM at ESCA with the aim to confirm its nature and the content of carbon in solid solution.

Profcssar F E Kennedv (Dartmouth College, Hanover, NH, USA). I do not understand the inlluence of slide-roll ratio C on temperature distribution of the roller (or ball) surface. It seems like the amount of sliding increases as C increases. I would expect that the peak temperature should move toward the contact exit as C increases (the hot oil should heat the trailing edge of the contact). That seems to be true for C=O.S, 1.0 and 2.0 but not for C=4. Can you esplain why the T distribution is nearly symmetric for C=4?

Pmer VII (iii) ‘Infrared Techniaue for MeasurinP Temt)erature Distributions in EHD Contact n n e : Part 1 Techniauc: Part 2 Esi)erimental Results’ by W X Qui, S Z Wen and A K Tieu (University of Wollongong. NSW, Australia).

R e ~ l v hv Mr Weinine Oiu (University of Wollongong. NSW, Australia). The phenomenon of the tcniperature distribution being symmetrical could only occiir when the system is completely symmetrical as discussed in the answer to Dr A V Olver’s question. We did not have a completely symmetrical case here. We would try to esplain the reason why the T distribution nioves back towards the centre of the contact when C>2. as following: I n the papcr, the slidc-roll ratio C is given by the formula: C = A U / U = 2 ( U b - U S)/(Ub+U s). The case of C<2 can be simulated by a motion such that tlic plate has a velocity in the same direction as the ball as shown in Fig.a (ub=O/.33 d s , u ,=0.20 nds and 0.11 nds). It can be scen that C=2 is a turning point. In this case, the ball rotates at ub=O.33 m / s while the plate is at a standstill as shown in Fig.b. The case of C>2 can be simulated by the plate moving in thc opposite direction to the ball (C=4 whcn ub=0.33 m/s. u,=O.11 nds) as shown in Fig.c.

Dr A V Olver (Imperial Collcgc. London. UK) The maximum temperature might be cspectcd to be near the centre of the contact as the slide-roll ratio ( Au / u ) + m because under these conditions. the system is esactly symmetrical:

n

Do the authors concur with this csplanation or can they offer an alternative?

Rei)lv hv Mr Wcisine Qiu (University of Wollongong, NSW, Australia). We concur with this explanation. If the lubricant is supplicd at two sides of the contact area and the two contact parts are made of the same material and have the same size, whcn the slide-roll ratio C-+ 0 0 . the systcm is esactly symmetrical and the masimum tempcrature is expected to be at the centre of the contact and the temperature distribution may also bc symmetrical.

727

When C<2, we agree that the peak tempcrature should move towards the exit as C incrcases because the hot oil is heating the trailing edge of the contact. But when C>2, the condition is different. In this experiment, plenty of oil was adsorbcd onto the plate surface all the time. Having a velocity opposing that of the ball, the plate carried a portion of cooler oil into the contact. Meanwhile the hot oil at the trailing edge of the contact would be partially transported towards the centre by the plate. So the peak temperature would move back towards the centre. If the ball stopped, then the peak temperature would pass the contact centre to the other side of thc contact, just likc the case of c<2. professor Y Okamoto (Ibaraki University, Japan). When you need InSb as an infrared radiometer, it is quite important to consider the water content in the air. How can you make a direct calibration of the relative humidity using the InSb radiometcr?

Reelv hv M r Weixine Oiu (University of Wollongong, NSW, Australia). It is truc that considering the water content in the air is quite important when photoelectric materials such as InSb are used as an infrared sensor. The watcr content in the air can be controllcd by adjusting the room temperature and the relalive humidity in the laboratory by an air conditioner. The detector used in the experiments is InSb photovoltaic sensor cooled by liquefied Nitrogen to a temperature of 77°K. In the esperinients and calibration, both the room temperature and rclative humidity were strictly controlled by the air conditioner to 20°C k0.5 “C and 6%. respectively. From the manufacturer’s data, we have taken into account the effect of humidity and temperature in the calibration of the sensor.

Dr J L Tevaanverk (Emerson Motor Technology Ccntcr, St Louis. Missouri. USA). Was tne correction needed because of source generation assumptions or because of model problems? Where on the con rods were the temperatures measured? What is the circumferential temperature distribution around the rod bearing? Professor F E Kennedy (Dartmouth College, Hanover, NH, USA). Where were the expcrimcntal temperature measurements made, in thc oil or in the bearing? How wcre the measurements made? Rei)lv hv Dr A 0 Miiin (T & N Technology Ltd, Cawston, Wanvickshire. UK) and Mr G J Jones (Glacier, UK). The authors would like to thank M e w s Tevaarwerk and Kennedy for their questions an this paper. The correction tcrm for the power loss figure was not used bccause of problems with the thermal modcl, which has proved very robust in tcrms of obtaining a convergcd solution for the bearing temperature. The corrcctioii was introduccd in an attempt to niodcl the trcnds observed in tcmperature nicasurenicnts in an engine. Figure 1 shows the nieasurcd tcmpcrature rise, relative to gallery, in a big-cnd bcaring. plotted against engine speed. 50

I---

0

P a i w VWiv) ‘An Iterative Heat Balance Techniaiie for Raikl Estimation of Engine Bearing Temrwatures’ by A 0 Mian (T & N Technology Ltd, UK) and G J Jones (Glacier, UK).

- - Pwtinn 1 I

2000

4000

6000

Engine speed (rev/inin)

Figure 1. Big-end bcaring temperature rise Values for four locations around the bearing are shown. Above 6000 rev/min there was a distinct

728 change i n the rate of temperature rise with speed. As explained in the paper, this effcct cannot be accountcd for by viscous losses alone. Some other phenomena must have been contributing to the heat generated in the bearing for such an increase in temperature to occur. It has been suggested that the bearing was starting to operate in the mised lubrication regime which would lcad to a higher effective coefficient of friction, and hence powcr loss and temperature rise. The correction term. calculated from the predicted film thickness and typical values of surface roughness of the bcaring and journal, was used in the model to account for this cffcct. This concept is well cstablishcd and is in routine use for engine bearing studies, as reported by Ligier and Gojon (1).

I *4

Cold junction 1

Figiirc 3 Two bar tclcmctry linkage From Figire 1 it can be scen that the variation around the bcaring was consistent and was at most 1-5C. Comparison bctween different builds of the engine suggest that these variations may have been due, in part, to spstcmatic errors in the system. One possiblc sourcc of such error may have been variations in thc dcpth of the thcrmocouple below the bearing surface which has proved very difficult to control.

Figure 2 Location of thermocouples on connccting rod

Figure 2 shows the positions on the connecting rod wlicre temperatures were measured. Four flat-

729 bottomed holes were drilled from the back of tlic shell into the bearing lining to within 0.25nini of the bearing surface. Thermocouples wcrc then placed against the bottom of these holes and cemented into place. The signals from the thermocouples were carried back to the instrumentation via a two bar telemctry linkage, as shown in Figure 3. To avoid having to carry thermocouple wire via this linkage, cold junctions were formed on each part of the rod and the temperatures of these points mcasurcd by calibrated thermistors.

I 11 Ligier, J L and Gojon, R: Fonctionnerncnt tribologique dcs cousstncts en rcgiiiie Itinitc. Matcriaur & Tcchniaucs, 1995. 3-4, 23-32.

Thc authors h:nc sonic cspcricncc i n relation to this phcnonicnon \I liicli is sccn as bcing important by many. I t is now possiblc to include an asscssnient of this and those intcrcstcd are referred to rcfcrcnce [ I ] , It is observed that traditional Mobility analysis includes neither consideration of shear rate viscosity dcpcndcnce nor effects of pressure upon viscosity, and these effects work against each other. Work presented in reference [ I ] indicates that as a first approsimation they may be considcrcd to cancel each other out.

Reference [l]. D Han “on-Ncwtonian Effects in Engine Bearing Analysis’. PhD thesis, Dcpartnicnt of Mcchi>nical Enginccring. Univcrsity of Lccds. I993 D r R I TiI\lot- (Shcll Rcscarcli Ltd. Chcstcr, UK)

SESSION V l l l - INVITED LEC‘I’UHES Paiwr Vlll(i) ‘Friction Modelling for Internal Cornhiistion Engines’, by D Dowson. C M Taylor and L Yang (Thc University of Lccds, UK).

Dr J L Tevaanverk (Emerson Motor Technology Center, St Louis, Missouri. USA). For the steady state power loss analysis. did you use thc Ross & Slaymaker mcthod? How docs your nicthod compare? Was the shear rate viscosity dcpcndcncc includcd in the analysis of journal bearings. Rci)lv by Professor D Dowson, Professor C M Tavlor and D r L S Yanp(1nstitute of Tribology, University of Leeds, UK). The Ross & Slayniakcr mctliod was not used in the data prcscntcd i n the paper. A range of approachcs from thc very siriiplc :Petroff analysis) to the more sophisticatcd [Mobility analysis of dynaniically loaded bearings with consideration of detailed asscssnicnt of powcr loss due lo viscous shcar including cavitation :ffects) has been considered. Thc authors are unable to comment on what the comparison tvith the Ross & Slaymaker method would be. Shear rate viscosity dcpendcnce was not includcd in the results which were prcscntcd in the paper.

The iiiodcl scciiis to undcrprcdict, compared to apcrinicnt. at high engine spccds for this particular cngiiie Could this bc due to the neglect Df frictioii losscs that depend on fucl consumption? Rci)lv lw Professor D Donson, Professor C hl Tiivlor i i i i t l D r L S Yiing (Institute of Tribology, University of Lccds. UK). Thc obscnation that the prcdictioii of power loss for all the major tribological C O I I I ~ O I I C I ~ Isccnis S l o be loivcr than cspcrimciit:il \,nlucs is true. At the current time we arc unsure of tlic reason for this. Part of the problcm lics i n the clarity of the data provided to us to dctail the cspcrimcntal conditions under whicli tlic cspcriiiiciital work was carried out. In p;irticular. at high engine speeds, the predictions associated with the piston asscrnbly considerably underestiniatc tlic predicted nicasure of power loss. Oiic of tlic major features in relation to this is the lcmpcrature conditions which wcrc appropriate for thc niotorcd cspcrinicrits which ivere carried out. Thc prcdiction of losses would be particularly scnsitivc to tlic tcnipcrature for motored spcrinicnts and tlic authors are pursuing furtlier dctails. I t is noted. however. that for engine speeds up to about 4000 rpm the agrccnicnt between the prcdictioiis of thc riiodcl and thc espcrinicntally 3btaincd data is not unsatisfactory and for the vast majority of situations automobiles would spend little t h e opcrating at speeds above this value.

730 Professor H Kato, (Tohoku University. Senolai, Japan). For the theoretical calculation, do you use the initial surface roughness or resultant surface roughness after running-in? If we consider the resultant surface roughness, is it sensitive to changes in engine speed?

mounted on a “frictionless” support and this enables direct nicasurenient of shear stress in the contact as a function of lubricant, load applied and temperature. In this way direct measurements of liniitiiig shear stress can be made.

Reiilv bv Professor D Dowon, Professor C M Tavlor and Dr L S Yang (Institute of Tribology, University of Leeds, UK). Professor Kato raises an important observation in relation to predictions of power loss in automobile engines, particularly associated with the piston assembly. The initial surface roughness of the major tribological components in the engine will certainly be modified during a running-in process. Since the analysis may call for the introduction of a boundary friction coeflicicnt or limiting shear stress, it is important that a sensible value of the running surface roughness is adopted. In relation to the experimental data provided in the paper, such information is not available, although in current engine tests being carried out by the authors at the University of Leeds, very detailed measurements are being made, particularly i n the early stages of running. Little evidence appears to be available in relation to the changes of surface roughness with engine speed after an initial running-in period. Howevcr. the authors believe that this would not be a significant factor. The particular importance of the surface topography of the cylinder liner in relation to its role in providing reservoirs of lubricants and its method of honing, is an area which has attracted the interest of researchers and practitioners for many years and continues to do

Paiier VWii) “on-laminar flow in Hytlrodvnamic Lubrication” by Professor J Frene (Universite de Poitiers, LMSo, France) and Professor V N Coiistantinescu (Universitt “Polytecnica” de Bucarest, Romania).

so.

Dr J Greenwood (The University of Cambridge, UK). Can you say more about the limiting shear stress used for your cam friction? In EHL there is considerable argument about how this depends on temperature and pressure: have you been able to do better than use a standard value of SMPa? Rei~lvhv Professor D Domson. Professor C M Taslor and Dr L S Yang (Institute of Tribology, University of Lecds, UK). The duthors have a two disc apparatus in which both discs can rotate at different controlled speeds. One of the discs is

Dr J Grecnivood (The University of Cambridge, UK). You haw demonstrated that non-laminar effects in bearings need to be considered: but where in the whole spectrum of engineering bcarings should we worry? For example, is Professor Taylor wrong to ignore non-laminar effects in his engine main bearing? Rei)lv hv Professor J Frene (Universite de Poitiers. LMSo, France) and Professor V N Cnnstantincscu (Universite “Polylecnica” de Bucarest. Romania). It is evident that many fluid bearings are working under laminar conditions. That is tlie case for all engine bearings lubricated with oil. For example for very high speed engines (15000 rpni) tlie mean Reynolds number is less than 500 which corresponds to laminar flow. But for very large bearings eg 1000 mm diameter, for power plant turbines which run at 1500 rpm the Reynolds number is of the order of 4500 and in this case the flow in the bearing is mainly turbulent. This is also the case for small bearings lubricated with very low viscosity lubricants; for esample a journal bearing of 100 mm diameter running at 12000 rpni lubricated with water presents a mean Reynolds number of 2500. Professor C M Taylor (Institute of Tribology. University of Leeds, UK). The turbulent thin film flow models you have described represent a range of relatively early hypotheses enabling a direct Reynolds number influence to be incorporated into flow considerations. In the last twenty years more comples turbulence models have been developed in association with non-tribological flow situations such as combustion. Does the application of these

73 1 more complex models to the lubrication situation enable significant improvements to be made to the ability to predict the behaviour of lubricated machine elements where non-laminar flow occurs? R e ~ l v bv Professor J Frcne (Universite de Poitiers, LMSo, France) and Professor V N Constantinescu (Universite “Polytecnica” de Bucarest, Romania). Indeed, as shown in the additional references, in the last years more complex turbulence models have been used in lubrication, namely the k-1 and the k-E energetic models. The ability of this model is to treat in a more accurate way flow regimes where the simplifying assumptions of the classical approaches are not correct, eg the transition region. The global resistance coefficients used in the Reynolds equation, k, and k, being integrated quantities are not very sensitive to such refinements. The values of the coefficients predicted by this model are very close to the classical ones in the usual range of Reynolds numbers and pressure gradients. Additional references. Di Pasquantonio, P; Saia, P; “Influence of thermal Field on the Resistance Law in Turbulent Bearing Lubrication Theory”, J Tribol, Trans ASME, Vol 106, pp 368-376, 1981. Launder, B E; Leschziner. M: “Flow in Finite Width Thrust Bearings Including Inertial Effects, Part 11: Turbulent Flow”, J Lub Tech Trans ASME, VOI 100, pp 330-334, 1978. The authors would like to espress their appreciation of the discussions written by Professor Greenwood and Professor C M Taylor. Dr J Greenwood (The University of Cambridge, UK). Having been brought up in Bowden and Tabors’ laboratory, it is heresy to hear that heating the plasticine will lower the coefficient of friction;

- and softening the body will reduce (s) and (p) by the same amount. How is plasticine different? Renlr bv Professor Mike Adams (Unilever Research, Wirral, UK). In our work, the heated platens were in contact with the “Plasticine” for a relatively short time interval such that only a thin

layer was heated. Consequently, the interfacial shear stress was reduced without any effect on the normal stress. This is analogous to Tabor’s study of nylon friction using a spherical steel slider. He found that, in the presence of water for short contact times, the friction coefficient was reduced due to plasticisation of the surface layer. As an additional point, for long contact times the friction increased due to an increase in contact area arising from bulk plasticisation. For a soft solid such as “Plasticine”, this effect would not occur because the real area of contact is approximately equal to the apparent value.

SESSTON 1X - GRANULAR LUBRICATION Paner IX(i). ‘Numerical Exgeriments with Flows of Elongated Granules’ by Professor H Elrod (Old Saybrook, USA). Professor Y Kimura (University of Tokyo, Japan). The pressure, ie the normal stress, you showed has a nearly symmetrical distribution, while ones with fluid lubricants tend to have their peaks close to the exit. Do you suggest any implication in this difference? The shearing stresses on the slider and the pad seem to have different levels. How can we understand the balance of forces? Reelv bv Professor H Elrod (Old Saybrook, USA). No. My understanding of granular flows is not yet good enough to hazard an explanation. As shown in Fig 14, even with no inclination of the slider, there is a substantial normal stress. The so-called “shear stress” on the slider surface includes an s-wise component of force due to the inclination of that surface. In Ref 1, which treated pure Couette flow, the same model of granulegranule interaction yielded a match for both normal and tangential stresses.

Dr J Greenwood (The University of Cambridge, UK). In a fluid-lubricated bearing we normally consider only the viscosity and ignore the density.

732 In powder lubrication there appears to be only one parameter, the mass of the particles or, effectively, the density of the powder: can you confirm that all the forces calculated simply scale with the particle mass? If so, is this what we would expect: do the forces involved in powder technology nearly disappear with light powders?

yet considered because it severely alters the particle geometry, and thus complicates the solution process. On the other hand, different particlc geometries are being studied.

Renlv bv Professor H Elrod (Old Saybrook, USA). For the calculations shown in the present work, single values of the force and hardness ratios were employed. Thus the parameter G$(M,U,Z) was maintained fixed. In other words, the stiffness, G, was scaled with the mass, M,. No inference can be drawn concerning the effect on forces due to the variation of M, by itsclf. For a fixed force ratio, fr, G,/(M,U,Z) varies dircctly as hr, and in Ref 1. Fig 6, it was shown that for a parallel-plate separation of 7 granule diametcrs, the effect of hr was small for densities less 60% solids, and significant for higher densities. The author appreciates the interest shown by Professor Kimura and Dr Greenwood.

SESSION X - SOLTD LUBRTCANTS

Paiwr IX(iii) ‘A S i r n i k Motlel for Granular Lubrication; Influence of Boundaries’ by A A

Lubrecht, C Chan-Tien and Y Bcrthier (INSA. LMC, France). Dr D Schiiiiw (University of Twente, The Netherlands). Both friction. especially static friction between and fracture of the particles is neglected. Therefore, the clustering of particles, 5 to 10 particles, is severely suppressed. As a consequence the transition from a strongly fluctuating friction to a smooth fluctuating friction will occur at much higher film thicknesses. The value of it will strongly dcpend on the friction between and, for instance, the toughness of the particles. How do the authors want to copc with this real problem?

Reiilv hv Professor Ton Luhrecht (INSA, LMC. France). The basic idea is that the particle interaction laws can be extended in the future, to account for more realistic behaviour. Inter particle adhesion is one of the extensions considered, as is elastic/plastic deformation. Particle fracture is not

Pailer X (iii) “Role of the T h i r d Bodv i n Life Enhancement of MoSC by Dr Kathryn J Wahl

and Dr I L Singer (Naval Research Laboratory, Washington DC, USA). What would happen to the intermcdiate end patches if the long passes followcd the short one, such that the patch Mas traversed completely in subsequent passes?

Ananvmnits

Rcplv hv Dr Kilthrvn J Wahl and Dr I L Singer (Naval Research Laboratory, Washington, DC. USA). The questioner has proposed an interesting variation in the stripe testing experiment. While we have not done this experiment, one might espect that the end patches would be smoothed over and re-distributed to the wear track and ball surfaces. At what rate and to what estent this may occur could be dctcrmined esperimcntally. The influence of introducing additional lubricant from the previously unworn portion of the track could bc investigated as wcll.

Pill)er X (iv) ‘Significance of Transfer L a v e r s h D r v Frictianirl Al)l)liciitions’ by Dr R Holinski

(Molgkote, Munich. Germany) Professor J-M Georges (Ecole Centrale de Lyon -

LTDS. France). Does the film contain organic material? Is the filni composition constant for the different applications presented? Rei)lv h v Dr R Holinski (Molykote, Munich. Germany). The investigated transfer films only consist of inorganic solid compounds. For various applications such as carbon brushes, plain bearings and brake linings dinerent compositions have to be used because the substrate is different, varying from copper to steel. By experiments it was found

733 that tailormade additives contribute best to certain applications, which cannot be transferred to others with the same improvements.

SESSTON XI - HYDRODYNAMTC LUBRICATION Paner XI (i) ‘Pressure D r w in a Hydrostatic Pocket. Exnerimental and Theoretical Results’ by Mr M Arghir, Mr S Attar and Mr D Nicolas (Univ de Poitiers. Laboratoire de Mtc des Solides. France) Dr B Bou-Said (INSA, Lyon, France). What is the significance of the logarithmic assumption for the boundary condition? Rei~lvbv Mr M Arehir (Universite de Poitiers. Laboratoire de Mec des Solidcs, France). The authors would like to espress their appreciation of Dr Bou-Said’s discussion. In viscous flow the wall boundaly conditions for the velocity components are the non-slip conditions. This means that the fluid particles have the velocity of the wall and this constraint is introduced as a Dirichlet type boundary condition. In turbulent flow, very steep velocity gradients occur near the wall. Normally, very fine meshes are needed when integrating the flow equations to the wall. For complex flows this would imply a large number of discretisation points. I n order to have a reasonable computational effort, the esact boundary condition of the velocity component parallel to the wall is replaced by an approsiniate one deduced from the logarithmic law. This approach was first proposed by Patanker and Spalding in [ 121 and is widely used. One considers that the logarithmic law is valid at all points in the neighbourhood of the wall. It is obvious that this hypothesis is not valid close to separation zones, but one considers that the errors which are introduced are limited. The logarithmic law is used as a non-linear algcbraic equation to determine the friction velicity (u T ) and the wall derivative of the velocity relations (22c) and (22d) . The derivation of the velocity component parallel

to tlie wall is used as a Newmann-type boundary condition and replaces the Dirichlet-type one. So the integration of the momentum equation is pcrformed only to the first grid point near the boundary. which must lie in the logarithmic zone, and the grid might be coarse. P w e r XI lii) ‘At)i)lication o f the Homogenized Motlcl to Thin Film Gas Lubrication’ by Professor G Bayada (INSA, LMC, France) and Mr M Jai (INSA, Centre de Mathematiques, France) Dr B Bou-Said (INSA, Lyon, France). What is the domain of validity of your approach if you consider, for instance, 3 0 0 p m between two gas layers? Ret)lv hv Professor G Bovada (INSA, LMC, France). Thc domain of validity of this study is strictly rclatcd to the validity of the so-called modified Reynolds equation. The usual references give this validity related to the local Knudsen number (see Y T Hsia and G A Domoto paper, Asme J of Tribology, 105, p120 (1983)) for clearances as low as 0.075 microns. For smaller clearance, the rigorous derivation of a Reynolds equation is unclcar. leading for esample to the introduction of a supplementary term defined as the Boltzniann correction factor inside the Reynolds basic equation (see Y Mitsuya and T Koumura. Asme J of Tribology, 117, p430 (1995). A good knowlcdge of this corrcctor could, perhaps, enable us to perform the same asymptotic analysis to obtain a new average equation. Mr M Arrrhir (Universite de Poitiers, Laboratoire de Mdc des Solides. France). The Reynolds equation is dcduced after making very restrictive assumptions in the Navier-Stokes equations (eg small (dNds)). From this standpoint, what are the limits of the modcl employed for describing the surface roughness and deformation. Rei~lv hv Professor G Bit\fatla (INSA, LMC, France). As most of the papers related to the roughness in gas bearings deal with the modified Reynolds equation, the question of the limits of this niodcl has to be posed. A rigorous proof of thc validity of the Reynolds equation when roughness

134 is taken into account can be found in G Bayada. M Chambat, Asme J of Tribology, 111, p323 (1989). In this paper the incompressible Stokes equation is taken as a starting point and both clearance and small roughness periods are assumed. Depending on the relative ratio of these two small parameters, various asymptiotic equations, all of these of a Reynolds kind, have been derived. The same study can be performed from the incompressible Stokes equation. making clear the validity criteria of the Reynolds equation here used which is that devices must have small local slope. This assumption, although very rarely mentioned, is crucial to use the averaged equation here obtained.

Paner XI (iii) ‘Boundarv Conditions for Resnoltls Eauation with Particdar Rcfercnce to Piston Ring Luhrication’ by Mr M A Priest, Dr R I Taylor*, Professor D Dowson and Professor C M Taylor (Institute of Tribology, University of Leeds. UK; *Shell Research Ltd, Thornlon Research Centre, Cheshire, UK) Dr A 0 Mian (T & N Technology Ltd, Cawston, Warwickshire, UK). Could the authors comment on the expected behaviour of the oil film; ring and boundary conditions during the brief ‘ring lifting’ part of the engine cycle? Rcnlv bv M r M A Priest (Institute of Tribology, The University of Leeds, UK). The analysis presented in this paper considers the piston ring 10 be located on the top or bottom of the piston groove or to be free floating in between under the action of a number of large and dynamic forces. These situations are, however, considered to be quasistatic with no detailed account being taken of the axial motion of the ring and the effect this has on the lubricant film. It seems reasonable to propose that the ring lifting motion will distort the boundaries of the oil film due to the high speed of the event. Such events are, however, as pointed out in the question, brief and unlikely to have a major effect on the results of the analysis. What may prove more important in the long term is distortion of the oil film boundaries due to torsional twisting of the ring relative to the cylinder wall. The analysis is

insufficiently advanced at this stage to incorporate this effect.

P a l m XI (iv) ‘Effect of Comr)liance on the Estent of 0i)timum Comulinnt Air Thrust Bearing Oiieratinp R a n d by Mr I Iordanoff (ABG SENCA, France) and Mr P Stefan (Universite P Sabatier, Toulouse, France) Professor J F r h e (Universite de Poitiers, Laboratoire de MCcanique des Solides, France). Have you performed any experiments to enable your theoretical results to be compared with the esperimental data? Reids hs M r I lortlanoff (ABG SEMCA, France) and M r P Stefan (Universite P Sabatier, Toulouse, France). Some esperiments have recently been carried out in ordcr to compare the complete calculation with esperiniental data. By taking a nominal filni thickness between 2.5 and 3.5 p m, the complete calculation gives the masimum load carrying capacity found esperimentally. Thus, we propose to take a 3.5 p m noiiiinal film thickness (h,,) for the simple model and for the complete calculation, in order to underprcdict the real masimum load capacity.

PaiJer XI (v) ‘Esi)erimcntal Measurinp of Vclocitv Profiles in Herrinphone Grooved Journal Bcilrins’ by Dr J Absi and Mr D Bonncau (IUT Angouleme, France) Dr J L Tcvaanverk (Emerson Motor Technology Center, St Louis, Mo, USA) (i) Is the model dimensionally correct? (ie can it be scaled?) (ii) What type of boundary conditions did you use?

Rci)lv bv Dr J Ahsi and M r D Bonneau (IUT AngoulCme, France) (i) The dimensions of the model are chosen such that the Reynolds number is less than 50. The scale factor between model and reality is approsiniately 10. (ii) The boundary conditions used are the normal operating conditions, including ambient atmospheric pressure. The journal bearing functions without an esternal oil supply.

735

SESSION XI1 - COATINGS Paner XI1 fil ‘An Investigation into the Contact Behnviour of Thin Solid Coatiiws Using an Outical Techniaue’ by Dr A V Olver, Dr P M E

Cann and L C Lorie (Imperial College, London, UK) Professor J S Sheashy (The University of Western Ontario, Ontario, Canada). Can use be made of the Newton fringes down the sides of the contact to get a better estimate of the contact width? Renlv hv Dr A V Olver (Imperial College, London, UK). In principle, yes. However. in the present experiment where the layer thickncss is comparable to the contact semi-width, the location of the first dark fringe is found to be insensitive to the layer modulus. In consequence, it has not been used in the modulus determination. Dr I

L

Singer (Naval Research Laboratory.

Washington, DC, USA). How do you estract the elastic modulus (E) of the coatings from the total deflection of the wire? What model do you use? Rer)lv hv Dr A V Olver (Imperial Collcge, London, UK). This is explained in the paper. The model used was that of refercwe [2] Cole & Sayles.

-

Paner XI1 (ii) ‘Trihological analysis of Friction Damage on Coated PliIstics Through the Third B o t h Concei)t’ by Professors J Denape. P Etienne,

very high for the chosen application, but despite such conditions, the scratch resistances of our coated polymers are superior to the resistance of the base polymer given the fact that the coating reduces or even avoids the degradation mechanisms (cracking or material removal) that occur an the substrate. Similar processes for thin film coating are already industrially performed, therefore no major disadvantages could limit its commercial viability. Finally, softer base materials could take advantage of these coatings, but it must be noted that the higher the gap between hardness (or elastic modulus) of the coating and substrate, the lower the performance achieved. Dr I L Singer (Naval Rcsearch Laboratory,

Washington, DC. USA). You stated that radial cracks in colloidal coatings are due to “plastic response”. Please esplain how “plastic response” gives radial cracks. Rei)lv hv Professor J Denaile (Ecole Nationale D’Ingenicurs. Tarbes, France). We used this espression with analogy to the radial crack pattern observed on brittle materials in indentation tests. Such cracks obviously spread in an elastic stress field but their initiation starts from a limited plastic zone just below the contact zone; so these cracks are always associated with a local plastic response. In this study, the cracks qualified as radial cracks have the same morphology and follow the same behaviour as those described in indentation and scratch tests.

J Y Paris, J Phalippour and R Sempere (Ecole Nationale D’Ingenieurs, Tarbes, France).

PillIer XI1 (iii) ‘Friction and W e a r Bchaviour of a Plasmi1-SI)rilvcd Cr203 Coating in Drv Sliding Agilinst AlSJ D 2 Steel’ by Professor J E

Professor A Bid1 (University of Cape Town. South

Fernandez Rico, Y Wang and R Tucho (Ovicdo University. Gijon. Spain).

Africa). Can you state with confidence that the scratch resistance of your coated polymer is superior to the resistance of the base polymer? Is the process therefore commercially viable? Would the process work for softer base materials - eg polyethylene or polypropylene? Renlv hv Professor J Denaile (Ecole Nationale D’Ingenieurs, Tarbes, France). We can reply yes to your three questions. Our loading conditions are

Dr I L Singer (Naval Research Laboratory,

Washington, DC. USA). Please clarifjl “adhesive wear” of Crz03(at low speeds). Rei)lv hv Professor J E Fcrnandez Rico (Oviedo University, Gijon. Spain). This question is answered in parts of the paper. On page 4, Point 3.2 SEM and EDS analysis is esplained. Figures 7 and 8 show the worn surface of Cr203coatings in

736 dry sliding against AISI D2 stecl under 133N normal load at 0.25 and 0.50 nds and these figures reveal that severe steel transfer esisted. On the other hand, adhesion damage was also observed. Therefore, the wear mechanism in this case was adhesion damage to the CrrO3 coating and material transfer from the steel to the CrzO3 coating. Also on Page 7 and Figure 11 we explain the relation between the percentage of variation of adhesion, by transfer of iron to Cr203coating and the increase of speed.

SESSION XI11 - DYNAMIC EHL Paner XI11 (i) ‘Kinematics of Roughness in

EHL’ by

Dr G E Morales-Espejel (ITESM, Monterrey, Mexico), Dr J A Greenwood (Cambridge University, UK) and J L Mclgar (ITESM, Montcrrey, Mesico).

Professor R C Cov (Shell Rescarch Ltd, Thornton Research Centre, Cheshire, UK) In your simulation, do you consider the fluid to be compressible. If so, what effect does lubricant compressibility have on your results? Rei)lv bv Dr G

E Morales-Esi)eicl (ITESM.

Monterrey, Mexico). The authors would like to thank Professor R C Coy for his written question. We are certainly considering a compressible lubricant in our schcme, as can be seen in the test. However, if compressibility is equation 4. removed, equation (12) suggests that the film thickness ripples in the steady state part of the solution would be completely flattencd, producing pressure ripples of finite amplitude given by equation (8). More estensive studies of the effccts of compressibility in roughness are given in the references IS], [ 6 ]and [ 101.

Paner XI11 (ii) ‘Influence of the Slitling Si~eed on the Elastohvdrodvnamicnllv Luhricated Film Thickness Shaile of Waviness Contacts’ by Mr F Couhier. Professor A A Lubrecht, D Nclias and

Professor L Flamand (INSA, LMC, France)

Dr J L Tcvaanwrk (Emerson Motor Technology Center, St Louis, Mo, USA). From a practical point of view, is the different roughness frequencies of the ball and race partially responsible for non-repetitive run-out?

Renlv hv Professor A A Lubrecht (INSA, LMC, France) I would espect that “roughness” effects get effcctively damped (averaged) by the contact size itself. Consequently, I would suspect features with wavelengths larger than the contact size, since they might also have more important amplitudes. Dr J A Grccnn.ood (Cambridge University, UK).

I believe that I understand the origin of components of the film thickness with differcnt spatial wavelengths: but can you explain how the presence of an (H’)term in the Reynolds equation in the iiilct can lead to a second harmonic in the Fourier analysis with respect to time? (If the flow ratc is ( I +

r =(I

+

3

E

coso) I)’, thcn:-

2) +3& (I +

3E

- cos2ot

$)

cosot+

E3 +cos3wt

2 4 Ignore the constant flow. (3 E coso t) is the hndamcntal cscitation. The second harmonic is a a factor ( - ) smallcr. but is not negligible. The third 2 E2

harmonic - is smallcr and can be ignored). 12 Rei)lv hv Professor a A Luhrccht (INSA, LMC. France). The authors would like to thank Dr Greenwood for his comments.

P a l m XI11 (iii) ‘Surface Rouphness Modelling for Piston Ring Luhricatian’ by Dr M Visscher,

Professor D Dowson and Professor C M Taylor (Institute of Tribology, Department of Mechanical Enginecring, The University of Leeds, UK)

737 Professor J-M Georges (Ecole Centrale de Lyon. LTDS, France). I would like to know how you take into account the isotropy of the roughness due to the running process. Reillv bv Dr M Visscher, Professor D Dowson and Professor C M Tavlor (Institute of Tribology, Department of Mechanical Engineering, The University of Leeds, UK). The procedure is described in the paper. However, Professor Georges probably refers to the change in the roughness texture of the cylinder liner due to the wear process, which will change the lubrication conditions and therefore the piston ring friction. This must be taken into account when predicting the piston ring performance over the engine’s life cycle, which subject is currently under investigation at the University of Leeds. The experiments by Radcliffe (1993), referrcd to in the paper, were performed in a motored engine, rather than a fired one, and at relatively low load, so that the wear rate over the engine’s run time was negligible. Under normal firing conditions, vertical grooves may develop in the liner surface while the original honing marks may disappear, as shown in experiments by Barber and Ludenia (1987). In that case, the surface topography may become very anisotropic. Then, the Patir and Cheng average flow model can still be applied. as it accounts for anisotropy. On the other hand. there may be a problem with the Greenwood and Tripp contact model, which assumes isotropy. It is, however, expected that the grooves themselves are not important for the asperity contact problem, but smaller scale asperities present on the larger scale grooves. These asperities will be anisotropic as well (as are all individual asperities, see Greenwood, 1992) but McCool (1986) showed that the simpler models, which assume isotropic roughness, can still be used with confidence. References: Barber, G C and Ludema, K C, 1987, “The Break-in Stage of Cylinder-Ring Wear: A Correlation between Fired Engines and a Laboratory Simulator”, Wear, Vol 118, pp.57-75 Greenwood, J A, 1992, “ Problems with Surface Roughness”, Fundamentals of Friction: Macroscopic and Microscopic Processes (Proc

NATO Adv Study Inst on Fundamentals of Friction). NATO AS1 Series E: Applied Sciences, VOI220, ~ ~ 5 7 - 7 6 McCool, J I, 1986, “Comparison of Models for the Contact of Rough Surfaces”, Wear, Vol 107, No 1, ~~37-60. Dr R I Tavlor (Shell Research Limited, Thornton Research Centre, Cheshire, UK). To obtain a Gaussian distribution, you neglect the deep valleys ie the honing marks on the liner. However, the honing marks are crucial to the efficient operation of the piston. Is it reasonable to ignore these deep valleys? Reillv hv D r M Visscher. Professor D Dowson and Professor C M Tnvlor (Institute of Tribology, Department of Mechanical Engineering, The University of Leeds, UK). It is important to distinguish between friction effects and lubrication. It is well known that the honing marks are important for lubrication, the general concept being that they provide reservoirs of lubricant. Our paper addressed the problem of friction and power loss predictions. taking account of the highly nonGaussian surface topography of cylinder liners. The direct influcnce of the deep grooves on friction is negligible.

P a r w XI11 (iv) ‘A Numerical Solution of Elastohydrodvnamic Analysis of Hieh Pressure Sleeve Seal’ by Dr H Xu, Dr P L Wong (The City University of Hong Kong, Kowloon, Hong Korrg) and Professor Z Zhang (Shanghai University, China) Dr C Radcliffe (Institute of Tribology, Department of Mechanical Engineering, The University of Lecds. UK). (i) What material is used for the shaft and seal? (ii) What is the critical static clearance between shaft and seal? Renlv bv Dr P L Wong (The City University of Hong Kong, Kowloon, Hong Kong). (i) The shaft is normally made of high strength materials such as high speed steel and WC, whilst the material for the sleeve is usually beryllium bronze for its superior elastic and anti-scuffing properties. In our present analysis, we chose a

738 steel/steel combination for the materials of the shaft and sleeve. (ii) For a given structure and under given operating parameters, there must be an optimum initial clearance which gives lowest leakage and no metal-to-metal contact for the high pressure sleeve seal. On the other hand, if an initial clearance is fixed, there is a critical pressure beyond which metal-to-metal contacts will occur. Due to the shortage of numerical results, the determination of the initial clearance is usually based on the manufacturers’ own esperiences. Hence, the seal is easily worn out.

Parler XI11 (v) ‘The Evaluation of the Minimum Film Thickness in Bdl-Plirne Irnimt Exneriments’ by Dr I Musca. T Morosanu and E Diaconescu (University of Suceava, Rouniania). Professor B 0 Jacobson (SKF Engineering & Research Centre, BV, The Netherlands). Do you know the surface roughness of the impacting ball and the impacted flat? How rough are they compared to the estimated film thickness? Renlv bv Dr 1 Muscr (University of Suceava. Roumania). The balls used for the impact esperiments are typical ball bearing balls. The roughness Ra is 0.1-0.2p m. The flat surface is very highly polished and the roughness can be neglected. The theoretical calculation assumes zero roughness on the contacting bodies. If the film thickness is less than the cuniulated roughness of the bodies, metal-metal contact occurs and the oscillogramme changes. All esperi ments whcre direct contact was observed were eliminated. The calculated values of the film thickness are greater than the roughness value. Professor D Dowson (Institute of Tribology. Department of Mechanical Engineering, The University of Leeds, UK) and Mr R Larsson (Division of Machine Elements, LuleA University of Technology, Sweden). The authors of this paper describe an interesting esperimental method to measure the minimum film thickness during ballplane impacts. They measure the maximum capacitance during the impact and compute the corresponding film thickness by assuming the

solids to be deformed in a Hertzian manner. The latter assumption does not, however, reflect the shape of the solids during lubricated impact. It is now known 11-41 that a ‘dimple’ forms at the ccntre of the contact. The assumption of a Hetzian flat film shape can thus lead to some discrepancy in the derived minimum film thickness. The authors kindly provided data from their experiments and we have been able to simulate some of the experiments numerically. The theoretical minimum film thickness h,, and the theoretical film thickness profile were obtained. This profile was then used instead of the Hertzian shape to give a better estimate of the minimum film thickness from the capacitance readings in the different experiments.

Thcoretical Motlclling The analysis of an elastic ball impacting onto a lubricated plate is described in references [2,3] and will be repcated only briefly here. Reynolds equation. the film thickness equation and the ball’s equation of motion are solved transiently. The computation starts whcn the ball just reaches the lubricant layer and continues until the ball has impacted and rcboundcd. The lubricant was assumed to be Newtonian, having a viscosity-pressure relationship according to the Roclands equation. The density-pressure relationship adopted was the same as that described by Musca et al. The surfaces of the ball and the plate were assumed to be perfectly smooth and to deform according to linear elastic theory. Isothermal conditions were assumed to previal. The theoretical capacitance was derived from the film profile. Tlic shape of this profile was retained and h,, was adjusted until theoretical and experimental capacitances coincided. The permittivity of the lubricant was derived from the theoretical pressure distribution. Results Espcriments 1.1 to 1.6 have been simulated. All these cases implied pure impact with an entry velocity varying between 1.50 and 3.43 d s . The ball radius was 5.555 mm and the mass was 5.64g. The lubricant viscosity was 0.1 Pas and the pressure-viscosity coeflicicnt 1.5 s lo-* Pa-’. The effective elastic modulus of both surfaces was assumed to be that for steel, 23 1 GPa.

739

Figure 1 shows the minimum film thickiiesscs at different impact velocities. For comparison the experimental results of Musca et a1 have been added. It is seen that an increase in impact velocity causes the theoretical minimum film thickness to increase slightly. The experiments give the opposite effect. Figure 2 shows a comparison between tlie nieasured maximum capacitance and the theoretically derived capacitance at the point of time where h,, occurs. The increase in impact velocity causes an increase in capacitance for both cases. It should be noted that maximum theoretical capacitance does not occur at the same time as h,,,. Masimum capacitance will, in these cases. occur somewhat earlier, at tlie time that the impact force reaches its maximum. Since these espcrinicnts are performed with relatively high impact velocity the impact is almost pcrfcctly elastic and the phase shift in time between niasimum impact force and minimum film thickness is small. Consequently, there is a small difference between the niasirnum capacitance and that at whicli h,,, occurs. Figure 3 shows the effect of using the theoretical film thickness profile instead of that of the Hertzian flat. The minimum film thickness has been adjusted to give a theoretical capacitance cqual to the measured capacitance. It is seen that the dimple causes a reduction of h,,,,. That is cxpectcd, since the central region of the contact gives a small contribution to the capacitance than that of the corresponding Hcrlziari flat.

1.5

2 2.5 Impact velocity [ d s ]

3

35

Figure 2 Esperiinental and Theoretical Capacitance

I

41

J 1.5

2

2.5

3

3.5

Impad wloclty [ d s ]

Figure 3 h,, Derivcd from Hcrtzian Flat and the Tlicorctical Film Thickness Profile

0.5

t

1

1.5

2

2.5

3

I 3.5

Impad velocity [Ws]

Figure 1 Experimental and Theoretical Minimum Film Thickness

D i scu ssi an As seen i n Figure 1 thcre is one serious difference bctween tlie values of h,, derived from the authors’ assuniption of a Hcrtzian profile and those based upon the computed film shapes in that the former suggests that tlie minimum film thickness should dccreasc as tlie impact velocity increases, whcreas adoption of the theoretical dimple profile shows the opposite effcct. The phenomenon cannot, howcver. be explained by the adaptation of the assuniption of a Hertzian flat (Figure 3). It should. however. be pointcd out that the test

740 conditions are severe, with very high impact pressure (>5 GPa). Plastic flow is likely to have taken place during the impact and in that way it is impossible to make proper theoretical predictions with a linear elastic model. The composite dielectric coefficient is another uncertainty. The influence of the outer regions of the contact is quite large at the lower impact velocities. In that region there is a misture of oil and air and it is not easy to find out what the correct oil and air fractions are. The ball squeezes some oil out to the outer regions during its impact and the lubricant layer becomes thicker than it was initially. Cavitation seems to play a minor role. The importance of taking account of the dimpled film shape in the interpretation of capacitance readings is shown in Figure 3. The assuniption that the shape of the gap between the solids is given by the corresponding Herlzian ‘flat’ solution for dry contact can over estimate the minimum film thickness by at least 40 percent and by as much as 200 percent at the highest impact velocities, over the range of conditions considered. References: (11 Dowson, D and Jones, D A ‘Lubricant

Entrapment between Approaching Elastic Solids’, Nature, 2 14 (1967). 509 I , pp9-17-948. [2] Dowson, D and Wang, D ‘An Analysis of the Normal Bouncing of a Solid Elastic Ball on an Oily Plate’, Presented at Nordtrib ‘94, Uppsala, Sweden, June 1994. [3] Larsson R and Haglund E ‘Numerical Simulation of a Ball Impacting and Rebounding a Lubricated Surface’, 1995, ASME J of Tribology, Vol 117, No 1, pp94102. [4] Dowson D and Wang D ‘Impact Elastohydrodynamics’,Proceedings of the 2 1st Leeds-Lyon Symposium on Tribology, ‘Lubricants and Lubrication’, Elsevier, Tribology Series 30, pp565-582. Renlv bv Dr I Musca (University of Suceava, Roumania). I would like to express my appreciation of the very interesting discussion by Professor D Dowson and Mr R Larson. The main objective of the paper was to present the method of film thickness evaluation. It is obvious

that the oil affects the film shape and thickness. So this discussion permits a more realistic evaluation of film thickness.

SESSION XIV - INVITED LECTURES Pawr XW (i) ‘HOWLubricants Behave in EHL COntiIctS’ by Professor B 0 Jacobson (SKF, ERC. Nieuwegein, The Netherlands) Dr J L Tcvaanverl< (Emerson Motor Technology Center, St Louis, Mo. USA). This is very nice and elegant work that will provide much needed insight into roughness and sliding effects. A question I have is, if there is some mechanism whereby the film can be re-built while the asperity in question is in the contact? Are there some surface topographies that lend themselves more towards this re-building of the film than others? R e ~ l vhv Professor B 0 Jacobson (SKF, ERC, Nieuwegein, The Netherlands). As far as I understand. the only way to relubricate an asperity in nietal-to-metal contact with the opposite surface during its passage through the Herlzian contact is to decrease the local asperity contact pressure. If a high top in the surface structure of one of the surfaces slides down into a valley in the other surface, the local pressure might decrease so much that a Newlonian type of behaviour of the lubricant can make it possible to entrain some lubricant under the asperity top. For this to happen it is necessary that some oil is present in the surface structure valley, and that the pressure there is below the glass transition pressure at the local temperature. It is further necessary that both surfaces in contact have similar surface roughnesses as otherwise the rough surface asperities will break through the oil film and daniage the smooth surface. After such a collapse of the rough surface asperity lubrication, the pure sliding without squeeze motion will not be able to re-establish an oil film. It seems thus that if the surfaces were very smooth and similar in structure, it might be possible to

741 “relubricate” a collapsed surface aspcrity if the local pressure is below the glass transition pressure.

Paner XIV (ii) ‘Elastohsdrodsnamic Films with Emulsions’ by Professor Y Kimura, K Okada and

W Liu University of Tokyo, Japan) Dr P Cann (Imperial College, London, UK) (1) In the entrapment model do you assume that

the emulsion particle size distribution is the same in the inlet as in the bulk, so that there is no ‘filtering’ of particle size? (2) What is the effect of rolling spccd on the experimental film thickness results and the agreement with the model? Rei)lv bv Professor Y Kimiirn (University of Tokyo, Japan). The authors appreciatc instructive comments of Dr Cann on our work. Although several EHL theories with emulsions have been proposed which show reasonable quantitative agreement with experimentally dctcrniincd minimum film thicknesses. direct observation of the behaviour of the particles of the disperscd phase has been reported only for liniited conditions. The following comments are based on them. With O/W emulsions, Nakahara et al found that the behaviour of oil particles in the inlet region to an EHL conjunction can be classified into tlirce groups [ 5 ] . The particles in the first group, the “penetration droplets” in thcir terminology, are entrained into the conjunction. Those in the second group, the “stay droplcts”, are staying at certain locations and those in the third group, the “reverse droplets” go back after reaching certain proximity to the conjunction. According to tlicir results, the first and the second group contain particles of similar diameter ranges, whilc the third group is composed of slightly smallcr particles. If this can be assumed, the “filtering” the discusscr mentioned takes place by expelling smaller particles. However, the fact that the differences in the particle diameters between the groups are slight and that the smaller particles are espcllcd, which means their volumetric contribution is smaller, suggests that the effect of the “filtering” on the film thickness is small, if any. No results of

obscrvation of watcr particles in W/O emulsions in the EHL inlet rcgion are at hand. Eflects of the entraining speed on the EHL film thickness is an interesting problem. Actually Zhu et al [S] rcportcd that the minimum EHL film thickncss with O/W emulsions decreased at higher speeds, and discussion by Schmid and Wilson on their paper pointcd out that the decrease was due to starvation common to the case with a single phase lubricant. Although the present authors have not esperimentally esamined the speed effect, two other reasons for the decrease at higher speeds in the film thickness in EHL with O/W emulsions can be conceived. One is the possible change in the initial cniulsion concentration. In the present and otlicr analyscs it has bcen assumed that the emulsion conccntration is kept constant at the far upper strcani. Whilc the speed is low, the flow in the greater inlct rcgion may be laminar. This means the coming-in and the reverse flow make scparate strata, and the assumption holds. At higher specds, turbulence must start at the upper stream where the film thickness is large, and mising of the rcjcctcd water and the supplied emulsion niay occur, gradually decreasing the initial oil conccntration. The other reason is the effectiveness of thc trapping of oil particles by lipopliilic surfaccs at higher speeds. Even though the film thickncss bccomes equal to or smaller than the diameter of a particle causing tentative trapping, a high shear rate in the film might “untrap” the particle to be escluded together with These, of course, necd the smaller oncs. espcriinental confinnation.

SESSION XV - SURFACE DEGRADATIONS P w e r X V (i) ‘Smoothing Effect of the Third Both Comi)action on Aluminit Surface in Sliding

Contact’ by Mr K Adachi, Professor K Kato and R Takizura (Tohoku University, Japan). Dr I L Sinver (Naval Research Laboratory, Washington, DC, USA). Have you identified the

742 3rd bodies that result in smoothing of Al2O3 i n water at 20°C?

Rei~lv bv Mr K Adachi (Tohoku University, Japan). Yes, we have identified smooth wear surface of alumina in water at 20°C, which is composed of worn alumina grain and agglomcrated third bodies. Figure 7 shows one example of a smooth worn surface obtained under such conditions. In Figure 7,the convex part corresponds to worn alumina grain and the other part corresponds to agglomorated third bodies, as we show in Section 3.2. Furthermore, each representative phenomenon as shown in Figures 6(a) and (b). have also been observed.

PaiIer XV (ii) 'Friction in Abrasion of Aluminit Fihre and Silicon Carbide Particle Reinforced Aluminium' by Dr N Asen (Dcpartmcnt of

Materials Science, University of Cambridge. UK) Dr A Olver (Imperial College, London, UK). Does the protuberant reinforcing phase beconie subjected to a locally higher pressure and what is the influence, if any, of local elastic dcflcctions?

Reilly bv Dr N AsCn (Department of Materials Science, University of Cambridge, UK). It should first be pointed out that the study is on steady-state wear and friction. I would find it reasonable to assume that the pressure distribution over the phases changes during an initial wear pcriod eg because of the building up of protuberances. but this is not what we have studied. The idea behind the model work is that during steady-state wear there should be a stable (but maybe not even) load distribution bctween the phases. For the prediction of the tribological properties of a multiphase material in a certain tribosystem, the load distribution is considcrcd as fundamental a parameter as the wcar resistance and friction values of the phase materials. With this viewpoint, protruding phases are a result of the load distribution, not vice versa. As far as I understand, it is not obvious to predict the load distribution for a certain tribosystem. A more wear resistant phase protruding over another,

possibly taking a higher load fraction as the question suggcsts, is one mechanism affecting the load distribution, but far from the only one. As dcscribed in the paper, also the type of abrasives used, the matrix hardness, and also the stiffness of the countersurface etc, all influence the load distribution. I have had to satisfy with studying the direction of inllucnce from some of these parameters. However, under the assumptions of our load distribution model, presented in Refs 7 and 17, the load distribution can be derived from measured wear or friction results. The procedure to do this is described in a paper by Hutchings and myself, to appcar in Materials Science and Tcchnology. It is an assumption in the model that the intrinsic material propertics are the same when tested individually as when tested as a phase in a composite. This includes the elastic properties, which the sccond part of the question concerns. It is my feeling that this is a reasonable assumption for elastic properties. The fracture toughness of eg a metal matris can, however, quite clearly be influenced by the introduction of brittle reinforcements (Ref I), something the model fails to describe. Dr J A Williams (Department of Engineering, Univcrsity of Cambridge, UK). On your final slide you show a range of values of p from 1 to 2. What physical mcclianisms lead to such high values bctween the abrasive and specimen surface.

N A s h (Department of Materials Science, University of Cambridge, UK). This question is really based on a misunderstanding of the figures on that slide. I have therefore decided not to give an answer to the question. Rci~lvhv Dr

Pitl)cr

XV (iii) 'Adhered Film Formation on

Surface hv 1mi)inecment of H a r d P;ii-ticles' by Mr N Hayashi, Y Kagimoto and H

Steel

Akiyama (Mitsibushi Heavy Nagasaki. Japan)

Industries Ltd,

Professor T H C Childs (Institute of Tribology, Department of Mechanical Engineering, The University of Leeds. UK). You say that if (R) and (v) are too large. the protective film is fractured

743

and wear protection is lost. I wondcr if another explanation is that the protective film is not formcd in the first place? I have in mind the spalling of hard coatings:if the coating is too thick, elastic energy is enough to fracture an adhering intcrface. Perhaps at large (R) and (v), fractured fragments of hard particles become larger (perhaps larger than l O p m thick) so that they spall from the soft surface almost as soon as they are formcd?

Rci~ly hv Mr N Havashi (Mitsibushi Heavy Industrics Ltd. Nagasaki, Japan). As we described in the paper, the wear rate I showed was a converted value, considering the difference of particle supply rate. The densities of the particles we used in the tests were almost equal. So the ranking of wear rate does not change by the change of the unit from p ndhour to pn3/ g .

Renlv bv Mr N Hayashi (Mitsibushi Heavy Industries Ltd, Nagasaki, Japan). In our synopsis we showed the data obtained by the test using large foundry sand (average particle diameter was about 7 5 p m ) as eroding particle. And the contcnts of Si, the main chemical component of particle, on the worn surface decreased if the impingcmcnt velocity increased. When we perfornicd the tcst using ash of coal as eroding particle undcr same velocity condition, however, the contents of particle components was smallcr than the contcnts using foundry sand. So we thought that the mechanism of wear was fracture of adhered film when we used the foundry sand. We observed the cross section of the worn surface eroded by foundry sand, and found the crack forniation i n the film.

P a i w XV (iv) ‘The Wear Mechanism of Ductile Mctals hs S1urrics:Fatime or Ratchetting’ by Professor A A Torrance, B Crosby and Y Yang (Trinity College, Dublin, Ireland)

We have never performed the test under vcry large particle impingement energy which cause the fracture of particle at first. But the data of the foundry sand tcst suggests that if particle impingement energy become larger thc aniount of adhesion become smaller. So there is a possibility that if impingement energy is very large the fracture of particle occur bcfore the formation of adhered film. Professor A Bill1 (Dcpartment of Materials Engineering, The University of Cape Town, South Africa). Your use of wcar dcpth per hour ( p d h o u r ) for two materials and two particle diameters could be confusing. It is normal to use volume loss per mass of erodcnt ( 1 . ~ 1 1 1/ ~g) to eliminate density differences of the targct materials and differences in feed rates for thc diffcrcnt erodent particles. How would your conclusions be changed if you used these units‘?

Dr J A Williains (Dcpartment of Engineering, Univcrsity of Cambridge, UK). Do you see the mcclianisms of cyclic fatigue and ratchetting as bcing esscntially cooperative or competitive? Both involve the introduction and accumulation of damage - dislocations - within the material. Would we espcct different dislocation structures within the specimen from each mechanism? Rci)lv bv Prafessor A A Torrance (Trinrty Collcge. Dublin, Ircland). In our wedge tests we have attcmptcd to achieve plane strain, with a stable plastic wave ahcad of the wedge. However, Kapoor and Johnson [ I ] have argued that ratchetting is to be espcctcd when straining the surface causes it to estrude over an “edge”, for esaniplc the sidc of an aspcrity. The set-up of the wedge test probably prevented such conditions arising - hence wcar was mainly by fatigue, and the wear particles wcre quite large and thick [2] in contrast to the “filmy” particles envisaged for ratchetting [ I ] . I n contrast, the conditions of the abrasive wear tcsts allowed straincd material to flow i n any dircction. thus pcriiiitting the estrusion ncedcd for ratchctting. Rcfcrcnccs: 1. Kapoor, A and Johnson, K L, “Plastic Ratchctting as a Mcchanism of Metallic Wear’ Proc Roy SOCLondon, A, 445( l994), 367-38 1. 2.Torrance. A A and Zhou, F, “Fracture Modes in Wear Particle Forination”, Proc 20th Leeds-Lyon Symposium on Tribology, Elsevier, Ed. D Dowson and M Godct. 1994. 521-529.

144 P a l m XWv) ‘Surface Deeratlation and Third Bodv Formation in Trihocorrosion Svstenis’ by Dr S Mischler, S Debaud, E A Rosset and D Landolt (EPFL, Lausanne, Switzerland) Professor J-M Georves (Ecole Centrale de Lyon, LTDS, France). What is the thickness of the passive film? Is this film removed or not?

Renlv bv Dr S Mischler (EPFL, Lausanne, Switzerland). The passive film thickness on stainless steels lies usually between 2nm and 2nm. The very high corrosion rate observed during rubbing indicates that the corrosion protection efficiency of the passive film becomes smaller. This may occur either by total passive film removal (at least locally) with subsequent esposiire of reactive metal or by thinning of the passive film as a consequence of wear. The relative iniportance of these two possible mechanisms is at present not known. One of our PhD students is trying to quantify the increase in current due to each of these mechanisms by using a numerical model which describes the passive film formation by considering two separate steps ie the nucleation and the growth of the passive film. By comparing the simulation with the experimental observations we hope to be able to answer in more detail your second question. Professor A Ball (Department of Materials Engineering, University of Cape Town, South Africa). Is it possible that your observcd increases in mechanical loss under passive coiiditioiis are due to abrasion by particles of the Cr203 passive film itselfl It would be interesting to investigate the effect of reducing the frequency of oscillation and do similar esperiments on mild steel. Have you considered these situations?

RCIIIY bv Dr S Mischler (EPFL, Lausanne, Switzerland). 1 cannot give a dclinitive answer to your first question. However, in this particular case there are some points indicating that two body abrasion occurs at the passive potential. The width of the grooves observed in the wear track lies typically in the range 0.5-1 p m and thcrefore the size of the abrading bodies is expected to be in the same order of magnitude. However we could not observe any wear debris even of this relative large

size whilst the roughness of the alumina pin (Ra 0.7 p m) correlates well with the obsewed groove Of course these considerations are width. speculative and, in general, your question remains open. We have not carried out low frequency experiments on mild steel yet. However, at 5 HZ we observed on mild steel in the passive condition a current density under rubbing by two orders of magnitude more important than with the 3 16L steel. This can be esplained by the fact that the passive film formation on mild steel is much slower than on 316L steel, so that the mild steel has no time to repassivate between the strokes and thus remains very reactive. By adequately reducing the frequency it should be possible to observe the repassivation of mild steel between two strokes.

Pi1t)er XV (vi) ‘Modellinp Fluid Interactions in Magnetic Fluid Grinding or Snot the Third Both’ by Professor T H C Childs and Mr F Y Chang (Institute of Tribology, Department of Mechanical Engineering, The University of Leeds)

-

Dr J A Williams (Department of Engineering, University of Cambridge, UK). If the function of the magnetic field is only to provide the load on the balls and float and to counteract gravity, why not invert the rig and use gravity to provide the positive load? Professor F E Kennedy (Dartmouth College, Hanover, NH,USA). What role does the magnetic field play in your model? Renlv hv Professor T H C Childs (Institute of Tribology, Department of Mechanical Engineering, The University of Lecds, UK). “Why cannot one invert the rig” is a very good question. Maybe one can, and we are carrying out a series of alternative studies ourselves. The fact is that variants of this type have not to date proved successful. I believe the magnetic fluid fulfills some subtle secondary feaatures. If one calculates the compliance of the float in the fluid, one finds the magnetic forces create an extremely soil spring system. Maybe this is important to avoid damage at the high sliding speeds involved. In the current version, the grinding grits are also prevented, by magnetic

745

-

levitation, from settling out one might of course introduce grits into the system in other ways than by magnetic suspension. As far as the role of the magnetic fluid in the modelling is concerned, it provides the contact loads and it has a viscosity: that is all. There are no aspects of magnetic fluid dynamics.

SESSTON XM - FRICTION Paner XVI (i) 'A Justification of Friction Law' by J F Ganghoffer, Professor A Brillard and J Schultz (Universite Haute Alsace, Laboratoire de Math, Mulhouse, France) Professor F Sicloroff (Ecole Centrale de Lyon. LTDS, France). (1) Do your results remain true in the limit z + l? In this case you should recover Tresca's condition for friction. On the other hand, with this kind of physics it seems to me that you will never get a friction condition involving the normal stress, like Coulomb's. (2)What is the fundamental reason for your using the Hellinger Reissner variational principle instead of the classical one? Rei~lvhv Professor A Brillard (Universite Haute Alsace, Laboratoire de Math, Mulhouse, France). (1) When the exponent q of Norton's law tends to infinity, one recovers Tresca friction condition, as shown by Licht ('Un probltme d'elasticite avec frottement visqueux non-lineaire', Journal de Mecanique theorique et appliquee, Vol 4, N"1, 1985, pp15-26). Indeed, the friction law reads as

I- I

bounded, one must have o now

if

less than one. If

10 "1 = 1 , one recovers Tresca friction law, ie

h , o ';'= [u:

]

. With this respect, Norton's

law does not involve any threshold condition. When considering a thin fluid layer, it is clear that one recovers only one part of Coulomb's friction law, since the threshold condition involving the normal stress must be added as a postulate in the original equations, imposing for instance that sliding will occur when the deviatoric part of the energy stored within the layer will exceed a fraction of the hydrostatic part. At the limit, I think one shall recover Coulomb's threshold. Lastly, the unilaterality condition is here verified in a strong sense, due to the incompressibility of the third layer and since we do not consider situations in which the two solids and the third body might not be in contact. (2) The reason for using a mised (HellingerReissner) variational formulation is that the derivation of the limit solution through an asymptotic espansion (when the thickness of the third layer tends towards zero) involves less technical effort, compared to a one field forinulation. This can be attributed to the fact that the mised formulation places an equal weight on displacement and stresses. P a l m XVI (iii) 'Effects of Thin Laver on Friction and Wear of Cast Iron Under Severe Sliding Conditions' by Professor K Kayashi, K Hirasanta, K Yamamoto and K Sugita (Osaka Sangyo University, Japan) Professor F E Kennedy (Dartmouth College. Hanover, NH, USA). (1) Can you comment on the wear of the mild steel disk? Was it measured? (2) Have you tried to relate coefficient of friction and wear rate to contact temperature? Ret)lv hv Professor K Havashi (Osaka Sangyo University, Japan). (1) The cast iron pin was harder than the mild steel disk under the condition of room temperature. So, for a while after starting of sliding, namely in the mild wear region, the wear amount of the mild steel disk might be larger than that of the cast iron pin. But the temperature of the cast iron pin near the sliding surface rapidly went up with the

146

increment of sliding distance and its hardness remarkably fell down because of the high sliding speed and the high contact pressure. In this condition, the wear rate of the cast iron pin notably increased and the mild steel disk might be no longer worn (the severe wear region or so-called thermal wear region). Though we did not measure the wear of the mild steel disk in detail because we focussed on the thermal wear of the cast iron pin in this paper. In the next step, however, we think that the more detailed investigations of the wear of the mild steel disk will become necessary. (2) the exact contact temperatures could not be directly measured in the present experiments. Instead of them, we measured the temperature rises of the side surface of the cast iron pin near the sliding surface by using the infra-red imaging system. The relations among the coefficient of friction, the wear rate and temperature of the cast iron pin near the sliding surface have been discussed through the variations of thickness of “the fluidity layer” in this paper.

Paner XVI (iv) ‘An Elastic-Plastic Model with Adhesion for the Sphere-FliIt Contact’ by Professor A M Tudor and L Seiciu (University Politechnica Bucharest, Roumania). Anonymous How do you explain micro stick slip? Rei)lv by Professor A M Tudor (University Politechnica Bucharest, Roumania). The micro stick-slip phenomenon is explained in Sections 4 and 5 of the paper.

SESSION XVII MIXED/BOUNDARY LUBRlCATlON Paner XVII (i) ‘Influence of Materiids on Lubrication in Ameous Solutions’ by Dr S Mischler, Dr E Rosset and D Landolt (EPFL, Lausanne, Switzerland)

Dr J A Greenwood (University of Cambridge, Engineering Department, Cambridge). My very limited experience of measuring wetting angles is that the answers are highly variable as bad as trying to measure wear. Can you really say with conlidence that your materials were wetted or not in the tribometer? Is there the possibility of changing the answers by using a wetting agent? No response received.

-

Paijer XVII (ii) ‘An Examination of Additive Debris to Give Insight into Boundary Lubrication’ by Professor J S Sheasby, T A Caughlin, S Terranova and A Cohen (University of Western Ontario, Canada) Dr R J Smallev (SKF Engineering & Research, Nieuwegein, The Netherlands). Could you give some idea on the mechanical properties of the additive film debris? Rci)lv bv Professor J S Sheashv (University of Western Ontario, Canada). No measurements have been made yet, however an IFM is under construction to do just this.

Dr S Mischler (EPFL, Lausanne, Switzerland). what are the chemical reactions leading to the formation of the “good’ third body? Rei)lv hv Professor J S Sheashy (University of Western Ontario, Canada). The chemical structure of the ZDDP antiwear material is the best understood although the reaction path to its formation is contentious (P A Willermet, D P Dailey, R 0 Carter, P J Schmitz and W Zhu ‘On The Meclianisin of Formation of Antiwear Films from Zinc Dialkyldithiophosphates’, to be published). The nature of the antiweear material formed from the other additives has yet to be established. Dr J A Greenwood (University of Cambridge, Engineering Department, UK). You examined the wear scars on the first body and sometimes found a bare scar: but can you say there was no film on the second body?

Renlv bv Professor J S Sheashy (University of Western Ontario, Canada). Scars on the first body were in fact never bare, though they could appear that way by optical microscopy and conventional SEM. Second body scars have not been examined as critically, but so far appear similar to those on the first body. Paiwr XVII (iv) ‘The lnflucnce of Plastic Bulk Deformation on Surface Roughness and Frictional Behaviour During Deei) Drawing Processes’ by Mr H Lubbinge, R ter Haar and Dr D Schipper (University of Twente, The Netherlands). Dr J A Greenwood (University of Cambridge. Engineering Department, UK). I share Professor Lubrecht’s worry about the different results from and area (k).If the profile studying profile (h) heights were taken as a slice of the area results. then the only possibility seems to be in the different datum lines used: the mean line for the profile and the mean plane for the area measurements. It seems possible that a wavincss on the scale of the area might well lead to different datums and so esplain the diffcrences - especially recalling that the overall changes were not large.

Rei~lvbv Ir H Luhhinw (University of Twente. The Netherlands). There are mainly two reasons for the differences between the profile and the surface measurements. Firstly, by taking a slice of the area for calculating the & profile, the mean line indeed differs from the overall mean plane of the surface h. Secondly, there is a large difference between the number of datapoints used for calculating the R, profile and the R, surface. Despite the fact that for the profile measurements nine measurements were performed and for the area measurements only five measurements, the number of datapoints used for the area measurements is much more (one surface measurement corresponds with 693 12 datapoints, one profile measurement with 3 17 datapoints). When comparing the R, profile measurements with the surface & measurements, for the profile measurements therefore a much higher scattering (standard deviation) on the mean value is shown.

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LIST OF DELEGATES

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75 1

22nd LEEDS-LYON SYMPOSIUM ON TRIBOLOGY ‘The Third Body Corrcrpt :Ititrrpretatiort of Tribological Plie~ionierra’ Lyon 5th - 8th September 1995

List of Delegates Title Name Dr ABSI J.

Affiliation I.U.T.dA1igoul2ine Dept. Genie Mecaiiique 4, avenue de Varsovie 16021 blgoLlice France

Title Name Mr

ARGHIRM.

Mr

LABORATORY OF TRIBOLOGY School of Mechaiiical Engineering, Tohoku (Joiversity 980 77 Seiidai Japan

Mr

ARMBRUSTER M. AEROSPATIALE 37 Boulevard de Montinoreiicy 7578 I Paris cedex 16 France

IJNLEVER RESEARCH Port Sunlight Laboratory Quarry Road East L63 3.W Bebington, Wirral

Mr.

ARTEROR.

ADACHIK

Prof ADAMS M.

Affiliation Laboratoire de Mecanique des Solides SP2MI BD 3 T e k p ~ r2t - BP 179 86960 Futuroscope France

INSA LYON Laboratoire de Mecaiiique

des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

IJK Prof ANDRADEFERREIRA L

DEMECiVFEIJl’ Rua dos bragas 4099 Port0 codex Portugal

Mr

AUSLANDERF.

ECOLE CENTRALE DE LYON LTDS B.P. 163 69 I3 1 Ecully cedex France

Ms

IMPERIAL COLLEGE Departineiit of Mechanical Engineering Exhibition Road SW7 2BX London 1J.K.

Dr

AXE”.

IJNIVERSITY OF CAMBRIDGE Dept. of Materials Science and Metallurgy CB2 342 Cambridge UK

I JCB DCpt. de Physique des MatCriaux 43Bld. d u I I . N o v . 1918 69622 Villeurbaiuie cedex France

Mr.

BAILLETL

WSA LYON Laboratoire de Mecmique des Contacts 20 Ave A. Einstein 6962 1 Villeurbame cedex France

ANGHELV.

Miss ANNARELLI C

752 Title Name Mr

BAKERR.

Affiliation IMPERIAL COLLEGE llept. of Mechanical Eiigineerig Exhibition Road SW7 2HX London 1J.K

Title Name Mr

BERNARDF.

Affiliation UCB LYON I Departemelit de Physique des MatCriaux 43 Bld. du 1 1 Nov. 1918 69622 Villeurbaiuie cedex France

Prof BALL A.

UNIVERSITY OF CAPE TOWN Department of Materials Engineering Rondebosch 7700 Cape Town, South Africa

Prof BERT J.

UCB LYON I Departemerit de Physique des Materiaux 43 Bld. du I 1 Nov. 1918 69622 Villeurbanne cedex France

Ms

ECOLE CENTRALE r)E LY ( IN Dkpartement MMP B.P. 163

Dr

BERTHIER Y.

INSA LYON Laboratoire de MCcanique des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

INSA LYON Laboratoire de Mecanique des Colltacts 20 Ave A Eiiistciii 6962 I Villeurhaiiiie cedex France

Ms

BLAKE Y.

TRINITY COLLEGE Parsons Building Dublin 2, Ireland

Prof BAYADA G .

INSA LYON Labomtoire de Mkcanique des Contacts 20 Ave A Eiiisteiii 6962 I Villeurbaiuie cedex France

Prof BLOUET J.

Dr

BECS.

ECOLE CENTRALE I)E LYON - I,ms B P 163 69 I3 1 Ecully ccdex France

Dr

BOU-SAU3 B.

INSA LYON Laboratoire de Mkcanique des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

Dr

BELINM.

ECOLE CENTRALE DE LYON - LTDS B.P. 163 69 I3 I Ecully cedex France

Dr

BRENDLE M.

histitut de Chimie des Surfaces et Interfaces 15, rue Jean Starcky B.P. 2478 68057 Mulhouse cedex France

BARTHOUC.

69 13 I Ecully cedex France

Mr.

BAUD S.

I.S.M.C.M. Laboratoire de Tribologie 3 rue Feniand Hainaut 93407 Saint-Ouen FraIice

753 Title Name Mr.

BRETONE.

Mr

BRIFFETT G .

Name -

Affiliation INSA LYON Laboratoire de Mticanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbaime cedex France

p t J

1JNIVERSITY OF LEEDS

M r.

CHAN TIEN C.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbanne cedex France

Miss CATALDO G.

Department of Mechanical Eiigineering LS2 9JT Leeds, 1J.K.

Affiliation POLITECNICO DI TORINO Dipartiineiito di big. Aeronautica e Spaziale Corso Duca Delgi Abruzzi, 24 I0 I29 Torino, Italy

Prof BRIL ARD A.

IJNIVERSITE HA1JTE ALSACE Laboratoire de Math. 4 rue des Frkres Lumikre 68093 Mulhouse cedex France

Mr

CHANG F.Y.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds 1J.K.

Prof BRISCOE B.

W E R I A L COLLEGE Department of Cheinical Engineering SW7 2BY London IJ.K.

Dr

CHAOMLEFFEL J.-P.

INSA LYON Laboratoire de Mecanique

Miss CAHOUET V.

INSA LYON Laborntoire de MCcanique des Coutacts 20 Ave A. Einstein 6962 I Villeurbanne cedex France

Dr

CHATEAUMINOIS ECOLE CENTRALE DE A. LYON Dkpartement MMF’ B.P. 163 69 13 I Ecully cedex France

Dr

IMPERIAL COLLEGE Department of Mechanical Engineering Exhibition Road SW7 2BX London 1J.K.

M r.

CHEVALIER F.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbanne cedex France

FRAMATOME Centre Technique B.P. 13 7 I370 Saint Marcel France

Prof CHILDS T.H.C.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds U.K.

CANNP.

Miss CARPENTIER L.

des Contacts 20 Ave A. Einstein 6962 1 Villeurbanne cedex France

154 Title Name Dr

CHOUSTERL

Dr

CIUREA L

Prof CLERIC0 M.

Title Name

Affiliation Rue K. Marcs, 12 450025 Oulb Russia

Prof COY R.C.

MAN(.JFACTI.JREROLEX S.A. La Haute Route 82 2502 Bieme Switzerland PC)LITECNIC(1 DI T( Dipartiineiito di hig. Acroiiautica e Spaziale Corso Duca Degli Abruzzi, 24 10 129 torino. Italy

)

Affiliation SHELL RESEARCH Ltd. Thoniton Research Centre P.O. Box I CHI 3SH Chester U.K.

Prof DALMAZ G.

LNSA LYON Laboratoire de MCcanique des Contacts 20 Ave A. Einstein 6962 I Villeurbaime cedex France

Mr

GLYCO-METALL-WERKE P.O. Box 13 03 35 D-6509 1 Wieshaden, Genniuiy

DAMOLIR P.

Dr

COLIN F.

INSA LYON Laboratoire de Mkcaiiique des Coiitacts 20 Ave A. Einstein 6962 1 Villeurhaniie cedex France

Prof DENAPE J.

ECOLE NATIONALE DINGENIEURS Labo. Genie de Production B.P. 1629 650 I6 Tarhes cedex France

Ms

COLIN A.

1JN'IVERSITE LIBRE DE BRIJXELLES CRI Nivelles 24 rue de I'hidustrie 1400 Nivelles, Nelgique

Dr

PECHINEY CRV B.P. 27 38340 Voreppe France

Dr

CONTEM.

INSA LYON Lahoratoire de MCcanique des Colltacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

Mrs DESCARTES S.

INSA LYON Lahoratoire de Meciuiique des Contacts 20 Ave A. Eiiisteiii 6962 I Villeurbaiuie cedex France

Mr

COUHIERF.

INSA LYON Lahoratoire de Mecaiiique des Contacts 20 Ave A. Eiiisteiii 6962 I Villeurhamie cedex France

Mr

INSA LYON Laboratoire de MCciuiique des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

DENEWILLE P.

DESRAYAUDC.

755

Affiliation ECOLE CENTRALE DE LYON LTDS B.P. 163 69 I3 I Ecully cedex France

Title Name -

Prof DOWSON D.

IJNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds I1.K

Prof ELROD H.

14 Croinwell Court 06475 Old Saybrook, CT USA

Dr

INSA LYON Laboratoire de MCcaiiique des Contacts 20 Ave A. Einstein 6962 I Villeurhaii~iecedex France

Dr

INSA LYON Laboratoire de MCcaiiique des Contacts 20 Ave A. Einstein 69621 Villeurbaiuie cedex France

INSA LYON Lahoratoire dc MCcaiiique des Colitacts 20 Ave A Etiisteiri 6962 I Villeurbatuie cedex Fra11ce

Prof FERNANDEZ RICO E.T.S. INGENIEROS J. E. INDI JSTRIALES Oviedo Ihiiversity Crta. Castiello SM 33204 Gijoii, Spaiii

Title Name -

Dr

DONNETC.

DUBOURG M.-C.

MS DUMONT M.-L.

Dr

DUPUY-PHILON J. IICB LYON I Dkpt. de Pysique des Matiriaux 43 Bld. du I I Nov. 1918 69622 Villeurhariiie cedex France

Dr

DWYER-JOYCE R.S.

Dr

EHRETP.

1 JNIVERSITY (IF

Prof ELEOD A.

FANTINOB.

Prof FLAMAND L.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 I Villeurbatuie cedex France

Mr

ECOLE CENTRALE DE LYON DCpartement MMP B.P 163 69 I3 1 Ecully cedex France

FOUVRYS.

SHEFFIELD Department of Mechanical Rr. Process Engineering Mappiii Street S I 3SD Sheflield I J.K IJNIVERSITY OF LEEDS Departinelit of Mechaiiical Engineering LS2 9JT Leeds, I JK

Affiliation Uiiiversite Technique de Budapest Dept. of Machine Elernelit Bertalrui L.u.2 H- I I I Budapest, Hungary

Prof FRANEK F.

TECHNISCHE IJNIVERSITAT WIEN Institute f& Feiiiwerktecluiik Floragasse 7 1040 Wien, Austria

756 Title Name Prof FRENE J.

A ffi Iiii t ion Laboratoire de Mbcaiiique des Solides srj MI 13d. 3 Tkltiport 2 BP 179 86960 Futuroscope cedex France

Title Name -

Mr

HARDING R.T.

Prof GEORGES J.-M.

ECOLE C E N T W E DE LYON - LTDS B.P. 163 69 I3 I Ecully ccdex Fratice

Mr

HAYASHIN.

-7

TRIBOLOGY LAB. Nagasaki Research & Dev. Center Mitsubishi Heavy hid, Ltd. I - I Akunoura-machi 850-91 Nagasaki, Japan

Prof HAYASHI K.

83 hiari-oiunae-cho, Fukakusa, Fushimi-ku Kyoto, Japaii

IMPERIAL COLLEGE Lkpartineiit of Mechanical Eiigiiiecriiig Exhibition Road SW7 2HX Loiidoii ll.K.

Mr

HIRSTD.

IMPERIAL COLLEGE Department of Mechanical Enginceriug Exhibition Road SW7 2BX London, U.K.

GUETTECHE Y.

INSA LYON 1,ahorntoire de Mbcaniqtie des Colllacts 20 Ave A. Einstein 6962 I Villeurhaiitie ccdcx France

Dr

HOLINSKIR.

MOLYKOI’E A division of Dow Coming CiriibH Postfach 500 160 8097 I Munchen, Geniiany

HAMILTON R.

IMI’ERIN, COLLEGE

Mr

IORDANOFF I.

ABG SEMCA 408 avenue des Etats IJtiis, B.P. 2010 3 10 I6 Toulouse cedex France

Dr

GREENWOOD J.A. IJNIVERSITY OF CAMI3RIMiE 1Iniversity Eiigrg Depl Trtiiiipiiigtoii Street C132 11’7 Cambridge, 1I.K.

Dr

GUANGTENG G .

Mr

Mr

Department of Mcchnnical Engincoring Exhibition Road s w 7 2r3x Lolldoll I J K

Dr

Affi Iia t ion UNIVERSITY OF LEEDS Department of Mechanical Eiigiiieeriiig LS2 9JT Leeds U.K.

HAMZAOUI B.

INSA LYON

Laboratoh de MCcanique des Contacts 20 Ave A. Einstein 6962 I Villcurhanne cedex France

Prnf JACOBSON B.O.

SKI; ENCilNEEIUNG & RESEARCH CENTRE BV Postbus 2350 3430 LIT Nieuwegeiii The Nertherlands

757 Title Name Mrs JACQUEMARD P.

Affiliation INSA LYON Laboratoire de MCcaiiique des Contacts 20 Ave A. Einstein 6962 I Villeitrbaiitie cedex Fraiice

Title Name -

Dr

JOHNSTON G.J.

MOBIL RESEARCH & DEVELOPMENT C O W . Paulsboro Research Lab. Post Ollice Box 480 08066-0480 Paulsboro, N.J [J.S.A.

Prof KATO K

TOHOKU UNIVERSITY Laboratory of Tribology, School of Mechanical Engineering 980-77 Sendai, Japan

Dr

JONESK.

ELSEVLER SCIENCE B.V F' 0. Box 103 I000 AC Amsterdam The Netherlands

Prof KEER L M .

NORTHWESTERN IJNIVERSITY Civil Engineering Dept. 2145 Sheridan Road 60208 Evanston, 11. 1J.S.A.

Mr

J0NESD.A.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds 1J.K

Prof KENNEDY F.E.

DARTMOUTH COLLEGE Thayer School of Engineering 03755 Haiiover, NH,USA

Mr

JONES G.J.

ARGYLE HOI JSE Joel Street, HA6 ILN Northwood Hills 1J.K.

Mr

MPERIAL COLLEGE Departinelit of Mechanical Engineering Exhibition Road SW7 2BX London. U.K.

Prof KALKER J.J.

T L J DELFT TWI-Et Mekelweg 4 2628 CD Dell1 The Nctherlands

Prof KIMUFU Y

IJNIVERSITY OF TOKYO histitute of hidustrial Science 7-22- I - Roppongi, Miiiato-ku I06 Tokyo Japan

Miss KAMELM.

INSA LYON Lahoratoire de MCcanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbamie cedex France

Prof KO P.L.

NATIONAL RESEARCH COUNCIL OF CANADA 3650 Wesbrook Mall V6S 2L2 Vancouver B.C. Canada

.__-

Prof W S A P.

KIMT.

Affiliation ECOLE CENTRALE DE LYON L.T.D.S. B.P. 163 69 I3 1 Ecully cedex France

758

Title NHme

Affilintion MECI-IANICAL ENGINEERING LABORATORY N ~ I I I I1-2 ~I 305 Tsukuba, Ibaraki Japan

Title Name Mr

LUBBLNGEH.

Affiliation BWAP INTERNATIONAL BV PO Box 1300 4700 BH Roosetidaal The Netherlands

Mr

KORENAGA A.

Ms

LAMACQV.

INSA LYON Laboratoire de Mkcaiiique des Contacts 20 Ave A Einstein 6962 I Villeurbaiuie cedex France

Prof LUBRECHT T.

INSA LYON Laboratoire de Mecaiiique des Contacts 20 Ave A. Einstein 6962 I Villeurbrume cedex France

Dr

LARACINE M.

INSA LYON Laboratoire de Mkcaiiique des Contacts 20 Ave A Eiiisteiii 6962 I Villeurhaiiiie cedex Frillice

Prof LUDEMA K.

UNIVERSITY OF MICHIGAN Mech.1 Engineering Dept. GG Brown Building 48109-2125 k m Arbor, MI IJSA

Mr

LARSSON R.

Ll JLEA IJNWERSITY ( )F TECHNOL( )C;Y Division 01‘ Machiile Elements s-971 87 Lulea Swcdcn

Dr

MAATARM.

LNSA LYON Laboratoire de MCcaiiique des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

Mr

LEE-PRUDHOE I.

IMI’ERIAL COLLEGE Department of Mechanical Eiigiiiecriiig Exlitbition Road SW7 2UX London 11 K

Dr

MANNU.

F.Z.G.

Mr

LEMOGNE T.

ECOLE CENTRALE I)E LYON LTDS H.P. 163 69 I3 I Ecully cedcs France

Mr

MARCHANDP.

INSTITUT FRANCNS DU PETROLE B.P. 3 69390 Veniaison cedex France

Mr

LORIC J.-C.

IMPERIAL COLLEGE

Dr

MARTWJ.-M.

ECOLE CENTRALE DE LYON LTDS B.P. 163 69 I3 I Ecully cedex France

Department of Mechanical Eiigiiieeriiig Exhibition Road SW7 2HX Loadon, lI.K

Technische Uiiiversitat Arcisstrasse 2 I 80333 Muiicheii Geniiaiiy

759 Title --

Name

AMil ia t ion ECOLE CENTRALE DE LYON Dcpartement MMP B. P. 163 691 3 I Ecully cedex France

Title Name Dr

MIRANDAA.A.S.

Affiliation UNIVERSIDADE Do MINHO Dept. Eng. Mecanica 4800 Guimaraes Portugal

Ms

MARTINB.

Dr.

MAYEURC.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbaiine cedex France

Dr

MISCHLER S.

EPFL DMX-LMCH CH- 10 I 5 Lausanne Switzerland

Dr

MAZUYERD.

ECOLE CENTRALE DE LYON LTDS L3.P. 163 69 I3 I Ecully cedex France

Ms

MOORES.

UNIVERSITY OF LEEDS Departinelit of Mechanical Engineering LS2 9JT Leeds 1J.K.

Dr

McNICOLA.

I JNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds 1J.K.

Dr

MORALESESPEJEL G.E.

I.T.E.S.M. Centro de Sisteinas de Maiiufactura SUC.de Correos 64849 Monterrey N.L. Mexico

Mr

MEHENNYD.

I JNIVERSITY ( IF LEEDS Department of Mechanical Engineering LS2 9JT Leeds U.K.

Dr

MUSCAI.

IJNIVERSITY OF SUCEAVA 1 IJniversity Street 5800 Suceava Roinania

Dr

MEURISSE M.-H.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 I Villeurbanne cedex France

Mr

NOELB.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbamie cedex France

Dr

MIANO.

T & N Tecluiology Ltd. Engineering Analysis Dept Cawston House, Cawston CV22 7SA Rugby Warwickshire 1J.K.

Ms

NOLLN.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 1 Villeurbanne cedex France

760 Title Name Prof OKAMOTO Y.

Affiliation BARAKI IJNIVERSITY 4-12-1 Nakaiiarusawa 3 14 Hitachi, Ibaraki Japan

Title Name Mr

PRIEST M.

Affiliation UNIVERSITY OF LEEDS Department of Mectianical Engineering LS2 9JT Leeds, U.K.

Dr

OLVERA.

IMPERIAL COLLEGE Departinerit of Mechanical Engineering Exhibition Road SW7 2BX London. 1J.K.

Dr

QUERRY M.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Eiristeiii 6962 1 Villeurbaiuie cedex France

Mr.

OUCHERIF F.

INSA LYON Lahoratoire cle MCcanique des Contacts 20 Avc A. Einstein 6962 I Villeurbamie cedex France

M r.

RACLOT J.-P.

INSA LYON Lahoratoire de MCcanique des Contacts 20 Ave A. Einstein 6962 I Villeurbaiuie cedex France

Mr

PAUSCHITZ A.

TECHNISCHE I JNIVERSITAT WIEN Iiist i tiit fur Fciiiwerktecliriik Floragasse 7 1040 Wieii, Austria

Dr

RADCLIFFE C.D.

UNIVERSITY or: LEEDS Departiiieiit of Mechanical Eiigiiieeriiig LS2 9JT Leeds, 1J.K.

INSA LYON Laboratoire de Mkcaiiiqiie des Contacts 20 Ave A. Eiiisteiii 6962 I Villeiirhaiuie cedex France

Mr

RAMOS COMES J. M.

IJNIVERSIDADE DO MlNHC) Deparamento de Engelharia MecBiiica 4800 Guimaraes, Portugal

1JNIVERSITY ()F

Dr

RAOUS M.

CNRS LMA 3 I Cliemin Joseph Aiguier I3402 Marseille cedex 20 France

Ms

RAT01 M.

IMPERIAL COLLEGE Department of Mechanical Engineering Exhibition Road SW7 2BX London, U.K.

Miss PLUMET S.

Mr

PODGORNIK B.

I n JHLJANA Faculty of Mcc. Engrg CTD Center of'rrihology 6 1000 Ljubljana, Slovenia

Mr

PRATP.

INSA LYON Laboratoire de MCcaniquc des Contacts 20 Ave A. Eiiisteiii 6962 I Villeurbaiiiie ccdex France

76 1 Title Name -

Affiliation THE UNIVERSITY OF WESTERN ONTARIO Faculty of Engineering Science N6A 5B9 London, Ontario Canada

Title Name Dr ROSSETE.

Affiliation EPFL DMX-LMCH Groupe de Tribologie CH- I0 I 5 Lausanlie Switerzlaiid

Mr

ECOLE CENTRALE DE LYON, LTDS B.P. 163 69 131 Ecully cedex France

Prof SIDOROFF F.

ECOLE CENTRALE DE LYON LTDS B.P. 163 69 13I Ecully cedex France

Prof ROZEANU L.

TECHNIC IN Department of Materials Eiigiiieeriiig Haifa, Israel

Dr

SINGERLL.

NAVAL RESEARCH LAB. Code 6170 - NIU 20375 Washiiigtoii DC IJSA

Mr

RUTLWH.

W E R I A L COLLEGE Department of Mechanical Engineering Exhibition Road SW7 2BX London, 1.J.K.

Mr

SMALLEY R.J.

SKF Engineering &

Dr

SAWSOTP.

INSA LYON Lahoratoire de Mkcanique des Contacts 20 Ave A. Eiiisteiii 6962 I Villeurbaiuie cedex Fraiice

Mr

SMEETHM.

IMPERIAL COLLEGE Department of Mechanical Engineering Exhibition Road SW7 2BX London, U.K.

Mr

SAUGERE.

ECOLE CENTRALE DE LYON Dkpartcinciit Mh4P B.P. 163 69 I3 I Ecully cedex France

Mr.

SOUCHON F.

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 6962 I Villeurbaruie cedex France

Dr

SCHIPPERD.

I JNIVERSUY ()I: TWENTE Dr Fac Mech Engiiieeriiig, Tribology Seclioii P O Box217 7500 Enschede AE The Netherlands

TAYLOR R. I.

SHELL RESEARCH LIMITED Thoniton Research Centre P.O. Box I CHI 3SH Chester, U.K.

-

L

_

ROUCHON J.-F.

Prof SHEASBY J.S.

Research Post Box 2350 3430 DT Nieuwegeiii The Netherlands

762 Title Name Prof TAYLOR C.M.

Affiliation UNIVERSITY OF LEEDS Department of Mechanical Eiigiiiecriiig LS2 9JT Leeds, lJ.K.

Title Nnme Prof TORRANCE A.A.

TOSI L

Affiliation TRINITY COLLEGE Parsons Building Dublin 2 Ireland

INSA LYON Laboratoire de Mecanique des Contacts 20 Ave A. Einstein 69621 Villeurbanne cedex France

Dr

TEVAARWERK J. L

Mr. EMERSON M( )T( )R TECHNOLOGY CENTER 8100 W. Florissaiit P.O. Box 36912 63 I36 St Louis, MO, IJSA

Dr

THIEBAUT B.

ROHM AND HAAS Laboratoires EuropCeiis Sophia Antipolis 06560 Valhoiiiie France

Prof TUDOR A.M.

IJMVERSITY POLITEHNIC A B u c w s - r Spl. hidependentei 3 I3 79590 Bucharest Romania

Ms

THOMSON A.

1JNIVERSITY OF LEEDS Department of Mechanical Eiigiiieeriiig LS2 9JT Leeds. 1J.K.

Dr

VANNESB.

ECOLE CENTRALE DE LYON DCparteinent MMP B.P. 163 69 131 Ecully cedex France

Prof TICHY J.

IENSSELAER POLYTECHNIC LNST Dept of Mechanical Engllieeriiig I2 180-3590 Troy, NY 1JSA

Mr

VARENNESE.

ECOLE CENTRALE DE LYON LTDS B.P. 163 69 I3 I Ecully cedex France

Prof TIEU A.K.

I Jaiversity of Wollo~igo~ig Dr Dept. of Mechanical Eiigiiieeriiig NSW 2522, Australia

VELEXP

INSA LYON Laboratoire de Mecaiiique des Contacts

Dr

TONCKA.

ECOLE CENTRALE DE LYON LTDS D.P. 163 69 I3 I Ecully cedex Fra1ice

Dr

20 Ave A. Einstein 6962 I Villeurbaiuie cedex France VERGNEP.

LNSA LYON Laboratoire de MCcaiiique des Contacts 20 Ave A. Einstein 6962 1 Villeurbaiuie cedex

France

763 Title Name -

Prof VINCENT L.

Dr

VISSCHER M.

Affliatinn ECOLE CENTRALE DE LYON Dkpartement M M P D.P. 163 69 I3 I Ecully cedex France 1JNIVERSITY OF LEEDS

Name Title -

Affiliation CITY UNIVERSITY OF HONG KONG Dept. of Manufacturing Engineering Tat Chee Avenue Kowloon Hoiig Kong

Dr

WONG P.L.

Mr

Y AMASHITA R.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LS2 9JT Leeds, U.K.

Departinelit of Mechanical Engineering LS2 9JT Leeds, 1J.K

Prof VIZINTIN J.

I NVERSITY OF LnJBLJANA Faculty of Mech. Eiigrg CTD-Center of Tribology 6 1000 Ljubljana Slovenia

Dr

ZAHOUANI H.

ECOLE CENTRALE DE LYON LTDS B.P. 163 69 I3 I Ecully cedex France

Mr

WE1 JUN

EC( )LE CENTRALE I)E LYON DCpartcineiit Mh4P B.P. 163 69 13 I Ecully cedcx France

Dr

ZAMBELLI G .

EPFL Laboratoire de Mktallurgie Physique, MX-G Ecubleiis CH-I01 5 Lausaiuie Switzerland

Mr

WEMEKAMP A.W. SKF ENCiINEERINCi & RESEARCH CENTRE Postbus 2350 3430 Nieuwcgeiii DT -rile Netherlands

Mr

ZBINDEN M.

EDF Departenleiit MTC Les Renardieres BP 1 77250 Moret sur Loing France

Mr

WILKINSON C.

Mr

ZHOU Z.

ECOLE CENTRALE DE LYON DCpartement MMP B.P. 163 69 I3 I Ecully cedex France

Dr

WILLIAMS J.A.

IM€'EIUAL COLLE(iE Ikpartment of Mechanical Eiigiiieeriiig Exhibition Road SW7 2BX Loiidoii, lJ.K. UNIVERSITY OF

CAMBRIDCIE Departinelit Mechanical Eiigiiieeriiig Tnanpington Street CB2 IPZ Cambridge 1J.K.

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